Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(211,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.211");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.l (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.35983195036\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 295.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.295 |
Dual form | 546.2.l.d.211.1 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −2.00000 | −0.894427 | −0.447214 | − | 0.894427i | \(-0.647584\pi\) | ||||
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | 0.500000 | + | 0.866025i | 0.204124 | + | 0.353553i | ||||
\(7\) | 0.500000 | + | 0.866025i | 0.188982 | + | 0.327327i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −1.00000 | + | 1.73205i | −0.316228 | + | 0.547723i | ||||
\(11\) | 2.00000 | − | 3.46410i | 0.603023 | − | 1.04447i | −0.389338 | − | 0.921095i | \(-0.627296\pi\) |
0.992361 | − | 0.123371i | \(-0.0393705\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −3.50000 | − | 0.866025i | −0.970725 | − | 0.240192i | ||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 1.00000 | − | 1.73205i | 0.258199 | − | 0.447214i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −3.50000 | − | 6.06218i | −0.848875 | − | 1.47029i | −0.882213 | − | 0.470850i | \(-0.843947\pi\) |
0.0333386 | − | 0.999444i | \(-0.489386\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.00000 | − | 1.73205i | −0.229416 | − | 0.397360i | 0.728219 | − | 0.685344i | \(-0.240348\pi\) |
−0.957635 | + | 0.287984i | \(0.907015\pi\) | |||||||
\(20\) | 1.00000 | + | 1.73205i | 0.223607 | + | 0.387298i | ||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −2.00000 | − | 3.46410i | −0.426401 | − | 0.738549i | ||||
\(23\) | 0.500000 | − | 0.866025i | 0.104257 | − | 0.180579i | −0.809177 | − | 0.587565i | \(-0.800087\pi\) |
0.913434 | + | 0.406986i | \(0.133420\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −2.50000 | + | 2.59808i | −0.490290 | + | 0.509525i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.500000 | − | 0.866025i | 0.0944911 | − | 0.163663i | ||||
\(29\) | 1.00000 | − | 1.73205i | 0.185695 | − | 0.321634i | −0.758115 | − | 0.652121i | \(-0.773880\pi\) |
0.943811 | + | 0.330487i | \(0.107213\pi\) | |||||||
\(30\) | −1.00000 | − | 1.73205i | −0.182574 | − | 0.316228i | ||||
\(31\) | −9.00000 | −1.61645 | −0.808224 | − | 0.588875i | \(-0.799571\pi\) | ||||
−0.808224 | + | 0.588875i | \(0.799571\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 2.00000 | + | 3.46410i | 0.348155 | + | 0.603023i | ||||
\(34\) | −7.00000 | −1.20049 | ||||||||
\(35\) | −1.00000 | − | 1.73205i | −0.169031 | − | 0.292770i | ||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | 1.00000 | − | 1.73205i | 0.164399 | − | 0.284747i | −0.772043 | − | 0.635571i | \(-0.780765\pi\) |
0.936442 | + | 0.350823i | \(0.114098\pi\) | |||||||
\(38\) | −2.00000 | −0.324443 | ||||||||
\(39\) | 2.50000 | − | 2.59808i | 0.400320 | − | 0.416025i | ||||
\(40\) | 2.00000 | 0.316228 | ||||||||
\(41\) | −1.00000 | + | 1.73205i | −0.156174 | + | 0.270501i | −0.933486 | − | 0.358614i | \(-0.883249\pi\) |
0.777312 | + | 0.629115i | \(0.216583\pi\) | |||||||
\(42\) | −0.500000 | + | 0.866025i | −0.0771517 | + | 0.133631i | ||||
\(43\) | 2.50000 | + | 4.33013i | 0.381246 | + | 0.660338i | 0.991241 | − | 0.132068i | \(-0.0421616\pi\) |
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | −4.00000 | −0.603023 | ||||||||
\(45\) | 1.00000 | + | 1.73205i | 0.149071 | + | 0.258199i | ||||
\(46\) | −0.500000 | − | 0.866025i | −0.0737210 | − | 0.127688i | ||||
\(47\) | 6.00000 | 0.875190 | 0.437595 | − | 0.899172i | \(-0.355830\pi\) | ||||
0.437595 | + | 0.899172i | \(0.355830\pi\) | |||||||
\(48\) | −0.500000 | − | 0.866025i | −0.0721688 | − | 0.125000i | ||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | −0.500000 | + | 0.866025i | −0.0707107 | + | 0.122474i | ||||
\(51\) | 7.00000 | 0.980196 | ||||||||
\(52\) | 1.00000 | + | 3.46410i | 0.138675 | + | 0.480384i | ||||
\(53\) | 3.00000 | 0.412082 | 0.206041 | − | 0.978543i | \(-0.433942\pi\) | ||||
0.206041 | + | 0.978543i | \(0.433942\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | −4.00000 | + | 6.92820i | −0.539360 | + | 0.934199i | ||||
\(56\) | −0.500000 | − | 0.866025i | −0.0668153 | − | 0.115728i | ||||
\(57\) | 2.00000 | 0.264906 | ||||||||
\(58\) | −1.00000 | − | 1.73205i | −0.131306 | − | 0.227429i | ||||
\(59\) | −7.50000 | − | 12.9904i | −0.976417 | − | 1.69120i | −0.675178 | − | 0.737655i | \(-0.735933\pi\) |
−0.301239 | − | 0.953549i | \(-0.597400\pi\) | |||||||
\(60\) | −2.00000 | −0.258199 | ||||||||
\(61\) | 3.50000 | + | 6.06218i | 0.448129 | + | 0.776182i | 0.998264 | − | 0.0588933i | \(-0.0187572\pi\) |
−0.550135 | + | 0.835076i | \(0.685424\pi\) | |||||||
\(62\) | −4.50000 | + | 7.79423i | −0.571501 | + | 0.989868i | ||||
\(63\) | 0.500000 | − | 0.866025i | 0.0629941 | − | 0.109109i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 7.00000 | + | 1.73205i | 0.868243 | + | 0.214834i | ||||
\(66\) | 4.00000 | 0.492366 | ||||||||
\(67\) | 2.50000 | − | 4.33013i | 0.305424 | − | 0.529009i | −0.671932 | − | 0.740613i | \(-0.734535\pi\) |
0.977356 | + | 0.211604i | \(0.0678686\pi\) | |||||||
\(68\) | −3.50000 | + | 6.06218i | −0.424437 | + | 0.735147i | ||||
\(69\) | 0.500000 | + | 0.866025i | 0.0601929 | + | 0.104257i | ||||
\(70\) | −2.00000 | −0.239046 | ||||||||
\(71\) | −0.500000 | − | 0.866025i | −0.0593391 | − | 0.102778i | 0.834830 | − | 0.550508i | \(-0.185566\pi\) |
−0.894169 | + | 0.447730i | \(0.852233\pi\) | |||||||
\(72\) | 0.500000 | + | 0.866025i | 0.0589256 | + | 0.102062i | ||||
\(73\) | 12.0000 | 1.40449 | 0.702247 | − | 0.711934i | \(-0.252180\pi\) | ||||
0.702247 | + | 0.711934i | \(0.252180\pi\) | |||||||
\(74\) | −1.00000 | − | 1.73205i | −0.116248 | − | 0.201347i | ||||
\(75\) | 0.500000 | − | 0.866025i | 0.0577350 | − | 0.100000i | ||||
\(76\) | −1.00000 | + | 1.73205i | −0.114708 | + | 0.198680i | ||||
\(77\) | 4.00000 | 0.455842 | ||||||||
\(78\) | −1.00000 | − | 3.46410i | −0.113228 | − | 0.392232i | ||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 1.00000 | − | 1.73205i | 0.111803 | − | 0.193649i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 1.00000 | + | 1.73205i | 0.110432 | + | 0.191273i | ||||
\(83\) | −1.00000 | −0.109764 | −0.0548821 | − | 0.998493i | \(-0.517478\pi\) | ||||
−0.0548821 | + | 0.998493i | \(0.517478\pi\) | |||||||
\(84\) | 0.500000 | + | 0.866025i | 0.0545545 | + | 0.0944911i | ||||
\(85\) | 7.00000 | + | 12.1244i | 0.759257 | + | 1.31507i | ||||
\(86\) | 5.00000 | 0.539164 | ||||||||
\(87\) | 1.00000 | + | 1.73205i | 0.107211 | + | 0.185695i | ||||
\(88\) | −2.00000 | + | 3.46410i | −0.213201 | + | 0.369274i | ||||
\(89\) | −1.50000 | + | 2.59808i | −0.159000 | + | 0.275396i | −0.934508 | − | 0.355942i | \(-0.884160\pi\) |
0.775509 | + | 0.631337i | \(0.217494\pi\) | |||||||
\(90\) | 2.00000 | 0.210819 | ||||||||
\(91\) | −1.00000 | − | 3.46410i | −0.104828 | − | 0.363137i | ||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 4.50000 | − | 7.79423i | 0.466628 | − | 0.808224i | ||||
\(94\) | 3.00000 | − | 5.19615i | 0.309426 | − | 0.535942i | ||||
\(95\) | 2.00000 | + | 3.46410i | 0.205196 | + | 0.355409i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 8.00000 | + | 13.8564i | 0.812277 | + | 1.40690i | 0.911267 | + | 0.411816i | \(0.135106\pi\) |
−0.0989899 | + | 0.995088i | \(0.531561\pi\) | |||||||
\(98\) | 0.500000 | + | 0.866025i | 0.0505076 | + | 0.0874818i | ||||
\(99\) | −4.00000 | −0.402015 | ||||||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 3.50000 | − | 6.06218i | 0.346552 | − | 0.600245i | ||||
\(103\) | −11.0000 | −1.08386 | −0.541931 | − | 0.840423i | \(-0.682307\pi\) | ||||
−0.541931 | + | 0.840423i | \(0.682307\pi\) | |||||||
\(104\) | 3.50000 | + | 0.866025i | 0.343203 | + | 0.0849208i | ||||
\(105\) | 2.00000 | 0.195180 | ||||||||
\(106\) | 1.50000 | − | 2.59808i | 0.145693 | − | 0.252347i | ||||
\(107\) | 3.00000 | − | 5.19615i | 0.290021 | − | 0.502331i | −0.683793 | − | 0.729676i | \(-0.739671\pi\) |
0.973814 | + | 0.227345i | \(0.0730044\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | −16.0000 | −1.53252 | −0.766261 | − | 0.642529i | \(-0.777885\pi\) | ||||
−0.766261 | + | 0.642529i | \(0.777885\pi\) | |||||||
\(110\) | 4.00000 | + | 6.92820i | 0.381385 | + | 0.660578i | ||||
\(111\) | 1.00000 | + | 1.73205i | 0.0949158 | + | 0.164399i | ||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 4.00000 | + | 6.92820i | 0.376288 | + | 0.651751i | 0.990519 | − | 0.137376i | \(-0.0438669\pi\) |
−0.614231 | + | 0.789127i | \(0.710534\pi\) | |||||||
\(114\) | 1.00000 | − | 1.73205i | 0.0936586 | − | 0.162221i | ||||
\(115\) | −1.00000 | + | 1.73205i | −0.0932505 | + | 0.161515i | ||||
\(116\) | −2.00000 | −0.185695 | ||||||||
\(117\) | 1.00000 | + | 3.46410i | 0.0924500 | + | 0.320256i | ||||
\(118\) | −15.0000 | −1.38086 | ||||||||
\(119\) | 3.50000 | − | 6.06218i | 0.320844 | − | 0.555719i | ||||
\(120\) | −1.00000 | + | 1.73205i | −0.0912871 | + | 0.158114i | ||||
\(121\) | −2.50000 | − | 4.33013i | −0.227273 | − | 0.393648i | ||||
\(122\) | 7.00000 | 0.633750 | ||||||||
\(123\) | −1.00000 | − | 1.73205i | −0.0901670 | − | 0.156174i | ||||
