Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(499,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.499");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.o (of order \(6\), 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: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 499.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.499 |
Dual form | 1050.2.o.k.949.1 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0.866025 | − | 2.50000i | 0.327327 | − | 0.944911i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | + | 3.46410i | 0.603023 | + | 1.04447i | 0.992361 | + | 0.123371i | \(0.0393705\pi\) |
−0.389338 | + | 0.921095i | \(0.627296\pi\) | |||||||
\(12\) | −0.866025 | − | 0.500000i | −0.250000 | − | 0.144338i | ||||
\(13\) | − | 1.00000i | − | 0.277350i | −0.990338 | − | 0.138675i | \(-0.955716\pi\) | ||
0.990338 | − | 0.138675i | \(-0.0442844\pi\) | |||||||
\(14\) | −2.00000 | + | 1.73205i | −0.534522 | + | 0.462910i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.73205 | − | 1.00000i | 0.420084 | − | 0.242536i | −0.275029 | − | 0.961436i | \(-0.588688\pi\) |
0.695113 | + | 0.718900i | \(0.255354\pi\) | |||||||
\(18\) | −0.866025 | + | 0.500000i | −0.204124 | + | 0.117851i | ||||
\(19\) | 0.500000 | − | 0.866025i | 0.114708 | − | 0.198680i | −0.802955 | − | 0.596040i | \(-0.796740\pi\) |
0.917663 | + | 0.397360i | \(0.130073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.500000 | + | 2.59808i | 0.109109 | + | 0.566947i | ||||
\(22\) | − | 4.00000i | − | 0.852803i | ||||||
\(23\) | −1.73205 | − | 1.00000i | −0.361158 | − | 0.208514i | 0.308431 | − | 0.951247i | \(-0.400196\pi\) |
−0.669588 | + | 0.742732i | \(0.733529\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.500000 | + | 0.866025i | −0.0980581 | + | 0.169842i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 2.59808 | − | 0.500000i | 0.490990 | − | 0.0944911i | ||||
\(29\) | −4.00000 | −0.742781 | −0.371391 | − | 0.928477i | \(-0.621119\pi\) | ||||
−0.371391 | + | 0.928477i | \(0.621119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | −3.46410 | − | 2.00000i | −0.603023 | − | 0.348155i | ||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −2.59808 | − | 1.50000i | −0.427121 | − | 0.246598i | 0.270998 | − | 0.962580i | \(-0.412646\pi\) |
−0.698119 | + | 0.715981i | \(0.745980\pi\) | |||||||
\(38\) | −0.866025 | + | 0.500000i | −0.140488 | + | 0.0811107i | ||||
\(39\) | 0.500000 | + | 0.866025i | 0.0800641 | + | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.0000 | 1.87409 | 0.937043 | − | 0.349215i | \(-0.113552\pi\) | ||||
0.937043 | + | 0.349215i | \(0.113552\pi\) | |||||||
\(42\) | 0.866025 | − | 2.50000i | 0.133631 | − | 0.385758i | ||||
\(43\) | − | 8.00000i | − | 1.21999i | −0.792406 | − | 0.609994i | \(-0.791172\pi\) | ||
0.792406 | − | 0.609994i | \(-0.208828\pi\) | |||||||
\(44\) | −2.00000 | + | 3.46410i | −0.301511 | + | 0.522233i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | + | 1.73205i | 0.147442 | + | 0.255377i | ||||
\(47\) | 5.19615 | + | 3.00000i | 0.757937 | + | 0.437595i | 0.828554 | − | 0.559908i | \(-0.189164\pi\) |
−0.0706177 | + | 0.997503i | \(0.522497\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | −5.50000 | − | 4.33013i | −0.785714 | − | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.00000 | + | 1.73205i | −0.140028 | + | 0.242536i | ||||
\(52\) | 0.866025 | − | 0.500000i | 0.120096 | − | 0.0693375i | ||||
\(53\) | −1.73205 | + | 1.00000i | −0.237915 | + | 0.137361i | −0.614218 | − | 0.789136i | \(-0.710529\pi\) |
0.376303 | + | 0.926497i | \(0.377195\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.50000 | − | 0.866025i | −0.334077 | − | 0.115728i | ||||
\(57\) | 1.00000i | 0.132453i | ||||||||
\(58\) | 3.46410 | + | 2.00000i | 0.454859 | + | 0.262613i | ||||
\(59\) | 3.00000 | + | 5.19615i | 0.390567 | + | 0.676481i | 0.992524 | − | 0.122047i | \(-0.0389457\pi\) |
−0.601958 | + | 0.798528i | \(0.705612\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.50000 | − | 11.2583i | 0.832240 | − | 1.44148i | −0.0640184 | − | 0.997949i | \(-0.520392\pi\) |
0.896258 | − | 0.443533i | \(-0.146275\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.73205 | − | 2.00000i | −0.218218 | − | 0.251976i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.00000 | + | 3.46410i | 0.246183 | + | 0.426401i | ||||
\(67\) | 2.59808 | − | 1.50000i | 0.317406 | − | 0.183254i | −0.332830 | − | 0.942987i | \(-0.608004\pi\) |
0.650236 | + | 0.759733i | \(0.274670\pi\) | |||||||
\(68\) | 1.73205 | + | 1.00000i | 0.210042 | + | 0.121268i | ||||
\(69\) | 2.00000 | 0.240772 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.0000 | 1.89885 | 0.949425 | − | 0.313993i | \(-0.101667\pi\) | ||||
0.949425 | + | 0.313993i | \(0.101667\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | 9.52628 | − | 5.50000i | 1.11497 | − | 0.643726i | 0.174855 | − | 0.984594i | \(-0.444054\pi\) |
0.940111 | + | 0.340868i | \(0.110721\pi\) | |||||||
\(74\) | 1.50000 | + | 2.59808i | 0.174371 | + | 0.302020i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 10.3923 | − | 2.00000i | 1.18431 | − | 0.227921i | ||||
\(78\) | − | 1.00000i | − | 0.113228i | ||||||
\(79\) | 6.50000 | − | 11.2583i | 0.731307 | − | 1.26666i | −0.225018 | − | 0.974355i | \(-0.572244\pi\) |
0.956325 | − | 0.292306i | \(-0.0944227\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −10.3923 | − | 6.00000i | −1.14764 | − | 0.662589i | ||||
\(83\) | 6.00000i | 0.658586i | 0.944228 | + | 0.329293i | \(0.106810\pi\) | ||||
−0.944228 | + | 0.329293i | \(0.893190\pi\) | |||||||
\(84\) | −2.00000 | + | 1.73205i | −0.218218 | + | 0.188982i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.00000 | + | 6.92820i | −0.431331 | + | 0.747087i | ||||
\(87\) | 3.46410 | − | 2.00000i | 0.371391 | − | 0.214423i | ||||
\(88\) | 3.46410 | − | 2.00000i | 0.369274 | − | 0.213201i | ||||
\(89\) | −1.00000 | + | 1.73205i | −0.106000 | + | 0.183597i | −0.914146 | − | 0.405385i | \(-0.867138\pi\) |
0.808146 | + | 0.588982i | \(0.200471\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.50000 | − | 0.866025i | −0.262071 | − | 0.0907841i | ||||
\(92\) | − | 2.00000i | − | 0.208514i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.00000 | − | 5.19615i | −0.309426 | − | 0.535942i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | 17.0000i | 1.72609i | 0.505128 | + | 0.863044i | \(0.331445\pi\) | ||||
−0.505128 | + | 0.863044i | \(0.668555\pi\) | |||||||
\(98\) | 2.59808 | + | 6.50000i | 0.262445 | + | 0.656599i | ||||
\(99\) | 4.00000 | 0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | − | 10.3923i | −0.597022 | − | 1.03407i | −0.993258 | − | 0.115924i | \(-0.963017\pi\) |
0.396236 | − | 0.918149i | \(-0.370316\pi\) | |||||||
\(102\) | 1.73205 | − | 1.00000i | 0.171499 | − | 0.0990148i | ||||
\(103\) | 6.06218 | + | 3.50000i | 0.597324 | + | 0.344865i | 0.767988 | − | 0.640464i | \(-0.221258\pi\) |
−0.170664 | + | 0.985329i | \(0.554591\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.00000 | 0.194257 | ||||||||
\(107\) | −5.19615 | − | 3.00000i | −0.502331 | − | 0.290021i | 0.227345 | − | 0.973814i | \(-0.426996\pi\) |
−0.729676 | + | 0.683793i | \(0.760329\pi\) | |||||||
\(108\) | −0.866025 | + | 0.500000i | −0.0833333 | + | 0.0481125i | ||||
\(109\) | −9.50000 | − | 16.4545i | −0.909935 | − | 1.57605i | −0.814152 | − | 0.580651i | \(-0.802798\pi\) |
−0.0957826 | − | 0.995402i | \(-0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.00000 | 0.284747 | ||||||||
\(112\) | 1.73205 | + | 2.00000i | 0.163663 | + | 0.188982i | ||||
\(113\) | − | 18.0000i | − | 1.69330i | −0.532152 | − | 0.846649i | \(-0.678617\pi\) | ||
0.532152 | − | 0.846649i | \(-0.321383\pi\) | |||||||
\(114\) | 0.500000 | − | 0.866025i | 0.0468293 | − | 0.0811107i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.00000 | − | 3.46410i | −0.185695 | − | 0.321634i | ||||
\(117\) | −0.866025 | − | 0.500000i | −0.0800641 | − | 0.0462250i | ||||
\(118\) | − | 6.00000i | − | 0.552345i | ||||||
\(119\) | −1.00000 | − | 5.19615i | −0.0916698 | − | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.50000 | + | 4.33013i | −0.227273 | + | 0.393648i | ||||
\(122\) | −11.2583 | + | 6.50000i | −1.01928 | + | 0.588482i | ||||
\(123\) | −10.3923 | + | 6.00000i | −0.937043 | + | 0.541002i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.500000 | + | 2.59808i | 0.0445435 | + | 0.231455i | ||||
\(127\) | − | 1.00000i | − | 0.0887357i | −0.999015 | − | 0.0443678i | \(-0.985873\pi\) | ||
0.999015 | − | 0.0443678i | \(-0.0141274\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 4.00000 | + | 6.92820i | 0.352180 | + | 0.609994i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.00000 | + | 1.73205i | −0.0873704 | + | 0.151330i | −0.906399 | − | 0.422423i | \(-0.861180\pi\) |
0.819028 | + | 0.573753i | \(0.194513\pi\) | |||||||
\(132\) | − | 4.00000i | − | 0.348155i | ||||||
\(133\) | −1.73205 | − | 2.00000i | −0.150188 | − | 0.173422i | ||||
\(134\) | −3.00000 | −0.259161 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.00000 | − | 1.73205i | −0.0857493 | − | 0.148522i | ||||
\(137\) | 8.66025 | − | 5.00000i | 0.739895 | − | 0.427179i | −0.0821359 | − | 0.996621i | \(-0.526174\pi\) |
0.822031 | + | 0.569442i | \(0.192841\pi\) | |||||||
\(138\) | −1.73205 | − | 1.00000i | −0.147442 | − | 0.0851257i | ||||
\(139\) | 13.0000 | 1.10265 | 0.551323 | − | 0.834292i | \(-0.314123\pi\) | ||||
0.551323 | + | 0.834292i | \(0.314123\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | −13.8564 | − | 8.00000i | −1.16280 | − | 0.671345i | ||||
\(143\) | 3.46410 | − | 2.00000i | 0.289683 | − | 0.167248i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −11.0000 | −0.910366 | ||||||||
\(147\) | 6.92820 | + | 1.00000i | 0.571429 | + | 0.0824786i | ||||
\(148\) | − | 3.00000i | − | 0.246598i | ||||||
\(149\) | −8.00000 | + | 13.8564i | −0.655386 | + | 1.13516i | 0.326411 | + | 0.945228i | \(0.394160\pi\) |
−0.981797 | + | 0.189933i | \(0.939173\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.50000 | − | 16.4545i | −0.773099 | − | 1.33905i | −0.935857 | − | 0.352381i | \(-0.885372\pi\) |
0.162758 | − | 0.986666i | \(-0.447961\pi\) | |||||||
\(152\) | −0.866025 | − | 0.500000i | −0.0702439 | − | 0.0405554i | ||||
\(153\) | − | 2.00000i | − | 0.161690i | ||||||
\(154\) | −10.0000 | − | 3.46410i | −0.805823 | − | 0.279145i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.500000 | + | 0.866025i | −0.0400320 | + | 0.0693375i | ||||
\(157\) | −18.1865 | + | 10.5000i | −1.45144 | + | 0.837991i | −0.998564 | − | 0.0535803i | \(-0.982937\pi\) |
−0.452880 | + | 0.891572i | \(0.649603\pi\) | |||||||
\(158\) | −11.2583 | + | 6.50000i | −0.895665 | + | 0.517112i | ||||
\(159\) | 1.00000 | − | 1.73205i | 0.0793052 | − | 0.137361i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.00000 | + | 3.46410i | −0.315244 | + | 0.273009i | ||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 19.9186 | + | 11.5000i | 1.56014 | + | 0.900750i | 0.997241 | + | 0.0742262i | \(0.0236487\pi\) |
0.562902 | + | 0.826523i | \(0.309685\pi\) | |||||||
\(164\) | 6.00000 | + | 10.3923i | 0.468521 | + | 0.811503i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.00000 | − | 5.19615i | 0.232845 | − | 0.403300i | ||||
\(167\) | 10.0000i | 0.773823i | 0.922117 | + | 0.386912i | \(0.126458\pi\) | ||||
−0.922117 | + | 0.386912i | \(0.873542\pi\) | |||||||
\(168\) | 2.59808 | − | 0.500000i | 0.200446 | − | 0.0385758i | ||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.500000 | − | 0.866025i | −0.0382360 | − | 0.0662266i | ||||
\(172\) | 6.92820 | − | 4.00000i | 0.528271 | − | 0.304997i | ||||
\(173\) | −5.19615 | − | 3.00000i | −0.395056 | − | 0.228086i | 0.289292 | − | 0.957241i | \(-0.406580\pi\) |
−0.684349 | + | 0.729155i | \(0.739913\pi\) | |||||||
\(174\) | −4.00000 | −0.303239 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.00000 | −0.301511 | ||||||||
\(177\) | −5.19615 | − | 3.00000i | −0.390567 | − | 0.225494i | ||||
\(178\) | 1.73205 | − | 1.00000i | 0.129823 | − | 0.0749532i | ||||
\(179\) | −4.00000 | − | 6.92820i | −0.298974 | − | 0.517838i | 0.676927 | − | 0.736050i | \(-0.263311\pi\) |
−0.975901 | + | 0.218212i | \(0.929978\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.0000 | −1.33793 | −0.668965 | − | 0.743294i | \(-0.733262\pi\) | ||||
−0.668965 | + | 0.743294i | \(0.733262\pi\) | |||||||
\(182\) | 1.73205 | + | 2.00000i | 0.128388 | + | 0.148250i | ||||
\(183\) | 13.0000i | 0.960988i | ||||||||
\(184\) | −1.00000 | + | 1.73205i | −0.0737210 | + | 0.127688i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.92820 | + | 4.00000i | 0.506640 | + | 0.292509i | ||||
\(188\) | 6.00000i | 0.437595i | ||||||||
\(189\) | 2.50000 | + | 0.866025i | 0.181848 | + | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.0000 | + | 17.3205i | −0.723575 | + | 1.25327i | 0.235983 | + | 0.971757i | \(0.424169\pi\) |
−0.959558 | + | 0.281511i | \(0.909164\pi\) | |||||||
\(192\) | 0.866025 | − | 0.500000i | 0.0625000 | − | 0.0360844i | ||||
\(193\) | 8.66025 | − | 5.00000i | 0.623379 | − | 0.359908i | −0.154805 | − | 0.987945i | \(-0.549475\pi\) |
0.778183 | + | 0.628037i | \(0.216141\pi\) | |||||||
\(194\) | 8.50000 | − | 14.7224i | 0.610264 | − | 1.05701i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | − | 6.92820i | 0.0714286 | − | 0.494872i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | −3.46410 | − | 2.00000i | −0.246183 | − | 0.142134i | ||||
\(199\) | 7.50000 | + | 12.9904i | 0.531661 | + | 0.920864i | 0.999317 | + | 0.0369532i | \(0.0117652\pi\) |
−0.467656 | + | 0.883911i | \(0.654901\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.50000 | + | 2.59808i | −0.105802 | + | 0.183254i | ||||
\(202\) | 12.0000i | 0.844317i | ||||||||
\(203\) | −3.46410 | + | 10.0000i | −0.243132 | + | 0.701862i | ||||
\(204\) | −2.00000 | −0.140028 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.50000 | − | 6.06218i | −0.243857 | − | 0.422372i | ||||
\(207\) | −1.73205 | + | 1.00000i | −0.120386 | + | 0.0695048i | ||||
\(208\) | 0.866025 | + | 0.500000i | 0.0600481 | + | 0.0346688i | ||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.00000 | 0.206529 | 0.103264 | − | 0.994654i | \(-0.467071\pi\) | ||||
0.103264 | + | 0.994654i | \(0.467071\pi\) | |||||||
\(212\) | −1.73205 | − | 1.00000i | −0.118958 | − | 0.0686803i | ||||
\(213\) | −13.8564 | + | 8.00000i | −0.949425 | + | 0.548151i | ||||
\(214\) | 3.00000 | + | 5.19615i | 0.205076 | + | 0.355202i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 19.0000i | 1.28684i | ||||||||
\(219\) | −5.50000 | + | 9.52628i | −0.371656 | + | 0.643726i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.00000 | − | 1.73205i | −0.0672673 | − | 0.116510i | ||||
\(222\) | −2.59808 | − | 1.50000i | −0.174371 | − | 0.100673i | ||||
\(223\) | 19.0000i | 1.27233i | 0.771551 | + | 0.636167i | \(0.219481\pi\) | ||||
−0.771551 | + | 0.636167i | \(0.780519\pi\) | |||||||
\(224\) | −0.500000 | − | 2.59808i | −0.0334077 | − | 0.173591i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.00000 | + | 15.5885i | −0.598671 | + | 1.03693i | ||||
\(227\) | −6.92820 | + | 4.00000i | −0.459841 | + | 0.265489i | −0.711977 | − | 0.702202i | \(-0.752200\pi\) |
0.252136 | + | 0.967692i | \(0.418867\pi\) | |||||||
\(228\) | −0.866025 | + | 0.500000i | −0.0573539 | + | 0.0331133i | ||||
\(229\) | −3.50000 | + | 6.06218i | −0.231287 | + | 0.400600i | −0.958187 | − | 0.286143i | \(-0.907627\pi\) |
0.726900 | + | 0.686743i | \(0.240960\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.00000 | + | 6.92820i | −0.526361 | + | 0.455842i | ||||
\(232\) | 4.00000i | 0.262613i | ||||||||
\(233\) | −3.46410 | − | 2.00000i | −0.226941 | − | 0.131024i | 0.382219 | − | 0.924072i | \(-0.375160\pi\) |
−0.609160 | + | 0.793047i | \(0.708493\pi\) | |||||||
\(234\) | 0.500000 | + | 0.866025i | 0.0326860 | + | 0.0566139i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.00000 | + | 5.19615i | −0.195283 | + | 0.338241i | ||||
\(237\) | 13.0000i | 0.844441i | ||||||||
\(238\) | −1.73205 | + | 5.00000i | −0.112272 | + | 0.324102i | ||||
\(239\) | 12.0000 | 0.776215 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.50000 | − | 11.2583i | −0.418702 | − | 0.725213i | 0.577107 | − | 0.816668i | \(-0.304181\pi\) |
−0.995809 | + | 0.0914555i | \(0.970848\pi\) | |||||||
\(242\) | 4.33013 | − | 2.50000i | 0.278351 | − | 0.160706i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 13.0000 | 0.832240 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 12.0000 | 0.765092 | ||||||||
\(247\) | −0.866025 | − | 0.500000i | −0.0551039 | − | 0.0318142i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.00000 | − | 5.19615i | −0.190117 | − | 0.329293i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.0000 | 1.51487 | 0.757433 | − | 0.652913i | \(-0.226453\pi\) | ||||
0.757433 | + | 0.652913i | \(0.226453\pi\) | |||||||
\(252\) | 0.866025 | − | 2.50000i | 0.0545545 | − | 0.157485i | ||||
\(253\) | − | 8.00000i | − | 0.502956i | ||||||
\(254\) | −0.500000 | + | 0.866025i | −0.0313728 | + | 0.0543393i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 6.92820 | + | 4.00000i | 0.432169 | + | 0.249513i | 0.700270 | − | 0.713878i | \(-0.253063\pi\) |
−0.268101 | + | 0.963391i | \(0.586396\pi\) | |||||||
\(258\) | − | 8.00000i | − | 0.498058i | ||||||
\(259\) | −6.00000 | + | 5.19615i | −0.372822 | + | 0.322873i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.00000 | + | 3.46410i | −0.123797 | + | 0.214423i | ||||
\(262\) | 1.73205 | − | 1.00000i | 0.107006 | − | 0.0617802i | ||||
\(263\) | −27.7128 | + | 16.0000i | −1.70885 | + | 0.986602i | −0.772851 | + | 0.634588i | \(0.781170\pi\) |
−0.935995 | + | 0.352014i | \(0.885497\pi\) | |||||||
\(264\) | −2.00000 | + | 3.46410i | −0.123091 | + | 0.213201i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.500000 | + | 2.59808i | 0.0306570 | + | 0.159298i | ||||
\(267\) | − | 2.00000i | − | 0.122398i | ||||||
\(268\) | 2.59808 | + | 1.50000i | 0.158703 | + | 0.0916271i | ||||
\(269\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.0000 | − | 17.3205i | 0.607457 | − | 1.05215i | −0.384201 | − | 0.923249i | \(-0.625523\pi\) |
0.991658 | − | 0.128897i | \(-0.0411435\pi\) | |||||||
\(272\) | 2.00000i | 0.121268i | ||||||||
\(273\) | 2.59808 | − | 0.500000i | 0.157243 | − | 0.0302614i | ||||
\(274\) | −10.0000 | −0.604122 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.00000 | + | 1.73205i | 0.0601929 | + | 0.104257i | ||||
\(277\) | 0.866025 | − | 0.500000i | 0.0520344 | − | 0.0300421i | −0.473757 | − | 0.880656i | \(-0.657103\pi\) |
0.525792 | + | 0.850613i | \(0.323769\pi\) | |||||||
\(278\) | −11.2583 | − | 6.50000i | −0.675230 | − | 0.389844i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.0000 | −1.07379 | −0.536895 | − | 0.843649i | \(-0.680403\pi\) | ||||
−0.536895 | + | 0.843649i | \(0.680403\pi\) | |||||||
\(282\) | 5.19615 | + | 3.00000i | 0.309426 | + | 0.178647i | ||||
\(283\) | −11.2583 | + | 6.50000i | −0.669238 | + | 0.386385i | −0.795788 | − | 0.605575i | \(-0.792943\pi\) |
0.126550 | + | 0.991960i | \(0.459610\pi\) | |||||||
\(284\) | 8.00000 | + | 13.8564i | 0.474713 | + | 0.822226i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.00000 | −0.236525 | ||||||||
\(287\) | 10.3923 | − | 30.0000i | 0.613438 | − | 1.77084i | ||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | −6.50000 | + | 11.2583i | −0.382353 | + | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.50000 | − | 14.7224i | −0.498279 | − | 0.863044i | ||||
\(292\) | 9.52628 | + | 5.50000i | 0.557483 | + | 0.321863i | ||||
\(293\) | − | 12.0000i | − | 0.701047i | −0.936554 | − | 0.350524i | \(-0.886004\pi\) | ||
0.936554 | − | 0.350524i | \(-0.113996\pi\) | |||||||
\(294\) | −5.50000 | − | 4.33013i | −0.320767 | − | 0.252538i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.50000 | + | 2.59808i | −0.0871857 | + | 0.151010i | ||||
\(297\) | −3.46410 | + | 2.00000i | −0.201008 | + | 0.116052i | ||||
\(298\) | 13.8564 | − | 8.00000i | 0.802680 | − | 0.463428i | ||||
\(299\) | −1.00000 | + | 1.73205i | −0.0578315 | + | 0.100167i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.0000 | − | 6.92820i | −1.15278 | − | 0.399335i | ||||
\(302\) | 19.0000i | 1.09333i | ||||||||
\(303\) | 10.3923 | + | 6.00000i | 0.597022 | + | 0.344691i | ||||
\(304\) | 0.500000 | + | 0.866025i | 0.0286770 | + | 0.0496700i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.00000 | + | 1.73205i | −0.0571662 | + | 0.0990148i | ||||
\(307\) | 20.0000i | 1.14146i | 0.821138 | + | 0.570730i | \(0.193340\pi\) | ||||
−0.821138 | + | 0.570730i | \(0.806660\pi\) | |||||||
\(308\) | 6.92820 | + | 8.00000i | 0.394771 | + | 0.455842i | ||||
\(309\) | −7.00000 | −0.398216 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.00000 | + | 12.1244i | 0.396934 | + | 0.687509i | 0.993346 | − | 0.115169i | \(-0.0367410\pi\) |
−0.596412 | + | 0.802678i | \(0.703408\pi\) | |||||||
\(312\) | 0.866025 | − | 0.500000i | 0.0490290 | − | 0.0283069i | ||||
\(313\) | −15.5885 | − | 9.00000i | −0.881112 | − | 0.508710i | −0.0100869 | − | 0.999949i | \(-0.503211\pi\) |
−0.871025 | + | 0.491239i | \(0.836544\pi\) | |||||||
\(314\) | 21.0000 | 1.18510 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.0000 | 0.731307 | ||||||||
\(317\) | −19.0526 | − | 11.0000i | −1.07010 | − | 0.617822i | −0.141890 | − | 0.989882i | \(-0.545318\pi\) |
−0.928208 | + | 0.372061i | \(0.878651\pi\) | |||||||
\(318\) | −1.73205 | + | 1.00000i | −0.0971286 | + | 0.0560772i | ||||
\(319\) | −8.00000 | − | 13.8564i | −0.447914 | − | 0.775810i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.00000 | 0.334887 | ||||||||
\(322\) | 5.19615 | − | 1.00000i | 0.289570 | − | 0.0557278i | ||||
\(323\) | − | 2.00000i | − | 0.111283i | ||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −11.5000 | − | 19.9186i | −0.636926 | − | 1.10319i | ||||
\(327\) | 16.4545 | + | 9.50000i | 0.909935 | + | 0.525351i | ||||
\(328\) | − | 12.0000i | − | 0.662589i | ||||||
\(329\) | 12.0000 | − | 10.3923i | 0.661581 | − | 0.572946i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.5000 | + | 18.1865i | −0.577132 | + | 0.999622i | 0.418674 | + | 0.908137i | \(0.362495\pi\) |
−0.995806 | + | 0.0914858i | \(0.970838\pi\) | |||||||
\(332\) | −5.19615 | + | 3.00000i | −0.285176 | + | 0.164646i | ||||
\(333\) | −2.59808 | + | 1.50000i | −0.142374 | + | 0.0821995i | ||||
\(334\) | 5.00000 | − | 8.66025i | 0.273588 | − | 0.473868i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.50000 | − | 0.866025i | −0.136386 | − | 0.0472456i | ||||
\(337\) | − | 18.0000i | − | 0.980522i | −0.871576 | − | 0.490261i | \(-0.836901\pi\) | ||
0.871576 | − | 0.490261i | \(-0.163099\pi\) | |||||||
\(338\) | −10.3923 | − | 6.00000i | −0.565267 | − | 0.326357i | ||||
\(339\) | 9.00000 | + | 15.5885i | 0.488813 | + | 0.846649i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 1.00000i | 0.0540738i | ||||||||
\(343\) | −15.5885 | + | 10.0000i | −0.841698 | + | 0.539949i | ||||
\(344\) | −8.00000 | −0.431331 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.00000 | + | 5.19615i | 0.161281 | + | 0.279347i | ||||
\(347\) | −19.0526 | + | 11.0000i | −1.02279 | + | 0.590511i | −0.914912 | − | 0.403653i | \(-0.867740\pi\) |
−0.107883 | + | 0.994164i | \(0.534407\pi\) | |||||||
\(348\) | 3.46410 | + | 2.00000i | 0.185695 | + | 0.107211i | ||||
\(349\) | −2.00000 | −0.107058 | −0.0535288 | − | 0.998566i | \(-0.517047\pi\) | ||||
−0.0535288 | + | 0.998566i | \(0.517047\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 3.46410 | + | 2.00000i | 0.184637 | + | 0.106600i | ||||
\(353\) | 17.3205 | − | 10.0000i | 0.921878 | − | 0.532246i | 0.0376440 | − | 0.999291i | \(-0.488015\pi\) |
0.884234 | + | 0.467045i | \(0.154681\pi\) | |||||||
\(354\) | 3.00000 | + | 5.19615i | 0.159448 | + | 0.276172i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.00000 | −0.106000 | ||||||||
\(357\) | 3.46410 | + | 4.00000i | 0.183340 | + | 0.211702i | ||||
\(358\) | 8.00000i | 0.422813i | ||||||||
\(359\) | −3.00000 | + | 5.19615i | −0.158334 | + | 0.274242i | −0.934268 | − | 0.356572i | \(-0.883946\pi\) |
0.775934 | + | 0.630814i | \(0.217279\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | + | 15.5885i | 0.473684 | + | 0.820445i | ||||
\(362\) | 15.5885 | + | 9.00000i | 0.819311 | + | 0.473029i | ||||
\(363\) | − | 5.00000i | − | 0.262432i | ||||||
\(364\) | −0.500000 | − | 2.59808i | −0.0262071 | − | 0.136176i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.50000 | − | 11.2583i | 0.339760 | − | 0.588482i | ||||
\(367\) | −6.92820 | + | 4.00000i | −0.361649 | + | 0.208798i | −0.669804 | − | 0.742538i | \(-0.733622\pi\) |
0.308155 | + | 0.951336i | \(0.400289\pi\) | |||||||
\(368\) | 1.73205 | − | 1.00000i | 0.0902894 | − | 0.0521286i | ||||
\(369\) | 6.00000 | − | 10.3923i | 0.312348 | − | 0.541002i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.00000 | + | 5.19615i | 0.0519174 | + | 0.269771i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.9186 | + | 11.5000i | 1.03135 | + | 0.595447i | 0.917370 | − | 0.398036i | \(-0.130308\pi\) |
0.113975 | + | 0.993484i | \(0.463641\pi\) | |||||||
\(374\) | −4.00000 | − | 6.92820i | −0.206835 | − | 0.358249i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.00000 | − | 5.19615i | 0.154713 | − | 0.267971i | ||||
\(377\) | 4.00000i | 0.206010i | ||||||||
\(378\) | −1.73205 | − | 2.00000i | −0.0890871 | − | 0.102869i | ||||
\(379\) | 5.00000 | 0.256833 | 0.128416 | − | 0.991720i | \(-0.459011\pi\) | ||||
0.128416 | + | 0.991720i | \(0.459011\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.500000 | + | 0.866025i | 0.0256158 | + | 0.0443678i | ||||
