Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4031,2,Mod(1,4031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4031, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4031 = 29 \cdot 139 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4031.a (trivial) |
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: | yes |
Analytic conductor: | \(32.1876970548\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4031.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.414214 | −0.292893 | −0.146447 | − | 0.989219i | \(-0.546784\pi\) | ||||
−0.146447 | + | 0.989219i | \(0.546784\pi\) | |||||||
\(3\) | −0.414214 | −0.239146 | −0.119573 | − | 0.992825i | \(-0.538153\pi\) | ||||
−0.119573 | + | 0.992825i | \(0.538153\pi\) | |||||||
\(4\) | −1.82843 | −0.914214 | ||||||||
\(5\) | 2.00000 | 0.894427 | 0.447214 | − | 0.894427i | \(-0.352416\pi\) | ||||
0.447214 | + | 0.894427i | \(0.352416\pi\) | |||||||
\(6\) | 0.171573 | 0.0700443 | ||||||||
\(7\) | 1.82843 | 0.691080 | 0.345540 | − | 0.938404i | \(-0.387696\pi\) | ||||
0.345540 | + | 0.938404i | \(0.387696\pi\) | |||||||
\(8\) | 1.58579 | 0.560660 | ||||||||
\(9\) | −2.82843 | −0.942809 | ||||||||
\(10\) | −0.828427 | −0.261972 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0.757359 | 0.218631 | ||||||||
\(13\) | 5.00000 | 1.38675 | 0.693375 | − | 0.720577i | \(-0.256123\pi\) | ||||
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | −0.757359 | −0.202413 | ||||||||
\(15\) | −0.828427 | −0.213899 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | 1.58579 | 0.384610 | 0.192305 | − | 0.981335i | \(-0.438404\pi\) | ||||
0.192305 | + | 0.981335i | \(0.438404\pi\) | |||||||
\(18\) | 1.17157 | 0.276142 | ||||||||
\(19\) | 3.24264 | 0.743913 | 0.371956 | − | 0.928250i | \(-0.378687\pi\) | ||||
0.371956 | + | 0.928250i | \(0.378687\pi\) | |||||||
\(20\) | −3.65685 | −0.817697 | ||||||||
\(21\) | −0.757359 | −0.165269 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.82843 | 1.84085 | 0.920427 | − | 0.390914i | \(-0.127841\pi\) | ||||
0.920427 | + | 0.390914i | \(0.127841\pi\) | |||||||
\(24\) | −0.656854 | −0.134080 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −2.07107 | −0.406170 | ||||||||
\(27\) | 2.41421 | 0.464616 | ||||||||
\(28\) | −3.34315 | −0.631795 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0.343146 | 0.0626496 | ||||||||
\(31\) | −0.828427 | −0.148790 | −0.0743950 | − | 0.997229i | \(-0.523703\pi\) | ||||
−0.0743950 | + | 0.997229i | \(0.523703\pi\) | |||||||
\(32\) | −4.41421 | −0.780330 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.656854 | −0.112650 | ||||||||
\(35\) | 3.65685 | 0.618121 | ||||||||
\(36\) | 5.17157 | 0.861929 | ||||||||
\(37\) | −8.48528 | −1.39497 | −0.697486 | − | 0.716599i | \(-0.745698\pi\) | ||||
−0.697486 | + | 0.716599i | \(0.745698\pi\) | |||||||
\(38\) | −1.34315 | −0.217887 | ||||||||
\(39\) | −2.07107 | −0.331636 | ||||||||
\(40\) | 3.17157 | 0.501470 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0.313708 | 0.0484063 | ||||||||
\(43\) | 0.414214 | 0.0631670 | 0.0315835 | − | 0.999501i | \(-0.489945\pi\) | ||||
0.0315835 | + | 0.999501i | \(0.489945\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.65685 | −0.843274 | ||||||||
\(46\) | −3.65685 | −0.539174 | ||||||||
\(47\) | −0.828427 | −0.120839 | −0.0604193 | − | 0.998173i | \(-0.519244\pi\) | ||||
−0.0604193 | + | 0.998173i | \(0.519244\pi\) | |||||||
\(48\) | −1.24264 | −0.179360 | ||||||||
\(49\) | −3.65685 | −0.522408 | ||||||||
\(50\) | 0.414214 | 0.0585786 | ||||||||
\(51\) | −0.656854 | −0.0919780 | ||||||||
\(52\) | −9.14214 | −1.26779 | ||||||||
\(53\) | 1.17157 | 0.160928 | 0.0804640 | − | 0.996758i | \(-0.474360\pi\) | ||||
0.0804640 | + | 0.996758i | \(0.474360\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.89949 | 0.387461 | ||||||||
\(57\) | −1.34315 | −0.177904 | ||||||||
\(58\) | −0.414214 | −0.0543889 | ||||||||
\(59\) | −0.343146 | −0.0446738 | −0.0223369 | − | 0.999751i | \(-0.507111\pi\) | ||||
−0.0223369 | + | 0.999751i | \(0.507111\pi\) | |||||||
\(60\) | 1.51472 | 0.195549 | ||||||||
\(61\) | −8.89949 | −1.13946 | −0.569732 | − | 0.821831i | \(-0.692953\pi\) | ||||
−0.569732 | + | 0.821831i | \(0.692953\pi\) | |||||||
\(62\) | 0.343146 | 0.0435796 | ||||||||
\(63\) | −5.17157 | −0.651557 | ||||||||
\(64\) | −4.17157 | −0.521447 | ||||||||
\(65\) | 10.0000 | 1.24035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.3137 | 1.26002 | 0.630010 | − | 0.776587i | \(-0.283051\pi\) | ||||
0.630010 | + | 0.776587i | \(0.283051\pi\) | |||||||
\(68\) | −2.89949 | −0.351615 | ||||||||
\(69\) | −3.65685 | −0.440234 | ||||||||
\(70\) | −1.51472 | −0.181044 | ||||||||
\(71\) | 8.31371 | 0.986656 | 0.493328 | − | 0.869843i | \(-0.335780\pi\) | ||||
0.493328 | + | 0.869843i | \(0.335780\pi\) | |||||||
\(72\) | −4.48528 | −0.528595 | ||||||||
\(73\) | 10.0711 | 1.17873 | 0.589365 | − | 0.807867i | \(-0.299378\pi\) | ||||
0.589365 | + | 0.807867i | \(0.299378\pi\) | |||||||
\(74\) | 3.51472 | 0.408578 | ||||||||
\(75\) | 0.414214 | 0.0478293 | ||||||||
\(76\) | −5.92893 | −0.680095 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.857864 | 0.0971340 | ||||||||
\(79\) | 14.4853 | 1.62972 | 0.814861 | − | 0.579657i | \(-0.196813\pi\) | ||||
0.814861 | + | 0.579657i | \(0.196813\pi\) | |||||||
\(80\) | 6.00000 | 0.670820 | ||||||||
\(81\) | 7.48528 | 0.831698 | ||||||||
\(82\) | −0.828427 | −0.0914845 | ||||||||
\(83\) | −7.00000 | −0.768350 | −0.384175 | − | 0.923260i | \(-0.625514\pi\) | ||||
−0.384175 | + | 0.923260i | \(0.625514\pi\) | |||||||
\(84\) | 1.38478 | 0.151091 | ||||||||
\(85\) | 3.17157 | 0.344005 | ||||||||
\(86\) | −0.171573 | −0.0185012 | ||||||||
\(87\) | −0.414214 | −0.0444084 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.1716 | −1.18418 | −0.592092 | − | 0.805870i | \(-0.701698\pi\) | ||||
−0.592092 | + | 0.805870i | \(0.701698\pi\) | |||||||
\(90\) | 2.34315 | 0.246989 | ||||||||
\(91\) | 9.14214 | 0.958356 | ||||||||
\(92\) | −16.1421 | −1.68293 | ||||||||
\(93\) | 0.343146 | 0.0355826 | ||||||||
\(94\) | 0.343146 | 0.0353928 | ||||||||
\(95\) | 6.48528 | 0.665376 | ||||||||
\(96\) | 1.82843 | 0.186613 | ||||||||
\(97\) | 0.757359 | 0.0768982 | 0.0384491 | − | 0.999261i | \(-0.487758\pi\) | ||||
0.0384491 | + | 0.999261i | \(0.487758\pi\) | |||||||
\(98\) | 1.51472 | 0.153010 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.82843 | 0.182843 | ||||||||
\(101\) | 10.1421 | 1.00918 | 0.504590 | − | 0.863359i | \(-0.331644\pi\) | ||||
0.504590 | + | 0.863359i | \(0.331644\pi\) | |||||||
\(102\) | 0.272078 | 0.0269397 | ||||||||
\(103\) | −6.82843 | −0.672825 | −0.336412 | − | 0.941715i | \(-0.609214\pi\) | ||||
−0.336412 | + | 0.941715i | \(0.609214\pi\) | |||||||
\(104\) | 7.92893 | 0.777496 | ||||||||
\(105\) | −1.51472 | −0.147821 | ||||||||
\(106\) | −0.485281 | −0.0471347 | ||||||||
\(107\) | −19.4853 | −1.88371 | −0.941857 | − | 0.336015i | \(-0.890921\pi\) | ||||
−0.941857 | + | 0.336015i | \(0.890921\pi\) | |||||||
\(108\) | −4.41421 | −0.424758 | ||||||||
