Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5610,2,Mod(1,5610)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5610, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("5610.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5610.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: | \(44.7960755339\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 8 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5610.1 |
$q$-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 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −3.37228 | −1.27460 | −0.637301 | − | 0.770615i | \(-0.719949\pi\) | ||||
−0.637301 | + | 0.770615i | \(0.719949\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −4.00000 | −1.10940 | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 3.37228 | 0.901280 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 4.00000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 3.37228 | 0.735892 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −7.37228 | −1.53723 | −0.768613 | − | 0.639713i | \(-0.779053\pi\) | ||||
−0.768613 | + | 0.639713i | \(0.779053\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.00000 | 0.784465 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −3.37228 | −0.637301 | ||||||||
\(29\) | −0.627719 | −0.116564 | −0.0582822 | − | 0.998300i | \(-0.518562\pi\) | ||||
−0.0582822 | + | 0.998300i | \(0.518562\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 8.11684 | 1.45783 | 0.728914 | − | 0.684605i | \(-0.240025\pi\) | ||||
0.728914 | + | 0.684605i | \(0.240025\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | −3.37228 | −0.570020 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −2.74456 | −0.451203 | −0.225602 | − | 0.974220i | \(-0.572435\pi\) | ||||
−0.225602 | + | 0.974220i | \(0.572435\pi\) | |||||||
\(38\) | −4.00000 | −0.648886 | ||||||||
\(39\) | 4.00000 | 0.640513 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −0.744563 | −0.116281 | −0.0581406 | − | 0.998308i | \(-0.518517\pi\) | ||||
−0.0581406 | + | 0.998308i | \(0.518517\pi\) | |||||||
\(42\) | −3.37228 | −0.520354 | ||||||||
\(43\) | −4.62772 | −0.705720 | −0.352860 | − | 0.935676i | \(-0.614791\pi\) | ||||
−0.352860 | + | 0.935676i | \(0.614791\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 7.37228 | 1.08698 | ||||||||
\(47\) | −0.744563 | −0.108606 | −0.0543028 | − | 0.998525i | \(-0.517294\pi\) | ||||
−0.0543028 | + | 0.998525i | \(0.517294\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 4.37228 | 0.624612 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −4.00000 | −0.554700 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 3.37228 | 0.450640 | ||||||||
\(57\) | −4.00000 | −0.529813 | ||||||||
\(58\) | 0.627719 | 0.0824235 | ||||||||
\(59\) | 1.25544 | 0.163444 | 0.0817220 | − | 0.996655i | \(-0.473958\pi\) | ||||
0.0817220 | + | 0.996655i | \(0.473958\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | −11.4891 | −1.47103 | −0.735516 | − | 0.677507i | \(-0.763060\pi\) | ||||
−0.735516 | + | 0.677507i | \(0.763060\pi\) | |||||||
\(62\) | −8.11684 | −1.03084 | ||||||||
\(63\) | −3.37228 | −0.424868 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.00000 | −0.496139 | ||||||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | 1.00000 | 0.121268 | ||||||||
\(69\) | 7.37228 | 0.887518 | ||||||||
\(70\) | 3.37228 | 0.403065 | ||||||||
\(71\) | −6.74456 | −0.800432 | −0.400216 | − | 0.916421i | \(-0.631065\pi\) | ||||
−0.400216 | + | 0.916421i | \(0.631065\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −6.00000 | −0.702247 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | 2.74456 | 0.319049 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 4.00000 | 0.458831 | ||||||||
\(77\) | −3.37228 | −0.384307 | ||||||||
\(78\) | −4.00000 | −0.452911 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.744563 | 0.0822232 | ||||||||
\(83\) | 9.48913 | 1.04157 | 0.520783 | − | 0.853689i | \(-0.325640\pi\) | ||||
0.520783 | + | 0.853689i | \(0.325640\pi\) | |||||||
\(84\) | 3.37228 | 0.367946 | ||||||||
\(85\) | 1.00000 | 0.108465 | ||||||||
\(86\) | 4.62772 | 0.499020 | ||||||||
\(87\) | 0.627719 | 0.0672985 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 8.74456 | 0.926922 | 0.463461 | − | 0.886117i | \(-0.346607\pi\) | ||||
0.463461 | + | 0.886117i | \(0.346607\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 13.4891 | 1.41404 | ||||||||
\(92\) | −7.37228 | −0.768613 | ||||||||
\(93\) | −8.11684 | −0.841678 | ||||||||
\(94\) | 0.744563 | 0.0767958 | ||||||||
\(95\) | 4.00000 | 0.410391 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 10.8614 | 1.10281 | 0.551404 | − | 0.834238i | \(-0.314092\pi\) | ||||
0.551404 | + | 0.834238i | \(0.314092\pi\) | |||||||
\(98\) | −4.37228 | −0.441667 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 2.00000 | 0.199007 | 0.0995037 | − | 0.995037i | \(-0.468274\pi\) | ||||
0.0995037 | + | 0.995037i | \(0.468274\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | 12.6277 | 1.24425 | 0.622123 | − | 0.782919i | \(-0.286270\pi\) | ||||
0.622123 | + | 0.782919i | \(0.286270\pi\) | |||||||
\(104\) | 4.00000 | 0.392232 | ||||||||
\(105\) | 3.37228 | 0.329101 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.62772 | 0.447378 | 0.223689 | − | 0.974661i | \(-0.428190\pi\) | ||||
0.223689 | + | 0.974661i | \(0.428190\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −18.2337 | −1.74647 | −0.873235 | − | 0.487299i | \(-0.837982\pi\) | ||||
−0.873235 | + | 0.487299i | \(0.837982\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | 2.74456 | 0.260502 | ||||||||
\(112\) | −3.37228 | −0.318651 | ||||||||
\(113\) | −15.4891 | −1.45709 | −0.728547 | − | 0.684996i | \(-0.759804\pi\) | ||||
−0.728547 | + | 0.684996i | \(0.759804\pi\) | |||||||
\(114\) | 4.00000 | 0.374634 | ||||||||
\(115\) | −7.37228 | −0.687469 | ||||||||
\(116\) | −0.627719 | −0.0582822 | ||||||||
\(117\) | −4.00000 | −0.369800 | ||||||||
\(118\) | −1.25544 | −0.115572 | ||||||||
\(119\) | −3.37228 | −0.309137 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 11.4891 | 1.04018 | ||||||||
\(123\) | 0.744563 | 0.0671350 | ||||||||
\(124\) | 8.11684 | 0.728914 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 3.37228 | 0.300427 | ||||||||
\(127\) | 11.4891 | 1.01950 | 0.509748 | − | 0.860324i | \(-0.329739\pi\) | ||||
0.509748 | + | 0.860324i | \(0.329739\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 4.62772 | 0.407448 | ||||||||
\(130\) | 4.00000 | 0.350823 | ||||||||
\(131\) | 8.00000 | 0.698963 | 0.349482 | − | 0.936943i | \(-0.386358\pi\) | ||||
0.349482 | + | 0.936943i | \(0.386358\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | −13.4891 | −1.16966 | ||||||||
\(134\) | −4.00000 | −0.345547 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | −16.1168 | −1.37695 | −0.688477 | − | 0.725258i | \(-0.741721\pi\) | ||||
−0.688477 | + | 0.725258i | \(0.741721\pi\) | |||||||
\(138\) | −7.37228 | −0.627570 | ||||||||
\(139\) | 7.37228 | 0.625309 | 0.312654 | − | 0.949867i | \(-0.398782\pi\) | ||||
0.312654 | + | 0.949867i | \(0.398782\pi\) | |||||||
\(140\) | −3.37228 | −0.285010 | ||||||||
\(141\) | 0.744563 | 0.0627035 | ||||||||
\(142\) | 6.74456 | 0.565991 | ||||||||
\(143\) | −4.00000 | −0.334497 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −0.627719 | −0.0521292 | ||||||||
\(146\) | 6.00000 | 0.496564 | ||||||||
\(147\) | −4.37228 | −0.360620 | ||||||||
\(148\) | −2.74456 | −0.225602 | ||||||||
\(149\) | 3.25544 | 0.266696 | 0.133348 | − | 0.991069i | \(-0.457427\pi\) | ||||
0.133348 | + | 0.991069i | \(0.457427\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | −18.2337 | −1.48384 | −0.741918 | − | 0.670490i | \(-0.766084\pi\) | ||||
−0.741918 | + | 0.670490i | \(0.766084\pi\) | |||||||
\(152\) | −4.00000 | −0.324443 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 3.37228 | 0.271746 | ||||||||
\(155\) | 8.11684 | 0.651961 | ||||||||
\(156\) | 4.00000 | 0.320256 | ||||||||
\(157\) | 10.0000 | 0.798087 | 0.399043 | − | 0.916932i | \(-0.369342\pi\) | ||||
0.399043 | + | 0.916932i | \(0.369342\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 24.8614 | 1.95935 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 20.8614 | 1.63399 | 0.816996 | − | 0.576644i | \(-0.195638\pi\) | ||||
0.816996 | + | 0.576644i | \(0.195638\pi\) | |||||||
\(164\) | −0.744563 | −0.0581406 | ||||||||
\(165\) | −1.00000 | −0.0778499 | ||||||||
\(166\) | −9.48913 | −0.736499 | ||||||||
\(167\) | −3.48913 | −0.269997 | −0.134998 | − | 0.990846i | \(-0.543103\pi\) | ||||
−0.134998 | + | 0.990846i | \(0.543103\pi\) | |||||||
\(168\) | −3.37228 | −0.260177 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | −1.00000 | −0.0766965 | ||||||||
\(171\) | 4.00000 | 0.305888 | ||||||||
\(172\) | −4.62772 | −0.352860 | ||||||||
\(173\) | 20.2337 | 1.53834 | 0.769169 | − | 0.639045i | \(-0.220670\pi\) | ||||
0.769169 | + | 0.639045i | \(0.220670\pi\) | |||||||
\(174\) | −0.627719 | −0.0475872 | ||||||||
\(175\) | −3.37228 | −0.254921 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −1.25544 | −0.0943645 | ||||||||
\(178\) | −8.74456 | −0.655433 | ||||||||
\(179\) | 10.7446 | 0.803086 | 0.401543 | − | 0.915840i | \(-0.368474\pi\) | ||||
0.401543 | + | 0.915840i | \(0.368474\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | −8.62772 | −0.641293 | −0.320647 | − | 0.947199i | \(-0.603900\pi\) | ||||
−0.320647 | + | 0.947199i | \(0.603900\pi\) | |||||||
\(182\) | −13.4891 | −0.999880 | ||||||||
\(183\) | 11.4891 | 0.849301 | ||||||||
\(184\) | 7.37228 | 0.543492 | ||||||||
\(185\) | −2.74456 | −0.201784 | ||||||||
\(186\) | 8.11684 | 0.595156 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | −0.744563 | −0.0543028 | ||||||||
\(189\) | 3.37228 | 0.245297 | ||||||||
\(190\) | −4.00000 | −0.290191 | ||||||||
\(191\) | 13.3723 | 0.967584 | 0.483792 | − | 0.875183i | \(-0.339259\pi\) | ||||
0.483792 | + | 0.875183i | \(0.339259\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 19.4891 | 1.40286 | 0.701429 | − | 0.712739i | \(-0.252546\pi\) | ||||
0.701429 | + | 0.712739i | \(0.252546\pi\) | |||||||
\(194\) | −10.8614 | −0.779804 | ||||||||
\(195\) | 4.00000 | 0.286446 | ||||||||
\(196\) | 4.37228 | 0.312306 | ||||||||
\(197\) | 9.48913 | 0.676072 | 0.338036 | − | 0.941133i | \(-0.390237\pi\) | ||||
0.338036 | + | 0.941133i | \(0.390237\pi\) | |||||||
\(198\) | −1.00000 | −0.0710669 | ||||||||
\(199\) | −3.25544 | −0.230772 | −0.115386 | − | 0.993321i | \(-0.536810\pi\) | ||||
−0.115386 | + | 0.993321i | \(0.536810\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −4.00000 | −0.282138 | ||||||||
\(202\) | −2.00000 | −0.140720 | ||||||||
\(203\) | 2.11684 | 0.148573 | ||||||||
\(204\) | −1.00000 | −0.0700140 | ||||||||
\(205\) | −0.744563 | −0.0520025 | ||||||||
\(206\) | −12.6277 | −0.879815 | ||||||||
\(207\) | −7.37228 | −0.512409 | ||||||||
\(208\) | −4.00000 | −0.277350 | ||||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | −3.37228 | −0.232710 | ||||||||
\(211\) | −15.3723 | −1.05827 | −0.529136 | − | 0.848537i | \(-0.677484\pi\) | ||||
−0.529136 | + | 0.848537i | \(0.677484\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.74456 | 0.462130 | ||||||||
\(214\) | −4.62772 | −0.316344 | ||||||||
\(215\) | −4.62772 | −0.315608 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −27.3723 | −1.85815 | ||||||||
\(218\) | 18.2337 | 1.23494 | ||||||||
\(219\) | 6.00000 | 0.405442 | ||||||||
\(220\) | 1.00000 | 0.0674200 | ||||||||
\(221\) | −4.00000 | −0.269069 | ||||||||
\(222\) | −2.74456 | −0.184203 | ||||||||
\(223\) | 14.1168 | 0.945334 | 0.472667 | − | 0.881241i | \(-0.343291\pi\) | ||||
0.472667 | + | 0.881241i | \(0.343291\pi\) | |||||||
\(224\) | 3.37228 | 0.225320 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 15.4891 | 1.03032 | ||||||||
\(227\) | −4.86141 | −0.322663 | −0.161331 | − | 0.986900i | \(-0.551579\pi\) | ||||
−0.161331 | + | 0.986900i | \(0.551579\pi\) | |||||||
\(228\) | −4.00000 | −0.264906 | ||||||||
\(229\) | −12.7446 | −0.842184 | −0.421092 | − | 0.907018i | \(-0.638353\pi\) | ||||
−0.421092 | + | 0.907018i | \(0.638353\pi\) | |||||||
\(230\) | 7.37228 | 0.486114 | ||||||||
\(231\) | 3.37228 | 0.221880 | ||||||||
\(232\) | 0.627719 | 0.0412118 | ||||||||
\(233\) | 16.1168 | 1.05585 | 0.527925 | − | 0.849291i | \(-0.322970\pi\) | ||||
0.527925 | + | 0.849291i | \(0.322970\pi\) | |||||||
\(234\) | 4.00000 | 0.261488 | ||||||||
\(235\) | −0.744563 | −0.0485699 | ||||||||
\(236\) | 1.25544 | 0.0817220 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.37228 | 0.218593 | ||||||||
\(239\) | 4.23369 | 0.273855 | 0.136927 | − | 0.990581i | \(-0.456277\pi\) | ||||
0.136927 | + | 0.990581i | \(0.456277\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | −17.6060 | −1.13410 | −0.567050 | − | 0.823683i | \(-0.691915\pi\) | ||||
−0.567050 | + | 0.823683i | \(0.691915\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −11.4891 | −0.735516 | ||||||||
\(245\) | 4.37228 | 0.279335 | ||||||||
\(246\) | −0.744563 | −0.0474716 | ||||||||
\(247\) | −16.0000 | −1.01806 | ||||||||
\(248\) | −8.11684 | −0.515420 | ||||||||
\(249\) | −9.48913 | −0.601349 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | −3.37228 | −0.212434 | ||||||||
\(253\) | −7.37228 | −0.463491 | ||||||||
\(254\) | −11.4891 | −0.720892 | ||||||||
\(255\) | −1.00000 | −0.0626224 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.11684 | 0.506315 | 0.253157 | − | 0.967425i | \(-0.418531\pi\) | ||||
0.253157 | + | 0.967425i | \(0.418531\pi\) | |||||||
\(258\) | −4.62772 | −0.288109 | ||||||||
\(259\) | 9.25544 | 0.575105 | ||||||||
\(260\) | −4.00000 | −0.248069 | ||||||||
\(261\) | −0.627719 | −0.0388548 | ||||||||
\(262\) | −8.00000 | −0.494242 | ||||||||
\(263\) | −1.88316 | −0.116120 | −0.0580602 | − | 0.998313i | \(-0.518492\pi\) | ||||
−0.0580602 | + | 0.998313i | \(0.518492\pi\) | |||||||
\(264\) | 1.00000 | 0.0615457 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 13.4891 | 0.827071 | ||||||||
\(267\) | −8.74456 | −0.535159 | ||||||||
\(268\) | 4.00000 | 0.244339 | ||||||||
\(269\) | 14.0000 | 0.853595 | 0.426798 | − | 0.904347i | \(-0.359642\pi\) | ||||
0.426798 | + | 0.904347i | \(0.359642\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | −13.3723 | −0.812308 | −0.406154 | − | 0.913805i | \(-0.633130\pi\) | ||||
−0.406154 | + | 0.913805i | \(0.633130\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | −13.4891 | −0.816399 | ||||||||
\(274\) | 16.1168 | 0.973654 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 7.37228 | 0.443759 | ||||||||
\(277\) | −7.48913 | −0.449978 | −0.224989 | − | 0.974361i | \(-0.572235\pi\) | ||||
−0.224989 | + | 0.974361i | \(0.572235\pi\) | |||||||
\(278\) | −7.37228 | −0.442160 | ||||||||
\(279\) | 8.11684 | 0.485943 | ||||||||
\(280\) | 3.37228 | 0.201532 | ||||||||
\(281\) | −14.8614 | −0.886557 | −0.443279 | − | 0.896384i | \(-0.646185\pi\) | ||||
−0.443279 | + | 0.896384i | \(0.646185\pi\) | |||||||
\(282\) | −0.744563 | −0.0443381 | ||||||||
\(283\) | −13.2554 | −0.787954 | −0.393977 | − | 0.919120i | \(-0.628901\pi\) | ||||
−0.393977 | + | 0.919120i | \(0.628901\pi\) | |||||||
\(284\) | −6.74456 | −0.400216 | ||||||||
\(285\) | −4.00000 | −0.236940 | ||||||||
\(286\) | 4.00000 | 0.236525 | ||||||||
\(287\) | 2.51087 | 0.148212 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0.627719 | 0.0368609 | ||||||||
\(291\) | −10.8614 | −0.636707 | ||||||||
\(292\) | −6.00000 | −0.351123 | ||||||||
\(293\) | 20.1168 | 1.17524 | 0.587619 | − | 0.809138i | \(-0.300065\pi\) | ||||
0.587619 | + | 0.809138i | \(0.300065\pi\) | |||||||
\(294\) | 4.37228 | 0.254997 | ||||||||
\(295\) | 1.25544 | 0.0730944 | ||||||||
\(296\) | 2.74456 | 0.159524 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −3.25544 | −0.188582 | ||||||||
\(299\) | 29.4891 | 1.70540 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 15.6060 | 0.899513 | ||||||||
\(302\) | 18.2337 | 1.04923 | ||||||||
\(303\) | −2.00000 | −0.114897 | ||||||||
\(304\) | 4.00000 | 0.229416 | ||||||||
\(305\) | −11.4891 | −0.657865 | ||||||||
\(306\) | −1.00000 | −0.0571662 | ||||||||
\(307\) | −12.0000 | −0.684876 | −0.342438 | − | 0.939540i | \(-0.611253\pi\) | ||||
−0.342438 | + | 0.939540i | \(0.611253\pi\) | |||||||
\(308\) | −3.37228 | −0.192154 | ||||||||
\(309\) | −12.6277 | −0.718366 | ||||||||
\(310\) | −8.11684 | −0.461006 | ||||||||
\(311\) | 33.4891 | 1.89899 | 0.949497 | − | 0.313776i | \(-0.101594\pi\) | ||||
0.949497 | + | 0.313776i | \(0.101594\pi\) | |||||||
\(312\) | −4.00000 | −0.226455 | ||||||||
\(313\) | −1.37228 | −0.0775659 | −0.0387830 | − | 0.999248i | \(-0.512348\pi\) | ||||
−0.0387830 | + | 0.999248i | \(0.512348\pi\) | |||||||
\(314\) | −10.0000 | −0.564333 | ||||||||
\(315\) | −3.37228 | −0.190007 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.1168 | 0.905212 | 0.452606 | − | 0.891711i | \(-0.350494\pi\) | ||||
0.452606 | + | 0.891711i | \(0.350494\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.627719 | −0.0351455 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −4.62772 | −0.258294 | ||||||||
\(322\) | −24.8614 | −1.38547 | ||||||||
\(323\) | 4.00000 | 0.222566 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −4.00000 | −0.221880 | ||||||||
\(326\) | −20.8614 | −1.15541 | ||||||||
\(327\) | 18.2337 | 1.00833 | ||||||||
\(328\) | 0.744563 | 0.0411116 | ||||||||
\(329\) | 2.51087 | 0.138429 | ||||||||
\(330\) | 1.00000 | 0.0550482 | ||||||||
\(331\) | 9.88316 | 0.543227 | 0.271614 | − | 0.962406i | \(-0.412443\pi\) | ||||
0.271614 | + | 0.962406i | \(0.412443\pi\) | |||||||
\(332\) | 9.48913 | 0.520783 | ||||||||
\(333\) | −2.74456 | −0.150401 | ||||||||
\(334\) | 3.48913 | 0.190916 | ||||||||
\(335\) | 4.00000 | 0.218543 | ||||||||
\(336\) | 3.37228 | 0.183973 | ||||||||
\(337\) | 11.4891 | 0.625853 | 0.312926 | − | 0.949777i | \(-0.398691\pi\) | ||||
0.312926 | + | 0.949777i | \(0.398691\pi\) | |||||||
\(338\) | −3.00000 | −0.163178 | ||||||||
\(339\) | 15.4891 | 0.841254 | ||||||||
\(340\) | 1.00000 | 0.0542326 | ||||||||
\(341\) | 8.11684 | 0.439552 | ||||||||
\(342\) | −4.00000 | −0.216295 | ||||||||
\(343\) | 8.86141 | 0.478471 | ||||||||
\(344\) | 4.62772 | 0.249510 | ||||||||
\(345\) | 7.37228 | 0.396910 | ||||||||
\(346\) | −20.2337 | −1.08777 | ||||||||
\(347\) | −5.48913 | −0.294672 | −0.147336 | − | 0.989087i | \(-0.547070\pi\) | ||||
−0.147336 | + | 0.989087i | \(0.547070\pi\) | |||||||
\(348\) | 0.627719 | 0.0336493 | ||||||||
\(349\) | 4.23369 | 0.226624 | 0.113312 | − | 0.993559i | \(-0.463854\pi\) | ||||
0.113312 | + | 0.993559i | \(0.463854\pi\) | |||||||
\(350\) | 3.37228 | 0.180256 | ||||||||
\(351\) | 4.00000 | 0.213504 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 25.3723 | 1.35043 | 0.675215 | − | 0.737621i | \(-0.264051\pi\) | ||||
0.675215 | + | 0.737621i | \(0.264051\pi\) | |||||||
\(354\) | 1.25544 | 0.0667257 | ||||||||
\(355\) | −6.74456 | −0.357964 | ||||||||
\(356\) | 8.74456 | 0.463461 | ||||||||
\(357\) | 3.37228 | 0.178480 | ||||||||
\(358\) | −10.7446 | −0.567868 | ||||||||
\(359\) | 13.2554 | 0.699595 | 0.349798 | − | 0.936825i | \(-0.386250\pi\) | ||||
0.349798 | + | 0.936825i | \(0.386250\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 8.62772 | 0.453463 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 13.4891 | 0.707022 | ||||||||
\(365\) | −6.00000 | −0.314054 | ||||||||
\(366\) | −11.4891 | −0.600546 | ||||||||
\(367\) | 23.4891 | 1.22612 | 0.613061 | − | 0.790035i | \(-0.289938\pi\) | ||||
0.613061 | + | 0.790035i | \(0.289938\pi\) | |||||||
\(368\) | −7.37228 | −0.384307 | ||||||||
\(369\) | −0.744563 | −0.0387604 | ||||||||
\(370\) | 2.74456 | 0.142683 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −8.11684 | −0.420839 | ||||||||
\(373\) | −21.7228 | −1.12476 | −0.562382 | − | 0.826877i | \(-0.690115\pi\) | ||||
−0.562382 | + | 0.826877i | \(0.690115\pi\) | |||||||
\(374\) | −1.00000 | −0.0517088 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0.744563 | 0.0383979 | ||||||||
\(377\) | 2.51087 | 0.129317 | ||||||||
\(378\) | −3.37228 | −0.173451 | ||||||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 4.00000 | 0.205196 | ||||||||
\(381\) | −11.4891 | −0.588606 | ||||||||
\(382\) | −13.3723 | −0.684185 | ||||||||
\(383\) | 8.74456 | 0.446826 | 0.223413 | − | 0.974724i | \(-0.428280\pi\) | ||||
0.223413 | + | 0.974724i | \(0.428280\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −3.37228 | −0.171867 | ||||||||
\(386\) | −19.4891 | −0.991970 | ||||||||
\(387\) | −4.62772 | −0.235240 | ||||||||
\(388\) | 10.8614 | 0.551404 | ||||||||
\(389\) | 9.25544 | 0.469269 | 0.234635 | − | 0.972084i | \(-0.424611\pi\) | ||||
0.234635 | + | 0.972084i | \(0.424611\pi\) | |||||||
\(390\) | −4.00000 | −0.202548 | ||||||||
\(391\) | −7.37228 | −0.372832 | ||||||||
\(392\) | −4.37228 | −0.220834 | ||||||||
\(393\) | −8.00000 | −0.403547 | ||||||||
\(394\) | −9.48913 | −0.478055 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | −12.2337 | −0.613991 | −0.306996 | − | 0.951711i | \(-0.599324\pi\) | ||||
−0.306996 | + | 0.951711i | \(0.599324\pi\) | |||||||
\(398\) | 3.25544 | 0.163180 | ||||||||
\(399\) | 13.4891 | 0.675301 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 1.13859 | 0.0568586 | 0.0284293 | − | 0.999596i | \(-0.490949\pi\) | ||||
0.0284293 | + | 0.999596i | \(0.490949\pi\) | |||||||
\(402\) | 4.00000 | 0.199502 | ||||||||
\(403\) | −32.4674 | −1.61732 | ||||||||
\(404\) | 2.00000 | 0.0995037 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −2.11684 | −0.105057 | ||||||||
\(407\) | −2.74456 | −0.136043 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | −22.2337 | −1.09939 | −0.549693 | − | 0.835367i | \(-0.685255\pi\) | ||||
−0.549693 | + | 0.835367i | \(0.685255\pi\) | |||||||
\(410\) | 0.744563 | 0.0367713 | ||||||||
\(411\) | 16.1168 | 0.794985 | ||||||||
\(412\) | 12.6277 | 0.622123 | ||||||||
\(413\) | −4.23369 | −0.208326 | ||||||||
\(414\) | 7.37228 | 0.362328 | ||||||||
\(415\) | 9.48913 | 0.465803 | ||||||||
\(416\) | 4.00000 | 0.196116 | ||||||||
\(417\) | −7.37228 | −0.361022 | ||||||||
\(418\) | −4.00000 | −0.195646 | ||||||||
\(419\) | 32.6277 | 1.59397 | 0.796984 | − | 0.604000i | \(-0.206427\pi\) | ||||
0.796984 | + | 0.604000i | \(0.206427\pi\) | |||||||
\(420\) | 3.37228 | 0.164550 | ||||||||
\(421\) | −36.7446 | −1.79082 | −0.895410 | − | 0.445242i | \(-0.853118\pi\) | ||||
−0.895410 | + | 0.445242i | \(0.853118\pi\) | |||||||
\(422\) | 15.3723 | 0.748311 | ||||||||
\(423\) | −0.744563 | −0.0362019 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.00000 | 0.0485071 | ||||||||
\(426\) | −6.74456 | −0.326775 | ||||||||
\(427\) | 38.7446 | 1.87498 | ||||||||
\(428\) | 4.62772 | 0.223689 | ||||||||
\(429\) | 4.00000 | 0.193122 | ||||||||
\(430\) | 4.62772 | 0.223168 | ||||||||
\(431\) | 10.8614 | 0.523176 | 0.261588 | − | 0.965180i | \(-0.415754\pi\) | ||||
0.261588 | + | 0.965180i | \(0.415754\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 7.25544 | 0.348674 | 0.174337 | − | 0.984686i | \(-0.444222\pi\) | ||||
0.174337 | + | 0.984686i | \(0.444222\pi\) | |||||||
\(434\) | 27.3723 | 1.31391 | ||||||||
\(435\) | 0.627719 | 0.0300968 | ||||||||
\(436\) | −18.2337 | −0.873235 | ||||||||
\(437\) | −29.4891 | −1.41066 | ||||||||
\(438\) | −6.00000 | −0.286691 | ||||||||
\(439\) | 21.2554 | 1.01447 | 0.507233 | − | 0.861809i | \(-0.330668\pi\) | ||||
0.507233 | + | 0.861809i | \(0.330668\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | 4.37228 | 0.208204 | ||||||||
\(442\) | 4.00000 | 0.190261 | ||||||||
\(443\) | 4.62772 | 0.219870 | 0.109935 | − | 0.993939i | \(-0.464936\pi\) | ||||
0.109935 | + | 0.993939i | \(0.464936\pi\) | |||||||
\(444\) | 2.74456 | 0.130251 | ||||||||
\(445\) | 8.74456 | 0.414532 | ||||||||
\(446\) | −14.1168 | −0.668452 | ||||||||
\(447\) | −3.25544 | −0.153977 | ||||||||
\(448\) | −3.37228 | −0.159325 | ||||||||
\(449\) | 26.8614 | 1.26767 | 0.633834 | − | 0.773469i | \(-0.281480\pi\) | ||||
0.633834 | + | 0.773469i | \(0.281480\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | −0.744563 | −0.0350601 | ||||||||
\(452\) | −15.4891 | −0.728547 | ||||||||
\(453\) | 18.2337 | 0.856693 | ||||||||
\(454\) | 4.86141 | 0.228157 | ||||||||
\(455\) | 13.4891 | 0.632380 | ||||||||
\(456\) | 4.00000 | 0.187317 | ||||||||
\(457\) | 28.9783 | 1.35555 | 0.677773 | − | 0.735271i | \(-0.262945\pi\) | ||||
0.677773 | + | 0.735271i | \(0.262945\pi\) | |||||||
\(458\) | 12.7446 | 0.595514 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −7.37228 | −0.343734 | ||||||||
\(461\) | 0.510875 | 0.0237938 | 0.0118969 | − | 0.999929i | \(-0.496213\pi\) | ||||
0.0118969 | + | 0.999929i | \(0.496213\pi\) | |||||||
\(462\) | −3.37228 | −0.156893 | ||||||||
\(463\) | 8.00000 | 0.371792 | 0.185896 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(464\) | −0.627719 | −0.0291411 | ||||||||
\(465\) | −8.11684 | −0.376410 | ||||||||
\(466\) | −16.1168 | −0.746598 | ||||||||
\(467\) | −14.9783 | −0.693111 | −0.346555 | − | 0.938030i | \(-0.612649\pi\) | ||||
−0.346555 | + | 0.938030i | \(0.612649\pi\) | |||||||
\(468\) | −4.00000 | −0.184900 | ||||||||
\(469\) | −13.4891 | −0.622870 | ||||||||
\(470\) | 0.744563 | 0.0343441 | ||||||||
\(471\) | −10.0000 | −0.460776 | ||||||||
\(472\) | −1.25544 | −0.0577862 | ||||||||
\(473\) | −4.62772 | −0.212783 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | −3.37228 | −0.154568 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.23369 | −0.193644 | ||||||||
\(479\) | −15.8832 | −0.725720 | −0.362860 | − | 0.931844i | \(-0.618200\pi\) | ||||
−0.362860 | + | 0.931844i | \(0.618200\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 10.9783 | 0.500565 | ||||||||
\(482\) | 17.6060 | 0.801930 | ||||||||
\(483\) | −24.8614 | −1.13123 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 10.8614 | 0.493191 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −15.4891 | −0.701879 | −0.350940 | − | 0.936398i | \(-0.614138\pi\) | ||||
−0.350940 | + | 0.936398i | \(0.614138\pi\) | |||||||
\(488\) | 11.4891 | 0.520088 | ||||||||
\(489\) | −20.8614 | −0.943385 | ||||||||
\(490\) | −4.37228 | −0.197520 | ||||||||
\(491\) | 41.4891 | 1.87238 | 0.936189 | − | 0.351497i | \(-0.114327\pi\) | ||||
0.936189 | + | 0.351497i | \(0.114327\pi\) | |||||||
\(492\) | 0.744563 | 0.0335675 | ||||||||
\(493\) | −0.627719 | −0.0282710 | ||||||||
\(494\) | 16.0000 | 0.719874 | ||||||||
\(495\) | 1.00000 | 0.0449467 | ||||||||
\(496\) | 8.11684 | 0.364457 | ||||||||
\(497\) | 22.7446 | 1.02023 | ||||||||
\(498\) | 9.48913 | 0.425218 | ||||||||
\(499\) | 36.0000 | 1.61158 | 0.805791 | − | 0.592200i | \(-0.201741\pi\) | ||||
0.805791 | + | 0.592200i | \(0.201741\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 3.48913 | 0.155883 | ||||||||
\(502\) | −12.0000 | −0.535586 | ||||||||
\(503\) | −23.7228 | −1.05775 | −0.528874 | − | 0.848700i | \(-0.677386\pi\) | ||||
−0.528874 | + | 0.848700i | \(0.677386\pi\) | |||||||
\(504\) | 3.37228 | 0.150213 | ||||||||
\(505\) | 2.00000 | 0.0889988 | ||||||||
\(506\) | 7.37228 | 0.327738 | ||||||||
\(507\) | −3.00000 | −0.133235 | ||||||||
\(508\) | 11.4891 | 0.509748 | ||||||||
\(509\) | 9.25544 | 0.410240 | 0.205120 | − | 0.978737i | \(-0.434242\pi\) | ||||
0.205120 | + | 0.978737i | \(0.434242\pi\) | |||||||
\(510\) | 1.00000 | 0.0442807 | ||||||||
\(511\) | 20.2337 | 0.895086 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −4.00000 | −0.176604 | ||||||||
\(514\) | −8.11684 | −0.358019 | ||||||||
\(515\) | 12.6277 | 0.556444 | ||||||||
\(516\) | 4.62772 | 0.203724 | ||||||||
\(517\) | −0.744563 | −0.0327458 | ||||||||
\(518\) | −9.25544 | −0.406661 | ||||||||
\(519\) | −20.2337 | −0.888160 | ||||||||
\(520\) | 4.00000 | 0.175412 | ||||||||
\(521\) | 2.00000 | 0.0876216 | 0.0438108 | − | 0.999040i | \(-0.486050\pi\) | ||||
0.0438108 | + | 0.999040i | \(0.486050\pi\) | |||||||
\(522\) | 0.627719 | 0.0274745 | ||||||||
\(523\) | −14.1168 | −0.617286 | −0.308643 | − | 0.951178i | \(-0.599875\pi\) | ||||
−0.308643 | + | 0.951178i | \(0.599875\pi\) | |||||||
\(524\) | 8.00000 | 0.349482 | ||||||||
\(525\) | 3.37228 | 0.147178 | ||||||||
\(526\) | 1.88316 | 0.0821095 | ||||||||
\(527\) | 8.11684 | 0.353575 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | 31.3505 | 1.36307 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.25544 | 0.0544813 | ||||||||
\(532\) | −13.4891 | −0.584828 | ||||||||
\(533\) | 2.97825 | 0.129002 | ||||||||
\(534\) | 8.74456 | 0.378414 | ||||||||
\(535\) | 4.62772 | 0.200074 | ||||||||
\(536\) | −4.00000 | −0.172774 | ||||||||
\(537\) | −10.7446 | −0.463662 | ||||||||
\(538\) | −14.0000 | −0.603583 | ||||||||
\(539\) | 4.37228 | 0.188327 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | 2.23369 | 0.0960337 | 0.0480169 | − | 0.998847i | \(-0.484710\pi\) | ||||
0.0480169 | + | 0.998847i | \(0.484710\pi\) | |||||||
\(542\) | 13.3723 | 0.574389 | ||||||||
\(543\) | 8.62772 | 0.370251 | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | −18.2337 | −0.781045 | ||||||||
\(546\) | 13.4891 | 0.577281 | ||||||||
\(547\) | 5.25544 | 0.224706 | 0.112353 | − | 0.993668i | \(-0.464161\pi\) | ||||
0.112353 | + | 0.993668i | \(0.464161\pi\) | |||||||
\(548\) | −16.1168 | −0.688477 | ||||||||
\(549\) | −11.4891 | −0.490344 | ||||||||
\(550\) | −1.00000 | −0.0426401 | ||||||||
\(551\) | −2.51087 | −0.106967 | ||||||||
\(552\) | −7.37228 | −0.313785 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 7.48913 | 0.318182 | ||||||||
\(555\) | 2.74456 | 0.116500 | ||||||||
\(556\) | 7.37228 | 0.312654 | ||||||||
\(557\) | −1.13859 | −0.0482437 | −0.0241219 | − | 0.999709i | \(-0.507679\pi\) | ||||
−0.0241219 | + | 0.999709i | \(0.507679\pi\) | |||||||
\(558\) | −8.11684 | −0.343613 | ||||||||
\(559\) | 18.5109 | 0.782927 | ||||||||
\(560\) | −3.37228 | −0.142505 | ||||||||
\(561\) | −1.00000 | −0.0422200 | ||||||||
\(562\) | 14.8614 | 0.626891 | ||||||||
\(563\) | 33.4891 | 1.41140 | 0.705699 | − | 0.708512i | \(-0.250633\pi\) | ||||
0.705699 | + | 0.708512i | \(0.250633\pi\) | |||||||
\(564\) | 0.744563 | 0.0313517 | ||||||||
\(565\) | −15.4891 | −0.651632 | ||||||||
\(566\) | 13.2554 | 0.557168 | ||||||||
\(567\) | −3.37228 | −0.141623 | ||||||||
\(568\) | 6.74456 | 0.282996 | ||||||||
\(569\) | 6.00000 | 0.251533 | 0.125767 | − | 0.992060i | \(-0.459861\pi\) | ||||
0.125767 | + | 0.992060i | \(0.459861\pi\) | |||||||
\(570\) | 4.00000 | 0.167542 | ||||||||
\(571\) | 4.00000 | 0.167395 | 0.0836974 | − | 0.996491i | \(-0.473327\pi\) | ||||
0.0836974 | + | 0.996491i | \(0.473327\pi\) | |||||||
\(572\) | −4.00000 | −0.167248 | ||||||||
\(573\) | −13.3723 | −0.558635 | ||||||||
\(574\) | −2.51087 | −0.104802 | ||||||||
\(575\) | −7.37228 | −0.307445 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 38.4674 | 1.60142 | 0.800709 | − | 0.599054i | \(-0.204456\pi\) | ||||
0.800709 | + | 0.599054i | \(0.204456\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | −19.4891 | −0.809940 | ||||||||
\(580\) | −0.627719 | −0.0260646 | ||||||||
\(581\) | −32.0000 | −1.32758 | ||||||||
\(582\) | 10.8614 | 0.450220 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 6.00000 | 0.248282 | ||||||||
\(585\) | −4.00000 | −0.165380 | ||||||||
\(586\) | −20.1168 | −0.831019 | ||||||||
\(587\) | 22.3505 | 0.922505 | 0.461253 | − | 0.887269i | \(-0.347400\pi\) | ||||
0.461253 | + | 0.887269i | \(0.347400\pi\) | |||||||
\(588\) | −4.37228 | −0.180310 | ||||||||
\(589\) | 32.4674 | 1.33779 | ||||||||
\(590\) | −1.25544 | −0.0516855 | ||||||||
\(591\) | −9.48913 | −0.390330 | ||||||||
\(592\) | −2.74456 | −0.112801 | ||||||||
\(593\) | 40.9783 | 1.68278 | 0.841388 | − | 0.540432i | \(-0.181739\pi\) | ||||
0.841388 | + | 0.540432i | \(0.181739\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | −3.37228 | −0.138250 | ||||||||
\(596\) | 3.25544 | 0.133348 | ||||||||
\(597\) | 3.25544 | 0.133236 | ||||||||
\(598\) | −29.4891 | −1.20590 | ||||||||
\(599\) | 44.1168 | 1.80257 | 0.901283 | − | 0.433231i | \(-0.142627\pi\) | ||||
0.901283 | + | 0.433231i | \(0.142627\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | 36.9783 | 1.50837 | 0.754187 | − | 0.656660i | \(-0.228031\pi\) | ||||
0.754187 | + | 0.656660i | \(0.228031\pi\) | |||||||
\(602\) | −15.6060 | −0.636052 | ||||||||
\(603\) | 4.00000 | 0.162893 | ||||||||
\(604\) | −18.2337 | −0.741918 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 2.00000 | 0.0812444 | ||||||||
\(607\) | 8.00000 | 0.324710 | 0.162355 | − | 0.986732i | \(-0.448091\pi\) | ||||
0.162355 | + | 0.986732i | \(0.448091\pi\) | |||||||
\(608\) | −4.00000 | −0.162221 | ||||||||
\(609\) | −2.11684 | −0.0857788 | ||||||||
\(610\) | 11.4891 | 0.465181 | ||||||||
\(611\) | 2.97825 | 0.120487 | ||||||||
\(612\) | 1.00000 | 0.0404226 | ||||||||
\(613\) | −5.25544 | −0.212265 | −0.106133 | − | 0.994352i | \(-0.533847\pi\) | ||||
−0.106133 | + | 0.994352i | \(0.533847\pi\) | |||||||
\(614\) | 12.0000 | 0.484281 | ||||||||
\(615\) | 0.744563 | 0.0300237 | ||||||||
\(616\) | 3.37228 | 0.135873 | ||||||||
\(617\) | 26.4674 | 1.06554 | 0.532768 | − | 0.846261i | \(-0.321152\pi\) | ||||
0.532768 | + | 0.846261i | \(0.321152\pi\) | |||||||
\(618\) | 12.6277 | 0.507961 | ||||||||
\(619\) | −16.2337 | −0.652487 | −0.326244 | − | 0.945286i | \(-0.605783\pi\) | ||||
−0.326244 | + | 0.945286i | \(0.605783\pi\) | |||||||
\(620\) | 8.11684 | 0.325980 | ||||||||
\(621\) | 7.37228 | 0.295839 | ||||||||
\(622\) | −33.4891 | −1.34279 | ||||||||
\(623\) | −29.4891 | −1.18146 | ||||||||
\(624\) | 4.00000 | 0.160128 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 1.37228 | 0.0548474 | ||||||||
\(627\) | −4.00000 | −0.159745 | ||||||||
\(628\) | 10.0000 | 0.399043 | ||||||||
\(629\) | −2.74456 | −0.109433 | ||||||||
\(630\) | 3.37228 | 0.134355 | ||||||||
\(631\) | −0.233688 | −0.00930297 | −0.00465148 | − | 0.999989i | \(-0.501481\pi\) | ||||
−0.00465148 | + | 0.999989i | \(0.501481\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.3723 | 0.610993 | ||||||||
\(634\) | −16.1168 | −0.640082 | ||||||||
\(635\) | 11.4891 | 0.455932 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.4891 | −0.692944 | ||||||||
\(638\) | 0.627719 | 0.0248516 | ||||||||
\(639\) | −6.74456 | −0.266811 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −36.1168 | −1.42653 | −0.713265 | − | 0.700895i | \(-0.752784\pi\) | ||||
−0.713265 | + | 0.700895i | \(0.752784\pi\) | |||||||
\(642\) | 4.62772 | 0.182641 | ||||||||
\(643\) | 4.62772 | 0.182499 | 0.0912497 | − | 0.995828i | \(-0.470914\pi\) | ||||
0.0912497 | + | 0.995828i | \(0.470914\pi\) | |||||||
\(644\) | 24.8614 | 0.979677 | ||||||||
\(645\) | 4.62772 | 0.182216 | ||||||||
\(646\) | −4.00000 | −0.157378 | ||||||||
\(647\) | 12.9783 | 0.510228 | 0.255114 | − | 0.966911i | \(-0.417887\pi\) | ||||
0.255114 | + | 0.966911i | \(0.417887\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 1.25544 | 0.0492802 | ||||||||
\(650\) | 4.00000 | 0.156893 | ||||||||
\(651\) | 27.3723 | 1.07280 | ||||||||
\(652\) | 20.8614 | 0.816996 | ||||||||
\(653\) | 22.6277 | 0.885491 | 0.442746 | − | 0.896647i | \(-0.354005\pi\) | ||||
0.442746 | + | 0.896647i | \(0.354005\pi\) | |||||||
\(654\) | −18.2337 | −0.712994 | ||||||||
\(655\) | 8.00000 | 0.312586 | ||||||||
\(656\) | −0.744563 | −0.0290703 | ||||||||
\(657\) | −6.00000 | −0.234082 | ||||||||
\(658\) | −2.51087 | −0.0978841 | ||||||||
\(659\) | 8.62772 | 0.336088 | 0.168044 | − | 0.985779i | \(-0.446255\pi\) | ||||
0.168044 | + | 0.985779i | \(0.446255\pi\) | |||||||
\(660\) | −1.00000 | −0.0389249 | ||||||||
\(661\) | 28.7446 | 1.11803 | 0.559017 | − | 0.829156i | \(-0.311179\pi\) | ||||
0.559017 | + | 0.829156i | \(0.311179\pi\) | |||||||
\(662\) | −9.88316 | −0.384120 | ||||||||
\(663\) | 4.00000 | 0.155347 | ||||||||
\(664\) | −9.48913 | −0.368249 | ||||||||
\(665\) | −13.4891 | −0.523086 | ||||||||
\(666\) | 2.74456 | 0.106350 | ||||||||
\(667\) | 4.62772 | 0.179186 | ||||||||
\(668\) | −3.48913 | −0.134998 | ||||||||
\(669\) | −14.1168 | −0.545789 | ||||||||
\(670\) | −4.00000 | −0.154533 | ||||||||
\(671\) | −11.4891 | −0.443533 | ||||||||
\(672\) | −3.37228 | −0.130089 | ||||||||
\(673\) | 10.2337 | 0.394480 | 0.197240 | − | 0.980355i | \(-0.436802\pi\) | ||||
0.197240 | + | 0.980355i | \(0.436802\pi\) | |||||||
\(674\) | −11.4891 | −0.442545 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 3.00000 | 0.115385 | ||||||||
\(677\) | −34.7446 | −1.33534 | −0.667671 | − | 0.744456i | \(-0.732709\pi\) | ||||
−0.667671 | + | 0.744456i | \(0.732709\pi\) | |||||||
\(678\) | −15.4891 | −0.594856 | ||||||||
\(679\) | −36.6277 | −1.40564 | ||||||||
\(680\) | −1.00000 | −0.0383482 | ||||||||
\(681\) | 4.86141 | 0.186290 | ||||||||
\(682\) | −8.11684 | −0.310810 | ||||||||
\(683\) | 1.02175 | 0.0390962 | 0.0195481 | − | 0.999809i | \(-0.493777\pi\) | ||||
0.0195481 | + | 0.999809i | \(0.493777\pi\) | |||||||
\(684\) | 4.00000 | 0.152944 | ||||||||
\(685\) | −16.1168 | −0.615793 | ||||||||
\(686\) | −8.86141 | −0.338330 | ||||||||
\(687\) | 12.7446 | 0.486235 | ||||||||
\(688\) | −4.62772 | −0.176430 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −7.37228 | −0.280658 | ||||||||
\(691\) | 8.00000 | 0.304334 | 0.152167 | − | 0.988355i | \(-0.451375\pi\) | ||||
0.152167 | + | 0.988355i | \(0.451375\pi\) | |||||||
\(692\) | 20.2337 | 0.769169 | ||||||||
\(693\) | −3.37228 | −0.128102 | ||||||||
\(694\) | 5.48913 | 0.208364 | ||||||||
\(695\) | 7.37228 | 0.279647 | ||||||||
\(696\) | −0.627719 | −0.0237936 | ||||||||
\(697\) | −0.744563 | −0.0282023 | ||||||||
\(698\) | −4.23369 | −0.160247 | ||||||||
\(699\) | −16.1168 | −0.609595 | ||||||||
\(700\) | −3.37228 | −0.127460 | ||||||||
\(701\) | 6.00000 | 0.226617 | 0.113308 | − | 0.993560i | \(-0.463855\pi\) | ||||
0.113308 | + | 0.993560i | \(0.463855\pi\) | |||||||
\(702\) | −4.00000 | −0.150970 | ||||||||
\(703\) | −10.9783 | −0.414053 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0.744563 | 0.0280419 | ||||||||
\(706\) | −25.3723 | −0.954898 | ||||||||
\(707\) | −6.74456 | −0.253655 | ||||||||
\(708\) | −1.25544 | −0.0471822 | ||||||||
\(709\) | −22.7446 | −0.854190 | −0.427095 | − | 0.904207i | \(-0.640463\pi\) | ||||
−0.427095 | + | 0.904207i | \(0.640463\pi\) | |||||||
\(710\) | 6.74456 | 0.253119 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8.74456 | −0.327716 | ||||||||
\(713\) | −59.8397 | −2.24101 | ||||||||
\(714\) | −3.37228 | −0.126204 | ||||||||
\(715\) | −4.00000 | −0.149592 | ||||||||
\(716\) | 10.7446 | 0.401543 | ||||||||
\(717\) | −4.23369 | −0.158110 | ||||||||
\(718\) | −13.2554 | −0.494689 | ||||||||
\(719\) | 12.2337 | 0.456240 | 0.228120 | − | 0.973633i | \(-0.426742\pi\) | ||||
0.228120 | + | 0.973633i | \(0.426742\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | −42.5842 | −1.58592 | ||||||||
\(722\) | 3.00000 | 0.111648 | ||||||||
\(723\) | 17.6060 | 0.654773 | ||||||||
\(724\) | −8.62772 | −0.320647 | ||||||||
\(725\) | −0.627719 | −0.0233129 | ||||||||
\(726\) | 1.00000 | 0.0371135 | ||||||||
\(727\) | 6.11684 | 0.226861 | 0.113431 | − | 0.993546i | \(-0.463816\pi\) | ||||
0.113431 | + | 0.993546i | \(0.463816\pi\) | |||||||
\(728\) | −13.4891 | −0.499940 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 6.00000 | 0.222070 | ||||||||
\(731\) | −4.62772 | −0.171162 | ||||||||
\(732\) | 11.4891 | 0.424650 | ||||||||
\(733\) | 9.48913 | 0.350489 | 0.175244 | − | 0.984525i | \(-0.443928\pi\) | ||||
0.175244 | + | 0.984525i | \(0.443928\pi\) | |||||||
\(734\) | −23.4891 | −0.866999 | ||||||||
\(735\) | −4.37228 | −0.161274 | ||||||||
\(736\) | 7.37228 | 0.271746 | ||||||||
\(737\) | 4.00000 | 0.147342 | ||||||||
\(738\) | 0.744563 | 0.0274077 | ||||||||
\(739\) | 36.2337 | 1.33288 | 0.666439 | − | 0.745560i | \(-0.267818\pi\) | ||||
0.666439 | + | 0.745560i | \(0.267818\pi\) | |||||||
\(740\) | −2.74456 | −0.100892 | ||||||||
\(741\) | 16.0000 | 0.587775 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −45.2119 | −1.65867 | −0.829333 | − | 0.558755i | \(-0.811279\pi\) | ||||
−0.829333 | + | 0.558755i | \(0.811279\pi\) | |||||||
\(744\) | 8.11684 | 0.297578 | ||||||||
\(745\) | 3.25544 | 0.119270 | ||||||||
\(746\) | 21.7228 | 0.795329 | ||||||||
\(747\) | 9.48913 | 0.347189 | ||||||||
\(748\) | 1.00000 | 0.0365636 | ||||||||
\(749\) | −15.6060 | −0.570230 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | −0.116844 | −0.00426370 | −0.00213185 | − | 0.999998i | \(-0.500679\pi\) | ||||
−0.00213185 | + | 0.999998i | \(0.500679\pi\) | |||||||
\(752\) | −0.744563 | −0.0271514 | ||||||||
\(753\) | −12.0000 | −0.437304 | ||||||||
\(754\) | −2.51087 | −0.0914407 | ||||||||
\(755\) | −18.2337 | −0.663592 | ||||||||
\(756\) | 3.37228 | 0.122649 | ||||||||
\(757\) | −14.6277 | −0.531653 | −0.265827 | − | 0.964021i | \(-0.585645\pi\) | ||||
−0.265827 | + | 0.964021i | \(0.585645\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.37228 | 0.267597 | ||||||||
\(760\) | −4.00000 | −0.145095 | ||||||||
\(761\) | −39.0951 | −1.41720 | −0.708598 | − | 0.705612i | \(-0.750672\pi\) | ||||
−0.708598 | + | 0.705612i | \(0.750672\pi\) | |||||||
\(762\) | 11.4891 | 0.416207 | ||||||||
\(763\) | 61.4891 | 2.22606 | ||||||||
\(764\) | 13.3723 | 0.483792 | ||||||||
\(765\) | 1.00000 | 0.0361551 | ||||||||
\(766\) | −8.74456 | −0.315954 | ||||||||
\(767\) | −5.02175 | −0.181325 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 24.9783 | 0.900739 | 0.450369 | − | 0.892842i | \(-0.351292\pi\) | ||||
0.450369 | + | 0.892842i | \(0.351292\pi\) | |||||||
\(770\) | 3.37228 | 0.121529 | ||||||||
\(771\) | −8.11684 | −0.292321 | ||||||||
\(772\) | 19.4891 | 0.701429 | ||||||||
\(773\) | −33.4891 | −1.20452 | −0.602260 | − | 0.798300i | \(-0.705733\pi\) | ||||
−0.602260 | + | 0.798300i | \(0.705733\pi\) | |||||||
\(774\) | 4.62772 | 0.166340 | ||||||||
\(775\) | 8.11684 | 0.291566 | ||||||||
\(776\) | −10.8614 | −0.389902 | ||||||||
\(777\) | −9.25544 | −0.332037 | ||||||||
\(778\) | −9.25544 | −0.331824 | ||||||||
\(779\) | −2.97825 | −0.106707 | ||||||||
\(780\) | 4.00000 | 0.143223 | ||||||||
\(781\) | −6.74456 | −0.241339 | ||||||||
\(782\) | 7.37228 | 0.263632 | ||||||||
\(783\) | 0.627719 | 0.0224328 | ||||||||
\(784\) | 4.37228 | 0.156153 | ||||||||
\(785\) | 10.0000 | 0.356915 | ||||||||
\(786\) | 8.00000 | 0.285351 | ||||||||
\(787\) | −9.48913 | −0.338251 | −0.169125 | − | 0.985595i | \(-0.554094\pi\) | ||||
−0.169125 | + | 0.985595i | \(0.554094\pi\) | |||||||
\(788\) | 9.48913 | 0.338036 | ||||||||
\(789\) | 1.88316 | 0.0670421 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 52.2337 | 1.85722 | ||||||||
\(792\) | −1.00000 | −0.0355335 | ||||||||
\(793\) | 45.9565 | 1.63196 | ||||||||
\(794\) | 12.2337 | 0.434157 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.25544 | −0.115386 | ||||||||
\(797\) | −5.48913 | −0.194435 | −0.0972174 | − | 0.995263i | \(-0.530994\pi\) | ||||
−0.0972174 | + | 0.995263i | \(0.530994\pi\) | |||||||
\(798\) | −13.4891 | −0.477510 | ||||||||
\(799\) | −0.744563 | −0.0263407 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 8.74456 | 0.308974 | ||||||||
\(802\) | −1.13859 | −0.0402051 | ||||||||
\(803\) | −6.00000 | −0.211735 | ||||||||
\(804\) | −4.00000 | −0.141069 | ||||||||
\(805\) | 24.8614 | 0.876249 | ||||||||
\(806\) | 32.4674 | 1.14361 | ||||||||
\(807\) | −14.0000 | −0.492823 | ||||||||
\(808\) | −2.00000 | −0.0703598 | ||||||||
\(809\) | 40.9783 | 1.44072 | 0.720359 | − | 0.693601i | \(-0.243977\pi\) | ||||
0.720359 | + | 0.693601i | \(0.243977\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | −9.48913 | −0.333208 | −0.166604 | − | 0.986024i | \(-0.553280\pi\) | ||||
−0.166604 | + | 0.986024i | \(0.553280\pi\) | |||||||
\(812\) | 2.11684 | 0.0742867 | ||||||||
\(813\) | 13.3723 | 0.468986 | ||||||||
\(814\) | 2.74456 | 0.0961969 | ||||||||
\(815\) | 20.8614 | 0.730743 | ||||||||
\(816\) | −1.00000 | −0.0350070 | ||||||||
\(817\) | −18.5109 | −0.647614 | ||||||||
\(818\) | 22.2337 | 0.777383 | ||||||||
\(819\) | 13.4891 | 0.471348 | ||||||||
\(820\) | −0.744563 | −0.0260013 | ||||||||
\(821\) | −27.3723 | −0.955299 | −0.477650 | − | 0.878550i | \(-0.658511\pi\) | ||||
−0.477650 | + | 0.878550i | \(0.658511\pi\) | |||||||
\(822\) | −16.1168 | −0.562139 | ||||||||
\(823\) | 10.0000 | 0.348578 | 0.174289 | − | 0.984695i | \(-0.444237\pi\) | ||||
0.174289 | + | 0.984695i | \(0.444237\pi\) | |||||||
\(824\) | −12.6277 | −0.439907 | ||||||||
\(825\) | −1.00000 | −0.0348155 | ||||||||
\(826\) | 4.23369 | 0.147309 | ||||||||
\(827\) | 23.8397 | 0.828986 | 0.414493 | − | 0.910052i | \(-0.363959\pi\) | ||||
0.414493 | + | 0.910052i | \(0.363959\pi\) | |||||||
\(828\) | −7.37228 | −0.256204 | ||||||||
\(829\) | 24.9783 | 0.867531 | 0.433765 | − | 0.901026i | \(-0.357185\pi\) | ||||
0.433765 | + | 0.901026i | \(0.357185\pi\) | |||||||
\(830\) | −9.48913 | −0.329372 | ||||||||
\(831\) | 7.48913 | 0.259795 | ||||||||
\(832\) | −4.00000 | −0.138675 | ||||||||
\(833\) | 4.37228 | 0.151491 | ||||||||
\(834\) | 7.37228 | 0.255281 | ||||||||
\(835\) | −3.48913 | −0.120746 | ||||||||
\(836\) | 4.00000 | 0.138343 | ||||||||
\(837\) | −8.11684 | −0.280559 | ||||||||
\(838\) | −32.6277 | −1.12711 | ||||||||
\(839\) | −13.7228 | −0.473764 | −0.236882 | − | 0.971538i | \(-0.576125\pi\) | ||||
−0.236882 | + | 0.971538i | \(0.576125\pi\) | |||||||
\(840\) | −3.37228 | −0.116355 | ||||||||
\(841\) | −28.6060 | −0.986413 | ||||||||
\(842\) | 36.7446 | 1.26630 | ||||||||
\(843\) | 14.8614 | 0.511854 | ||||||||
\(844\) | −15.3723 | −0.529136 | ||||||||
\(845\) | 3.00000 | 0.103203 | ||||||||
\(846\) | 0.744563 | 0.0255986 | ||||||||
\(847\) | −3.37228 | −0.115873 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.2554 | 0.454925 | ||||||||
\(850\) | −1.00000 | −0.0342997 | ||||||||
\(851\) | 20.2337 | 0.693602 | ||||||||
\(852\) | 6.74456 | 0.231065 | ||||||||
\(853\) | −4.11684 | −0.140958 | −0.0704790 | − | 0.997513i | \(-0.522453\pi\) | ||||
−0.0704790 | + | 0.997513i | \(0.522453\pi\) | |||||||
\(854\) | −38.7446 | −1.32581 | ||||||||
\(855\) | 4.00000 | 0.136797 | ||||||||
\(856\) | −4.62772 | −0.158172 | ||||||||
\(857\) | 18.8614 | 0.644293 | 0.322147 | − | 0.946690i | \(-0.395596\pi\) | ||||
0.322147 | + | 0.946690i | \(0.395596\pi\) | |||||||
\(858\) | −4.00000 | −0.136558 | ||||||||
\(859\) | −39.8397 | −1.35931 | −0.679656 | − | 0.733531i | \(-0.737871\pi\) | ||||
−0.679656 | + | 0.733531i | \(0.737871\pi\) | |||||||
\(860\) | −4.62772 | −0.157804 | ||||||||
\(861\) | −2.51087 | −0.0855704 | ||||||||
\(862\) | −10.8614 | −0.369941 | ||||||||
\(863\) | 19.7228 | 0.671372 | 0.335686 | − | 0.941974i | \(-0.391032\pi\) | ||||
0.335686 | + | 0.941974i | \(0.391032\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 20.2337 | 0.687966 | ||||||||
\(866\) | −7.25544 | −0.246550 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −27.3723 | −0.929076 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −0.627719 | −0.0212817 | ||||||||
\(871\) | −16.0000 | −0.542139 | ||||||||
\(872\) | 18.2337 | 0.617471 | ||||||||
\(873\) | 10.8614 | 0.367603 | ||||||||
\(874\) | 29.4891 | 0.997485 | ||||||||
\(875\) | −3.37228 | −0.114004 | ||||||||
\(876\) | 6.00000 | 0.202721 | ||||||||
\(877\) | −18.6277 | −0.629013 | −0.314507 | − | 0.949255i | \(-0.601839\pi\) | ||||
−0.314507 | + | 0.949255i | \(0.601839\pi\) | |||||||
\(878\) | −21.2554 | −0.717336 | ||||||||
\(879\) | −20.1168 | −0.678524 | ||||||||
\(880\) | 1.00000 | 0.0337100 | ||||||||
\(881\) | −11.8832 | −0.400354 | −0.200177 | − | 0.979760i | \(-0.564152\pi\) | ||||
−0.200177 | + | 0.979760i | \(0.564152\pi\) | |||||||
\(882\) | −4.37228 | −0.147222 | ||||||||
\(883\) | 1.48913 | 0.0501131 | 0.0250565 | − | 0.999686i | \(-0.492023\pi\) | ||||
0.0250565 | + | 0.999686i | \(0.492023\pi\) | |||||||
\(884\) | −4.00000 | −0.134535 | ||||||||
\(885\) | −1.25544 | −0.0422011 | ||||||||
\(886\) | −4.62772 | −0.155471 | ||||||||
\(887\) | −11.7228 | −0.393614 | −0.196807 | − | 0.980442i | \(-0.563057\pi\) | ||||
−0.196807 | + | 0.980442i | \(0.563057\pi\) | |||||||
\(888\) | −2.74456 | −0.0921015 | ||||||||
\(889\) | −38.7446 | −1.29945 | ||||||||
\(890\) | −8.74456 | −0.293118 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 14.1168 | 0.472667 | ||||||||
\(893\) | −2.97825 | −0.0996634 | ||||||||
\(894\) | 3.25544 | 0.108878 | ||||||||
\(895\) | 10.7446 | 0.359151 | ||||||||
\(896\) | 3.37228 | 0.112660 | ||||||||
\(897\) | −29.4891 | −0.984613 | ||||||||
\(898\) | −26.8614 | −0.896377 | ||||||||
\(899\) | −5.09509 | −0.169931 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0.744563 | 0.0247912 | ||||||||
\(903\) | −15.6060 | −0.519334 | ||||||||
\(904\) | 15.4891 | 0.515161 | ||||||||
\(905\) | −8.62772 | −0.286795 | ||||||||
\(906\) | −18.2337 | −0.605774 | ||||||||
\(907\) | 19.1386 | 0.635487 | 0.317743 | − | 0.948177i | \(-0.397075\pi\) | ||||
0.317743 | + | 0.948177i | \(0.397075\pi\) | |||||||
\(908\) | −4.86141 | −0.161331 | ||||||||
\(909\) | 2.00000 | 0.0663358 | ||||||||
\(910\) | −13.4891 | −0.447160 | ||||||||
\(911\) | −40.4674 | −1.34074 | −0.670372 | − | 0.742025i | \(-0.733865\pi\) | ||||
−0.670372 | + | 0.742025i | \(0.733865\pi\) | |||||||
\(912\) | −4.00000 | −0.132453 | ||||||||
\(913\) | 9.48913 | 0.314044 | ||||||||
\(914\) | −28.9783 | −0.958515 | ||||||||
\(915\) | 11.4891 | 0.379819 | ||||||||
\(916\) | −12.7446 | −0.421092 | ||||||||
\(917\) | −26.9783 | −0.890900 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | 27.8832 | 0.919780 | 0.459890 | − | 0.887976i | \(-0.347889\pi\) | ||||
0.459890 | + | 0.887976i | \(0.347889\pi\) | |||||||
\(920\) | 7.37228 | 0.243057 | ||||||||
\(921\) | 12.0000 | 0.395413 | ||||||||
\(922\) | −0.510875 | −0.0168248 | ||||||||
\(923\) | 26.9783 | 0.888000 | ||||||||
\(924\) | 3.37228 | 0.110940 | ||||||||
\(925\) | −2.74456 | −0.0902407 | ||||||||
\(926\) | −8.00000 | −0.262896 | ||||||||
\(927\) | 12.6277 | 0.414749 | ||||||||
\(928\) | 0.627719 | 0.0206059 | ||||||||
\(929\) | 25.3723 | 0.832438 | 0.416219 | − | 0.909265i | \(-0.363355\pi\) | ||||
0.416219 | + | 0.909265i | \(0.363355\pi\) | |||||||
\(930\) | 8.11684 | 0.266162 | ||||||||
\(931\) | 17.4891 | 0.573183 | ||||||||
\(932\) | 16.1168 | 0.527925 | ||||||||
\(933\) | −33.4891 | −1.09638 | ||||||||
\(934\) | 14.9783 | 0.490103 | ||||||||
\(935\) | 1.00000 | 0.0327035 | ||||||||
\(936\) | 4.00000 | 0.130744 | ||||||||
\(937\) | −34.4674 | −1.12600 | −0.563000 | − | 0.826457i | \(-0.690353\pi\) | ||||
−0.563000 | + | 0.826457i | \(0.690353\pi\) | |||||||
\(938\) | 13.4891 | 0.440436 | ||||||||
\(939\) | 1.37228 | 0.0447827 | ||||||||
\(940\) | −0.744563 | −0.0242850 | ||||||||
\(941\) | −14.7446 | −0.480659 | −0.240330 | − | 0.970691i | \(-0.577255\pi\) | ||||
−0.240330 | + | 0.970691i | \(0.577255\pi\) | |||||||
\(942\) | 10.0000 | 0.325818 | ||||||||
\(943\) | 5.48913 | 0.178751 | ||||||||
\(944\) | 1.25544 | 0.0408610 | ||||||||
\(945\) | 3.37228 | 0.109700 | ||||||||
\(946\) | 4.62772 | 0.150460 | ||||||||
\(947\) | −34.7446 | −1.12905 | −0.564523 | − | 0.825417i | \(-0.690940\pi\) | ||||
−0.564523 | + | 0.825417i | \(0.690940\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.0000 | 0.779073 | ||||||||
\(950\) | −4.00000 | −0.129777 | ||||||||
\(951\) | −16.1168 | −0.522624 | ||||||||
\(952\) | 3.37228 | 0.109296 | ||||||||
\(953\) | −7.02175 | −0.227457 | −0.113728 | − | 0.993512i | \(-0.536279\pi\) | ||||
−0.113728 | + | 0.993512i | \(0.536279\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.3723 | 0.432717 | ||||||||
\(956\) | 4.23369 | 0.136927 | ||||||||
\(957\) | 0.627719 | 0.0202913 | ||||||||
\(958\) | 15.8832 | 0.513161 | ||||||||
\(959\) | 54.3505 | 1.75507 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 34.8832 | 1.12526 | ||||||||
\(962\) | −10.9783 | −0.353953 | ||||||||
\(963\) | 4.62772 | 0.149126 | ||||||||
\(964\) | −17.6060 | −0.567050 | ||||||||
\(965\) | 19.4891 | 0.627377 | ||||||||
\(966\) | 24.8614 | 0.799903 | ||||||||
\(967\) | 26.4674 | 0.851133 | 0.425567 | − | 0.904927i | \(-0.360075\pi\) | ||||
0.425567 | + | 0.904927i | \(0.360075\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −4.00000 | −0.128499 | ||||||||
\(970\) | −10.8614 | −0.348739 | ||||||||
\(971\) | 48.4674 | 1.55539 | 0.777696 | − | 0.628640i | \(-0.216388\pi\) | ||||
0.777696 | + | 0.628640i | \(0.216388\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −24.8614 | −0.797020 | ||||||||
\(974\) | 15.4891 | 0.496304 | ||||||||
\(975\) | 4.00000 | 0.128103 | ||||||||
\(976\) | −11.4891 | −0.367758 | ||||||||
\(977\) | −11.4891 | −0.367570 | −0.183785 | − | 0.982966i | \(-0.558835\pi\) | ||||
−0.183785 | + | 0.982966i | \(0.558835\pi\) | |||||||
\(978\) | 20.8614 | 0.667074 | ||||||||
\(979\) | 8.74456 | 0.279477 | ||||||||
\(980\) | 4.37228 | 0.139667 | ||||||||
\(981\) | −18.2337 | −0.582157 | ||||||||
\(982\) | −41.4891 | −1.32397 | ||||||||
\(983\) | −5.88316 | −0.187644 | −0.0938218 | − | 0.995589i | \(-0.529908\pi\) | ||||
−0.0938218 | + | 0.995589i | \(0.529908\pi\) | |||||||
\(984\) | −0.744563 | −0.0237358 | ||||||||
\(985\) | 9.48913 | 0.302349 | ||||||||
\(986\) | 0.627719 | 0.0199906 | ||||||||
\(987\) | −2.51087 | −0.0799220 | ||||||||
\(988\) | −16.0000 | −0.509028 | ||||||||
\(989\) | 34.1168 | 1.08485 | ||||||||
\(990\) | −1.00000 | −0.0317821 | ||||||||
\(991\) | 13.3723 | 0.424785 | 0.212392 | − | 0.977184i | \(-0.431875\pi\) | ||||
0.212392 | + | 0.977184i | \(0.431875\pi\) | |||||||
\(992\) | −8.11684 | −0.257710 | ||||||||
\(993\) | −9.88316 | −0.313632 | ||||||||
\(994\) | −22.7446 | −0.721414 | ||||||||
\(995\) | −3.25544 | −0.103204 | ||||||||
\(996\) | −9.48913 | −0.300674 | ||||||||
\(997\) | 24.1168 | 0.763788 | 0.381894 | − | 0.924206i | \(-0.375272\pi\) | ||||
0.381894 | + | 0.924206i | \(0.375272\pi\) | |||||||
\(998\) | −36.0000 | −1.13956 | ||||||||
\(999\) | 2.74456 | 0.0868341 |
(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 | 5610.2.a.bq.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5610.2.a.bq.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial |