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: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 30x^{7} + 7x^{6} + 284x^{5} + 100x^{4} - 777x^{3} - 250x^{2} + 574x - 68 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.731055\) 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 | ||||||||
\(5\) | 0.268945 | 0.120276 | 0.0601379 | − | 0.998190i | \(-0.480846\pi\) | ||||
0.0601379 | + | 0.998190i | \(0.480846\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 3.42672 | 1.29518 | 0.647589 | − | 0.761990i | \(-0.275777\pi\) | ||||
0.647589 | + | 0.761990i | \(0.275777\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.268945 | 0.0850479 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 1.26655 | 0.351278 | 0.175639 | − | 0.984455i | \(-0.443801\pi\) | ||||
0.175639 | + | 0.984455i | \(0.443801\pi\) | |||||||
\(14\) | 3.42672 | 0.915829 | ||||||||
\(15\) | 0.268945 | 0.0694413 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.867540 | 0.210409 | 0.105205 | − | 0.994451i | \(-0.466450\pi\) | ||||
0.105205 | + | 0.994451i | \(0.466450\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 6.18750 | 1.41951 | 0.709755 | − | 0.704449i | \(-0.248806\pi\) | ||||
0.709755 | + | 0.704449i | \(0.248806\pi\) | |||||||
\(20\) | 0.268945 | 0.0601379 | ||||||||
\(21\) | 3.42672 | 0.747771 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −8.86224 | −1.84791 | −0.923953 | − | 0.382506i | \(-0.875061\pi\) | ||||
−0.923953 | + | 0.382506i | \(0.875061\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.92767 | −0.985534 | ||||||||
\(26\) | 1.26655 | 0.248391 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 3.42672 | 0.647589 | ||||||||
\(29\) | 1.57247 | 0.292001 | 0.146001 | − | 0.989285i | \(-0.453360\pi\) | ||||
0.146001 | + | 0.989285i | \(0.453360\pi\) | |||||||
\(30\) | 0.268945 | 0.0491024 | ||||||||
\(31\) | −6.59330 | −1.18419 | −0.592096 | − | 0.805868i | \(-0.701699\pi\) | ||||
−0.592096 | + | 0.805868i | \(0.701699\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 0.867540 | 0.148782 | ||||||||
\(35\) | 0.921599 | 0.155779 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 8.55030 | 1.40566 | 0.702830 | − | 0.711358i | \(-0.251919\pi\) | ||||
0.702830 | + | 0.711358i | \(0.251919\pi\) | |||||||
\(38\) | 6.18750 | 1.00374 | ||||||||
\(39\) | 1.26655 | 0.202811 | ||||||||
\(40\) | 0.268945 | 0.0425239 | ||||||||
\(41\) | 3.44241 | 0.537614 | 0.268807 | − | 0.963194i | \(-0.413371\pi\) | ||||
0.268807 | + | 0.963194i | \(0.413371\pi\) | |||||||
\(42\) | 3.42672 | 0.528754 | ||||||||
\(43\) | 12.3719 | 1.88669 | 0.943345 | − | 0.331813i | \(-0.107660\pi\) | ||||
0.943345 | + | 0.331813i | \(0.107660\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0.268945 | 0.0400920 | ||||||||
\(46\) | −8.86224 | −1.30667 | ||||||||
\(47\) | 5.99112 | 0.873894 | 0.436947 | − | 0.899487i | \(-0.356060\pi\) | ||||
0.436947 | + | 0.899487i | \(0.356060\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 4.74240 | 0.677485 | ||||||||
\(50\) | −4.92767 | −0.696878 | ||||||||
\(51\) | 0.867540 | 0.121480 | ||||||||
\(52\) | 1.26655 | 0.175639 | ||||||||
\(53\) | 4.13724 | 0.568293 | 0.284147 | − | 0.958781i | \(-0.408290\pi\) | ||||
0.284147 | + | 0.958781i | \(0.408290\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0.268945 | 0.0362645 | ||||||||
\(56\) | 3.42672 | 0.457914 | ||||||||
\(57\) | 6.18750 | 0.819554 | ||||||||
\(58\) | 1.57247 | 0.206476 | ||||||||
\(59\) | −13.3632 | −1.73974 | −0.869870 | − | 0.493281i | \(-0.835797\pi\) | ||||
−0.869870 | + | 0.493281i | \(0.835797\pi\) | |||||||
\(60\) | 0.268945 | 0.0347207 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | −6.59330 | −0.837350 | ||||||||
\(63\) | 3.42672 | 0.431726 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.340633 | 0.0422503 | ||||||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | −0.380487 | −0.0464839 | −0.0232420 | − | 0.999730i | \(-0.507399\pi\) | ||||
−0.0232420 | + | 0.999730i | \(0.507399\pi\) | |||||||
\(68\) | 0.867540 | 0.105205 | ||||||||
\(69\) | −8.86224 | −1.06689 | ||||||||
\(70\) | 0.921599 | 0.110152 | ||||||||
\(71\) | −10.4281 | −1.23759 | −0.618796 | − | 0.785551i | \(-0.712379\pi\) | ||||
−0.618796 | + | 0.785551i | \(0.712379\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −2.36638 | −0.276964 | −0.138482 | − | 0.990365i | \(-0.544222\pi\) | ||||
−0.138482 | + | 0.990365i | \(0.544222\pi\) | |||||||
\(74\) | 8.55030 | 0.993952 | ||||||||
\(75\) | −4.92767 | −0.568998 | ||||||||
\(76\) | 6.18750 | 0.709755 | ||||||||
\(77\) | 3.42672 | 0.390511 | ||||||||
\(78\) | 1.26655 | 0.143409 | ||||||||
\(79\) | −8.37132 | −0.941847 | −0.470924 | − | 0.882174i | \(-0.656079\pi\) | ||||
−0.470924 | + | 0.882174i | \(0.656079\pi\) | |||||||
\(80\) | 0.268945 | 0.0300690 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.44241 | 0.380150 | ||||||||
\(83\) | 2.32547 | 0.255254 | 0.127627 | − | 0.991822i | \(-0.459264\pi\) | ||||
0.127627 | + | 0.991822i | \(0.459264\pi\) | |||||||
\(84\) | 3.42672 | 0.373886 | ||||||||
\(85\) | 0.233320 | 0.0253072 | ||||||||
\(86\) | 12.3719 | 1.33409 | ||||||||
\(87\) | 1.57247 | 0.168587 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −11.6165 | −1.23134 | −0.615671 | − | 0.788004i | \(-0.711115\pi\) | ||||
−0.615671 | + | 0.788004i | \(0.711115\pi\) | |||||||
\(90\) | 0.268945 | 0.0283493 | ||||||||
\(91\) | 4.34011 | 0.454968 | ||||||||
\(92\) | −8.86224 | −0.923953 | ||||||||
\(93\) | −6.59330 | −0.683693 | ||||||||
\(94\) | 5.99112 | 0.617937 | ||||||||
\(95\) | 1.66410 | 0.170733 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −11.5077 | −1.16843 | −0.584215 | − | 0.811599i | \(-0.698597\pi\) | ||||
−0.584215 | + | 0.811599i | \(0.698597\pi\) | |||||||
\(98\) | 4.74240 | 0.479054 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −4.92767 | −0.492767 | ||||||||
\(101\) | −10.6426 | −1.05898 | −0.529489 | − | 0.848317i | \(-0.677616\pi\) | ||||
−0.529489 | + | 0.848317i | \(0.677616\pi\) | |||||||
\(102\) | 0.867540 | 0.0858992 | ||||||||
\(103\) | 1.00764 | 0.0992852 | 0.0496426 | − | 0.998767i | \(-0.484192\pi\) | ||||
0.0496426 | + | 0.998767i | \(0.484192\pi\) | |||||||
\(104\) | 1.26655 | 0.124196 | ||||||||
\(105\) | 0.921599 | 0.0899388 | ||||||||
\(106\) | 4.13724 | 0.401844 | ||||||||
\(107\) | −6.78676 | −0.656101 | −0.328051 | − | 0.944660i | \(-0.606392\pi\) | ||||
−0.328051 | + | 0.944660i | \(0.606392\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −10.9790 | −1.05160 | −0.525800 | − | 0.850608i | \(-0.676234\pi\) | ||||
−0.525800 | + | 0.850608i | \(0.676234\pi\) | |||||||
\(110\) | 0.268945 | 0.0256429 | ||||||||
\(111\) | 8.55030 | 0.811558 | ||||||||
\(112\) | 3.42672 | 0.323794 | ||||||||
\(113\) | −0.304968 | −0.0286890 | −0.0143445 | − | 0.999897i | \(-0.504566\pi\) | ||||
−0.0143445 | + | 0.999897i | \(0.504566\pi\) | |||||||
\(114\) | 6.18750 | 0.579512 | ||||||||
\(115\) | −2.38346 | −0.222258 | ||||||||
\(116\) | 1.57247 | 0.146001 | ||||||||
\(117\) | 1.26655 | 0.117093 | ||||||||