\(382\) | 17.3205 | − | 10.0000i | 0.886194 | − | 0.511645i | ||||
\(383\) | −12.1244 | − | 7.00000i | −0.619526 | − | 0.357683i | 0.157159 | − | 0.987573i | \(-0.449767\pi\) |
−0.776684 | + | 0.629890i | \(0.783100\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.0000 | −0.508987 | ||||||||
\(387\) | −6.92820 | − | 4.00000i | −0.352180 | − | 0.203331i | ||||
\(388\) | −14.7224 | + | 8.50000i | −0.747418 | + | 0.431522i | ||||
\(389\) | −10.0000 | − | 17.3205i | −0.507020 | − | 0.878185i | −0.999967 | − | 0.00812520i | \(-0.997414\pi\) |
0.492947 | − | 0.870059i | \(-0.335920\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.00000 | −0.202289 | ||||||||
\(392\) | −4.33013 | + | 5.50000i | −0.218704 | + | 0.277792i | ||||
\(393\) | − | 2.00000i | − | 0.100887i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.00000 | + | 3.46410i | 0.100504 | + | 0.174078i | ||||
\(397\) | 15.5885 | + | 9.00000i | 0.782362 | + | 0.451697i | 0.837267 | − | 0.546795i | \(-0.184152\pi\) |
−0.0549046 | + | 0.998492i | \(0.517485\pi\) | |||||||
\(398\) | − | 15.0000i | − | 0.751882i | ||||||
\(399\) | 2.50000 | + | 0.866025i | 0.125157 | + | 0.0433555i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.00000 | + | 3.46410i | −0.0998752 | + | 0.172989i | −0.911633 | − | 0.411005i | \(-0.865178\pi\) |
0.811758 | + | 0.583994i | \(0.198511\pi\) | |||||||
\(402\) | 2.59808 | − | 1.50000i | 0.129580 | − | 0.0748132i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 6.00000 | − | 10.3923i | 0.298511 | − | 0.517036i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.00000 | − | 6.92820i | 0.397033 | − | 0.343841i | ||||
\(407\) | − | 12.0000i | − | 0.594818i | ||||||
\(408\) | 1.73205 | + | 1.00000i | 0.0857493 | + | 0.0495074i | ||||
\(409\) | −5.50000 | − | 9.52628i | −0.271957 | − | 0.471044i | 0.697406 | − | 0.716677i | \(-0.254338\pi\) |
−0.969363 | + | 0.245633i | \(0.921004\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.00000 | + | 8.66025i | −0.246632 | + | 0.427179i | ||||
\(412\) | 7.00000i | 0.344865i | ||||||||
\(413\) | 15.5885 | − | 3.00000i | 0.767058 | − | 0.147620i | ||||
\(414\) | 2.00000 | 0.0982946 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.500000 | − | 0.866025i | −0.0245145 | − | 0.0424604i | ||||
\(417\) | −11.2583 | + | 6.50000i | −0.551323 | + | 0.318306i | ||||
\(418\) | −3.46410 | − | 2.00000i | −0.169435 | − | 0.0978232i | ||||
\(419\) | 16.0000 | 0.781651 | 0.390826 | − | 0.920465i | \(-0.372190\pi\) | ||||
0.390826 | + | 0.920465i | \(0.372190\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.00000 | 0.0487370 | 0.0243685 | − | 0.999703i | \(-0.492242\pi\) | ||||
0.0243685 | + | 0.999703i | \(0.492242\pi\) | |||||||
\(422\) | −2.59808 | − | 1.50000i | −0.126472 | − | 0.0730189i | ||||
\(423\) | 5.19615 | − | 3.00000i | 0.252646 | − | 0.145865i | ||||
\(424\) | 1.00000 | + | 1.73205i | 0.0485643 | + | 0.0841158i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 16.0000 | 0.775203 | ||||||||
\(427\) | −22.5167 | − | 26.0000i | −1.08966 | − | 1.25823i | ||||
\(428\) | − | 6.00000i | − | 0.290021i | ||||||
\(429\) | −2.00000 | + | 3.46410i | −0.0965609 | + | 0.167248i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.00000 | − | 5.19615i | −0.144505 | − | 0.250290i | 0.784683 | − | 0.619897i | \(-0.212826\pi\) |
−0.929188 | + | 0.369607i | \(0.879492\pi\) | |||||||
\(432\) | −0.866025 | − | 0.500000i | −0.0416667 | − | 0.0240563i | ||||
\(433\) | 2.00000i | 0.0961139i | 0.998845 | + | 0.0480569i | \(0.0153029\pi\) | ||||
−0.998845 | + | 0.0480569i | \(0.984697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.50000 | − | 16.4545i | 0.454967 | − | 0.788027i | ||||
\(437\) | −1.73205 | + | 1.00000i | −0.0828552 | + | 0.0478365i | ||||
\(438\) | 9.52628 | − | 5.50000i | 0.455183 | − | 0.262800i | ||||
\(439\) | −11.5000 | + | 19.9186i | −0.548865 | + | 0.950662i | 0.449488 | + | 0.893287i | \(0.351607\pi\) |
−0.998353 | + | 0.0573756i | \(0.981727\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.50000 | + | 2.59808i | −0.309524 | + | 0.123718i | ||||
\(442\) | 2.00000i | 0.0951303i | ||||||||
\(443\) | 5.19615 | + | 3.00000i | 0.246877 | + | 0.142534i | 0.618333 | − | 0.785916i | \(-0.287808\pi\) |
−0.371457 | + | 0.928450i | \(0.621142\pi\) | |||||||
\(444\) | 1.50000 | + | 2.59808i | 0.0711868 | + | 0.123299i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9.50000 | − | 16.4545i | 0.449838 | − | 0.779142i | ||||
\(447\) | − | 16.0000i | − | 0.756774i | ||||||
\(448\) | −0.866025 | + | 2.50000i | −0.0409159 | + | 0.118114i | ||||
\(449\) | −2.00000 | −0.0943858 | −0.0471929 | − | 0.998886i | \(-0.515028\pi\) | ||||
−0.0471929 | + | 0.998886i | \(0.515028\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.0000 | + | 41.5692i | 1.13012 | + | 1.95742i | ||||
\(452\) | 15.5885 | − | 9.00000i | 0.733219 | − | 0.423324i | ||||
\(453\) | 16.4545 | + | 9.50000i | 0.773099 | + | 0.446349i | ||||
\(454\) | 8.00000 | 0.375459 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | −32.0429 | − | 18.5000i | −1.49891 | − | 0.865393i | −0.498906 | − | 0.866656i | \(-0.666265\pi\) |
−0.999999 | + | 0.00126243i | \(0.999598\pi\) | |||||||
\(458\) | 6.06218 | − | 3.50000i | 0.283267 | − | 0.163544i | ||||
\(459\) | 1.00000 | + | 1.73205i | 0.0466760 | + | 0.0808452i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.0000 | 1.21094 | 0.605470 | − | 0.795868i | \(-0.292985\pi\) | ||||
0.605470 | + | 0.795868i | \(0.292985\pi\) | |||||||
\(462\) | 10.3923 | − | 2.00000i | 0.483494 | − | 0.0930484i | ||||
\(463\) | 3.00000i | 0.139422i | 0.997567 | + | 0.0697109i | \(0.0222077\pi\) | ||||
−0.997567 | + | 0.0697109i | \(0.977792\pi\) | |||||||
\(464\) | 2.00000 | − | 3.46410i | 0.0928477 | − | 0.160817i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.00000 | + | 3.46410i | 0.0926482 | + | 0.160471i | ||||
\(467\) | −25.9808 | − | 15.0000i | −1.20225 | − | 0.694117i | −0.241192 | − | 0.970477i | \(-0.577538\pi\) |
−0.961054 | + | 0.276360i | \(0.910872\pi\) | |||||||
\(468\) | − | 1.00000i | − | 0.0462250i | ||||||
\(469\) | −1.50000 | − | 7.79423i | −0.0692636 | − | 0.359904i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.5000 | − | 18.1865i | 0.483814 | − | 0.837991i | ||||
\(472\) | 5.19615 | − | 3.00000i | 0.239172 | − | 0.138086i | ||||
\(473\) | 27.7128 | − | 16.0000i | 1.27424 | − | 0.735681i | ||||
\(474\) | 6.50000 | − | 11.2583i | 0.298555 | − | 0.517112i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.00000 | − | 3.46410i | 0.183340 | − | 0.158777i | ||||
\(477\) | 2.00000i | 0.0915737i | ||||||||
\(478\) | −10.3923 | − | 6.00000i | −0.475333 | − | 0.274434i | ||||
\(479\) | −17.0000 | − | 29.4449i | −0.776750 | − | 1.34537i | −0.933806 | − | 0.357780i | \(-0.883534\pi\) |
0.157056 | − | 0.987590i | \(-0.449800\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.50000 | + | 2.59808i | −0.0683941 | + | 0.118462i | ||||
\(482\) | 13.0000i | 0.592134i | ||||||||
\(483\) | 1.73205 | − | 5.00000i | 0.0788110 | − | 0.227508i | ||||
\(484\) | −5.00000 | −0.227273 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | 34.6410 | − | 20.0000i | 1.56973 | − | 0.906287i | 0.573535 | − | 0.819181i | \(-0.305572\pi\) |
0.996199 | − | 0.0871056i | \(-0.0277618\pi\) | |||||||
\(488\) | −11.2583 | − | 6.50000i | −0.509641 | − | 0.294241i | ||||
\(489\) | −23.0000 | −1.04010 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.0000 | 0.812329 | 0.406164 | − | 0.913800i | \(-0.366866\pi\) | ||||
0.406164 | + | 0.913800i | \(0.366866\pi\) | |||||||
\(492\) | −10.3923 | − | 6.00000i | −0.468521 | − | 0.270501i | ||||
\(493\) | −6.92820 | + | 4.00000i | −0.312031 | + | 0.180151i | ||||
\(494\) | 0.500000 | + | 0.866025i | 0.0224961 | + | 0.0389643i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.8564 | − | 40.0000i | 0.621545 | − | 1.79425i | ||||
\(498\) | 6.00000i | 0.268866i | ||||||||
\(499\) | −13.5000 | + | 23.3827i | −0.604343 | + | 1.04675i | 0.387812 | + | 0.921739i | \(0.373231\pi\) |
−0.992155 | + | 0.125014i | \(0.960102\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.00000 | − | 8.66025i | −0.223384 | − | 0.386912i | ||||
\(502\) | −20.7846 | − | 12.0000i | −0.927663 | − | 0.535586i | ||||
\(503\) | − | 4.00000i | − | 0.178351i | −0.996016 | − | 0.0891756i | \(-0.971577\pi\) | ||
0.996016 | − | 0.0891756i | \(-0.0284232\pi\) | |||||||
\(504\) | −2.00000 | + | 1.73205i | −0.0890871 | + | 0.0771517i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.00000 | + | 6.92820i | −0.177822 | + | 0.307996i | ||||