\(109\) | −1.17157 | −0.112216 | −0.0561082 | − | 0.998425i | \(-0.517869\pi\) | ||||
−0.0561082 | + | 0.998425i | \(0.517869\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.51472 | 0.333602 | ||||||||
\(112\) | 5.48528 | 0.518310 | ||||||||
\(113\) | −2.48528 | −0.233796 | −0.116898 | − | 0.993144i | \(-0.537295\pi\) | ||||
−0.116898 | + | 0.993144i | \(0.537295\pi\) | |||||||
\(114\) | 0.556349 | 0.0521069 | ||||||||
\(115\) | 17.6569 | 1.64651 | ||||||||
\(116\) | −1.82843 | −0.169765 | ||||||||
\(117\) | −14.1421 | −1.30744 | ||||||||
\(118\) | 0.142136 | 0.0130846 | ||||||||
\(119\) | 2.89949 | 0.265796 | ||||||||
\(120\) | −1.31371 | −0.119925 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 3.68629 | 0.333741 | ||||||||
\(123\) | −0.828427 | −0.0746968 | ||||||||
\(124\) | 1.51472 | 0.136026 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 2.14214 | 0.190837 | ||||||||
\(127\) | 6.48528 | 0.575476 | 0.287738 | − | 0.957709i | \(-0.407097\pi\) | ||||
0.287738 | + | 0.957709i | \(0.407097\pi\) | |||||||
\(128\) | 10.5563 | 0.933058 | ||||||||
\(129\) | −0.171573 | −0.0151061 | ||||||||
\(130\) | −4.14214 | −0.363289 | ||||||||
\(131\) | 4.34315 | 0.379462 | 0.189731 | − | 0.981836i | \(-0.439238\pi\) | ||||
0.189731 | + | 0.981836i | \(0.439238\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.92893 | 0.514104 | ||||||||
\(134\) | −4.27208 | −0.369051 | ||||||||
\(135\) | 4.82843 | 0.415565 | ||||||||
\(136\) | 2.51472 | 0.215635 | ||||||||
\(137\) | 22.4853 | 1.92105 | 0.960524 | − | 0.278198i | \(-0.0897373\pi\) | ||||
0.960524 | + | 0.278198i | \(0.0897373\pi\) | |||||||
\(138\) | 1.51472 | 0.128941 | ||||||||
\(139\) | −1.00000 | −0.0848189 | ||||||||
\(140\) | −6.68629 | −0.565095 | ||||||||
\(141\) | 0.343146 | 0.0288981 | ||||||||
\(142\) | −3.44365 | −0.288985 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −8.48528 | −0.707107 | ||||||||
\(145\) | 2.00000 | 0.166091 | ||||||||
\(146\) | −4.17157 | −0.345242 | ||||||||
\(147\) | 1.51472 | 0.124932 | ||||||||
\(148\) | 15.5147 | 1.27530 | ||||||||
\(149\) | −0.828427 | −0.0678674 | −0.0339337 | − | 0.999424i | \(-0.510804\pi\) | ||||
−0.0339337 | + | 0.999424i | \(0.510804\pi\) | |||||||
\(150\) | −0.171573 | −0.0140089 | ||||||||
\(151\) | −12.0000 | −0.976546 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(152\) | 5.14214 | 0.417082 | ||||||||
\(153\) | −4.48528 | −0.362614 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.65685 | −0.133082 | ||||||||
\(156\) | 3.78680 | 0.303186 | ||||||||
\(157\) | 18.2132 | 1.45357 | 0.726786 | − | 0.686864i | \(-0.241013\pi\) | ||||
0.726786 | + | 0.686864i | \(0.241013\pi\) | |||||||
\(158\) | −6.00000 | −0.477334 | ||||||||
\(159\) | −0.485281 | −0.0384853 | ||||||||
\(160\) | −8.82843 | −0.697948 | ||||||||
\(161\) | 16.1421 | 1.27218 | ||||||||
\(162\) | −3.10051 | −0.243599 | ||||||||
\(163\) | 24.6274 | 1.92897 | 0.964484 | − | 0.264141i | \(-0.0850884\pi\) | ||||
0.964484 | + | 0.264141i | \(0.0850884\pi\) | |||||||
\(164\) | −3.65685 | −0.285552 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.89949 | 0.225044 | ||||||||
\(167\) | 2.34315 | 0.181318 | 0.0906590 | − | 0.995882i | \(-0.471103\pi\) | ||||
0.0906590 | + | 0.995882i | \(0.471103\pi\) | |||||||
\(168\) | −1.20101 | −0.0926599 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | −1.31371 | −0.100757 | ||||||||
\(171\) | −9.17157 | −0.701368 | ||||||||
\(172\) | −0.757359 | −0.0577481 | ||||||||
\(173\) | 4.17157 | 0.317159 | 0.158579 | − | 0.987346i | \(-0.449309\pi\) | ||||
0.158579 | + | 0.987346i | \(0.449309\pi\) | |||||||
\(174\) | 0.171573 | 0.0130069 | ||||||||
\(175\) | −1.82843 | −0.138216 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.142136 | 0.0106836 | ||||||||
\(178\) | 4.62742 | 0.346840 | ||||||||
\(179\) | −17.7990 | −1.33036 | −0.665179 | − | 0.746684i | \(-0.731645\pi\) | ||||
−0.665179 | + | 0.746684i | \(0.731645\pi\) | |||||||
\(180\) | 10.3431 | 0.770933 | ||||||||
\(181\) | −17.8284 | −1.32518 | −0.662588 | − | 0.748984i | \(-0.730542\pi\) | ||||
−0.662588 | + | 0.748984i | \(0.730542\pi\) | |||||||
\(182\) | −3.78680 | −0.280696 | ||||||||
\(183\) | 3.68629 | 0.272499 | ||||||||
\(184\) | 14.0000 | 1.03209 | ||||||||
\(185\) | −16.9706 | −1.24770 | ||||||||
\(186\) | −0.142136 | −0.0104219 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1.51472 | 0.110472 | ||||||||
\(189\) | 4.41421 | 0.321087 | ||||||||
\(190\) | −2.68629 | −0.194884 | ||||||||
\(191\) | −11.6569 | −0.843460 | −0.421730 | − | 0.906721i | \(-0.638577\pi\) | ||||
−0.421730 | + | 0.906721i | \(0.638577\pi\) | |||||||
\(192\) | 1.72792 | 0.124702 | ||||||||
\(193\) | 19.1716 | 1.38000 | 0.690000 | − | 0.723809i | \(-0.257611\pi\) | ||||
0.690000 | + | 0.723809i | \(0.257611\pi\) | |||||||
\(194\) | −0.313708 | −0.0225230 | ||||||||
\(195\) | −4.14214 | −0.296624 | ||||||||
\(196\) | 6.68629 | 0.477592 | ||||||||
\(197\) | 24.1421 | 1.72006 | 0.860028 | − | 0.510247i | \(-0.170446\pi\) | ||||
0.860028 | + | 0.510247i | \(0.170446\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.7990 | −1.11996 | −0.559980 | − | 0.828506i | \(-0.689191\pi\) | ||||
−0.559980 | + | 0.828506i | \(0.689191\pi\) | |||||||
\(200\) | −1.58579 | −0.112132 | ||||||||
\(201\) | −4.27208 | −0.301329 | ||||||||
\(202\) | −4.20101 | −0.295582 | ||||||||
\(203\) | 1.82843 | 0.128330 | ||||||||
\(204\) | 1.20101 | 0.0840875 | ||||||||
\(205\) | 4.00000 | 0.279372 | ||||||||
\(206\) | 2.82843 | 0.197066 | ||||||||
\(207\) | −24.9706 | −1.73557 | ||||||||
\(208\) | 15.0000 | 1.04006 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.627417 | 0.0432959 | ||||||||
\(211\) | −9.92893 | −0.683536 | −0.341768 | − | 0.939784i | \(-0.611026\pi\) | ||||
−0.341768 | + | 0.939784i | \(0.611026\pi\) | |||||||
\(212\) | −2.14214 | −0.147122 | ||||||||
\(213\) | −3.44365 | −0.235955 | ||||||||
\(214\) | 8.07107 | 0.551727 | ||||||||
\(215\) | 0.828427 | 0.0564983 | ||||||||
\(216\) | 3.82843 | 0.260491 | ||||||||
\(217\) | −1.51472 | −0.102826 | ||||||||
\(218\) | 0.485281 | 0.0328674 | ||||||||
\(219\) | −4.17157 | −0.281889 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.92893 | 0.533358 | ||||||||
\(222\) | −1.45584 | −0.0977099 | ||||||||
\(223\) | 16.8284 | 1.12691 | 0.563457 | − | 0.826145i | \(-0.309471\pi\) | ||||
0.563457 | + | 0.826145i | \(0.309471\pi\) | |||||||
\(224\) | −8.07107 | −0.539271 | ||||||||
\(225\) | 2.82843 | 0.188562 | ||||||||
\(226\) | 1.02944 | 0.0684771 | ||||||||
\(227\) | −24.6274 | −1.63458 | −0.817290 | − | 0.576227i | \(-0.804524\pi\) | ||||
−0.817290 | + | 0.576227i | \(0.804524\pi\) | |||||||
\(228\) | 2.45584 | 0.162642 | ||||||||
\(229\) | −20.4853 | −1.35371 | −0.676853 | − | 0.736118i | \(-0.736657\pi\) | ||||
−0.676853 | + | 0.736118i | \(0.736657\pi\) | |||||||
\(230\) | −7.31371 | −0.482252 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.58579 | 0.104112 | ||||||||
\(233\) | 23.7990 | 1.55912 | 0.779562 | − | 0.626325i | \(-0.215442\pi\) | ||||
0.779562 | + | 0.626325i | \(0.215442\pi\) | |||||||
\(234\) | 5.85786 | 0.382941 | ||||||||
\(235\) | −1.65685 | −0.108081 | ||||||||
\(236\) | 0.627417 | 0.0408414 | ||||||||
\(237\) | −6.00000 | −0.389742 | ||||||||
\(238\) | −1.20101 | −0.0778499 | ||||||||
\(239\) | 15.8284 | 1.02386 | 0.511928 | − | 0.859028i | \(-0.328931\pi\) | ||||
0.511928 | + | 0.859028i | \(0.328931\pi\) | |||||||
\(240\) | −2.48528 | −0.160424 | ||||||||
\(241\) | −20.9706 | −1.35083 | −0.675416 | − | 0.737437i | \(-0.736036\pi\) | ||||
−0.675416 | + | 0.737437i | \(0.736036\pi\) | |||||||
\(242\) | 4.55635 | 0.292893 | ||||||||
\(243\) | −10.3431 | −0.663513 | ||||||||
\(244\) | 16.2721 | 1.04171 | ||||||||
\(245\) | −7.31371 | −0.467256 | ||||||||
\(246\) | 0.343146 | 0.0218782 | ||||||||
\(247\) | 16.2132 | 1.03162 | ||||||||
\(248\) | −1.31371 | −0.0834206 | ||||||||
\(249\) | 2.89949 | 0.183748 | ||||||||
\(250\) | 4.97056 | 0.314366 | ||||||||
\(251\) | 28.9706 | 1.82861 | 0.914303 | − | 0.405031i | \(-0.132739\pi\) | ||||
0.914303 | + | 0.405031i | \(0.132739\pi\) | |||||||
\(252\) | 9.45584 | 0.595662 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −2.68629 | −0.168553 | ||||||||
\(255\) | −1.31371 | −0.0822676 | ||||||||
\(256\) | 3.97056 | 0.248160 | ||||||||
\(257\) | 29.3137 | 1.82854 | 0.914269 | − | 0.405107i | \(-0.132766\pi\) | ||||
0.914269 | + | 0.405107i | \(0.132766\pi\) | |||||||
\(258\) | 0.0710678 | 0.00442449 | ||||||||
\(259\) | −15.5147 | −0.964038 | ||||||||
\(260\) | −18.2843 | −1.13394 | ||||||||
\(261\) | −2.82843 | −0.175075 | ||||||||
\(262\) | −1.79899 | −0.111142 | ||||||||
\(263\) | −1.51472 | −0.0934016 | −0.0467008 | − | 0.998909i | \(-0.514871\pi\) | ||||
−0.0467008 | + | 0.998909i | \(0.514871\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.34315 | 0.143938 | ||||||||
\(266\) | −2.45584 | −0.150577 | ||||||||
\(267\) | 4.62742 | 0.283193 | ||||||||
\(268\) | −18.8579 | −1.15193 | ||||||||
\(269\) | −7.72792 | −0.471180 | −0.235590 | − | 0.971853i | \(-0.575702\pi\) | ||||
−0.235590 | + | 0.971853i | \(0.575702\pi\) | |||||||
\(270\) | −2.00000 | −0.121716 | ||||||||
\(271\) | 18.4142 | 1.11858 | 0.559292 | − | 0.828971i | \(-0.311073\pi\) | ||||
0.559292 | + | 0.828971i | \(0.311073\pi\) | |||||||
\(272\) | 4.75736 | 0.288457 | ||||||||
\(273\) | −3.78680 | −0.229187 | ||||||||
\(274\) | −9.31371 | −0.562662 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.68629 | 0.402467 | ||||||||
\(277\) | 21.1716 | 1.27208 | 0.636038 | − | 0.771658i | \(-0.280572\pi\) | ||||
0.636038 | + | 0.771658i | \(0.280572\pi\) | |||||||
\(278\) | 0.414214 | 0.0248429 | ||||||||
\(279\) | 2.34315 | 0.140280 | ||||||||
\(280\) | 5.79899 | 0.346556 | ||||||||
\(281\) | 13.6569 | 0.814700 | 0.407350 | − | 0.913272i | \(-0.366453\pi\) | ||||
0.407350 | + | 0.913272i | \(0.366453\pi\) | |||||||
\(282\) | −0.142136 | −0.00846405 | ||||||||
\(283\) | 27.9706 | 1.66268 | 0.831339 | − | 0.555766i | \(-0.187575\pi\) | ||||
0.831339 | + | 0.555766i | \(0.187575\pi\) | |||||||
\(284\) | −15.2010 | −0.902014 | ||||||||
\(285\) | −2.68629 | −0.159122 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.65685 | 0.215857 | ||||||||
\(288\) | 12.4853 | 0.735702 | ||||||||
\(289\) | −14.4853 | −0.852075 | ||||||||
\(290\) | −0.828427 | −0.0486469 | ||||||||
\(291\) | −0.313708 | −0.0183899 | ||||||||
\(292\) | −18.4142 | −1.07761 | ||||||||
\(293\) | 20.4853 | 1.19676 | 0.598381 | − | 0.801211i | \(-0.295811\pi\) | ||||
0.598381 | + | 0.801211i | \(0.295811\pi\) | |||||||
\(294\) | −0.627417 | −0.0365917 | ||||||||
\(295\) | −0.686292 | −0.0399574 | ||||||||
\(296\) | −13.4558 | −0.782105 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.343146 | 0.0198779 | ||||||||
\(299\) | 44.1421 | 2.55281 | ||||||||
\(300\) | −0.757359 | −0.0437262 | ||||||||
\(301\) | 0.757359 | 0.0436535 | ||||||||
\(302\) | 4.97056 | 0.286024 | ||||||||
\(303\) | −4.20101 | −0.241342 | ||||||||
\(304\) | 9.72792 | 0.557935 | ||||||||
\(305\) | −17.7990 | −1.01917 | ||||||||
\(306\) | 1.85786 | 0.106207 | ||||||||
\(307\) | 27.3137 | 1.55888 | 0.779438 | − | 0.626480i | \(-0.215505\pi\) | ||||
0.779438 | + | 0.626480i | \(0.215505\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.82843 | 0.160904 | ||||||||
\(310\) | 0.686292 | 0.0389787 | ||||||||
\(311\) | 3.65685 | 0.207361 | 0.103681 | − | 0.994611i | \(-0.466938\pi\) | ||||
0.103681 | + | 0.994611i | \(0.466938\pi\) | |||||||
\(312\) | −3.28427 | −0.185935 | ||||||||
\(313\) | 29.1421 | 1.64721 | 0.823605 | − | 0.567163i | \(-0.191959\pi\) | ||||
0.823605 | + | 0.567163i | \(0.191959\pi\) | |||||||
\(314\) | −7.54416 | −0.425741 | ||||||||
\(315\) | −10.3431 | −0.582770 | ||||||||
\(316\) | −26.4853 | −1.48991 | ||||||||
\(317\) | 10.8284 | 0.608185 | 0.304093 | − | 0.952643i | \(-0.401647\pi\) | ||||
0.304093 | + | 0.952643i | \(0.401647\pi\) | |||||||
\(318\) | 0.201010 | 0.0112721 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −8.34315 | −0.466396 | ||||||||
\(321\) | 8.07107 | 0.450483 | ||||||||
\(322\) | −6.68629 | −0.372612 | ||||||||
\(323\) | 5.14214 | 0.286116 | ||||||||
\(324\) | −13.6863 | −0.760350 | ||||||||
\(325\) | −5.00000 | −0.277350 | ||||||||
\(326\) | −10.2010 | −0.564982 | ||||||||
\(327\) | 0.485281 | 0.0268361 | ||||||||
\(328\) | 3.17157 | 0.175121 | ||||||||
\(329\) | −1.51472 | −0.0835091 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.02944 | −0.0565830 | −0.0282915 | − | 0.999600i | \(-0.509007\pi\) | ||||
−0.0282915 | + | 0.999600i | \(0.509007\pi\) | |||||||
\(332\) | 12.7990 | 0.702436 | ||||||||
\(333\) | 24.0000 | 1.31519 | ||||||||
\(334\) | −0.970563 | −0.0531068 | ||||||||
\(335\) | 20.6274 | 1.12700 | ||||||||
\(336\) | −2.27208 | −0.123952 | ||||||||
\(337\) | 10.7574 | 0.585991 | 0.292995 | − | 0.956114i | \(-0.405348\pi\) | ||||
0.292995 | + | 0.956114i | \(0.405348\pi\) | |||||||
\(338\) | −4.97056 | −0.270363 | ||||||||
\(339\) | 1.02944 | 0.0559114 | ||||||||
\(340\) | −5.79899 | −0.314494 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 3.79899 | 0.205426 | ||||||||
\(343\) | −19.4853 | −1.05211 | ||||||||
\(344\) | 0.656854 | 0.0354152 | ||||||||
\(345\) | −7.31371 | −0.393757 | ||||||||
\(346\) | −1.72792 | −0.0928937 | ||||||||
\(347\) | −12.9706 | −0.696296 | −0.348148 | − | 0.937440i | \(-0.613189\pi\) | ||||
−0.348148 | + | 0.937440i | \(0.613189\pi\) | |||||||
\(348\) | 0.757359 | 0.0405987 | ||||||||
\(349\) | 5.97056 | 0.319597 | 0.159798 | − | 0.987150i | \(-0.448916\pi\) | ||||
0.159798 | + | 0.987150i | \(0.448916\pi\) | |||||||
\(350\) | 0.757359 | 0.0404826 | ||||||||
\(351\) | 12.0711 | 0.644306 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.4558 | −0.822632 | −0.411316 | − | 0.911493i | \(-0.634931\pi\) | ||||
−0.411316 | + | 0.911493i | \(0.634931\pi\) | |||||||
\(354\) | −0.0588745 | −0.00312914 | ||||||||
\(355\) | 16.6274 | 0.882492 | ||||||||
\(356\) | 20.4264 | 1.08260 | ||||||||
\(357\) | −1.20101 | −0.0635642 | ||||||||
\(358\) | 7.37258 | 0.389653 | ||||||||
\(359\) | 8.48528 | 0.447836 | 0.223918 | − | 0.974608i | \(-0.428115\pi\) | ||||
0.223918 | + | 0.974608i | \(0.428115\pi\) | |||||||
\(360\) | −8.97056 | −0.472790 | ||||||||
\(361\) | −8.48528 | −0.446594 | ||||||||
\(362\) | 7.38478 | 0.388135 | ||||||||
\(363\) | 4.55635 | 0.239146 | ||||||||
\(364\) | −16.7157 | −0.876142 | ||||||||
\(365\) | 20.1421 | 1.05429 | ||||||||
\(366\) | −1.52691 | −0.0798130 | ||||||||
\(367\) | −10.1421 | −0.529415 | −0.264708 | − | 0.964329i | \(-0.585275\pi\) | ||||
−0.264708 | + | 0.964329i | \(0.585275\pi\) | |||||||
\(368\) | 26.4853 | 1.38064 | ||||||||
\(369\) | −5.65685 | −0.294484 | ||||||||
\(370\) | 7.02944 | 0.365443 | ||||||||
\(371\) | 2.14214 | 0.111214 | ||||||||
\(372\) | −0.627417 | −0.0325301 | ||||||||
\(373\) | 20.0000 | 1.03556 | 0.517780 | − | 0.855514i | \(-0.326758\pi\) | ||||
0.517780 | + | 0.855514i | \(0.326758\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.97056 | 0.256679 | ||||||||
\(376\) | −1.31371 | −0.0677493 | ||||||||
\(377\) | 5.00000 | 0.257513 | ||||||||
\(378\) | −1.82843 | −0.0940441 | ||||||||
\(379\) | −33.7279 | −1.73249 | −0.866243 | − | 0.499622i | \(-0.833472\pi\) | ||||
−0.866243 | + | 0.499622i | \(0.833472\pi\) | |||||||
\(380\) | −11.8579 | −0.608296 | ||||||||
\(381\) | −2.68629 | −0.137623 | ||||||||
\(382\) | 4.82843 | 0.247044 | ||||||||
\(383\) | −15.7990 | −0.807291 | −0.403645 | − | 0.914916i | \(-0.632257\pi\) | ||||
−0.403645 | + | 0.914916i | \(0.632257\pi\) | |||||||
\(384\) | −4.37258 | −0.223137 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.94113 | −0.404193 | ||||||||
\(387\) | −1.17157 | −0.0595544 | ||||||||
\(388\) | −1.38478 | −0.0703014 | ||||||||
\(389\) | 29.0416 | 1.47247 | 0.736235 | − | 0.676726i | \(-0.236602\pi\) | ||||
0.736235 | + | 0.676726i | \(0.236602\pi\) | |||||||
\(390\) | 1.71573 | 0.0868793 | ||||||||
\(391\) | 14.0000 | 0.708010 | ||||||||
\(392\) | −5.79899 | −0.292893 | ||||||||
\(393\) | −1.79899 | −0.0907470 | ||||||||
\(394\) | −10.0000 | −0.503793 | ||||||||
\(395\) | 28.9706 | 1.45767 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.00000 | −0.200754 | −0.100377 | − | 0.994949i | \(-0.532005\pi\) | ||||
−0.100377 | + | 0.994949i | \(0.532005\pi\) | |||||||
\(398\) | 6.54416 | 0.328029 | ||||||||
\(399\) | −2.45584 | −0.122946 | ||||||||
\(400\) | −3.00000 | −0.150000 | ||||||||
\(401\) | −10.9706 | −0.547844 | −0.273922 | − | 0.961752i | \(-0.588321\pi\) | ||||
−0.273922 | + | 0.961752i | \(0.588321\pi\) | |||||||
\(402\) | 1.76955 | 0.0882573 | ||||||||
\(403\) | −4.14214 | −0.206334 | ||||||||
\(404\) | −18.5442 | −0.922606 | ||||||||
\(405\) | 14.9706 | 0.743893 | ||||||||
\(406\) | −0.757359 | −0.0375871 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −1.04163 | −0.0515684 | ||||||||
\(409\) | −20.1421 | −0.995965 | −0.497982 | − | 0.867187i | \(-0.665926\pi\) | ||||
−0.497982 | + | 0.867187i | \(0.665926\pi\) | |||||||
\(410\) | −1.65685 | −0.0818262 | ||||||||
\(411\) | −9.31371 | −0.459411 | ||||||||
\(412\) | 12.4853 | 0.615106 | ||||||||
\(413\) | −0.627417 | −0.0308732 | ||||||||
\(414\) | 10.3431 | 0.508338 | ||||||||
\(415\) | −14.0000 | −0.687233 | ||||||||
\(416\) | −22.0711 | −1.08212 | ||||||||
\(417\) | 0.414214 | 0.0202841 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.7990 | 1.55348 | 0.776741 | − | 0.629820i | \(-0.216871\pi\) | ||||
0.776741 | + | 0.629820i | \(0.216871\pi\) | |||||||
\(420\) | 2.76955 | 0.135140 | ||||||||
\(421\) | 12.6863 | 0.618292 | 0.309146 | − | 0.951015i | \(-0.399957\pi\) | ||||
0.309146 | + | 0.951015i | \(0.399957\pi\) | |||||||
\(422\) | 4.11270 | 0.200203 | ||||||||
\(423\) | 2.34315 | 0.113928 | ||||||||
\(424\) | 1.85786 | 0.0902259 | ||||||||
\(425\) | −1.58579 | −0.0769219 | ||||||||
\(426\) | 1.42641 | 0.0691096 | ||||||||
\(427\) | −16.2721 | −0.787461 | ||||||||
\(428\) | 35.6274 | 1.72212 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.343146 | −0.0165480 | ||||||||
\(431\) | 5.17157 | 0.249106 | 0.124553 | − | 0.992213i | \(-0.460250\pi\) | ||||
0.124553 | + | 0.992213i | \(0.460250\pi\) | |||||||
\(432\) | 7.24264 | 0.348462 | ||||||||
\(433\) | 15.6569 | 0.752420 | 0.376210 | − | 0.926534i | \(-0.377227\pi\) | ||||
0.376210 | + | 0.926534i | \(0.377227\pi\) | |||||||
\(434\) | 0.627417 | 0.0301170 | ||||||||
\(435\) | −0.828427 | −0.0397200 | ||||||||
\(436\) | 2.14214 | 0.102590 | ||||||||
\(437\) | 28.6274 | 1.36944 | ||||||||
\(438\) | 1.72792 | 0.0825633 | ||||||||
\(439\) | −17.4558 | −0.833122 | −0.416561 | − | 0.909108i | \(-0.636765\pi\) | ||||
−0.416561 | + | 0.909108i | \(0.636765\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.3431 | 0.492531 | ||||||||
\(442\) | −3.28427 | −0.156217 | ||||||||
\(443\) | −38.9706 | −1.85155 | −0.925774 | − | 0.378078i | \(-0.876585\pi\) | ||||
−0.925774 | + | 0.378078i | \(0.876585\pi\) | |||||||
\(444\) | −6.42641 | −0.304984 | ||||||||
\(445\) | −22.3431 | −1.05917 | ||||||||
\(446\) | −6.97056 | −0.330066 | ||||||||
\(447\) | 0.343146 | 0.0162302 | ||||||||
\(448\) | −7.62742 | −0.360362 | ||||||||
\(449\) | 37.5269 | 1.77100 | 0.885502 | − | 0.464635i | \(-0.153814\pi\) | ||||
0.885502 | + | 0.464635i | \(0.153814\pi\) | |||||||
\(450\) | −1.17157 | −0.0552285 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 4.54416 | 0.213739 | ||||||||
\(453\) | 4.97056 | 0.233537 | ||||||||
\(454\) | 10.2010 | 0.478757 | ||||||||
\(455\) | 18.2843 | 0.857180 | ||||||||
\(456\) | −2.12994 | −0.0997437 | ||||||||
\(457\) | −21.6569 | −1.01306 | −0.506532 | − | 0.862221i | \(-0.669073\pi\) | ||||
−0.506532 | + | 0.862221i | \(0.669073\pi\) | |||||||
\(458\) | 8.48528 | 0.396491 | ||||||||
\(459\) | 3.82843 | 0.178696 | ||||||||
\(460\) | −32.2843 | −1.50526 | ||||||||
\(461\) | −15.1716 | −0.706611 | −0.353305 | − | 0.935508i | \(-0.614942\pi\) | ||||
−0.353305 | + | 0.935508i | \(0.614942\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.1716 | 1.40219 | 0.701096 | − | 0.713067i | \(-0.252694\pi\) | ||||
0.701096 | + | 0.713067i | \(0.252694\pi\) | |||||||
\(464\) | 3.00000 | 0.139272 | ||||||||
\(465\) | 0.686292 | 0.0318260 | ||||||||
\(466\) | −9.85786 | −0.456657 | ||||||||
\(467\) | −35.6569 | −1.65000 | −0.825001 | − | 0.565131i | \(-0.808826\pi\) | ||||
−0.825001 | + | 0.565131i | \(0.808826\pi\) | |||||||
\(468\) | 25.8579 | 1.19528 | ||||||||
\(469\) | 18.8579 | 0.870775 | ||||||||
\(470\) | 0.686292 | 0.0316563 | ||||||||
\(471\) | −7.54416 | −0.347616 | ||||||||
\(472\) | −0.544156 | −0.0250468 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 2.48528 | 0.114153 | ||||||||
\(475\) | −3.24264 | −0.148783 | ||||||||
\(476\) | −5.30152 | −0.242995 | ||||||||
\(477\) | −3.31371 | −0.151724 | ||||||||
\(478\) | −6.55635 | −0.299880 | ||||||||
\(479\) | 2.68629 | 0.122740 | 0.0613699 | − | 0.998115i | \(-0.480453\pi\) | ||||
0.0613699 | + | 0.998115i | \(0.480453\pi\) | |||||||
\(480\) | 3.65685 | 0.166912 | ||||||||
\(481\) | −42.4264 | −1.93448 | ||||||||
\(482\) | 8.68629 | 0.395650 | ||||||||
\(483\) | −6.68629 | −0.304237 | ||||||||
\(484\) | 20.1127 | 0.914214 | ||||||||
\(485\) | 1.51472 | 0.0687798 | ||||||||
\(486\) | 4.28427 | 0.194338 | ||||||||
\(487\) | −38.1421 | −1.72839 | −0.864193 | − | 0.503161i | \(-0.832170\pi\) | ||||
−0.864193 | + | 0.503161i | \(0.832170\pi\) | |||||||
\(488\) | −14.1127 | −0.638852 | ||||||||
\(489\) | −10.2010 | −0.461306 | ||||||||
\(490\) | 3.02944 | 0.136856 | ||||||||
\(491\) | −34.2843 | −1.54723 | −0.773614 | − | 0.633657i | \(-0.781553\pi\) | ||||
−0.773614 | + | 0.633657i | \(0.781553\pi\) | |||||||
\(492\) | 1.51472 | 0.0682888 | ||||||||
\(493\) | 1.58579 | 0.0714202 | ||||||||
\(494\) | −6.71573 | −0.302155 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.48528 | −0.111592 | ||||||||
\(497\) | 15.2010 | 0.681858 | ||||||||
\(498\) | −1.20101 | −0.0538186 | ||||||||
\(499\) | 10.6274 | 0.475749 | 0.237874 | − | 0.971296i | \(-0.423549\pi\) | ||||
0.237874 | + | 0.971296i | \(0.423549\pi\) | |||||||
\(500\) | 21.9411 | 0.981237 | ||||||||
\(501\) | −0.970563 | −0.0433615 | ||||||||
\(502\) | −12.0000 | −0.535586 | ||||||||
\(503\) | −15.3137 | −0.682805 | −0.341402 | − | 0.939917i | \(-0.610902\pi\) | ||||
−0.341402 | + | 0.939917i | \(0.610902\pi\) | |||||||
\(504\) | −8.20101 | −0.365302 | ||||||||
\(505\) | 20.2843 | 0.902638 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.97056 | −0.220750 | ||||||||
\(508\) | −11.8579 | −0.526108 | ||||||||
\(509\) | 4.48528 | 0.198807 | 0.0994033 | − | 0.995047i | \(-0.468307\pi\) | ||||
0.0994033 | + | 0.995047i | \(0.468307\pi\) | |||||||
\(510\) | 0.544156 | 0.0240956 | ||||||||
\(511\) | 18.4142 | 0.814597 | ||||||||
\(512\) | −22.7574 | −1.00574 | ||||||||
\(513\) | 7.82843 | 0.345634 | ||||||||
\(514\) | −12.1421 | −0.535567 | ||||||||
\(515\) | −13.6569 | −0.601793 | ||||||||
\(516\) | 0.313708 | 0.0138102 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 6.42641 | 0.282360 | ||||||||
\(519\) | −1.72792 | −0.0758474 | ||||||||
\(520\) | 15.8579 | 0.695413 | ||||||||
\(521\) | −2.82843 | −0.123916 | −0.0619578 | − | 0.998079i | \(-0.519734\pi\) | ||||
−0.0619578 | + | 0.998079i | \(0.519734\pi\) | |||||||
\(522\) | 1.17157 | 0.0512784 | ||||||||
\(523\) | 10.5147 | 0.459777 | 0.229888 | − | 0.973217i | \(-0.426164\pi\) | ||||
0.229888 | + | 0.973217i | \(0.426164\pi\) | |||||||
\(524\) | −7.94113 | −0.346910 | ||||||||
\(525\) | 0.757359 | 0.0330539 | ||||||||
\(526\) | 0.627417 | 0.0273567 | ||||||||
\(527\) | −1.31371 | −0.0572260 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 54.9411 | 2.38874 | ||||||||
\(530\) | −0.970563 | −0.0421586 | ||||||||
\(531\) | 0.970563 | 0.0421188 | ||||||||
\(532\) | −10.8406 | −0.470001 | ||||||||
\(533\) | 10.0000 | 0.433148 | ||||||||
\(534\) | −1.91674 | −0.0829454 | ||||||||
\(535\) | −38.9706 | −1.68484 | ||||||||
\(536\) | 16.3553 | 0.706443 | ||||||||
\(537\) | 7.37258 | 0.318150 | ||||||||
\(538\) | 3.20101 | 0.138005 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −8.82843 | −0.379915 | ||||||||
\(541\) | −10.0000 | −0.429934 | −0.214967 | − | 0.976621i | \(-0.568964\pi\) | ||||
−0.214967 | + | 0.976621i | \(0.568964\pi\) | |||||||
\(542\) | −7.62742 | −0.327626 | ||||||||
\(543\) | 7.38478 | 0.316911 | ||||||||
\(544\) | −7.00000 | −0.300123 | ||||||||
\(545\) | −2.34315 | −0.100369 | ||||||||
\(546\) | 1.56854 | 0.0671274 | ||||||||
\(547\) | 10.1421 | 0.433646 | 0.216823 | − | 0.976211i | \(-0.430430\pi\) | ||||
0.216823 | + | 0.976211i | \(0.430430\pi\) | |||||||
\(548\) | −41.1127 | −1.75625 | ||||||||
\(549\) | 25.1716 | 1.07430 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.24264 | 0.138141 | ||||||||
\(552\) | −5.79899 | −0.246821 | ||||||||
\(553\) | 26.4853 | 1.12627 | ||||||||
\(554\) | −8.76955 | −0.372583 | ||||||||
\(555\) | 7.02944 | 0.298383 | ||||||||
\(556\) | 1.82843 | 0.0775426 | ||||||||
\(557\) | 11.6569 | 0.493917 | 0.246958 | − | 0.969026i | \(-0.420569\pi\) | ||||
0.246958 | + | 0.969026i | \(0.420569\pi\) | |||||||
\(558\) | −0.970563 | −0.0410872 | ||||||||
\(559\) | 2.07107 | 0.0875968 | ||||||||
\(560\) | 10.9706 | 0.463591 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.65685 | −0.238620 | ||||||||
\(563\) | −17.1127 | −0.721214 | −0.360607 | − | 0.932718i | \(-0.617430\pi\) | ||||
−0.360607 | + | 0.932718i | \(0.617430\pi\) | |||||||
\(564\) | −0.627417 | −0.0264190 | ||||||||
\(565\) | −4.97056 | −0.209113 | ||||||||
\(566\) | −11.5858 | −0.486987 | ||||||||
\(567\) | 13.6863 | 0.574770 | ||||||||
\(568\) | 13.1838 | 0.553179 | ||||||||
\(569\) | −11.7990 | −0.494639 | −0.247320 | − | 0.968934i | \(-0.579550\pi\) | ||||
−0.247320 | + | 0.968934i | \(0.579550\pi\) | |||||||
\(570\) | 1.11270 | 0.0466058 | ||||||||
\(571\) | −20.6274 | −0.863231 | −0.431615 | − | 0.902058i | \(-0.642056\pi\) | ||||
−0.431615 | + | 0.902058i | \(0.642056\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.82843 | 0.201710 | ||||||||
\(574\) | −1.51472 | −0.0632231 | ||||||||
\(575\) | −8.82843 | −0.368171 | ||||||||
\(576\) | 11.7990 | 0.491625 | ||||||||
\(577\) | −25.2426 | −1.05086 | −0.525432 | − | 0.850835i | \(-0.676096\pi\) | ||||
−0.525432 | + | 0.850835i | \(0.676096\pi\) | |||||||
\(578\) | 6.00000 | 0.249567 | ||||||||
\(579\) | −7.94113 | −0.330022 | ||||||||
\(580\) | −3.65685 | −0.151843 | ||||||||
\(581\) | −12.7990 | −0.530992 | ||||||||
\(582\) | 0.129942 | 0.00538628 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 15.9706 | 0.660867 | ||||||||
\(585\) | −28.2843 | −1.16941 | ||||||||
\(586\) | −8.48528 | −0.350524 | ||||||||
\(587\) | 2.65685 | 0.109660 | 0.0548301 | − | 0.998496i | \(-0.482538\pi\) | ||||
0.0548301 | + | 0.998496i | \(0.482538\pi\) | |||||||
\(588\) | −2.76955 | −0.114214 | ||||||||
\(589\) | −2.68629 | −0.110687 | ||||||||
\(590\) | 0.284271 | 0.0117033 | ||||||||
\(591\) | −10.0000 | −0.411345 | ||||||||
\(592\) | −25.4558 | −1.04623 | ||||||||
\(593\) | −30.9411 | −1.27060 | −0.635300 | − | 0.772266i | \(-0.719123\pi\) | ||||
−0.635300 | + | 0.772266i | \(0.719123\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.79899 | 0.237735 | ||||||||
\(596\) | 1.51472 | 0.0620453 | ||||||||
\(597\) | 6.54416 | 0.267834 | ||||||||
\(598\) | −18.2843 | −0.747699 | ||||||||
\(599\) | −34.2843 | −1.40082 | −0.700409 | − | 0.713742i | \(-0.746999\pi\) | ||||
−0.700409 | + | 0.713742i | \(0.746999\pi\) | |||||||
\(600\) | 0.656854 | 0.0268160 | ||||||||
\(601\) | 44.4853 | 1.81459 | 0.907296 | − | 0.420492i | \(-0.138143\pi\) | ||||
0.907296 | + | 0.420492i | \(0.138143\pi\) | |||||||
\(602\) | −0.313708 | −0.0127858 | ||||||||
\(603\) | −29.1716 | −1.18796 | ||||||||
\(604\) | 21.9411 | 0.892772 | ||||||||
\(605\) | −22.0000 | −0.894427 | ||||||||
\(606\) | 1.74012 | 0.0706874 | ||||||||
\(607\) | −25.1716 | −1.02168 | −0.510841 | − | 0.859675i | \(-0.670666\pi\) | ||||
−0.510841 | + | 0.859675i | \(0.670666\pi\) | |||||||
\(608\) | −14.3137 | −0.580498 | ||||||||
\(609\) | −0.757359 | −0.0306897 | ||||||||
\(610\) | 7.37258 | 0.298507 | ||||||||
\(611\) | −4.14214 | −0.167573 | ||||||||
\(612\) | 8.20101 | 0.331506 | ||||||||
\(613\) | −24.7990 | −1.00162 | −0.500811 | − | 0.865557i | \(-0.666965\pi\) | ||||
−0.500811 | + | 0.865557i | \(0.666965\pi\) | |||||||
\(614\) | −11.3137 | −0.456584 | ||||||||
\(615\) | −1.65685 | −0.0668108 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.3848 | −0.699885 | −0.349942 | − | 0.936771i | \(-0.613799\pi\) | ||||
−0.349942 | + | 0.936771i | \(0.613799\pi\) | |||||||
\(618\) | −1.17157 | −0.0471276 | ||||||||
\(619\) | 1.65685 | 0.0665946 | 0.0332973 | − | 0.999445i | \(-0.489399\pi\) | ||||
0.0332973 | + | 0.999445i | \(0.489399\pi\) | |||||||
\(620\) | 3.02944 | 0.121665 | ||||||||
\(621\) | 21.3137 | 0.855290 | ||||||||
\(622\) | −1.51472 | −0.0607347 | ||||||||
\(623\) | −20.4264 | −0.818367 | ||||||||
\(624\) | −6.21320 | −0.248727 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | −12.0711 | −0.482457 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −33.3015 | −1.32888 | ||||||||
\(629\) | −13.4558 | −0.536520 | ||||||||
\(630\) | 4.28427 | 0.170689 | ||||||||
\(631\) | −10.4853 | −0.417412 | −0.208706 | − | 0.977978i | \(-0.566925\pi\) | ||||
−0.208706 | + | 0.977978i | \(0.566925\pi\) | |||||||
\(632\) | 22.9706 | 0.913720 | ||||||||
\(633\) | 4.11270 | 0.163465 | ||||||||
\(634\) | −4.48528 | −0.178133 | ||||||||
\(635\) | 12.9706 | 0.514721 | ||||||||
\(636\) | 0.887302 | 0.0351838 | ||||||||
\(637\) | −18.2843 | −0.724449 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23.5147 | −0.930228 | ||||||||
\(640\) | 21.1127 | 0.834553 | ||||||||
\(641\) | 1.17157 | 0.0462743 | 0.0231372 | − | 0.999732i | \(-0.492635\pi\) | ||||
0.0231372 | + | 0.999732i | \(0.492635\pi\) | |||||||
\(642\) | −3.34315 | −0.131943 | ||||||||
\(643\) | 35.6569 | 1.40617 | 0.703085 | − | 0.711106i | \(-0.251806\pi\) | ||||
0.703085 | + | 0.711106i | \(0.251806\pi\) | |||||||
\(644\) | −29.5147 | −1.16304 | ||||||||
\(645\) | −0.343146 | −0.0135114 | ||||||||
\(646\) | −2.12994 | −0.0838015 | ||||||||
\(647\) | −21.3431 | −0.839086 | −0.419543 | − | 0.907736i | \(-0.637810\pi\) | ||||
−0.419543 | + | 0.907736i | \(0.637810\pi\) | |||||||
\(648\) | 11.8701 | 0.466300 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.07107 | 0.0812340 | ||||||||
\(651\) | 0.627417 | 0.0245904 | ||||||||
\(652\) | −45.0294 | −1.76349 | ||||||||
\(653\) | 27.7279 | 1.08508 | 0.542539 | − | 0.840031i | \(-0.317463\pi\) | ||||
0.542539 | + | 0.840031i | \(0.317463\pi\) | |||||||
\(654\) | −0.201010 | −0.00786012 | ||||||||
\(655\) | 8.68629 | 0.339401 | ||||||||
\(656\) | 6.00000 | 0.234261 | ||||||||
\(657\) | −28.4853 | −1.11132 | ||||||||
\(658\) | 0.627417 | 0.0244593 | ||||||||
\(659\) | −10.4142 | −0.405680 | −0.202840 | − | 0.979212i | \(-0.565017\pi\) | ||||
−0.202840 | + | 0.979212i | \(0.565017\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.6863 | −0.882394 | −0.441197 | − | 0.897410i | \(-0.645446\pi\) | ||||
−0.441197 | + | 0.897410i | \(0.645446\pi\) | |||||||
\(662\) | 0.426407 | 0.0165728 | ||||||||
\(663\) | −3.28427 | −0.127551 | ||||||||
\(664\) | −11.1005 | −0.430783 | ||||||||
\(665\) | 11.8579 | 0.459828 | ||||||||
\(666\) | −9.94113 | −0.385211 | ||||||||
\(667\) | 8.82843 | 0.341838 | ||||||||
\(668\) | −4.28427 | −0.165763 | ||||||||
\(669\) | −6.97056 | −0.269498 | ||||||||
\(670\) | −8.54416 | −0.330090 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 3.34315 | 0.128965 | ||||||||
\(673\) | 31.4853 | 1.21367 | 0.606834 | − | 0.794828i | \(-0.292439\pi\) | ||||
0.606834 | + | 0.794828i | \(0.292439\pi\) | |||||||
\(674\) | −4.45584 | −0.171633 | ||||||||
\(675\) | −2.41421 | −0.0929231 | ||||||||
\(676\) | −21.9411 | −0.843889 | ||||||||
\(677\) | −45.9411 | −1.76566 | −0.882830 | − | 0.469692i | \(-0.844365\pi\) | ||||
−0.882830 | + | 0.469692i | \(0.844365\pi\) | |||||||
\(678\) | −0.426407 | −0.0163761 | ||||||||
\(679\) | 1.38478 | 0.0531428 | ||||||||
\(680\) | 5.02944 | 0.192870 | ||||||||
\(681\) | 10.2010 | 0.390904 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.1421 | −0.579398 | −0.289699 | − | 0.957118i | \(-0.593555\pi\) | ||||
−0.289699 | + | 0.957118i | \(0.593555\pi\) | |||||||
\(684\) | 16.7696 | 0.641200 | ||||||||
\(685\) | 44.9706 | 1.71824 | ||||||||
\(686\) | 8.07107 | 0.308155 | ||||||||
\(687\) | 8.48528 | 0.323734 | ||||||||
\(688\) | 1.24264 | 0.0473752 | ||||||||
\(689\) | 5.85786 | 0.223167 | ||||||||
\(690\) | 3.02944 | 0.115329 | ||||||||
\(691\) | 18.4853 | 0.703213 | 0.351607 | − | 0.936148i | \(-0.385635\pi\) | ||||
0.351607 | + | 0.936148i | \(0.385635\pi\) | |||||||
\(692\) | −7.62742 | −0.289951 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.37258 | 0.203940 | ||||||||
\(695\) | −2.00000 | −0.0758643 | ||||||||
\(696\) | −0.656854 | −0.0248980 | ||||||||
\(697\) | 3.17157 | 0.120132 | ||||||||
\(698\) | −2.47309 | −0.0936078 | ||||||||
\(699\) | −9.85786 | −0.372859 | ||||||||
\(700\) | 3.34315 | 0.126359 | ||||||||
\(701\) | −52.3137 | −1.97586 | −0.987931 | − | 0.154896i | \(-0.950496\pi\) | ||||
−0.987931 | + | 0.154896i | \(0.950496\pi\) | |||||||
\(702\) | −5.00000 | −0.188713 | ||||||||
\(703\) | −27.5147 | −1.03774 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.686292 | 0.0258472 | ||||||||
\(706\) | 6.40202 | 0.240943 | ||||||||
\(707\) | 18.5442 | 0.697425 | ||||||||
\(708\) | −0.259885 | −0.00976706 | ||||||||
\(709\) | −21.1716 | −0.795115 | −0.397558 | − | 0.917577i | \(-0.630142\pi\) | ||||
−0.397558 | + | 0.917577i | \(0.630142\pi\) | |||||||
\(710\) | −6.88730 | −0.258476 | ||||||||
\(711\) | −40.9706 | −1.53652 | ||||||||
\(712\) | −17.7157 | −0.663925 | ||||||||
\(713\) | −7.31371 | −0.273901 | ||||||||
\(714\) | 0.497475 | 0.0186175 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 32.5442 | 1.21623 | ||||||||
\(717\) | −6.55635 | −0.244851 | ||||||||
\(718\) | −3.51472 | −0.131168 | ||||||||
\(719\) | 32.3137 | 1.20510 | 0.602549 | − | 0.798082i | \(-0.294152\pi\) | ||||
0.602549 | + | 0.798082i | \(0.294152\pi\) | |||||||
\(720\) | −16.9706 | −0.632456 | ||||||||
\(721\) | −12.4853 | −0.464976 | ||||||||
\(722\) | 3.51472 | 0.130804 | ||||||||
\(723\) | 8.68629 | 0.323047 | ||||||||
\(724\) | 32.5980 | 1.21149 | ||||||||
\(725\) | −1.00000 | −0.0371391 | ||||||||
\(726\) | −1.88730 | −0.0700443 | ||||||||
\(727\) | 27.8701 | 1.03364 | 0.516822 | − | 0.856093i | \(-0.327115\pi\) | ||||
0.516822 | + | 0.856093i | \(0.327115\pi\) | |||||||
\(728\) | 14.4975 | 0.537312 | ||||||||
\(729\) | −18.1716 | −0.673021 | ||||||||
\(730\) | −8.34315 | −0.308794 | ||||||||
\(731\) | 0.656854 | 0.0242946 | ||||||||
\(732\) | −6.74012 | −0.249122 | ||||||||
\(733\) | 6.97056 | 0.257464 | 0.128732 | − | 0.991679i | \(-0.458909\pi\) | ||||
0.128732 | + | 0.991679i | \(0.458909\pi\) | |||||||
\(734\) | 4.20101 | 0.155062 | ||||||||
\(735\) | 3.02944 | 0.111742 | ||||||||
\(736\) | −38.9706 | −1.43647 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 2.34315 | 0.0862524 | ||||||||
\(739\) | 13.1127 | 0.482358 | 0.241179 | − | 0.970481i | \(-0.422466\pi\) | ||||
0.241179 | + | 0.970481i | \(0.422466\pi\) | |||||||
\(740\) | 31.0294 | 1.14066 | ||||||||
\(741\) | −6.71573 | −0.246708 | ||||||||
\(742\) | −0.887302 | −0.0325739 | ||||||||
\(743\) | 15.5858 | 0.571787 | 0.285894 | − | 0.958261i | \(-0.407710\pi\) | ||||
0.285894 | + | 0.958261i | \(0.407710\pi\) | |||||||
\(744\) | 0.544156 | 0.0199497 | ||||||||
\(745\) | −1.65685 | −0.0607024 | ||||||||
\(746\) | −8.28427 | −0.303309 | ||||||||
\(747\) | 19.7990 | 0.724407 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −35.6274 | −1.30180 | ||||||||
\(750\) | −2.05887 | −0.0751795 | ||||||||
\(751\) | 4.07107 | 0.148555 | 0.0742777 | − | 0.997238i | \(-0.476335\pi\) | ||||
0.0742777 | + | 0.997238i | \(0.476335\pi\) | |||||||
\(752\) | −2.48528 | −0.0906289 | ||||||||
\(753\) | −12.0000 | −0.437304 | ||||||||
\(754\) | −2.07107 | −0.0754238 | ||||||||
\(755\) | −24.0000 | −0.873449 | ||||||||
\(756\) | −8.07107 | −0.293542 | ||||||||
\(757\) | 32.7696 | 1.19103 | 0.595515 | − | 0.803344i | \(-0.296948\pi\) | ||||
0.595515 | + | 0.803344i | \(0.296948\pi\) | |||||||
\(758\) | 13.9706 | 0.507434 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.2843 | 0.373050 | ||||||||
\(761\) | −47.4853 | −1.72134 | −0.860670 | − | 0.509163i | \(-0.829955\pi\) | ||||
−0.860670 | + | 0.509163i | \(0.829955\pi\) | |||||||
\(762\) | 1.11270 | 0.0403088 | ||||||||
\(763\) | −2.14214 | −0.0775505 | ||||||||
\(764\) | 21.3137 | 0.771103 | ||||||||
\(765\) | −8.97056 | −0.324331 | ||||||||
\(766\) | 6.54416 | 0.236450 | ||||||||
\(767\) | −1.71573 | −0.0619514 | ||||||||
\(768\) | −1.64466 | −0.0593466 | ||||||||
\(769\) | −26.8284 | −0.967458 | −0.483729 | − | 0.875218i | \(-0.660718\pi\) | ||||
−0.483729 | + | 0.875218i | \(0.660718\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.1421 | −0.437288 | ||||||||
\(772\) | −35.0538 | −1.26161 | ||||||||
\(773\) | 37.1716 | 1.33697 | 0.668484 | − | 0.743726i | \(-0.266943\pi\) | ||||
0.668484 | + | 0.743726i | \(0.266943\pi\) | |||||||
\(774\) | 0.485281 | 0.0174431 | ||||||||
\(775\) | 0.828427 | 0.0297580 | ||||||||
\(776\) | 1.20101 | 0.0431138 | ||||||||
\(777\) | 6.42641 | 0.230546 | ||||||||
\(778\) | −12.0294 | −0.431276 | ||||||||
\(779\) | 6.48528 | 0.232359 | ||||||||
\(780\) | 7.57359 | 0.271178 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −5.79899 | −0.207371 | ||||||||
\(783\) | 2.41421 | 0.0862770 | ||||||||
\(784\) | −10.9706 | −0.391806 | ||||||||
\(785\) | 36.4264 | 1.30011 | ||||||||
\(786\) | 0.745166 | 0.0265792 | ||||||||
\(787\) | 11.6569 | 0.415522 | 0.207761 | − | 0.978180i | \(-0.433382\pi\) | ||||
0.207761 | + | 0.978180i | \(0.433382\pi\) | |||||||
\(788\) | −44.1421 | −1.57250 | ||||||||
\(789\) | 0.627417 | 0.0223366 | ||||||||
\(790\) | −12.0000 | −0.426941 | ||||||||
\(791\) | −4.54416 | −0.161572 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −44.4975 | −1.58015 | ||||||||
\(794\) | 1.65685 | 0.0587996 | ||||||||
\(795\) | −0.970563 | −0.0344223 | ||||||||
\(796\) | 28.8873 | 1.02388 | ||||||||
\(797\) | 17.0416 | 0.603646 | 0.301823 | − | 0.953364i | \(-0.402405\pi\) | ||||
0.301823 | + | 0.953364i | \(0.402405\pi\) | |||||||
\(798\) | 1.01724 | 0.0360100 | ||||||||
\(799\) | −1.31371 | −0.0464757 | ||||||||
\(800\) | 4.41421 | 0.156066 | ||||||||
\(801\) | 31.5980 | 1.11646 | ||||||||
\(802\) | 4.54416 | 0.160460 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 7.81118 | 0.275479 | ||||||||
\(805\) | 32.2843 | 1.13787 | ||||||||
\(806\) | 1.71573 | 0.0604340 | ||||||||
\(807\) | 3.20101 | 0.112681 | ||||||||
\(808\) | 16.0833 | 0.565807 | ||||||||
\(809\) | −25.3848 | −0.892481 | −0.446241 | − | 0.894913i | \(-0.647237\pi\) | ||||
−0.446241 | + | 0.894913i | \(0.647237\pi\) | |||||||
\(810\) | −6.20101 | −0.217881 | ||||||||
\(811\) | −25.6569 | −0.900934 | −0.450467 | − | 0.892793i | \(-0.648743\pi\) | ||||
−0.450467 | + | 0.892793i | \(0.648743\pi\) | |||||||
\(812\) | −3.34315 | −0.117321 | ||||||||
\(813\) | −7.62742 | −0.267505 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 49.2548 | 1.72532 | ||||||||
\(816\) | −1.97056 | −0.0689835 | ||||||||
\(817\) | 1.34315 | 0.0469907 | ||||||||
\(818\) | 8.34315 | 0.291711 | ||||||||
\(819\) | −25.8579 | −0.903547 | ||||||||
\(820\) | −7.31371 | −0.255406 | ||||||||
\(821\) | 30.4264 | 1.06189 | 0.530944 | − | 0.847407i | \(-0.321837\pi\) | ||||
0.530944 | + | 0.847407i | \(0.321837\pi\) | |||||||
\(822\) | 3.85786 | 0.134558 | ||||||||
\(823\) | −2.41421 | −0.0841542 | −0.0420771 | − | 0.999114i | \(-0.513398\pi\) | ||||
−0.0420771 | + | 0.999114i | \(0.513398\pi\) | |||||||
\(824\) | −10.8284 | −0.377226 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.259885 | 0.00904254 | ||||||||
\(827\) | −24.7574 | −0.860898 | −0.430449 | − | 0.902615i | \(-0.641645\pi\) | ||||
−0.430449 | + | 0.902615i | \(0.641645\pi\) | |||||||
\(828\) | 45.6569 | 1.58669 | ||||||||
\(829\) | 40.7696 | 1.41599 | 0.707993 | − | 0.706220i | \(-0.249601\pi\) | ||||
0.707993 | + | 0.706220i | \(0.249601\pi\) | |||||||
\(830\) | 5.79899 | 0.201286 | ||||||||
\(831\) | −8.76955 | −0.304212 | ||||||||
\(832\) | −20.8579 | −0.723116 | ||||||||
\(833\) | −5.79899 | −0.200923 | ||||||||
\(834\) | −0.171573 | −0.00594108 | ||||||||
\(835\) | 4.68629 | 0.162176 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.00000 | −0.0691301 | ||||||||
\(838\) | −13.1716 | −0.455004 | ||||||||
\(839\) | 22.0000 | 0.759524 | 0.379762 | − | 0.925084i | \(-0.376006\pi\) | ||||
0.379762 | + | 0.925084i | \(0.376006\pi\) | |||||||
\(840\) | −2.40202 | −0.0828776 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −5.25483 | −0.181094 | ||||||||
\(843\) | −5.65685 | −0.194832 | ||||||||
\(844\) | 18.1543 | 0.624898 | ||||||||
\(845\) | 24.0000 | 0.825625 | ||||||||
\(846\) | −0.970563 | −0.0333686 | ||||||||
\(847\) | −20.1127 | −0.691080 | ||||||||
\(848\) | 3.51472 | 0.120696 | ||||||||
\(849\) | −11.5858 | −0.397623 | ||||||||
\(850\) | 0.656854 | 0.0225299 | ||||||||
\(851\) | −74.9117 | −2.56794 | ||||||||
\(852\) | 6.29646 | 0.215713 | ||||||||
\(853\) | 50.8995 | 1.74277 | 0.871383 | − | 0.490604i | \(-0.163224\pi\) | ||||
0.871383 | + | 0.490604i | \(0.163224\pi\) | |||||||
\(854\) | 6.74012 | 0.230642 | ||||||||
\(855\) | −18.3431 | −0.627322 | ||||||||
\(856\) | −30.8995 | −1.05612 | ||||||||
\(857\) | −47.9411 | −1.63764 | −0.818819 | − | 0.574052i | \(-0.805371\pi\) | ||||
−0.818819 | + | 0.574052i | \(0.805371\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(860\) | −1.51472 | −0.0516515 | ||||||||
\(861\) | −1.51472 | −0.0516215 | ||||||||
\(862\) | −2.14214 | −0.0729614 | ||||||||
\(863\) | 48.9706 | 1.66698 | 0.833489 | − | 0.552537i | \(-0.186340\pi\) | ||||
0.833489 | + | 0.552537i | \(0.186340\pi\) | |||||||
\(864\) | −10.6569 | −0.362554 | ||||||||
\(865\) | 8.34315 | 0.283675 | ||||||||
\(866\) | −6.48528 | −0.220379 | ||||||||
\(867\) | 6.00000 | 0.203771 | ||||||||
\(868\) | 2.76955 | 0.0940047 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0.343146 | 0.0116337 | ||||||||
\(871\) | 51.5685 | 1.74733 | ||||||||
\(872\) | −1.85786 | −0.0629152 | ||||||||
\(873\) | −2.14214 | −0.0725003 | ||||||||
\(874\) | −11.8579 | −0.401098 | ||||||||
\(875\) | −21.9411 | −0.741745 | ||||||||
\(876\) | 7.62742 | 0.257707 | ||||||||
\(877\) | −6.68629 | −0.225780 | −0.112890 | − | 0.993607i | \(-0.536011\pi\) | ||||
−0.112890 | + | 0.993607i | \(0.536011\pi\) | |||||||
\(878\) | 7.23045 | 0.244016 | ||||||||
\(879\) | −8.48528 | −0.286201 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.6274 | 0.762337 | 0.381169 | − | 0.924506i | \(-0.375522\pi\) | ||||
0.381169 | + | 0.924506i | \(0.375522\pi\) | |||||||
\(882\) | −4.28427 | −0.144259 | ||||||||
\(883\) | −35.4264 | −1.19219 | −0.596097 | − | 0.802913i | \(-0.703283\pi\) | ||||
−0.596097 | + | 0.802913i | \(0.703283\pi\) | |||||||
\(884\) | −14.4975 | −0.487603 | ||||||||
\(885\) | 0.284271 | 0.00955567 | ||||||||
\(886\) | 16.1421 | 0.542306 | ||||||||
\(887\) | 38.4142 | 1.28982 | 0.644912 | − | 0.764257i | \(-0.276894\pi\) | ||||
0.644912 | + | 0.764257i | \(0.276894\pi\) | |||||||
\(888\) | 5.57359 | 0.187038 | ||||||||
\(889\) | 11.8579 | 0.397700 | ||||||||
\(890\) | 9.25483 | 0.310223 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −30.7696 | −1.03024 | ||||||||
\(893\) | −2.68629 | −0.0898933 | ||||||||
\(894\) | −0.142136 | −0.00475373 | ||||||||
\(895\) | −35.5980 | −1.18991 | ||||||||
\(896\) | 19.3015 | 0.644818 | ||||||||
\(897\) | −18.2843 | −0.610494 | ||||||||
\(898\) | −15.5442 | −0.518715 | ||||||||
\(899\) | −0.828427 | −0.0276296 | ||||||||
\(900\) | −5.17157 | −0.172386 | ||||||||
\(901\) | 1.85786 | 0.0618944 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.313708 | −0.0104396 | ||||||||
\(904\) | −3.94113 | −0.131080 | ||||||||
\(905\) | −35.6569 | −1.18527 | ||||||||
\(906\) | −2.05887 | −0.0684015 | ||||||||
\(907\) | 21.3137 | 0.707710 | 0.353855 | − | 0.935300i | \(-0.384871\pi\) | ||||
0.353855 | + | 0.935300i | \(0.384871\pi\) | |||||||
\(908\) | 45.0294 | 1.49435 | ||||||||
\(909\) | −28.6863 | −0.951464 | ||||||||
\(910\) | −7.57359 | −0.251062 | ||||||||
\(911\) | −19.1716 | −0.635183 | −0.317591 | − | 0.948228i | \(-0.602874\pi\) | ||||
−0.317591 | + | 0.948228i | \(0.602874\pi\) | |||||||
\(912\) | −4.02944 | −0.133428 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 8.97056 | 0.296720 | ||||||||
\(915\) | 7.37258 | 0.243730 | ||||||||
\(916\) | 37.4558 | 1.23758 | ||||||||
\(917\) | 7.94113 | 0.262239 | ||||||||
\(918\) | −1.58579 | −0.0523388 | ||||||||
\(919\) | 13.6569 | 0.450498 | 0.225249 | − | 0.974301i | \(-0.427680\pi\) | ||||
0.225249 | + | 0.974301i | \(0.427680\pi\) | |||||||
\(920\) | 28.0000 | 0.923133 | ||||||||
\(921\) | −11.3137 | −0.372799 | ||||||||
\(922\) | 6.28427 | 0.206961 | ||||||||
\(923\) | 41.5685 | 1.36825 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.48528 | 0.278994 | ||||||||
\(926\) | −12.4975 | −0.410693 | ||||||||
\(927\) | 19.3137 | 0.634345 | ||||||||
\(928\) | −4.41421 | −0.144904 | ||||||||
\(929\) | −26.9706 | −0.884875 | −0.442438 | − | 0.896799i | \(-0.645886\pi\) | ||||
−0.442438 | + | 0.896799i | \(0.645886\pi\) | |||||||
\(930\) | −0.284271 | −0.00932162 | ||||||||
\(931\) | −11.8579 | −0.388626 | ||||||||
\(932\) | −43.5147 | −1.42537 | ||||||||
\(933\) | −1.51472 | −0.0495897 | ||||||||
\(934\) | 14.7696 | 0.483275 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −22.4264 | −0.733030 | ||||||||
\(937\) | 24.8284 | 0.811109 | 0.405555 | − | 0.914071i | \(-0.367078\pi\) | ||||
0.405555 | + | 0.914071i | \(0.367078\pi\) | |||||||
\(938\) | −7.81118 | −0.255044 | ||||||||
\(939\) | −12.0711 | −0.393924 | ||||||||
\(940\) | 3.02944 | 0.0988093 | ||||||||
\(941\) | −17.0294 | −0.555144 | −0.277572 | − | 0.960705i | \(-0.589530\pi\) | ||||
−0.277572 | + | 0.960705i | \(0.589530\pi\) | |||||||
\(942\) | 3.12489 | 0.101814 | ||||||||
\(943\) | 17.6569 | 0.574986 | ||||||||
\(944\) | −1.02944 | −0.0335053 | ||||||||
\(945\) | 8.82843 | 0.287189 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.1716 | −0.817966 | −0.408983 | − | 0.912542i | \(-0.634117\pi\) | ||||
−0.408983 | + | 0.912542i | \(0.634117\pi\) | |||||||
\(948\) | 10.9706 | 0.356307 | ||||||||
\(949\) | 50.3553 | 1.63460 | ||||||||
\(950\) | 1.34315 | 0.0435774 | ||||||||
\(951\) | −4.48528 | −0.145445 | ||||||||
\(952\) | 4.59798 | 0.149021 | ||||||||
\(953\) | −0.343146 | −0.0111156 | −0.00555779 | − | 0.999985i | \(-0.501769\pi\) | ||||
−0.00555779 | + | 0.999985i | \(0.501769\pi\) | |||||||
\(954\) | 1.37258 | 0.0444390 | ||||||||
\(955\) | −23.3137 | −0.754414 | ||||||||
\(956\) | −28.9411 | −0.936023 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.11270 | −0.0359497 | ||||||||
\(959\) | 41.1127 | 1.32760 | ||||||||
\(960\) | 3.45584 | 0.111537 | ||||||||
\(961\) | −30.3137 | −0.977862 | ||||||||
\(962\) | 17.5736 | 0.566595 | ||||||||
\(963\) | 55.1127 | 1.77598 | ||||||||
\(964\) | 38.3431 | 1.23495 | ||||||||
\(965\) | 38.3431 | 1.23431 | ||||||||
\(966\) | 2.76955 | 0.0891089 | ||||||||
\(967\) | 34.2843 | 1.10251 | 0.551254 | − | 0.834338i | \(-0.314150\pi\) | ||||
0.551254 | + | 0.834338i | \(0.314150\pi\) | |||||||
\(968\) | −17.4437 | −0.560660 | ||||||||
\(969\) | −2.12994 | −0.0684236 | ||||||||
\(970\) | −0.627417 | −0.0201451 | ||||||||
\(971\) | −39.5980 | −1.27076 | −0.635380 | − | 0.772200i | \(-0.719156\pi\) | ||||
−0.635380 | + | 0.772200i | \(0.719156\pi\) | |||||||
\(972\) | 18.9117 | 0.606593 | ||||||||
\(973\) | −1.82843 | −0.0586167 | ||||||||
\(974\) | 15.7990 | 0.506232 | ||||||||
\(975\) | 2.07107 | 0.0663273 | ||||||||
\(976\) | −26.6985 | −0.854598 | ||||||||
\(977\) | 14.0294 | 0.448841 | 0.224421 | − | 0.974492i | \(-0.427951\pi\) | ||||
0.224421 | + | 0.974492i | \(0.427951\pi\) | |||||||
\(978\) | 4.22540 | 0.135113 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 13.3726 | 0.427171 | ||||||||
\(981\) | 3.31371 | 0.105799 | ||||||||
\(982\) | 14.2010 | 0.453172 | ||||||||
\(983\) | −48.2132 | −1.53776 | −0.768881 | − | 0.639392i | \(-0.779186\pi\) | ||||
−0.768881 | + | 0.639392i | \(0.779186\pi\) | |||||||
\(984\) | −1.31371 | −0.0418795 | ||||||||
\(985\) | 48.2843 | 1.53846 | ||||||||
\(986\) | −0.656854 | −0.0209185 | ||||||||
\(987\) | 0.627417 | 0.0199709 | ||||||||
\(988\) | −29.6447 | −0.943122 | ||||||||
\(989\) | 3.65685 | 0.116281 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.9706 | 0.602620 | 0.301310 | − | 0.953526i | \(-0.402576\pi\) | ||||
0.301310 | + | 0.953526i | \(0.402576\pi\) | |||||||
\(992\) | 3.65685 | 0.116105 | ||||||||
\(993\) | 0.426407 | 0.0135316 | ||||||||
\(994\) | −6.29646 | −0.199712 | ||||||||
\(995\) | −31.5980 | −1.00172 | ||||||||
\(996\) | −5.30152 | −0.167985 | ||||||||
\(997\) | 21.7990 | 0.690381 | 0.345190 | − | 0.938533i | \(-0.387814\pi\) | ||||
0.345190 | + | 0.938533i | \(0.387814\pi\) | |||||||
\(998\) | −4.40202 | −0.139344 | ||||||||
\(999\) | −20.4853 | −0.648126 |
(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 | 4031.2.a.a.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4031.2.a.a.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial |