Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [378,2,Mod(215,378)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(378, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("378.215");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.k (of order \(6\), 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: | \(3.01834519640\) |
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 | 269.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 378.269 |
Dual form | 378.2.k.b.215.1 |
$q$-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 \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 1.73205 | + | 3.00000i | 0.774597 | + | 1.34164i | 0.935021 | + | 0.354593i | \(0.115380\pi\) |
−0.160424 | + | 0.987048i | \(0.551286\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | + | 1.73205i | 0.755929 | + | 0.654654i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.00000 | − | 1.73205i | −0.948683 | − | 0.547723i | ||||
\(11\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.19615i | − | 1.44115i | −0.693375 | − | 0.720577i | \(-0.743877\pi\) | ||
0.693375 | − | 0.720577i | \(-0.256123\pi\) | |||||||
\(14\) | −2.59808 | − | 0.500000i | −0.694365 | − | 0.133631i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3.46410 | + | 6.00000i | −0.840168 | + | 1.45521i | 0.0495842 | + | 0.998770i | \(0.484210\pi\) |
−0.889752 | + | 0.456444i | \(0.849123\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.00000 | + | 1.73205i | −0.688247 | + | 0.397360i | −0.802955 | − | 0.596040i | \(-0.796740\pi\) |
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 3.46410 | 0.774597 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.19615 | − | 3.00000i | 1.08347 | − | 0.625543i | 0.151642 | − | 0.988436i | \(-0.451544\pi\) |
0.931831 | + | 0.362892i | \(0.118211\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.50000 | + | 6.06218i | −0.700000 | + | 1.21244i | ||||
\(26\) | 2.59808 | + | 4.50000i | 0.509525 | + | 0.882523i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.50000 | − | 0.866025i | 0.472456 | − | 0.163663i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.50000 | + | 4.33013i | 1.34704 | + | 0.777714i | 0.987829 | − | 0.155543i | \(-0.0497126\pi\) |
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 6.92820i | − | 1.18818i | ||||||
\(35\) | −1.73205 | + | 9.00000i | −0.292770 | + | 1.52128i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.50000 | + | 4.33013i | 0.410997 | + | 0.711868i | 0.994999 | − | 0.0998840i | \(-0.0318472\pi\) |
−0.584002 | + | 0.811752i | \(0.698514\pi\) | |||||||
\(38\) | 1.73205 | − | 3.00000i | 0.280976 | − | 0.486664i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.00000 | + | 1.73205i | −0.474342 | + | 0.273861i | ||||
\(41\) | −6.92820 | −1.08200 | −0.541002 | − | 0.841021i | \(-0.681955\pi\) | ||||
−0.541002 | + | 0.841021i | \(0.681955\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | 0.152499 | 0.0762493 | − | 0.997089i | \(-0.475706\pi\) | ||||
0.0762493 | + | 0.997089i | \(0.475706\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.00000 | + | 5.19615i | −0.442326 | + | 0.766131i | ||||
\(47\) | −3.46410 | − | 6.00000i | −0.505291 | − | 0.875190i | −0.999981 | − | 0.00612051i | \(-0.998052\pi\) |
0.494690 | − | 0.869069i | \(-0.335282\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | − | 7.00000i | − | 0.989949i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.50000 | − | 2.59808i | −0.624038 | − | 0.360288i | ||||
\(53\) | −5.19615 | − | 3.00000i | −0.713746 | − | 0.412082i | 0.0987002 | − | 0.995117i | \(-0.468532\pi\) |
−0.812447 | + | 0.583036i | \(0.801865\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.73205 | + | 2.00000i | −0.231455 | + | 0.267261i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.46410 | − | 6.00000i | 0.450988 | − | 0.781133i | −0.547460 | − | 0.836832i | \(-0.684405\pi\) |
0.998448 | + | 0.0556984i | \(0.0177385\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.50000 | + | 0.866025i | −0.192055 | + | 0.110883i | −0.592944 | − | 0.805243i | \(-0.702035\pi\) |
0.400889 | + | 0.916127i | \(0.368701\pi\) | |||||||
\(62\) | −8.66025 | −1.09985 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 15.5885 | − | 9.00000i | 1.93351 | − | 1.11631i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.50000 | − | 11.2583i | 0.794101 | − | 1.37542i | −0.129307 | − | 0.991605i | \(-0.541275\pi\) |
0.923408 | − | 0.383819i | \(-0.125391\pi\) | |||||||
\(68\) | 3.46410 | + | 6.00000i | 0.420084 | + | 0.727607i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.00000 | − | 8.66025i | −0.358569 | − | 1.03510i | ||||
\(71\) | − | 6.00000i | − | 0.712069i | −0.934473 | − | 0.356034i | \(-0.884129\pi\) | ||
0.934473 | − | 0.356034i | \(-0.115871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | − | 3.46410i | −0.702247 | − | 0.405442i | 0.105937 | − | 0.994373i | \(-0.466216\pi\) |
−0.808184 | + | 0.588930i | \(0.799549\pi\) | |||||||
\(74\) | −4.33013 | − | 2.50000i | −0.503367 | − | 0.290619i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.46410i | 0.397360i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.50000 | + | 6.06218i | 0.393781 | + | 0.682048i | 0.992945 | − | 0.118578i | \(-0.0378336\pi\) |
−0.599164 | + | 0.800626i | \(0.704500\pi\) | |||||||
\(80\) | 1.73205 | − | 3.00000i | 0.193649 | − | 0.335410i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.00000 | − | 3.46410i | 0.662589 | − | 0.382546i | ||||
\(83\) | 3.46410 | 0.380235 | 0.190117 | − | 0.981761i | \(-0.439113\pi\) | ||||
0.190117 | + | 0.981761i | \(0.439113\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −24.0000 | −2.60317 | ||||||||
\(86\) | −0.866025 | + | 0.500000i | −0.0933859 | + | 0.0539164i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.19615 | + | 9.00000i | 0.550791 | + | 0.953998i | 0.998218 | + | 0.0596775i | \(0.0190072\pi\) |
−0.447427 | + | 0.894321i | \(0.647659\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.00000 | − | 10.3923i | 0.943456 | − | 1.08941i | ||||
\(92\) | − | 6.00000i | − | 0.625543i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.00000 | + | 3.46410i | 0.618853 | + | 0.357295i | ||||
\(95\) | −10.3923 | − | 6.00000i | −1.06623 | − | 0.615587i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.73205i | 0.175863i | 0.996127 | + | 0.0879316i | \(0.0280257\pi\) | ||||
−0.996127 | + | 0.0879316i | \(0.971974\pi\) | |||||||
\(98\) | −4.33013 | − | 5.50000i | −0.437409 | − | 0.555584i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.50000 | + | 6.06218i | 0.350000 | + | 0.606218i | ||||
\(101\) | 5.19615 | − | 9.00000i | 0.517036 | − | 0.895533i | −0.482768 | − | 0.875748i | \(-0.660368\pi\) |
0.999804 | − | 0.0197851i | \(-0.00629819\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.50000 | − | 2.59808i | 0.443398 | − | 0.255996i | −0.261640 | − | 0.965166i | \(-0.584263\pi\) |
0.705038 | + | 0.709170i | \(0.250930\pi\) | |||||||
\(104\) | 5.19615 | 0.509525 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | 5.19615 | − | 3.00000i | 0.502331 | − | 0.290021i | −0.227345 | − | 0.973814i | \(-0.573004\pi\) |
0.729676 | + | 0.683793i | \(0.239671\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.50000 | − | 9.52628i | 0.526804 | − | 0.912452i | −0.472708 | − | 0.881219i | \(-0.656723\pi\) |
0.999512 | − | 0.0312328i | \(-0.00994332\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.500000 | − | 2.59808i | 0.0472456 | − | 0.245495i | ||||
\(113\) | − | 18.0000i | − | 1.69330i | −0.532152 | − | 0.846649i | \(-0.678617\pi\) | ||
0.532152 | − | 0.846649i | \(-0.321383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 18.0000 | + | 10.3923i | 1.67851 | + | 0.969087i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.92820i | 0.637793i | ||||||||
\(119\) | −17.3205 | + | 6.00000i | −1.58777 | + | 0.550019i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.50000 | − | 9.52628i | −0.500000 | − | 0.866025i | ||||
\(122\) | 0.866025 | − | 1.50000i | 0.0784063 | − | 0.135804i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.50000 | − | 4.33013i | 0.673520 | − | 0.388857i | ||||
\(125\) | −6.92820 | −0.619677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.00000 | −0.621150 | −0.310575 | − | 0.950549i | \(-0.600522\pi\) | ||||
−0.310575 | + | 0.950549i | \(0.600522\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −9.00000 | + | 15.5885i | −0.789352 | + | 1.36720i | ||||
\(131\) | 10.3923 | + | 18.0000i | 0.907980 | + | 1.57267i | 0.816866 | + | 0.576827i | \(0.195709\pi\) |
0.0911134 | + | 0.995841i | \(0.470957\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.00000 | − | 1.73205i | −0.780399 | − | 0.150188i | ||||
\(134\) | 13.0000i | 1.12303i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.00000 | − | 3.46410i | −0.514496 | − | 0.297044i | ||||
\(137\) | −15.5885 | − | 9.00000i | −1.33181 | − | 0.768922i | −0.346235 | − | 0.938148i | \(-0.612540\pi\) |
−0.985577 | + | 0.169226i | \(0.945873\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 5.19615i | − | 0.440732i | −0.975417 | − | 0.220366i | \(-0.929275\pi\) | ||
0.975417 | − | 0.220366i | \(-0.0707252\pi\) | |||||||
\(140\) | 6.92820 | + | 6.00000i | 0.585540 | + | 0.507093i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.00000 | + | 5.19615i | 0.251754 | + | 0.436051i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.92820 | 0.573382 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.00000 | 0.410997 | ||||||||
\(149\) | −5.19615 | + | 3.00000i | −0.425685 | + | 0.245770i | −0.697507 | − | 0.716578i | \(-0.745707\pi\) |
0.271821 | + | 0.962348i | \(0.412374\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.500000 | + | 0.866025i | −0.0406894 | + | 0.0704761i | −0.885653 | − | 0.464348i | \(-0.846289\pi\) |
0.844963 | + | 0.534824i | \(0.179622\pi\) | |||||||
\(152\) | −1.73205 | − | 3.00000i | −0.140488 | − | 0.243332i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 30.0000i | 2.40966i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(158\) | −6.06218 | − | 3.50000i | −0.482281 | − | 0.278445i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.46410i | 0.273861i | ||||||||
\(161\) | 15.5885 | + | 3.00000i | 1.22854 | + | 0.236433i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.50000 | − | 9.52628i | −0.430793 | − | 0.746156i | 0.566149 | − | 0.824303i | \(-0.308433\pi\) |
−0.996942 | + | 0.0781474i | \(0.975100\pi\) | |||||||
\(164\) | −3.46410 | + | 6.00000i | −0.270501 | + | 0.468521i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.00000 | + | 1.73205i | −0.232845 | + | 0.134433i | ||||
\(167\) | −3.46410 | −0.268060 | −0.134030 | − | 0.990977i | \(-0.542792\pi\) | ||||
−0.134030 | + | 0.990977i | \(0.542792\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −14.0000 | −1.07692 | ||||||||
\(170\) | 20.7846 | − | 12.0000i | 1.59411 | − | 0.920358i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.500000 | − | 0.866025i | 0.0381246 | − | 0.0660338i | ||||
\(173\) | 10.3923 | + | 18.0000i | 0.790112 | + | 1.36851i | 0.925897 | + | 0.377776i | \(0.123311\pi\) |
−0.135785 | + | 0.990738i | \(0.543356\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −17.5000 | + | 6.06218i | −1.32288 | + | 0.458258i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9.00000 | − | 5.19615i | −0.674579 | − | 0.389468i | ||||
\(179\) | −5.19615 | − | 3.00000i | −0.388379 | − | 0.224231i | 0.293079 | − | 0.956088i | \(-0.405320\pi\) |
−0.681457 | + | 0.731858i | \(0.738654\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.8564i | 1.02994i | 0.857209 | + | 0.514969i | \(0.172197\pi\) | ||||
−0.857209 | + | 0.514969i | \(0.827803\pi\) | |||||||
\(182\) | −2.59808 | + | 13.5000i | −0.192582 | + | 1.00069i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.00000 | + | 5.19615i | 0.221163 | + | 0.383065i | ||||
\(185\) | −8.66025 | + | 15.0000i | −0.636715 | + | 1.10282i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −6.92820 | −0.505291 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.0000 | 0.870572 | ||||||||
\(191\) | 5.19615 | − | 3.00000i | 0.375980 | − | 0.217072i | −0.300088 | − | 0.953912i | \(-0.597016\pi\) |
0.676068 | + | 0.736839i | \(0.263683\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.500000 | + | 0.866025i | −0.0359908 | + | 0.0623379i | −0.883460 | − | 0.468507i | \(-0.844792\pi\) |
0.847469 | + | 0.530845i | \(0.178125\pi\) | |||||||
\(194\) | −0.866025 | − | 1.50000i | −0.0621770 | − | 0.107694i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.50000 | + | 2.59808i | 0.464286 | + | 0.185577i | ||||
\(197\) | − | 24.0000i | − | 1.70993i | −0.518686 | − | 0.854965i | \(-0.673579\pi\) | ||
0.518686 | − | 0.854965i | \(-0.326421\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.50000 | − | 0.866025i | −0.106332 | − | 0.0613909i | 0.445891 | − | 0.895087i | \(-0.352887\pi\) |
−0.552223 | + | 0.833696i | \(0.686220\pi\) | |||||||
\(200\) | −6.06218 | − | 3.50000i | −0.428661 | − | 0.247487i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.3923i | 0.731200i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.0000 | − | 20.7846i | −0.838116 | − | 1.45166i | ||||
\(206\) | −2.59808 | + | 4.50000i | −0.181017 | + | 0.313530i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.50000 | + | 2.59808i | −0.312019 | + | 0.180144i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.0000 | 1.72107 | 0.860535 | − | 0.509390i | \(-0.170129\pi\) | ||||
0.860535 | + | 0.509390i | \(0.170129\pi\) | |||||||
\(212\) | −5.19615 | + | 3.00000i | −0.356873 | + | 0.206041i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.00000 | + | 5.19615i | −0.205076 | + | 0.355202i | ||||
\(215\) | 1.73205 | + | 3.00000i | 0.118125 | + | 0.204598i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.50000 | + | 21.6506i | 0.509133 | + | 1.46974i | ||||
\(218\) | 11.0000i | 0.745014i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 31.1769 | + | 18.0000i | 2.09719 | + | 1.21081i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 10.3923i | − | 0.695920i | −0.937509 | − | 0.347960i | \(-0.886874\pi\) | ||
0.937509 | − | 0.347960i | \(-0.113126\pi\) | |||||||
\(224\) | 0.866025 | + | 2.50000i | 0.0578638 | + | 0.167038i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.00000 | + | 15.5885i | 0.598671 | + | 1.03693i | ||||
\(227\) | 5.19615 | − | 9.00000i | 0.344881 | − | 0.597351i | −0.640451 | − | 0.767999i | \(-0.721253\pi\) |
0.985332 | + | 0.170648i | \(0.0545860\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.50000 | − | 0.866025i | 0.0991228 | − | 0.0572286i | −0.449619 | − | 0.893220i | \(-0.648440\pi\) |
0.548742 | + | 0.835992i | \(0.315107\pi\) | |||||||
\(230\) | −20.7846 | −1.37050 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.3923 | + | 6.00000i | −0.680823 | + | 0.393073i | −0.800165 | − | 0.599780i | \(-0.795255\pi\) |
0.119342 | + | 0.992853i | \(0.461921\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.0000 | − | 20.7846i | 0.782794 | − | 1.35584i | ||||
\(236\) | −3.46410 | − | 6.00000i | −0.225494 | − | 0.390567i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 12.0000 | − | 13.8564i | 0.777844 | − | 0.898177i | ||||
\(239\) | 6.00000i | 0.388108i | 0.980991 | + | 0.194054i | \(0.0621637\pi\) | ||||
−0.980991 | + | 0.194054i | \(0.937836\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.50000 | + | 0.866025i | 0.0966235 | + | 0.0557856i | 0.547533 | − | 0.836784i | \(-0.315567\pi\) |
−0.450910 | + | 0.892570i | \(0.648900\pi\) | |||||||
\(242\) | 9.52628 | + | 5.50000i | 0.612372 | + | 0.353553i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.73205i | 0.110883i | ||||||||
\(245\) | −19.0526 | + | 15.0000i | −1.21722 | + | 0.958315i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.00000 | + | 15.5885i | 0.572656 | + | 0.991870i | ||||
\(248\) | −4.33013 | + | 7.50000i | −0.274963 | + | 0.476250i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.00000 | − | 3.46410i | 0.379473 | − | 0.219089i | ||||
\(251\) | 17.3205 | 1.09326 | 0.546630 | − | 0.837374i | \(-0.315910\pi\) | ||||
0.546630 | + | 0.837374i | \(0.315910\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 6.06218 | − | 3.50000i | 0.380375 | − | 0.219610i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 5.19615 | + | 9.00000i | 0.324127 | + | 0.561405i | 0.981335 | − | 0.192304i | \(-0.0615961\pi\) |
−0.657208 | + | 0.753709i | \(0.728263\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.50000 | + | 12.9904i | −0.155342 | + | 0.807183i | ||||
\(260\) | − | 18.0000i | − | 1.11631i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −18.0000 | − | 10.3923i | −1.11204 | − | 0.642039i | ||||
\(263\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 20.7846i | − | 1.27679i | ||||||
\(266\) | 8.66025 | − | 3.00000i | 0.530994 | − | 0.183942i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.50000 | − | 11.2583i | −0.397051 | − | 0.687712i | ||||
\(269\) | 13.8564 | − | 24.0000i | 0.844840 | − | 1.46331i | −0.0409201 | − | 0.999162i | \(-0.513029\pi\) |
0.885760 | − | 0.464143i | \(-0.153638\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.5000 | + | 14.7224i | −1.54901 | + | 0.894324i | −0.550797 | + | 0.834639i | \(0.685676\pi\) |
−0.998217 | + | 0.0596851i | \(0.980990\pi\) | |||||||
\(272\) | 6.92820 | 0.420084 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 18.0000 | 1.08742 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.500000 | − | 0.866025i | 0.0300421 | − | 0.0520344i | −0.850613 | − | 0.525792i | \(-0.823769\pi\) |
0.880656 | + | 0.473757i | \(0.157103\pi\) | |||||||
\(278\) | 2.59808 | + | 4.50000i | 0.155822 | + | 0.269892i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −9.00000 | − | 1.73205i | −0.537853 | − | 0.103510i | ||||
\(281\) | 18.0000i | 1.07379i | 0.843649 | + | 0.536895i | \(0.180403\pi\) | ||||
−0.843649 | + | 0.536895i | \(0.819597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.5000 | − | 9.52628i | −0.980823 | − | 0.566279i | −0.0783046 | − | 0.996929i | \(-0.524951\pi\) |
−0.902519 | + | 0.430651i | \(0.858284\pi\) | |||||||
\(284\) | −5.19615 | − | 3.00000i | −0.308335 | − | 0.178017i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.8564 | − | 12.0000i | −0.817918 | − | 0.708338i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.5000 | − | 26.8468i | −0.911765 | − | 1.57922i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.00000 | + | 3.46410i | −0.351123 | + | 0.202721i | ||||
\(293\) | −27.7128 | −1.61900 | −0.809500 | − | 0.587120i | \(-0.800262\pi\) | ||||
−0.809500 | + | 0.587120i | \(0.800262\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.0000 | 1.39733 | ||||||||
\(296\) | −4.33013 | + | 2.50000i | −0.251684 | + | 0.145310i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.00000 | − | 5.19615i | 0.173785 | − | 0.301005i | ||||
\(299\) | −15.5885 | − | 27.0000i | −0.901504 | − | 1.56145i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.00000 | + | 1.73205i | 0.115278 | + | 0.0998337i | ||||
\(302\) | − | 1.00000i | − | 0.0575435i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.00000 | + | 1.73205i | 0.172062 | + | 0.0993399i | ||||
\(305\) | −5.19615 | − | 3.00000i | −0.297531 | − | 0.171780i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 8.66025i | − | 0.494267i | −0.968981 | − | 0.247133i | \(-0.920511\pi\) | ||
0.968981 | − | 0.247133i | \(-0.0794886\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −15.0000 | − | 25.9808i | −0.851943 | − | 1.47561i | ||||
\(311\) | 1.73205 | − | 3.00000i | 0.0982156 | − | 0.170114i | −0.812731 | − | 0.582640i | \(-0.802020\pi\) |
0.910946 | + | 0.412525i | \(0.135353\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.00000 | + | 3.46410i | −0.339140 | + | 0.195803i | −0.659892 | − | 0.751361i | \(-0.729398\pi\) |
0.320752 | + | 0.947163i | \(0.396065\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.00000 | 0.393781 | ||||||||
\(317\) | −20.7846 | + | 12.0000i | −1.16738 | + | 0.673987i | −0.953062 | − | 0.302777i | \(-0.902086\pi\) |
−0.214318 | + | 0.976764i | \(0.568753\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.73205 | − | 3.00000i | −0.0968246 | − | 0.167705i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −15.0000 | + | 5.19615i | −0.835917 | + | 0.289570i | ||||
\(323\) | − | 24.0000i | − | 1.33540i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 31.5000 | + | 18.1865i | 1.74731 | + | 1.00881i | ||||
\(326\) | 9.52628 | + | 5.50000i | 0.527612 | + | 0.304617i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 6.92820i | − | 0.382546i | ||||||
\(329\) | 3.46410 | − | 18.0000i | 0.190982 | − | 0.992372i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.00000 | + | 6.92820i | 0.219860 | + | 0.380808i | 0.954765 | − | 0.297361i | \(-0.0961066\pi\) |
−0.734905 | + | 0.678170i | \(0.762773\pi\) | |||||||
\(332\) | 1.73205 | − | 3.00000i | 0.0950586 | − | 0.164646i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.00000 | − | 1.73205i | 0.164153 | − | 0.0947736i | ||||
\(335\) | 45.0333 | 2.46043 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.0000 | 1.19842 | 0.599208 | − | 0.800593i | \(-0.295482\pi\) | ||||
0.599208 | + | 0.800593i | \(0.295482\pi\) | |||||||
\(338\) | 12.1244 | − | 7.00000i | 0.659478 | − | 0.380750i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −12.0000 | + | 20.7846i | −0.650791 | + | 1.12720i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 1.00000i | 0.0539164i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.0000 | − | 10.3923i | −0.967686 | − | 0.558694i | ||||
\(347\) | −20.7846 | − | 12.0000i | −1.11578 | − | 0.644194i | −0.175457 | − | 0.984487i | \(-0.556140\pi\) |
−0.940319 | + | 0.340293i | \(0.889474\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.0526i | 1.01986i | 0.860216 | + | 0.509930i | \(0.170329\pi\) | ||||
−0.860216 | + | 0.509930i | \(0.829671\pi\) | |||||||
\(350\) | 12.1244 | − | 14.0000i | 0.648074 | − | 0.748331i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.46410 | + | 6.00000i | −0.184376 | + | 0.319348i | −0.943366 | − | 0.331754i | \(-0.892360\pi\) |
0.758990 | + | 0.651102i | \(0.225693\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.0000 | − | 10.3923i | 0.955341 | − | 0.551566i | ||||
\(356\) | 10.3923 | 0.550791 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.00000 | 0.317110 | ||||||||
\(359\) | 5.19615 | − | 3.00000i | 0.274242 | − | 0.158334i | −0.356572 | − | 0.934268i | \(-0.616054\pi\) |
0.630814 | + | 0.775934i | \(0.282721\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.50000 | + | 6.06218i | −0.184211 | + | 0.319062i | ||||
\(362\) | −6.92820 | − | 12.0000i | −0.364138 | − | 0.630706i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.50000 | − | 12.9904i | −0.235864 | − | 0.680881i | ||||
\(365\) | − | 24.0000i | − | 1.25622i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.0000 | + | 8.66025i | 0.782994 | + | 0.452062i | 0.837490 | − | 0.546452i | \(-0.184022\pi\) |
−0.0544966 | + | 0.998514i | \(0.517355\pi\) | |||||||
\(368\) | −5.19615 | − | 3.00000i | −0.270868 | − | 0.156386i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 17.3205i | − | 0.900450i | ||||||
\(371\) | −5.19615 | − | 15.0000i | −0.269771 | − | 0.778761i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.0000 | + | 19.0526i | 0.569558 | + | 0.986504i | 0.996610 | + | 0.0822766i | \(0.0262191\pi\) |
−0.427051 | + | 0.904227i | \(0.640448\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.00000 | − | 3.46410i | 0.309426 | − | 0.178647i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.0000 | −1.18143 | −0.590715 | − | 0.806880i | \(-0.701154\pi\) | ||||
−0.590715 | + | 0.806880i | \(0.701154\pi\) | |||||||
\(380\) | −10.3923 | + | 6.00000i | −0.533114 | + | 0.307794i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.00000 | + | 5.19615i | −0.153493 | + | 0.265858i | ||||
\(383\) | −1.73205 | − | 3.00000i | −0.0885037 | − | 0.153293i | 0.818375 | − | 0.574684i | \(-0.194875\pi\) |
−0.906879 | + | 0.421392i | \(0.861542\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 1.00000i | − | 0.0508987i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.50000 | + | 0.866025i | 0.0761510 | + | 0.0439658i | ||||
\(389\) | 10.3923 | + | 6.00000i | 0.526911 | + | 0.304212i | 0.739758 | − | 0.672874i | \(-0.234940\pi\) |
−0.212847 | + | 0.977086i | \(0.568274\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 41.5692i | 2.10225i | ||||||||
\(392\) | −6.92820 | + | 1.00000i | −0.349927 | + | 0.0505076i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.0000 | + | 20.7846i | 0.604551 | + | 1.04711i | ||||
\(395\) | −12.1244 | + | 21.0000i | −0.610043 | + | 1.05662i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.50000 | − | 4.33013i | 0.376414 | − | 0.217323i | −0.299843 | − | 0.953989i | \(-0.596934\pi\) |
0.676257 | + | 0.736666i | \(0.263601\pi\) | |||||||
\(398\) | 1.73205 | 0.0868199 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.00000 | 0.350000 | ||||||||
\(401\) | 20.7846 | − | 12.0000i | 1.03793 | − | 0.599251i | 0.118686 | − | 0.992932i | \(-0.462132\pi\) |
0.919247 | + | 0.393680i | \(0.128798\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.5000 | − | 38.9711i | 1.12080 | − | 1.94129i | ||||
\(404\) | −5.19615 | − | 9.00000i | −0.258518 | − | 0.447767i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.5000 | − | 7.79423i | −0.667532 | − | 0.385400i | 0.127609 | − | 0.991825i | \(-0.459270\pi\) |
−0.795141 | + | 0.606425i | \(0.792603\pi\) | |||||||
\(410\) | 20.7846 | + | 12.0000i | 1.02648 | + | 0.592638i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 5.19615i | − | 0.255996i | ||||||
\(413\) | 17.3205 | − | 6.00000i | 0.852286 | − | 0.295241i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.00000 | + | 10.3923i | 0.294528 | + | 0.510138i | ||||
\(416\) | 2.59808 | − | 4.50000i | 0.127381 | − | 0.220631i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.2487 | −1.18463 | −0.592314 | − | 0.805708i | \(-0.701785\pi\) | ||||
−0.592314 | + | 0.805708i | \(0.701785\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.0000 | −1.07221 | −0.536107 | − | 0.844150i | \(-0.680106\pi\) | ||||
−0.536107 | + | 0.844150i | \(0.680106\pi\) | |||||||
\(422\) | −21.6506 | + | 12.5000i | −1.05394 | + | 0.608490i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.00000 | − | 5.19615i | 0.145693 | − | 0.252347i | ||||
\(425\) | −24.2487 | − | 42.0000i | −1.17624 | − | 2.03730i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.50000 | − | 0.866025i | −0.217770 | − | 0.0419099i | ||||
\(428\) | − | 6.00000i | − | 0.290021i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.00000 | − | 1.73205i | −0.144673 | − | 0.0835269i | ||||
\(431\) | 31.1769 | + | 18.0000i | 1.50174 | + | 0.867029i | 0.999998 | + | 0.00201168i | \(0.000640338\pi\) |
0.501741 | + | 0.865018i | \(0.332693\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 39.8372i | 1.91445i | 0.289341 | + | 0.957226i | \(0.406564\pi\) | ||||
−0.289341 | + | 0.957226i | \(0.593436\pi\) | |||||||
\(434\) | −17.3205 | − | 15.0000i | −0.831411 | − | 0.720023i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.50000 | − | 9.52628i | −0.263402 | − | 0.456226i | ||||
\(437\) | −10.3923 | + | 18.0000i | −0.497131 | + | 0.861057i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.0000 | + | 15.5885i | −1.28864 | + | 0.743996i | −0.978412 | − | 0.206666i | \(-0.933739\pi\) |
−0.310228 | + | 0.950662i | \(0.600405\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −36.0000 | −1.71235 | ||||||||
\(443\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.0000 | + | 31.1769i | −0.853282 | + | 1.47793i | ||||
\(446\) | 5.19615 | + | 9.00000i | 0.246045 | + | 0.426162i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.00000 | − | 1.73205i | −0.0944911 | − | 0.0818317i | ||||
\(449\) | 30.0000i | 1.41579i | 0.706319 | + | 0.707894i | \(0.250354\pi\) | ||||
−0.706319 | + | 0.707894i | \(0.749646\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −15.5885 | − | 9.00000i | −0.733219 | − | 0.423324i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10.3923i | 0.487735i | ||||||||
\(455\) | 46.7654 | + | 9.00000i | 2.19239 | + | 0.421927i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.5000 | − | 26.8468i | −0.725059 | − | 1.25584i | −0.958950 | − | 0.283577i | \(-0.908479\pi\) |
0.233890 | − | 0.972263i | \(-0.424854\pi\) | |||||||
\(458\) | −0.866025 | + | 1.50000i | −0.0404667 | + | 0.0700904i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 18.0000 | − | 10.3923i | 0.839254 | − | 0.484544i | ||||
\(461\) | 13.8564 | 0.645357 | 0.322679 | − | 0.946509i | \(-0.395417\pi\) | ||||
0.322679 | + | 0.946509i | \(0.395417\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −40.0000 | −1.85896 | −0.929479 | − | 0.368875i | \(-0.879743\pi\) | ||||
−0.929479 | + | 0.368875i | \(0.879743\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.00000 | − | 10.3923i | 0.277945 | − | 0.481414i | ||||
\(467\) | −5.19615 | − | 9.00000i | −0.240449 | − | 0.416470i | 0.720393 | − | 0.693566i | \(-0.243961\pi\) |
−0.960842 | + | 0.277096i | \(0.910628\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 32.5000 | − | 11.2583i | 1.50071 | − | 0.519861i | ||||
\(470\) | 24.0000i | 1.10704i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.00000 | + | 3.46410i | 0.276172 | + | 0.159448i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 24.2487i | − | 1.11261i | ||||||
\(476\) | −3.46410 | + | 18.0000i | −0.158777 | + | 0.825029i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.00000 | − | 5.19615i | −0.137217 | − | 0.237666i | ||||
\(479\) | −1.73205 | + | 3.00000i | −0.0791394 | + | 0.137073i | −0.902879 | − | 0.429895i | \(-0.858551\pi\) |
0.823739 | + | 0.566969i | \(0.191884\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.5000 | − | 12.9904i | 1.02591 | − | 0.592310i | ||||
\(482\) | −1.73205 | −0.0788928 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.0000 | −0.500000 | ||||||||
\(485\) | −5.19615 | + | 3.00000i | −0.235945 | + | 0.136223i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.00000 | − | 6.92820i | 0.181257 | − | 0.313947i | −0.761052 | − | 0.648691i | \(-0.775317\pi\) |
0.942309 | + | 0.334744i | \(0.108650\pi\) | |||||||
\(488\) | −0.866025 | − | 1.50000i | −0.0392031 | − | 0.0679018i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 9.00000 | − | 22.5167i | 0.406579 | − | 1.01720i | ||||
\(491\) | 6.00000i | 0.270776i | 0.990793 | + | 0.135388i | \(0.0432281\pi\) | ||||
−0.990793 | + | 0.135388i | \(0.956772\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −15.5885 | − | 9.00000i | −0.701358 | − | 0.404929i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 8.66025i | − | 0.388857i | ||||||
\(497\) | 10.3923 | − | 12.0000i | 0.466159 | − | 0.538274i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.5000 | + | 19.9186i | 0.514811 | + | 0.891678i | 0.999852 | + | 0.0171872i | \(0.00547113\pi\) |
−0.485042 | + | 0.874491i | \(0.661196\pi\) | |||||||
\(500\) | −3.46410 | + | 6.00000i | −0.154919 | + | 0.268328i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −15.0000 | + | 8.66025i | −0.669483 | + | 0.386526i | ||||
\(503\) | −38.1051 | −1.69902 | −0.849512 | − | 0.527570i | \(-0.823103\pi\) | ||||
−0.849512 | + | 0.527570i | \(0.823103\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 36.0000 | 1.60198 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.50000 | + | 6.06218i | −0.155287 | + | 0.268966i | ||||
\(509\) | −12.1244 | − | 21.0000i | −0.537403 | − | 0.930809i | −0.999043 | − | 0.0437414i | \(-0.986072\pi\) |
0.461640 | − | 0.887067i | \(-0.347261\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.00000 | − | 17.3205i | −0.265424 | − | 0.766214i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9.00000 | − | 5.19615i | −0.396973 | − | 0.229192i | ||||
\(515\) | 15.5885 | + | 9.00000i | 0.686909 | + | 0.396587i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −4.33013 | − | 12.5000i | −0.190255 | − | 0.549218i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.00000 | + | 15.5885i | 0.394676 | + | 0.683599i | ||||
\(521\) | −12.1244 | + | 21.0000i | −0.531178 | + | 0.920027i | 0.468160 | + | 0.883644i | \(0.344917\pi\) |
−0.999338 | + | 0.0363831i | \(0.988416\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.50000 | + | 2.59808i | −0.196771 | + | 0.113606i | −0.595149 | − | 0.803616i | \(-0.702907\pi\) |
0.398377 | + | 0.917222i | \(0.369573\pi\) | |||||||
\(524\) | 20.7846 | 0.907980 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −51.9615 | + | 30.0000i | −2.26348 | + | 1.30682i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.50000 | − | 11.2583i | 0.282609 | − | 0.489493i | ||||
\(530\) | 10.3923 | + | 18.0000i | 0.451413 | + | 0.781870i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.00000 | + | 6.92820i | −0.260133 | + | 0.300376i | ||||
\(533\) | 36.0000i | 1.55933i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.0000 | + | 10.3923i | 0.778208 | + | 0.449299i | ||||
\(536\) | 11.2583 | + | 6.50000i | 0.486286 | + | 0.280757i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 27.7128i | 1.19478i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.00000 | − | 1.73205i | −0.0429934 | − | 0.0744667i | 0.843728 | − | 0.536771i | \(-0.180356\pi\) |
−0.886721 | + | 0.462304i | \(0.847023\pi\) | |||||||
\(542\) | 14.7224 | − | 25.5000i | 0.632383 | − | 1.09532i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.00000 | + | 3.46410i | −0.257248 | + | 0.148522i | ||||
\(545\) | 38.1051 | 1.63224 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.00000 | −0.0427569 | −0.0213785 | − | 0.999771i | \(-0.506805\pi\) | ||||
−0.0213785 | + | 0.999771i | \(0.506805\pi\) | |||||||
\(548\) | −15.5885 | + | 9.00000i | −0.665906 | + | 0.384461i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.50000 | + | 18.1865i | −0.148835 | + | 0.773370i | ||||
\(554\) | 1.00000i | 0.0424859i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.50000 | − | 2.59808i | −0.190843 | − | 0.110183i | ||||
\(557\) | 15.5885 | + | 9.00000i | 0.660504 | + | 0.381342i | 0.792469 | − | 0.609912i | \(-0.208795\pi\) |
−0.131965 | + | 0.991254i | \(0.542129\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 5.19615i | − | 0.219774i | ||||||
\(560\) | 8.66025 | − | 3.00000i | 0.365963 | − | 0.126773i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.00000 | − | 15.5885i | −0.379642 | − | 0.657559i | ||||
\(563\) | 5.19615 | − | 9.00000i | 0.218992 | − | 0.379305i | −0.735508 | − | 0.677516i | \(-0.763057\pi\) |
0.954500 | + | 0.298211i | \(0.0963899\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 54.0000 | − | 31.1769i | 2.27180 | − | 1.31162i | ||||
\(566\) | 19.0526 | 0.800839 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.00000 | 0.251754 | ||||||||
\(569\) | −5.19615 | + | 3.00000i | −0.217834 | + | 0.125767i | −0.604947 | − | 0.796266i | \(-0.706806\pi\) |
0.387113 | + | 0.922032i | \(0.373472\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.00000 | − | 3.46410i | 0.0836974 | − | 0.144968i | −0.821138 | − | 0.570730i | \(-0.806660\pi\) |
0.904835 | + | 0.425762i | \(0.139994\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 18.0000 | + | 3.46410i | 0.751305 | + | 0.144589i | ||||
\(575\) | 42.0000i | 1.75152i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.5000 | + | 18.1865i | 1.31136 | + | 0.757115i | 0.982322 | − | 0.187201i | \(-0.0599414\pi\) |
0.329040 | + | 0.944316i | \(0.393275\pi\) | |||||||
\(578\) | 26.8468 | + | 15.5000i | 1.11668 | + | 0.644715i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.92820 | + | 6.00000i | 0.287430 | + | 0.248922i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 3.46410 | − | 6.00000i | 0.143346 | − | 0.248282i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.0000 | − | 13.8564i | 0.991431 | − | 0.572403i | ||||
\(587\) | 10.3923 | 0.428936 | 0.214468 | − | 0.976731i | \(-0.431198\pi\) | ||||
0.214468 | + | 0.976731i | \(0.431198\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −30.0000 | −1.23613 | ||||||||
\(590\) | −20.7846 | + | 12.0000i | −0.855689 | + | 0.494032i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.50000 | − | 4.33013i | 0.102749 | − | 0.177967i | ||||
\(593\) | 8.66025 | + | 15.0000i | 0.355634 | + | 0.615976i | 0.987226 | − | 0.159325i | \(-0.0509316\pi\) |
−0.631592 | + | 0.775301i | \(0.717598\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −48.0000 | − | 41.5692i | −1.96781 | − | 1.70417i | ||||
\(596\) | 6.00000i | 0.245770i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 27.0000 | + | 15.5885i | 1.10411 | + | 0.637459i | ||||
\(599\) | 20.7846 | + | 12.0000i | 0.849236 | + | 0.490307i | 0.860393 | − | 0.509631i | \(-0.170218\pi\) |
−0.0111569 | + | 0.999938i | \(0.503551\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 19.0526i | − | 0.777170i | −0.921413 | − | 0.388585i | \(-0.872964\pi\) | ||
0.921413 | − | 0.388585i | \(-0.127036\pi\) | |||||||
\(602\) | −2.59808 | − | 0.500000i | −0.105890 | − | 0.0203785i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.500000 | + | 0.866025i | 0.0203447 | + | 0.0352381i | ||||
\(605\) | 19.0526 | − | 33.0000i | 0.774597 | − | 1.34164i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.0000 | + | 8.66025i | −0.608831 | + | 0.351509i | −0.772508 | − | 0.635005i | \(-0.780998\pi\) |
0.163677 | + | 0.986514i | \(0.447665\pi\) | |||||||
\(608\) | −3.46410 | −0.140488 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.00000 | 0.242933 | ||||||||
\(611\) | −31.1769 | + | 18.0000i | −1.26128 | + | 0.728202i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.50000 | + | 14.7224i | −0.343312 | + | 0.594633i | −0.985046 | − | 0.172294i | \(-0.944882\pi\) |
0.641734 | + | 0.766927i | \(0.278215\pi\) | |||||||
\(614\) | 4.33013 | + | 7.50000i | 0.174750 | + | 0.302675i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 12.0000i | − | 0.483102i | −0.970388 | − | 0.241551i | \(-0.922344\pi\) | ||
0.970388 | − | 0.241551i | \(-0.0776561\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.5000 | − | 7.79423i | −0.542611 | − | 0.313276i | 0.203526 | − | 0.979070i | \(-0.434760\pi\) |
−0.746136 | + | 0.665793i | \(0.768093\pi\) | |||||||
\(620\) | 25.9808 | + | 15.0000i | 1.04341 | + | 0.602414i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.46410i | 0.138898i | ||||||||
\(623\) | −5.19615 | + | 27.0000i | −0.208179 | + | 1.08173i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | 3.46410 | − | 6.00000i | 0.138453 | − | 0.239808i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −34.6410 | −1.38123 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.0000 | −0.995234 | −0.497617 | − | 0.867397i | \(-0.665792\pi\) | ||||
−0.497617 | + | 0.867397i | \(0.665792\pi\) | |||||||
\(632\) | −6.06218 | + | 3.50000i | −0.241140 | + | 0.139223i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 12.0000 | − | 20.7846i | 0.476581 | − | 0.825462i | ||||
\(635\) | −12.1244 | − | 21.0000i | −0.481140 | − | 0.833360i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 36.0000 | − | 5.19615i | 1.42637 | − | 0.205879i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.00000 | + | 1.73205i | 0.118585 | + | 0.0684653i | ||||
\(641\) | −20.7846 | − | 12.0000i | −0.820943 | − | 0.473972i | 0.0297987 | − | 0.999556i | \(-0.490513\pi\) |
−0.850741 | + | 0.525584i | \(0.823847\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 43.3013i | − | 1.70764i | −0.520572 | − | 0.853818i | \(-0.674281\pi\) | ||
0.520572 | − | 0.853818i | \(-0.325719\pi\) | |||||||
\(644\) | 10.3923 | − | 12.0000i | 0.409514 | − | 0.472866i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.0000 | + | 20.7846i | 0.472134 | + | 0.817760i | ||||
\(647\) | −10.3923 | + | 18.0000i | −0.408564 | + | 0.707653i | −0.994729 | − | 0.102538i | \(-0.967304\pi\) |
0.586165 | + | 0.810191i | \(0.300637\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −36.3731 | −1.42667 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.0000 | −0.430793 | ||||||||
\(653\) | 5.19615 | − | 3.00000i | 0.203341 | − | 0.117399i | −0.394872 | − | 0.918736i | \(-0.629211\pi\) |
0.598213 | + | 0.801337i | \(0.295878\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −36.0000 | + | 62.3538i | −1.40664 | + | 2.43637i | ||||
\(656\) | 3.46410 | + | 6.00000i | 0.135250 | + | 0.234261i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.00000 | + | 17.3205i | 0.233904 | + | 0.675224i | ||||
\(659\) | − | 18.0000i | − | 0.701180i | −0.936529 | − | 0.350590i | \(-0.885981\pi\) | ||
0.936529 | − | 0.350590i | \(-0.114019\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.0000 | − | 17.3205i | −1.16686 | − | 0.673690i | −0.213925 | − | 0.976850i | \(-0.568625\pi\) |
−0.952940 | + | 0.303160i | \(0.901958\pi\) | |||||||
\(662\) | −6.92820 | − | 4.00000i | −0.269272 | − | 0.155464i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.46410i | 0.134433i | ||||||||
\(665\) | −10.3923 | − | 30.0000i | −0.402996 | − | 1.16335i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −1.73205 | + | 3.00000i | −0.0670151 | + | 0.116073i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −39.0000 | + | 22.5167i | −1.50670 | + | 0.869894i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.0000 | −0.539660 | −0.269830 | − | 0.962908i | \(-0.586968\pi\) | ||||
−0.269830 | + | 0.962908i | \(0.586968\pi\) | |||||||
\(674\) | −19.0526 | + | 11.0000i | −0.733877 | + | 0.423704i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.00000 | + | 12.1244i | −0.269231 | + | 0.466321i | ||||
\(677\) | −20.7846 | − | 36.0000i | −0.798817 | − | 1.38359i | −0.920387 | − | 0.391009i | \(-0.872126\pi\) |
0.121569 | − | 0.992583i | \(-0.461207\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.00000 | + | 3.46410i | −0.115129 | + | 0.132940i | ||||
\(680\) | − | 24.0000i | − | 0.920358i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.5885 | + | 9.00000i | 0.596476 | + | 0.344375i | 0.767654 | − | 0.640865i | \(-0.221424\pi\) |
−0.171178 | + | 0.985240i | \(0.554757\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 62.3538i | − | 2.38242i | ||||||
\(686\) | 0.866025 | − | 18.5000i | 0.0330650 | − | 0.706333i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.500000 | − | 0.866025i | −0.0190623 | − | 0.0330169i | ||||
\(689\) | −15.5885 | + | 27.0000i | −0.593873 | + | 1.02862i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.5000 | + | 16.4545i | −1.08419 | + | 0.625958i | −0.932024 | − | 0.362397i | \(-0.881959\pi\) |
−0.152167 | + | 0.988355i | \(0.548625\pi\) | |||||||
\(692\) | 20.7846 | 0.790112 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.0000 | 0.911028 | ||||||||
\(695\) | 15.5885 | − | 9.00000i | 0.591304 | − | 0.341389i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.0000 | − | 41.5692i | 0.909065 | − | 1.57455i | ||||
\(698\) | −9.52628 | − | 16.5000i | −0.360575 | − | 0.624534i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.50000 | + | 18.1865i | −0.132288 | + | 0.687386i | ||||
\(701\) | 36.0000i | 1.35970i | 0.733351 | + | 0.679851i | \(0.237955\pi\) | ||||
−0.733351 | + | 0.679851i | \(0.762045\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.0000 | − | 8.66025i | −0.565736 | − | 0.326628i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 6.92820i | − | 0.260746i | ||||||
\(707\) | 25.9808 | − | 9.00000i | 0.977107 | − | 0.338480i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.500000 | − | 0.866025i | −0.0187779 | − | 0.0325243i | 0.856484 | − | 0.516174i | \(-0.172644\pi\) |
−0.875262 | + | 0.483650i | \(0.839311\pi\) | |||||||
\(710\) | −10.3923 | + | 18.0000i | −0.390016 | + | 0.675528i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.00000 | + | 5.19615i | −0.337289 | + | 0.194734i | ||||
\(713\) | 51.9615 | 1.94597 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.19615 | + | 3.00000i | −0.194189 | + | 0.112115i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.00000 | + | 5.19615i | −0.111959 | + | 0.193919i | ||||
\(719\) | −1.73205 | − | 3.00000i | −0.0645946 | − | 0.111881i | 0.831919 | − | 0.554896i | \(-0.187242\pi\) |
−0.896514 | + | 0.443015i | \(0.853909\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.5000 | + | 2.59808i | 0.502766 | + | 0.0967574i | ||||
\(722\) | − | 7.00000i | − | 0.260513i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 12.0000 | + | 6.92820i | 0.445976 | + | 0.257485i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.0526i | 0.706620i | 0.935506 | + | 0.353310i | \(0.114944\pi\) | ||||
−0.935506 | + | 0.353310i | \(0.885056\pi\) | |||||||
\(728\) | 10.3923 | + | 9.00000i | 0.385164 | + | 0.333562i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 12.0000 | + | 20.7846i | 0.444140 | + | 0.769273i | ||||
\(731\) | −3.46410 | + | 6.00000i | −0.128124 | + | 0.221918i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.50000 | + | 0.866025i | −0.0554038 | + | 0.0319874i | −0.527446 | − | 0.849589i | \(-0.676850\pi\) |
0.472042 | + | 0.881576i | \(0.343517\pi\) | |||||||
\(734\) | −17.3205 | −0.639312 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.00000 | 0.221163 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.5000 | + | 30.3109i | −0.643748 | + | 1.11500i | 0.340841 | + | 0.940121i | \(0.389288\pi\) |
−0.984589 | + | 0.174883i | \(0.944045\pi\) | |||||||
\(740\) | 8.66025 | + | 15.0000i | 0.318357 | + | 0.551411i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.0000 | + | 10.3923i | 0.440534 | + | 0.381514i | ||||
\(743\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.0000 | − | 10.3923i | −0.659469 | − | 0.380745i | ||||
\(746\) | −19.0526 | − | 11.0000i | −0.697564 | − | 0.402739i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.5885 | + | 3.00000i | 0.569590 | + | 0.109618i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.0000 | + | 17.3205i | 0.364905 | + | 0.632034i | 0.988761 | − | 0.149505i | \(-0.0477681\pi\) |
−0.623856 | + | 0.781540i | \(0.714435\pi\) | |||||||
\(752\) | −3.46410 | + | 6.00000i | −0.126323 | + | 0.218797i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.46410 | −0.126072 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.0000 | 0.908640 | 0.454320 | − | 0.890838i | \(-0.349882\pi\) | ||||
0.454320 | + | 0.890838i | \(0.349882\pi\) | |||||||
\(758\) | 19.9186 | − | 11.5000i | 0.723476 | − | 0.417699i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.00000 | − | 10.3923i | 0.217643 | − | 0.376969i | ||||
\(761\) | 3.46410 | + | 6.00000i | 0.125574 | + | 0.217500i | 0.921957 | − | 0.387292i | \(-0.126590\pi\) |
−0.796383 | + | 0.604792i | \(0.793256\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 27.5000 | − | 9.52628i | 0.995567 | − | 0.344874i | ||||
\(764\) | − | 6.00000i | − | 0.217072i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.00000 | + | 1.73205i | 0.108394 | + | 0.0625815i | ||||
\(767\) | −31.1769 | − | 18.0000i | −1.12573 | − | 0.649942i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.92820i | 0.249837i | 0.992167 | + | 0.124919i | \(0.0398670\pi\) | ||||
−0.992167 | + | 0.124919i | \(0.960133\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.500000 | + | 0.866025i | 0.0179954 | + | 0.0311689i | ||||
\(773\) | 17.3205 | − | 30.0000i | 0.622975 | − | 1.07903i | −0.365953 | − | 0.930633i | \(-0.619257\pi\) |
0.988929 | − | 0.148392i | \(-0.0474097\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −52.5000 | + | 30.3109i | −1.88586 | + | 1.08880i | ||||
\(776\) | −1.73205 | −0.0621770 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12.0000 | −0.430221 | ||||||||
\(779\) | 20.7846 | − | 12.0000i | 0.744686 | − | 0.429945i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −20.7846 | − | 36.0000i | −0.743256 | − | 1.28736i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.50000 | − | 4.33013i | 0.196429 | − | 0.154647i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.50000 | − | 0.866025i | −0.0534692 | − | 0.0308705i | 0.473027 | − | 0.881048i | \(-0.343161\pi\) |
−0.526496 | + | 0.850177i | \(0.676495\pi\) | |||||||
\(788\) | −20.7846 | − | 12.0000i | −0.740421 | − | 0.427482i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 24.2487i | − | 0.862730i | ||||||
\(791\) | 31.1769 | − | 36.0000i | 1.10852 | − | 1.28001i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.50000 | + | 7.79423i | 0.159800 | + | 0.276781i | ||||
\(794\) | −4.33013 | + | 7.50000i | −0.153670 | + | 0.266165i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.50000 | + | 0.866025i | −0.0531661 | + | 0.0306955i | ||||
\(797\) | 20.7846 | 0.736229 | 0.368114 | − | 0.929781i | \(-0.380004\pi\) | ||||
0.368114 | + | 0.929781i | \(0.380004\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 48.0000 | 1.69812 | ||||||||
\(800\) | −6.06218 | + | 3.50000i | −0.214330 | + | 0.123744i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −12.0000 | + | 20.7846i | −0.423735 | + | 0.733930i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.0000 | + | 51.9615i | 0.634417 | + | 1.83140i | ||||
\(806\) | 45.0000i | 1.58506i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.00000 | + | 5.19615i | 0.316619 | + | 0.182800i | ||||
\(809\) | −25.9808 | − | 15.0000i | −0.913435 | − | 0.527372i | −0.0319002 | − | 0.999491i | \(-0.510156\pi\) |
−0.881535 | + | 0.472119i | \(0.843489\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 10.3923i | − | 0.364923i | −0.983213 | − | 0.182462i | \(-0.941593\pi\) | ||
0.983213 | − | 0.182462i | \(-0.0584065\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.0526 | − | 33.0000i | 0.667382 | − | 1.15594i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.00000 | + | 1.73205i | −0.104957 | + | 0.0605968i | ||||
\(818\) | 15.5885 | 0.545038 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −24.0000 | −0.838116 | ||||||||
\(821\) | −15.5885 | + | 9.00000i | −0.544041 | + | 0.314102i | −0.746715 | − | 0.665144i | \(-0.768370\pi\) |
0.202674 | + | 0.979246i | \(0.435037\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.5000 | − | 42.4352i | 0.854016 | − | 1.47920i | −0.0235383 | − | 0.999723i | \(-0.507493\pi\) |
0.877555 | − | 0.479477i | \(-0.159174\pi\) | |||||||
\(824\) | 2.59808 | + | 4.50000i | 0.0905083 | + | 0.156765i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.0000 | + | 13.8564i | −0.417533 | + | 0.482126i | ||||
\(827\) | − | 48.0000i | − | 1.66912i | −0.550914 | − | 0.834562i | \(-0.685721\pi\) | ||
0.550914 | − | 0.834562i | \(-0.314279\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.0000 | − | 6.92820i | −0.416777 | − | 0.240626i | 0.276920 | − | 0.960893i | \(-0.410686\pi\) |
−0.693698 | + | 0.720266i | \(0.744020\pi\) | |||||||
\(830\) | −10.3923 | − | 6.00000i | −0.360722 | − | 0.208263i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.19615i | 0.180144i | ||||||||
\(833\) | −45.0333 | − | 18.0000i | −1.56031 | − | 0.623663i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.00000 | − | 10.3923i | −0.207639 | − | 0.359641i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 21.0000 | − | 12.1244i | 0.725433 | − | 0.418829i | ||||
\(839\) | −45.0333 | −1.55472 | −0.777361 | − | 0.629054i | \(-0.783442\pi\) | ||||
−0.777361 | + | 0.629054i | \(0.783442\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 19.0526 | − | 11.0000i | 0.656595 | − | 0.379085i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12.5000 | − | 21.6506i | 0.430268 | − | 0.745246i | ||||
\(845\) | −24.2487 | − | 42.0000i | −0.834181 | − | 1.44484i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.50000 | − | 28.5788i | 0.188982 | − | 0.981981i | ||||
\(848\) | 6.00000i | 0.206041i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 42.0000 | + | 24.2487i | 1.44059 | + | 0.831724i | ||||
\(851\) | 25.9808 | + | 15.0000i | 0.890609 | + | 0.514193i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.8564i | 0.474434i | 0.971457 | + | 0.237217i | \(0.0762353\pi\) | ||||
−0.971457 | + | 0.237217i | \(0.923765\pi\) | |||||||
\(854\) | 4.33013 | − | 1.50000i | 0.148174 | − | 0.0513289i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.00000 | + | 5.19615i | 0.102538 | + | 0.177601i | ||||
\(857\) | −8.66025 | + | 15.0000i | −0.295829 | + | 0.512390i | −0.975177 | − | 0.221425i | \(-0.928929\pi\) |
0.679349 | + | 0.733816i | \(0.262262\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.50000 | + | 4.33013i | −0.255897 | + | 0.147742i | −0.622461 | − | 0.782651i | \(-0.713867\pi\) |
0.366565 | + | 0.930393i | \(0.380534\pi\) | |||||||
\(860\) | 3.46410 | 0.118125 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −36.0000 | −1.22616 | ||||||||
\(863\) | 31.1769 | − | 18.0000i | 1.06127 | − | 0.612727i | 0.135490 | − | 0.990779i | \(-0.456739\pi\) |
0.925785 | + | 0.378052i | \(0.123406\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −36.0000 | + | 62.3538i | −1.22404 | + | 2.12009i | ||||
\(866\) | −19.9186 | − | 34.5000i | −0.676861 | − | 1.17236i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 22.5000 | + | 4.33013i | 0.763700 | + | 0.146974i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −58.5000 | − | 33.7750i | −1.98220 | − | 1.14442i | ||||
\(872\) | 9.52628 | + | 5.50000i | 0.322601 | + | 0.186254i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 20.7846i | − | 0.703050i | ||||||
\(875\) | −13.8564 | − | 12.0000i | −0.468432 | − | 0.405674i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.5000 | − | 35.5070i | −0.692236 | − | 1.19899i | −0.971104 | − | 0.238658i | \(-0.923292\pi\) |
0.278868 | − | 0.960329i | \(-0.410041\pi\) | |||||||
\(878\) | 15.5885 | − | 27.0000i | 0.526085 | − | 0.911206i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.1769 | 1.05038 | 0.525188 | − | 0.850986i | \(-0.323995\pi\) | ||||
0.525188 | + | 0.850986i | \(0.323995\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 52.0000 | 1.74994 | 0.874970 | − | 0.484178i | \(-0.160881\pi\) | ||||
0.874970 | + | 0.484178i | \(0.160881\pi\) | |||||||
\(884\) | 31.1769 | − | 18.0000i | 1.04859 | − | 0.605406i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.73205 | + | 3.00000i | 0.0581566 | + | 0.100730i | 0.893638 | − | 0.448789i | \(-0.148144\pi\) |
−0.835481 | + | 0.549519i | \(0.814811\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.0000 | − | 12.1244i | −0.469545 | − | 0.406638i | ||||
\(890\) | − | 36.0000i | − | 1.20672i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.00000 | − | 5.19615i | −0.301342 | − | 0.173980i | ||||
\(893\) | 20.7846 | + | 12.0000i | 0.695530 | + | 0.401565i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 20.7846i | − | 0.694753i | ||||||
\(896\) | 2.59808 | + | 0.500000i | 0.0867956 | + | 0.0167038i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15.0000 | − | 25.9808i | −0.500556 | − | 0.866989i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.0000 | − | 20.7846i | 1.19933 | − | 0.692436i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18.0000 | 0.598671 | ||||||||
\(905\) | −41.5692 | + | 24.0000i | −1.38181 | + | 0.797787i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.5000 | − | 40.7032i | 0.780305 | − | 1.35153i | −0.151460 | − | 0.988463i | \(-0.548397\pi\) |
0.931764 | − | 0.363064i | \(-0.118269\pi\) | |||||||
\(908\) | −5.19615 | − | 9.00000i | −0.172440 | − | 0.298675i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −45.0000 | + | 15.5885i | −1.49174 | + | 0.516752i | ||||
\(911\) | − | 48.0000i | − | 1.59031i | −0.606406 | − | 0.795155i | \(-0.707389\pi\) | ||
0.606406 | − | 0.795155i | \(-0.292611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 26.8468 | + | 15.5000i | 0.888013 | + | 0.512694i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 1.73205i | − | 0.0572286i | ||||||
\(917\) | −10.3923 | + | 54.0000i | −0.343184 | + | 1.78324i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.5000 | − | 21.6506i | −0.412337 | − | 0.714189i | 0.582808 | − | 0.812610i | \(-0.301954\pi\) |
−0.995145 | + | 0.0984214i | \(0.968621\pi\) | |||||||
\(920\) | −10.3923 | + | 18.0000i | −0.342624 | + | 0.593442i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12.0000 | + | 6.92820i | −0.395199 | + | 0.228168i | ||||
\(923\) | −31.1769 | −1.02620 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −35.0000 | −1.15079 | ||||||||
\(926\) | 34.6410 | − | 20.0000i | 1.13837 | − | 0.657241i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.5167 | + | 39.0000i | 0.738748 | + | 1.27955i | 0.953059 | + | 0.302783i | \(0.0979158\pi\) |
−0.214312 | + | 0.976765i | \(0.568751\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.0000 | − | 19.0526i | −0.491605 | − | 0.624422i | ||||
\(932\) | 12.0000i | 0.393073i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 9.00000 | + | 5.19615i | 0.294489 | + | 0.170023i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.19615i | 0.169751i | 0.996392 | + | 0.0848755i | \(0.0270492\pi\) | ||||
−0.996392 | + | 0.0848755i | \(0.972951\pi\) | |||||||
\(938\) | −22.5167 | + | 26.0000i | −0.735195 | + | 0.848930i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −12.0000 | − | 20.7846i | −0.391397 | − | 0.677919i | ||||
\(941\) | −6.92820 | + | 12.0000i | −0.225853 | + | 0.391189i | −0.956575 | − | 0.291486i | \(-0.905850\pi\) |
0.730722 | + | 0.682675i | \(0.239184\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −36.0000 | + | 20.7846i | −1.17232 | + | 0.676840i | ||||
\(944\) | −6.92820 | −0.225494 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.1769 | + | 18.0000i | −1.01311 | + | 0.584921i | −0.912102 | − | 0.409964i | \(-0.865541\pi\) |
−0.101012 | + | 0.994885i | \(0.532208\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.0000 | + | 31.1769i | −0.584305 | + | 1.01205i | ||||
\(950\) | 12.1244 | + | 21.0000i | 0.393366 | + | 0.681330i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.00000 | − | 17.3205i | −0.194461 | − | 0.561361i | ||||
\(953\) | 6.00000i | 0.194359i | 0.995267 | + | 0.0971795i | \(0.0309821\pi\) | ||||
−0.995267 | + | 0.0971795i | \(0.969018\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.0000 | + | 10.3923i | 0.582466 | + | 0.336287i | ||||
\(956\) | 5.19615 | + | 3.00000i | 0.168056 | + | 0.0970269i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 3.46410i | − | 0.111920i | ||||||
\(959\) | −15.5885 | − | 45.0000i | −0.503378 | − | 1.45313i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.0000 | + | 38.1051i | 0.709677 | + | 1.22920i | ||||
\(962\) | −12.9904 | + | 22.5000i | −0.418827 | + | 0.725429i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.50000 | − | 0.866025i | 0.0483117 | − | 0.0278928i | ||||
\(965\) | −3.46410 | −0.111513 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.0000 | −0.996893 | −0.498446 | − | 0.866921i | \(-0.666096\pi\) | ||||
−0.498446 | + | 0.866921i | \(0.666096\pi\) | |||||||
\(968\) | 9.52628 | − | 5.50000i | 0.306186 | − | 0.176777i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.00000 | − | 5.19615i | 0.0963242 | − | 0.166838i | ||||
\(971\) | 13.8564 | + | 24.0000i | 0.444673 | + | 0.770197i | 0.998029 | − | 0.0627481i | \(-0.0199865\pi\) |
−0.553356 | + | 0.832945i | \(0.686653\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.00000 | − | 10.3923i | 0.288527 | − | 0.333162i | ||||
\(974\) | 8.00000i | 0.256337i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.50000 | + | 0.866025i | 0.0480138 | + | 0.0277208i | ||||
\(977\) | −5.19615 | − | 3.00000i | −0.166240 | − | 0.0959785i | 0.414572 | − | 0.910017i | \(-0.363931\pi\) |
−0.580812 | + | 0.814038i | \(0.697265\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 3.46410 | + | 24.0000i | 0.110657 | + | 0.766652i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.00000 | − | 5.19615i | −0.0957338 | − | 0.165816i | ||||
\(983\) | −12.1244 | + | 21.0000i | −0.386707 | + | 0.669796i | −0.992004 | − | 0.126203i | \(-0.959721\pi\) |
0.605298 | + | 0.795999i | \(0.293054\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 72.0000 | − | 41.5692i | 2.29411 | − | 1.32451i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18.0000 | 0.572656 | ||||||||
\(989\) | 5.19615 | − | 3.00000i | 0.165228 | − | 0.0953945i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.50000 | + | 11.2583i | −0.206479 | + | 0.357633i | −0.950603 | − | 0.310409i | \(-0.899534\pi\) |
0.744124 | + | 0.668042i | \(0.232867\pi\) | |||||||
\(992\) | 4.33013 | + | 7.50000i | 0.137482 | + | 0.238125i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.00000 | + | 15.5885i | −0.0951542 | + | 0.494436i | ||||
\(995\) | − | 6.00000i | − | 0.190213i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.5000 | + | 16.4545i | 0.902604 | + | 0.521119i | 0.878044 | − | 0.478580i | \(-0.158848\pi\) |
0.0245599 | + | 0.999698i | \(0.492182\pi\) | |||||||
\(998\) | −19.9186 | − | 11.5000i | −0.630512 | − | 0.364026i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 378.2.k.b.269.1 | yes | 4 | |
3.2 | odd | 2 | inner | 378.2.k.b.269.2 | yes | 4 | |
7.3 | odd | 6 | 2646.2.d.b.2645.2 | 4 | |||
7.4 | even | 3 | 2646.2.d.b.2645.1 | 4 | |||
7.5 | odd | 6 | inner | 378.2.k.b.215.2 | yes | 4 | |
9.2 | odd | 6 | 1134.2.t.b.1025.1 | 4 | |||
9.4 | even | 3 | 1134.2.l.a.269.1 | 4 | |||
9.5 | odd | 6 | 1134.2.l.a.269.2 | 4 | |||
9.7 | even | 3 | 1134.2.t.b.1025.2 | 4 | |||
21.5 | even | 6 | inner | 378.2.k.b.215.1 | ✓ | 4 | |
21.11 | odd | 6 | 2646.2.d.b.2645.4 | 4 | |||
21.17 | even | 6 | 2646.2.d.b.2645.3 | 4 | |||
63.5 | even | 6 | 1134.2.t.b.593.2 | 4 | |||
63.40 | odd | 6 | 1134.2.t.b.593.1 | 4 | |||
63.47 | even | 6 | 1134.2.l.a.215.2 | 4 | |||
63.61 | odd | 6 | 1134.2.l.a.215.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.2.k.b.215.1 | ✓ | 4 | 21.5 | even | 6 | inner | |
378.2.k.b.215.2 | yes | 4 | 7.5 | odd | 6 | inner | |
378.2.k.b.269.1 | yes | 4 | 1.1 | even | 1 | trivial | |
378.2.k.b.269.2 | yes | 4 | 3.2 | odd | 2 | inner | |
1134.2.l.a.215.1 | 4 | 63.61 | odd | 6 | |||
1134.2.l.a.215.2 | 4 | 63.47 | even | 6 | |||
1134.2.l.a.269.1 | 4 | 9.4 | even | 3 | |||
1134.2.l.a.269.2 | 4 | 9.5 | odd | 6 | |||
1134.2.t.b.593.1 | 4 | 63.40 | odd | 6 | |||
1134.2.t.b.593.2 | 4 | 63.5 | even | 6 | |||
1134.2.t.b.1025.1 | 4 | 9.2 | odd | 6 | |||
1134.2.t.b.1025.2 | 4 | 9.7 | even | 3 | |||
2646.2.d.b.2645.1 | 4 | 7.4 | even | 3 | |||
2646.2.d.b.2645.2 | 4 | 7.3 | odd | 6 | |||
2646.2.d.b.2645.3 | 4 | 21.17 | even | 6 | |||
2646.2.d.b.2645.4 | 4 | 21.11 | odd | 6 |