Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(793,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.793");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.k (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 154) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 991.2 | ||
Root | \(1.32288 + 2.29129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.991 |
Dual form | 1386.2.k.s.793.2 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 1.82288 | + | 3.15731i | 0.815215 | + | 1.41199i | 0.909174 | + | 0.416417i | \(0.136714\pi\) |
−0.0939588 | + | 0.995576i | \(0.529952\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.32288 | + | 2.29129i | 0.500000 | + | 0.866025i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.82288 | − | 3.15731i | 0.576444 | − | 0.998430i | ||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.00000 | 1.38675 | 0.693375 | − | 0.720577i | \(-0.256123\pi\) | ||||
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | 1.32288 | − | 2.29129i | 0.353553 | − | 0.612372i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 3.00000 | − | 5.19615i | 0.727607 | − | 1.26025i | −0.230285 | − | 0.973123i | \(-0.573966\pi\) |
0.957892 | − | 0.287129i | \(-0.0927008\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.177124 | + | 0.306788i | 0.0406351 | + | 0.0703821i | 0.885628 | − | 0.464396i | \(-0.153729\pi\) |
−0.844993 | + | 0.534778i | \(0.820395\pi\) | |||||||
\(20\) | −3.64575 | −0.815215 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −1.82288 | − | 3.15731i | −0.380096 | − | 0.658345i | 0.610980 | − | 0.791646i | \(-0.290776\pi\) |
−0.991076 | + | 0.133301i | \(0.957442\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.14575 | + | 7.18065i | −0.829150 | + | 1.43613i | ||||
\(26\) | −2.50000 | − | 4.33013i | −0.490290 | − | 0.849208i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.64575 | −0.500000 | ||||||||
\(29\) | 4.29150 | 0.796912 | 0.398456 | − | 0.917187i | \(-0.369546\pi\) | ||||
0.398456 | + | 0.917187i | \(0.369546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | − | 3.46410i | 0.359211 | − | 0.622171i | −0.628619 | − | 0.777714i | \(-0.716379\pi\) |
0.987829 | + | 0.155543i | \(0.0497126\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.00000 | −1.02899 | ||||||||
\(35\) | −4.82288 | + | 8.35347i | −0.815215 | + | 1.41199i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.822876 | + | 1.42526i | 0.135280 | + | 0.234312i | 0.925704 | − | 0.378248i | \(-0.123473\pi\) |
−0.790424 | + | 0.612560i | \(0.790140\pi\) | |||||||
\(38\) | 0.177124 | − | 0.306788i | 0.0287334 | − | 0.0497676i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.82288 | + | 3.15731i | 0.288222 | + | 0.499215i | ||||
\(41\) | 4.93725 | 0.771070 | 0.385535 | − | 0.922693i | \(-0.374017\pi\) | ||||
0.385535 | + | 0.922693i | \(0.374017\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0.500000 | + | 0.866025i | 0.0753778 | + | 0.130558i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.82288 | + | 3.15731i | −0.268768 | + | 0.465520i | ||||
\(47\) | 6.64575 | + | 11.5108i | 0.969382 | + | 1.67902i | 0.697349 | + | 0.716732i | \(0.254363\pi\) |
0.272034 | + | 0.962288i | \(0.412304\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.50000 | + | 6.06218i | −0.500000 | + | 0.866025i | ||||
\(50\) | 8.29150 | 1.17260 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.50000 | + | 4.33013i | −0.346688 | + | 0.600481i | ||||
\(53\) | −1.82288 | + | 3.15731i | −0.250391 | + | 0.433690i | −0.963634 | − | 0.267227i | \(-0.913893\pi\) |
0.713242 | + | 0.700918i | \(0.247226\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.64575 | 0.491593 | ||||||||
\(56\) | 1.32288 | + | 2.29129i | 0.176777 | + | 0.306186i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.14575 | − | 3.71655i | −0.281751 | − | 0.488007i | ||||
\(59\) | −0.322876 | + | 0.559237i | −0.0420348 | + | 0.0728065i | −0.886277 | − | 0.463155i | \(-0.846717\pi\) |
0.844243 | + | 0.535961i | \(0.180051\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.85425 | − | 3.21165i | −0.237412 | − | 0.411210i | 0.722559 | − | 0.691310i | \(-0.242966\pi\) |
−0.959971 | + | 0.280099i | \(0.909633\pi\) | |||||||
\(62\) | −4.00000 | −0.508001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 9.11438 | + | 15.7866i | 1.13050 | + | 1.95808i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.96863 | + | 3.40976i | −0.240506 | + | 0.416569i | −0.960859 | − | 0.277039i | \(-0.910647\pi\) |
0.720352 | + | 0.693608i | \(0.243980\pi\) | |||||||
\(68\) | 3.00000 | + | 5.19615i | 0.363803 | + | 0.630126i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 9.64575 | 1.15289 | ||||||||
\(71\) | −9.64575 | −1.14474 | −0.572370 | − | 0.819995i | \(-0.693976\pi\) | ||||
−0.572370 | + | 0.819995i | \(0.693976\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.82288 | + | 4.88936i | −0.330393 | + | 0.572257i | −0.982589 | − | 0.185793i | \(-0.940514\pi\) |
0.652196 | + | 0.758050i | \(0.273848\pi\) | |||||||
\(74\) | 0.822876 | − | 1.42526i | 0.0956574 | − | 0.165683i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.354249 | −0.0406351 | ||||||||
\(77\) | 2.64575 | 0.301511 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.32288 | − | 2.29129i | −0.148835 | − | 0.257790i | 0.781962 | − | 0.623326i | \(-0.214219\pi\) |
−0.930797 | + | 0.365536i | \(0.880886\pi\) | |||||||
\(80\) | 1.82288 | − | 3.15731i | 0.203804 | − | 0.352998i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.46863 | − | 4.27579i | −0.272614 | − | 0.472182i | ||||
\(83\) | −13.2915 | −1.45893 | −0.729466 | − | 0.684017i | \(-0.760231\pi\) | ||||
−0.729466 | + | 0.684017i | \(0.760231\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 21.8745 | 2.37262 | ||||||||
\(86\) | 2.00000 | + | 3.46410i | 0.215666 | + | 0.373544i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.500000 | − | 0.866025i | 0.0533002 | − | 0.0923186i | ||||
\(89\) | −7.29150 | − | 12.6293i | −0.772898 | − | 1.33870i | −0.935968 | − | 0.352084i | \(-0.885473\pi\) |
0.163071 | − | 0.986614i | \(-0.447860\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.61438 | + | 11.4564i | 0.693375 | + | 1.20096i | ||||
\(92\) | 3.64575 | 0.380096 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.64575 | − | 11.5108i | 0.685457 | − | 1.18725i | ||||
\(95\) | −0.645751 | + | 1.11847i | −0.0662527 | + | 0.114753i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.70850 | −0.579610 | −0.289805 | − | 0.957086i | \(-0.593590\pi\) | ||||
−0.289805 | + | 0.957086i | \(0.593590\pi\) | |||||||
\(98\) | 7.00000 | 0.707107 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.14575 | − | 7.18065i | −0.414575 | − | 0.718065i | ||||
\(101\) | 1.50000 | − | 2.59808i | 0.149256 | − | 0.258518i | −0.781697 | − | 0.623658i | \(-0.785646\pi\) |
0.930953 | + | 0.365140i | \(0.118979\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.46863 | − | 11.2040i | −0.637373 | − | 1.10396i | −0.986007 | − | 0.166703i | \(-0.946688\pi\) |
0.348634 | − | 0.937259i | \(-0.386646\pi\) | |||||||
\(104\) | 5.00000 | 0.490290 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.64575 | 0.354107 | ||||||||
\(107\) | 2.46863 | + | 4.27579i | 0.238651 | + | 0.413356i | 0.960327 | − | 0.278875i | \(-0.0899614\pi\) |
−0.721676 | + | 0.692231i | \(0.756628\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.29150 | + | 9.16515i | −0.506834 | + | 0.877862i | 0.493135 | + | 0.869953i | \(0.335851\pi\) |
−0.999969 | + | 0.00790932i | \(0.997482\pi\) | |||||||
\(110\) | −1.82288 | − | 3.15731i | −0.173804 | − | 0.301038i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.32288 | − | 2.29129i | 0.125000 | − | 0.216506i | ||||
\(113\) | 7.70850 | 0.725154 | 0.362577 | − | 0.931954i | \(-0.381897\pi\) | ||||
0.362577 | + | 0.931954i | \(0.381897\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.64575 | − | 11.5108i | 0.619720 | − | 1.07339i | ||||
\(116\) | −2.14575 | + | 3.71655i | −0.199228 | + | 0.345073i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.645751 | 0.0594462 | ||||||||