\(118\) | −13.3632 | −1.23018 | ||||||||
\(119\) | 2.97281 | 0.272517 | ||||||||
\(120\) | 0.268945 | 0.0245512 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.00000 | −0.0905357 | ||||||||
\(123\) | 3.44241 | 0.310391 | ||||||||
\(124\) | −6.59330 | −0.592096 | ||||||||
\(125\) | −2.67000 | −0.238812 | ||||||||
\(126\) | 3.42672 | 0.305276 | ||||||||
\(127\) | 18.8689 | 1.67435 | 0.837174 | − | 0.546936i | \(-0.184206\pi\) | ||||
0.837174 | + | 0.546936i | \(0.184206\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 12.3719 | 1.08928 | ||||||||
\(130\) | 0.340633 | 0.0298755 | ||||||||
\(131\) | 3.68893 | 0.322304 | 0.161152 | − | 0.986930i | \(-0.448479\pi\) | ||||
0.161152 | + | 0.986930i | \(0.448479\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | 21.2028 | 1.83852 | ||||||||
\(134\) | −0.380487 | −0.0328691 | ||||||||
\(135\) | 0.268945 | 0.0231471 | ||||||||
\(136\) | 0.867540 | 0.0743909 | ||||||||
\(137\) | 8.47305 | 0.723901 | 0.361951 | − | 0.932197i | \(-0.382111\pi\) | ||||
0.361951 | + | 0.932197i | \(0.382111\pi\) | |||||||
\(138\) | −8.86224 | −0.754404 | ||||||||
\(139\) | 14.3911 | 1.22064 | 0.610320 | − | 0.792155i | \(-0.291041\pi\) | ||||
0.610320 | + | 0.792155i | \(0.291041\pi\) | |||||||
\(140\) | 0.921599 | 0.0778893 | ||||||||
\(141\) | 5.99112 | 0.504543 | ||||||||
\(142\) | −10.4281 | −0.875110 | ||||||||
\(143\) | 1.26655 | 0.105914 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0.422909 | 0.0351207 | ||||||||
\(146\) | −2.36638 | −0.195843 | ||||||||
\(147\) | 4.74240 | 0.391146 | ||||||||
\(148\) | 8.55030 | 0.702830 | ||||||||
\(149\) | 19.6765 | 1.61196 | 0.805980 | − | 0.591943i | \(-0.201639\pi\) | ||||
0.805980 | + | 0.591943i | \(0.201639\pi\) | |||||||
\(150\) | −4.92767 | −0.402342 | ||||||||
\(151\) | 8.71508 | 0.709223 | 0.354611 | − | 0.935014i | \(-0.384613\pi\) | ||||
0.354611 | + | 0.935014i | \(0.384613\pi\) | |||||||
\(152\) | 6.18750 | 0.501872 | ||||||||
\(153\) | 0.867540 | 0.0701364 | ||||||||
\(154\) | 3.42672 | 0.276133 | ||||||||
\(155\) | −1.77324 | −0.142430 | ||||||||
\(156\) | 1.26655 | 0.101405 | ||||||||
\(157\) | 22.7483 | 1.81551 | 0.907755 | − | 0.419501i | \(-0.137795\pi\) | ||||
0.907755 | + | 0.419501i | \(0.137795\pi\) | |||||||
\(158\) | −8.37132 | −0.665986 | ||||||||
\(159\) | 4.13724 | 0.328104 | ||||||||
\(160\) | 0.268945 | 0.0212620 | ||||||||
\(161\) | −30.3684 | −2.39337 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −16.9197 | −1.32526 | −0.662628 | − | 0.748948i | \(-0.730559\pi\) | ||||
−0.662628 | + | 0.748948i | \(0.730559\pi\) | |||||||
\(164\) | 3.44241 | 0.268807 | ||||||||
\(165\) | 0.268945 | 0.0209373 | ||||||||
\(166\) | 2.32547 | 0.180492 | ||||||||
\(167\) | 24.5798 | 1.90204 | 0.951021 | − | 0.309125i | \(-0.100036\pi\) | ||||
0.951021 | + | 0.309125i | \(0.100036\pi\) | |||||||
\(168\) | 3.42672 | 0.264377 | ||||||||
\(169\) | −11.3958 | −0.876604 | ||||||||
\(170\) | 0.233320 | 0.0178949 | ||||||||
\(171\) | 6.18750 | 0.473170 | ||||||||
\(172\) | 12.3719 | 0.943345 | ||||||||
\(173\) | 16.0917 | 1.22343 | 0.611715 | − | 0.791078i | \(-0.290480\pi\) | ||||
0.611715 | + | 0.791078i | \(0.290480\pi\) | |||||||
\(174\) | 1.57247 | 0.119209 | ||||||||
\(175\) | −16.8857 | −1.27644 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −13.3632 | −1.00444 | ||||||||
\(178\) | −11.6165 | −0.870690 | ||||||||
\(179\) | −20.5271 | −1.53427 | −0.767133 | − | 0.641488i | \(-0.778317\pi\) | ||||
−0.767133 | + | 0.641488i | \(0.778317\pi\) | |||||||
\(180\) | 0.268945 | 0.0200460 | ||||||||
\(181\) | −14.6239 | −1.08699 | −0.543494 | − | 0.839413i | \(-0.682899\pi\) | ||||
−0.543494 | + | 0.839413i | \(0.682899\pi\) | |||||||
\(182\) | 4.34011 | 0.321711 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | −8.86224 | −0.653333 | ||||||||
\(185\) | 2.29956 | 0.169067 | ||||||||
\(186\) | −6.59330 | −0.483444 | ||||||||
\(187\) | 0.867540 | 0.0634408 | ||||||||
\(188\) | 5.99112 | 0.436947 | ||||||||
\(189\) | 3.42672 | 0.249257 | ||||||||
\(190\) | 1.66410 | 0.120726 | ||||||||
\(191\) | −5.11491 | −0.370102 | −0.185051 | − | 0.982729i | \(-0.559245\pi\) | ||||
−0.185051 | + | 0.982729i | \(0.559245\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −18.9293 | −1.36256 | −0.681281 | − | 0.732022i | \(-0.738577\pi\) | ||||
−0.681281 | + | 0.732022i | \(0.738577\pi\) | |||||||
\(194\) | −11.5077 | −0.826204 | ||||||||
\(195\) | 0.340633 | 0.0243932 | ||||||||
\(196\) | 4.74240 | 0.338743 | ||||||||
\(197\) | 8.98440 | 0.640112 | 0.320056 | − | 0.947399i | \(-0.396298\pi\) | ||||
0.320056 | + | 0.947399i | \(0.396298\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | 15.1438 | 1.07352 | 0.536758 | − | 0.843736i | \(-0.319649\pi\) | ||||
0.536758 | + | 0.843736i | \(0.319649\pi\) | |||||||
\(200\) | −4.92767 | −0.348439 | ||||||||
\(201\) | −0.380487 | −0.0268375 | ||||||||
\(202\) | −10.6426 | −0.748810 | ||||||||
\(203\) | 5.38842 | 0.378193 | ||||||||
\(204\) | 0.867540 | 0.0607399 | ||||||||
\(205\) | 0.925818 | 0.0646620 | ||||||||
\(206\) | 1.00764 | 0.0702053 | ||||||||
\(207\) | −8.86224 | −0.615969 | ||||||||
\(208\) | 1.26655 | 0.0878196 | ||||||||
\(209\) | 6.18750 | 0.427998 | ||||||||
\(210\) | 0.921599 | 0.0635964 | ||||||||
\(211\) | 25.8348 | 1.77854 | 0.889271 | − | 0.457381i | \(-0.151212\pi\) | ||||
0.889271 | + | 0.457381i | \(0.151212\pi\) | |||||||
\(212\) | 4.13724 | 0.284147 | ||||||||
\(213\) | −10.4281 | −0.714525 | ||||||||
\(214\) | −6.78676 | −0.463934 | ||||||||
\(215\) | 3.32735 | 0.226923 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −22.5934 | −1.53374 | ||||||||
\(218\) | −10.9790 | −0.743594 | ||||||||
\(219\) | −2.36638 | −0.159905 | ||||||||
\(220\) | 0.268945 | 0.0181323 | ||||||||
\(221\) | 1.09878 | 0.0739122 | ||||||||
\(222\) | 8.55030 | 0.573858 | ||||||||
\(223\) | 9.89572 | 0.662666 | 0.331333 | − | 0.943514i | \(-0.392502\pi\) | ||||
0.331333 | + | 0.943514i | \(0.392502\pi\) | |||||||
\(224\) | 3.42672 | 0.228957 | ||||||||
\(225\) | −4.92767 | −0.328511 | ||||||||
\(226\) | −0.304968 | −0.0202862 | ||||||||
\(227\) | 1.05470 | 0.0700032 | 0.0350016 | − | 0.999387i | \(-0.488856\pi\) | ||||
0.0350016 | + | 0.999387i | \(0.488856\pi\) | |||||||
\(228\) | 6.18750 | 0.409777 | ||||||||
\(229\) | −6.19110 | −0.409119 | −0.204560 | − | 0.978854i | \(-0.565576\pi\) | ||||
−0.204560 | + | 0.978854i | \(0.565576\pi\) | |||||||
\(230\) | −2.38346 | −0.157160 | ||||||||
\(231\) | 3.42672 | 0.225461 | ||||||||
\(232\) | 1.57247 | 0.103238 | ||||||||
\(233\) | −28.9847 | −1.89885 | −0.949426 | − | 0.313990i | \(-0.898334\pi\) | ||||
−0.949426 | + | 0.313990i | \(0.898334\pi\) | |||||||
\(234\) | 1.26655 | 0.0827971 | ||||||||
\(235\) | 1.61128 | 0.105108 | ||||||||
\(236\) | −13.3632 | −0.869870 | ||||||||
\(237\) | −8.37132 | −0.543776 | ||||||||
\(238\) | 2.97281 | 0.192699 | ||||||||
\(239\) | −4.63720 | −0.299955 | −0.149978 | − | 0.988689i | \(-0.547920\pi\) | ||||
−0.149978 | + | 0.988689i | \(0.547920\pi\) | |||||||
\(240\) | 0.268945 | 0.0173603 | ||||||||