\(507\) | −10.3923 | + | 6.00000i | −0.461538 | + | 0.266469i | ||||
\(508\) | 0.866025 | − | 0.500000i | 0.0384237 | − | 0.0221839i | ||||
\(509\) | −18.0000 | + | 31.1769i | −0.797836 | + | 1.38189i | 0.123187 | + | 0.992384i | \(0.460689\pi\) |
−0.921023 | + | 0.389509i | \(0.872645\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.50000 | − | 28.5788i | −0.243306 | − | 1.26425i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0.866025 | + | 0.500000i | 0.0382360 | + | 0.0220755i | ||||
\(514\) | −4.00000 | − | 6.92820i | −0.176432 | − | 0.305590i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.00000 | + | 6.92820i | −0.176090 | + | 0.304997i | ||||
\(517\) | 24.0000i | 1.05552i | ||||||||
\(518\) | 7.79423 | − | 1.50000i | 0.342459 | − | 0.0659062i | ||||
\(519\) | 6.00000 | 0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.00000 | − | 5.19615i | −0.131432 | − | 0.227648i | 0.792797 | − | 0.609486i | \(-0.208624\pi\) |
−0.924229 | + | 0.381839i | \(0.875291\pi\) | |||||||
\(522\) | 3.46410 | − | 2.00000i | 0.151620 | − | 0.0875376i | ||||
\(523\) | 13.8564 | + | 8.00000i | 0.605898 | + | 0.349816i | 0.771358 | − | 0.636401i | \(-0.219578\pi\) |
−0.165460 | + | 0.986216i | \(0.552911\pi\) | |||||||
\(524\) | −2.00000 | −0.0873704 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 32.0000 | 1.39527 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 3.46410 | − | 2.00000i | 0.150756 | − | 0.0870388i | ||||
\(529\) | −9.50000 | − | 16.4545i | −0.413043 | − | 0.715412i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.00000 | 0.260378 | ||||||||
\(532\) | 0.866025 | − | 2.50000i | 0.0375470 | − | 0.108389i | ||||
\(533\) | − | 12.0000i | − | 0.519778i | ||||||
\(534\) | −1.00000 | + | 1.73205i | −0.0432742 | + | 0.0749532i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.50000 | − | 2.59808i | −0.0647901 | − | 0.112220i | ||||
\(537\) | 6.92820 | + | 4.00000i | 0.298974 | + | 0.172613i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.00000 | − | 27.7128i | 0.172292 | − | 1.19368i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.50000 | + | 14.7224i | −0.365444 | + | 0.632967i | −0.988847 | − | 0.148933i | \(-0.952416\pi\) |
0.623404 | + | 0.781900i | \(0.285749\pi\) | |||||||
\(542\) | −17.3205 | + | 10.0000i | −0.743980 | + | 0.429537i | ||||
\(543\) | 15.5885 | − | 9.00000i | 0.668965 | − | 0.386227i | ||||
\(544\) | 1.00000 | − | 1.73205i | 0.0428746 | − | 0.0742611i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.50000 | − | 0.866025i | −0.106990 | − | 0.0370625i | ||||
\(547\) | − | 12.0000i | − | 0.513083i | −0.966533 | − | 0.256541i | \(-0.917417\pi\) | ||
0.966533 | − | 0.256541i | \(-0.0825830\pi\) | |||||||
\(548\) | 8.66025 | + | 5.00000i | 0.369948 | + | 0.213589i | ||||
\(549\) | −6.50000 | − | 11.2583i | −0.277413 | − | 0.480494i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.00000 | + | 3.46410i | −0.0852029 | + | 0.147576i | ||||
\(552\) | − | 2.00000i | − | 0.0851257i | ||||||
\(553\) | −22.5167 | − | 26.0000i | −0.957506 | − | 1.10563i | ||||
\(554\) | −1.00000 | −0.0424859 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.50000 | + | 11.2583i | 0.275661 | + | 0.477460i | ||||
\(557\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.00000 | −0.337760 | ||||||||
\(562\) | 15.5885 | + | 9.00000i | 0.657559 | + | 0.379642i | ||||
\(563\) | 24.2487 | − | 14.0000i | 1.02196 | − | 0.590030i | 0.107290 | − | 0.994228i | \(-0.465783\pi\) |
0.914671 | + | 0.404198i | \(0.132449\pi\) | |||||||
\(564\) | −3.00000 | − | 5.19615i | −0.126323 | − | 0.218797i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 13.0000 | 0.546431 | ||||||||
\(567\) | −2.59808 | + | 0.500000i | −0.109109 | + | 0.0209980i | ||||
\(568\) | − | 16.0000i | − | 0.671345i | ||||||
\(569\) | −20.0000 | + | 34.6410i | −0.838444 | + | 1.45223i | 0.0527519 | + | 0.998608i | \(0.483201\pi\) |
−0.891196 | + | 0.453619i | \(0.850133\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.5000 | + | 30.3109i | 0.732352 | + | 1.26847i | 0.955875 | + | 0.293773i | \(0.0949108\pi\) |
−0.223523 | + | 0.974699i | \(0.571756\pi\) | |||||||
\(572\) | 3.46410 | + | 2.00000i | 0.144841 | + | 0.0836242i | ||||
\(573\) | − | 20.0000i | − | 0.835512i | ||||||
\(574\) | −24.0000 | + | 20.7846i | −1.00174 | + | 0.867533i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 19.0526 | − | 11.0000i | 0.793168 | − | 0.457936i | −0.0479084 | − | 0.998852i | \(-0.515256\pi\) |
0.841077 | + | 0.540916i | \(0.181922\pi\) | |||||||
\(578\) | 11.2583 | − | 6.50000i | 0.468285 | − | 0.270364i | ||||
\(579\) | −5.00000 | + | 8.66025i | −0.207793 | + | 0.359908i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.0000 | + | 5.19615i | 0.622305 | + | 0.215573i | ||||
\(582\) | 17.0000i | 0.704673i | ||||||||
\(583\) | −6.92820 | − | 4.00000i | −0.286937 | − | 0.165663i | ||||
\(584\) | −5.50000 | − | 9.52628i | −0.227592 | − | 0.394200i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.00000 | + | 10.3923i | −0.247858 | + | 0.429302i | ||||
\(587\) | − | 42.0000i | − | 1.73353i | −0.498721 | − | 0.866763i | \(-0.666197\pi\) | ||
0.498721 | − | 0.866763i | \(-0.333803\pi\) | |||||||
\(588\) | 2.59808 | + | 6.50000i | 0.107143 | + | 0.268055i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.59808 | − | 1.50000i | 0.106780 | − | 0.0616496i | ||||
\(593\) | 36.3731 | + | 21.0000i | 1.49366 | + | 0.862367i | 0.999974 | − | 0.00727173i | \(-0.00231468\pi\) |
0.493689 | + | 0.869638i | \(0.335648\pi\) | |||||||
\(594\) | 4.00000 | 0.164122 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −16.0000 | −0.655386 | ||||||||
\(597\) | −12.9904 | − | 7.50000i | −0.531661 | − | 0.306955i | ||||
\(598\) | 1.73205 | − | 1.00000i | 0.0708288 | − | 0.0408930i | ||||
\(599\) | −3.00000 | − | 5.19615i | −0.122577 | − | 0.212309i | 0.798206 | − | 0.602384i | \(-0.205782\pi\) |
−0.920783 | + | 0.390075i | \(0.872449\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.0000 | −1.18293 | −0.591467 | − | 0.806329i | \(-0.701451\pi\) | ||||
−0.591467 | + | 0.806329i | \(0.701451\pi\) | |||||||
\(602\) | 13.8564 | + | 16.0000i | 0.564745 | + | 0.652111i | ||||
\(603\) | − | 3.00000i | − | 0.122169i | ||||||
\(604\) | 9.50000 | − | 16.4545i | 0.386550 | − | 0.669523i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.00000 | − | 10.3923i | −0.243733 | − | 0.422159i | ||||
\(607\) | −0.866025 | − | 0.500000i | −0.0351509 | − | 0.0202944i | 0.482322 | − | 0.875994i | \(-0.339794\pi\) |
−0.517472 | + | 0.855700i | \(0.673127\pi\) | |||||||
\(608\) | − | 1.00000i | − | 0.0405554i | ||||||
\(609\) | −2.00000 | − | 10.3923i | −0.0810441 | − | 0.421117i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.00000 | − | 5.19615i | 0.121367 | − | 0.210214i | ||||
\(612\) | 1.73205 | − | 1.00000i | 0.0700140 | − | 0.0404226i | ||||
\(613\) | −5.19615 | + | 3.00000i | −0.209871 | + | 0.121169i | −0.601251 | − | 0.799060i | \(-0.705331\pi\) |
0.391381 | + | 0.920229i | \(0.371998\pi\) | |||||||
\(614\) | 10.0000 | − | 17.3205i | 0.403567 | − | 0.698999i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.00000 | − | 10.3923i | −0.0805823 | − | 0.418718i | ||||
\(617\) | 44.0000i | 1.77137i | 0.464283 | + | 0.885687i | \(0.346312\pi\) | ||||
−0.464283 | + | 0.885687i | \(0.653688\pi\) | |||||||
\(618\) | 6.06218 | + | 3.50000i | 0.243857 | + | 0.140791i | ||||
\(619\) | 22.0000 | + | 38.1051i | 0.884255 | + | 1.53157i | 0.846566 | + | 0.532284i | \(0.178666\pi\) |
0.0376891 | + | 0.999290i | \(0.488000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | − | 1.73205i | 0.0401286 | − | 0.0695048i | ||||
\(622\) | − | 14.0000i | − | 0.561349i | ||||||
\(623\) | 3.46410 | + | 4.00000i | 0.138786 | + | 0.160257i | ||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 9.00000 | + | 15.5885i | 0.359712 | + | 0.623040i | ||||
\(627\) | −3.46410 | + | 2.00000i | −0.138343 | + | 0.0798723i | ||||
\(628\) | −18.1865 | − | 10.5000i | −0.725722 | − | 0.418996i | ||||
\(629\) | −6.00000 | −0.239236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.0000 | 0.676759 | 0.338380 | − | 0.941010i | \(-0.390121\pi\) | ||||
0.338380 | + | 0.941010i | \(0.390121\pi\) | |||||||
\(632\) | −11.2583 | − | 6.50000i | −0.447832 | − | 0.258556i | ||||
\(633\) | −2.59808 | + | 1.50000i | −0.103264 | + | 0.0596196i | ||||
\(634\) | 11.0000 | + | 19.0526i | 0.436866 | + | 0.756674i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.00000 | 0.0793052 | ||||||||
\(637\) | −4.33013 | + | 5.50000i | −0.171566 | + | 0.217918i | ||||
\(638\) | 16.0000i | 0.633446i | ||||||||
\(639\) | 8.00000 | − | 13.8564i | 0.316475 | − | 0.548151i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.00000 | − | 13.8564i | −0.315981 | − | 0.547295i | 0.663665 | − | 0.748030i | \(-0.269000\pi\) |
−0.979646 | + | 0.200735i | \(0.935667\pi\) | |||||||
\(642\) | −5.19615 | − | 3.00000i | −0.205076 | − | 0.118401i | ||||
\(643\) | − | 11.0000i | − | 0.433798i | −0.976194 | − | 0.216899i | \(-0.930406\pi\) | ||
0.976194 | − | 0.216899i | \(-0.0695942\pi\) | |||||||
\(644\) | −5.00000 | − | 1.73205i | −0.197028 | − | 0.0682524i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.00000 | + | 1.73205i | −0.0393445 | + | 0.0681466i | ||||
\(647\) | 10.3923 | − | 6.00000i | 0.408564 | − | 0.235884i | −0.281609 | − | 0.959529i | \(-0.590868\pi\) |
0.690172 | + | 0.723645i | \(0.257535\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | −12.0000 | + | 20.7846i | −0.471041 | + | 0.815867i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 23.0000i | 0.900750i | ||||||||
\(653\) | −13.8564 | − | 8.00000i | −0.542243 | − | 0.313064i | 0.203744 | − | 0.979024i | \(-0.434689\pi\) |
−0.745988 | + | 0.665960i | \(0.768022\pi\) | |||||||
\(654\) | −9.50000 | − | 16.4545i | −0.371479 | − | 0.643421i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.00000 | + | 10.3923i | −0.234261 | + | 0.405751i | ||||
\(657\) | − | 11.0000i | − | 0.429151i | ||||||
\(658\) | −15.5885 | + | 3.00000i | −0.607701 | + | 0.116952i | ||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.5000 | + | 21.6506i | 0.486194 | + | 0.842112i | 0.999874 | − | 0.0158695i | \(-0.00505163\pi\) |
−0.513680 | + | 0.857982i | \(0.671718\pi\) | |||||||
\(662\) | 18.1865 | − | 10.5000i | 0.706840 | − | 0.408094i | ||||
\(663\) | 1.73205 | + | 1.00000i | 0.0672673 | + | 0.0388368i | ||||
\(664\) | 6.00000 | 0.232845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.00000 | 0.116248 | ||||||||
\(667\) | 6.92820 | + | 4.00000i | 0.268261 | + | 0.154881i | ||||
\(668\) | −8.66025 | + | 5.00000i | −0.335075 | + | 0.193456i | ||||
\(669\) | −9.50000 | − | 16.4545i | −0.367291 | − | 0.636167i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 52.0000 | 2.00744 | ||||||||
\(672\) | 1.73205 | + | 2.00000i | 0.0668153 | + | 0.0771517i | ||||
\(673\) | 9.00000i | 0.346925i | 0.984841 | + | 0.173462i | \(0.0554955\pi\) | ||||
−0.984841 | + | 0.173462i | \(0.944505\pi\) | |||||||
\(674\) | −9.00000 | + | 15.5885i | −0.346667 | + | 0.600445i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.00000 | + | 10.3923i | 0.230769 | + | 0.399704i | ||||
\(677\) | 1.73205 | + | 1.00000i | 0.0665681 | + | 0.0384331i | 0.532915 | − | 0.846169i | \(-0.321097\pi\) |
−0.466347 | + | 0.884602i | \(0.654430\pi\) | |||||||
\(678\) | − | 18.0000i | − | 0.691286i | ||||||
\(679\) | 42.5000 | + | 14.7224i | 1.63100 | + | 0.564995i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.00000 | − | 6.92820i | 0.153280 | − | 0.265489i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −41.5692 | + | 24.0000i | −1.59060 | + | 0.918334i | −0.597398 | + | 0.801945i | \(0.703799\pi\) |
−0.993204 | + | 0.116390i | \(0.962868\pi\) | |||||||
\(684\) | 0.500000 | − | 0.866025i | 0.0191180 | − | 0.0331133i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 18.5000 | − | 0.866025i | 0.706333 | − | 0.0330650i | ||||
\(687\) | − | 7.00000i | − | 0.267067i | ||||||
\(688\) | 6.92820 | + | 4.00000i | 0.264135 | + | 0.152499i | ||||
\(689\) | 1.00000 | + | 1.73205i | 0.0380970 | + | 0.0659859i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.5000 | − | 33.7750i | 0.741815 | − | 1.28486i | −0.209853 | − | 0.977733i | \(-0.567299\pi\) |
0.951668 | − | 0.307128i | \(-0.0993681\pi\) | |||||||
\(692\) | − | 6.00000i | − | 0.228086i | ||||||
\(693\) | 3.46410 | − | 10.0000i | 0.131590 | − | 0.379869i | ||||
\(694\) | 22.0000 | 0.835109 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.00000 | − | 3.46410i | −0.0758098 | − | 0.131306i | ||||
\(697\) | 20.7846 | − | 12.0000i | 0.787273 | − | 0.454532i | ||||
\(698\) | 1.73205 | + | 1.00000i | 0.0655591 | + | 0.0378506i | ||||
\(699\) | 4.00000 | 0.151294 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.0000 | −0.679851 | −0.339925 | − | 0.940452i | \(-0.610402\pi\) | ||||
−0.339925 | + | 0.940452i | \(0.610402\pi\) | |||||||
\(702\) | −0.866025 | − | 0.500000i | −0.0326860 | − | 0.0188713i | ||||
\(703\) | −2.59808 | + | 1.50000i | −0.0979883 | + | 0.0565736i | ||||
\(704\) | −2.00000 | − | 3.46410i | −0.0753778 | − | 0.130558i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −20.0000 | −0.752710 | ||||||||
\(707\) | −31.1769 | + | 6.00000i | −1.17253 | + | 0.225653i | ||||
\(708\) | − | 6.00000i | − | 0.225494i | ||||||
\(709\) | −5.50000 | + | 9.52628i | −0.206557 | + | 0.357767i | −0.950628 | − | 0.310334i | \(-0.899559\pi\) |
0.744071 | + | 0.668101i | \(0.232892\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.50000 | − | 11.2583i | −0.243769 | − | 0.422220i | ||||
\(712\) | 1.73205 | + | 1.00000i | 0.0649113 | + | 0.0374766i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −1.00000 | − | 5.19615i | −0.0374241 | − | 0.194461i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.00000 | − | 6.92820i | 0.149487 | − | 0.258919i | ||||
\(717\) | −10.3923 | + | 6.00000i | −0.388108 | + | 0.224074i | ||||
\(718\) | 5.19615 | − | 3.00000i | 0.193919 | − | 0.111959i | ||||
\(719\) | 4.00000 | − | 6.92820i | 0.149175 | − | 0.258378i | −0.781748 | − | 0.623595i | \(-0.785672\pi\) |
0.930923 | + | 0.365216i | \(0.119005\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.0000 | − | 12.1244i | 0.521387 | − | 0.451535i | ||||
\(722\) | − | 18.0000i | − | 0.669891i | ||||||
\(723\) | 11.2583 | + | 6.50000i | 0.418702 | + | 0.241738i | ||||
\(724\) | −9.00000 | − | 15.5885i | −0.334482 | − | 0.579340i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.50000 | + | 4.33013i | −0.0927837 | + | 0.160706i | ||||
\(727\) | − | 1.00000i | − | 0.0370879i | −0.999828 | − | 0.0185440i | \(-0.994097\pi\) | ||
0.999828 | − | 0.0185440i | \(-0.00590307\pi\) | |||||||
\(728\) | −0.866025 | + | 2.50000i | −0.0320970 | + | 0.0926562i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.00000 | − | 13.8564i | −0.295891 | − | 0.512498i | ||||
\(732\) | −11.2583 | + | 6.50000i | −0.416120 | + | 0.240247i | ||||
\(733\) | −30.3109 | − | 17.5000i | −1.11956 | − | 0.646377i | −0.178270 | − | 0.983982i | \(-0.557050\pi\) |
−0.941288 | + | 0.337604i | \(0.890383\pi\) | |||||||
\(734\) | 8.00000 | 0.295285 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.00000 | −0.0737210 | ||||||||
\(737\) | 10.3923 | + | 6.00000i | 0.382805 | + | 0.221013i | ||||
\(738\) | −10.3923 | + | 6.00000i | −0.382546 | + | 0.220863i | ||||
\(739\) | −0.500000 | − | 0.866025i | −0.0183928 | − | 0.0318573i | 0.856683 | − | 0.515844i | \(-0.172522\pi\) |
−0.875075 | + | 0.483987i | \(0.839188\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.00000 | 0.0367359 | ||||||||
\(742\) | 1.73205 | − | 5.00000i | 0.0635856 | − | 0.183556i | ||||
\(743\) | 6.00000i | 0.220119i | 0.993925 | + | 0.110059i | \(0.0351041\pi\) | ||||
−0.993925 | + | 0.110059i | \(0.964896\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −11.5000 | − | 19.9186i | −0.421045 | − | 0.729271i | ||||
\(747\) | 5.19615 | + | 3.00000i | 0.190117 | + | 0.109764i | ||||
\(748\) | 8.00000i | 0.292509i | ||||||||
\(749\) | −12.0000 | + | 10.3923i | −0.438470 | + | 0.379727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.50000 | + | 16.4545i | −0.346660 | + | 0.600433i | −0.985654 | − | 0.168779i | \(-0.946018\pi\) |
0.638994 | + | 0.769212i | \(0.279351\pi\) | |||||||
\(752\) | −5.19615 | + | 3.00000i | −0.189484 | + | 0.109399i | ||||
\(753\) | −20.7846 | + | 12.0000i | −0.757433 | + | 0.437304i | ||||
\(754\) | 2.00000 | − | 3.46410i | 0.0728357 | − | 0.126155i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.500000 | + | 2.59808i | 0.0181848 | + | 0.0944911i | ||||
\(757\) | 1.00000i | 0.0363456i | 0.999835 | + | 0.0181728i | \(0.00578490\pi\) | ||||
−0.999835 | + | 0.0181728i | \(0.994215\pi\) | |||||||
\(758\) | −4.33013 | − | 2.50000i | −0.157277 | − | 0.0908041i | ||||
\(759\) | 4.00000 | + | 6.92820i | 0.145191 | + | 0.251478i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.0000 | + | 29.4449i | −0.616250 | + | 1.06738i | 0.373914 | + | 0.927463i | \(0.378015\pi\) |
−0.990164 | + | 0.139912i | \(0.955318\pi\) | |||||||
\(762\) | − | 1.00000i | − | 0.0362262i | ||||||
\(763\) | −49.3634 | + | 9.50000i | −1.78708 | + | 0.343923i | ||||
\(764\) | −20.0000 | −0.723575 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.00000 | + | 12.1244i | 0.252920 | + | 0.438071i | ||||
\(767\) | 5.19615 | − | 3.00000i | 0.187622 | − | 0.108324i | ||||
\(768\) | 0.866025 | + | 0.500000i | 0.0312500 | + | 0.0180422i | ||||
\(769\) | 50.0000 | 1.80305 | 0.901523 | − | 0.432731i | \(-0.142450\pi\) | ||||
0.901523 | + | 0.432731i | \(0.142450\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.00000 | −0.288113 | ||||||||
\(772\) | 8.66025 | + | 5.00000i | 0.311689 | + | 0.179954i | ||||
\(773\) | 27.7128 | − | 16.0000i | 0.996761 | − | 0.575480i | 0.0894724 | − | 0.995989i | \(-0.471482\pi\) |
0.907288 | + | 0.420509i | \(0.138149\pi\) | |||||||
\(774\) | 4.00000 | + | 6.92820i | 0.143777 | + | 0.249029i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 17.0000 | 0.610264 | ||||||||
\(777\) | 2.59808 | − | 7.50000i | 0.0932055 | − | 0.269061i | ||||
\(778\) | 20.0000i | 0.717035i | ||||||||
\(779\) | 6.00000 | − | 10.3923i | 0.214972 | − | 0.372343i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.0000 | + | 55.4256i | 1.14505 | + | 1.98328i | ||||
\(782\) | 3.46410 | + | 2.00000i | 0.123876 | + | 0.0715199i | ||||
\(783\) | − | 4.00000i | − | 0.142948i | ||||||
\(784\) | 6.50000 | − | 2.59808i | 0.232143 | − | 0.0927884i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.00000 | + | 1.73205i | −0.0356688 | + | 0.0617802i | ||||
\(787\) | 19.9186 | − | 11.5000i | 0.710021 | − | 0.409931i | −0.101048 | − | 0.994882i | \(-0.532220\pi\) |
0.811069 | + | 0.584951i | \(0.198886\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.0000 | − | 27.7128i | 0.569615 | − | 0.986602i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −45.0000 | − | 15.5885i | −1.60002 | − | 0.554262i | ||||
\(792\) | − | 4.00000i | − | 0.142134i | ||||||
\(793\) | −11.2583 | − | 6.50000i | −0.399795 | − | 0.230822i | ||||
\(794\) | −9.00000 | − | 15.5885i | −0.319398 | − | 0.553214i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.50000 | + | 12.9904i | −0.265830 | + | 0.460432i | ||||
\(797\) | 42.0000i | 1.48772i | 0.668338 | + | 0.743858i | \(0.267006\pi\) | ||||
−0.668338 | + | 0.743858i | \(0.732994\pi\) | |||||||
\(798\) | −1.73205 | − | 2.00000i | −0.0613139 | − | 0.0707992i | ||||
\(799\) | 12.0000 | 0.424529 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.00000 | + | 1.73205i | 0.0353333 | + | 0.0611990i | ||||
\(802\) | 3.46410 | − | 2.00000i | 0.122322 | − | 0.0706225i | ||||
\(803\) | 38.1051 | + | 22.0000i | 1.34470 | + | 0.776363i | ||||
\(804\) | −3.00000 | −0.105802 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10.3923 | + | 6.00000i | −0.365600 | + | 0.211079i | ||||
\(809\) | 7.00000 | + | 12.1244i | 0.246107 | + | 0.426270i | 0.962442 | − | 0.271487i | \(-0.0875152\pi\) |
−0.716335 | + | 0.697756i | \(0.754182\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.00000 | −0.175574 | −0.0877869 | − | 0.996139i | \(-0.527979\pi\) | ||||
−0.0877869 | + | 0.996139i | \(0.527979\pi\) | |||||||
\(812\) | −10.3923 | + | 2.00000i | −0.364698 | + | 0.0701862i | ||||
\(813\) | 20.0000i | 0.701431i | ||||||||
\(814\) | −6.00000 | + | 10.3923i | −0.210300 | + | 0.364250i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.00000 | − | 1.73205i | −0.0350070 | − | 0.0606339i | ||||
\(817\) | −6.92820 | − | 4.00000i | −0.242387 | − | 0.139942i | ||||
\(818\) | 11.0000i | 0.384606i | ||||||||
\(819\) | −2.00000 | + | 1.73205i | −0.0698857 | + | 0.0605228i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.0000 | − | 38.1051i | 0.767805 | − | 1.32988i | −0.170945 | − | 0.985281i | \(-0.554682\pi\) |
0.938751 | − | 0.344597i | \(-0.111985\pi\) | |||||||
\(822\) | 8.66025 | − | 5.00000i | 0.302061 | − | 0.174395i | ||||
\(823\) | −7.79423 | + | 4.50000i | −0.271690 | + | 0.156860i | −0.629655 | − | 0.776875i | \(-0.716804\pi\) |
0.357966 | + | 0.933735i | \(0.383471\pi\) | |||||||
\(824\) | 3.50000 | − | 6.06218i | 0.121928 | − | 0.211186i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.0000 | − | 5.19615i | −0.521917 | − | 0.180797i | ||||
\(827\) | 40.0000i | 1.39094i | 0.718557 | + | 0.695468i | \(0.244803\pi\) | ||||
−0.718557 | + | 0.695468i | \(0.755197\pi\) | |||||||
\(828\) | −1.73205 | − | 1.00000i | −0.0601929 | − | 0.0347524i | ||||
\(829\) | −1.50000 | − | 2.59808i | −0.0520972 | − | 0.0902349i | 0.838801 | − | 0.544438i | \(-0.183257\pi\) |
−0.890898 | + | 0.454204i | \(0.849924\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.500000 | + | 0.866025i | −0.0173448 | + | 0.0300421i | ||||
\(832\) | 1.00000i | 0.0346688i | ||||||||
\(833\) | −13.8564 | − | 2.00000i | −0.480096 | − | 0.0692959i | ||||
\(834\) | 13.0000 | 0.450153 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.00000 | + | 3.46410i | 0.0691714 | + | 0.119808i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −13.8564 | − | 8.00000i | −0.478662 | − | 0.276355i | ||||
\(839\) | −50.0000 | −1.72619 | −0.863096 | − | 0.505040i | \(-0.831478\pi\) | ||||
−0.863096 | + | 0.505040i | \(0.831478\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | −0.866025 | − | 0.500000i | −0.0298452 | − | 0.0172311i | ||||
\(843\) | 15.5885 | − | 9.00000i | 0.536895 | − | 0.309976i | ||||
\(844\) | 1.50000 | + | 2.59808i | 0.0516321 | + | 0.0894295i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.00000 | −0.206284 | ||||||||
\(847\) | 8.66025 | + | 10.0000i | 0.297570 | + | 0.343604i | ||||
\(848\) | − | 2.00000i | − | 0.0686803i | ||||||
\(849\) | 6.50000 | − | 11.2583i | 0.223079 | − | 0.386385i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.00000 | + | 5.19615i | 0.102839 | + | 0.178122i | ||||
\(852\) | −13.8564 | − | 8.00000i | −0.474713 | − | 0.274075i | ||||
\(853\) | 38.0000i | 1.30110i | 0.759465 | + | 0.650548i | \(0.225461\pi\) | ||||
−0.759465 | + | 0.650548i | \(0.774539\pi\) | |||||||
\(854\) | 6.50000 | + | 33.7750i | 0.222425 | + | 1.15576i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.00000 | + | 5.19615i | −0.102538 | + | 0.177601i | ||||
\(857\) | 22.5167 | − | 13.0000i | 0.769154 | − | 0.444072i | −0.0634184 | − | 0.997987i | \(-0.520200\pi\) |
0.832573 | + | 0.553915i | \(0.186867\pi\) | |||||||
\(858\) | 3.46410 | − | 2.00000i | 0.118262 | − | 0.0682789i | ||||
\(859\) | 2.00000 | − | 3.46410i | 0.0682391 | − | 0.118194i | −0.829887 | − | 0.557931i | \(-0.811595\pi\) |
0.898126 | + | 0.439738i | \(0.144929\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.00000 | + | 31.1769i | 0.204479 | + | 1.06251i | ||||
\(862\) | 6.00000i | 0.204361i | ||||||||
\(863\) | −29.4449 | − | 17.0000i | −1.00231 | − | 0.578687i | −0.0933825 | − | 0.995630i | \(-0.529768\pi\) |
−0.908932 | + | 0.416944i | \(0.863101\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.00000 | − | 1.73205i | 0.0339814 | − | 0.0588575i | ||||
\(867\) | − | 13.0000i | − | 0.441503i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 52.0000 | 1.76398 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.50000 | − | 2.59808i | −0.0508256 | − | 0.0880325i | ||||
\(872\) | −16.4545 | + | 9.50000i | −0.557219 | + | 0.321711i | ||||
\(873\) | 14.7224 | + | 8.50000i | 0.498279 | + | 0.287681i | ||||
\(874\) | 2.00000 | 0.0676510 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −11.0000 | −0.371656 | ||||||||
\(877\) | 11.2583 | + | 6.50000i | 0.380167 | + | 0.219489i | 0.677891 | − | 0.735163i | \(-0.262894\pi\) |
−0.297724 | + | 0.954652i | \(0.596228\pi\) | |||||||
\(878\) | 19.9186 | − | 11.5000i | 0.672220 | − | 0.388106i | ||||
\(879\) | 6.00000 | + | 10.3923i | 0.202375 | + | 0.350524i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40.0000 | −1.34763 | −0.673817 | − | 0.738898i | \(-0.735346\pi\) | ||||
−0.673817 | + | 0.738898i | \(0.735346\pi\) | |||||||
\(882\) | 6.92820 | + | 1.00000i | 0.233285 | + | 0.0336718i | ||||
\(883\) | 1.00000i | 0.0336527i | 0.999858 | + | 0.0168263i | \(0.00535624\pi\) | ||||
−0.999858 | + | 0.0168263i | \(0.994644\pi\) | |||||||
\(884\) | 1.00000 | − | 1.73205i | 0.0336336 | − | 0.0582552i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.00000 | − | 5.19615i | −0.100787 | − | 0.174568i | ||||
\(887\) | 39.8372 | + | 23.0000i | 1.33760 | + | 0.772264i | 0.986451 | − | 0.164055i | \(-0.0524574\pi\) |
0.351150 | + | 0.936319i | \(0.385791\pi\) | |||||||
\(888\) | − | 3.00000i | − | 0.100673i | ||||||
\(889\) | −2.50000 | − | 0.866025i | −0.0838473 | − | 0.0290456i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.00000 | − | 3.46410i | 0.0670025 | − | 0.116052i | ||||
\(892\) | −16.4545 | + | 9.50000i | −0.550937 | + | 0.318084i | ||||
\(893\) | 5.19615 | − | 3.00000i | 0.173883 | − | 0.100391i | ||||
\(894\) | −8.00000 | + | 13.8564i | −0.267560 | + | 0.463428i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.00000 | − | 1.73205i | 0.0668153 | − | 0.0578638i | ||||
\(897\) | − | 2.00000i | − | 0.0667781i | ||||||
\(898\) | 1.73205 | + | 1.00000i | 0.0577993 | + | 0.0333704i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.00000 | + | 3.46410i | −0.0666297 | + | 0.115406i | ||||
\(902\) | − | 48.0000i | − | 1.59823i | ||||||
\(903\) | 20.7846 | − | 4.00000i | 0.691669 | − | 0.133112i | ||||
\(904\) | −18.0000 | −0.598671 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −9.50000 | − | 16.4545i | −0.315616 | − | 0.546664i | ||||
\(907\) | −40.7032 | + | 23.5000i | −1.35153 | + | 0.780305i | −0.988463 | − | 0.151460i | \(-0.951603\pi\) |
−0.363064 | + | 0.931764i | \(0.618269\pi\) | |||||||
\(908\) | −6.92820 | − | 4.00000i | −0.229920 | − | 0.132745i | ||||
\(909\) | −12.0000 | −0.398015 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.0000 | −1.52405 | −0.762024 | − | 0.647549i | \(-0.775794\pi\) | ||||
−0.762024 | + | 0.647549i | \(0.775794\pi\) | |||||||
\(912\) | −0.866025 | − | 0.500000i | −0.0286770 | − | 0.0165567i | ||||
\(913\) | −20.7846 | + | 12.0000i | −0.687870 | + | 0.397142i | ||||
\(914\) | 18.5000 | + | 32.0429i | 0.611926 | + | 1.05989i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.00000 | −0.231287 | ||||||||
\(917\) | 3.46410 | + | 4.00000i | 0.114395 | + | 0.132092i | ||||
\(918\) | − | 2.00000i | − | 0.0660098i | ||||||
\(919\) | 8.00000 | − | 13.8564i | 0.263896 | − | 0.457081i | −0.703378 | − | 0.710816i | \(-0.748326\pi\) |
0.967274 | + | 0.253735i | \(0.0816592\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.0000 | − | 17.3205i | −0.329511 | − | 0.570730i | ||||
\(922\) | −22.5167 | − | 13.0000i | −0.741547 | − | 0.428132i | ||||
\(923\) | − | 16.0000i | − | 0.526646i | ||||||
\(924\) | −10.0000 | − | 3.46410i | −0.328976 | − | 0.113961i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.50000 | − | 2.59808i | 0.0492931 | − | 0.0853781i | ||||
\(927\) | 6.06218 | − | 3.50000i | 0.199108 | − | 0.114955i | ||||
\(928\) | −3.46410 | + | 2.00000i | −0.113715 | + | 0.0656532i | ||||
\(929\) | −10.0000 | + | 17.3205i | −0.328089 | + | 0.568267i | −0.982133 | − | 0.188190i | \(-0.939738\pi\) |
0.654043 | + | 0.756457i | \(0.273071\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.50000 | + | 2.59808i | −0.213029 | + | 0.0851485i | ||||
\(932\) | − | 4.00000i | − | 0.131024i | ||||||
\(933\) | −12.1244 | − | 7.00000i | −0.396934 | − | 0.229170i | ||||
\(934\) | 15.0000 | + | 25.9808i | 0.490815 | + | 0.850117i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.500000 | + | 0.866025i | −0.0163430 | + | 0.0283069i | ||||
\(937\) | 46.0000i | 1.50275i | 0.659873 | + | 0.751377i | \(0.270610\pi\) | ||||
−0.659873 | + | 0.751377i | \(0.729390\pi\) | |||||||
\(938\) | −2.59808 | + | 7.50000i | −0.0848302 | + | 0.244884i | ||||
\(939\) | 18.0000 | 0.587408 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.0000 | − | 36.3731i | −0.684580 | − | 1.18573i | −0.973568 | − | 0.228395i | \(-0.926652\pi\) |
0.288988 | − | 0.957333i | \(-0.406681\pi\) | |||||||
\(942\) | −18.1865 | + | 10.5000i | −0.592549 | + | 0.342108i | ||||
\(943\) | −20.7846 | − | 12.0000i | −0.676840 | − | 0.390774i | ||||
\(944\) | −6.00000 | −0.195283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −32.0000 | −1.04041 | ||||||||
\(947\) | 32.9090 | + | 19.0000i | 1.06940 | + | 0.617417i | 0.928017 | − | 0.372538i | \(-0.121512\pi\) |
0.141381 | + | 0.989955i | \(0.454846\pi\) | |||||||
\(948\) | −11.2583 | + | 6.50000i | −0.365654 | + | 0.211110i | ||||
\(949\) | −5.50000 | − | 9.52628i | −0.178538 | − | 0.309236i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.0000 | 0.713399 | ||||||||
\(952\) | −5.19615 | + | 1.00000i | −0.168408 | + | 0.0324102i | ||||
\(953\) | 4.00000i | 0.129573i | 0.997899 | + | 0.0647864i | \(0.0206366\pi\) | ||||
−0.997899 | + | 0.0647864i | \(0.979363\pi\) | |||||||
\(954\) | 1.00000 | − | 1.73205i | 0.0323762 | − | 0.0560772i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6.00000 | + | 10.3923i | 0.194054 | + | 0.336111i | ||||
\(957\) | 13.8564 | + | 8.00000i | 0.447914 | + | 0.258603i | ||||
\(958\) | 34.0000i | 1.09849i | ||||||||
\(959\) | −5.00000 | − | 25.9808i | −0.161458 | − | 0.838963i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.5000 | − | 26.8468i | 0.500000 | − | 0.866025i | ||||
\(962\) | 2.59808 | − | 1.50000i | 0.0837653 | − | 0.0483619i | ||||
\(963\) | −5.19615 | + | 3.00000i | −0.167444 | + | 0.0966736i | ||||
\(964\) | 6.50000 | − | 11.2583i | 0.209351 | − | 0.362606i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.00000 | + | 3.46410i | −0.128698 | + | 0.111456i | ||||
\(967\) | − | 11.0000i | − | 0.353736i | −0.984235 | − | 0.176868i | \(-0.943403\pi\) | ||
0.984235 | − | 0.176868i | \(-0.0565966\pi\) | |||||||
\(968\) | 4.33013 | + | 2.50000i | 0.139176 | + | 0.0803530i | ||||
\(969\) | 1.00000 | + | 1.73205i | 0.0321246 | + | 0.0556415i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.00000 | + | 13.8564i | −0.256732 | + | 0.444673i | −0.965365 | − | 0.260905i | \(-0.915979\pi\) |
0.708632 | + | 0.705578i | \(0.249313\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 11.2583 | − | 32.5000i | 0.360925 | − | 1.04190i | ||||
\(974\) | −40.0000 | −1.28168 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.50000 | + | 11.2583i | 0.208060 | + | 0.360370i | ||||
\(977\) | −41.5692 | + | 24.0000i | −1.32992 | + | 0.767828i | −0.985287 | − | 0.170910i | \(-0.945329\pi\) |
−0.344631 | + | 0.938738i | \(0.611996\pi\) | |||||||
\(978\) | 19.9186 | + | 11.5000i | 0.636926 | + | 0.367729i | ||||
\(979\) | −8.00000 | −0.255681 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.0000 | −0.606623 | ||||||||
\(982\) | −15.5885 | − | 9.00000i | −0.497448 | − | 0.287202i | ||||
\(983\) | −36.3731 | + | 21.0000i | −1.16012 | + | 0.669796i | −0.951333 | − | 0.308165i | \(-0.900285\pi\) |
−0.208788 | + | 0.977961i | \(0.566952\pi\) | |||||||
\(984\) | 6.00000 | + | 10.3923i | 0.191273 | + | 0.331295i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 8.00000 | 0.254772 | ||||||||
\(987\) | −5.19615 | + | 15.0000i | −0.165395 | + | 0.477455i | ||||
\(988\) | − | 1.00000i | − | 0.0318142i | ||||||
\(989\) | −8.00000 | + | 13.8564i | −0.254385 | + | 0.440608i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.00000 | + | 6.92820i | 0.127064 | + | 0.220082i | 0.922538 | − | 0.385906i | \(-0.126111\pi\) |
−0.795474 | + | 0.605988i | \(0.792778\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 21.0000i | − | 0.666415i | ||||||
\(994\) | −32.0000 | + | 27.7128i | −1.01498 | + | 0.878997i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.00000 | − | 5.19615i | 0.0950586 | − | 0.164646i | ||||
\(997\) | 26.8468 | − | 15.5000i | 0.850246 | − | 0.490890i | −0.0104877 | − | 0.999945i | \(-0.503338\pi\) |
0.860734 | + | 0.509055i | \(0.170005\pi\) | |||||||
\(998\) | 23.3827 | − | 13.5000i | 0.740166 | − | 0.427335i | ||||
\(999\) | 1.50000 | − | 2.59808i | 0.0474579 | − | 0.0821995i |
(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 | 1050.2.o.k.499.1 | 4 | ||
5.2 | odd | 4 | 1050.2.i.t.751.1 | yes | 2 | ||
5.3 | odd | 4 | 1050.2.i.a.751.1 | yes | 2 | ||
5.4 | even | 2 | inner | 1050.2.o.k.499.2 | 4 | ||
7.4 | even | 3 | inner | 1050.2.o.k.949.2 | 4 | ||
35.2 | odd | 12 | 7350.2.a.c.1.1 | 1 | |||
35.4 | even | 6 | inner | 1050.2.o.k.949.1 | 4 | ||
35.12 | even | 12 | 7350.2.a.y.1.1 | 1 | |||
35.18 | odd | 12 | 1050.2.i.a.151.1 | ✓ | 2 | ||
35.23 | odd | 12 | 7350.2.a.cl.1.1 | 1 | |||
35.32 | odd | 12 | 1050.2.i.t.151.1 | yes | 2 | ||
35.33 | even | 12 | 7350.2.a.bp.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.2.i.a.151.1 | ✓ | 2 | 35.18 | odd | 12 | ||
1050.2.i.a.751.1 | yes | 2 | 5.3 | odd | 4 | ||
1050.2.i.t.151.1 | yes | 2 | 35.32 | odd | 12 | ||
1050.2.i.t.751.1 | yes | 2 | 5.2 | odd | 4 | ||
1050.2.o.k.499.1 | 4 | 1.1 | even | 1 | trivial | ||
1050.2.o.k.499.2 | 4 | 5.4 | even | 2 | inner | ||
1050.2.o.k.949.1 | 4 | 35.4 | even | 6 | inner | ||
1050.2.o.k.949.2 | 4 | 7.4 | even | 3 | inner | ||
7350.2.a.c.1.1 | 1 | 35.2 | odd | 12 | |||
7350.2.a.y.1.1 | 1 | 35.12 | even | 12 | |||
7350.2.a.bp.1.1 | 1 | 35.33 | even | 12 | |||
7350.2.a.cl.1.1 | 1 | 35.23 | odd | 12 |