Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4026,2,Mod(1,4026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4026.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: | \(32.1477718538\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 18x^{5} - 10x^{4} + 91x^{3} + 90x^{2} - 66x - 56 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.70776\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4026.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.745947 | −0.333598 | −0.166799 | − | 0.985991i | \(-0.553343\pi\) | ||||
−0.166799 | + | 0.985991i | \(0.553343\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.28209 | −0.484586 | −0.242293 | − | 0.970203i | \(-0.577900\pi\) | ||||
−0.242293 | + | 0.970203i | \(0.577900\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.745947 | 0.235889 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.02684 | 0.284795 | 0.142398 | − | 0.989810i | \(-0.454519\pi\) | ||||
0.142398 | + | 0.989810i | \(0.454519\pi\) | |||||||
\(14\) | 1.28209 | 0.342654 | ||||||||
\(15\) | 0.745947 | 0.192603 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.94118 | −0.955877 | −0.477939 | − | 0.878393i | \(-0.658616\pi\) | ||||
−0.477939 | + | 0.878393i | \(0.658616\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 1.02435 | 0.235003 | 0.117502 | − | 0.993073i | \(-0.462512\pi\) | ||||
0.117502 | + | 0.993073i | \(0.462512\pi\) | |||||||
\(20\) | −0.745947 | −0.166799 | ||||||||
\(21\) | 1.28209 | 0.279776 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 2.77474 | 0.578574 | 0.289287 | − | 0.957242i | \(-0.406582\pi\) | ||||
0.289287 | + | 0.957242i | \(0.406582\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.44356 | −0.888713 | ||||||||
\(26\) | −1.02684 | −0.201381 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.28209 | −0.242293 | ||||||||
\(29\) | 4.28967 | 0.796571 | 0.398286 | − | 0.917261i | \(-0.369605\pi\) | ||||
0.398286 | + | 0.917261i | \(0.369605\pi\) | |||||||
\(30\) | −0.745947 | −0.136191 | ||||||||
\(31\) | −5.11863 | −0.919333 | −0.459666 | − | 0.888092i | \(-0.652031\pi\) | ||||
−0.459666 | + | 0.888092i | \(0.652031\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 3.94118 | 0.675907 | ||||||||
\(35\) | 0.956374 | 0.161657 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −1.64876 | −0.271055 | −0.135527 | − | 0.990774i | \(-0.543273\pi\) | ||||
−0.135527 | + | 0.990774i | \(0.543273\pi\) | |||||||
\(38\) | −1.02435 | −0.166172 | ||||||||
\(39\) | −1.02684 | −0.164427 | ||||||||
\(40\) | 0.745947 | 0.117945 | ||||||||
\(41\) | 5.94995 | 0.929226 | 0.464613 | − | 0.885514i | \(-0.346193\pi\) | ||||
0.464613 | + | 0.885514i | \(0.346193\pi\) | |||||||
\(42\) | −1.28209 | −0.197831 | ||||||||
\(43\) | 3.78917 | 0.577842 | 0.288921 | − | 0.957353i | \(-0.406703\pi\) | ||||
0.288921 | + | 0.957353i | \(0.406703\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −0.745947 | −0.111199 | ||||||||
\(46\) | −2.77474 | −0.409113 | ||||||||
\(47\) | 6.38880 | 0.931903 | 0.465951 | − | 0.884810i | \(-0.345712\pi\) | ||||
0.465951 | + | 0.884810i | \(0.345712\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −5.35623 | −0.765176 | ||||||||
\(50\) | 4.44356 | 0.628415 | ||||||||
\(51\) | 3.94118 | 0.551876 | ||||||||
\(52\) | 1.02684 | 0.142398 | ||||||||
\(53\) | −0.306449 | −0.0420939 | −0.0210470 | − | 0.999778i | \(-0.506700\pi\) | ||||
−0.0210470 | + | 0.999778i | \(0.506700\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −0.745947 | −0.100583 | ||||||||
\(56\) | 1.28209 | 0.171327 | ||||||||
\(57\) | −1.02435 | −0.135679 | ||||||||
\(58\) | −4.28967 | −0.563261 | ||||||||
\(59\) | −6.02604 | −0.784524 | −0.392262 | − | 0.919854i | \(-0.628307\pi\) | ||||
−0.392262 | + | 0.919854i | \(0.628307\pi\) | |||||||
\(60\) | 0.745947 | 0.0963014 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | 5.11863 | 0.650066 | ||||||||
\(63\) | −1.28209 | −0.161529 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.765971 | −0.0950070 | ||||||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | −9.15286 | −1.11820 | −0.559100 | − | 0.829100i | \(-0.688853\pi\) | ||||
−0.559100 | + | 0.829100i | \(0.688853\pi\) | |||||||
\(68\) | −3.94118 | −0.477939 | ||||||||
\(69\) | −2.77474 | −0.334040 | ||||||||
\(70\) | −0.956374 | −0.114309 | ||||||||
\(71\) | 7.77380 | 0.922580 | 0.461290 | − | 0.887249i | \(-0.347387\pi\) | ||||
0.461290 | + | 0.887249i | \(0.347387\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −0.861474 | −0.100828 | −0.0504140 | − | 0.998728i | \(-0.516054\pi\) | ||||
−0.0504140 | + | 0.998728i | \(0.516054\pi\) | |||||||
\(74\) | 1.64876 | 0.191664 | ||||||||
\(75\) | 4.44356 | 0.513098 | ||||||||
\(76\) | 1.02435 | 0.117502 | ||||||||
\(77\) | −1.28209 | −0.146108 | ||||||||
\(78\) | 1.02684 | 0.116267 | ||||||||
\(79\) | −3.78432 | −0.425769 | −0.212884 | − | 0.977077i | \(-0.568286\pi\) | ||||
−0.212884 | + | 0.977077i | \(0.568286\pi\) | |||||||
\(80\) | −0.745947 | −0.0833994 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.94995 | −0.657062 | ||||||||
\(83\) | −10.9806 | −1.20528 | −0.602640 | − | 0.798013i | \(-0.705885\pi\) | ||||
−0.602640 | + | 0.798013i | \(0.705885\pi\) | |||||||
\(84\) | 1.28209 | 0.139888 | ||||||||
\(85\) | 2.93991 | 0.318878 | ||||||||
\(86\) | −3.78917 | −0.408596 | ||||||||
\(87\) | −4.28967 | −0.459901 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 9.92651 | 1.05221 | 0.526104 | − | 0.850420i | \(-0.323652\pi\) | ||||
0.526104 | + | 0.850420i | \(0.323652\pi\) | |||||||
\(90\) | 0.745947 | 0.0786297 | ||||||||
\(91\) | −1.31651 | −0.138008 | ||||||||
\(92\) | 2.77474 | 0.289287 | ||||||||
\(93\) | 5.11863 | 0.530777 | ||||||||
\(94\) | −6.38880 | −0.658955 | ||||||||
\(95\) | −0.764114 | −0.0783965 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 3.30314 | 0.335383 | 0.167692 | − | 0.985839i | \(-0.446369\pi\) | ||||
0.167692 | + | 0.985839i | \(0.446369\pi\) | |||||||
\(98\) | 5.35623 | 0.541061 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −4.44356 | −0.444356 | ||||||||
\(101\) | 6.19552 | 0.616477 | 0.308239 | − | 0.951309i | \(-0.400260\pi\) | ||||
0.308239 | + | 0.951309i | \(0.400260\pi\) | |||||||
\(102\) | −3.94118 | −0.390235 | ||||||||
\(103\) | −1.68344 | −0.165875 | −0.0829373 | − | 0.996555i | \(-0.526430\pi\) | ||||
−0.0829373 | + | 0.996555i | \(0.526430\pi\) | |||||||
\(104\) | −1.02684 | −0.100690 | ||||||||
\(105\) | −0.956374 | −0.0933326 | ||||||||
\(106\) | 0.306449 | 0.0297649 | ||||||||
\(107\) | −16.8399 | −1.62798 | −0.813989 | − | 0.580880i | \(-0.802709\pi\) | ||||
−0.813989 | + | 0.580880i | \(0.802709\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −1.16123 | −0.111226 | −0.0556130 | − | 0.998452i | \(-0.517711\pi\) | ||||
−0.0556130 | + | 0.998452i | \(0.517711\pi\) | |||||||
\(110\) | 0.745947 | 0.0711233 | ||||||||
\(111\) | 1.64876 | 0.156493 | ||||||||
\(112\) | −1.28209 | −0.121147 | ||||||||
\(113\) | 14.0142 | 1.31834 | 0.659171 | − | 0.751993i | \(-0.270908\pi\) | ||||
0.659171 | + | 0.751993i | \(0.270908\pi\) | |||||||
\(114\) | 1.02435 | 0.0959396 | ||||||||
\(115\) | −2.06981 | −0.193011 | ||||||||
\(116\) | 4.28967 | 0.398286 | ||||||||
\(117\) | 1.02684 | 0.0949317 | ||||||||
\(118\) | 6.02604 | 0.554742 | ||||||||
\(119\) | 5.05297 | 0.463205 | ||||||||
\(120\) | −0.745947 | −0.0680953 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.00000 | 0.0905357 | ||||||||
\(123\) | −5.94995 | −0.536489 | ||||||||
\(124\) | −5.11863 | −0.459666 | ||||||||
\(125\) | 7.04440 | 0.630070 | ||||||||
\(126\) | 1.28209 | 0.114218 | ||||||||
\(127\) | 19.0865 | 1.69366 | 0.846828 | − | 0.531867i | \(-0.178509\pi\) | ||||
0.846828 | + | 0.531867i | \(0.178509\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −3.78917 | −0.333617 | ||||||||
\(130\) | 0.765971 | 0.0671801 | ||||||||
\(131\) | 17.6945 | 1.54597 | 0.772986 | − | 0.634423i | \(-0.218762\pi\) | ||||
0.772986 | + | 0.634423i | \(0.218762\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | −1.31332 | −0.113879 | ||||||||
\(134\) | 9.15286 | 0.790687 | ||||||||
\(135\) | 0.745947 | 0.0642009 | ||||||||
\(136\) | 3.94118 | 0.337954 | ||||||||
\(137\) | −15.6557 | −1.33755 | −0.668777 | − | 0.743463i | \(-0.733182\pi\) | ||||
−0.668777 | + | 0.743463i | \(0.733182\pi\) | |||||||
\(138\) | 2.77474 | 0.236202 | ||||||||
\(139\) | 0.617102 | 0.0523419 | 0.0261710 | − | 0.999657i | \(-0.491669\pi\) | ||||
0.0261710 | + | 0.999657i | \(0.491669\pi\) | |||||||
\(140\) | 0.956374 | 0.0808284 | ||||||||
\(141\) | −6.38880 | −0.538034 | ||||||||
\(142\) | −7.77380 | −0.652362 | ||||||||
\(143\) | 1.02684 | 0.0858690 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −3.19986 | −0.265734 | ||||||||
\(146\) | 0.861474 | 0.0712961 | ||||||||
\(147\) | 5.35623 | 0.441775 | ||||||||
\(148\) | −1.64876 | −0.135527 | ||||||||
\(149\) | −1.52056 | −0.124569 | −0.0622847 | − | 0.998058i | \(-0.519839\pi\) | ||||
−0.0622847 | + | 0.998058i | \(0.519839\pi\) | |||||||
\(150\) | −4.44356 | −0.362815 | ||||||||
\(151\) | −9.36299 | −0.761949 | −0.380974 | − | 0.924586i | \(-0.624411\pi\) | ||||
−0.380974 | + | 0.924586i | \(0.624411\pi\) | |||||||
\(152\) | −1.02435 | −0.0830861 | ||||||||
\(153\) | −3.94118 | −0.318626 | ||||||||
\(154\) | 1.28209 | 0.103314 | ||||||||
\(155\) | 3.81823 | 0.306687 | ||||||||
\(156\) | −1.02684 | −0.0822133 | ||||||||
\(157\) | 15.0841 | 1.20384 | 0.601922 | − | 0.798555i | \(-0.294402\pi\) | ||||
0.601922 | + | 0.798555i | \(0.294402\pi\) | |||||||
\(158\) | 3.78432 | 0.301064 | ||||||||
\(159\) | 0.306449 | 0.0243029 | ||||||||
\(160\) | 0.745947 | 0.0589723 | ||||||||
\(161\) | −3.55748 | −0.280369 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 23.0806 | 1.80781 | 0.903906 | − | 0.427731i | \(-0.140687\pi\) | ||||
0.903906 | + | 0.427731i | \(0.140687\pi\) | |||||||
\(164\) | 5.94995 | 0.464613 | ||||||||
\(165\) | 0.745947 | 0.0580719 | ||||||||
\(166\) | 10.9806 | 0.852262 | ||||||||
\(167\) | 16.6333 | 1.28712 | 0.643561 | − | 0.765395i | \(-0.277456\pi\) | ||||
0.643561 | + | 0.765395i | \(0.277456\pi\) | |||||||
\(168\) | −1.28209 | −0.0989157 | ||||||||
\(169\) | −11.9456 | −0.918892 | ||||||||
\(170\) | −2.93991 | −0.225481 | ||||||||
\(171\) | 1.02435 | 0.0783343 | ||||||||
\(172\) | 3.78917 | 0.288921 | ||||||||
\(173\) | −19.1561 | −1.45641 | −0.728205 | − | 0.685360i | \(-0.759645\pi\) | ||||
−0.728205 | + | 0.685360i | \(0.759645\pi\) | |||||||
\(174\) | 4.28967 | 0.325199 | ||||||||
\(175\) | 5.69707 | 0.430658 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 6.02604 | 0.452945 | ||||||||
\(178\) | −9.92651 | −0.744024 | ||||||||
\(179\) | 15.0366 | 1.12389 | 0.561943 | − | 0.827176i | \(-0.310054\pi\) | ||||
0.561943 | + | 0.827176i | \(0.310054\pi\) | |||||||
\(180\) | −0.745947 | −0.0555996 | ||||||||
\(181\) | 3.34104 | 0.248337 | 0.124169 | − | 0.992261i | \(-0.460374\pi\) | ||||
0.124169 | + | 0.992261i | \(0.460374\pi\) | |||||||
\(182\) | 1.31651 | 0.0975862 | ||||||||
\(183\) | 1.00000 | 0.0739221 | ||||||||
\(184\) | −2.77474 | −0.204557 | ||||||||
\(185\) | 1.22989 | 0.0904232 | ||||||||
\(186\) | −5.11863 | −0.375316 | ||||||||
\(187\) | −3.94118 | −0.288208 | ||||||||
\(188\) | 6.38880 | 0.465951 | ||||||||
\(189\) | 1.28209 | 0.0932586 | ||||||||
\(190\) | 0.764114 | 0.0554347 | ||||||||
\(191\) | 23.6842 | 1.71373 | 0.856865 | − | 0.515541i | \(-0.172409\pi\) | ||||
0.856865 | + | 0.515541i | \(0.172409\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −25.2226 | −1.81556 | −0.907781 | − | 0.419444i | \(-0.862225\pi\) | ||||
−0.907781 | + | 0.419444i | \(0.862225\pi\) | |||||||
\(194\) | −3.30314 | −0.237152 | ||||||||
\(195\) | 0.765971 | 0.0548523 | ||||||||
\(196\) | −5.35623 | −0.382588 | ||||||||
\(197\) | −19.7129 | −1.40449 | −0.702243 | − | 0.711937i | \(-0.747818\pi\) | ||||
−0.702243 | + | 0.711937i | \(0.747818\pi\) | |||||||
\(198\) | −1.00000 | −0.0710669 | ||||||||
\(199\) | −13.3077 | −0.943361 | −0.471681 | − | 0.881770i | \(-0.656352\pi\) | ||||
−0.471681 | + | 0.881770i | \(0.656352\pi\) | |||||||
\(200\) | 4.44356 | 0.314207 | ||||||||
\(201\) | 9.15286 | 0.645593 | ||||||||
\(202\) | −6.19552 | −0.435915 | ||||||||
\(203\) | −5.49976 | −0.386007 | ||||||||
\(204\) | 3.94118 | 0.275938 | ||||||||
\(205\) | −4.43835 | −0.309988 | ||||||||
\(206\) | 1.68344 | 0.117291 | ||||||||
\(207\) | 2.77474 | 0.192858 | ||||||||
\(208\) | 1.02684 | 0.0711988 | ||||||||
\(209\) | 1.02435 | 0.0708561 | ||||||||
\(210\) | 0.956374 | 0.0659961 | ||||||||
\(211\) | 13.9516 | 0.960468 | 0.480234 | − | 0.877140i | \(-0.340552\pi\) | ||||
0.480234 | + | 0.877140i | \(0.340552\pi\) | |||||||
\(212\) | −0.306449 | −0.0210470 | ||||||||
\(213\) | −7.77380 | −0.532652 | ||||||||
\(214\) | 16.8399 | 1.15115 | ||||||||
\(215\) | −2.82652 | −0.192767 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 6.56256 | 0.445496 | ||||||||
\(218\) | 1.16123 | 0.0786487 | ||||||||
\(219\) | 0.861474 | 0.0582130 | ||||||||
\(220\) | −0.745947 | −0.0502917 | ||||||||
\(221\) | −4.04698 | −0.272229 | ||||||||
\(222\) | −1.64876 | −0.110658 | ||||||||
\(223\) | 2.90024 | 0.194214 | 0.0971071 | − | 0.995274i | \(-0.469041\pi\) | ||||
0.0971071 | + | 0.995274i | \(0.469041\pi\) | |||||||
\(224\) | 1.28209 | 0.0856635 | ||||||||
\(225\) | −4.44356 | −0.296238 | ||||||||
\(226\) | −14.0142 | −0.932208 | ||||||||
\(227\) | 8.77009 | 0.582091 | 0.291046 | − | 0.956709i | \(-0.405997\pi\) | ||||
0.291046 | + | 0.956709i | \(0.405997\pi\) | |||||||
\(228\) | −1.02435 | −0.0678395 | ||||||||
\(229\) | 12.6487 | 0.835850 | 0.417925 | − | 0.908481i | \(-0.362757\pi\) | ||||
0.417925 | + | 0.908481i | \(0.362757\pi\) | |||||||
\(230\) | 2.06981 | 0.136479 | ||||||||
\(231\) | 1.28209 | 0.0843556 | ||||||||
\(232\) | −4.28967 | −0.281630 | ||||||||
\(233\) | −6.13121 | −0.401669 | −0.200834 | − | 0.979625i | \(-0.564365\pi\) | ||||
−0.200834 | + | 0.979625i | \(0.564365\pi\) | |||||||
\(234\) | −1.02684 | −0.0671269 | ||||||||
\(235\) | −4.76571 | −0.310881 | ||||||||
\(236\) | −6.02604 | −0.392262 | ||||||||
\(237\) | 3.78432 | 0.245818 | ||||||||
\(238\) | −5.05297 | −0.327535 | ||||||||
\(239\) | 17.9825 | 1.16319 | 0.581597 | − | 0.813477i | \(-0.302428\pi\) | ||||
0.581597 | + | 0.813477i | \(0.302428\pi\) | |||||||
\(240\) | 0.745947 | 0.0481507 | ||||||||
\(241\) | 29.8941 | 1.92565 | 0.962826 | − | 0.270124i | \(-0.0870647\pi\) | ||||
0.962826 | + | 0.270124i | \(0.0870647\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.00000 | −0.0640184 | ||||||||
\(245\) | 3.99547 | 0.255261 | ||||||||
\(246\) | 5.94995 | 0.379355 | ||||||||
\(247\) | 1.05185 | 0.0669277 | ||||||||
\(248\) | 5.11863 | 0.325033 | ||||||||
\(249\) | 10.9806 | 0.695869 | ||||||||
\(250\) | −7.04440 | −0.445527 | ||||||||
\(251\) | 24.7252 | 1.56064 | 0.780320 | − | 0.625380i | \(-0.215056\pi\) | ||||
0.780320 | + | 0.625380i | \(0.215056\pi\) | |||||||
\(252\) | −1.28209 | −0.0807643 | ||||||||
\(253\) | 2.77474 | 0.174446 | ||||||||
\(254\) | −19.0865 | −1.19760 | ||||||||
\(255\) | −2.93991 | −0.184105 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 26.9857 | 1.68332 | 0.841660 | − | 0.540008i | \(-0.181579\pi\) | ||||
0.841660 | + | 0.540008i | \(0.181579\pi\) | |||||||
\(258\) | 3.78917 | 0.235903 | ||||||||
\(259\) | 2.11387 | 0.131349 | ||||||||
\(260\) | −0.765971 | −0.0475035 | ||||||||
\(261\) | 4.28967 | 0.265524 | ||||||||
\(262\) | −17.6945 | −1.09317 | ||||||||
\(263\) | 5.78655 | 0.356814 | 0.178407 | − | 0.983957i | \(-0.442906\pi\) | ||||
0.178407 | + | 0.983957i | \(0.442906\pi\) | |||||||
\(264\) | 1.00000 | 0.0615457 | ||||||||
\(265\) | 0.228594 | 0.0140424 | ||||||||
\(266\) | 1.31332 | 0.0805247 | ||||||||
\(267\) | −9.92651 | −0.607493 | ||||||||
\(268\) | −9.15286 | −0.559100 | ||||||||
\(269\) | 11.6113 | 0.707952 | 0.353976 | − | 0.935254i | \(-0.384829\pi\) | ||||
0.353976 | + | 0.935254i | \(0.384829\pi\) | |||||||
\(270\) | −0.745947 | −0.0453969 | ||||||||
\(271\) | −25.1036 | −1.52494 | −0.762468 | − | 0.647025i | \(-0.776013\pi\) | ||||
−0.762468 | + | 0.647025i | \(0.776013\pi\) | |||||||
\(272\) | −3.94118 | −0.238969 | ||||||||
\(273\) | 1.31651 | 0.0796788 | ||||||||
\(274\) | 15.6557 | 0.945794 | ||||||||
\(275\) | −4.44356 | −0.267957 | ||||||||
\(276\) | −2.77474 | −0.167020 | ||||||||
\(277\) | 2.63951 | 0.158593 | 0.0792964 | − | 0.996851i | \(-0.474733\pi\) | ||||
0.0792964 | + | 0.996851i | \(0.474733\pi\) | |||||||
\(278\) | −0.617102 | −0.0370113 | ||||||||
\(279\) | −5.11863 | −0.306444 | ||||||||
\(280\) | −0.956374 | −0.0571543 | ||||||||
\(281\) | 0.322393 | 0.0192324 | 0.00961618 | − | 0.999954i | \(-0.496939\pi\) | ||||
0.00961618 | + | 0.999954i | \(0.496939\pi\) | |||||||
\(282\) | 6.38880 | 0.380448 | ||||||||
\(283\) | −14.2970 | −0.849867 | −0.424933 | − | 0.905225i | \(-0.639702\pi\) | ||||
−0.424933 | + | 0.905225i | \(0.639702\pi\) | |||||||
\(284\) | 7.77380 | 0.461290 | ||||||||
\(285\) | 0.764114 | 0.0452622 | ||||||||
\(286\) | −1.02684 | −0.0607185 | ||||||||
\(287\) | −7.62840 | −0.450290 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −1.46708 | −0.0862988 | ||||||||
\(290\) | 3.19986 | 0.187903 | ||||||||
\(291\) | −3.30314 | −0.193634 | ||||||||
\(292\) | −0.861474 | −0.0504140 | ||||||||
\(293\) | 7.05756 | 0.412307 | 0.206153 | − | 0.978520i | \(-0.433905\pi\) | ||||
0.206153 | + | 0.978520i | \(0.433905\pi\) | |||||||
\(294\) | −5.35623 | −0.312382 | ||||||||
\(295\) | 4.49511 | 0.261715 | ||||||||
\(296\) | 1.64876 | 0.0958322 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 1.52056 | 0.0880838 | ||||||||
\(299\) | 2.84922 | 0.164775 | ||||||||
\(300\) | 4.44356 | 0.256549 | ||||||||
\(301\) | −4.85807 | −0.280014 | ||||||||
\(302\) | 9.36299 | 0.538779 | ||||||||
\(303\) | −6.19552 | −0.355923 | ||||||||
\(304\) | 1.02435 | 0.0587508 | ||||||||
\(305\) | 0.745947 | 0.0427128 | ||||||||
\(306\) | 3.94118 | 0.225302 | ||||||||
\(307\) | −2.22142 | −0.126783 | −0.0633916 | − | 0.997989i | \(-0.520192\pi\) | ||||
−0.0633916 | + | 0.997989i | \(0.520192\pi\) | |||||||
\(308\) | −1.28209 | −0.0730541 | ||||||||
\(309\) | 1.68344 | 0.0957677 | ||||||||
\(310\) | −3.81823 | −0.216861 | ||||||||
\(311\) | 23.8939 | 1.35490 | 0.677451 | − | 0.735568i | \(-0.263085\pi\) | ||||
0.677451 | + | 0.735568i | \(0.263085\pi\) | |||||||
\(312\) | 1.02684 | 0.0581336 | ||||||||
\(313\) | 25.0026 | 1.41323 | 0.706616 | − | 0.707597i | \(-0.250221\pi\) | ||||
0.706616 | + | 0.707597i | \(0.250221\pi\) | |||||||
\(314\) | −15.0841 | −0.851247 | ||||||||
\(315\) | 0.956374 | 0.0538856 | ||||||||
\(316\) | −3.78432 | −0.212884 | ||||||||
\(317\) | −1.61195 | −0.0905364 | −0.0452682 | − | 0.998975i | \(-0.514414\pi\) | ||||
−0.0452682 | + | 0.998975i | \(0.514414\pi\) | |||||||
\(318\) | −0.306449 | −0.0171848 | ||||||||
\(319\) | 4.28967 | 0.240175 | ||||||||
\(320\) | −0.745947 | −0.0416997 | ||||||||
\(321\) | 16.8399 | 0.939914 | ||||||||
\(322\) | 3.55748 | 0.198251 | ||||||||
\(323\) | −4.03717 | −0.224634 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −4.56284 | −0.253101 | ||||||||
\(326\) | −23.0806 | −1.27832 | ||||||||
\(327\) | 1.16123 | 0.0642164 | ||||||||
\(328\) | −5.94995 | −0.328531 | ||||||||
\(329\) | −8.19105 | −0.451587 | ||||||||
\(330\) | −0.745947 | −0.0410630 | ||||||||
\(331\) | 30.4671 | 1.67462 | 0.837312 | − | 0.546725i | \(-0.184126\pi\) | ||||
0.837312 | + | 0.546725i | \(0.184126\pi\) | |||||||
\(332\) | −10.9806 | −0.602640 | ||||||||
\(333\) | −1.64876 | −0.0903515 | ||||||||
\(334\) | −16.6333 | −0.910133 | ||||||||
\(335\) | 6.82755 | 0.373029 | ||||||||
\(336\) | 1.28209 | 0.0699440 | ||||||||
\(337\) | −0.665639 | −0.0362597 | −0.0181298 | − | 0.999836i | \(-0.505771\pi\) | ||||
−0.0181298 | + | 0.999836i | \(0.505771\pi\) | |||||||
\(338\) | 11.9456 | 0.649755 | ||||||||
\(339\) | −14.0142 | −0.761145 | ||||||||
\(340\) | 2.93991 | 0.159439 | ||||||||
\(341\) | −5.11863 | −0.277189 | ||||||||
\(342\) | −1.02435 | −0.0553907 | ||||||||
\(343\) | 15.8419 | 0.855380 | ||||||||
\(344\) | −3.78917 | −0.204298 | ||||||||
\(345\) | 2.06981 | 0.111435 | ||||||||
\(346\) | 19.1561 | 1.02984 | ||||||||
\(347\) | 12.6629 | 0.679781 | 0.339891 | − | 0.940465i | \(-0.389610\pi\) | ||||
0.339891 | + | 0.940465i | \(0.389610\pi\) | |||||||
\(348\) | −4.28967 | −0.229950 | ||||||||
\(349\) | 8.77444 | 0.469685 | 0.234843 | − | 0.972033i | \(-0.424543\pi\) | ||||
0.234843 | + | 0.972033i | \(0.424543\pi\) | |||||||
\(350\) | −5.69707 | −0.304521 | ||||||||
\(351\) | −1.02684 | −0.0548089 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 15.1214 | 0.804834 | 0.402417 | − | 0.915457i | \(-0.368170\pi\) | ||||
0.402417 | + | 0.915457i | \(0.368170\pi\) | |||||||
\(354\) | −6.02604 | −0.320281 | ||||||||
\(355\) | −5.79884 | −0.307770 | ||||||||
\(356\) | 9.92651 | 0.526104 | ||||||||
\(357\) | −5.05297 | −0.267431 | ||||||||
\(358\) | −15.0366 | −0.794708 | ||||||||
\(359\) | 32.1499 | 1.69681 | 0.848404 | − | 0.529349i | \(-0.177564\pi\) | ||||
0.848404 | + | 0.529349i | \(0.177564\pi\) | |||||||
\(360\) | 0.745947 | 0.0393149 | ||||||||
\(361\) | −17.9507 | −0.944774 | ||||||||
\(362\) | −3.34104 | −0.175601 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −1.31651 | −0.0690039 | ||||||||
\(365\) | 0.642614 | 0.0336360 | ||||||||
\(366\) | −1.00000 | −0.0522708 | ||||||||
\(367\) | 22.0197 | 1.14942 | 0.574709 | − | 0.818358i | \(-0.305115\pi\) | ||||
0.574709 | + | 0.818358i | \(0.305115\pi\) | |||||||
\(368\) | 2.77474 | 0.144643 | ||||||||
\(369\) | 5.94995 | 0.309742 | ||||||||
\(370\) | −1.22989 | −0.0639388 | ||||||||
\(371\) | 0.392896 | 0.0203981 | ||||||||
\(372\) | 5.11863 | 0.265388 | ||||||||
\(373\) | −37.3428 | −1.93354 | −0.966769 | − | 0.255653i | \(-0.917709\pi\) | ||||
−0.966769 | + | 0.255653i | \(0.917709\pi\) | |||||||
\(374\) | 3.94118 | 0.203794 | ||||||||
\(375\) | −7.04440 | −0.363771 | ||||||||
\(376\) | −6.38880 | −0.329477 | ||||||||
\(377\) | 4.40482 | 0.226860 | ||||||||
\(378\) | −1.28209 | −0.0659438 | ||||||||
\(379\) | −19.1507 | −0.983706 | −0.491853 | − | 0.870678i | \(-0.663680\pi\) | ||||
−0.491853 | + | 0.870678i | \(0.663680\pi\) | |||||||
\(380\) | −0.764114 | −0.0391982 | ||||||||
\(381\) | −19.0865 | −0.977833 | ||||||||
\(382\) | −23.6842 | −1.21179 | ||||||||
\(383\) | 7.54042 | 0.385298 | 0.192649 | − | 0.981268i | \(-0.438292\pi\) | ||||
0.192649 | + | 0.981268i | \(0.438292\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0.956374 | 0.0487414 | ||||||||
\(386\) | 25.2226 | 1.28380 | ||||||||
\(387\) | 3.78917 | 0.192614 | ||||||||
\(388\) | 3.30314 | 0.167692 | ||||||||
\(389\) | −2.78201 | −0.141053 | −0.0705267 | − | 0.997510i | \(-0.522468\pi\) | ||||
−0.0705267 | + | 0.997510i | \(0.522468\pi\) | |||||||
\(390\) | −0.765971 | −0.0387864 | ||||||||
\(391\) | −10.9358 | −0.553045 | ||||||||
\(392\) | 5.35623 | 0.270531 | ||||||||
\(393\) | −17.6945 | −0.892567 | ||||||||
\(394\) | 19.7129 | 0.993122 | ||||||||
\(395\) | 2.82290 | 0.142036 | ||||||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | −33.5450 | −1.68357 | −0.841787 | − | 0.539810i | \(-0.818496\pi\) | ||||
−0.841787 | + | 0.539810i | \(0.818496\pi\) | |||||||
\(398\) | 13.3077 | 0.667057 | ||||||||
\(399\) | 1.31332 | 0.0657482 | ||||||||
\(400\) | −4.44356 | −0.222178 | ||||||||
\(401\) | 2.67571 | 0.133619 | 0.0668093 | − | 0.997766i | \(-0.478718\pi\) | ||||
0.0668093 | + | 0.997766i | \(0.478718\pi\) | |||||||
\(402\) | −9.15286 | −0.456503 | ||||||||
\(403\) | −5.25603 | −0.261822 | ||||||||
\(404\) | 6.19552 | 0.308239 | ||||||||
\(405\) | −0.745947 | −0.0370664 | ||||||||
\(406\) | 5.49976 | 0.272948 | ||||||||
\(407\) | −1.64876 | −0.0817260 | ||||||||
\(408\) | −3.94118 | −0.195118 | ||||||||
\(409\) | −0.271591 | −0.0134293 | −0.00671465 | − | 0.999977i | \(-0.502137\pi\) | ||||
−0.00671465 | + | 0.999977i | \(0.502137\pi\) | |||||||
\(410\) | 4.43835 | 0.219194 | ||||||||
\(411\) | 15.6557 | 0.772237 | ||||||||
\(412\) | −1.68344 | −0.0829373 | ||||||||
\(413\) | 7.72595 | 0.380169 | ||||||||
\(414\) | −2.77474 | −0.136371 | ||||||||
\(415\) | 8.19097 | 0.402079 | ||||||||
\(416\) | −1.02684 | −0.0503451 | ||||||||
\(417\) | −0.617102 | −0.0302196 | ||||||||
\(418\) | −1.02435 | −0.0501028 | ||||||||
\(419\) | −4.66064 | −0.227687 | −0.113844 | − | 0.993499i | \(-0.536316\pi\) | ||||
−0.113844 | + | 0.993499i | \(0.536316\pi\) | |||||||
\(420\) | −0.956374 | −0.0466663 | ||||||||
\(421\) | 31.9442 | 1.55686 | 0.778432 | − | 0.627729i | \(-0.216016\pi\) | ||||
0.778432 | + | 0.627729i | \(0.216016\pi\) | |||||||
\(422\) | −13.9516 | −0.679153 | ||||||||
\(423\) | 6.38880 | 0.310634 | ||||||||
\(424\) | 0.306449 | 0.0148825 | ||||||||
\(425\) | 17.5129 | 0.849500 | ||||||||
\(426\) | 7.77380 | 0.376642 | ||||||||
\(427\) | 1.28209 | 0.0620449 | ||||||||
\(428\) | −16.8399 | −0.813989 | ||||||||
\(429\) | −1.02684 | −0.0495765 | ||||||||
\(430\) | 2.82652 | 0.136307 | ||||||||
\(431\) | 30.6753 | 1.47758 | 0.738789 | − | 0.673936i | \(-0.235398\pi\) | ||||
0.738789 | + | 0.673936i | \(0.235398\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 24.0788 | 1.15715 | 0.578577 | − | 0.815628i | \(-0.303608\pi\) | ||||
0.578577 | + | 0.815628i | \(0.303608\pi\) | |||||||
\(434\) | −6.56256 | −0.315013 | ||||||||
\(435\) | 3.19986 | 0.153422 | ||||||||
\(436\) | −1.16123 | −0.0556130 | ||||||||
\(437\) | 2.84232 | 0.135967 | ||||||||
\(438\) | −0.861474 | −0.0411628 | ||||||||
\(439\) | 8.48940 | 0.405177 | 0.202589 | − | 0.979264i | \(-0.435065\pi\) | ||||
0.202589 | + | 0.979264i | \(0.435065\pi\) | |||||||
\(440\) | 0.745947 | 0.0355616 | ||||||||
\(441\) | −5.35623 | −0.255059 | ||||||||
\(442\) | 4.04698 | 0.192495 | ||||||||
\(443\) | 32.7393 | 1.55549 | 0.777745 | − | 0.628580i | \(-0.216364\pi\) | ||||
0.777745 | + | 0.628580i | \(0.216364\pi\) | |||||||
\(444\) | 1.64876 | 0.0782467 | ||||||||
\(445\) | −7.40466 | −0.351014 | ||||||||
\(446\) | −2.90024 | −0.137330 | ||||||||
\(447\) | 1.52056 | 0.0719201 | ||||||||
\(448\) | −1.28209 | −0.0605733 | ||||||||
\(449\) | −26.1057 | −1.23200 | −0.616002 | − | 0.787745i | \(-0.711249\pi\) | ||||
−0.616002 | + | 0.787745i | \(0.711249\pi\) | |||||||
\(450\) | 4.44356 | 0.209472 | ||||||||
\(451\) | 5.94995 | 0.280172 | ||||||||
\(452\) | 14.0142 | 0.659171 | ||||||||
\(453\) | 9.36299 | 0.439911 | ||||||||
\(454\) | −8.77009 | −0.411601 | ||||||||
\(455\) | 0.982047 | 0.0460391 | ||||||||
\(456\) | 1.02435 | 0.0479698 | ||||||||
\(457\) | 15.2573 | 0.713708 | 0.356854 | − | 0.934160i | \(-0.383849\pi\) | ||||
0.356854 | + | 0.934160i | \(0.383849\pi\) | |||||||
\(458\) | −12.6487 | −0.591036 | ||||||||
\(459\) | 3.94118 | 0.183959 | ||||||||
\(460\) | −2.06981 | −0.0965054 | ||||||||
\(461\) | 29.7034 | 1.38343 | 0.691713 | − | 0.722173i | \(-0.256856\pi\) | ||||
0.691713 | + | 0.722173i | \(0.256856\pi\) | |||||||
\(462\) | −1.28209 | −0.0596484 | ||||||||
\(463\) | −7.74787 | −0.360074 | −0.180037 | − | 0.983660i | \(-0.557622\pi\) | ||||
−0.180037 | + | 0.983660i | \(0.557622\pi\) | |||||||
\(464\) | 4.28967 | 0.199143 | ||||||||
\(465\) | −3.81823 | −0.177066 | ||||||||
\(466\) | 6.13121 | 0.284023 | ||||||||
\(467\) | −18.7407 | −0.867215 | −0.433607 | − | 0.901102i | \(-0.642760\pi\) | ||||
−0.433607 | + | 0.901102i | \(0.642760\pi\) | |||||||
\(468\) | 1.02684 | 0.0474659 | ||||||||
\(469\) | 11.7348 | 0.541864 | ||||||||
\(470\) | 4.76571 | 0.219826 | ||||||||
\(471\) | −15.0841 | −0.695040 | ||||||||
\(472\) | 6.02604 | 0.277371 | ||||||||
\(473\) | 3.78917 | 0.174226 | ||||||||
\(474\) | −3.78432 | −0.173819 | ||||||||
\(475\) | −4.55178 | −0.208850 | ||||||||
\(476\) | 5.05297 | 0.231602 | ||||||||
\(477\) | −0.306449 | −0.0140313 | ||||||||
\(478\) | −17.9825 | −0.822502 | ||||||||
\(479\) | −8.02669 | −0.366749 | −0.183374 | − | 0.983043i | \(-0.558702\pi\) | ||||
−0.183374 | + | 0.983043i | \(0.558702\pi\) | |||||||
\(480\) | −0.745947 | −0.0340477 | ||||||||
\(481\) | −1.69302 | −0.0771950 | ||||||||
\(482\) | −29.8941 | −1.36164 | ||||||||
\(483\) | 3.55748 | 0.161871 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −2.46397 | −0.111883 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 6.25479 | 0.283431 | 0.141716 | − | 0.989907i | \(-0.454738\pi\) | ||||
0.141716 | + | 0.989907i | \(0.454738\pi\) | |||||||
\(488\) | 1.00000 | 0.0452679 | ||||||||
\(489\) | −23.0806 | −1.04374 | ||||||||
\(490\) | −3.99547 | −0.180497 | ||||||||
\(491\) | −4.48630 | −0.202464 | −0.101232 | − | 0.994863i | \(-0.532278\pi\) | ||||
−0.101232 | + | 0.994863i | \(0.532278\pi\) | |||||||
\(492\) | −5.94995 | −0.268245 | ||||||||
\(493\) | −16.9064 | −0.761424 | ||||||||
\(494\) | −1.05185 | −0.0473250 | ||||||||
\(495\) | −0.745947 | −0.0335278 | ||||||||
\(496\) | −5.11863 | −0.229833 | ||||||||
\(497\) | −9.96674 | −0.447069 | ||||||||
\(498\) | −10.9806 | −0.492054 | ||||||||
\(499\) | 28.6832 | 1.28404 | 0.642018 | − | 0.766689i | \(-0.278097\pi\) | ||||
0.642018 | + | 0.766689i | \(0.278097\pi\) | |||||||
\(500\) | 7.04440 | 0.315035 | ||||||||
\(501\) | −16.6333 | −0.743120 | ||||||||
\(502\) | −24.7252 | −1.10354 | ||||||||
\(503\) | 42.1944 | 1.88136 | 0.940678 | − | 0.339299i | \(-0.110190\pi\) | ||||
0.940678 | + | 0.339299i | \(0.110190\pi\) | |||||||
\(504\) | 1.28209 | 0.0571090 | ||||||||
\(505\) | −4.62153 | −0.205655 | ||||||||
\(506\) | −2.77474 | −0.123352 | ||||||||
\(507\) | 11.9456 | 0.530522 | ||||||||
\(508\) | 19.0865 | 0.846828 | ||||||||
\(509\) | 39.9620 | 1.77128 | 0.885642 | − | 0.464369i | \(-0.153719\pi\) | ||||
0.885642 | + | 0.464369i | \(0.153719\pi\) | |||||||
\(510\) | 2.93991 | 0.130182 | ||||||||
\(511\) | 1.10449 | 0.0488598 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.02435 | −0.0452264 | ||||||||
\(514\) | −26.9857 | −1.19029 | ||||||||
\(515\) | 1.25576 | 0.0553354 | ||||||||
\(516\) | −3.78917 | −0.166809 | ||||||||
\(517\) | 6.38880 | 0.280979 | ||||||||
\(518\) | −2.11387 | −0.0928779 | ||||||||
\(519\) | 19.1561 | 0.840858 | ||||||||
\(520\) | 0.765971 | 0.0335901 | ||||||||
\(521\) | −23.4648 | −1.02801 | −0.514007 | − | 0.857786i | \(-0.671839\pi\) | ||||
−0.514007 | + | 0.857786i | \(0.671839\pi\) | |||||||
\(522\) | −4.28967 | −0.187754 | ||||||||
\(523\) | 6.63988 | 0.290342 | 0.145171 | − | 0.989407i | \(-0.453627\pi\) | ||||
0.145171 | + | 0.989407i | \(0.453627\pi\) | |||||||
\(524\) | 17.6945 | 0.772986 | ||||||||
\(525\) | −5.69707 | −0.248640 | ||||||||
\(526\) | −5.78655 | −0.252306 | ||||||||
\(527\) | 20.1734 | 0.878769 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | −15.3008 | −0.665253 | ||||||||
\(530\) | −0.228594 | −0.00992951 | ||||||||
\(531\) | −6.02604 | −0.261508 | ||||||||
\(532\) | −1.31332 | −0.0569396 | ||||||||
\(533\) | 6.10967 | 0.264639 | ||||||||
\(534\) | 9.92651 | 0.429562 | ||||||||
\(535\) | 12.5617 | 0.543090 | ||||||||
\(536\) | 9.15286 | 0.395343 | ||||||||
\(537\) | −15.0366 | −0.648876 | ||||||||
\(538\) | −11.6113 | −0.500598 | ||||||||
\(539\) | −5.35623 | −0.230709 | ||||||||
\(540\) | 0.745947 | 0.0321005 | ||||||||
\(541\) | 9.23968 | 0.397245 | 0.198622 | − | 0.980076i | \(-0.436353\pi\) | ||||
0.198622 | + | 0.980076i | \(0.436353\pi\) | |||||||
\(542\) | 25.1036 | 1.07829 | ||||||||
\(543\) | −3.34104 | −0.143378 | ||||||||
\(544\) | 3.94118 | 0.168977 | ||||||||
\(545\) | 0.866219 | 0.0371048 | ||||||||
\(546\) | −1.31651 | −0.0563414 | ||||||||
\(547\) | −9.44136 | −0.403684 | −0.201842 | − | 0.979418i | \(-0.564693\pi\) | ||||
−0.201842 | + | 0.979418i | \(0.564693\pi\) | |||||||
\(548\) | −15.6557 | −0.668777 | ||||||||
\(549\) | −1.00000 | −0.0426790 | ||||||||
\(550\) | 4.44356 | 0.189474 | ||||||||
\(551\) | 4.39414 | 0.187197 | ||||||||
\(552\) | 2.77474 | 0.118101 | ||||||||
\(553\) | 4.85185 | 0.206322 | ||||||||
\(554\) | −2.63951 | −0.112142 | ||||||||
\(555\) | −1.22989 | −0.0522058 | ||||||||
\(556\) | 0.617102 | 0.0261710 | ||||||||
\(557\) | −29.5229 | −1.25092 | −0.625462 | − | 0.780255i | \(-0.715089\pi\) | ||||
−0.625462 | + | 0.780255i | \(0.715089\pi\) | |||||||
\(558\) | 5.11863 | 0.216689 | ||||||||
\(559\) | 3.89088 | 0.164567 | ||||||||
\(560\) | 0.956374 | 0.0404142 | ||||||||
\(561\) | 3.94118 | 0.166397 | ||||||||
\(562\) | −0.322393 | −0.0135993 | ||||||||
\(563\) | 27.9114 | 1.17632 | 0.588162 | − | 0.808743i | \(-0.299852\pi\) | ||||
0.588162 | + | 0.808743i | \(0.299852\pi\) | |||||||
\(564\) | −6.38880 | −0.269017 | ||||||||
\(565\) | −10.4538 | −0.439796 | ||||||||
\(566\) | 14.2970 | 0.600947 | ||||||||
\(567\) | −1.28209 | −0.0538429 | ||||||||
\(568\) | −7.77380 | −0.326181 | ||||||||
\(569\) | −33.2074 | −1.39213 | −0.696063 | − | 0.717980i | \(-0.745067\pi\) | ||||
−0.696063 | + | 0.717980i | \(0.745067\pi\) | |||||||
\(570\) | −0.764114 | −0.0320052 | ||||||||
\(571\) | 40.3175 | 1.68724 | 0.843618 | − | 0.536943i | \(-0.180421\pi\) | ||||
0.843618 | + | 0.536943i | \(0.180421\pi\) | |||||||
\(572\) | 1.02684 | 0.0429345 | ||||||||
\(573\) | −23.6842 | −0.989423 | ||||||||
\(574\) | 7.62840 | 0.318403 | ||||||||
\(575\) | −12.3297 | −0.514186 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −6.24593 | −0.260022 | −0.130011 | − | 0.991513i | \(-0.541501\pi\) | ||||
−0.130011 | + | 0.991513i | \(0.541501\pi\) | |||||||
\(578\) | 1.46708 | 0.0610225 | ||||||||
\(579\) | 25.2226 | 1.04822 | ||||||||
\(580\) | −3.19986 | −0.132867 | ||||||||
\(581\) | 14.0782 | 0.584062 | ||||||||
\(582\) | 3.30314 | 0.136920 | ||||||||
\(583\) | −0.306449 | −0.0126918 | ||||||||
\(584\) | 0.861474 | 0.0356480 | ||||||||
\(585\) | −0.765971 | −0.0316690 | ||||||||
\(586\) | −7.05756 | −0.291545 | ||||||||
\(587\) | 10.0478 | 0.414718 | 0.207359 | − | 0.978265i | \(-0.433513\pi\) | ||||
0.207359 | + | 0.978265i | \(0.433513\pi\) | |||||||
\(588\) | 5.35623 | 0.220887 | ||||||||
\(589\) | −5.24329 | −0.216046 | ||||||||
\(590\) | −4.49511 | −0.185061 | ||||||||
\(591\) | 19.7129 | 0.810881 | ||||||||
\(592\) | −1.64876 | −0.0677636 | ||||||||
\(593\) | −13.6042 | −0.558656 | −0.279328 | − | 0.960196i | \(-0.590112\pi\) | ||||
−0.279328 | + | 0.960196i | \(0.590112\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | −3.76925 | −0.154524 | ||||||||
\(596\) | −1.52056 | −0.0622847 | ||||||||
\(597\) | 13.3077 | 0.544650 | ||||||||
\(598\) | −2.84922 | −0.116513 | ||||||||
\(599\) | −19.2922 | −0.788258 | −0.394129 | − | 0.919055i | \(-0.628954\pi\) | ||||
−0.394129 | + | 0.919055i | \(0.628954\pi\) | |||||||
\(600\) | −4.44356 | −0.181408 | ||||||||
\(601\) | 39.0394 | 1.59245 | 0.796224 | − | 0.605001i | \(-0.206827\pi\) | ||||
0.796224 | + | 0.605001i | \(0.206827\pi\) | |||||||
\(602\) | 4.85807 | 0.198000 | ||||||||
\(603\) | −9.15286 | −0.372733 | ||||||||
\(604\) | −9.36299 | −0.380974 | ||||||||
\(605\) | −0.745947 | −0.0303271 | ||||||||
\(606\) | 6.19552 | 0.251676 | ||||||||
\(607\) | −41.7549 | −1.69478 | −0.847389 | − | 0.530972i | \(-0.821827\pi\) | ||||
−0.847389 | + | 0.530972i | \(0.821827\pi\) | |||||||
\(608\) | −1.02435 | −0.0415431 | ||||||||
\(609\) | 5.49976 | 0.222861 | ||||||||
\(610\) | −0.745947 | −0.0302025 | ||||||||
\(611\) | 6.56030 | 0.265401 | ||||||||
\(612\) | −3.94118 | −0.159313 | ||||||||
\(613\) | 2.89232 | 0.116820 | 0.0584098 | − | 0.998293i | \(-0.481397\pi\) | ||||
0.0584098 | + | 0.998293i | \(0.481397\pi\) | |||||||
\(614\) | 2.22142 | 0.0896492 | ||||||||
\(615\) | 4.43835 | 0.178972 | ||||||||
\(616\) | 1.28209 | 0.0516570 | ||||||||
\(617\) | 22.2130 | 0.894260 | 0.447130 | − | 0.894469i | \(-0.352446\pi\) | ||||
0.447130 | + | 0.894469i | \(0.352446\pi\) | |||||||
\(618\) | −1.68344 | −0.0677180 | ||||||||
\(619\) | 25.9433 | 1.04275 | 0.521374 | − | 0.853328i | \(-0.325420\pi\) | ||||
0.521374 | + | 0.853328i | \(0.325420\pi\) | |||||||
\(620\) | 3.81823 | 0.153344 | ||||||||
\(621\) | −2.77474 | −0.111347 | ||||||||
\(622\) | −23.8939 | −0.958060 | ||||||||
\(623\) | −12.7267 | −0.509885 | ||||||||
\(624\) | −1.02684 | −0.0411066 | ||||||||
\(625\) | 16.9631 | 0.678523 | ||||||||
\(626\) | −25.0026 | −0.999307 | ||||||||
\(627\) | −1.02435 | −0.0409088 | ||||||||
\(628\) | 15.0841 | 0.601922 | ||||||||
\(629\) | 6.49806 | 0.259095 | ||||||||
\(630\) | −0.956374 | −0.0381029 | ||||||||
\(631\) | −31.2154 | −1.24267 | −0.621333 | − | 0.783547i | \(-0.713408\pi\) | ||||
−0.621333 | + | 0.783547i | \(0.713408\pi\) | |||||||
\(632\) | 3.78432 | 0.150532 | ||||||||
\(633\) | −13.9516 | −0.554526 | ||||||||
\(634\) | 1.61195 | 0.0640189 | ||||||||
\(635\) | −14.2375 | −0.565000 | ||||||||
\(636\) | 0.306449 | 0.0121515 | ||||||||
\(637\) | −5.50002 | −0.217919 | ||||||||
\(638\) | −4.28967 | −0.169830 | ||||||||
\(639\) | 7.77380 | 0.307527 | ||||||||
\(640\) | 0.745947 | 0.0294862 | ||||||||
\(641\) | −7.75435 | −0.306278 | −0.153139 | − | 0.988205i | \(-0.548938\pi\) | ||||
−0.153139 | + | 0.988205i | \(0.548938\pi\) | |||||||
\(642\) | −16.8399 | −0.664620 | ||||||||
\(643\) | −33.1226 | −1.30623 | −0.653114 | − | 0.757260i | \(-0.726538\pi\) | ||||
−0.653114 | + | 0.757260i | \(0.726538\pi\) | |||||||
\(644\) | −3.55748 | −0.140184 | ||||||||
\(645\) | 2.82652 | 0.111294 | ||||||||
\(646\) | 4.03717 | 0.158840 | ||||||||
\(647\) | −34.8551 | −1.37030 | −0.685148 | − | 0.728404i | \(-0.740262\pi\) | ||||
−0.685148 | + | 0.728404i | \(0.740262\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −6.02604 | −0.236543 | ||||||||
\(650\) | 4.56284 | 0.178969 | ||||||||
\(651\) | −6.56256 | −0.257207 | ||||||||
\(652\) | 23.0806 | 0.903906 | ||||||||
\(653\) | −41.5559 | −1.62621 | −0.813105 | − | 0.582117i | \(-0.802224\pi\) | ||||
−0.813105 | + | 0.582117i | \(0.802224\pi\) | |||||||
\(654\) | −1.16123 | −0.0454079 | ||||||||
\(655\) | −13.1991 | −0.515733 | ||||||||
\(656\) | 5.94995 | 0.232307 | ||||||||
\(657\) | −0.861474 | −0.0336093 | ||||||||
\(658\) | 8.19105 | 0.319320 | ||||||||
\(659\) | −21.6449 | −0.843165 | −0.421582 | − | 0.906790i | \(-0.638525\pi\) | ||||
−0.421582 | + | 0.906790i | \(0.638525\pi\) | |||||||
\(660\) | 0.745947 | 0.0290360 | ||||||||
\(661\) | 28.8759 | 1.12314 | 0.561570 | − | 0.827429i | \(-0.310197\pi\) | ||||
0.561570 | + | 0.827429i | \(0.310197\pi\) | |||||||
\(662\) | −30.4671 | −1.18414 | ||||||||
\(663\) | 4.04698 | 0.157172 | ||||||||
\(664\) | 10.9806 | 0.426131 | ||||||||
\(665\) | 0.979666 | 0.0379898 | ||||||||
\(666\) | 1.64876 | 0.0638882 | ||||||||
\(667\) | 11.9027 | 0.460875 | ||||||||
\(668\) | 16.6333 | 0.643561 | ||||||||
\(669\) | −2.90024 | −0.112130 | ||||||||
\(670\) | −6.82755 | −0.263771 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | −1.28209 | −0.0494579 | ||||||||
\(673\) | −17.4235 | −0.671626 | −0.335813 | − | 0.941929i | \(-0.609011\pi\) | ||||
−0.335813 | + | 0.941929i | \(0.609011\pi\) | |||||||
\(674\) | 0.665639 | 0.0256395 | ||||||||
\(675\) | 4.44356 | 0.171033 | ||||||||
\(676\) | −11.9456 | −0.459446 | ||||||||
\(677\) | −48.9322 | −1.88062 | −0.940308 | − | 0.340324i | \(-0.889463\pi\) | ||||
−0.940308 | + | 0.340324i | \(0.889463\pi\) | |||||||
\(678\) | 14.0142 | 0.538210 | ||||||||
\(679\) | −4.23494 | −0.162522 | ||||||||
\(680\) | −2.93991 | −0.112741 | ||||||||
\(681\) | −8.77009 | −0.336070 | ||||||||
\(682\) | 5.11863 | 0.196002 | ||||||||
\(683\) | 31.4190 | 1.20221 | 0.601107 | − | 0.799168i | \(-0.294726\pi\) | ||||
0.601107 | + | 0.799168i | \(0.294726\pi\) | |||||||
\(684\) | 1.02435 | 0.0391672 | ||||||||
\(685\) | 11.6783 | 0.446205 | ||||||||
\(686\) | −15.8419 | −0.604845 | ||||||||
\(687\) | −12.6487 | −0.482579 | ||||||||
\(688\) | 3.78917 | 0.144461 | ||||||||
\(689\) | −0.314675 | −0.0119882 | ||||||||
\(690\) | −2.06981 | −0.0787963 | ||||||||
\(691\) | −21.0351 | −0.800215 | −0.400107 | − | 0.916468i | \(-0.631027\pi\) | ||||
−0.400107 | + | 0.916468i | \(0.631027\pi\) | |||||||
\(692\) | −19.1561 | −0.728205 | ||||||||
\(693\) | −1.28209 | −0.0487027 | ||||||||
\(694\) | −12.6629 | −0.480678 | ||||||||
\(695\) | −0.460325 | −0.0174611 | ||||||||
\(696\) | 4.28967 | 0.162599 | ||||||||
\(697\) | −23.4498 | −0.888226 | ||||||||
\(698\) | −8.77444 | −0.332117 | ||||||||
\(699\) | 6.13121 | 0.231904 | ||||||||
\(700\) | 5.69707 | 0.215329 | ||||||||
\(701\) | −1.43256 | −0.0541071 | −0.0270535 | − | 0.999634i | \(-0.508612\pi\) | ||||
−0.0270535 | + | 0.999634i | \(0.508612\pi\) | |||||||
\(702\) | 1.02684 | 0.0387557 | ||||||||
\(703\) | −1.68891 | −0.0636986 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 4.76571 | 0.179487 | ||||||||
\(706\) | −15.1214 | −0.569103 | ||||||||
\(707\) | −7.94324 | −0.298736 | ||||||||
\(708\) | 6.02604 | 0.226473 | ||||||||
\(709\) | 14.8380 | 0.557254 | 0.278627 | − | 0.960399i | \(-0.410121\pi\) | ||||
0.278627 | + | 0.960399i | \(0.410121\pi\) | |||||||
\(710\) | 5.79884 | 0.217627 | ||||||||
\(711\) | −3.78432 | −0.141923 | ||||||||
\(712\) | −9.92651 | −0.372012 | ||||||||
\(713\) | −14.2029 | −0.531902 | ||||||||
\(714\) | 5.05297 | 0.189103 | ||||||||
\(715\) | −0.765971 | −0.0286457 | ||||||||
\(716\) | 15.0366 | 0.561943 | ||||||||
\(717\) | −17.9825 | −0.671570 | ||||||||
\(718\) | −32.1499 | −1.19983 | ||||||||
\(719\) | 33.7422 | 1.25837 | 0.629187 | − | 0.777254i | \(-0.283388\pi\) | ||||
0.629187 | + | 0.777254i | \(0.283388\pi\) | |||||||
\(720\) | −0.745947 | −0.0277998 | ||||||||
\(721\) | 2.15833 | 0.0803805 | ||||||||
\(722\) | 17.9507 | 0.668056 | ||||||||
\(723\) | −29.8941 | −1.11178 | ||||||||
\(724\) | 3.34104 | 0.124169 | ||||||||
\(725\) | −19.0614 | −0.707923 | ||||||||
\(726\) | 1.00000 | 0.0371135 | ||||||||
\(727\) | 27.2283 | 1.00984 | 0.504922 | − | 0.863165i | \(-0.331521\pi\) | ||||
0.504922 | + | 0.863165i | \(0.331521\pi\) | |||||||
\(728\) | 1.31651 | 0.0487931 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.642614 | −0.0237842 | ||||||||
\(731\) | −14.9338 | −0.552346 | ||||||||
\(732\) | 1.00000 | 0.0369611 | ||||||||
\(733\) | 27.1243 | 1.00186 | 0.500930 | − | 0.865488i | \(-0.332992\pi\) | ||||
0.500930 | + | 0.865488i | \(0.332992\pi\) | |||||||
\(734\) | −22.0197 | −0.812762 | ||||||||
\(735\) | −3.99547 | −0.147375 | ||||||||
\(736\) | −2.77474 | −0.102278 | ||||||||
\(737\) | −9.15286 | −0.337150 | ||||||||
\(738\) | −5.94995 | −0.219021 | ||||||||
\(739\) | 28.2274 | 1.03836 | 0.519181 | − | 0.854664i | \(-0.326237\pi\) | ||||
0.519181 | + | 0.854664i | \(0.326237\pi\) | |||||||
\(740\) | 1.22989 | 0.0452116 | ||||||||
\(741\) | −1.05185 | −0.0386407 | ||||||||
\(742\) | −0.392896 | −0.0144237 | ||||||||
\(743\) | −51.4169 | −1.88630 | −0.943152 | − | 0.332362i | \(-0.892154\pi\) | ||||
−0.943152 | + | 0.332362i | \(0.892154\pi\) | |||||||
\(744\) | −5.11863 | −0.187658 | ||||||||
\(745\) | 1.13426 | 0.0415560 | ||||||||
\(746\) | 37.3428 | 1.36722 | ||||||||
\(747\) | −10.9806 | −0.401760 | ||||||||
\(748\) | −3.94118 | −0.144104 | ||||||||
\(749\) | 21.5904 | 0.788896 | ||||||||
\(750\) | 7.04440 | 0.257225 | ||||||||
\(751\) | −23.3658 | −0.852631 | −0.426315 | − | 0.904575i | \(-0.640189\pi\) | ||||
−0.426315 | + | 0.904575i | \(0.640189\pi\) | |||||||
\(752\) | 6.38880 | 0.232976 | ||||||||
\(753\) | −24.7252 | −0.901036 | ||||||||
\(754\) | −4.40482 | −0.160414 | ||||||||
\(755\) | 6.98429 | 0.254184 | ||||||||
\(756\) | 1.28209 | 0.0466293 | ||||||||
\(757\) | 1.01078 | 0.0367372 | 0.0183686 | − | 0.999831i | \(-0.494153\pi\) | ||||
0.0183686 | + | 0.999831i | \(0.494153\pi\) | |||||||
\(758\) | 19.1507 | 0.695585 | ||||||||
\(759\) | −2.77474 | −0.100717 | ||||||||
\(760\) | 0.764114 | 0.0277173 | ||||||||
\(761\) | −41.7770 | −1.51441 | −0.757207 | − | 0.653175i | \(-0.773437\pi\) | ||||
−0.757207 | + | 0.653175i | \(0.773437\pi\) | |||||||
\(762\) | 19.0865 | 0.691432 | ||||||||
\(763\) | 1.48881 | 0.0538986 | ||||||||
\(764\) | 23.6842 | 0.856865 | ||||||||
\(765\) | 2.93991 | 0.106293 | ||||||||
\(766\) | −7.54042 | −0.272447 | ||||||||
\(767\) | −6.18780 | −0.223429 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 8.66749 | 0.312558 | 0.156279 | − | 0.987713i | \(-0.450050\pi\) | ||||
0.156279 | + | 0.987713i | \(0.450050\pi\) | |||||||
\(770\) | −0.956374 | −0.0344653 | ||||||||
\(771\) | −26.9857 | −0.971865 | ||||||||
\(772\) | −25.2226 | −0.907781 | ||||||||
\(773\) | −2.50838 | −0.0902201 | −0.0451101 | − | 0.998982i | \(-0.514364\pi\) | ||||
−0.0451101 | + | 0.998982i | \(0.514364\pi\) | |||||||
\(774\) | −3.78917 | −0.136199 | ||||||||
\(775\) | 22.7449 | 0.817023 | ||||||||
\(776\) | −3.30314 | −0.118576 | ||||||||
\(777\) | −2.11387 | −0.0758345 | ||||||||
\(778\) | 2.78201 | 0.0997398 | ||||||||
\(779\) | 6.09486 | 0.218371 | ||||||||
\(780\) | 0.765971 | 0.0274262 | ||||||||
\(781\) | 7.77380 | 0.278168 | ||||||||
\(782\) | 10.9358 | 0.391062 | ||||||||
\(783\) | −4.28967 | −0.153300 | ||||||||
\(784\) | −5.35623 | −0.191294 | ||||||||
\(785\) | −11.2520 | −0.401600 | ||||||||
\(786\) | 17.6945 | 0.631140 | ||||||||
\(787\) | −49.1920 | −1.75350 | −0.876752 | − | 0.480943i | \(-0.840295\pi\) | ||||
−0.876752 | + | 0.480943i | \(0.840295\pi\) | |||||||
\(788\) | −19.7129 | −0.702243 | ||||||||
\(789\) | −5.78655 | −0.206007 | ||||||||
\(790\) | −2.82290 | −0.100434 | ||||||||
\(791\) | −17.9675 | −0.638850 | ||||||||
\(792\) | −1.00000 | −0.0355335 | ||||||||
\(793\) | −1.02684 | −0.0364643 | ||||||||
\(794\) | 33.5450 | 1.19047 | ||||||||
\(795\) | −0.228594 | −0.00810741 | ||||||||
\(796\) | −13.3077 | −0.471681 | ||||||||
\(797\) | −20.4915 | −0.725847 | −0.362923 | − | 0.931819i | \(-0.618221\pi\) | ||||
−0.362923 | + | 0.931819i | \(0.618221\pi\) | |||||||
\(798\) | −1.31332 | −0.0464910 | ||||||||
\(799\) | −25.1794 | −0.890785 | ||||||||
\(800\) | 4.44356 | 0.157104 | ||||||||
\(801\) | 9.92651 | 0.350736 | ||||||||
\(802\) | −2.67571 | −0.0944826 | ||||||||
\(803\) | −0.861474 | −0.0304008 | ||||||||
\(804\) | 9.15286 | 0.322797 | ||||||||
\(805\) | 2.65369 | 0.0935303 | ||||||||
\(806\) | 5.25603 | 0.185136 | ||||||||
\(807\) | −11.6113 | −0.408736 | ||||||||
\(808\) | −6.19552 | −0.217958 | ||||||||
\(809\) | −7.49309 | −0.263443 | −0.131721 | − | 0.991287i | \(-0.542050\pi\) | ||||
−0.131721 | + | 0.991287i | \(0.542050\pi\) | |||||||
\(810\) | 0.745947 | 0.0262099 | ||||||||
\(811\) | −9.87970 | −0.346923 | −0.173462 | − | 0.984841i | \(-0.555495\pi\) | ||||
−0.173462 | + | 0.984841i | \(0.555495\pi\) | |||||||
\(812\) | −5.49976 | −0.193004 | ||||||||
\(813\) | 25.1036 | 0.880423 | ||||||||
\(814\) | 1.64876 | 0.0577890 | ||||||||
\(815\) | −17.2169 | −0.603082 | ||||||||
\(816\) | 3.94118 | 0.137969 | ||||||||
\(817\) | 3.88145 | 0.135795 | ||||||||
\(818\) | 0.271591 | 0.00949595 | ||||||||
\(819\) | −1.31651 | −0.0460026 | ||||||||
\(820\) | −4.43835 | −0.154994 | ||||||||
\(821\) | −21.0894 | −0.736027 | −0.368013 | − | 0.929820i | \(-0.619962\pi\) | ||||
−0.368013 | + | 0.929820i | \(0.619962\pi\) | |||||||
\(822\) | −15.6557 | −0.546054 | ||||||||
\(823\) | 10.0204 | 0.349290 | 0.174645 | − | 0.984631i | \(-0.444122\pi\) | ||||
0.174645 | + | 0.984631i | \(0.444122\pi\) | |||||||
\(824\) | 1.68344 | 0.0586455 | ||||||||
\(825\) | 4.44356 | 0.154705 | ||||||||
\(826\) | −7.72595 | −0.268820 | ||||||||
\(827\) | 29.9687 | 1.04211 | 0.521056 | − | 0.853522i | \(-0.325538\pi\) | ||||
0.521056 | + | 0.853522i | \(0.325538\pi\) | |||||||
\(828\) | 2.77474 | 0.0964289 | ||||||||
\(829\) | −6.81946 | −0.236850 | −0.118425 | − | 0.992963i | \(-0.537784\pi\) | ||||
−0.118425 | + | 0.992963i | \(0.537784\pi\) | |||||||
\(830\) | −8.19097 | −0.284313 | ||||||||
\(831\) | −2.63951 | −0.0915636 | ||||||||
\(832\) | 1.02684 | 0.0355994 | ||||||||
\(833\) | 21.1099 | 0.731415 | ||||||||
\(834\) | 0.617102 | 0.0213685 | ||||||||
\(835\) | −12.4076 | −0.429381 | ||||||||
\(836\) | 1.02435 | 0.0354280 | ||||||||
\(837\) | 5.11863 | 0.176926 | ||||||||
\(838\) | 4.66064 | 0.160999 | ||||||||
\(839\) | 20.0108 | 0.690850 | 0.345425 | − | 0.938446i | \(-0.387735\pi\) | ||||
0.345425 | + | 0.938446i | \(0.387735\pi\) | |||||||
\(840\) | 0.956374 | 0.0329981 | ||||||||
\(841\) | −10.5988 | −0.365475 | ||||||||
\(842\) | −31.9442 | −1.10087 | ||||||||
\(843\) | −0.322393 | −0.0111038 | ||||||||
\(844\) | 13.9516 | 0.480234 | ||||||||
\(845\) | 8.91078 | 0.306540 | ||||||||
\(846\) | −6.38880 | −0.219652 | ||||||||
\(847\) | −1.28209 | −0.0440533 | ||||||||
\(848\) | −0.306449 | −0.0105235 | ||||||||
\(849\) | 14.2970 | 0.490671 | ||||||||
\(850\) | −17.5129 | −0.600687 | ||||||||
\(851\) | −4.57488 | −0.156825 | ||||||||
\(852\) | −7.77380 | −0.266326 | ||||||||
\(853\) | −21.0335 | −0.720175 | −0.360087 | − | 0.932919i | \(-0.617253\pi\) | ||||
−0.360087 | + | 0.932919i | \(0.617253\pi\) | |||||||
\(854\) | −1.28209 | −0.0438724 | ||||||||
\(855\) | −0.764114 | −0.0261322 | ||||||||
\(856\) | 16.8399 | 0.575577 | ||||||||
\(857\) | −8.50611 | −0.290563 | −0.145282 | − | 0.989390i | \(-0.546409\pi\) | ||||
−0.145282 | + | 0.989390i | \(0.546409\pi\) | |||||||
\(858\) | 1.02684 | 0.0350559 | ||||||||
\(859\) | 42.1631 | 1.43859 | 0.719293 | − | 0.694707i | \(-0.244466\pi\) | ||||
0.719293 | + | 0.694707i | \(0.244466\pi\) | |||||||
\(860\) | −2.82652 | −0.0963834 | ||||||||
\(861\) | 7.62840 | 0.259975 | ||||||||
\(862\) | −30.6753 | −1.04481 | ||||||||
\(863\) | −43.3604 | −1.47601 | −0.738003 | − | 0.674798i | \(-0.764231\pi\) | ||||
−0.738003 | + | 0.674798i | \(0.764231\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 14.2894 | 0.485855 | ||||||||
\(866\) | −24.0788 | −0.818232 | ||||||||
\(867\) | 1.46708 | 0.0498246 | ||||||||
\(868\) | 6.56256 | 0.222748 | ||||||||
\(869\) | −3.78432 | −0.128374 | ||||||||
\(870\) | −3.19986 | −0.108486 | ||||||||
\(871\) | −9.39856 | −0.318458 | ||||||||
\(872\) | 1.16123 | 0.0393244 | ||||||||