\(241\) | 13.8531 | 0.892354 | 0.446177 | − | 0.894945i | \(-0.352785\pi\) | ||||
0.446177 | + | 0.894945i | \(0.352785\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −1.00000 | −0.0640184 | ||||||||
\(245\) | 1.27544 | 0.0814851 | ||||||||
\(246\) | 3.44241 | 0.219480 | ||||||||
\(247\) | 7.83679 | 0.498643 | ||||||||
\(248\) | −6.59330 | −0.418675 | ||||||||
\(249\) | 2.32547 | 0.147371 | ||||||||
\(250\) | −2.67000 | −0.168865 | ||||||||
\(251\) | −8.63040 | −0.544746 | −0.272373 | − | 0.962192i | \(-0.587808\pi\) | ||||
−0.272373 | + | 0.962192i | \(0.587808\pi\) | |||||||
\(252\) | 3.42672 | 0.215863 | ||||||||
\(253\) | −8.86224 | −0.557165 | ||||||||
\(254\) | 18.8689 | 1.18394 | ||||||||
\(255\) | 0.233320 | 0.0146111 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.33011 | 0.0829700 | 0.0414850 | − | 0.999139i | \(-0.486791\pi\) | ||||
0.0414850 | + | 0.999139i | \(0.486791\pi\) | |||||||
\(258\) | 12.3719 | 0.770238 | ||||||||
\(259\) | 29.2995 | 1.82058 | ||||||||
\(260\) | 0.340633 | 0.0211251 | ||||||||
\(261\) | 1.57247 | 0.0973337 | ||||||||
\(262\) | 3.68893 | 0.227903 | ||||||||
\(263\) | −29.1042 | −1.79464 | −0.897321 | − | 0.441378i | \(-0.854490\pi\) | ||||
−0.897321 | + | 0.441378i | \(0.854490\pi\) | |||||||
\(264\) | 1.00000 | 0.0615457 | ||||||||
\(265\) | 1.11269 | 0.0683520 | ||||||||
\(266\) | 21.2028 | 1.30003 | ||||||||
\(267\) | −11.6165 | −0.710915 | ||||||||
\(268\) | −0.380487 | −0.0232420 | ||||||||
\(269\) | −2.29032 | −0.139643 | −0.0698215 | − | 0.997560i | \(-0.522243\pi\) | ||||
−0.0698215 | + | 0.997560i | \(0.522243\pi\) | |||||||
\(270\) | 0.268945 | 0.0163675 | ||||||||
\(271\) | −23.4290 | −1.42321 | −0.711604 | − | 0.702580i | \(-0.752031\pi\) | ||||
−0.711604 | + | 0.702580i | \(0.752031\pi\) | |||||||
\(272\) | 0.867540 | 0.0526023 | ||||||||
\(273\) | 4.34011 | 0.262676 | ||||||||
\(274\) | 8.47305 | 0.511875 | ||||||||
\(275\) | −4.92767 | −0.297150 | ||||||||
\(276\) | −8.86224 | −0.533444 | ||||||||
\(277\) | 18.8839 | 1.13463 | 0.567313 | − | 0.823502i | \(-0.307983\pi\) | ||||
0.567313 | + | 0.823502i | \(0.307983\pi\) | |||||||
\(278\) | 14.3911 | 0.863123 | ||||||||
\(279\) | −6.59330 | −0.394730 | ||||||||
\(280\) | 0.921599 | 0.0550761 | ||||||||
\(281\) | −10.0216 | −0.597840 | −0.298920 | − | 0.954278i | \(-0.596626\pi\) | ||||
−0.298920 | + | 0.954278i | \(0.596626\pi\) | |||||||
\(282\) | 5.99112 | 0.356766 | ||||||||
\(283\) | 2.41609 | 0.143622 | 0.0718108 | − | 0.997418i | \(-0.477122\pi\) | ||||
0.0718108 | + | 0.997418i | \(0.477122\pi\) | |||||||
\(284\) | −10.4281 | −0.618796 | ||||||||
\(285\) | 1.66410 | 0.0985726 | ||||||||
\(286\) | 1.26655 | 0.0748928 | ||||||||
\(287\) | 11.7962 | 0.696305 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −16.2474 | −0.955728 | ||||||||
\(290\) | 0.422909 | 0.0248341 | ||||||||
\(291\) | −11.5077 | −0.674593 | ||||||||
\(292\) | −2.36638 | −0.138482 | ||||||||
\(293\) | 4.40067 | 0.257090 | 0.128545 | − | 0.991704i | \(-0.458969\pi\) | ||||
0.128545 | + | 0.991704i | \(0.458969\pi\) | |||||||
\(294\) | 4.74240 | 0.276582 | ||||||||
\(295\) | −3.59396 | −0.209249 | ||||||||
\(296\) | 8.55030 | 0.496976 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 19.6765 | 1.13983 | ||||||||
\(299\) | −11.2245 | −0.649129 | ||||||||
\(300\) | −4.92767 | −0.284499 | ||||||||
\(301\) | 42.3949 | 2.44360 | ||||||||
\(302\) | 8.71508 | 0.501496 | ||||||||
\(303\) | −10.6426 | −0.611401 | ||||||||
\(304\) | 6.18750 | 0.354877 | ||||||||
\(305\) | −0.268945 | −0.0153997 | ||||||||
\(306\) | 0.867540 | 0.0495939 | ||||||||
\(307\) | −17.0682 | −0.974136 | −0.487068 | − | 0.873364i | \(-0.661934\pi\) | ||||
−0.487068 | + | 0.873364i | \(0.661934\pi\) | |||||||
\(308\) | 3.42672 | 0.195255 | ||||||||
\(309\) | 1.00764 | 0.0573224 | ||||||||
\(310\) | −1.77324 | −0.100713 | ||||||||
\(311\) | −28.3715 | −1.60880 | −0.804400 | − | 0.594088i | \(-0.797513\pi\) | ||||
−0.804400 | + | 0.594088i | \(0.797513\pi\) | |||||||
\(312\) | 1.26655 | 0.0717044 | ||||||||
\(313\) | −9.88599 | −0.558789 | −0.279395 | − | 0.960176i | \(-0.590134\pi\) | ||||
−0.279395 | + | 0.960176i | \(0.590134\pi\) | |||||||
\(314\) | 22.7483 | 1.28376 | ||||||||
\(315\) | 0.921599 | 0.0519262 | ||||||||
\(316\) | −8.37132 | −0.470924 | ||||||||
\(317\) | 5.91378 | 0.332151 | 0.166075 | − | 0.986113i | \(-0.446890\pi\) | ||||
0.166075 | + | 0.986113i | \(0.446890\pi\) | |||||||
\(318\) | 4.13724 | 0.232005 | ||||||||
\(319\) | 1.57247 | 0.0880416 | ||||||||
\(320\) | 0.268945 | 0.0150345 | ||||||||
\(321\) | −6.78676 | −0.378800 | ||||||||
\(322\) | −30.3684 | −1.69237 | ||||||||
\(323\) | 5.36790 | 0.298678 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −6.24115 | −0.346197 | ||||||||
\(326\) | −16.9197 | −0.937098 | ||||||||
\(327\) | −10.9790 | −0.607142 | ||||||||
\(328\) | 3.44241 | 0.190075 | ||||||||
\(329\) | 20.5299 | 1.13185 | ||||||||
\(330\) | 0.268945 | 0.0148049 | ||||||||
\(331\) | 18.4377 | 1.01343 | 0.506714 | − | 0.862114i | \(-0.330860\pi\) | ||||
0.506714 | + | 0.862114i | \(0.330860\pi\) | |||||||
\(332\) | 2.32547 | 0.127627 | ||||||||
\(333\) | 8.55030 | 0.468553 | ||||||||
\(334\) | 24.5798 | 1.34495 | ||||||||
\(335\) | −0.102330 | −0.00559090 | ||||||||
\(336\) | 3.42672 | 0.186943 | ||||||||
\(337\) | 35.4326 | 1.93014 | 0.965069 | − | 0.261998i | \(-0.0843813\pi\) | ||||
0.965069 | + | 0.261998i | \(0.0843813\pi\) | |||||||
\(338\) | −11.3958 | −0.619852 | ||||||||
\(339\) | −0.304968 | −0.0165636 | ||||||||
\(340\) | 0.233320 | 0.0126536 | ||||||||
\(341\) | −6.59330 | −0.357047 | ||||||||
\(342\) | 6.18750 | 0.334582 | ||||||||
\(343\) | −7.73617 | −0.417714 | ||||||||
\(344\) | 12.3719 | 0.667046 | ||||||||
\(345\) | −2.38346 | −0.128321 | ||||||||
\(346\) | 16.0917 | 0.865096 | ||||||||
\(347\) | 32.0180 | 1.71881 | 0.859407 | − | 0.511292i | \(-0.170833\pi\) | ||||
0.859407 | + | 0.511292i | \(0.170833\pi\) | |||||||
\(348\) | 1.57247 | 0.0842935 | ||||||||
\(349\) | 0.763609 | 0.0408751 | 0.0204375 | − | 0.999791i | \(-0.493494\pi\) | ||||
0.0204375 | + | 0.999791i | \(0.493494\pi\) | |||||||
\(350\) | −16.8857 | −0.902580 | ||||||||
\(351\) | 1.26655 | 0.0676035 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 16.4468 | 0.875376 | 0.437688 | − | 0.899127i | \(-0.355798\pi\) | ||||
0.437688 | + | 0.899127i | \(0.355798\pi\) | |||||||
\(354\) | −13.3632 | −0.710246 | ||||||||
\(355\) | −2.80460 | −0.148853 | ||||||||
\(356\) | −11.6165 | −0.615671 | ||||||||
\(357\) | 2.97281 | 0.157338 | ||||||||
\(358\) | −20.5271 | −1.08489 | ||||||||
\(359\) | 19.7050 | 1.03999 | 0.519995 | − | 0.854169i | \(-0.325934\pi\) | ||||
0.519995 | + | 0.854169i | \(0.325934\pi\) | |||||||
\(360\) | 0.268945 | 0.0141746 | ||||||||
\(361\) | 19.2851 | 1.01501 | ||||||||
\(362\) | −14.6239 | −0.768616 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 4.34011 | 0.227484 | ||||||||
\(365\) | −0.636427 | −0.0333121 | ||||||||
\(366\) | −1.00000 | −0.0522708 | ||||||||
\(367\) | −20.4095 | −1.06537 | −0.532684 | − | 0.846314i | \(-0.678817\pi\) | ||||
−0.532684 | + | 0.846314i | \(0.678817\pi\) | |||||||
\(368\) | −8.86224 | −0.461976 | ||||||||
\(369\) | 3.44241 | 0.179205 | ||||||||
\(370\) | 2.29956 | 0.119548 | ||||||||
\(371\) | 14.1772 | 0.736041 | ||||||||
\(372\) | −6.59330 | −0.341847 | ||||||||
\(373\) | −35.9190 | −1.85982 | −0.929908 | − | 0.367793i | \(-0.880114\pi\) | ||||
−0.929908 | + | 0.367793i | \(0.880114\pi\) | |||||||
\(374\) | 0.867540 | 0.0448594 | ||||||||
\(375\) | −2.67000 | −0.137878 | ||||||||
\(376\) | 5.99112 | 0.308968 | ||||||||
\(377\) | 1.99162 | 0.102574 | ||||||||
\(378\) | 3.42672 | 0.176251 | ||||||||
\(379\) | 29.2039 | 1.50010 | 0.750051 | − | 0.661380i | \(-0.230029\pi\) | ||||
0.750051 | + | 0.661380i | \(0.230029\pi\) | |||||||
\(380\) | 1.66410 | 0.0853664 | ||||||||
\(381\) | 18.8689 | 0.966686 | ||||||||
\(382\) | −5.11491 | −0.261702 | ||||||||
\(383\) | −30.2591 | −1.54617 | −0.773083 | − | 0.634305i | \(-0.781286\pi\) | ||||
−0.773083 | + | 0.634305i | \(0.781286\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0.921599 | 0.0469690 | ||||||||
\(386\) | −18.9293 | −0.963477 | ||||||||
\(387\) | 12.3719 | 0.628897 | ||||||||
\(388\) | −11.5077 | −0.584215 | ||||||||
\(389\) | −6.13420 | −0.311016 | −0.155508 | − | 0.987835i | \(-0.549702\pi\) | ||||
−0.155508 | + | 0.987835i | \(0.549702\pi\) | |||||||
\(390\) | 0.340633 | 0.0172486 | ||||||||
\(391\) | −7.68835 | −0.388816 | ||||||||
\(392\) | 4.74240 | 0.239527 | ||||||||
\(393\) | 3.68893 | 0.186082 | ||||||||
\(394\) | 8.98440 | 0.452628 | ||||||||
\(395\) | −2.25142 | −0.113281 | ||||||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | 7.09173 | 0.355924 | 0.177962 | − | 0.984037i | \(-0.443050\pi\) | ||||
0.177962 | + | 0.984037i | \(0.443050\pi\) | |||||||
\(398\) | 15.1438 | 0.759091 | ||||||||
\(399\) | 21.2028 | 1.06147 | ||||||||
\(400\) | −4.92767 | −0.246383 | ||||||||
\(401\) | −29.9023 | −1.49325 | −0.746626 | − | 0.665244i | \(-0.768328\pi\) | ||||
−0.746626 | + | 0.665244i | \(0.768328\pi\) | |||||||
\(402\) | −0.380487 | −0.0189770 | ||||||||
\(403\) | −8.35075 | −0.415981 | ||||||||
\(404\) | −10.6426 | −0.529489 | ||||||||
\(405\) | 0.268945 | 0.0133640 | ||||||||
\(406\) | 5.38842 | 0.267423 | ||||||||
\(407\) | 8.55030 | 0.423822 | ||||||||
\(408\) | 0.867540 | 0.0429496 | ||||||||
\(409\) | −31.4377 | −1.55449 | −0.777246 | − | 0.629197i | \(-0.783384\pi\) | ||||
−0.777246 | + | 0.629197i | \(0.783384\pi\) | |||||||
\(410\) | 0.925818 | 0.0457229 | ||||||||
\(411\) | 8.47305 | 0.417945 | ||||||||
\(412\) | 1.00764 | 0.0496426 | ||||||||
\(413\) | −45.7919 | −2.25327 | ||||||||
\(414\) | −8.86224 | −0.435556 | ||||||||
\(415\) | 0.625425 | 0.0307009 | ||||||||
\(416\) | 1.26655 | 0.0620978 | ||||||||
\(417\) | 14.3911 | 0.704737 | ||||||||
\(418\) | 6.18750 | 0.302640 | ||||||||
\(419\) | −6.06492 | −0.296291 | −0.148145 | − | 0.988966i | \(-0.547330\pi\) | ||||
−0.148145 | + | 0.988966i | \(0.547330\pi\) | |||||||
\(420\) | 0.921599 | 0.0449694 | ||||||||
\(421\) | −11.9703 | −0.583397 | −0.291698 | − | 0.956510i | \(-0.594220\pi\) | ||||
−0.291698 | + | 0.956510i | \(0.594220\pi\) | |||||||
\(422\) | 25.8348 | 1.25762 | ||||||||
\(423\) | 5.99112 | 0.291298 | ||||||||
\(424\) | 4.13724 | 0.200922 | ||||||||
\(425\) | −4.27495 | −0.207365 | ||||||||
\(426\) | −10.4281 | −0.505245 | ||||||||
\(427\) | −3.42672 | −0.165831 | ||||||||
\(428\) | −6.78676 | −0.328051 | ||||||||
\(429\) | 1.26655 | 0.0611497 | ||||||||
\(430\) | 3.32735 | 0.160459 | ||||||||
\(431\) | 4.23679 | 0.204079 | 0.102039 | − | 0.994780i | \(-0.467463\pi\) | ||||
0.102039 | + | 0.994780i | \(0.467463\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −12.6590 | −0.608352 | −0.304176 | − | 0.952616i | \(-0.598381\pi\) | ||||
−0.304176 | + | 0.952616i | \(0.598381\pi\) | |||||||
\(434\) | −22.5934 | −1.08452 | ||||||||
\(435\) | 0.422909 | 0.0202769 | ||||||||
\(436\) | −10.9790 | −0.525800 | ||||||||
\(437\) | −54.8351 | −2.62312 | ||||||||
\(438\) | −2.36638 | −0.113070 | ||||||||
\(439\) | −26.5844 | −1.26881 | −0.634403 | − | 0.773003i | \(-0.718754\pi\) | ||||
−0.634403 | + | 0.773003i | \(0.718754\pi\) | |||||||
\(440\) | 0.268945 | 0.0128215 | ||||||||
\(441\) | 4.74240 | 0.225828 | ||||||||
\(442\) | 1.09878 | 0.0522638 | ||||||||
\(443\) | 26.5443 | 1.26116 | 0.630579 | − | 0.776125i | \(-0.282817\pi\) | ||||
0.630579 | + | 0.776125i | \(0.282817\pi\) | |||||||
\(444\) | 8.55030 | 0.405779 | ||||||||
\(445\) | −3.12419 | −0.148101 | ||||||||
\(446\) | 9.89572 | 0.468576 | ||||||||
\(447\) | 19.6765 | 0.930665 | ||||||||
\(448\) | 3.42672 | 0.161897 | ||||||||
\(449\) | 33.4432 | 1.57828 | 0.789140 | − | 0.614213i | \(-0.210526\pi\) | ||||
0.789140 | + | 0.614213i | \(0.210526\pi\) | |||||||
\(450\) | −4.92767 | −0.232293 | ||||||||
\(451\) | 3.44241 | 0.162097 | ||||||||
\(452\) | −0.304968 | −0.0143445 | ||||||||
\(453\) | 8.71508 | 0.409470 | ||||||||
\(454\) | 1.05470 | 0.0494997 | ||||||||
\(455\) | 1.16725 | 0.0547216 | ||||||||
\(456\) | 6.18750 | 0.289756 | ||||||||
\(457\) | −39.3979 | −1.84296 | −0.921479 | − | 0.388428i | \(-0.873018\pi\) | ||||
−0.921479 | + | 0.388428i | \(0.873018\pi\) | |||||||
\(458\) | −6.19110 | −0.289291 | ||||||||
\(459\) | 0.867540 | 0.0404933 | ||||||||
\(460\) | −2.38346 | −0.111129 | ||||||||
\(461\) | 2.36247 | 0.110031 | 0.0550155 | − | 0.998485i | \(-0.482479\pi\) | ||||
0.0550155 | + | 0.998485i | \(0.482479\pi\) | |||||||
\(462\) | 3.42672 | 0.159425 | ||||||||
\(463\) | 29.4582 | 1.36904 | 0.684520 | − | 0.728994i | \(-0.260012\pi\) | ||||
0.684520 | + | 0.728994i | \(0.260012\pi\) | |||||||
\(464\) | 1.57247 | 0.0730003 | ||||||||
\(465\) | −1.77324 | −0.0822318 | ||||||||
\(466\) | −28.9847 | −1.34269 | ||||||||
\(467\) | −1.97701 | −0.0914850 | −0.0457425 | − | 0.998953i | \(-0.514565\pi\) | ||||
−0.0457425 | + | 0.998953i | \(0.514565\pi\) | |||||||
\(468\) | 1.26655 | 0.0585464 | ||||||||
\(469\) | −1.30382 | −0.0602050 | ||||||||
\(470\) | 1.61128 | 0.0743229 | ||||||||
\(471\) | 22.7483 | 1.04818 | ||||||||
\(472\) | −13.3632 | −0.615091 | ||||||||
\(473\) | 12.3719 | 0.568859 | ||||||||
\(474\) | −8.37132 | −0.384507 | ||||||||
\(475\) | −30.4899 | −1.39897 | ||||||||
\(476\) | 2.97281 | 0.136259 | ||||||||
\(477\) | 4.13724 | 0.189431 | ||||||||
\(478\) | −4.63720 | −0.212100 | ||||||||
\(479\) | −26.1584 | −1.19521 | −0.597604 | − | 0.801791i | \(-0.703880\pi\) | ||||
−0.597604 | + | 0.801791i | \(0.703880\pi\) | |||||||
\(480\) | 0.268945 | 0.0122756 | ||||||||
\(481\) | 10.8294 | 0.493778 | ||||||||
\(482\) | 13.8531 | 0.630990 | ||||||||
\(483\) | −30.3684 | −1.38181 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −3.09494 | −0.140534 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −28.6097 | −1.29643 | −0.648215 | − | 0.761457i | \(-0.724484\pi\) | ||||
−0.648215 | + | 0.761457i | \(0.724484\pi\) | |||||||
\(488\) | −1.00000 | −0.0452679 | ||||||||
\(489\) | −16.9197 | −0.765137 | ||||||||
\(490\) | 1.27544 | 0.0576187 | ||||||||
\(491\) | −12.1722 | −0.549322 | −0.274661 | − | 0.961541i | \(-0.588566\pi\) | ||||
−0.274661 | + | 0.961541i | \(0.588566\pi\) | |||||||
\(492\) | 3.44241 | 0.155196 | ||||||||
\(493\) | 1.36418 | 0.0614397 | ||||||||
\(494\) | 7.83679 | 0.352594 | ||||||||
\(495\) | 0.268945 | 0.0120882 | ||||||||
\(496\) | −6.59330 | −0.296048 | ||||||||
\(497\) | −35.7343 | −1.60290 | ||||||||
\(498\) | 2.32547 | 0.104207 | ||||||||
\(499\) | −18.9089 | −0.846481 | −0.423240 | − | 0.906017i | \(-0.639107\pi\) | ||||
−0.423240 | + | 0.906017i | \(0.639107\pi\) | |||||||
\(500\) | −2.67000 | −0.119406 | ||||||||
\(501\) | 24.5798 | 1.09814 | ||||||||
\(502\) | −8.63040 | −0.385194 | ||||||||
\(503\) | −16.0313 | −0.714800 | −0.357400 | − | 0.933951i | \(-0.616337\pi\) | ||||
−0.357400 | + | 0.933951i | \(0.616337\pi\) | |||||||
\(504\) | 3.42672 | 0.152638 | ||||||||
\(505\) | −2.86227 | −0.127369 | ||||||||
\(506\) | −8.86224 | −0.393975 | ||||||||
\(507\) | −11.3958 | −0.506107 | ||||||||
\(508\) | 18.8689 | 0.837174 | ||||||||
\(509\) | 41.6067 | 1.84418 | 0.922092 | − | 0.386971i | \(-0.126479\pi\) | ||||
0.922092 | + | 0.386971i | \(0.126479\pi\) | |||||||
\(510\) | 0.233320 | 0.0103316 | ||||||||
\(511\) | −8.10893 | −0.358718 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 6.18750 | 0.273185 | ||||||||
\(514\) | 1.33011 | 0.0586687 | ||||||||
\(515\) | 0.270998 | 0.0119416 | ||||||||
\(516\) | 12.3719 | 0.544641 | ||||||||
\(517\) | 5.99112 | 0.263489 | ||||||||
\(518\) | 29.2995 | 1.28734 | ||||||||
\(519\) | 16.0917 | 0.706348 | ||||||||
\(520\) | 0.340633 | 0.0149377 | ||||||||
\(521\) | 28.9241 | 1.26719 | 0.633593 | − | 0.773667i | \(-0.281579\pi\) | ||||
0.633593 | + | 0.773667i | \(0.281579\pi\) | |||||||
\(522\) | 1.57247 | 0.0688253 | ||||||||
\(523\) | 18.7161 | 0.818400 | 0.409200 | − | 0.912445i | \(-0.365808\pi\) | ||||
0.409200 | + | 0.912445i | \(0.365808\pi\) | |||||||
\(524\) | 3.68893 | 0.161152 | ||||||||
\(525\) | −16.8857 | −0.736954 | ||||||||
\(526\) | −29.1042 | −1.26900 | ||||||||
\(527\) | −5.71995 | −0.249165 | ||||||||
\(528\) | 1.00000 | 0.0435194 | ||||||||
\(529\) | 55.5394 | 2.41476 | ||||||||
\(530\) | 1.11269 | 0.0483322 | ||||||||
\(531\) | −13.3632 | −0.579913 | ||||||||
\(532\) | 21.2028 | 0.919259 | ||||||||
\(533\) | 4.35999 | 0.188852 | ||||||||
\(534\) | −11.6165 | −0.502693 | ||||||||
\(535\) | −1.82527 | −0.0789131 | ||||||||
\(536\) | −0.380487 | −0.0164346 | ||||||||
\(537\) | −20.5271 | −0.885809 | ||||||||
\(538\) | −2.29032 | −0.0987425 | ||||||||
\(539\) | 4.74240 | 0.204269 | ||||||||
\(540\) | 0.268945 | 0.0115736 | ||||||||
\(541\) | −6.77164 | −0.291136 | −0.145568 | − | 0.989348i | \(-0.546501\pi\) | ||||
−0.145568 | + | 0.989348i | \(0.546501\pi\) | |||||||
\(542\) | −23.4290 | −1.00636 | ||||||||
\(543\) | −14.6239 | −0.627573 | ||||||||
\(544\) | 0.867540 | 0.0371955 | ||||||||
\(545\) | −2.95276 | −0.126482 | ||||||||
\(546\) | 4.34011 | 0.185740 | ||||||||
\(547\) | 11.8955 | 0.508616 | 0.254308 | − | 0.967123i | \(-0.418152\pi\) | ||||
0.254308 | + | 0.967123i | \(0.418152\pi\) | |||||||
\(548\) | 8.47305 | 0.361951 | ||||||||
\(549\) | −1.00000 | −0.0426790 | ||||||||
\(550\) | −4.92767 | −0.210116 | ||||||||
\(551\) | 9.72968 | 0.414498 | ||||||||
\(552\) | −8.86224 | −0.377202 | ||||||||
\(553\) | −28.6861 | −1.21986 | ||||||||
\(554\) | 18.8839 | 0.802301 | ||||||||
\(555\) | 2.29956 | 0.0976109 | ||||||||
\(556\) | 14.3911 | 0.610320 | ||||||||
\(557\) | −28.9513 | −1.22671 | −0.613354 | − | 0.789808i | \(-0.710180\pi\) | ||||
−0.613354 | + | 0.789808i | \(0.710180\pi\) | |||||||
\(558\) | −6.59330 | −0.279117 | ||||||||
\(559\) | 15.6696 | 0.662753 | ||||||||
\(560\) | 0.921599 | 0.0389447 | ||||||||
\(561\) | 0.867540 | 0.0366276 | ||||||||
\(562\) | −10.0216 | −0.422737 | ||||||||
\(563\) | −41.4776 | −1.74807 | −0.874036 | − | 0.485861i | \(-0.838506\pi\) | ||||
−0.874036 | + | 0.485861i | \(0.838506\pi\) | |||||||
\(564\) | 5.99112 | 0.252272 | ||||||||
\(565\) | −0.0820196 | −0.00345059 | ||||||||
\(566\) | 2.41609 | 0.101556 | ||||||||
\(567\) | 3.42672 | 0.143909 | ||||||||
\(568\) | −10.4281 | −0.437555 | ||||||||
\(569\) | −8.47596 | −0.355331 | −0.177665 | − | 0.984091i | \(-0.556854\pi\) | ||||
−0.177665 | + | 0.984091i | \(0.556854\pi\) | |||||||
\(570\) | 1.66410 | 0.0697014 | ||||||||
\(571\) | −14.6693 | −0.613892 | −0.306946 | − | 0.951727i | \(-0.599307\pi\) | ||||
−0.306946 | + | 0.951727i | \(0.599307\pi\) | |||||||
\(572\) | 1.26655 | 0.0529572 | ||||||||
\(573\) | −5.11491 | −0.213679 | ||||||||
\(574\) | 11.7962 | 0.492362 | ||||||||
\(575\) | 43.6702 | 1.82117 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −34.5189 | −1.43704 | −0.718520 | − | 0.695506i | \(-0.755180\pi\) | ||||
−0.718520 | + | 0.695506i | \(0.755180\pi\) | |||||||
\(578\) | −16.2474 | −0.675802 | ||||||||
\(579\) | −18.9293 | −0.786676 | ||||||||
\(580\) | 0.422909 | 0.0175603 | ||||||||
\(581\) | 7.96874 | 0.330599 | ||||||||
\(582\) | −11.5077 | −0.477009 | ||||||||
\(583\) | 4.13724 | 0.171347 | ||||||||
\(584\) | −2.36638 | −0.0979216 | ||||||||
\(585\) | 0.340633 | 0.0140834 | ||||||||
\(586\) | 4.40067 | 0.181790 | ||||||||
\(587\) | −38.5034 | −1.58920 | −0.794602 | − | 0.607131i | \(-0.792320\pi\) | ||||
−0.794602 | + | 0.607131i | \(0.792320\pi\) | |||||||
\(588\) | 4.74240 | 0.195573 | ||||||||
\(589\) | −40.7960 | −1.68097 | ||||||||
\(590\) | −3.59396 | −0.147961 | ||||||||
\(591\) | 8.98440 | 0.369569 | ||||||||
\(592\) | 8.55030 | 0.351415 | ||||||||
\(593\) | −13.1113 | −0.538416 | −0.269208 | − | 0.963082i | \(-0.586762\pi\) | ||||
−0.269208 | + | 0.963082i | \(0.586762\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | 0.799523 | 0.0327773 | ||||||||
\(596\) | 19.6765 | 0.805980 | ||||||||
\(597\) | 15.1438 | 0.619795 | ||||||||
\(598\) | −11.2245 | −0.459004 | ||||||||
\(599\) | −34.2308 | −1.39863 | −0.699316 | − | 0.714813i | \(-0.746512\pi\) | ||||
−0.699316 | + | 0.714813i | \(0.746512\pi\) | |||||||
\(600\) | −4.92767 | −0.201171 | ||||||||
\(601\) | −2.51772 | −0.102700 | −0.0513499 | − | 0.998681i | \(-0.516352\pi\) | ||||
−0.0513499 | + | 0.998681i | \(0.516352\pi\) | |||||||
\(602\) | 42.3949 | 1.72789 | ||||||||
\(603\) | −0.380487 | −0.0154946 | ||||||||
\(604\) | 8.71508 | 0.354611 | ||||||||
\(605\) | 0.268945 | 0.0109342 | ||||||||
\(606\) | −10.6426 | −0.432326 | ||||||||
\(607\) | −24.5474 | −0.996349 | −0.498174 | − | 0.867077i | \(-0.665996\pi\) | ||||
−0.498174 | + | 0.867077i | \(0.665996\pi\) | |||||||
\(608\) | 6.18750 | 0.250936 | ||||||||
\(609\) | 5.38842 | 0.218350 | ||||||||
\(610\) | −0.268945 | −0.0108893 | ||||||||
\(611\) | 7.58806 | 0.306980 | ||||||||
\(612\) | 0.867540 | 0.0350682 | ||||||||
\(613\) | 25.2944 | 1.02163 | 0.510816 | − | 0.859690i | \(-0.329343\pi\) | ||||
0.510816 | + | 0.859690i | \(0.329343\pi\) | |||||||
\(614\) | −17.0682 | −0.688818 | ||||||||
\(615\) | 0.925818 | 0.0373326 | ||||||||
\(616\) | 3.42672 | 0.138066 | ||||||||
\(617\) | 7.83562 | 0.315450 | 0.157725 | − | 0.987483i | \(-0.449584\pi\) | ||||
0.157725 | + | 0.987483i | \(0.449584\pi\) | |||||||
\(618\) | 1.00764 | 0.0405330 | ||||||||
\(619\) | 28.4337 | 1.14285 | 0.571424 | − | 0.820655i | \(-0.306391\pi\) | ||||
0.571424 | + | 0.820655i | \(0.306391\pi\) | |||||||
\(620\) | −1.77324 | −0.0712148 | ||||||||
\(621\) | −8.86224 | −0.355630 | ||||||||
\(622\) | −28.3715 | −1.13759 | ||||||||
\(623\) | −39.8063 | −1.59481 | ||||||||
\(624\) | 1.26655 | 0.0507026 | ||||||||
\(625\) | 23.9203 | 0.956810 | ||||||||
\(626\) | −9.88599 | −0.395124 | ||||||||
\(627\) | 6.18750 | 0.247105 | ||||||||
\(628\) | 22.7483 | 0.907755 | ||||||||
\(629\) | 7.41772 | 0.295764 | ||||||||
\(630\) | 0.921599 | 0.0367174 | ||||||||
\(631\) | 13.6904 | 0.545006 | 0.272503 | − | 0.962155i | \(-0.412149\pi\) | ||||
0.272503 | + | 0.962155i | \(0.412149\pi\) | |||||||
\(632\) | −8.37132 | −0.332993 | ||||||||
\(633\) | 25.8348 | 1.02684 | ||||||||
\(634\) | 5.91378 | 0.234866 | ||||||||
\(635\) | 5.07471 | 0.201384 | ||||||||
\(636\) | 4.13724 | 0.164052 | ||||||||
\(637\) | 6.00649 | 0.237986 | ||||||||
\(638\) | 1.57247 | 0.0622548 | ||||||||
\(639\) | −10.4281 | −0.412531 | ||||||||
\(640\) | 0.268945 | 0.0106310 | ||||||||
\(641\) | −16.9952 | −0.671271 | −0.335636 | − | 0.941992i | \(-0.608951\pi\) | ||||
−0.335636 | + | 0.941992i | \(0.608951\pi\) | |||||||
\(642\) | −6.78676 | −0.267852 | ||||||||
\(643\) | −25.4697 | −1.00443 | −0.502214 | − | 0.864743i | \(-0.667481\pi\) | ||||
−0.502214 | + | 0.864743i | \(0.667481\pi\) | |||||||
\(644\) | −30.3684 | −1.19668 | ||||||||
\(645\) | 3.32735 | 0.131014 | ||||||||
\(646\) | 5.36790 | 0.211197 | ||||||||
\(647\) | −23.3764 | −0.919021 | −0.459510 | − | 0.888172i | \(-0.651975\pi\) | ||||
−0.459510 | + | 0.888172i | \(0.651975\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −13.3632 | −0.524551 | ||||||||
\(650\) | −6.24115 | −0.244798 | ||||||||
\(651\) | −22.5934 | −0.885504 | ||||||||
\(652\) | −16.9197 | −0.662628 | ||||||||
\(653\) | −14.5309 | −0.568638 | −0.284319 | − | 0.958730i | \(-0.591767\pi\) | ||||
−0.284319 | + | 0.958730i | \(0.591767\pi\) | |||||||
\(654\) | −10.9790 | −0.429314 | ||||||||
\(655\) | 0.992120 | 0.0387654 | ||||||||
\(656\) | 3.44241 | 0.134403 | ||||||||
\(657\) | −2.36638 | −0.0923214 | ||||||||
\(658\) | 20.5299 | 0.800338 | ||||||||
\(659\) | −1.83670 | −0.0715475 | −0.0357738 | − | 0.999360i | \(-0.511390\pi\) | ||||
−0.0357738 | + | 0.999360i | \(0.511390\pi\) | |||||||
\(660\) | 0.268945 | 0.0104687 | ||||||||
\(661\) | 27.0191 | 1.05092 | 0.525460 | − | 0.850818i | \(-0.323893\pi\) | ||||
0.525460 | + | 0.850818i | \(0.323893\pi\) | |||||||
\(662\) | 18.4377 | 0.716602 | ||||||||
\(663\) | 1.09878 | 0.0426732 | ||||||||
\(664\) | 2.32547 | 0.0902459 | ||||||||
\(665\) | 5.70239 | 0.221129 | ||||||||
\(666\) | 8.55030 | 0.331317 | ||||||||
\(667\) | −13.9356 | −0.539590 | ||||||||
\(668\) | 24.5798 | 0.951021 | ||||||||
\(669\) | 9.89572 | 0.382591 | ||||||||
\(670\) | −0.102330 | −0.00395336 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 3.42672 | 0.132189 | ||||||||
\(673\) | 31.5860 | 1.21755 | 0.608775 | − | 0.793343i | \(-0.291661\pi\) | ||||
0.608775 | + | 0.793343i | \(0.291661\pi\) | |||||||
\(674\) | 35.4326 | 1.36481 | ||||||||
\(675\) | −4.92767 | −0.189666 | ||||||||
\(676\) | −11.3958 | −0.438302 | ||||||||
\(677\) | 33.9490 | 1.30477 | 0.652384 | − | 0.757889i | \(-0.273769\pi\) | ||||
0.652384 | + | 0.757889i | \(0.273769\pi\) | |||||||
\(678\) | −0.304968 | −0.0117122 | ||||||||
\(679\) | −39.4336 | −1.51332 | ||||||||
\(680\) | 0.233320 | 0.00894743 | ||||||||
\(681\) | 1.05470 | 0.0404164 | ||||||||
\(682\) | −6.59330 | −0.252470 | ||||||||
\(683\) | −5.96961 | −0.228421 | −0.114210 | − | 0.993457i | \(-0.536434\pi\) | ||||
−0.114210 | + | 0.993457i | \(0.536434\pi\) | |||||||
\(684\) | 6.18750 | 0.236585 | ||||||||
\(685\) | 2.27878 | 0.0870679 | ||||||||
\(686\) | −7.73617 | −0.295368 | ||||||||
\(687\) | −6.19110 | −0.236205 | ||||||||
\(688\) | 12.3719 | 0.471673 | ||||||||
\(689\) | 5.24003 | 0.199629 | ||||||||
\(690\) | −2.38346 | −0.0907366 | ||||||||
\(691\) | −17.1589 | −0.652757 | −0.326378 | − | 0.945239i | \(-0.605828\pi\) | ||||
−0.326378 | + | 0.945239i | \(0.605828\pi\) | |||||||
\(692\) | 16.0917 | 0.611715 | ||||||||
\(693\) | 3.42672 | 0.130170 | ||||||||
\(694\) | 32.0180 | 1.21538 | ||||||||
\(695\) | 3.87043 | 0.146814 | ||||||||
\(696\) | 1.57247 | 0.0596045 | ||||||||
\(697\) | 2.98642 | 0.113119 | ||||||||
\(698\) | 0.763609 | 0.0289030 | ||||||||
\(699\) | −28.9847 | −1.09630 | ||||||||
\(700\) | −16.8857 | −0.638221 | ||||||||
\(701\) | −23.4422 | −0.885399 | −0.442699 | − | 0.896670i | \(-0.645979\pi\) | ||||
−0.442699 | + | 0.896670i | \(0.645979\pi\) | |||||||
\(702\) | 1.26655 | 0.0478029 | ||||||||
\(703\) | 52.9049 | 1.99535 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 1.61128 | 0.0606844 | ||||||||
\(706\) | 16.4468 | 0.618984 | ||||||||
\(707\) | −36.4692 | −1.37156 | ||||||||
\(708\) | −13.3632 | −0.502220 | ||||||||
\(709\) | −12.4098 | −0.466061 | −0.233030 | − | 0.972469i | \(-0.574864\pi\) | ||||
−0.233030 | + | 0.972469i | \(0.574864\pi\) | |||||||
\(710\) | −2.80460 | −0.105255 | ||||||||
\(711\) | −8.37132 | −0.313949 | ||||||||
\(712\) | −11.6165 | −0.435345 | ||||||||
\(713\) | 58.4314 | 2.18827 | ||||||||
\(714\) | 2.97281 | 0.111255 | ||||||||
\(715\) | 0.340633 | 0.0127389 | ||||||||
\(716\) | −20.5271 | −0.767133 | ||||||||
\(717\) | −4.63720 | −0.173179 | ||||||||
\(718\) | 19.7050 | 0.735385 | ||||||||
\(719\) | 5.73145 | 0.213747 | 0.106874 | − | 0.994273i | \(-0.465916\pi\) | ||||
0.106874 | + | 0.994273i | \(0.465916\pi\) | |||||||
\(720\) | 0.268945 | 0.0100230 | ||||||||
\(721\) | 3.45288 | 0.128592 | ||||||||
\(722\) | 19.2851 | 0.717719 | ||||||||
\(723\) | 13.8531 | 0.515201 | ||||||||
\(724\) | −14.6239 | −0.543494 | ||||||||
\(725\) | −7.74863 | −0.287777 | ||||||||
\(726\) | 1.00000 | 0.0371135 | ||||||||
\(727\) | −38.7317 | −1.43648 | −0.718240 | − | 0.695795i | \(-0.755052\pi\) | ||||
−0.718240 | + | 0.695795i | \(0.755052\pi\) | |||||||
\(728\) | 4.34011 | 0.160855 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.636427 | −0.0235552 | ||||||||
\(731\) | 10.7331 | 0.396977 | ||||||||
\(732\) | −1.00000 | −0.0369611 | ||||||||
\(733\) | 30.5487 | 1.12834 | 0.564171 | − | 0.825658i | \(-0.309196\pi\) | ||||
0.564171 | + | 0.825658i | \(0.309196\pi\) | |||||||
\(734\) | −20.4095 | −0.753329 | ||||||||
\(735\) | 1.27544 | 0.0470454 | ||||||||
\(736\) | −8.86224 | −0.326667 | ||||||||
\(737\) | −0.380487 | −0.0140154 | ||||||||
\(738\) | 3.44241 | 0.126717 | ||||||||
\(739\) | 13.3787 | 0.492142 | 0.246071 | − | 0.969252i | \(-0.420860\pi\) | ||||
0.246071 | + | 0.969252i | \(0.420860\pi\) | |||||||
\(740\) | 2.29956 | 0.0845335 | ||||||||
\(741\) | 7.83679 | 0.287892 | ||||||||
\(742\) | 14.1772 | 0.520460 | ||||||||
\(743\) | 41.2178 | 1.51213 | 0.756067 | − | 0.654494i | \(-0.227118\pi\) | ||||
0.756067 | + | 0.654494i | \(0.227118\pi\) | |||||||
\(744\) | −6.59330 | −0.241722 | ||||||||
\(745\) | 5.29189 | 0.193880 | ||||||||
\(746\) | −35.9190 | −1.31509 | ||||||||
\(747\) | 2.32547 | 0.0850846 | ||||||||
\(748\) | 0.867540 | 0.0317204 | ||||||||
\(749\) | −23.2563 | −0.849768 | ||||||||
\(750\) | −2.67000 | −0.0974945 | ||||||||
\(751\) | 17.5229 | 0.639420 | 0.319710 | − | 0.947515i | \(-0.396414\pi\) | ||||
0.319710 | + | 0.947515i | \(0.396414\pi\) | |||||||
\(752\) | 5.99112 | 0.218474 | ||||||||
\(753\) | −8.63040 | −0.314509 | ||||||||
\(754\) | 1.99162 | 0.0725305 | ||||||||
\(755\) | 2.34388 | 0.0853024 | ||||||||
\(756\) | 3.42672 | 0.124629 | ||||||||
\(757\) | −17.5737 | −0.638726 | −0.319363 | − | 0.947632i | \(-0.603469\pi\) | ||||
−0.319363 | + | 0.947632i | \(0.603469\pi\) | |||||||
\(758\) | 29.2039 | 1.06073 | ||||||||
\(759\) | −8.86224 | −0.321679 | ||||||||
\(760\) | 1.66410 | 0.0603631 | ||||||||
\(761\) | −41.5905 | −1.50765 | −0.753827 | − | 0.657073i | \(-0.771794\pi\) | ||||
−0.753827 | + | 0.657073i | \(0.771794\pi\) | |||||||
\(762\) | 18.8689 | 0.683550 | ||||||||
\(763\) | −37.6220 | −1.36201 | ||||||||
\(764\) | −5.11491 | −0.185051 | ||||||||
\(765\) | 0.233320 | 0.00843572 | ||||||||
\(766\) | −30.2591 | −1.09330 | ||||||||
\(767\) | −16.9252 | −0.611133 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 22.8539 | 0.824132 | 0.412066 | − | 0.911154i | \(-0.364807\pi\) | ||||
0.412066 | + | 0.911154i | \(0.364807\pi\) | |||||||
\(770\) | 0.921599 | 0.0332121 | ||||||||
\(771\) | 1.33011 | 0.0479028 | ||||||||
\(772\) | −18.9293 | −0.681281 | ||||||||
\(773\) | −47.8479 | −1.72097 | −0.860485 | − | 0.509476i | \(-0.829839\pi\) | ||||
−0.860485 | + | 0.509476i | \(0.829839\pi\) | |||||||
\(774\) | 12.3719 | 0.444697 | ||||||||
\(775\) | 32.4896 | 1.16706 | ||||||||
\(776\) | −11.5077 | −0.413102 | ||||||||
\(777\) | 29.2995 | 1.05111 | ||||||||
\(778\) | −6.13420 | −0.219922 | ||||||||
\(779\) | 21.2999 | 0.763148 | ||||||||
\(780\) | 0.340633 | 0.0121966 | ||||||||
\(781\) | −10.4281 | −0.373148 | ||||||||
\(782\) | −7.68835 | −0.274935 | ||||||||
\(783\) | 1.57247 | 0.0561956 | ||||||||
\(784\) | 4.74240 | 0.169371 | ||||||||
\(785\) | 6.11803 | 0.218362 | ||||||||
\(786\) | 3.68893 | 0.131580 | ||||||||
\(787\) | 6.39840 | 0.228078 | 0.114039 | − | 0.993476i | \(-0.463621\pi\) | ||||
0.114039 | + | 0.993476i | \(0.463621\pi\) | |||||||
\(788\) | 8.98440 | 0.320056 | ||||||||
\(789\) | −29.1042 | −1.03614 | ||||||||
\(790\) | −2.25142 | −0.0801021 | ||||||||
\(791\) | −1.04504 | −0.0371573 | ||||||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | −1.26655 | −0.0449766 | ||||||||
\(794\) | 7.09173 | 0.251676 | ||||||||
\(795\) | 1.11269 | 0.0394630 | ||||||||
\(796\) | 15.1438 | 0.536758 | ||||||||
\(797\) | 23.0083 | 0.814996 | 0.407498 | − | 0.913206i | \(-0.366401\pi\) | ||||
0.407498 | + | 0.913206i | \(0.366401\pi\) | |||||||
\(798\) | 21.2028 | 0.750571 | ||||||||
\(799\) | 5.19753 | 0.183875 | ||||||||
\(800\) | −4.92767 | −0.174219 | ||||||||
\(801\) | −11.6165 | −0.410447 | ||||||||
\(802\) | −29.9023 | −1.05589 | ||||||||
\(803\) | −2.36638 | −0.0835079 | ||||||||
\(804\) | −0.380487 | −0.0134188 | ||||||||
\(805\) | −8.16743 | −0.287864 | ||||||||
\(806\) | −8.35075 | −0.294143 | ||||||||
\(807\) | −2.29032 | −0.0806229 | ||||||||
\(808\) | −10.6426 | −0.374405 | ||||||||
\(809\) | 23.5409 | 0.827653 | 0.413827 | − | 0.910356i | \(-0.364192\pi\) | ||||
0.413827 | + | 0.910356i | \(0.364192\pi\) | |||||||
\(810\) | 0.268945 | 0.00944976 | ||||||||
\(811\) | 13.2119 | 0.463932 | 0.231966 | − | 0.972724i | \(-0.425484\pi\) | ||||
0.231966 | + | 0.972724i | \(0.425484\pi\) | |||||||
\(812\) | 5.38842 | 0.189097 | ||||||||
\(813\) | −23.4290 | −0.821690 | ||||||||
\(814\) | 8.55030 | 0.299688 | ||||||||
\(815\) | −4.55048 | −0.159396 | ||||||||
\(816\) | 0.867540 | 0.0303700 | ||||||||
\(817\) | 76.5509 | 2.67818 | ||||||||
\(818\) | −31.4377 | −1.09919 | ||||||||
\(819\) | 4.34011 | 0.151656 | ||||||||
\(820\) | 0.925818 | 0.0323310 | ||||||||
\(821\) | 17.7547 | 0.619643 | 0.309821 | − | 0.950795i | \(-0.399731\pi\) | ||||
0.309821 | + | 0.950795i | \(0.399731\pi\) | |||||||
\(822\) | 8.47305 | 0.295531 | ||||||||
\(823\) | 32.3631 | 1.12811 | 0.564054 | − | 0.825738i | \(-0.309241\pi\) | ||||
0.564054 | + | 0.825738i | \(0.309241\pi\) | |||||||
\(824\) | 1.00764 | 0.0351026 | ||||||||
\(825\) | −4.92767 | −0.171559 | ||||||||
\(826\) | −45.7919 | −1.59330 | ||||||||
\(827\) | −40.4152 | −1.40537 | −0.702686 | − | 0.711500i | \(-0.748016\pi\) | ||||
−0.702686 | + | 0.711500i | \(0.748016\pi\) | |||||||
\(828\) | −8.86224 | −0.307984 | ||||||||
\(829\) | 22.9984 | 0.798767 | 0.399384 | − | 0.916784i | \(-0.369224\pi\) | ||||
0.399384 | + | 0.916784i | \(0.369224\pi\) | |||||||
\(830\) | 0.625425 | 0.0217088 | ||||||||
\(831\) | 18.8839 | 0.655076 | ||||||||
\(832\) | 1.26655 | 0.0439098 | ||||||||
\(833\) | 4.11422 | 0.142549 | ||||||||
\(834\) | 14.3911 | 0.498325 | ||||||||
\(835\) | 6.61062 | 0.228770 | ||||||||
\(836\) | 6.18750 | 0.213999 | ||||||||
\(837\) | −6.59330 | −0.227898 | ||||||||
\(838\) | −6.06492 | −0.209509 | ||||||||
\(839\) | −1.45169 | −0.0501179 | −0.0250589 | − | 0.999686i | \(-0.507977\pi\) | ||||
−0.0250589 | + | 0.999686i | \(0.507977\pi\) | |||||||
\(840\) | 0.921599 | 0.0317982 | ||||||||
\(841\) | −26.5273 | −0.914735 | ||||||||
\(842\) | −11.9703 | −0.412524 | ||||||||
\(843\) | −10.0216 | −0.345163 | ||||||||
\(844\) | 25.8348 | 0.889271 | ||||||||
\(845\) | −3.06486 | −0.105434 | ||||||||
\(846\) | 5.99112 | 0.205979 | ||||||||
\(847\) | 3.42672 | 0.117743 | ||||||||
\(848\) | 4.13724 | 0.142073 | ||||||||
\(849\) | 2.41609 | 0.0829200 | ||||||||
\(850\) | −4.27495 | −0.146629 | ||||||||
\(851\) | −75.7748 | −2.59753 | ||||||||
\(852\) | −10.4281 | −0.357262 | ||||||||
\(853\) | 42.6983 | 1.46196 | 0.730981 | − | 0.682398i | \(-0.239063\pi\) | ||||
0.730981 | + | 0.682398i | \(0.239063\pi\) | |||||||
\(854\) | −3.42672 | −0.117260 | ||||||||
\(855\) | 1.66410 | 0.0569109 | ||||||||
\(856\) | −6.78676 | −0.231967 | ||||||||
\(857\) | −4.02296 | −0.137422 | −0.0687108 | − | 0.997637i | \(-0.521889\pi\) | ||||
−0.0687108 | + | 0.997637i | \(0.521889\pi\) | |||||||
\(858\) | 1.26655 | 0.0432394 | ||||||||
\(859\) | −11.2054 | −0.382323 | −0.191162 | − | 0.981559i | \(-0.561225\pi\) | ||||
−0.191162 | + | 0.981559i | \(0.561225\pi\) | |||||||
\(860\) | 3.32735 | 0.113462 | ||||||||
\(861\) | 11.7962 | 0.402012 | ||||||||
\(862\) | 4.23679 | 0.144306 | ||||||||
\(863\) | −38.2809 | −1.30310 | −0.651548 | − | 0.758607i | \(-0.725880\pi\) | ||||
−0.651548 | + | 0.758607i | \(0.725880\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 4.32779 | 0.147149 | ||||||||
\(866\) | −12.6590 | −0.430170 | ||||||||
\(867\) | −16.2474 | −0.551790 | ||||||||
\(868\) | −22.5934 | −0.766869 | ||||||||
\(869\) | −8.37132 | −0.283978 | ||||||||
\(870\) | 0.422909 | 0.0143380 | ||||||||
\(871\) | −0.481907 | −0.0163288 | ||||||||
\(872\) | −10.9790 | −0.371797 | ||||||||
\(873\) | −11.5077 | −0.389476 | ||||||||
\(874\) | −54.8351 | −1.85483 | ||||||||
\(875\) | −9.14933 | −0.309304 | ||||||||
\(876\) | −2.36638 | −0.0799527 | ||||||||
\(877\) | 14.9533 | 0.504937 | 0.252468 | − | 0.967605i | \(-0.418758\pi\) | ||||
0.252468 | + | 0.967605i | \(0.418758\pi\) | |||||||
\(878\) | −26.5844 | −0.897181 | ||||||||
\(879\) | 4.40067 | 0.148431 | ||||||||
\(880\) | 0.268945 | 0.00906613 | ||||||||
\(881\) | −13.4894 | −0.454469 | −0.227234 | − | 0.973840i | \(-0.572968\pi\) | ||||
−0.227234 | + | 0.973840i | \(0.572968\pi\) | |||||||
\(882\) | 4.74240 | 0.159685 | ||||||||
\(883\) | −53.1259 | −1.78783 | −0.893915 | − | 0.448236i | \(-0.852052\pi\) | ||||
−0.893915 | + | 0.448236i | \(0.852052\pi\) | |||||||
\(884\) | 1.09878 | 0.0369561 | ||||||||
\(885\) | −3.59396 | −0.120810 | ||||||||
\(886\) | 26.5443 | 0.891773 | ||||||||
\(887\) | 33.1287 | 1.11235 | 0.556176 | − | 0.831065i | \(-0.312268\pi\) | ||||
0.556176 | + | 0.831065i | \(0.312268\pi\) | |||||||
\(888\) | 8.55030 | 0.286929 | ||||||||
\(889\) | 64.6586 | 2.16858 | ||||||||
\(890\) | −3.12419 | −0.104723 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 9.89572 | 0.331333 | ||||||||
\(893\) | 37.0700 | 1.24050 | ||||||||
\(894\) | 19.6765 | 0.658080 | ||||||||
\(895\) | −5.52066 | −0.184535 | ||||||||
\(896\) | 3.42672 | 0.114479 | ||||||||
\(897\) | −11.2245 | −0.374775 | ||||||||
\(898\) | 33.4432 | 1.11601 | ||||||||
\(899\) | −10.3678 | −0.345785 | ||||||||
\(900\) | −4.92767 | −0.164256 | ||||||||
\(901\) | 3.58922 | 0.119574 | ||||||||
\(902\) | 3.44241 | 0.114620 | ||||||||
\(903\) | 42.3949 | 1.41081 | ||||||||
\(904\) | −0.304968 | −0.0101431 | ||||||||
\(905\) | −3.93303 | −0.130738 | ||||||||
\(906\) | 8.71508 | 0.289539 | ||||||||
\(907\) | 35.6391 | 1.18338 | 0.591688 | − | 0.806167i | \(-0.298462\pi\) | ||||
0.591688 | + | 0.806167i | \(0.298462\pi\) | |||||||
\(908\) | 1.05470 | 0.0350016 | ||||||||
\(909\) | −10.6426 | −0.352993 | ||||||||
\(910\) | 1.16725 | 0.0386940 | ||||||||
\(911\) | −40.8527 | −1.35351 | −0.676755 | − | 0.736208i | \(-0.736614\pi\) | ||||
−0.676755 | + | 0.736208i | \(0.736614\pi\) | |||||||
\(912\) | 6.18750 | 0.204889 | ||||||||
\(913\) | 2.32547 | 0.0769619 | ||||||||
\(914\) | −39.3979 | −1.30317 | ||||||||
\(915\) | −0.268945 | −0.00889105 | ||||||||
\(916\) | −6.19110 | −0.204560 | ||||||||
\(917\) | 12.6409 | 0.417440 | ||||||||
\(918\) | 0.867540 | 0.0286331 | ||||||||
\(919\) | −6.75599 | −0.222860 | −0.111430 | − | 0.993772i | \(-0.535543\pi\) | ||||
−0.111430 | + | 0.993772i | \(0.535543\pi\) | |||||||
\(920\) | −2.38346 | −0.0785802 | ||||||||
\(921\) | −17.0682 | −0.562418 | ||||||||
\(922\) | 2.36247 | 0.0778037 | ||||||||
\(923\) | −13.2078 | −0.434739 | ||||||||
\(924\) | 3.42672 | 0.112731 | ||||||||
\(925\) | −42.1330 | −1.38533 | ||||||||
\(926\) | 29.4582 | 0.968057 | ||||||||
\(927\) | 1.00764 | 0.0330951 | ||||||||
\(928\) | 1.57247 | 0.0516190 | ||||||||
\(929\) | −30.3584 | −0.996026 | −0.498013 | − | 0.867170i | \(-0.665937\pi\) | ||||
−0.498013 | + | 0.867170i | \(0.665937\pi\) | |||||||
\(930\) | −1.77324 | −0.0581467 | ||||||||
\(931\) | 29.3436 | 0.961697 | ||||||||
\(932\) | −28.9847 | −0.949426 | ||||||||
\(933\) | −28.3715 | −0.928841 | ||||||||
\(934\) | −1.97701 | −0.0646896 | ||||||||
\(935\) | 0.233320 | 0.00763040 | ||||||||
\(936\) | 1.26655 | 0.0413985 | ||||||||
\(937\) | −7.42112 | −0.242437 | −0.121219 | − | 0.992626i | \(-0.538680\pi\) | ||||
−0.121219 | + | 0.992626i | \(0.538680\pi\) | |||||||
\(938\) | −1.30382 | −0.0425713 | ||||||||
\(939\) | −9.88599 | −0.322617 | ||||||||
\(940\) | 1.61128 | 0.0525542 | ||||||||
\(941\) | −36.7139 | −1.19684 | −0.598419 | − | 0.801183i | \(-0.704204\pi\) | ||||
−0.598419 | + | 0.801183i | \(0.704204\pi\) | |||||||
\(942\) | 22.7483 | 0.741179 | ||||||||
\(943\) | −30.5075 | −0.993459 | ||||||||
\(944\) | −13.3632 | −0.434935 | ||||||||
\(945\) | 0.921599 | 0.0299796 | ||||||||
\(946\) | 12.3719 | 0.402244 | ||||||||
\(947\) | 27.1926 | 0.883641 | 0.441821 | − | 0.897103i | \(-0.354333\pi\) | ||||
0.441821 | + | 0.897103i | \(0.354333\pi\) | |||||||
\(948\) | −8.37132 | −0.271888 | ||||||||
\(949\) | −2.99715 | −0.0972915 | ||||||||
\(950\) | −30.4899 | −0.989224 | ||||||||
\(951\) | 5.91378 | 0.191767 | ||||||||
\(952\) | 2.97281 | 0.0963494 | ||||||||
\(953\) | −11.2829 | −0.365488 | −0.182744 | − | 0.983161i | \(-0.558498\pi\) | ||||
−0.182744 | + | 0.983161i | \(0.558498\pi\) | |||||||
\(954\) | 4.13724 | 0.133948 | ||||||||
\(955\) | −1.37563 | −0.0445144 | ||||||||
\(956\) | −4.63720 | −0.149978 | ||||||||
\(957\) | 1.57247 | 0.0508309 | ||||||||
\(958\) | −26.1584 | −0.845140 | ||||||||
\(959\) | 29.0347 | 0.937581 | ||||||||
\(960\) | 0.268945 | 0.00868016 | ||||||||
\(961\) | 12.4716 | 0.402309 | ||||||||
\(962\) | 10.8294 | 0.349154 | ||||||||
\(963\) | −6.78676 | −0.218700 | ||||||||
\(964\) | 13.8531 | 0.446177 | ||||||||
\(965\) | −5.09095 | −0.163883 | ||||||||
\(966\) | −30.3684 | −0.977088 | ||||||||
\(967\) | 47.9113 | 1.54072 | 0.770361 | − | 0.637608i | \(-0.220076\pi\) | ||||
0.770361 | + | 0.637608i | \(0.220076\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 5.36790 | 0.172442 | ||||||||
\(970\) | −3.09494 | −0.0993724 | ||||||||
\(971\) | 27.4932 | 0.882298 | 0.441149 | − | 0.897434i | \(-0.354571\pi\) | ||||
0.441149 | + | 0.897434i | \(0.354571\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 49.3144 | 1.58095 | ||||||||
\(974\) | −28.6097 | −0.916715 | ||||||||
\(975\) | −6.24115 | −0.199877 | ||||||||
\(976\) | −1.00000 | −0.0320092 | ||||||||
\(977\) | 7.09610 | 0.227024 | 0.113512 | − | 0.993537i | \(-0.463790\pi\) | ||||
0.113512 | + | 0.993537i | \(0.463790\pi\) | |||||||
\(978\) | −16.9197 | −0.541034 | ||||||||
\(979\) | −11.6165 | −0.371263 | ||||||||
\(980\) | 1.27544 | 0.0407426 | ||||||||
\(981\) | −10.9790 | −0.350533 | ||||||||
\(982\) | −12.1722 | −0.388429 | ||||||||
\(983\) | 49.9351 | 1.59268 | 0.796342 | − | 0.604847i | \(-0.206766\pi\) | ||||
0.796342 | + | 0.604847i | \(0.206766\pi\) | |||||||
\(984\) | 3.44241 | 0.109740 | ||||||||
\(985\) | 2.41631 | 0.0769901 | ||||||||
\(986\) | 1.36418 | 0.0434445 | ||||||||
\(987\) | 20.5299 | 0.653473 | ||||||||
\(988\) | 7.83679 | 0.249321 | ||||||||
\(989\) | −109.642 | −3.48643 | ||||||||
\(990\) | 0.268945 | 0.00854763 | ||||||||
\(991\) | 25.0878 | 0.796942 | 0.398471 | − | 0.917181i | \(-0.369541\pi\) | ||||
0.398471 | + | 0.917181i | \(0.369541\pi\) | |||||||
\(992\) | −6.59330 | −0.209337 | ||||||||
\(993\) | 18.4377 | 0.585103 | ||||||||
\(994\) | −35.7343 | −1.13342 | ||||||||
\(995\) | 4.07286 | 0.129118 | ||||||||
\(996\) | 2.32547 | 0.0736855 | ||||||||
\(997\) | 55.0312 | 1.74285 | 0.871427 | − | 0.490525i | \(-0.163195\pi\) | ||||
0.871427 | + | 0.490525i | \(0.163195\pi\) | |||||||
\(998\) | −18.9089 | −0.598552 | ||||||||
\(999\) | 8.55030 | 0.270519 |
(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.bc.1.4 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4026.2.a.bc.1.4 | ✓ | 9 | 1.1 | even | 1 | trivial |