\(119\) | 15.8745 | 1.45521 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | −1.85425 | + | 3.21165i | −0.167876 | + | 0.290769i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.00000 | + | 3.46410i | 0.179605 | + | 0.311086i | ||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.0627461 | 0.00556781 | 0.00278391 | − | 0.999996i | \(-0.499114\pi\) | ||||
0.00278391 | + | 0.999996i | \(0.499114\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 9.11438 | − | 15.7866i | 0.799384 | − | 1.38457i | ||||
\(131\) | 7.82288 | + | 13.5496i | 0.683488 | + | 1.18384i | 0.973909 | + | 0.226937i | \(0.0728711\pi\) |
−0.290422 | + | 0.956899i | \(0.593796\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.468627 | + | 0.811686i | −0.0406351 | + | 0.0703821i | ||||
\(134\) | 3.93725 | 0.340127 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.00000 | − | 5.19615i | 0.257248 | − | 0.445566i | ||||
\(137\) | 9.43725 | − | 16.3458i | 0.806279 | − | 1.39652i | −0.109145 | − | 0.994026i | \(-0.534811\pi\) |
0.915424 | − | 0.402490i | \(-0.131855\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | −4.82288 | − | 8.35347i | −0.407607 | − | 0.705997i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.82288 | + | 8.35347i | 0.404727 | + | 0.701007i | ||||
\(143\) | 2.50000 | − | 4.33013i | 0.209061 | − | 0.362103i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.82288 | + | 13.5496i | 0.649654 | + | 1.12523i | ||||
\(146\) | 5.64575 | 0.467246 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.64575 | −0.135280 | ||||||||
\(149\) | −2.35425 | − | 4.07768i | −0.192868 | − | 0.334056i | 0.753332 | − | 0.657641i | \(-0.228445\pi\) |
−0.946199 | + | 0.323584i | \(0.895112\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.67712 | − | 2.90486i | 0.136482 | − | 0.236395i | −0.789680 | − | 0.613519i | \(-0.789754\pi\) |
0.926163 | + | 0.377124i | \(0.123087\pi\) | |||||||
\(152\) | 0.177124 | + | 0.306788i | 0.0143667 | + | 0.0248838i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.32288 | − | 2.29129i | −0.106600 | − | 0.184637i | ||||
\(155\) | 14.5830 | 1.17134 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.5830 | − | 18.3303i | 0.844616 | − | 1.46292i | −0.0413387 | − | 0.999145i | \(-0.513162\pi\) |
0.885954 | − | 0.463772i | \(-0.153504\pi\) | |||||||
\(158\) | −1.32288 | + | 2.29129i | −0.105242 | + | 0.182285i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.64575 | −0.288222 | ||||||||
\(161\) | 4.82288 | − | 8.35347i | 0.380096 | − | 0.658345i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.32288 | + | 4.02334i | 0.181942 | + | 0.315132i | 0.942542 | − | 0.334089i | \(-0.108428\pi\) |
−0.760600 | + | 0.649221i | \(0.775095\pi\) | |||||||
\(164\) | −2.46863 | + | 4.27579i | −0.192767 | + | 0.333883i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.64575 | + | 11.5108i | 0.515810 | + | 0.893410i | ||||
\(167\) | −15.2288 | −1.17844 | −0.589218 | − | 0.807974i | \(-0.700564\pi\) | ||||
−0.589218 | + | 0.807974i | \(0.700564\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | −10.9373 | − | 18.9439i | −0.838849 | − | 1.45293i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.00000 | − | 3.46410i | 0.152499 | − | 0.264135i | ||||
\(173\) | 5.14575 | + | 8.91270i | 0.391224 | + | 0.677620i | 0.992611 | − | 0.121338i | \(-0.0387184\pi\) |
−0.601387 | + | 0.798958i | \(0.705385\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −21.9373 | −1.65830 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.29150 | + | 12.6293i | −0.546521 | + | 0.946603i | ||||
\(179\) | −2.03137 | + | 3.51844i | −0.151832 | + | 0.262981i | −0.931901 | − | 0.362713i | \(-0.881851\pi\) |
0.780069 | + | 0.625693i | \(0.215184\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 6.61438 | − | 11.4564i | 0.490290 | − | 0.849208i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.82288 | − | 3.15731i | −0.134384 | − | 0.232760i | ||||
\(185\) | −3.00000 | + | 5.19615i | −0.220564 | + | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.00000 | − | 5.19615i | −0.219382 | − | 0.379980i | ||||
\(188\) | −13.2915 | −0.969382 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.29150 | 0.0936954 | ||||||||
\(191\) | −6.64575 | − | 11.5108i | −0.480870 | − | 0.832891i | 0.518889 | − | 0.854841i | \(-0.326346\pi\) |
−0.999759 | + | 0.0219507i | \(0.993012\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.76013 | − | 9.97684i | 0.414623 | − | 0.718148i | −0.580766 | − | 0.814071i | \(-0.697247\pi\) |
0.995389 | + | 0.0959224i | \(0.0305801\pi\) | |||||||
\(194\) | 2.85425 | + | 4.94370i | 0.204923 | + | 0.354937i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.50000 | − | 6.06218i | −0.250000 | − | 0.433013i | ||||
\(197\) | −18.8745 | −1.34475 | −0.672377 | − | 0.740209i | \(-0.734726\pi\) | ||||
−0.672377 | + | 0.740209i | \(0.734726\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.1144 | − | 19.2507i | 0.787877 | − | 1.36464i | −0.139388 | − | 0.990238i | \(-0.544513\pi\) |
0.927265 | − | 0.374406i | \(-0.122153\pi\) | |||||||
\(200\) | −4.14575 | + | 7.18065i | −0.293149 | + | 0.507749i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.00000 | −0.211079 | ||||||||
\(203\) | 5.67712 | + | 9.83307i | 0.398456 | + | 0.690146i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.00000 | + | 15.5885i | 0.628587 | + | 1.08875i | ||||
\(206\) | −6.46863 | + | 11.2040i | −0.450691 | + | 0.780619i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.50000 | − | 4.33013i | −0.173344 | − | 0.300240i | ||||
\(209\) | 0.354249 | 0.0245039 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.9373 | −1.02832 | −0.514161 | − | 0.857693i | \(-0.671897\pi\) | ||||
−0.514161 | + | 0.857693i | \(0.671897\pi\) | |||||||
\(212\) | −1.82288 | − | 3.15731i | −0.125196 | − | 0.216845i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.46863 | − | 4.27579i | 0.168752 | − | 0.292287i | ||||
\(215\) | −7.29150 | − | 12.6293i | −0.497276 | − | 0.861308i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.5830 | 0.718421 | ||||||||
\(218\) | 10.5830 | 0.716772 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.82288 | + | 3.15731i | −0.122898 | + | 0.212866i | ||||
\(221\) | 15.0000 | − | 25.9808i | 1.00901 | − | 1.74766i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.3542 | −0.827302 | −0.413651 | − | 0.910436i | \(-0.635747\pi\) | ||||
−0.413651 | + | 0.910436i | \(0.635747\pi\) | |||||||
\(224\) | −2.64575 | −0.176777 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.85425 | − | 6.67575i | −0.256381 | − | 0.444065i | ||||
\(227\) | −6.64575 | + | 11.5108i | −0.441094 | + | 0.763997i | −0.997771 | − | 0.0667318i | \(-0.978743\pi\) |
0.556677 | + | 0.830729i | \(0.312076\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.00000 | + | 13.8564i | 0.528655 | + | 0.915657i | 0.999442 | + | 0.0334101i | \(0.0106368\pi\) |
−0.470787 | + | 0.882247i | \(0.656030\pi\) | |||||||
\(230\) | −13.2915 | −0.876416 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.29150 | 0.281751 | ||||||||
\(233\) | 8.46863 | + | 14.6681i | 0.554798 | + | 0.960939i | 0.997919 | + | 0.0644769i | \(0.0205379\pi\) |
−0.443121 | + | 0.896462i | \(0.646129\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.2288 | + | 41.9654i | −1.58051 | + | 2.73752i | ||||
\(236\) | −0.322876 | − | 0.559237i | −0.0210174 | − | 0.0364032i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −7.93725 | − | 13.7477i | −0.514496 | − | 0.891133i | ||||
\(239\) | −9.22876 | −0.596959 | −0.298479 | − | 0.954416i | \(-0.596479\pi\) | ||||
−0.298479 | + | 0.954416i | \(0.596479\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.4059 | + | 19.7556i | −0.734717 | + | 1.27257i | 0.220130 | + | 0.975471i | \(0.429352\pi\) |
−0.954847 | + | 0.297097i | \(0.903981\pi\) | |||||||
\(242\) | −0.500000 | + | 0.866025i | −0.0321412 | + | 0.0556702i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.70850 | 0.237412 | ||||||||
\(245\) | −25.5203 | −1.63043 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.885622 | + | 1.53394i | 0.0563508 | + | 0.0976024i | ||||
\(248\) | 2.00000 | − | 3.46410i | 0.127000 | − | 0.219971i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.00000 | + | 10.3923i | 0.379473 | + | 0.657267i | ||||
\(251\) | −7.29150 | −0.460236 | −0.230118 | − | 0.973163i | \(-0.573911\pi\) | ||||
−0.230118 | + | 0.973163i | \(0.573911\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.64575 | −0.229206 | ||||||||
\(254\) | −0.0313730 | − | 0.0543397i | −0.00196852 | − | 0.00340958i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −0.208497 | − | 0.361128i | −0.0130057 | − | 0.0225265i | 0.859449 | − | 0.511221i | \(-0.170807\pi\) |
−0.872455 | + | 0.488694i | \(0.837473\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.17712 | + | 3.77089i | −0.135280 | + | 0.234312i | ||||
\(260\) | −18.2288 | −1.13050 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.82288 | − | 13.5496i | 0.483299 | − | 0.837098i | ||||
\(263\) | 2.03137 | − | 3.51844i | 0.125260 | − | 0.216956i | −0.796575 | − | 0.604540i | \(-0.793357\pi\) |
0.921834 | + | 0.387584i | \(0.126690\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.2915 | −0.816491 | ||||||||
\(266\) | 0.937254 | 0.0574667 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.96863 | − | 3.40976i | −0.120253 | − | 0.208284i | ||||
\(269\) | 13.2915 | − | 23.0216i | 0.810397 | − | 1.40365i | −0.102189 | − | 0.994765i | \(-0.532585\pi\) |
0.912586 | − | 0.408884i | \(-0.134082\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.96863 | + | 15.5341i | 0.544805 | + | 0.943630i | 0.998619 | + | 0.0525339i | \(0.0167298\pi\) |
−0.453814 | + | 0.891097i | \(0.649937\pi\) | |||||||
\(272\) | −6.00000 | −0.363803 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.8745 | −1.14025 | ||||||||
\(275\) | 4.14575 | + | 7.18065i | 0.249998 | + | 0.433010i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.85425 | − | 10.1399i | 0.351748 | − | 0.609245i | −0.634808 | − | 0.772670i | \(-0.718921\pi\) |
0.986556 | + | 0.163425i | \(0.0522542\pi\) | |||||||
\(278\) | 2.00000 | + | 3.46410i | 0.119952 | + | 0.207763i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.82288 | + | 8.35347i | −0.288222 | + | 0.499215i | ||||
\(281\) | 7.06275 | 0.421328 | 0.210664 | − | 0.977559i | \(-0.432437\pi\) | ||||
0.210664 | + | 0.977559i | \(0.432437\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.82288 | − | 6.62141i | 0.227246 | − | 0.393602i | −0.729745 | − | 0.683720i | \(-0.760361\pi\) |
0.956991 | + | 0.290118i | \(0.0936944\pi\) | |||||||
\(284\) | 4.82288 | − | 8.35347i | 0.286185 | − | 0.495687i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.00000 | −0.295656 | ||||||||
\(287\) | 6.53137 | + | 11.3127i | 0.385535 | + | 0.667766i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.50000 | − | 16.4545i | −0.558824 | − | 0.967911i | ||||
\(290\) | 7.82288 | − | 13.5496i | 0.459375 | − | 0.795661i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.82288 | − | 4.88936i | −0.165196 | − | 0.286128i | ||||
\(293\) | −12.0000 | −0.701047 | −0.350524 | − | 0.936554i | \(-0.613996\pi\) | ||||
−0.350524 | + | 0.936554i | \(0.613996\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.35425 | −0.137070 | ||||||||
\(296\) | 0.822876 | + | 1.42526i | 0.0478287 | + | 0.0828417i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.35425 | + | 4.07768i | −0.136378 | + | 0.236214i | ||||
\(299\) | −9.11438 | − | 15.7866i | −0.527098 | − | 0.912961i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.29150 | − | 9.16515i | −0.304997 | − | 0.528271i | ||||
\(302\) | −3.35425 | −0.193015 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.177124 | − | 0.306788i | 0.0101588 | − | 0.0175955i | ||||
\(305\) | 6.76013 | − | 11.7089i | 0.387084 | − | 0.670449i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.22876 | −0.241348 | −0.120674 | − | 0.992692i | \(-0.538506\pi\) | ||||
−0.120674 | + | 0.992692i | \(0.538506\pi\) | |||||||
\(308\) | −1.32288 | + | 2.29129i | −0.0753778 | + | 0.130558i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.29150 | − | 12.6293i | −0.414130 | − | 0.717293i | ||||
\(311\) | 8.46863 | − | 14.6681i | 0.480212 | − | 0.831751i | −0.519531 | − | 0.854452i | \(-0.673893\pi\) |
0.999742 | + | 0.0227007i | \(0.00722647\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.20850 | − | 2.09318i | −0.0683083 | − | 0.118313i | 0.829848 | − | 0.557989i | \(-0.188427\pi\) |
−0.898157 | + | 0.439675i | \(0.855093\pi\) | |||||||
\(314\) | −21.1660 | −1.19447 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.64575 | 0.148835 | ||||||||
\(317\) | 6.00000 | + | 10.3923i | 0.336994 | + | 0.583690i | 0.983866 | − | 0.178908i | \(-0.0572566\pi\) |
−0.646872 | + | 0.762598i | \(0.723923\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.14575 | − | 3.71655i | 0.120139 | − | 0.208087i | ||||
\(320\) | 1.82288 | + | 3.15731i | 0.101902 | + | 0.176499i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −9.64575 | −0.537537 | ||||||||
\(323\) | 2.12549 | 0.118266 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.7288 | + | 35.9033i | −1.14982 | + | 1.99155i | ||||
\(326\) | 2.32288 | − | 4.02334i | 0.128652 | − | 0.222832i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.93725 | 0.272614 | ||||||||
\(329\) | −17.5830 | + | 30.4547i | −0.969382 | + | 1.67902i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.67712 | + | 13.2972i | 0.421973 | + | 0.730879i | 0.996132 | − | 0.0878650i | \(-0.0280044\pi\) |
−0.574159 | + | 0.818743i | \(0.694671\pi\) | |||||||
\(332\) | 6.64575 | − | 11.5108i | 0.364733 | − | 0.631736i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.61438 | + | 13.1885i | 0.416640 | + | 0.721642i | ||||
\(335\) | −14.3542 | −0.784256 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.9373 | 1.35842 | 0.679209 | − | 0.733945i | \(-0.262323\pi\) | ||||
0.679209 | + | 0.733945i | \(0.262323\pi\) | |||||||
\(338\) | −6.00000 | − | 10.3923i | −0.326357 | − | 0.565267i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −10.9373 | + | 18.9439i | −0.593156 | + | 1.02738i | ||||
\(341\) | −2.00000 | − | 3.46410i | −0.108306 | − | 0.187592i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.5203 | −1.00000 | ||||||||
\(344\) | −4.00000 | −0.215666 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.14575 | − | 8.91270i | 0.276637 | − | 0.479150i | ||||
\(347\) | 13.4059 | − | 23.2197i | 0.719665 | − | 1.24650i | −0.241467 | − | 0.970409i | \(-0.577629\pi\) |
0.961132 | − | 0.276088i | \(-0.0890381\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.8745 | 1.59915 | 0.799573 | − | 0.600569i | \(-0.205059\pi\) | ||||
0.799573 | + | 0.600569i | \(0.205059\pi\) | |||||||
\(350\) | 10.9686 | + | 18.9982i | 0.586298 | + | 1.01550i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.500000 | + | 0.866025i | 0.0266501 | + | 0.0461593i | ||||
\(353\) | −17.5830 | + | 30.4547i | −0.935849 | + | 1.62094i | −0.162736 | + | 0.986670i | \(0.552032\pi\) |
−0.773113 | + | 0.634268i | \(0.781301\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −17.5830 | − | 30.4547i | −0.933209 | − | 1.61637i | ||||
\(356\) | 14.5830 | 0.772898 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.06275 | 0.214723 | ||||||||
\(359\) | −5.03137 | − | 8.71459i | −0.265546 | − | 0.459939i | 0.702161 | − | 0.712018i | \(-0.252219\pi\) |
−0.967706 | + | 0.252080i | \(0.918885\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.43725 | − | 16.3458i | 0.496698 | − | 0.860305i | ||||
\(362\) | 5.00000 | + | 8.66025i | 0.262794 | + | 0.455173i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −13.2288 | −0.693375 | ||||||||
\(365\) | −20.5830 | −1.07736 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.88562 | − | 8.46215i | 0.255027 | − | 0.441720i | −0.709876 | − | 0.704327i | \(-0.751249\pi\) |
0.964903 | + | 0.262607i | \(0.0845822\pi\) | |||||||
\(368\) | −1.82288 | + | 3.15731i | −0.0950240 | + | 0.164586i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.00000 | 0.311925 | ||||||||
\(371\) | −9.64575 | −0.500782 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.43725 | + | 9.41760i | 0.281530 | + | 0.487625i | 0.971762 | − | 0.235964i | \(-0.0758247\pi\) |
−0.690232 | + | 0.723589i | \(0.742491\pi\) | |||||||
\(374\) | −3.00000 | + | 5.19615i | −0.155126 | + | 0.268687i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.64575 | + | 11.5108i | 0.342728 | + | 0.593623i | ||||
\(377\) | 21.4575 | 1.10512 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.9373 | 1.12684 | 0.563421 | − | 0.826170i | \(-0.309485\pi\) | ||||
0.563421 | + | 0.826170i | \(0.309485\pi\) | |||||||
\(380\) | −0.645751 | − | 1.11847i | −0.0331263 | − | 0.0573765i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.64575 | + | 11.5108i | −0.340026 | + | 0.588943i | ||||
\(383\) | −17.0516 | − | 29.5343i | −0.871298 | − | 1.50913i | −0.860655 | − | 0.509189i | \(-0.829946\pi\) |
−0.0106427 | − | 0.999943i | \(-0.503388\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.82288 | + | 8.35347i | 0.245797 | + | 0.425732i | ||||
\(386\) | −11.5203 | −0.586366 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.85425 | − | 4.94370i | 0.144903 | − | 0.250979i | ||||
\(389\) | −10.4059 | + | 18.0235i | −0.527599 | + | 0.913828i | 0.471883 | + | 0.881661i | \(0.343574\pi\) |
−0.999482 | + | 0.0321675i | \(0.989759\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.8745 | −1.10624 | ||||||||
\(392\) | −3.50000 | + | 6.06218i | −0.176777 | + | 0.306186i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.43725 | + | 16.3458i | 0.475442 | + | 0.823490i | ||||
\(395\) | 4.82288 | − | 8.35347i | 0.242665 | − | 0.420308i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.5830 | − | 26.9906i | −0.782089 | − | 1.35462i | −0.930723 | − | 0.365725i | \(-0.880821\pi\) |
0.148634 | − | 0.988892i | \(-0.452512\pi\) | |||||||
\(398\) | −22.2288 | −1.11423 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.29150 | 0.414575 | ||||||||
\(401\) | 0.208497 | + | 0.361128i | 0.0104119 | + | 0.0180339i | 0.871184 | − | 0.490956i | \(-0.163352\pi\) |
−0.860773 | + | 0.508990i | \(0.830019\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.0000 | − | 17.3205i | 0.498135 | − | 0.862796i | ||||
\(404\) | 1.50000 | + | 2.59808i | 0.0746278 | + | 0.129259i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.67712 | − | 9.83307i | 0.281751 | − | 0.488007i | ||||
\(407\) | 1.64575 | 0.0815769 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.46863 | + | 16.4001i | −0.468193 | + | 0.810935i | −0.999339 | − | 0.0363456i | \(-0.988428\pi\) |
0.531146 | + | 0.847280i | \(0.321762\pi\) | |||||||
\(410\) | 9.00000 | − | 15.5885i | 0.444478 | − | 0.769859i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.9373 | 0.637373 | ||||||||
\(413\) | −1.70850 | −0.0840697 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.2288 | − | 41.9654i | −1.18934 | − | 2.06000i | ||||
\(416\) | −2.50000 | + | 4.33013i | −0.122573 | + | 0.212302i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.177124 | − | 0.306788i | −0.00866343 | − | 0.0150055i | ||||
\(419\) | −21.8745 | −1.06864 | −0.534320 | − | 0.845282i | \(-0.679432\pi\) | ||||
−0.534320 | + | 0.845282i | \(0.679432\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.1660 | −1.61641 | −0.808206 | − | 0.588900i | \(-0.799561\pi\) | ||||
−0.808206 | + | 0.588900i | \(0.799561\pi\) | |||||||
\(422\) | 7.46863 | + | 12.9360i | 0.363567 | + | 0.629717i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.82288 | + | 3.15731i | −0.0885267 | + | 0.153333i | ||||
\(425\) | 24.8745 | + | 43.0839i | 1.20659 | + | 2.08988i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.90588 | − | 8.49723i | 0.237412 | − | 0.411210i | ||||
\(428\) | −4.93725 | −0.238651 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.29150 | + | 12.6293i | −0.351627 | + | 0.609037i | ||||
\(431\) | 1.38562 | − | 2.39997i | 0.0667430 | − | 0.115602i | −0.830723 | − | 0.556686i | \(-0.812073\pi\) |
0.897466 | + | 0.441084i | \(0.145406\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.0000 | −0.768911 | −0.384455 | − | 0.923144i | \(-0.625611\pi\) | ||||
−0.384455 | + | 0.923144i | \(0.625611\pi\) | |||||||
\(434\) | −5.29150 | − | 9.16515i | −0.254000 | − | 0.439941i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.29150 | − | 9.16515i | −0.253417 | − | 0.438931i | ||||
\(437\) | 0.645751 | − | 1.11847i | 0.0308905 | − | 0.0535039i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.96863 | + | 10.3380i | 0.284867 | + | 0.493404i | 0.972577 | − | 0.232581i | \(-0.0747172\pi\) |
−0.687710 | + | 0.725986i | \(0.741384\pi\) | |||||||
\(440\) | 3.64575 | 0.173804 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −30.0000 | −1.42695 | ||||||||
\(443\) | −9.22876 | − | 15.9847i | −0.438471 | − | 0.759455i | 0.559100 | − | 0.829100i | \(-0.311147\pi\) |
−0.997572 | + | 0.0696451i | \(0.977813\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.5830 | − | 46.0431i | 1.26016 | − | 2.18265i | ||||
\(446\) | 6.17712 | + | 10.6991i | 0.292495 | + | 0.506617i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.32288 | + | 2.29129i | 0.0625000 | + | 0.108253i | ||||
\(449\) | −9.87451 | −0.466007 | −0.233003 | − | 0.972476i | \(-0.574855\pi\) | ||||
−0.233003 | + | 0.972476i | \(0.574855\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.46863 | − | 4.27579i | 0.116243 | − | 0.201339i | ||||
\(452\) | −3.85425 | + | 6.67575i | −0.181289 | + | 0.314001i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.2915 | 0.623801 | ||||||||
\(455\) | −24.1144 | + | 41.7673i | −1.13050 | + | 1.95808i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.5830 | + | 33.9188i | 0.916054 | + | 1.58665i | 0.805350 | + | 0.592799i | \(0.201977\pi\) |
0.110704 | + | 0.993853i | \(0.464689\pi\) | |||||||
\(458\) | 8.00000 | − | 13.8564i | 0.373815 | − | 0.647467i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.64575 | + | 11.5108i | 0.309860 | + | 0.536693i | ||||
\(461\) | 32.1660 | 1.49812 | 0.749060 | − | 0.662502i | \(-0.230505\pi\) | ||||
0.749060 | + | 0.662502i | \(0.230505\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.4575 | −1.04369 | −0.521845 | − | 0.853041i | \(-0.674756\pi\) | ||||
−0.521845 | + | 0.853041i | \(0.674756\pi\) | |||||||
\(464\) | −2.14575 | − | 3.71655i | −0.0996140 | − | 0.172537i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.46863 | − | 14.6681i | 0.392302 | − | 0.679486i | ||||
\(467\) | 5.35425 | + | 9.27383i | 0.247765 | + | 0.429142i | 0.962905 | − | 0.269839i | \(-0.0869706\pi\) |
−0.715140 | + | 0.698981i | \(0.753637\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.4170 | −0.481012 | ||||||||
\(470\) | 48.4575 | 2.23518 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.322876 | + | 0.559237i | −0.0148616 | + | 0.0257410i | ||||
\(473\) | −2.00000 | + | 3.46410i | −0.0919601 | + | 0.159280i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.93725 | −0.134770 | ||||||||
\(476\) | −7.93725 | + | 13.7477i | −0.363803 | + | 0.630126i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.61438 | + | 7.99234i | 0.211057 | + | 0.365561i | ||||
\(479\) | −12.9686 | + | 22.4623i | −0.592552 | + | 1.02633i | 0.401336 | + | 0.915931i | \(0.368546\pi\) |
−0.993887 | + | 0.110399i | \(0.964787\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.11438 | + | 7.12631i | 0.187600 | + | 0.324932i | ||||
\(482\) | 22.8118 | 1.03905 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −10.4059 | − | 18.0235i | −0.472507 | − | 0.818406i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.2915 | − | 26.4857i | 0.692924 | − | 1.20018i | −0.277951 | − | 0.960595i | \(-0.589655\pi\) |
0.970875 | − | 0.239585i | \(-0.0770113\pi\) | |||||||
\(488\) | −1.85425 | − | 3.21165i | −0.0839379 | − | 0.145385i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 12.7601 | + | 22.1012i | 0.576444 | + | 0.998430i | ||||
\(491\) | −10.7085 | −0.483268 | −0.241634 | − | 0.970367i | \(-0.577683\pi\) | ||||
−0.241634 | + | 0.970367i | \(0.577683\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.8745 | − | 22.2993i | 0.579839 | − | 1.00431i | ||||
\(494\) | 0.885622 | − | 1.53394i | 0.0398460 | − | 0.0690153i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | −12.7601 | − | 22.1012i | −0.572370 | − | 0.991374i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.93725 | − | 15.4798i | −0.400086 | − | 0.692970i | 0.593650 | − | 0.804724i | \(-0.297687\pi\) |
−0.993736 | + | 0.111754i | \(0.964353\pi\) | |||||||
\(500\) | 6.00000 | − | 10.3923i | 0.268328 | − | 0.464758i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.64575 | + | 6.31463i | 0.162718 | + | 0.281836i | ||||
\(503\) | 19.9373 | 0.888958 | 0.444479 | − | 0.895789i | \(-0.353389\pi\) | ||||
0.444479 | + | 0.895789i | \(0.353389\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.9373 | 0.486701 | ||||||||
\(506\) | 1.82288 | + | 3.15731i | 0.0810367 | + | 0.140360i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.0313730 | + | 0.0543397i | −0.00139195 | + | 0.00241093i | ||||
\(509\) | 10.2915 | + | 17.8254i | 0.456163 | + | 0.790097i | 0.998754 | − | 0.0498996i | \(-0.0158901\pi\) |
−0.542591 | + | 0.839997i | \(0.682557\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.9373 | −0.660785 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.208497 | + | 0.361128i | −0.00919643 | + | 0.0159287i | ||||
\(515\) | 23.5830 | − | 40.8470i | 1.03919 | − | 1.79993i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.2915 | 0.584560 | ||||||||
\(518\) | 4.35425 | 0.191315 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.11438 | + | 15.7866i | 0.399692 | + | 0.692287i | ||||
\(521\) | −1.06275 | + | 1.84073i | −0.0465598 | + | 0.0806439i | −0.888366 | − | 0.459136i | \(-0.848159\pi\) |
0.841806 | + | 0.539780i | \(0.181492\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.76013 | − | 13.4409i | −0.339327 | − | 0.587731i | 0.644979 | − | 0.764200i | \(-0.276866\pi\) |
−0.984306 | + | 0.176469i | \(0.943533\pi\) | |||||||
\(524\) | −15.6458 | −0.683488 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.06275 | −0.177144 | ||||||||
\(527\) | −12.0000 | − | 20.7846i | −0.522728 | − | 0.905392i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.85425 | − | 8.40781i | 0.211054 | − | 0.365557i | ||||
\(530\) | 6.64575 | + | 11.5108i | 0.288673 | + | 0.499996i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.468627 | − | 0.811686i | −0.0203176 | − | 0.0351910i | ||||
\(533\) | 24.6863 | 1.06928 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.00000 | + | 15.5885i | −0.389104 | + | 0.673948i | ||||
\(536\) | −1.96863 | + | 3.40976i | −0.0850317 | + | 0.147279i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −26.5830 | −1.14607 | ||||||||
\(539\) | 3.50000 | + | 6.06218i | 0.150756 | + | 0.261116i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.14575 | + | 7.18065i | 0.178240 | + | 0.308720i | 0.941278 | − | 0.337633i | \(-0.109626\pi\) |
−0.763038 | + | 0.646354i | \(0.776293\pi\) | |||||||
\(542\) | 8.96863 | − | 15.5341i | 0.385236 | − | 0.667247i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.00000 | + | 5.19615i | 0.128624 | + | 0.222783i | ||||
\(545\) | −38.5830 | −1.65271 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.5203 | 1.17668 | 0.588341 | − | 0.808613i | \(-0.299781\pi\) | ||||
0.588341 | + | 0.808613i | \(0.299781\pi\) | |||||||
\(548\) | 9.43725 | + | 16.3458i | 0.403140 | + | 0.698258i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.14575 | − | 7.18065i | 0.176775 | − | 0.306184i | ||||
\(551\) | 0.760130 | + | 1.31658i | 0.0323826 | + | 0.0560883i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.50000 | − | 6.06218i | 0.148835 | − | 0.257790i | ||||
\(554\) | −11.7085 | −0.497446 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.00000 | − | 3.46410i | 0.0848189 | − | 0.146911i | ||||
\(557\) | 15.8745 | − | 27.4955i | 0.672624 | − | 1.16502i | −0.304533 | − | 0.952502i | \(-0.598500\pi\) |
0.977157 | − | 0.212518i | \(-0.0681664\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.0000 | −0.845910 | ||||||||
\(560\) | 9.64575 | 0.407607 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.53137 | − | 6.11652i | −0.148962 | − | 0.258010i | ||||
\(563\) | 6.53137 | − | 11.3127i | 0.275265 | − | 0.476772i | −0.694937 | − | 0.719070i | \(-0.744568\pi\) |
0.970202 | + | 0.242298i | \(0.0779012\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.0516 | + | 24.3381i | 0.591157 | + | 1.02391i | ||||
\(566\) | −7.64575 | −0.321375 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.64575 | −0.404727 | ||||||||
\(569\) | −20.5830 | − | 35.6508i | −0.862884 | − | 1.49456i | −0.869133 | − | 0.494579i | \(-0.835322\pi\) |
0.00624806 | − | 0.999980i | \(-0.498011\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.4686 | − | 38.9168i | 0.940283 | − | 1.62862i | 0.175351 | − | 0.984506i | \(-0.443894\pi\) |
0.764932 | − | 0.644112i | \(-0.222773\pi\) | |||||||
\(572\) | 2.50000 | + | 4.33013i | 0.104530 | + | 0.181052i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.53137 | − | 11.3127i | 0.272614 | − | 0.472182i | ||||
\(575\) | 30.2288 | 1.26063 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.7288 | − | 22.0469i | 0.529905 | − | 0.917823i | −0.469486 | − | 0.882940i | \(-0.655561\pi\) |
0.999391 | − | 0.0348828i | \(-0.0111058\pi\) | |||||||
\(578\) | −9.50000 | + | 16.4545i | −0.395148 | + | 0.684416i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −15.6458 | −0.649654 | ||||||||
\(581\) | −17.5830 | − | 30.4547i | −0.729466 | − | 1.26347i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.82288 | + | 3.15731i | 0.0754958 | + | 0.130763i | ||||
\(584\) | −2.82288 | + | 4.88936i | −0.116811 | + | 0.202323i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.00000 | + | 10.3923i | 0.247858 | + | 0.429302i | ||||
\(587\) | 7.93725 | 0.327606 | 0.163803 | − | 0.986493i | \(-0.447624\pi\) | ||||
0.163803 | + | 0.986493i | \(0.447624\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.41699 | 0.0583863 | ||||||||
\(590\) | 1.17712 | + | 2.03884i | 0.0484614 | + | 0.0839377i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.822876 | − | 1.42526i | 0.0338200 | − | 0.0585779i | ||||
\(593\) | 11.4686 | + | 19.8642i | 0.470960 | + | 0.815727i | 0.999448 | − | 0.0332139i | \(-0.0105743\pi\) |
−0.528488 | + | 0.848941i | \(0.677241\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 28.9373 | + | 50.1208i | 1.18631 | + | 2.05475i | ||||
\(596\) | 4.70850 | 0.192868 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.11438 | + | 15.7866i | −0.372715 | + | 0.645561i | ||||
\(599\) | −9.87451 | + | 17.1031i | −0.403461 | + | 0.698816i | −0.994141 | − | 0.108090i | \(-0.965526\pi\) |
0.590680 | + | 0.806906i | \(0.298860\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.5830 | −1.00276 | −0.501381 | − | 0.865227i | \(-0.667174\pi\) | ||||
−0.501381 | + | 0.865227i | \(0.667174\pi\) | |||||||
\(602\) | −5.29150 | + | 9.16515i | −0.215666 | + | 0.373544i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.67712 | + | 2.90486i | 0.0682412 | + | 0.118197i | ||||
\(605\) | 1.82288 | − | 3.15731i | 0.0741104 | − | 0.128363i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.6458 | − | 18.4390i | −0.432098 | − | 0.748415i | 0.564956 | − | 0.825121i | \(-0.308893\pi\) |
−0.997054 | + | 0.0767058i | \(0.975560\pi\) | |||||||
\(608\) | −0.354249 | −0.0143667 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −13.5203 | −0.547419 | ||||||||
\(611\) | 33.2288 | + | 57.5539i | 1.34429 | + | 2.32838i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.00000 | + | 1.73205i | −0.0403896 | + | 0.0699569i | −0.885514 | − | 0.464614i | \(-0.846193\pi\) |
0.845124 | + | 0.534570i | \(0.179527\pi\) | |||||||
\(614\) | 2.11438 | + | 3.66221i | 0.0853294 | + | 0.147795i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.64575 | 0.106600 | ||||||||
\(617\) | 16.2915 | 0.655871 | 0.327936 | − | 0.944700i | \(-0.393647\pi\) | ||||
0.327936 | + | 0.944700i | \(0.393647\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.2915 | + | 29.9498i | −0.695004 | + | 1.20378i | 0.275175 | + | 0.961394i | \(0.411264\pi\) |
−0.970179 | + | 0.242388i | \(0.922069\pi\) | |||||||
\(620\) | −7.29150 | + | 12.6293i | −0.292834 | + | 0.507203i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −16.9373 | −0.679122 | ||||||||
\(623\) | 19.2915 | − | 33.4139i | 0.772898 | − | 1.33870i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.14575 | − | 1.98450i | −0.0458301 | − | 0.0793800i | ||||
\(626\) | −1.20850 | + | 2.09318i | −0.0483013 | + | 0.0836603i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.5830 | + | 18.3303i | 0.422308 | + | 0.731459i | ||||
\(629\) | 9.87451 | 0.393722 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.8118 | 1.38583 | 0.692917 | − | 0.721017i | \(-0.256325\pi\) | ||||
0.692917 | + | 0.721017i | \(0.256325\pi\) | |||||||
\(632\) | −1.32288 | − | 2.29129i | −0.0526212 | − | 0.0911425i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.00000 | − | 10.3923i | 0.238290 | − | 0.412731i | ||||
\(635\) | 0.114378 | + | 0.198109i | 0.00453896 | + | 0.00786172i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.5000 | + | 30.3109i | −0.693375 | + | 1.20096i | ||||
\(638\) | −4.29150 | −0.169902 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.82288 | − | 3.15731i | 0.0720555 | − | 0.124804i | ||||
\(641\) | −9.43725 | + | 16.3458i | −0.372749 | + | 0.645620i | −0.989987 | − | 0.141156i | \(-0.954918\pi\) |
0.617238 | + | 0.786776i | \(0.288251\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.52026 | 0.257134 | 0.128567 | − | 0.991701i | \(-0.458962\pi\) | ||||
0.128567 | + | 0.991701i | \(0.458962\pi\) | |||||||
\(644\) | 4.82288 | + | 8.35347i | 0.190048 | + | 0.329173i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.06275 | − | 1.84073i | −0.0418132 | − | 0.0724226i | ||||
\(647\) | 19.4059 | − | 33.6120i | 0.762924 | − | 1.32142i | −0.178413 | − | 0.983956i | \(-0.557096\pi\) |
0.941337 | − | 0.337467i | \(-0.109570\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.322876 | + | 0.559237i | 0.0126740 | + | 0.0219520i | ||||
\(650\) | 41.4575 | 1.62610 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.64575 | −0.181942 | ||||||||
\(653\) | 1.17712 | + | 2.03884i | 0.0460644 | + | 0.0797859i | 0.888138 | − | 0.459576i | \(-0.151999\pi\) |
−0.842074 | + | 0.539362i | \(0.818665\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −28.5203 | + | 49.3985i | −1.11438 | + | 1.93016i | ||||
\(656\) | −2.46863 | − | 4.27579i | −0.0963837 | − | 0.166941i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 35.1660 | 1.37091 | ||||||||
\(659\) | −14.5830 | −0.568073 | −0.284037 | − | 0.958813i | \(-0.591674\pi\) | ||||
−0.284037 | + | 0.958813i | \(0.591674\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.2915 | + | 24.7536i | −0.555875 | + | 0.962804i | 0.441960 | + | 0.897035i | \(0.354283\pi\) |
−0.997835 | + | 0.0657690i | \(0.979050\pi\) | |||||||
\(662\) | 7.67712 | − | 13.2972i | 0.298380 | − | 0.516809i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −13.2915 | −0.515810 | ||||||||
\(665\) | −3.41699 | −0.132505 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.82288 | − | 13.5496i | −0.302903 | − | 0.524643i | ||||
\(668\) | 7.61438 | − | 13.1885i | 0.294609 | − | 0.510278i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.17712 | + | 12.4311i | 0.277277 | + | 0.480257i | ||||
\(671\) | −3.70850 | −0.143165 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.9373 | −0.575789 | −0.287894 | − | 0.957662i | \(-0.592955\pi\) | ||||
−0.287894 | + | 0.957662i | \(0.592955\pi\) | |||||||
\(674\) | −12.4686 | − | 21.5963i | −0.480274 | − | 0.831858i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.00000 | + | 10.3923i | −0.230769 | + | 0.399704i | ||||
\(677\) | −1.06275 | − | 1.84073i | −0.0408446 | − | 0.0707450i | 0.844880 | − | 0.534955i | \(-0.179672\pi\) |
−0.885725 | + | 0.464210i | \(0.846338\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.55163 | − | 13.0798i | −0.289805 | − | 0.501957i | ||||
\(680\) | 21.8745 | 0.838849 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.00000 | + | 3.46410i | −0.0765840 | + | 0.132647i | ||||
\(683\) | −6.96863 | + | 12.0700i | −0.266647 | + | 0.461846i | −0.967994 | − | 0.250974i | \(-0.919249\pi\) |
0.701347 | + | 0.712820i | \(0.252582\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 68.8118 | 2.62916 | ||||||||
\(686\) | 9.26013 | + | 16.0390i | 0.353553 | + | 0.612372i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.00000 | + | 3.46410i | 0.0762493 | + | 0.132068i | ||||
\(689\) | −9.11438 | + | 15.7866i | −0.347230 | + | 0.601420i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.38562 | + | 16.2564i | 0.357046 | + | 0.618422i | 0.987466 | − | 0.157833i | \(-0.0504506\pi\) |
−0.630420 | + | 0.776254i | \(0.717117\pi\) | |||||||
\(692\) | −10.2915 | −0.391224 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −26.8118 | −1.01776 | ||||||||
\(695\) | −7.29150 | − | 12.6293i | −0.276582 | − | 0.479055i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.8118 | − | 25.6547i | 0.561035 | − | 0.971742i | ||||
\(698\) | −14.9373 | − | 25.8721i | −0.565383 | − | 0.979273i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 10.9686 | − | 18.9982i | 0.414575 | − | 0.718065i | ||||
\(701\) | 6.87451 | 0.259647 | 0.129823 | − | 0.991537i | \(-0.458559\pi\) | ||||
0.129823 | + | 0.991537i | \(0.458559\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.291503 | + | 0.504897i | −0.0109942 | + | 0.0190426i | ||||
\(704\) | 0.500000 | − | 0.866025i | 0.0188445 | − | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 35.1660 | 1.32349 | ||||||||
\(707\) | 7.93725 | 0.298511 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.40588 | + | 5.89916i | 0.127911 | + | 0.221548i | 0.922867 | − | 0.385119i | \(-0.125840\pi\) |
−0.794956 | + | 0.606667i | \(0.792506\pi\) | |||||||
\(710\) | −17.5830 | + | 30.4547i | −0.659878 | + | 1.14294i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.29150 | − | 12.6293i | −0.273261 | − | 0.473301i | ||||
\(713\) | −14.5830 | −0.546138 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.2288 | 0.681717 | ||||||||
\(716\) | −2.03137 | − | 3.51844i | −0.0759160 | − | 0.131490i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.03137 | + | 8.71459i | −0.187769 | + | 0.325226i | ||||
\(719\) | −1.93725 | − | 3.35542i | −0.0722474 | − | 0.125136i | 0.827639 | − | 0.561261i | \(-0.189684\pi\) |
−0.899886 | + | 0.436125i | \(0.856350\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.1144 | − | 29.6430i | 0.637373 | − | 1.10396i | ||||
\(722\) | −18.8745 | −0.702436 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.00000 | − | 8.66025i | 0.185824 | − | 0.321856i | ||||
\(725\) | −17.7915 | + | 30.8158i | −0.660760 | + | 1.14447i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.2915 | −0.641306 | −0.320653 | − | 0.947197i | \(-0.603902\pi\) | ||||
−0.320653 | + | 0.947197i | \(0.603902\pi\) | |||||||
\(728\) | 6.61438 | + | 11.4564i | 0.245145 | + | 0.424604i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10.2915 | + | 17.8254i | 0.380906 | + | 0.659748i | ||||
\(731\) | −12.0000 | + | 20.7846i | −0.443836 | + | 0.768747i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.7288 | − | 35.9033i | −0.765634 | − | 1.32612i | −0.939911 | − | 0.341420i | \(-0.889092\pi\) |
0.174277 | − | 0.984697i | \(-0.444241\pi\) | |||||||
\(734\) | −9.77124 | −0.360663 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.64575 | 0.134384 | ||||||||
\(737\) | 1.96863 | + | 3.40976i | 0.0725153 | + | 0.125600i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.93725 | − | 6.81952i | 0.144834 | − | 0.250860i | −0.784477 | − | 0.620158i | \(-0.787068\pi\) |
0.929311 | + | 0.369298i | \(0.120402\pi\) | |||||||
\(740\) | −3.00000 | − | 5.19615i | −0.110282 | − | 0.191014i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.82288 | + | 8.35347i | 0.177053 | + | 0.306665i | ||||
\(743\) | 34.7085 | 1.27333 | 0.636666 | − | 0.771140i | \(-0.280313\pi\) | ||||
0.636666 | + | 0.771140i | \(0.280313\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.58301 | − | 14.8662i | 0.314457 | − | 0.544655i | ||||
\(746\) | 5.43725 | − | 9.41760i | 0.199072 | − | 0.344803i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.00000 | 0.219382 | ||||||||
\(749\) | −6.53137 | + | 11.3127i | −0.238651 | + | 0.413356i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.00000 | + | 13.8564i | 0.291924 | + | 0.505627i | 0.974265 | − | 0.225407i | \(-0.0723712\pi\) |
−0.682341 | + | 0.731034i | \(0.739038\pi\) | |||||||
\(752\) | 6.64575 | − | 11.5108i | 0.242346 | − | 0.419755i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −10.7288 | − | 18.5828i | −0.390718 | − | 0.676744i | ||||
\(755\) | 12.2288 | 0.445050 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.1660 | 0.696600 | 0.348300 | − | 0.937383i | \(-0.386759\pi\) | ||||
0.348300 | + | 0.937383i | \(0.386759\pi\) | |||||||
\(758\) | −10.9686 | − | 18.9982i | −0.398398 | − | 0.690046i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.645751 | + | 1.11847i | −0.0234239 | + | 0.0405713i | ||||
\(761\) | −3.00000 | − | 5.19615i | −0.108750 | − | 0.188360i | 0.806514 | − | 0.591215i | \(-0.201351\pi\) |
−0.915264 | + | 0.402854i | \(0.868018\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −28.0000 | −1.01367 | ||||||||
\(764\) | 13.2915 | 0.480870 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17.0516 | + | 29.5343i | −0.616101 | + | 1.06712i | ||||
\(767\) | −1.61438 | + | 2.79619i | −0.0582918 | + | 0.100964i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.1660 | −0.546900 | −0.273450 | − | 0.961886i | \(-0.588165\pi\) | ||||
−0.273450 | + | 0.961886i | \(0.588165\pi\) | |||||||
\(770\) | 4.82288 | − | 8.35347i | 0.173804 | − | 0.301038i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.76013 | + | 9.97684i | 0.207312 | + | 0.359074i | ||||
\(773\) | 1.29150 | − | 2.23695i | 0.0464521 | − | 0.0804574i | −0.841864 | − | 0.539689i | \(-0.818542\pi\) |
0.888317 | + | 0.459232i | \(0.151875\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.5830 | + | 28.7226i | 0.595679 | + | 1.03175i | ||||
\(776\) | −5.70850 | −0.204923 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.8118 | 0.746138 | ||||||||
\(779\) | 0.874508 | + | 1.51469i | 0.0313325 | + | 0.0542695i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.82288 | + | 8.35347i | −0.172576 | + | 0.298911i | ||||
\(782\) | 10.9373 | + | 18.9439i | 0.391115 | + | 0.677432i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 7.00000 | 0.250000 | ||||||||
\(785\) | 77.1660 | 2.75417 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.405881 | − | 0.703006i | 0.0144681 | − | 0.0250595i | −0.858701 | − | 0.512477i | \(-0.828728\pi\) |
0.873169 | + | 0.487418i | \(0.162061\pi\) | |||||||
\(788\) | 9.43725 | − | 16.3458i | 0.336188 | − | 0.582295i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −9.64575 | −0.343180 | ||||||||
\(791\) | 10.1974 | + | 17.6624i | 0.362577 | + | 0.628002i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.27124 | − | 16.0583i | −0.329232 | − | 0.570246i | ||||
\(794\) | −15.5830 | + | 26.9906i | −0.553020 | + | 0.957859i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.1144 | + | 19.2507i | 0.393939 | + | 0.682322i | ||||
\(797\) | 35.1660 | 1.24564 | 0.622822 | − | 0.782364i | \(-0.285986\pi\) | ||||
0.622822 | + | 0.782364i | \(0.285986\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 79.7490 | 2.82132 | ||||||||
\(800\) | −4.14575 | − | 7.18065i | −0.146574 | − | 0.253874i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.208497 | − | 0.361128i | 0.00736230 | − | 0.0127519i | ||||
\(803\) | 2.82288 | + | 4.88936i | 0.0996171 | + | 0.172542i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 35.1660 | 1.23944 | ||||||||
\(806\) | −20.0000 | −0.704470 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.50000 | − | 2.59808i | 0.0527698 | − | 0.0914000i | ||||
\(809\) | 25.2915 | − | 43.8062i | 0.889202 | − | 1.54014i | 0.0483813 | − | 0.998829i | \(-0.484594\pi\) |
0.840821 | − | 0.541314i | \(-0.182073\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.7490 | 0.974400 | 0.487200 | − | 0.873290i | \(-0.338018\pi\) | ||||
0.487200 | + | 0.873290i | \(0.338018\pi\) | |||||||
\(812\) | −11.3542 | −0.398456 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.822876 | − | 1.42526i | −0.0288418 | − | 0.0499554i | ||||
\(815\) | −8.46863 | + | 14.6681i | −0.296643 | + | 0.513801i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.708497 | − | 1.22715i | −0.0247872 | − | 0.0429327i | ||||
\(818\) | 18.9373 | 0.662126 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −18.0000 | −0.628587 | ||||||||
\(821\) | −3.85425 | − | 6.67575i | −0.134514 | − | 0.232985i | 0.790898 | − | 0.611949i | \(-0.209614\pi\) |
−0.925412 | + | 0.378963i | \(0.876281\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.9373 | − | 37.9964i | 0.764685 | − | 1.32447i | −0.175729 | − | 0.984439i | \(-0.556228\pi\) |
0.940413 | − | 0.340034i | \(-0.110439\pi\) | |||||||
\(824\) | −6.46863 | − | 11.2040i | −0.225345 | − | 0.390310i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.854249 | + | 1.47960i | 0.0297231 | + | 0.0514819i | ||||
\(827\) | 35.3948 | 1.23080 | 0.615398 | − | 0.788216i | \(-0.288995\pi\) | ||||
0.615398 | + | 0.788216i | \(0.288995\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.6974 | + | 37.5810i | −0.753581 | + | 1.30524i | 0.192495 | + | 0.981298i | \(0.438342\pi\) |
−0.946077 | + | 0.323943i | \(0.894991\pi\) | |||||||
\(830\) | −24.2288 | + | 41.9654i | −0.840992 | + | 1.45664i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.00000 | 0.173344 | ||||||||
\(833\) | 21.0000 | + | 36.3731i | 0.727607 | + | 1.26025i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −27.7601 | − | 48.0820i | −0.960679 | − | 1.66394i | ||||
\(836\) | −0.177124 | + | 0.306788i | −0.00612597 | + | 0.0106105i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 10.9373 | + | 18.9439i | 0.377821 | + | 0.654405i | ||||
\(839\) | −27.8745 | −0.962335 | −0.481167 | − | 0.876629i | \(-0.659787\pi\) | ||||
−0.481167 | + | 0.876629i | \(0.659787\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.5830 | −0.364931 | ||||||||
\(842\) | 16.5830 | + | 28.7226i | 0.571488 | + | 0.989846i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.46863 | − | 12.9360i | 0.257081 | − | 0.445277i | ||||
\(845\) | 21.8745 | + | 37.8878i | 0.752506 | + | 1.30338i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.32288 | − | 2.29129i | 0.0454545 | − | 0.0787296i | ||||
\(848\) | 3.64575 | 0.125196 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 24.8745 | − | 43.0839i | 0.853189 | − | 1.47777i | ||||
\(851\) | 3.00000 | − | 5.19615i | 0.102839 | − | 0.178122i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.16601 | −0.108402 | −0.0542011 | − | 0.998530i | \(-0.517261\pi\) | ||||
−0.0542011 | + | 0.998530i | \(0.517261\pi\) | |||||||
\(854\) | −9.81176 | −0.335752 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.46863 | + | 4.27579i | 0.0843759 | + | 0.146143i | ||||
\(857\) | 18.0000 | − | 31.1769i | 0.614868 | − | 1.06498i | −0.375539 | − | 0.926806i | \(-0.622542\pi\) |
0.990408 | − | 0.138177i | \(-0.0441242\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.9059 | − | 32.7459i | −0.645060 | − | 1.11728i | −0.984288 | − | 0.176573i | \(-0.943499\pi\) |
0.339227 | − | 0.940704i | \(-0.389834\pi\) | |||||||
\(860\) | 14.5830 | 0.497276 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.77124 | −0.0943889 | ||||||||
\(863\) | −24.7601 | − | 42.8858i | −0.842845 | − | 1.45985i | −0.887480 | − | 0.460846i | \(-0.847546\pi\) |
0.0446353 | − | 0.999003i | \(-0.485787\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.7601 | + | 32.4935i | −0.637864 | + | 1.10481i | ||||
\(866\) | 8.00000 | + | 13.8564i | 0.271851 | + | 0.470860i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.29150 | + | 9.16515i | −0.179605 | + | 0.311086i | ||||
\(869\) | −2.64575 | −0.0897510 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.84313 | + | 17.0488i | −0.333522 | + | 0.577677i | ||||
\(872\) | −5.29150 | + | 9.16515i | −0.179193 | + | 0.310371i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.29150 | −0.0436857 | ||||||||
\(875\) | −15.8745 | − | 27.4955i | −0.536656 | − | 0.929516i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.43725 | − | 7.68555i | −0.149835 | − | 0.259523i | 0.781331 | − | 0.624117i | \(-0.214541\pi\) |
−0.931167 | + | 0.364594i | \(0.881208\pi\) | |||||||
\(878\) | 5.96863 | − | 10.3380i | 0.201431 | − | 0.348889i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.82288 | − | 3.15731i | −0.0614491 | − | 0.106433i | ||||
\(881\) | −6.87451 | −0.231608 | −0.115804 | − | 0.993272i | \(-0.536944\pi\) | ||||
−0.115804 | + | 0.993272i | \(0.536944\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.06275 | 0.204028 | 0.102014 | − | 0.994783i | \(-0.467471\pi\) | ||||
0.102014 | + | 0.994783i | \(0.467471\pi\) | |||||||
\(884\) | 15.0000 | + | 25.9808i | 0.504505 | + | 0.873828i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.22876 | + | 15.9847i | −0.310046 | + | 0.537016i | ||||
\(887\) | −6.55163 | − | 11.3478i | −0.219982 | − | 0.381020i | 0.734820 | − | 0.678262i | \(-0.237267\pi\) |
−0.954802 | + | 0.297242i | \(0.903933\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.0830052 | + | 0.143769i | 0.00278391 | + | 0.00482187i | ||||
\(890\) | −53.1660 | −1.78213 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.17712 | − | 10.6991i | 0.206825 | − | 0.358232i | ||||
\(893\) | −2.35425 | + | 4.07768i | −0.0787819 | + | 0.136454i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.8118 | −0.495103 | ||||||||
\(896\) | 1.32288 | − | 2.29129i | 0.0441942 | − | 0.0765466i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.93725 | + | 8.55157i | 0.164758 | + | 0.285370i | ||||
\(899\) | 8.58301 | − | 14.8662i | 0.286259 | − | 0.495816i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.9373 | + | 18.9439i | 0.364373 | + | 0.631112i | ||||
\(902\) | −4.93725 | −0.164393 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.70850 | 0.256381 | ||||||||
\(905\) | −18.2288 | − | 31.5731i | −0.605944 | − | 1.04953i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.22876 | − | 9.05647i | 0.173618 | − | 0.300715i | −0.766064 | − | 0.642764i | \(-0.777788\pi\) |
0.939682 | + | 0.342049i | \(0.111121\pi\) | |||||||
\(908\) | −6.64575 | − | 11.5108i | −0.220547 | − | 0.381999i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 48.2288 | 1.59877 | ||||||||
\(911\) | 1.29150 | 0.0427894 | 0.0213947 | − | 0.999771i | \(-0.493189\pi\) | ||||
0.0213947 | + | 0.999771i | \(0.493189\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.64575 | + | 11.5108i | −0.219942 | + | 0.380951i | ||||
\(914\) | 19.5830 | − | 33.9188i | 0.647748 | − | 1.12193i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.0000 | −0.528655 | ||||||||
\(917\) | −20.6974 | + | 35.8489i | −0.683488 | + | 1.18384i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.6458 | + | 30.5633i | 0.582080 | + | 1.00819i | 0.995233 | + | 0.0975298i | \(0.0310941\pi\) |
−0.413153 | + | 0.910662i | \(0.635573\pi\) | |||||||
\(920\) | 6.64575 | − | 11.5108i | 0.219104 | − | 0.379499i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −16.0830 | − | 27.8566i | −0.529666 | − | 0.917408i | ||||
\(923\) | −48.2288 | −1.58747 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.6458 | −0.448670 | ||||||||
\(926\) | 11.2288 | + | 19.4488i | 0.369000 | + | 0.639126i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.14575 | + | 3.71655i | −0.0704377 | + | 0.122002i | ||||
\(929\) | 17.7915 | + | 30.8158i | 0.583720 | + | 1.01103i | 0.995034 | + | 0.0995392i | \(0.0317369\pi\) |
−0.411313 | + | 0.911494i | \(0.634930\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.47974 | −0.0812702 | ||||||||
\(932\) | −16.9373 | −0.554798 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.35425 | − | 9.27383i | 0.175196 | − | 0.303449i | ||||
\(935\) | 10.9373 | − | 18.9439i | 0.357686 | − | 0.619531i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −46.6863 | −1.52517 | −0.762587 | − | 0.646886i | \(-0.776071\pi\) | ||||
−0.762587 | + | 0.646886i | \(0.776071\pi\) | |||||||
\(938\) | 5.20850 | + | 9.02138i | 0.170063 | + | 0.294559i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −24.2288 | − | 41.9654i | −0.790255 | − | 1.36876i | ||||
\(941\) | −22.3118 | + | 38.6451i | −0.727343 | + | 1.25979i | 0.230660 | + | 0.973034i | \(0.425912\pi\) |
−0.958002 | + | 0.286760i | \(0.907422\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.00000 | − | 15.5885i | −0.293080 | − | 0.507630i | ||||
\(944\) | 0.645751 | 0.0210174 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.00000 | 0.130051 | ||||||||
\(947\) | −16.9373 | − | 29.3362i | −0.550387 | − | 0.953298i | −0.998246 | − | 0.0591941i | \(-0.981147\pi\) |
0.447860 | − | 0.894104i | \(-0.352186\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.1144 | + | 24.4468i | −0.458172 | + | 0.793577i | ||||
\(950\) | 1.46863 | + | 2.54374i | 0.0476486 | + | 0.0825297i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 15.8745 | 0.514496 | ||||||||
\(953\) | 25.5203 | 0.826682 | 0.413341 | − | 0.910576i | \(-0.364362\pi\) | ||||
0.413341 | + | 0.910576i | \(0.364362\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.2288 | − | 41.9654i | 0.784024 | − | 1.35797i | ||||
\(956\) | 4.61438 | − | 7.99234i | 0.149240 | − | 0.258491i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 25.9373 | 0.837995 | ||||||||
\(959\) | 49.9373 | 1.61256 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | 4.11438 | − | 7.12631i | 0.132653 | − | 0.229762i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −11.4059 | − | 19.7556i | −0.367359 | − | 0.636284i | ||||
\(965\) | 42.0000 | 1.35203 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.3320 | −0.846781 | −0.423390 | − | 0.905947i | \(-0.639160\pi\) | ||||
−0.423390 | + | 0.905947i | \(0.639160\pi\) | |||||||
\(968\) | −0.500000 | − | 0.866025i | −0.0160706 | − | 0.0278351i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −10.4059 | + | 18.0235i | −0.334113 | + | 0.578700i | ||||
\(971\) | −12.9686 | − | 22.4623i | −0.416183 | − | 0.720850i | 0.579369 | − | 0.815066i | \(-0.303299\pi\) |
−0.995552 | + | 0.0942153i | \(0.969966\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.29150 | − | 9.16515i | −0.169638 | − | 0.293821i | ||||
\(974\) | −30.5830 | −0.979943 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.85425 | + | 3.21165i | −0.0593531 | + | 0.102803i | ||||
\(977\) | 18.2288 | − | 31.5731i | 0.583190 | − | 1.01011i | −0.411909 | − | 0.911225i | \(-0.635138\pi\) |
0.995098 | − | 0.0988890i | \(-0.0315289\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.5830 | −0.466075 | ||||||||
\(980\) | 12.7601 | − | 22.1012i | 0.407607 | − | 0.705997i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.35425 | + | 9.27383i | 0.170861 | + | 0.295940i | ||||
\(983\) | −18.6458 | + | 32.2954i | −0.594707 | + | 1.03006i | 0.398881 | + | 0.917003i | \(0.369399\pi\) |
−0.993588 | + | 0.113060i | \(0.963935\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −34.4059 | − | 59.5927i | −1.09626 | − | 1.89878i | ||||
\(986\) | −25.7490 | −0.820016 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.77124 | −0.0563508 | ||||||||
\(989\) | 7.29150 | + | 12.6293i | 0.231856 | + | 0.401587i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.3431 | + | 49.0917i | −0.900349 | + | 1.55945i | −0.0733083 | + | 0.997309i | \(0.523356\pi\) |
−0.827041 | + | 0.562141i | \(0.809978\pi\) | |||||||
\(992\) | 2.00000 | + | 3.46410i | 0.0635001 | + | 0.109985i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −12.7601 | + | 22.1012i | −0.404727 | + | 0.701007i | ||||
\(995\) | 81.0405 | 2.56916 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.2915 | − | 36.8780i | 0.674309 | − | 1.16794i | −0.302362 | − | 0.953193i | \(-0.597775\pi\) |
0.976670 | − | 0.214744i | \(-0.0688916\pi\) | |||||||
\(998\) | −8.93725 | + | 15.4798i | −0.282904 | + | 0.490004i | ||||
\(999\) | 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 | 1386.2.k.s.991.2 | 4 | ||
3.2 | odd | 2 | 154.2.e.f.67.2 | yes | 4 | ||
7.2 | even | 3 | inner | 1386.2.k.s.793.2 | 4 | ||
7.3 | odd | 6 | 9702.2.a.dr.1.2 | 2 | |||
7.4 | even | 3 | 9702.2.a.cz.1.1 | 2 | |||
12.11 | even | 2 | 1232.2.q.g.529.1 | 4 | |||
21.2 | odd | 6 | 154.2.e.f.23.2 | ✓ | 4 | ||
21.5 | even | 6 | 1078.2.e.v.177.1 | 4 | |||
21.11 | odd | 6 | 1078.2.a.s.1.1 | 2 | |||
21.17 | even | 6 | 1078.2.a.n.1.2 | 2 | |||
21.20 | even | 2 | 1078.2.e.v.67.1 | 4 | |||
84.11 | even | 6 | 8624.2.a.ca.1.2 | 2 | |||
84.23 | even | 6 | 1232.2.q.g.177.1 | 4 | |||
84.59 | odd | 6 | 8624.2.a.bk.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.e.f.23.2 | ✓ | 4 | 21.2 | odd | 6 | ||
154.2.e.f.67.2 | yes | 4 | 3.2 | odd | 2 | ||
1078.2.a.n.1.2 | 2 | 21.17 | even | 6 | |||
1078.2.a.s.1.1 | 2 | 21.11 | odd | 6 | |||
1078.2.e.v.67.1 | 4 | 21.20 | even | 2 | |||
1078.2.e.v.177.1 | 4 | 21.5 | even | 6 | |||
1232.2.q.g.177.1 | 4 | 84.23 | even | 6 | |||
1232.2.q.g.529.1 | 4 | 12.11 | even | 2 | |||
1386.2.k.s.793.2 | 4 | 7.2 | even | 3 | inner | ||
1386.2.k.s.991.2 | 4 | 1.1 | even | 1 | trivial | ||
8624.2.a.bk.1.1 | 2 | 84.59 | odd | 6 | |||
8624.2.a.ca.1.2 | 2 | 84.11 | even | 6 | |||
9702.2.a.cz.1.1 | 2 | 7.4 | even | 3 | |||
9702.2.a.dr.1.2 | 2 | 7.3 | odd | 6 |