\(124\) | 4.50000 | + | 7.79423i | 0.404112 | + | 0.699942i | ||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | −0.500000 | − | 0.866025i | −0.0445435 | − | 0.0771517i | ||||
\(127\) | −8.00000 | + | 13.8564i | −0.709885 | + | 1.22956i | 0.255014 | + | 0.966937i | \(0.417920\pi\) |
−0.964899 | + | 0.262620i | \(0.915413\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −5.00000 | −0.440225 | ||||||||
\(130\) | 5.00000 | − | 5.19615i | 0.438529 | − | 0.455733i | ||||
\(131\) | 15.0000 | 1.31056 | 0.655278 | − | 0.755388i | \(-0.272551\pi\) | ||||
0.655278 | + | 0.755388i | \(0.272551\pi\) | |||||||
\(132\) | 2.00000 | − | 3.46410i | 0.174078 | − | 0.301511i | ||||
\(133\) | 1.00000 | − | 1.73205i | 0.0867110 | − | 0.150188i | ||||
\(134\) | −2.50000 | − | 4.33013i | −0.215967 | − | 0.374066i | ||||
\(135\) | −2.00000 | −0.172133 | ||||||||
\(136\) | 3.50000 | + | 6.06218i | 0.300123 | + | 0.519827i | ||||
\(137\) | −2.00000 | − | 3.46410i | −0.170872 | − | 0.295958i | 0.767853 | − | 0.640626i | \(-0.221325\pi\) |
−0.938725 | + | 0.344668i | \(0.887992\pi\) | |||||||
\(138\) | 1.00000 | 0.0851257 | ||||||||
\(139\) | −8.00000 | − | 13.8564i | −0.678551 | − | 1.17529i | −0.975417 | − | 0.220366i | \(-0.929275\pi\) |
0.296866 | − | 0.954919i | \(-0.404058\pi\) | |||||||
\(140\) | −1.00000 | + | 1.73205i | −0.0845154 | + | 0.146385i | ||||
\(141\) | −3.00000 | + | 5.19615i | −0.252646 | + | 0.437595i | ||||
\(142\) | −1.00000 | −0.0839181 | ||||||||
\(143\) | −10.0000 | + | 10.3923i | −0.836242 | + | 0.869048i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −2.00000 | + | 3.46410i | −0.166091 | + | 0.287678i | ||||
\(146\) | 6.00000 | − | 10.3923i | 0.496564 | − | 0.860073i | ||||
\(147\) | −0.500000 | − | 0.866025i | −0.0412393 | − | 0.0714286i | ||||
\(148\) | −2.00000 | −0.164399 | ||||||||
\(149\) | −10.5000 | − | 18.1865i | −0.860194 | − | 1.48990i | −0.871742 | − | 0.489966i | \(-0.837009\pi\) |
0.0115483 | − | 0.999933i | \(-0.496324\pi\) | |||||||
\(150\) | −0.500000 | − | 0.866025i | −0.0408248 | − | 0.0707107i | ||||
\(151\) | 20.0000 | 1.62758 | 0.813788 | − | 0.581161i | \(-0.197401\pi\) | ||||
0.813788 | + | 0.581161i | \(0.197401\pi\) | |||||||
\(152\) | 1.00000 | + | 1.73205i | 0.0811107 | + | 0.140488i | ||||
\(153\) | −3.50000 | + | 6.06218i | −0.282958 | + | 0.490098i | ||||
\(154\) | 2.00000 | − | 3.46410i | 0.161165 | − | 0.279145i | ||||
\(155\) | 18.0000 | 1.44579 | ||||||||
\(156\) | −3.50000 | − | 0.866025i | −0.280224 | − | 0.0693375i | ||||
\(157\) | 10.0000 | 0.798087 | 0.399043 | − | 0.916932i | \(-0.369342\pi\) | ||||
0.399043 | + | 0.916932i | \(0.369342\pi\) | |||||||
\(158\) | −2.00000 | + | 3.46410i | −0.159111 | + | 0.275589i | ||||
\(159\) | −1.50000 | + | 2.59808i | −0.118958 | + | 0.206041i | ||||
\(160\) | −1.00000 | − | 1.73205i | −0.0790569 | − | 0.136931i | ||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0.500000 | + | 0.866025i | 0.0392837 | + | 0.0680414i | ||||
\(163\) | −10.5000 | − | 18.1865i | −0.822423 | − | 1.42448i | −0.903873 | − | 0.427802i | \(-0.859288\pi\) |
0.0814491 | − | 0.996678i | \(-0.474045\pi\) | |||||||
\(164\) | 2.00000 | 0.156174 | ||||||||
\(165\) | −4.00000 | − | 6.92820i | −0.311400 | − | 0.539360i | ||||
\(166\) | −0.500000 | + | 0.866025i | −0.0388075 | + | 0.0672166i | ||||
\(167\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | 11.5000 | + | 6.06218i | 0.884615 | + | 0.466321i | ||||
\(170\) | 14.0000 | 1.07375 | ||||||||
\(171\) | −1.00000 | + | 1.73205i | −0.0764719 | + | 0.132453i | ||||
\(172\) | 2.50000 | − | 4.33013i | 0.190623 | − | 0.330169i | ||||
\(173\) | 8.00000 | + | 13.8564i | 0.608229 | + | 1.05348i | 0.991532 | + | 0.129861i | \(0.0414530\pi\) |
−0.383304 | + | 0.923622i | \(0.625214\pi\) | |||||||
\(174\) | 2.00000 | 0.151620 | ||||||||
\(175\) | −0.500000 | − | 0.866025i | −0.0377964 | − | 0.0654654i | ||||
\(176\) | 2.00000 | + | 3.46410i | 0.150756 | + | 0.261116i | ||||
\(177\) | 15.0000 | 1.12747 | ||||||||
\(178\) | 1.50000 | + | 2.59808i | 0.112430 | + | 0.194734i | ||||
\(179\) | −3.00000 | + | 5.19615i | −0.224231 | + | 0.388379i | −0.956088 | − | 0.293079i | \(-0.905320\pi\) |
0.731858 | + | 0.681457i | \(0.238654\pi\) | |||||||
\(180\) | 1.00000 | − | 1.73205i | 0.0745356 | − | 0.129099i | ||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | −3.50000 | − | 0.866025i | −0.259437 | − | 0.0641941i | ||||
\(183\) | −7.00000 | −0.517455 | ||||||||
\(184\) | −0.500000 | + | 0.866025i | −0.0368605 | + | 0.0638442i | ||||
\(185\) | −2.00000 | + | 3.46410i | −0.147043 | + | 0.254686i | ||||
\(186\) | −4.50000 | − | 7.79423i | −0.329956 | − | 0.571501i | ||||
\(187\) | −28.0000 | −2.04756 | ||||||||
\(188\) | −3.00000 | − | 5.19615i | −0.218797 | − | 0.378968i | ||||
\(189\) | 0.500000 | + | 0.866025i | 0.0363696 | + | 0.0629941i | ||||
\(190\) | 4.00000 | 0.290191 | ||||||||
\(191\) | −1.50000 | − | 2.59808i | −0.108536 | − | 0.187990i | 0.806641 | − | 0.591041i | \(-0.201283\pi\) |
−0.915177 | + | 0.403051i | \(0.867950\pi\) | |||||||
\(192\) | −0.500000 | + | 0.866025i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | 11.0000 | − | 19.0526i | 0.791797 | − | 1.37143i | −0.133056 | − | 0.991109i | \(-0.542479\pi\) |
0.924853 | − | 0.380325i | \(-0.124188\pi\) | |||||||
\(194\) | 16.0000 | 1.14873 | ||||||||
\(195\) | −5.00000 | + | 5.19615i | −0.358057 | + | 0.372104i | ||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 4.50000 | − | 7.79423i | 0.320612 | − | 0.555316i | −0.660003 | − | 0.751263i | \(-0.729445\pi\) |
0.980614 | + | 0.195947i | \(0.0627782\pi\) | |||||||
\(198\) | −2.00000 | + | 3.46410i | −0.142134 | + | 0.246183i | ||||
\(199\) | 2.50000 | + | 4.33013i | 0.177220 | + | 0.306955i | 0.940927 | − | 0.338608i | \(-0.109956\pi\) |
−0.763707 | + | 0.645563i | \(0.776623\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 2.50000 | + | 4.33013i | 0.176336 | + | 0.305424i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.00000 | 0.140372 | ||||||||
\(204\) | −3.50000 | − | 6.06218i | −0.245049 | − | 0.424437i | ||||
\(205\) | 2.00000 | − | 3.46410i | 0.139686 | − | 0.241943i | ||||
\(206\) | −5.50000 | + | 9.52628i | −0.383203 | + | 0.663727i | ||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 2.50000 | − | 2.59808i | 0.173344 | − | 0.180144i | ||||
\(209\) | −8.00000 | −0.553372 | ||||||||
\(210\) | 1.00000 | − | 1.73205i | 0.0690066 | − | 0.119523i | ||||
\(211\) | −2.00000 | + | 3.46410i | −0.137686 | + | 0.238479i | −0.926620 | − | 0.375999i | \(-0.877300\pi\) |
0.788935 | + | 0.614477i | \(0.210633\pi\) | |||||||
\(212\) | −1.50000 | − | 2.59808i | −0.103020 | − | 0.178437i | ||||
\(213\) | 1.00000 | 0.0685189 | ||||||||
\(214\) | −3.00000 | − | 5.19615i | −0.205076 | − | 0.355202i | ||||
\(215\) | −5.00000 | − | 8.66025i | −0.340997 | − | 0.590624i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −4.50000 | − | 7.79423i | −0.305480 | − | 0.529107i | ||||
\(218\) | −8.00000 | + | 13.8564i | −0.541828 | + | 0.938474i | ||||
\(219\) | −6.00000 | + | 10.3923i | −0.405442 | + | 0.702247i | ||||
\(220\) | 8.00000 | 0.539360 | ||||||||
\(221\) | 7.00000 | + | 24.2487i | 0.470871 | + | 1.63114i | ||||
\(222\) | 2.00000 | 0.134231 | ||||||||
\(223\) | −1.50000 | + | 2.59808i | −0.100447 | + | 0.173980i | −0.911869 | − | 0.410481i | \(-0.865361\pi\) |
0.811422 | + | 0.584461i | \(0.198694\pi\) | |||||||
\(224\) | −0.500000 | + | 0.866025i | −0.0334077 | + | 0.0578638i | ||||
\(225\) | 0.500000 | + | 0.866025i | 0.0333333 | + | 0.0577350i | ||||
\(226\) | 8.00000 | 0.532152 | ||||||||
\(227\) | −14.0000 | − | 24.2487i | −0.929213 | − | 1.60944i | −0.784642 | − | 0.619949i | \(-0.787153\pi\) |
−0.144571 | − | 0.989494i | \(-0.546180\pi\) | |||||||
\(228\) | −1.00000 | − | 1.73205i | −0.0662266 | − | 0.114708i | ||||
\(229\) | 13.0000 | 0.859064 | 0.429532 | − | 0.903052i | \(-0.358679\pi\) | ||||
0.429532 | + | 0.903052i | \(0.358679\pi\) | |||||||
\(230\) | 1.00000 | + | 1.73205i | 0.0659380 | + | 0.114208i | ||||
\(231\) | −2.00000 | + | 3.46410i | −0.131590 | + | 0.227921i | ||||
\(232\) | −1.00000 | + | 1.73205i | −0.0656532 | + | 0.113715i | ||||
\(233\) | −16.0000 | −1.04819 | −0.524097 | − | 0.851658i | \(-0.675597\pi\) | ||||
−0.524097 | + | 0.851658i | \(0.675597\pi\) | |||||||
\(234\) | 3.50000 | + | 0.866025i | 0.228802 | + | 0.0566139i | ||||
\(235\) | −12.0000 | −0.782794 | ||||||||
\(236\) | −7.50000 | + | 12.9904i | −0.488208 | + | 0.845602i | ||||
\(237\) | 2.00000 | − | 3.46410i | 0.129914 | − | 0.225018i | ||||
\(238\) | −3.50000 | − | 6.06218i | −0.226871 | − | 0.392953i | ||||
\(239\) | −9.00000 | −0.582162 | −0.291081 | − | 0.956698i | \(-0.594015\pi\) | ||||
−0.291081 | + | 0.956698i | \(0.594015\pi\) | |||||||
\(240\) | 1.00000 | + | 1.73205i | 0.0645497 | + | 0.111803i | ||||
\(241\) | −7.00000 | − | 12.1244i | −0.450910 | − | 0.780998i | 0.547533 | − | 0.836784i | \(-0.315567\pi\) |
−0.998443 | + | 0.0557856i | \(0.982234\pi\) | |||||||
\(242\) | −5.00000 | −0.321412 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 3.50000 | − | 6.06218i | 0.224065 | − | 0.388091i | ||||
\(245\) | 1.00000 | − | 1.73205i | 0.0638877 | − | 0.110657i | ||||
\(246\) | −2.00000 | −0.127515 | ||||||||
\(247\) | 2.00000 | + | 6.92820i | 0.127257 | + | 0.440831i | ||||
\(248\) | 9.00000 | 0.571501 | ||||||||
\(249\) | 0.500000 | − | 0.866025i | 0.0316862 | − | 0.0548821i | ||||
\(250\) | 6.00000 | − | 10.3923i | 0.379473 | − | 0.657267i | ||||
\(251\) | −11.5000 | − | 19.9186i | −0.725874 | − | 1.25725i | −0.958613 | − | 0.284711i | \(-0.908102\pi\) |
0.232740 | − | 0.972539i | \(-0.425231\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | −2.00000 | − | 3.46410i | −0.125739 | − | 0.217786i | ||||
\(254\) | 8.00000 | + | 13.8564i | 0.501965 | + | 0.869428i | ||||
\(255\) | −14.0000 | −0.876714 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −13.5000 | + | 23.3827i | −0.842107 | + | 1.45857i | 0.0460033 | + | 0.998941i | \(0.485352\pi\) |
−0.888110 | + | 0.459631i | \(0.847982\pi\) | |||||||
\(258\) | −2.50000 | + | 4.33013i | −0.155643 | + | 0.269582i | ||||
\(259\) | 2.00000 | 0.124274 | ||||||||
\(260\) | −2.00000 | − | 6.92820i | −0.124035 | − | 0.429669i | ||||
\(261\) | −2.00000 | −0.123797 | ||||||||
\(262\) | 7.50000 | − | 12.9904i | 0.463352 | − | 0.802548i | ||||
\(263\) | −2.00000 | + | 3.46410i | −0.123325 | + | 0.213606i | −0.921077 | − | 0.389380i | \(-0.872689\pi\) |
0.797752 | + | 0.602986i | \(0.206023\pi\) | |||||||
\(264\) | −2.00000 | − | 3.46410i | −0.123091 | − | 0.213201i | ||||
\(265\) | −6.00000 | −0.368577 | ||||||||
\(266\) | −1.00000 | − | 1.73205i | −0.0613139 | − | 0.106199i | ||||
\(267\) | −1.50000 | − | 2.59808i | −0.0917985 | − | 0.159000i | ||||
\(268\) | −5.00000 | −0.305424 | ||||||||
\(269\) | −9.00000 | − | 15.5885i | −0.548740 | − | 0.950445i | −0.998361 | − | 0.0572259i | \(-0.981774\pi\) |
0.449622 | − | 0.893219i | \(-0.351559\pi\) | |||||||
\(270\) | −1.00000 | + | 1.73205i | −0.0608581 | + | 0.105409i | ||||
\(271\) | −4.50000 | + | 7.79423i | −0.273356 | + | 0.473466i | −0.969719 | − | 0.244224i | \(-0.921467\pi\) |
0.696363 | + | 0.717689i | \(0.254800\pi\) | |||||||
\(272\) | 7.00000 | 0.424437 | ||||||||
\(273\) | 3.50000 | + | 0.866025i | 0.211830 | + | 0.0524142i | ||||
\(274\) | −4.00000 | −0.241649 | ||||||||
\(275\) | −2.00000 | + | 3.46410i | −0.120605 | + | 0.208893i | ||||
\(276\) | 0.500000 | − | 0.866025i | 0.0300965 | − | 0.0521286i | ||||
\(277\) | 4.00000 | + | 6.92820i | 0.240337 | + | 0.416275i | 0.960810 | − | 0.277207i | \(-0.0894088\pi\) |
−0.720473 | + | 0.693482i | \(0.756075\pi\) | |||||||
\(278\) | −16.0000 | −0.959616 | ||||||||
\(279\) | 4.50000 | + | 7.79423i | 0.269408 | + | 0.466628i | ||||
\(280\) | 1.00000 | + | 1.73205i | 0.0597614 | + | 0.103510i | ||||
\(281\) | −26.0000 | −1.55103 | −0.775515 | − | 0.631329i | \(-0.782510\pi\) | ||||
−0.775515 | + | 0.631329i | \(0.782510\pi\) | |||||||
\(282\) | 3.00000 | + | 5.19615i | 0.178647 | + | 0.309426i | ||||
\(283\) | −7.00000 | + | 12.1244i | −0.416107 | + | 0.720718i | −0.995544 | − | 0.0942988i | \(-0.969939\pi\) |
0.579437 | + | 0.815017i | \(0.303272\pi\) | |||||||
\(284\) | −0.500000 | + | 0.866025i | −0.0296695 | + | 0.0513892i | ||||
\(285\) | −4.00000 | −0.236940 | ||||||||
\(286\) | 4.00000 | + | 13.8564i | 0.236525 | + | 0.819346i | ||||
\(287\) | −2.00000 | −0.118056 | ||||||||
\(288\) | 0.500000 | − | 0.866025i | 0.0294628 | − | 0.0510310i | ||||
\(289\) | −16.0000 | + | 27.7128i | −0.941176 | + | 1.63017i | ||||
\(290\) | 2.00000 | + | 3.46410i | 0.117444 | + | 0.203419i | ||||
\(291\) | −16.0000 | −0.937937 | ||||||||
\(292\) | −6.00000 | − | 10.3923i | −0.351123 | − | 0.608164i | ||||
\(293\) | 8.00000 | + | 13.8564i | 0.467365 | + | 0.809500i | 0.999305 | − | 0.0372823i | \(-0.0118701\pi\) |
−0.531940 | + | 0.846782i | \(0.678537\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | 15.0000 | + | 25.9808i | 0.873334 | + | 1.51266i | ||||
\(296\) | −1.00000 | + | 1.73205i | −0.0581238 | + | 0.100673i | ||||
\(297\) | 2.00000 | − | 3.46410i | 0.116052 | − | 0.201008i | ||||
\(298\) | −21.0000 | −1.21650 | ||||||||
\(299\) | −2.50000 | + | 2.59808i | −0.144579 | + | 0.150251i | ||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | −2.50000 | + | 4.33013i | −0.144098 | + | 0.249584i | ||||
\(302\) | 10.0000 | − | 17.3205i | 0.575435 | − | 0.996683i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.00000 | 0.114708 | ||||||||
\(305\) | −7.00000 | − | 12.1244i | −0.400819 | − | 0.694239i | ||||
\(306\) | 3.50000 | + | 6.06218i | 0.200082 | + | 0.346552i | ||||
\(307\) | 30.0000 | 1.71219 | 0.856095 | − | 0.516818i | \(-0.172884\pi\) | ||||
0.856095 | + | 0.516818i | \(0.172884\pi\) | |||||||
\(308\) | −2.00000 | − | 3.46410i | −0.113961 | − | 0.197386i | ||||
\(309\) | 5.50000 | − | 9.52628i | 0.312884 | − | 0.541931i | ||||
\(310\) | 9.00000 | − | 15.5885i | 0.511166 | − | 0.885365i | ||||
\(311\) | 30.0000 | 1.70114 | 0.850572 | − | 0.525859i | \(-0.176256\pi\) | ||||
0.850572 | + | 0.525859i | \(0.176256\pi\) | |||||||
\(312\) | −2.50000 | + | 2.59808i | −0.141535 | + | 0.147087i | ||||
\(313\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(314\) | 5.00000 | − | 8.66025i | 0.282166 | − | 0.488726i | ||||
\(315\) | −1.00000 | + | 1.73205i | −0.0563436 | + | 0.0975900i | ||||
\(316\) | 2.00000 | + | 3.46410i | 0.112509 | + | 0.194871i | ||||
\(317\) | 23.0000 | 1.29181 | 0.645904 | − | 0.763418i | \(-0.276480\pi\) | ||||
0.645904 | + | 0.763418i | \(0.276480\pi\) | |||||||
\(318\) | 1.50000 | + | 2.59808i | 0.0841158 | + | 0.145693i | ||||
\(319\) | −4.00000 | − | 6.92820i | −0.223957 | − | 0.387905i | ||||
\(320\) | −2.00000 | −0.111803 | ||||||||
\(321\) | 3.00000 | + | 5.19615i | 0.167444 | + | 0.290021i | ||||
\(322\) | 0.500000 | − | 0.866025i | 0.0278639 | − | 0.0482617i | ||||
\(323\) | −7.00000 | + | 12.1244i | −0.389490 | + | 0.674617i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 3.50000 | + | 0.866025i | 0.194145 | + | 0.0480384i | ||||
\(326\) | −21.0000 | −1.16308 | ||||||||
\(327\) | 8.00000 | − | 13.8564i | 0.442401 | − | 0.766261i | ||||
\(328\) | 1.00000 | − | 1.73205i | 0.0552158 | − | 0.0956365i | ||||
\(329\) | 3.00000 | + | 5.19615i | 0.165395 | + | 0.286473i | ||||
\(330\) | −8.00000 | −0.440386 | ||||||||
\(331\) | −18.0000 | − | 31.1769i | −0.989369 | − | 1.71364i | −0.620625 | − | 0.784107i | \(-0.713121\pi\) |
−0.368744 | − | 0.929531i | \(-0.620212\pi\) | |||||||
\(332\) | 0.500000 | + | 0.866025i | 0.0274411 | + | 0.0475293i | ||||
\(333\) | −2.00000 | −0.109599 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.00000 | + | 8.66025i | −0.273179 | + | 0.473160i | ||||
\(336\) | 0.500000 | − | 0.866025i | 0.0272772 | − | 0.0472456i | ||||
\(337\) | 18.0000 | 0.980522 | 0.490261 | − | 0.871576i | \(-0.336901\pi\) | ||||
0.490261 | + | 0.871576i | \(0.336901\pi\) | |||||||
\(338\) | 11.0000 | − | 6.92820i | 0.598321 | − | 0.376845i | ||||
\(339\) | −8.00000 | −0.434500 | ||||||||
\(340\) | 7.00000 | − | 12.1244i | 0.379628 | − | 0.657536i | ||||
\(341\) | −18.0000 | + | 31.1769i | −0.974755 | + | 1.68832i | ||||
\(342\) | 1.00000 | + | 1.73205i | 0.0540738 | + | 0.0936586i | ||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −2.50000 | − | 4.33013i | −0.134791 | − | 0.233465i | ||||
\(345\) | −1.00000 | − | 1.73205i | −0.0538382 | − | 0.0932505i | ||||
\(346\) | 16.0000 | 0.860165 | ||||||||
\(347\) | −5.00000 | − | 8.66025i | −0.268414 | − | 0.464907i | 0.700038 | − | 0.714105i | \(-0.253166\pi\) |
−0.968452 | + | 0.249198i | \(0.919833\pi\) | |||||||
\(348\) | 1.00000 | − | 1.73205i | 0.0536056 | − | 0.0928477i | ||||
\(349\) | 12.5000 | − | 21.6506i | 0.669110 | − | 1.15893i | −0.309044 | − | 0.951048i | \(-0.600009\pi\) |
0.978153 | − | 0.207884i | \(-0.0666577\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | −3.50000 | − | 0.866025i | −0.186816 | − | 0.0462250i | ||||
\(352\) | 4.00000 | 0.213201 | ||||||||
\(353\) | 17.5000 | − | 30.3109i | 0.931431 | − | 1.61329i | 0.150553 | − | 0.988602i | \(-0.451894\pi\) |
0.780878 | − | 0.624684i | \(-0.214772\pi\) | |||||||
\(354\) | 7.50000 | − | 12.9904i | 0.398621 | − | 0.690431i | ||||
\(355\) | 1.00000 | + | 1.73205i | 0.0530745 | + | 0.0919277i | ||||
\(356\) | 3.00000 | 0.159000 | ||||||||
\(357\) | 3.50000 | + | 6.06218i | 0.185240 | + | 0.320844i | ||||
\(358\) | 3.00000 | + | 5.19615i | 0.158555 | + | 0.274625i | ||||
\(359\) | −24.0000 | −1.26667 | −0.633336 | − | 0.773877i | \(-0.718315\pi\) | ||||
−0.633336 | + | 0.773877i | \(0.718315\pi\) | |||||||
\(360\) | −1.00000 | − | 1.73205i | −0.0527046 | − | 0.0912871i | ||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | −1.00000 | + | 1.73205i | −0.0525588 | + | 0.0910346i | ||||
\(363\) | 5.00000 | 0.262432 | ||||||||
\(364\) | −2.50000 | + | 2.59808i | −0.131036 | + | 0.136176i | ||||
\(365\) | −24.0000 | −1.25622 | ||||||||
\(366\) | −3.50000 | + | 6.06218i | −0.182948 | + | 0.316875i | ||||
\(367\) | 1.50000 | − | 2.59808i | 0.0782994 | − | 0.135618i | −0.824217 | − | 0.566274i | \(-0.808384\pi\) |
0.902516 | + | 0.430656i | \(0.141718\pi\) | |||||||
\(368\) | 0.500000 | + | 0.866025i | 0.0260643 | + | 0.0451447i | ||||
\(369\) | 2.00000 | 0.104116 | ||||||||
\(370\) | 2.00000 | + | 3.46410i | 0.103975 | + | 0.180090i | ||||
\(371\) | 1.50000 | + | 2.59808i | 0.0778761 | + | 0.134885i | ||||
\(372\) | −9.00000 | −0.466628 | ||||||||
\(373\) | −2.00000 | − | 3.46410i | −0.103556 | − | 0.179364i | 0.809591 | − | 0.586994i | \(-0.199689\pi\) |
−0.913147 | + | 0.407630i | \(0.866355\pi\) | |||||||
\(374\) | −14.0000 | + | 24.2487i | −0.723923 | + | 1.25387i | ||||
\(375\) | −6.00000 | + | 10.3923i | −0.309839 | + | 0.536656i | ||||
\(376\) | −6.00000 | −0.309426 | ||||||||
\(377\) | −5.00000 | + | 5.19615i | −0.257513 | + | 0.267615i | ||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | 10.0000 | − | 17.3205i | 0.513665 | − | 0.889695i | −0.486209 | − | 0.873843i | \(-0.661621\pi\) |
0.999874 | − | 0.0158521i | \(-0.00504609\pi\) | |||||||
\(380\) | 2.00000 | − | 3.46410i | 0.102598 | − | 0.177705i | ||||
\(381\) | −8.00000 | − | 13.8564i | −0.409852 | − | 0.709885i | ||||
\(382\) | −3.00000 | −0.153493 | ||||||||
\(383\) | −12.0000 | − | 20.7846i | −0.613171 | − | 1.06204i | −0.990702 | − | 0.136047i | \(-0.956560\pi\) |
0.377531 | − | 0.925997i | \(-0.376773\pi\) | |||||||
\(384\) | 0.500000 | + | 0.866025i | 0.0255155 | + | 0.0441942i | ||||
\(385\) | −8.00000 | −0.407718 | ||||||||
\(386\) | −11.0000 | − | 19.0526i | −0.559885 | − | 0.969750i | ||||
\(387\) | 2.50000 | − | 4.33013i | 0.127082 | − | 0.220113i | ||||
\(388\) | 8.00000 | − | 13.8564i | 0.406138 | − | 0.703452i | ||||
\(389\) | −1.00000 | −0.0507020 | −0.0253510 | − | 0.999679i | \(-0.508070\pi\) | ||||
−0.0253510 | + | 0.999679i | \(0.508070\pi\) | |||||||
\(390\) | 2.00000 | + | 6.92820i | 0.101274 | + | 0.350823i | ||||
\(391\) | −7.00000 | −0.354005 | ||||||||
\(392\) | 0.500000 | − | 0.866025i | 0.0252538 | − | 0.0437409i | ||||
\(393\) | −7.50000 | + | 12.9904i | −0.378325 | + | 0.655278i | ||||
\(394\) | −4.50000 | − | 7.79423i | −0.226707 | − | 0.392668i | ||||
\(395\) | 8.00000 | 0.402524 | ||||||||
\(396\) | 2.00000 | + | 3.46410i | 0.100504 | + | 0.174078i | ||||
\(397\) | 0.500000 | + | 0.866025i | 0.0250943 | + | 0.0434646i | 0.878300 | − | 0.478110i | \(-0.158678\pi\) |
−0.853206 | + | 0.521575i | \(0.825345\pi\) | |||||||
\(398\) | 5.00000 | 0.250627 | ||||||||
\(399\) | 1.00000 | + | 1.73205i | 0.0500626 | + | 0.0867110i | ||||
\(400\) | 0.500000 | − | 0.866025i | 0.0250000 | − | 0.0433013i | ||||
\(401\) | −16.0000 | + | 27.7128i | −0.799002 | + | 1.38391i | 0.121265 | + | 0.992620i | \(0.461305\pi\) |
−0.920267 | + | 0.391292i | \(0.872028\pi\) | |||||||
\(402\) | 5.00000 | 0.249377 | ||||||||
\(403\) | 31.5000 | + | 7.79423i | 1.56913 | + | 0.388258i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | − | 1.73205i | 0.0496904 | − | 0.0860663i | ||||
\(406\) | 1.00000 | − | 1.73205i | 0.0496292 | − | 0.0859602i | ||||
\(407\) | −4.00000 | − | 6.92820i | −0.198273 | − | 0.343418i | ||||
\(408\) | −7.00000 | −0.346552 | ||||||||
\(409\) | −7.00000 | − | 12.1244i | −0.346128 | − | 0.599511i | 0.639430 | − | 0.768849i | \(-0.279170\pi\) |
−0.985558 | + | 0.169338i | \(0.945837\pi\) | |||||||
\(410\) | −2.00000 | − | 3.46410i | −0.0987730 | − | 0.171080i | ||||
\(411\) | 4.00000 | 0.197305 | ||||||||
\(412\) | 5.50000 | + | 9.52628i | 0.270966 | + | 0.469326i | ||||
\(413\) | 7.50000 | − | 12.9904i | 0.369051 | − | 0.639215i | ||||
\(414\) | −0.500000 | + | 0.866025i | −0.0245737 | + | 0.0425628i | ||||
\(415\) | 2.00000 | 0.0981761 | ||||||||
\(416\) | −1.00000 | − | 3.46410i | −0.0490290 | − | 0.169842i | ||||
\(417\) | 16.0000 | 0.783523 | ||||||||
\(418\) | −4.00000 | + | 6.92820i | −0.195646 | + | 0.338869i | ||||
\(419\) | 15.5000 | − | 26.8468i | 0.757225 | − | 1.31155i | −0.187036 | − | 0.982353i | \(-0.559888\pi\) |
0.944261 | − | 0.329198i | \(-0.106778\pi\) | |||||||
\(420\) | −1.00000 | − | 1.73205i | −0.0487950 | − | 0.0845154i | ||||
\(421\) | 34.0000 | 1.65706 | 0.828529 | − | 0.559946i | \(-0.189178\pi\) | ||||
0.828529 | + | 0.559946i | \(0.189178\pi\) | |||||||
\(422\) | 2.00000 | + | 3.46410i | 0.0973585 | + | 0.168630i | ||||
\(423\) | −3.00000 | − | 5.19615i | −0.145865 | − | 0.252646i | ||||
\(424\) | −3.00000 | −0.145693 | ||||||||
\(425\) | 3.50000 | + | 6.06218i | 0.169775 | + | 0.294059i | ||||
\(426\) | 0.500000 | − | 0.866025i | 0.0242251 | − | 0.0419591i | ||||
\(427\) | −3.50000 | + | 6.06218i | −0.169377 | + | 0.293369i | ||||
\(428\) | −6.00000 | −0.290021 | ||||||||
\(429\) | −4.00000 | − | 13.8564i | −0.193122 | − | 0.668994i | ||||
\(430\) | −10.0000 | −0.482243 | ||||||||
\(431\) | 0.500000 | − | 0.866025i | 0.0240842 | − | 0.0417150i | −0.853732 | − | 0.520712i | \(-0.825666\pi\) |
0.877816 | + | 0.478997i | \(0.159000\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | −6.00000 | − | 10.3923i | −0.288342 | − | 0.499422i | 0.685072 | − | 0.728475i | \(-0.259771\pi\) |
−0.973414 | + | 0.229053i | \(0.926437\pi\) | |||||||
\(434\) | −9.00000 | −0.432014 | ||||||||
\(435\) | −2.00000 | − | 3.46410i | −0.0958927 | − | 0.166091i | ||||
\(436\) | 8.00000 | + | 13.8564i | 0.383131 | + | 0.663602i | ||||
\(437\) | −2.00000 | −0.0956730 | ||||||||
\(438\) | 6.00000 | + | 10.3923i | 0.286691 | + | 0.496564i | ||||
\(439\) | −2.00000 | + | 3.46410i | −0.0954548 | + | 0.165333i | −0.909798 | − | 0.415051i | \(-0.863764\pi\) |
0.814344 | + | 0.580383i | \(0.197097\pi\) | |||||||
\(440\) | 4.00000 | − | 6.92820i | 0.190693 | − | 0.330289i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 24.5000 | + | 6.06218i | 1.16535 | + | 0.288348i | ||||
\(443\) | −6.00000 | −0.285069 | −0.142534 | − | 0.989790i | \(-0.545525\pi\) | ||||
−0.142534 | + | 0.989790i | \(0.545525\pi\) | |||||||
\(444\) | 1.00000 | − | 1.73205i | 0.0474579 | − | 0.0821995i | ||||
\(445\) | 3.00000 | − | 5.19615i | 0.142214 | − | 0.246321i | ||||
\(446\) | 1.50000 | + | 2.59808i | 0.0710271 | + | 0.123022i | ||||
\(447\) | 21.0000 | 0.993266 | ||||||||
\(448\) | 0.500000 | + | 0.866025i | 0.0236228 | + | 0.0409159i | ||||
\(449\) | −9.00000 | − | 15.5885i | −0.424736 | − | 0.735665i | 0.571660 | − | 0.820491i | \(-0.306300\pi\) |
−0.996396 | + | 0.0848262i | \(0.972967\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 4.00000 | + | 6.92820i | 0.188353 | + | 0.326236i | ||||
\(452\) | 4.00000 | − | 6.92820i | 0.188144 | − | 0.325875i | ||||
\(453\) | −10.0000 | + | 17.3205i | −0.469841 | + | 0.813788i | ||||
\(454\) | −28.0000 | −1.31411 | ||||||||
\(455\) | 2.00000 | + | 6.92820i | 0.0937614 | + | 0.324799i | ||||
\(456\) | −2.00000 | −0.0936586 | ||||||||
\(457\) | 4.50000 | − | 7.79423i | 0.210501 | − | 0.364599i | −0.741370 | − | 0.671096i | \(-0.765824\pi\) |
0.951871 | + | 0.306497i | \(0.0991571\pi\) | |||||||
\(458\) | 6.50000 | − | 11.2583i | 0.303725 | − | 0.526067i | ||||
\(459\) | −3.50000 | − | 6.06218i | −0.163366 | − | 0.282958i | ||||
\(460\) | 2.00000 | 0.0932505 | ||||||||
\(461\) | 10.0000 | + | 17.3205i | 0.465746 | + | 0.806696i | 0.999235 | − | 0.0391109i | \(-0.0124526\pi\) |
−0.533488 | + | 0.845807i | \(0.679119\pi\) | |||||||
\(462\) | 2.00000 | + | 3.46410i | 0.0930484 | + | 0.161165i | ||||
\(463\) | 18.0000 | 0.836531 | 0.418265 | − | 0.908325i | \(-0.362638\pi\) | ||||
0.418265 | + | 0.908325i | \(0.362638\pi\) | |||||||
\(464\) | 1.00000 | + | 1.73205i | 0.0464238 | + | 0.0804084i | ||||
\(465\) | −9.00000 | + | 15.5885i | −0.417365 | + | 0.722897i | ||||
\(466\) | −8.00000 | + | 13.8564i | −0.370593 | + | 0.641886i | ||||
\(467\) | 37.0000 | 1.71216 | 0.856078 | − | 0.516847i | \(-0.172894\pi\) | ||||
0.856078 | + | 0.516847i | \(0.172894\pi\) | |||||||
\(468\) | 2.50000 | − | 2.59808i | 0.115563 | − | 0.120096i | ||||
\(469\) | 5.00000 | 0.230879 | ||||||||
\(470\) | −6.00000 | + | 10.3923i | −0.276759 | + | 0.479361i | ||||
\(471\) | −5.00000 | + | 8.66025i | −0.230388 | + | 0.399043i | ||||
\(472\) | 7.50000 | + | 12.9904i | 0.345215 | + | 0.597931i | ||||
\(473\) | 20.0000 | 0.919601 | ||||||||
\(474\) | −2.00000 | − | 3.46410i | −0.0918630 | − | 0.159111i | ||||
\(475\) | 1.00000 | + | 1.73205i | 0.0458831 | + | 0.0794719i | ||||
\(476\) | −7.00000 | −0.320844 | ||||||||
\(477\) | −1.50000 | − | 2.59808i | −0.0686803 | − | 0.118958i | ||||
\(478\) | −4.50000 | + | 7.79423i | −0.205825 | + | 0.356500i | ||||
\(479\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(480\) | 2.00000 | 0.0912871 | ||||||||
\(481\) | −5.00000 | + | 5.19615i | −0.227980 | + | 0.236924i | ||||
\(482\) | −14.0000 | −0.637683 | ||||||||
\(483\) | −0.500000 | + | 0.866025i | −0.0227508 | + | 0.0394055i | ||||
\(484\) | −2.50000 | + | 4.33013i | −0.113636 | + | 0.196824i | ||||
\(485\) | −16.0000 | − | 27.7128i | −0.726523 | − | 1.25837i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 14.0000 | + | 24.2487i | 0.634401 | + | 1.09881i | 0.986642 | + | 0.162905i | \(0.0520863\pi\) |
−0.352241 | + | 0.935909i | \(0.614580\pi\) | |||||||
\(488\) | −3.50000 | − | 6.06218i | −0.158438 | − | 0.274422i | ||||
\(489\) | 21.0000 | 0.949653 | ||||||||
\(490\) | −1.00000 | − | 1.73205i | −0.0451754 | − | 0.0782461i | ||||
\(491\) | 4.00000 | − | 6.92820i | 0.180517 | − | 0.312665i | −0.761539 | − | 0.648119i | \(-0.775556\pi\) |
0.942057 | + | 0.335453i | \(0.108889\pi\) | |||||||
\(492\) | −1.00000 | + | 1.73205i | −0.0450835 | + | 0.0780869i | ||||
\(493\) | −14.0000 | −0.630528 | ||||||||
\(494\) | 7.00000 | + | 1.73205i | 0.314945 | + | 0.0779287i | ||||
\(495\) | 8.00000 | 0.359573 | ||||||||
\(496\) | 4.50000 | − | 7.79423i | 0.202056 | − | 0.349971i | ||||
\(497\) | 0.500000 | − | 0.866025i | 0.0224281 | − | 0.0388465i | ||||
\(498\) | −0.500000 | − | 0.866025i | −0.0224055 | − | 0.0388075i | ||||
\(499\) | 7.00000 | 0.313363 | 0.156682 | − | 0.987649i | \(-0.449920\pi\) | ||||
0.156682 | + | 0.987649i | \(0.449920\pi\) | |||||||
\(500\) | −6.00000 | − | 10.3923i | −0.268328 | − | 0.464758i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −23.0000 | −1.02654 | ||||||||
\(503\) | 2.00000 | + | 3.46410i | 0.0891756 | + | 0.154457i | 0.907163 | − | 0.420780i | \(-0.138243\pi\) |
−0.817987 | + | 0.575236i | \(0.804910\pi\) | |||||||
\(504\) | −0.500000 | + | 0.866025i | −0.0222718 | + | 0.0385758i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.00000 | −0.177822 | ||||||||
\(507\) | −11.0000 | + | 6.92820i | −0.488527 | + | 0.307692i | ||||
\(508\) | 16.0000 | 0.709885 | ||||||||
\(509\) | 6.00000 | − | 10.3923i | 0.265945 | − | 0.460631i | −0.701866 | − | 0.712309i | \(-0.747649\pi\) |
0.967811 | + | 0.251679i | \(0.0809826\pi\) | |||||||
\(510\) | −7.00000 | + | 12.1244i | −0.309965 | + | 0.536875i | ||||
\(511\) | 6.00000 | + | 10.3923i | 0.265424 | + | 0.459728i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.00000 | − | 1.73205i | −0.0441511 | − | 0.0764719i | ||||
\(514\) | 13.5000 | + | 23.3827i | 0.595459 | + | 1.03137i | ||||
\(515\) | 22.0000 | 0.969436 | ||||||||
\(516\) | 2.50000 | + | 4.33013i | 0.110056 | + | 0.190623i | ||||
\(517\) | 12.0000 | − | 20.7846i | 0.527759 | − | 0.914106i | ||||
\(518\) | 1.00000 | − | 1.73205i | 0.0439375 | − | 0.0761019i | ||||
\(519\) | −16.0000 | −0.702322 | ||||||||
\(520\) | −7.00000 | − | 1.73205i | −0.306970 | − | 0.0759555i | ||||
\(521\) | −42.0000 | −1.84005 | −0.920027 | − | 0.391856i | \(-0.871833\pi\) | ||||
−0.920027 | + | 0.391856i | \(0.871833\pi\) | |||||||
\(522\) | −1.00000 | + | 1.73205i | −0.0437688 | + | 0.0758098i | ||||
\(523\) | 12.0000 | − | 20.7846i | 0.524723 | − | 0.908848i | −0.474862 | − | 0.880060i | \(-0.657502\pi\) |
0.999586 | − | 0.0287874i | \(-0.00916457\pi\) | |||||||
\(524\) | −7.50000 | − | 12.9904i | −0.327639 | − | 0.567487i | ||||
\(525\) | 1.00000 | 0.0436436 | ||||||||
\(526\) | 2.00000 | + | 3.46410i | 0.0872041 | + | 0.151042i | ||||
\(527\) | 31.5000 | + | 54.5596i | 1.37216 | + | 2.37665i | ||||
\(528\) | −4.00000 | −0.174078 | ||||||||
\(529\) | 11.0000 | + | 19.0526i | 0.478261 | + | 0.828372i | ||||
\(530\) | −3.00000 | + | 5.19615i | −0.130312 | + | 0.225706i | ||||
\(531\) | −7.50000 | + | 12.9904i | −0.325472 | + | 0.563735i | ||||
\(532\) | −2.00000 | −0.0867110 | ||||||||
\(533\) | 5.00000 | − | 5.19615i | 0.216574 | − | 0.225070i | ||||
\(534\) | −3.00000 | −0.129823 | ||||||||
\(535\) | −6.00000 | + | 10.3923i | −0.259403 | + | 0.449299i | ||||
\(536\) | −2.50000 | + | 4.33013i | −0.107984 | + | 0.187033i | ||||
\(537\) | −3.00000 | − | 5.19615i | −0.129460 | − | 0.224231i | ||||
\(538\) | −18.0000 | −0.776035 | ||||||||
\(539\) | 2.00000 | + | 3.46410i | 0.0861461 | + | 0.149209i | ||||
\(540\) | 1.00000 | + | 1.73205i | 0.0430331 | + | 0.0745356i | ||||
\(541\) | 34.0000 | 1.46177 | 0.730887 | − | 0.682498i | \(-0.239107\pi\) | ||||
0.730887 | + | 0.682498i | \(0.239107\pi\) | |||||||
\(542\) | 4.50000 | + | 7.79423i | 0.193292 | + | 0.334791i | ||||
\(543\) | 1.00000 | − | 1.73205i | 0.0429141 | − | 0.0743294i | ||||
\(544\) | 3.50000 | − | 6.06218i | 0.150061 | − | 0.259914i | ||||
\(545\) | 32.0000 | 1.37073 | ||||||||
\(546\) | 2.50000 | − | 2.59808i | 0.106990 | − | 0.111187i | ||||
\(547\) | −4.00000 | −0.171028 | −0.0855138 | − | 0.996337i | \(-0.527253\pi\) | ||||
−0.0855138 | + | 0.996337i | \(0.527253\pi\) | |||||||
\(548\) | −2.00000 | + | 3.46410i | −0.0854358 | + | 0.147979i | ||||
\(549\) | 3.50000 | − | 6.06218i | 0.149376 | − | 0.258727i | ||||
\(550\) | 2.00000 | + | 3.46410i | 0.0852803 | + | 0.147710i | ||||
\(551\) | −4.00000 | −0.170406 | ||||||||
\(552\) | −0.500000 | − | 0.866025i | −0.0212814 | − | 0.0368605i | ||||
\(553\) | −2.00000 | − | 3.46410i | −0.0850487 | − | 0.147309i | ||||
\(554\) | 8.00000 | 0.339887 | ||||||||
\(555\) | −2.00000 | − | 3.46410i | −0.0848953 | − | 0.147043i | ||||
\(556\) | −8.00000 | + | 13.8564i | −0.339276 | + | 0.587643i | ||||
\(557\) | −6.50000 | + | 11.2583i | −0.275414 | + | 0.477031i | −0.970239 | − | 0.242147i | \(-0.922148\pi\) |
0.694826 | + | 0.719178i | \(0.255482\pi\) | |||||||
\(558\) | 9.00000 | 0.381000 | ||||||||
\(559\) | −5.00000 | − | 17.3205i | −0.211477 | − | 0.732579i | ||||
\(560\) | 2.00000 | 0.0845154 | ||||||||
\(561\) | 14.0000 | − | 24.2487i | 0.591080 | − | 1.02378i | ||||
\(562\) | −13.0000 | + | 22.5167i | −0.548372 | + | 0.949808i | ||||
\(563\) | 20.0000 | + | 34.6410i | 0.842900 | + | 1.45994i | 0.887433 | + | 0.460937i | \(0.152487\pi\) |
−0.0445334 | + | 0.999008i | \(0.514180\pi\) | |||||||
\(564\) | 6.00000 | 0.252646 | ||||||||
\(565\) | −8.00000 | − | 13.8564i | −0.336563 | − | 0.582943i | ||||
\(566\) | 7.00000 | + | 12.1244i | 0.294232 | + | 0.509625i | ||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0.500000 | + | 0.866025i | 0.0209795 | + | 0.0363376i | ||||
\(569\) | −13.0000 | + | 22.5167i | −0.544988 | + | 0.943948i | 0.453619 | + | 0.891196i | \(0.350133\pi\) |
−0.998608 | + | 0.0527519i | \(0.983201\pi\) | |||||||
\(570\) | −2.00000 | + | 3.46410i | −0.0837708 | + | 0.145095i | ||||
\(571\) | 23.0000 | 0.962520 | 0.481260 | − | 0.876578i | \(-0.340179\pi\) | ||||
0.481260 | + | 0.876578i | \(0.340179\pi\) | |||||||
\(572\) | 14.0000 | + | 3.46410i | 0.585369 | + | 0.144841i | ||||
\(573\) | 3.00000 | 0.125327 | ||||||||
\(574\) | −1.00000 | + | 1.73205i | −0.0417392 | + | 0.0722944i | ||||
\(575\) | −0.500000 | + | 0.866025i | −0.0208514 | + | 0.0361158i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 6.00000 | 0.249783 | 0.124892 | − | 0.992170i | \(-0.460142\pi\) | ||||
0.124892 | + | 0.992170i | \(0.460142\pi\) | |||||||
\(578\) | 16.0000 | + | 27.7128i | 0.665512 | + | 1.15270i | ||||
\(579\) | 11.0000 | + | 19.0526i | 0.457144 | + | 0.791797i | ||||
\(580\) | 4.00000 | 0.166091 | ||||||||
\(581\) | −0.500000 | − | 0.866025i | −0.0207435 | − | 0.0359288i | ||||
\(582\) | −8.00000 | + | 13.8564i | −0.331611 | + | 0.574367i | ||||
\(583\) | 6.00000 | − | 10.3923i | 0.248495 | − | 0.430405i | ||||
\(584\) | −12.0000 | −0.496564 | ||||||||
\(585\) | −2.00000 | − | 6.92820i | −0.0826898 | − | 0.286446i | ||||
\(586\) | 16.0000 | 0.660954 | ||||||||
\(587\) | −22.5000 | + | 38.9711i | −0.928674 | + | 1.60851i | −0.143132 | + | 0.989704i | \(0.545717\pi\) |
−0.785543 | + | 0.618808i | \(0.787616\pi\) | |||||||
\(588\) | −0.500000 | + | 0.866025i | −0.0206197 | + | 0.0357143i | ||||
\(589\) | 9.00000 | + | 15.5885i | 0.370839 | + | 0.642311i | ||||
\(590\) | 30.0000 | 1.23508 | ||||||||
\(591\) | 4.50000 | + | 7.79423i | 0.185105 | + | 0.320612i | ||||
\(592\) | 1.00000 | + | 1.73205i | 0.0410997 | + | 0.0711868i | ||||
\(593\) | 29.0000 | 1.19089 | 0.595444 | − | 0.803397i | \(-0.296976\pi\) | ||||
0.595444 | + | 0.803397i | \(0.296976\pi\) | |||||||
\(594\) | −2.00000 | − | 3.46410i | −0.0820610 | − | 0.142134i | ||||
\(595\) | −7.00000 | + | 12.1244i | −0.286972 | + | 0.497050i | ||||
\(596\) | −10.5000 | + | 18.1865i | −0.430097 | + | 0.744949i | ||||
\(597\) | −5.00000 | −0.204636 | ||||||||
\(598\) | 1.00000 | + | 3.46410i | 0.0408930 | + | 0.141658i | ||||
\(599\) | 9.00000 | 0.367730 | 0.183865 | − | 0.982952i | \(-0.441139\pi\) | ||||
0.183865 | + | 0.982952i | \(0.441139\pi\) | |||||||
\(600\) | −0.500000 | + | 0.866025i | −0.0204124 | + | 0.0353553i | ||||
\(601\) | −19.0000 | + | 32.9090i | −0.775026 | + | 1.34238i | 0.159754 | + | 0.987157i | \(0.448930\pi\) |
−0.934780 | + | 0.355228i | \(0.884403\pi\) | |||||||
\(602\) | 2.50000 | + | 4.33013i | 0.101892 | + | 0.176483i | ||||
\(603\) | −5.00000 | −0.203616 | ||||||||
\(604\) | −10.0000 | − | 17.3205i | −0.406894 | − | 0.704761i | ||||
\(605\) | 5.00000 | + | 8.66025i | 0.203279 | + | 0.352089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.5000 | − | 40.7032i | −0.953836 | − | 1.65209i | −0.737011 | − | 0.675881i | \(-0.763763\pi\) |
−0.216825 | − | 0.976210i | \(-0.569570\pi\) | |||||||
\(608\) | 1.00000 | − | 1.73205i | 0.0405554 | − | 0.0702439i | ||||
\(609\) | −1.00000 | + | 1.73205i | −0.0405220 | + | 0.0701862i | ||||
\(610\) | −14.0000 | −0.566843 | ||||||||
\(611\) | −21.0000 | − | 5.19615i | −0.849569 | − | 0.210214i | ||||
\(612\) | 7.00000 | 0.282958 | ||||||||
\(613\) | −7.00000 | + | 12.1244i | −0.282727 | + | 0.489698i | −0.972056 | − | 0.234751i | \(-0.924572\pi\) |
0.689328 | + | 0.724449i | \(0.257906\pi\) | |||||||
\(614\) | 15.0000 | − | 25.9808i | 0.605351 | − | 1.04850i | ||||
\(615\) | 2.00000 | + | 3.46410i | 0.0806478 | + | 0.139686i | ||||
\(616\) | −4.00000 | −0.161165 | ||||||||
\(617\) | 10.0000 | + | 17.3205i | 0.402585 | + | 0.697297i | 0.994037 | − | 0.109043i | \(-0.0347785\pi\) |
−0.591452 | + | 0.806340i | \(0.701445\pi\) | |||||||
\(618\) | −5.50000 | − | 9.52628i | −0.221242 | − | 0.383203i | ||||
\(619\) | −22.0000 | −0.884255 | −0.442127 | − | 0.896952i | \(-0.645776\pi\) | ||||
−0.442127 | + | 0.896952i | \(0.645776\pi\) | |||||||
\(620\) | −9.00000 | − | 15.5885i | −0.361449 | − | 0.626048i | ||||
\(621\) | 0.500000 | − | 0.866025i | 0.0200643 | − | 0.0347524i | ||||
\(622\) | 15.0000 | − | 25.9808i | 0.601445 | − | 1.04173i | ||||
\(623\) | −3.00000 | −0.120192 | ||||||||
\(624\) | 1.00000 | + | 3.46410i | 0.0400320 | + | 0.138675i | ||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.00000 | − | 6.92820i | 0.159745 | − | 0.276686i | ||||
\(628\) | −5.00000 | − | 8.66025i | −0.199522 | − | 0.345582i | ||||
\(629\) | −14.0000 | −0.558217 | ||||||||
\(630\) | 1.00000 | + | 1.73205i | 0.0398410 | + | 0.0690066i | ||||
\(631\) | 10.0000 | + | 17.3205i | 0.398094 | + | 0.689519i | 0.993491 | − | 0.113913i | \(-0.0363385\pi\) |
−0.595397 | + | 0.803432i | \(0.703005\pi\) | |||||||
\(632\) | 4.00000 | 0.159111 | ||||||||
\(633\) | −2.00000 | − | 3.46410i | −0.0794929 | − | 0.137686i | ||||
\(634\) | 11.5000 | − | 19.9186i | 0.456723 | − | 0.791068i | ||||
\(635\) | 16.0000 | − | 27.7128i | 0.634941 | − | 1.09975i | ||||
\(636\) | 3.00000 | 0.118958 | ||||||||
\(637\) | 2.50000 | − | 2.59808i | 0.0990536 | − | 0.102940i | ||||
\(638\) | −8.00000 | −0.316723 | ||||||||
\(639\) | −0.500000 | + | 0.866025i | −0.0197797 | + | 0.0342594i | ||||
\(640\) | −1.00000 | + | 1.73205i | −0.0395285 | + | 0.0684653i | ||||
\(641\) | −16.0000 | − | 27.7128i | −0.631962 | − | 1.09459i | −0.987150 | − | 0.159795i | \(-0.948917\pi\) |
0.355188 | − | 0.934795i | \(-0.384417\pi\) | |||||||
\(642\) | 6.00000 | 0.236801 | ||||||||
\(643\) | −7.00000 | − | 12.1244i | −0.276053 | − | 0.478138i | 0.694347 | − | 0.719640i | \(-0.255693\pi\) |
−0.970400 | + | 0.241502i | \(0.922360\pi\) | |||||||
\(644\) | −0.500000 | − | 0.866025i | −0.0197028 | − | 0.0341262i | ||||
\(645\) | 10.0000 | 0.393750 | ||||||||
\(646\) | 7.00000 | + | 12.1244i | 0.275411 | + | 0.477026i | ||||
\(647\) | 3.00000 | − | 5.19615i | 0.117942 | − | 0.204282i | −0.801010 | − | 0.598651i | \(-0.795704\pi\) |
0.918952 | + | 0.394369i | \(0.129037\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | −60.0000 | −2.35521 | ||||||||
\(650\) | 2.50000 | − | 2.59808i | 0.0980581 | − | 0.101905i | ||||
\(651\) | 9.00000 | 0.352738 | ||||||||
\(652\) | −10.5000 | + | 18.1865i | −0.411212 | + | 0.712240i | ||||
\(653\) | −13.5000 | + | 23.3827i | −0.528296 | + | 0.915035i | 0.471160 | + | 0.882048i | \(0.343835\pi\) |
−0.999456 | + | 0.0329874i | \(0.989498\pi\) | |||||||
\(654\) | −8.00000 | − | 13.8564i | −0.312825 | − | 0.541828i | ||||
\(655\) | −30.0000 | −1.17220 | ||||||||
\(656\) | −1.00000 | − | 1.73205i | −0.0390434 | − | 0.0676252i | ||||
\(657\) | −6.00000 | − | 10.3923i | −0.234082 | − | 0.405442i | ||||
\(658\) | 6.00000 | 0.233904 | ||||||||
\(659\) | 3.00000 | + | 5.19615i | 0.116863 | + | 0.202413i | 0.918523 | − | 0.395367i | \(-0.129383\pi\) |
−0.801660 | + | 0.597781i | \(0.796049\pi\) | |||||||
\(660\) | −4.00000 | + | 6.92820i | −0.155700 | + | 0.269680i | ||||
\(661\) | 17.5000 | − | 30.3109i | 0.680671 | − | 1.17896i | −0.294105 | − | 0.955773i | \(-0.595022\pi\) |
0.974776 | − | 0.223184i | \(-0.0716450\pi\) | |||||||
\(662\) | −36.0000 | −1.39918 | ||||||||
\(663\) | −24.5000 | − | 6.06218i | −0.951501 | − | 0.235435i | ||||
\(664\) | 1.00000 | 0.0388075 | ||||||||
\(665\) | −2.00000 | + | 3.46410i | −0.0775567 | + | 0.134332i | ||||
\(666\) | −1.00000 | + | 1.73205i | −0.0387492 | + | 0.0671156i | ||||
\(667\) | −1.00000 | − | 1.73205i | −0.0387202 | − | 0.0670653i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.50000 | − | 2.59808i | −0.0579934 | − | 0.100447i | ||||
\(670\) | 5.00000 | + | 8.66025i | 0.193167 | + | 0.334575i | ||||
\(671\) | 28.0000 | 1.08093 | ||||||||
\(672\) | −0.500000 | − | 0.866025i | −0.0192879 | − | 0.0334077i | ||||
\(673\) | 16.5000 | − | 28.5788i | 0.636028 | − | 1.10163i | −0.350268 | − | 0.936650i | \(-0.613909\pi\) |
0.986296 | − | 0.164984i | \(-0.0527572\pi\) | |||||||
\(674\) | 9.00000 | − | 15.5885i | 0.346667 | − | 0.600445i | ||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −0.500000 | − | 12.9904i | −0.0192308 | − | 0.499630i | ||||
\(677\) | 28.0000 | 1.07613 | 0.538064 | − | 0.842904i | \(-0.319156\pi\) | ||||
0.538064 | + | 0.842904i | \(0.319156\pi\) | |||||||
\(678\) | −4.00000 | + | 6.92820i | −0.153619 | + | 0.266076i | ||||
\(679\) | −8.00000 | + | 13.8564i | −0.307012 | + | 0.531760i | ||||
\(680\) | −7.00000 | − | 12.1244i | −0.268438 | − | 0.464948i | ||||
\(681\) | 28.0000 | 1.07296 | ||||||||
\(682\) | 18.0000 | + | 31.1769i | 0.689256 | + | 1.19383i | ||||
\(683\) | −11.0000 | − | 19.0526i | −0.420903 | − | 0.729026i | 0.575125 | − | 0.818066i | \(-0.304953\pi\) |
−0.996028 | + | 0.0890398i | \(0.971620\pi\) | |||||||
\(684\) | 2.00000 | 0.0764719 | ||||||||
\(685\) | 4.00000 | + | 6.92820i | 0.152832 | + | 0.264713i | ||||
\(686\) | −0.500000 | + | 0.866025i | −0.0190901 | + | 0.0330650i | ||||
\(687\) | −6.50000 | + | 11.2583i | −0.247990 | + | 0.429532i | ||||
\(688\) | −5.00000 | −0.190623 | ||||||||
\(689\) | −10.5000 | − | 2.59808i | −0.400018 | − | 0.0989788i | ||||
\(690\) | −2.00000 | −0.0761387 | ||||||||
\(691\) | 22.0000 | − | 38.1051i | 0.836919 | − | 1.44959i | −0.0555386 | − | 0.998457i | \(-0.517688\pi\) |
0.892458 | − | 0.451130i | \(-0.148979\pi\) | |||||||
\(692\) | 8.00000 | − | 13.8564i | 0.304114 | − | 0.526742i | ||||
\(693\) | −2.00000 | − | 3.46410i | −0.0759737 | − | 0.131590i | ||||
\(694\) | −10.0000 | −0.379595 | ||||||||
\(695\) | 16.0000 | + | 27.7128i | 0.606915 | + | 1.05121i | ||||
\(696\) | −1.00000 | − | 1.73205i | −0.0379049 | − | 0.0656532i | ||||
\(697\) | 14.0000 | 0.530288 | ||||||||
\(698\) | −12.5000 | − | 21.6506i | −0.473132 | − | 0.819489i | ||||
\(699\) | 8.00000 | − | 13.8564i | 0.302588 | − | 0.524097i | ||||
\(700\) | −0.500000 | + | 0.866025i | −0.0188982 | + | 0.0327327i | ||||
\(701\) | −15.0000 | −0.566542 | −0.283271 | − | 0.959040i | \(-0.591420\pi\) | ||||
−0.283271 | + | 0.959040i | \(0.591420\pi\) | |||||||
\(702\) | −2.50000 | + | 2.59808i | −0.0943564 | + | 0.0980581i | ||||
\(703\) | −4.00000 | −0.150863 | ||||||||
\(704\) | 2.00000 | − | 3.46410i | 0.0753778 | − | 0.130558i | ||||
\(705\) | 6.00000 | − | 10.3923i | 0.225973 | − | 0.391397i | ||||
\(706\) | −17.5000 | − | 30.3109i | −0.658621 | − | 1.14077i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −7.50000 | − | 12.9904i | −0.281867 | − | 0.488208i | ||||
\(709\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(710\) | 2.00000 | 0.0750587 | ||||||||
\(711\) | 2.00000 | + | 3.46410i | 0.0750059 | + | 0.129914i | ||||
\(712\) | 1.50000 | − | 2.59808i | 0.0562149 | − | 0.0973670i | ||||
\(713\) | −4.50000 | + | 7.79423i | −0.168526 | + | 0.291896i | ||||
\(714\) | 7.00000 | 0.261968 | ||||||||
\(715\) | 20.0000 | − | 20.7846i | 0.747958 | − | 0.777300i | ||||
\(716\) | 6.00000 | 0.224231 | ||||||||
\(717\) | 4.50000 | − | 7.79423i | 0.168056 | − | 0.291081i | ||||
\(718\) | −12.0000 | + | 20.7846i | −0.447836 | + | 0.775675i | ||||
\(719\) | −10.0000 | − | 17.3205i | −0.372937 | − | 0.645946i | 0.617079 | − | 0.786901i | \(-0.288316\pi\) |
−0.990016 | + | 0.140955i | \(0.954983\pi\) | |||||||
\(720\) | −2.00000 | −0.0745356 | ||||||||
\(721\) | −5.50000 | − | 9.52628i | −0.204831 | − | 0.354777i | ||||
\(722\) | −7.50000 | − | 12.9904i | −0.279121 | − | 0.483452i | ||||
\(723\) | 14.0000 | 0.520666 | ||||||||
\(724\) | 1.00000 | + | 1.73205i | 0.0371647 | + | 0.0643712i | ||||
\(725\) | −1.00000 | + | 1.73205i | −0.0371391 | + | 0.0643268i | ||||
\(726\) | 2.50000 | − | 4.33013i | 0.0927837 | − | 0.160706i | ||||
\(727\) | −21.0000 | −0.778847 | −0.389423 | − | 0.921059i | \(-0.627326\pi\) | ||||
−0.389423 | + | 0.921059i | \(0.627326\pi\) | |||||||
\(728\) | 1.00000 | + | 3.46410i | 0.0370625 | + | 0.128388i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −12.0000 | + | 20.7846i | −0.444140 | + | 0.769273i | ||||
\(731\) | 17.5000 | − | 30.3109i | 0.647261 | − | 1.12109i | ||||
\(732\) | 3.50000 | + | 6.06218i | 0.129364 | + | 0.224065i | ||||
\(733\) | −21.0000 | −0.775653 | −0.387826 | − | 0.921732i | \(-0.626774\pi\) | ||||
−0.387826 | + | 0.921732i | \(0.626774\pi\) | |||||||
\(734\) | −1.50000 | − | 2.59808i | −0.0553660 | − | 0.0958967i | ||||
\(735\) | 1.00000 | + | 1.73205i | 0.0368856 | + | 0.0638877i | ||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −10.0000 | − | 17.3205i | −0.368355 | − | 0.638009i | ||||
\(738\) | 1.00000 | − | 1.73205i | 0.0368105 | − | 0.0637577i | ||||
\(739\) | −24.5000 | + | 42.4352i | −0.901247 | + | 1.56101i | −0.0753699 | + | 0.997156i | \(0.524014\pi\) |
−0.825877 | + | 0.563850i | \(0.809320\pi\) | |||||||
\(740\) | 4.00000 | 0.147043 | ||||||||
\(741\) | −7.00000 | − | 1.73205i | −0.257151 | − | 0.0636285i | ||||
\(742\) | 3.00000 | 0.110133 | ||||||||
\(743\) | 20.5000 | − | 35.5070i | 0.752072 | − | 1.30263i | −0.194745 | − | 0.980854i | \(-0.562388\pi\) |
0.946817 | − | 0.321773i | \(-0.104279\pi\) | |||||||
\(744\) | −4.50000 | + | 7.79423i | −0.164978 | + | 0.285750i | ||||
\(745\) | 21.0000 | + | 36.3731i | 0.769380 | + | 1.33261i | ||||
\(746\) | −4.00000 | −0.146450 | ||||||||
\(747\) | 0.500000 | + | 0.866025i | 0.0182940 | + | 0.0316862i | ||||
\(748\) | 14.0000 | + | 24.2487i | 0.511891 | + | 0.886621i | ||||
\(749\) | 6.00000 | 0.219235 | ||||||||
\(750\) | 6.00000 | + | 10.3923i | 0.219089 | + | 0.379473i | ||||
\(751\) | 13.0000 | − | 22.5167i | 0.474377 | − | 0.821645i | −0.525193 | − | 0.850983i | \(-0.676007\pi\) |
0.999570 | + | 0.0293387i | \(0.00934013\pi\) | |||||||
\(752\) | −3.00000 | + | 5.19615i | −0.109399 | + | 0.189484i | ||||
\(753\) | 23.0000 | 0.838167 | ||||||||
\(754\) | 2.00000 | + | 6.92820i | 0.0728357 | + | 0.252310i | ||||
\(755\) | −40.0000 | −1.45575 | ||||||||
\(756\) | 0.500000 | − | 0.866025i | 0.0181848 | − | 0.0314970i | ||||
\(757\) | −23.0000 | + | 39.8372i | −0.835949 | + | 1.44791i | 0.0573060 | + | 0.998357i | \(0.481749\pi\) |
−0.893255 | + | 0.449550i | \(0.851584\pi\) | |||||||
\(758\) | −10.0000 | − | 17.3205i | −0.363216 | − | 0.629109i | ||||
\(759\) | 4.00000 | 0.145191 | ||||||||
\(760\) | −2.00000 | − | 3.46410i | −0.0725476 | − | 0.125656i | ||||
\(761\) | −5.00000 | − | 8.66025i | −0.181250 | − | 0.313934i | 0.761057 | − | 0.648686i | \(-0.224681\pi\) |
−0.942306 | + | 0.334752i | \(0.891348\pi\) | |||||||
\(762\) | −16.0000 | −0.579619 | ||||||||
\(763\) | −8.00000 | − | 13.8564i | −0.289619 | − | 0.501636i | ||||
\(764\) | −1.50000 | + | 2.59808i | −0.0542681 | + | 0.0939951i | ||||
\(765\) | 7.00000 | − | 12.1244i | 0.253086 | − | 0.438357i | ||||
\(766\) | −24.0000 | −0.867155 | ||||||||
\(767\) | 15.0000 | + | 51.9615i | 0.541619 | + | 1.87622i | ||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −2.00000 | + | 3.46410i | −0.0721218 | + | 0.124919i | −0.899831 | − | 0.436239i | \(-0.856310\pi\) |
0.827709 | + | 0.561157i | \(0.189644\pi\) | |||||||
\(770\) | −4.00000 | + | 6.92820i | −0.144150 | + | 0.249675i | ||||
\(771\) | −13.5000 | − | 23.3827i | −0.486191 | − | 0.842107i | ||||
\(772\) | −22.0000 | −0.791797 | ||||||||
\(773\) | 5.00000 | + | 8.66025i | 0.179838 | + | 0.311488i | 0.941825 | − | 0.336104i | \(-0.109109\pi\) |
−0.761987 | + | 0.647592i | \(0.775776\pi\) | |||||||
\(774\) | −2.50000 | − | 4.33013i | −0.0898606 | − | 0.155643i | ||||
\(775\) | 9.00000 | 0.323290 | ||||||||
\(776\) | −8.00000 | − | 13.8564i | −0.287183 | − | 0.497416i | ||||
\(777\) | −1.00000 | + | 1.73205i | −0.0358748 | + | 0.0621370i | ||||
\(778\) | −0.500000 | + | 0.866025i | −0.0179259 | + | 0.0310485i | ||||
\(779\) | 4.00000 | 0.143315 | ||||||||
\(780\) | 7.00000 | + | 1.73205i | 0.250640 | + | 0.0620174i | ||||
\(781\) | −4.00000 | −0.143131 | ||||||||
\(782\) | −3.50000 | + | 6.06218i | −0.125160 | + | 0.216783i | ||||
\(783\) | 1.00000 | − | 1.73205i | 0.0357371 | − | 0.0618984i | ||||
\(784\) | −0.500000 | − | 0.866025i | −0.0178571 | − | 0.0309295i | ||||
\(785\) | −20.0000 | −0.713831 | ||||||||
\(786\) | 7.50000 | + | 12.9904i | 0.267516 | + | 0.463352i | ||||
\(787\) | −16.0000 | − | 27.7128i | −0.570338 | − | 0.987855i | −0.996531 | − | 0.0832226i | \(-0.973479\pi\) |
0.426193 | − | 0.904632i | \(-0.359855\pi\) | |||||||
\(788\) | −9.00000 | −0.320612 | ||||||||
\(789\) | −2.00000 | − | 3.46410i | −0.0712019 | − | 0.123325i | ||||
\(790\) | 4.00000 | − | 6.92820i | 0.142314 | − | 0.246494i | ||||
\(791\) | −4.00000 | + | 6.92820i | −0.142224 | + | 0.246339i | ||||
\(792\) | 4.00000 | 0.142134 | ||||||||
\(793\) | −7.00000 | − | 24.2487i | −0.248577 | − | 0.861097i | ||||
\(794\) | 1.00000 | 0.0354887 | ||||||||
\(795\) | 3.00000 | − | 5.19615i | 0.106399 | − | 0.184289i | ||||
\(796\) | 2.50000 | − | 4.33013i | 0.0886102 | − | 0.153477i | ||||
\(797\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(798\) | 2.00000 | 0.0707992 | ||||||||
\(799\) | −21.0000 | − | 36.3731i | −0.742927 | − | 1.28679i | ||||
\(800\) | −0.500000 | − | 0.866025i | −0.0176777 | − | 0.0306186i | ||||
\(801\) | 3.00000 | 0.106000 | ||||||||
\(802\) | 16.0000 | + | 27.7128i | 0.564980 | + | 0.978573i | ||||
\(803\) | 24.0000 | − | 41.5692i | 0.846942 | − | 1.46695i | ||||
\(804\) | 2.50000 | − | 4.33013i | 0.0881682 | − | 0.152712i | ||||
\(805\) | −2.00000 | −0.0704907 | ||||||||
\(806\) | 22.5000 | − | 23.3827i | 0.792529 | − | 0.823620i | ||||
\(807\) | 18.0000 | 0.633630 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.0000 | + | 20.7846i | −0.421898 | + | 0.730748i | −0.996125 | − | 0.0879478i | \(-0.971969\pi\) |
0.574228 | + | 0.818696i | \(0.305302\pi\) | |||||||
\(810\) | −1.00000 | − | 1.73205i | −0.0351364 | − | 0.0608581i | ||||
\(811\) | −4.00000 | −0.140459 | −0.0702295 | − | 0.997531i | \(-0.522373\pi\) | ||||
−0.0702295 | + | 0.997531i | \(0.522373\pi\) | |||||||
\(812\) | −1.00000 | − | 1.73205i | −0.0350931 | − | 0.0607831i | ||||
\(813\) | −4.50000 | − | 7.79423i | −0.157822 | − | 0.273356i | ||||
\(814\) | −8.00000 | −0.280400 | ||||||||
\(815\) | 21.0000 | + | 36.3731i | 0.735598 | + | 1.27409i | ||||
\(816\) | −3.50000 | + | 6.06218i | −0.122525 | + | 0.212219i | ||||
\(817\) | 5.00000 | − | 8.66025i | 0.174928 | − | 0.302984i | ||||
\(818\) | −14.0000 | −0.489499 | ||||||||
\(819\) | −2.50000 | + | 2.59808i | −0.0873571 | + | 0.0907841i | ||||
\(820\) | −4.00000 | −0.139686 | ||||||||
\(821\) | −21.5000 | + | 37.2391i | −0.750355 | + | 1.29965i | 0.197295 | + | 0.980344i | \(0.436784\pi\) |
−0.947651 | + | 0.319309i | \(0.896549\pi\) | |||||||
\(822\) | 2.00000 | − | 3.46410i | 0.0697580 | − | 0.120824i | ||||
\(823\) | 10.0000 | + | 17.3205i | 0.348578 | + | 0.603755i | 0.985997 | − | 0.166762i | \(-0.0533313\pi\) |
−0.637419 | + | 0.770517i | \(0.719998\pi\) | |||||||
\(824\) | 11.0000 | 0.383203 | ||||||||
\(825\) | −2.00000 | − | 3.46410i | −0.0696311 | − | 0.120605i | ||||
\(826\) | −7.50000 | − | 12.9904i | −0.260958 | − | 0.451993i | ||||
\(827\) | −8.00000 | −0.278187 | −0.139094 | − | 0.990279i | \(-0.544419\pi\) | ||||
−0.139094 | + | 0.990279i | \(0.544419\pi\) | |||||||
\(828\) | 0.500000 | + | 0.866025i | 0.0173762 | + | 0.0300965i | ||||
\(829\) | −21.0000 | + | 36.3731i | −0.729360 | + | 1.26329i | 0.227794 | + | 0.973709i | \(0.426849\pi\) |
−0.957154 | + | 0.289579i | \(0.906485\pi\) | |||||||
\(830\) | 1.00000 | − | 1.73205i | 0.0347105 | − | 0.0601204i | ||||
\(831\) | −8.00000 | −0.277517 | ||||||||
\(832\) | −3.50000 | − | 0.866025i | −0.121341 | − | 0.0300240i | ||||
\(833\) | 7.00000 | 0.242536 | ||||||||
\(834\) | 8.00000 | − | 13.8564i | 0.277017 | − | 0.479808i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.00000 | + | 6.92820i | 0.138343 | + | 0.239617i | ||||
\(837\) | −9.00000 | −0.311086 | ||||||||
\(838\) | −15.5000 | − | 26.8468i | −0.535439 | − | 0.927407i | ||||
\(839\) | −9.00000 | − | 15.5885i | −0.310715 | − | 0.538173i | 0.667803 | − | 0.744338i | \(-0.267235\pi\) |
−0.978517 | + | 0.206165i | \(0.933902\pi\) | |||||||
\(840\) | −2.00000 | −0.0690066 | ||||||||
\(841\) | 12.5000 | + | 21.6506i | 0.431034 | + | 0.746574i | ||||
\(842\) | 17.0000 | − | 29.4449i | 0.585859 | − | 1.01474i | ||||
\(843\) | 13.0000 | − | 22.5167i | 0.447744 | − | 0.775515i | ||||
\(844\) | 4.00000 | 0.137686 | ||||||||
\(845\) | −23.0000 | − | 12.1244i | −0.791224 | − | 0.417091i | ||||
\(846\) | −6.00000 | −0.206284 | ||||||||
\(847\) | 2.50000 | − | 4.33013i | 0.0859010 | − | 0.148785i | ||||
\(848\) | −1.50000 | + | 2.59808i | −0.0515102 | + | 0.0892183i | ||||
\(849\) | −7.00000 | − | 12.1244i | −0.240239 | − | 0.416107i | ||||
\(850\) | 7.00000 | 0.240098 | ||||||||
\(851\) | −1.00000 | − | 1.73205i | −0.0342796 | − | 0.0593739i | ||||
\(852\) | −0.500000 | − | 0.866025i | −0.0171297 | − | 0.0296695i | ||||
\(853\) | −29.0000 | −0.992941 | −0.496471 | − | 0.868054i | \(-0.665371\pi\) | ||||
−0.496471 | + | 0.868054i | \(0.665371\pi\) | |||||||
\(854\) | 3.50000 | + | 6.06218i | 0.119768 | + | 0.207443i | ||||
\(855\) | 2.00000 | − | 3.46410i | 0.0683986 | − | 0.118470i | ||||
\(856\) | −3.00000 | + | 5.19615i | −0.102538 | + | 0.177601i | ||||
\(857\) | 6.00000 | 0.204956 | 0.102478 | − | 0.994735i | \(-0.467323\pi\) | ||||
0.102478 | + | 0.994735i | \(0.467323\pi\) | |||||||
\(858\) | −14.0000 | − | 3.46410i | −0.477952 | − | 0.118262i | ||||
\(859\) | −14.0000 | −0.477674 | −0.238837 | − | 0.971060i | \(-0.576766\pi\) | ||||
−0.238837 | + | 0.971060i | \(0.576766\pi\) | |||||||
\(860\) | −5.00000 | + | 8.66025i | −0.170499 | + | 0.295312i | ||||
\(861\) | 1.00000 | − | 1.73205i | 0.0340799 | − | 0.0590281i | ||||
\(862\) | −0.500000 | − | 0.866025i | −0.0170301 | − | 0.0294969i | ||||
\(863\) | 48.0000 | 1.63394 | 0.816970 | − | 0.576681i | \(-0.195652\pi\) | ||||
0.816970 | + | 0.576681i | \(0.195652\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | −16.0000 | − | 27.7128i | −0.544016 | − | 0.942264i | ||||
\(866\) | −12.0000 | −0.407777 | ||||||||
\(867\) | −16.0000 | − | 27.7128i | −0.543388 | − | 0.941176i | ||||
\(868\) | −4.50000 | + | 7.79423i | −0.152740 | + | 0.264553i | ||||
\(869\) | −8.00000 | + | 13.8564i | −0.271381 | + | 0.470046i | ||||
\(870\) | −4.00000 | −0.135613 | ||||||||
\(871\) | −12.5000 | + | 12.9904i | −0.423546 | + | 0.440162i | ||||
\(872\) | 16.0000 | 0.541828 | ||||||||
\(873\) | 8.00000 | − | 13.8564i | 0.270759 | − | 0.468968i | ||||
\(874\) | −1.00000 | + | 1.73205i | −0.0338255 | + | 0.0585875i | ||||
\(875\) | 6.00000 | + | 10.3923i | 0.202837 | + | 0.351324i | ||||
\(876\) | 12.0000 | 0.405442 | ||||||||
\(877\) | −13.0000 | − | 22.5167i | −0.438979 | − | 0.760334i | 0.558632 | − | 0.829416i | \(-0.311326\pi\) |
−0.997611 | + | 0.0690819i | \(0.977993\pi\) | |||||||
\(878\) | 2.00000 | + | 3.46410i | 0.0674967 | + | 0.116908i | ||||
\(879\) | −16.0000 | −0.539667 | ||||||||
\(880\) | −4.00000 | − | 6.92820i | −0.134840 | − | 0.233550i | ||||
\(881\) | 23.5000 | − | 40.7032i | 0.791735 | − | 1.37133i | −0.133157 | − | 0.991095i | \(-0.542511\pi\) |
0.924892 | − | 0.380230i | \(-0.124155\pi\) | |||||||
\(882\) | 0.500000 | − | 0.866025i | 0.0168359 | − | 0.0291606i | ||||
\(883\) | −7.00000 | −0.235569 | −0.117784 | − | 0.993039i | \(-0.537579\pi\) | ||||
−0.117784 | + | 0.993039i | \(0.537579\pi\) | |||||||
\(884\) | 17.5000 | − | 18.1865i | 0.588589 | − | 0.611679i | ||||
\(885\) | −30.0000 | −1.00844 | ||||||||
\(886\) | −3.00000 | + | 5.19615i | −0.100787 | + | 0.174568i | ||||
\(887\) | −1.00000 | + | 1.73205i | −0.0335767 | + | 0.0581566i | −0.882325 | − | 0.470640i | \(-0.844023\pi\) |
0.848749 | + | 0.528796i | \(0.177356\pi\) | |||||||
\(888\) | −1.00000 | − | 1.73205i | −0.0335578 | − | 0.0581238i | ||||
\(889\) | −16.0000 | −0.536623 | ||||||||
\(890\) | −3.00000 | − | 5.19615i | −0.100560 | − | 0.174175i | ||||
\(891\) | 2.00000 | + | 3.46410i | 0.0670025 | + | 0.116052i | ||||
\(892\) | 3.00000 | 0.100447 | ||||||||
\(893\) | −6.00000 | − | 10.3923i | −0.200782 | − | 0.347765i | ||||
\(894\) | 10.5000 | − | 18.1865i | 0.351173 | − | 0.608249i | ||||
\(895\) | 6.00000 | − | 10.3923i | 0.200558 | − | 0.347376i | ||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −1.00000 | − | 3.46410i | −0.0333890 | − | 0.115663i | ||||
\(898\) | −18.0000 | −0.600668 | ||||||||
\(899\) | −9.00000 | + | 15.5885i | −0.300167 | + | 0.519904i | ||||
\(900\) | 0.500000 | − | 0.866025i | 0.0166667 | − | 0.0288675i | ||||
\(901\) | −10.5000 | − | 18.1865i | −0.349806 | − | 0.605881i | ||||
\(902\) | 8.00000 | 0.266371 | ||||||||
\(903\) | −2.50000 | − | 4.33013i | −0.0831948 | − | 0.144098i | ||||
\(904\) | −4.00000 | − | 6.92820i | −0.133038 | − | 0.230429i | ||||
\(905\) | 4.00000 | 0.132964 | ||||||||
\(906\) | 10.0000 | + | 17.3205i | 0.332228 | + | 0.575435i | ||||
\(907\) | −19.5000 | + | 33.7750i | −0.647487 | + | 1.12148i | 0.336234 | + | 0.941778i | \(0.390847\pi\) |
−0.983721 | + | 0.179702i | \(0.942487\pi\) | |||||||
\(908\) | −14.0000 | + | 24.2487i | −0.464606 | + | 0.804722i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7.00000 | + | 1.73205i | 0.232048 | + | 0.0574169i | ||||
\(911\) | −24.0000 | −0.795155 | −0.397578 | − | 0.917568i | \(-0.630149\pi\) | ||||
−0.397578 | + | 0.917568i | \(0.630149\pi\) | |||||||
\(912\) | −1.00000 | + | 1.73205i | −0.0331133 | + | 0.0573539i | ||||
\(913\) | −2.00000 | + | 3.46410i | −0.0661903 | + | 0.114645i | ||||
\(914\) | −4.50000 | − | 7.79423i | −0.148847 | − | 0.257810i | ||||
\(915\) | 14.0000 | 0.462826 | ||||||||
\(916\) | −6.50000 | − | 11.2583i | −0.214766 | − | 0.371986i | ||||
\(917\) | 7.50000 | + | 12.9904i | 0.247672 | + | 0.428980i | ||||
\(918\) | −7.00000 | −0.231034 | ||||||||
\(919\) | 23.0000 | + | 39.8372i | 0.758700 | + | 1.31411i | 0.943514 | + | 0.331333i | \(0.107498\pi\) |
−0.184814 | + | 0.982774i | \(0.559168\pi\) | |||||||
\(920\) | 1.00000 | − | 1.73205i | 0.0329690 | − | 0.0571040i | ||||
\(921\) | −15.0000 | + | 25.9808i | −0.494267 | + | 0.856095i | ||||
\(922\) | 20.0000 | 0.658665 | ||||||||
\(923\) | 1.00000 | + | 3.46410i | 0.0329154 | + | 0.114022i | ||||
\(924\) | 4.00000 | 0.131590 | ||||||||
\(925\) | −1.00000 | + | 1.73205i | −0.0328798 | + | 0.0569495i | ||||
\(926\) | 9.00000 | − | 15.5885i | 0.295758 | − | 0.512268i | ||||
\(927\) | 5.50000 | + | 9.52628i | 0.180644 | + | 0.312884i | ||||
\(928\) | 2.00000 | 0.0656532 | ||||||||
\(929\) | 13.5000 | + | 23.3827i | 0.442921 | + | 0.767161i | 0.997905 | − | 0.0646999i | \(-0.0206090\pi\) |
−0.554984 | + | 0.831861i | \(0.687276\pi\) | |||||||
\(930\) | 9.00000 | + | 15.5885i | 0.295122 | + | 0.511166i | ||||
\(931\) | 2.00000 | 0.0655474 | ||||||||
\(932\) | 8.00000 | + | 13.8564i | 0.262049 | + | 0.453882i | ||||
\(933\) | −15.0000 | + | 25.9808i | −0.491078 | + | 0.850572i | ||||
\(934\) | 18.5000 | − | 32.0429i | 0.605338 | − | 1.04848i | ||||
\(935\) | 56.0000 | 1.83140 | ||||||||
\(936\) | −1.00000 | − | 3.46410i | −0.0326860 | − | 0.113228i | ||||
\(937\) | −18.0000 | −0.588034 | −0.294017 | − | 0.955800i | \(-0.594992\pi\) | ||||
−0.294017 | + | 0.955800i | \(0.594992\pi\) | |||||||
\(938\) | 2.50000 | − | 4.33013i | 0.0816279 | − | 0.141384i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.00000 | + | 10.3923i | 0.195698 | + | 0.338960i | ||||
\(941\) | −28.0000 | −0.912774 | −0.456387 | − | 0.889781i | \(-0.650857\pi\) | ||||
−0.456387 | + | 0.889781i | \(0.650857\pi\) | |||||||
\(942\) | 5.00000 | + | 8.66025i | 0.162909 | + | 0.282166i | ||||
\(943\) | 1.00000 | + | 1.73205i | 0.0325645 | + | 0.0564033i | ||||
\(944\) | 15.0000 | 0.488208 | ||||||||
\(945\) | −1.00000 | − | 1.73205i | −0.0325300 | − | 0.0563436i | ||||
\(946\) | 10.0000 | − | 17.3205i | 0.325128 | − | 0.563138i | ||||
\(947\) | −2.00000 | + | 3.46410i | −0.0649913 | + | 0.112568i | −0.896690 | − | 0.442659i | \(-0.854035\pi\) |
0.831699 | + | 0.555227i | \(0.187369\pi\) | |||||||
\(948\) | −4.00000 | −0.129914 | ||||||||
\(949\) | −42.0000 | − | 10.3923i | −1.36338 | − | 0.337348i | ||||
\(950\) | 2.00000 | 0.0648886 | ||||||||
\(951\) | −11.5000 | + | 19.9186i | −0.372913 | + | 0.645904i | ||||
\(952\) | −3.50000 | + | 6.06218i | −0.113436 | + | 0.196476i | ||||
\(953\) | −7.00000 | − | 12.1244i | −0.226752 | − | 0.392746i | 0.730091 | − | 0.683349i | \(-0.239477\pi\) |
−0.956844 | + | 0.290603i | \(0.906144\pi\) | |||||||
\(954\) | −3.00000 | −0.0971286 | ||||||||
\(955\) | 3.00000 | + | 5.19615i | 0.0970777 | + | 0.168144i | ||||
\(956\) | 4.50000 | + | 7.79423i | 0.145540 | + | 0.252083i | ||||
\(957\) | 8.00000 | 0.258603 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.00000 | − | 3.46410i | 0.0645834 | − | 0.111862i | ||||
\(960\) | 1.00000 | − | 1.73205i | 0.0322749 | − | 0.0559017i | ||||
\(961\) | 50.0000 | 1.61290 | ||||||||
\(962\) | 2.00000 | + | 6.92820i | 0.0644826 | + | 0.223374i | ||||
\(963\) | −6.00000 | −0.193347 | ||||||||
\(964\) | −7.00000 | + | 12.1244i | −0.225455 | + | 0.390499i | ||||
\(965\) | −22.0000 | + | 38.1051i | −0.708205 | + | 1.22665i | ||||
\(966\) | 0.500000 | + | 0.866025i | 0.0160872 | + | 0.0278639i | ||||
\(967\) | 18.0000 | 0.578841 | 0.289420 | − | 0.957202i | \(-0.406537\pi\) | ||||
0.289420 | + | 0.957202i | \(0.406537\pi\) | |||||||
\(968\) | 2.50000 | + | 4.33013i | 0.0803530 | + | 0.139176i | ||||
\(969\) | −7.00000 | − | 12.1244i | −0.224872 | − | 0.389490i | ||||
\(970\) | −32.0000 | −1.02746 | ||||||||
\(971\) | −7.50000 | − | 12.9904i | −0.240686 | − | 0.416881i | 0.720224 | − | 0.693742i | \(-0.244039\pi\) |
−0.960910 | + | 0.276861i | \(0.910706\pi\) | |||||||
\(972\) | −0.500000 | + | 0.866025i | −0.0160375 | + | 0.0277778i | ||||
\(973\) | 8.00000 | − | 13.8564i | 0.256468 | − | 0.444216i | ||||
\(974\) | 28.0000 | 0.897178 | ||||||||
\(975\) | −2.50000 | + | 2.59808i | −0.0800641 | + | 0.0832050i | ||||
\(976\) | −7.00000 | −0.224065 | ||||||||
\(977\) | 24.0000 | − | 41.5692i | 0.767828 | − | 1.32992i | −0.170910 | − | 0.985287i | \(-0.554671\pi\) |
0.938738 | − | 0.344631i | \(-0.111996\pi\) | |||||||
\(978\) | 10.5000 | − | 18.1865i | 0.335753 | − | 0.581541i | ||||
\(979\) | 6.00000 | + | 10.3923i | 0.191761 | + | 0.332140i | ||||
\(980\) | −2.00000 | −0.0638877 | ||||||||
\(981\) | 8.00000 | + | 13.8564i | 0.255420 | + | 0.442401i | ||||
\(982\) | −4.00000 | − | 6.92820i | −0.127645 | − | 0.221088i | ||||
\(983\) | −46.0000 | −1.46717 | −0.733586 | − | 0.679597i | \(-0.762155\pi\) | ||||
−0.733586 | + | 0.679597i | \(0.762155\pi\) | |||||||
\(984\) | 1.00000 | + | 1.73205i | 0.0318788 | + | 0.0552158i | ||||
\(985\) | −9.00000 | + | 15.5885i | −0.286764 | + | 0.496690i | ||||
\(986\) | −7.00000 | + | 12.1244i | −0.222925 | + | 0.386118i | ||||
\(987\) | −6.00000 | −0.190982 | ||||||||
\(988\) | 5.00000 | − | 5.19615i | 0.159071 | − | 0.165312i | ||||
\(989\) | 5.00000 | 0.158991 | ||||||||
\(990\) | 4.00000 | − | 6.92820i | 0.127128 | − | 0.220193i | ||||
\(991\) | −9.00000 | + | 15.5885i | −0.285894 | + | 0.495184i | −0.972826 | − | 0.231539i | \(-0.925624\pi\) |
0.686931 | + | 0.726722i | \(0.258957\pi\) | |||||||
\(992\) | −4.50000 | − | 7.79423i | −0.142875 | − | 0.247467i | ||||
\(993\) | 36.0000 | 1.14243 | ||||||||
\(994\) | −0.500000 | − | 0.866025i | −0.0158590 | − | 0.0274687i | ||||
\(995\) | −5.00000 | − | 8.66025i | −0.158511 | − | 0.274549i | ||||
\(996\) | −1.00000 | −0.0316862 | ||||||||
\(997\) | 17.5000 | + | 30.3109i | 0.554231 | + | 0.959955i | 0.997963 | + | 0.0637961i | \(0.0203207\pi\) |
−0.443732 | + | 0.896159i | \(0.646346\pi\) | |||||||
\(998\) | 3.50000 | − | 6.06218i | 0.110791 | − | 0.191895i | ||||
\(999\) | 1.00000 | − | 1.73205i | 0.0316386 | − | 0.0547997i |
(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 | 546.2.l.d.295.1 | yes | 2 | |
3.2 | odd | 2 | 1638.2.r.k.1387.1 | 2 | |||
13.3 | even | 3 | inner | 546.2.l.d.211.1 | ✓ | 2 | |
13.4 | even | 6 | 7098.2.a.bf.1.1 | 1 | |||
13.9 | even | 3 | 7098.2.a.h.1.1 | 1 | |||
39.29 | odd | 6 | 1638.2.r.k.757.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.l.d.211.1 | ✓ | 2 | 13.3 | even | 3 | inner | |
546.2.l.d.295.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1638.2.r.k.757.1 | 2 | 39.29 | odd | 6 | |||
1638.2.r.k.1387.1 | 2 | 3.2 | odd | 2 | |||
7098.2.a.h.1.1 | 1 | 13.9 | even | 3 | |||
7098.2.a.bf.1.1 | 1 | 13.4 | even | 6 |