\(873\) | 3.30314 | 0.111794 | ||||||||
\(874\) | −2.84232 | −0.0961429 | ||||||||
\(875\) | −9.03158 | −0.305323 | ||||||||
\(876\) | 0.861474 | 0.0291065 | ||||||||
\(877\) | 15.3868 | 0.519576 | 0.259788 | − | 0.965666i | \(-0.416347\pi\) | ||||
0.259788 | + | 0.965666i | \(0.416347\pi\) | |||||||
\(878\) | −8.48940 | −0.286503 | ||||||||
\(879\) | −7.05756 | −0.238045 | ||||||||
\(880\) | −0.745947 | −0.0251459 | ||||||||
\(881\) | −44.2447 | −1.49064 | −0.745321 | − | 0.666705i | \(-0.767704\pi\) | ||||
−0.745321 | + | 0.666705i | \(0.767704\pi\) | |||||||
\(882\) | 5.35623 | 0.180354 | ||||||||
\(883\) | 27.0054 | 0.908803 | 0.454401 | − | 0.890797i | \(-0.349853\pi\) | ||||
0.454401 | + | 0.890797i | \(0.349853\pi\) | |||||||
\(884\) | −4.04698 | −0.136115 | ||||||||
\(885\) | −4.49511 | −0.151101 | ||||||||
\(886\) | −32.7393 | −1.09990 | ||||||||
\(887\) | 2.74028 | 0.0920095 | 0.0460047 | − | 0.998941i | \(-0.485351\pi\) | ||||
0.0460047 | + | 0.998941i | \(0.485351\pi\) | |||||||
\(888\) | −1.64876 | −0.0553288 | ||||||||
\(889\) | −24.4707 | −0.820722 | ||||||||
\(890\) | 7.40466 | 0.248205 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 2.90024 | 0.0971071 | ||||||||
\(893\) | 6.54440 | 0.219000 | ||||||||
\(894\) | −1.52056 | −0.0508552 | ||||||||
\(895\) | −11.2165 | −0.374926 | ||||||||
\(896\) | 1.28209 | 0.0428318 | ||||||||
\(897\) | −2.84922 | −0.0951329 | ||||||||
\(898\) | 26.1057 | 0.871158 | ||||||||
\(899\) | −21.9572 | −0.732314 | ||||||||
\(900\) | −4.44356 | −0.148119 | ||||||||
\(901\) | 1.20777 | 0.0402366 | ||||||||
\(902\) | −5.94995 | −0.198112 | ||||||||
\(903\) | 4.85807 | 0.161666 | ||||||||
\(904\) | −14.0142 | −0.466104 | ||||||||
\(905\) | −2.49224 | −0.0828448 | ||||||||
\(906\) | −9.36299 | −0.311064 | ||||||||
\(907\) | 43.7001 | 1.45104 | 0.725519 | − | 0.688202i | \(-0.241600\pi\) | ||||
0.725519 | + | 0.688202i | \(0.241600\pi\) | |||||||
\(908\) | 8.77009 | 0.291046 | ||||||||
\(909\) | 6.19552 | 0.205492 | ||||||||
\(910\) | −0.982047 | −0.0325545 | ||||||||
\(911\) | −10.7348 | −0.355661 | −0.177830 | − | 0.984061i | \(-0.556908\pi\) | ||||
−0.177830 | + | 0.984061i | \(0.556908\pi\) | |||||||
\(912\) | −1.02435 | −0.0339198 | ||||||||
\(913\) | −10.9806 | −0.363406 | ||||||||
\(914\) | −15.2573 | −0.504668 | ||||||||
\(915\) | −0.745947 | −0.0246603 | ||||||||
\(916\) | 12.6487 | 0.417925 | ||||||||
\(917\) | −22.6860 | −0.749156 | ||||||||
\(918\) | −3.94118 | −0.130078 | ||||||||
\(919\) | −31.8104 | −1.04933 | −0.524665 | − | 0.851309i | \(-0.675809\pi\) | ||||
−0.524665 | + | 0.851309i | \(0.675809\pi\) | |||||||
\(920\) | 2.06981 | 0.0682396 | ||||||||
\(921\) | 2.22142 | 0.0731983 | ||||||||
\(922\) | −29.7034 | −0.978230 | ||||||||
\(923\) | 7.98247 | 0.262746 | ||||||||
\(924\) | 1.28209 | 0.0421778 | ||||||||
\(925\) | 7.32637 | 0.240890 | ||||||||
\(926\) | 7.74787 | 0.254611 | ||||||||
\(927\) | −1.68344 | −0.0552915 | ||||||||
\(928\) | −4.28967 | −0.140815 | ||||||||
\(929\) | 5.77873 | 0.189594 | 0.0947969 | − | 0.995497i | \(-0.469780\pi\) | ||||
0.0947969 | + | 0.995497i | \(0.469780\pi\) | |||||||
\(930\) | 3.81823 | 0.125205 | ||||||||
\(931\) | −5.48668 | −0.179819 | ||||||||
\(932\) | −6.13121 | −0.200834 | ||||||||
\(933\) | −23.8939 | −0.782252 | ||||||||
\(934\) | 18.7407 | 0.613214 | ||||||||
\(935\) | 2.93991 | 0.0961455 | ||||||||
\(936\) | −1.02684 | −0.0335634 | ||||||||
\(937\) | −56.1605 | −1.83468 | −0.917342 | − | 0.398099i | \(-0.869670\pi\) | ||||
−0.917342 | + | 0.398099i | \(0.869670\pi\) | |||||||
\(938\) | −11.7348 | −0.383156 | ||||||||
\(939\) | −25.0026 | −0.815930 | ||||||||
\(940\) | −4.76571 | −0.155440 | ||||||||
\(941\) | −2.36918 | −0.0772329 | −0.0386165 | − | 0.999254i | \(-0.512295\pi\) | ||||
−0.0386165 | + | 0.999254i | \(0.512295\pi\) | |||||||
\(942\) | 15.0841 | 0.491468 | ||||||||
\(943\) | 16.5096 | 0.537626 | ||||||||
\(944\) | −6.02604 | −0.196131 | ||||||||
\(945\) | −0.956374 | −0.0311109 | ||||||||
\(946\) | −3.78917 | −0.123196 | ||||||||
\(947\) | 52.4163 | 1.70330 | 0.851650 | − | 0.524111i | \(-0.175602\pi\) | ||||
0.851650 | + | 0.524111i | \(0.175602\pi\) | |||||||
\(948\) | 3.78432 | 0.122909 | ||||||||
\(949\) | −0.884599 | −0.0287153 | ||||||||
\(950\) | 4.55178 | 0.147679 | ||||||||
\(951\) | 1.61195 | 0.0522712 | ||||||||
\(952\) | −5.05297 | −0.163768 | ||||||||
\(953\) | 17.5667 | 0.569041 | 0.284520 | − | 0.958670i | \(-0.408166\pi\) | ||||
0.284520 | + | 0.958670i | \(0.408166\pi\) | |||||||
\(954\) | 0.306449 | 0.00992164 | ||||||||
\(955\) | −17.6672 | −0.571696 | ||||||||
\(956\) | 17.9825 | 0.581597 | ||||||||
\(957\) | −4.28967 | −0.138665 | ||||||||
\(958\) | 8.02669 | 0.259330 | ||||||||
\(959\) | 20.0720 | 0.648160 | ||||||||
\(960\) | 0.745947 | 0.0240753 | ||||||||
\(961\) | −4.79965 | −0.154827 | ||||||||
\(962\) | 1.69302 | 0.0545851 | ||||||||
\(963\) | −16.8399 | −0.542660 | ||||||||
\(964\) | 29.8941 | 0.962826 | ||||||||
\(965\) | 18.8147 | 0.605668 | ||||||||
\(966\) | −3.55748 | −0.114460 | ||||||||
\(967\) | −43.8573 | −1.41036 | −0.705178 | − | 0.709031i | \(-0.749133\pi\) | ||||
−0.705178 | + | 0.709031i | \(0.749133\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 4.03717 | 0.129693 | ||||||||
\(970\) | 2.46397 | 0.0791133 | ||||||||
\(971\) | 48.5102 | 1.55677 | 0.778383 | − | 0.627789i | \(-0.216040\pi\) | ||||
0.778383 | + | 0.627789i | \(0.216040\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −0.791183 | −0.0253642 | ||||||||
\(974\) | −6.25479 | −0.200416 | ||||||||
\(975\) | 4.56284 | 0.146128 | ||||||||
\(976\) | −1.00000 | −0.0320092 | ||||||||
\(977\) | 29.9989 | 0.959751 | 0.479875 | − | 0.877337i | \(-0.340682\pi\) | ||||
0.479875 | + | 0.877337i | \(0.340682\pi\) | |||||||
\(978\) | 23.0806 | 0.738036 | ||||||||
\(979\) | 9.92651 | 0.317253 | ||||||||
\(980\) | 3.99547 | 0.127631 | ||||||||
\(981\) | −1.16123 | −0.0370754 | ||||||||
\(982\) | 4.48630 | 0.143164 | ||||||||
\(983\) | 17.3423 | 0.553133 | 0.276566 | − | 0.960995i | \(-0.410803\pi\) | ||||
0.276566 | + | 0.960995i | \(0.410803\pi\) | |||||||
\(984\) | 5.94995 | 0.189678 | ||||||||
\(985\) | 14.7048 | 0.468534 | ||||||||
\(986\) | 16.9064 | 0.538408 | ||||||||
\(987\) | 8.19105 | 0.260724 | ||||||||
\(988\) | 1.05185 | 0.0334639 | ||||||||
\(989\) | 10.5140 | 0.334324 | ||||||||
\(990\) | 0.745947 | 0.0237078 | ||||||||
\(991\) | −59.7452 | −1.89787 | −0.948935 | − | 0.315472i | \(-0.897837\pi\) | ||||
−0.948935 | + | 0.315472i | \(0.897837\pi\) | |||||||
\(992\) | 5.11863 | 0.162517 | ||||||||
\(993\) | −30.4671 | −0.966845 | ||||||||
\(994\) | 9.96674 | 0.316126 | ||||||||
\(995\) | 9.92688 | 0.314703 | ||||||||
\(996\) | 10.9806 | 0.347934 | ||||||||
\(997\) | 16.8895 | 0.534897 | 0.267449 | − | 0.963572i | \(-0.413819\pi\) | ||||
0.267449 | + | 0.963572i | \(0.413819\pi\) | |||||||
\(998\) | −28.6832 | −0.907951 | ||||||||
\(999\) | 1.64876 | 0.0521645 |
(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 | 4026.2.a.z.1.4 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4026.2.a.z.1.4 | ✓ | 7 | 1.1 | even | 1 | trivial |