Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(1469,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.1469");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.3317760000.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1469.8 | ||
Root | \(1.72286 + 0.178197i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.1469 |
Dual form | 1470.2.d.f.1469.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0.707107 | + | 1.58114i | 0.408248 | + | 0.912871i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.41421 | + | 1.73205i | −0.632456 | + | 0.774597i | ||||
\(6\) | 0.707107 | + | 1.58114i | 0.288675 | + | 0.645497i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.00000 | + | 2.23607i | −0.666667 | + | 0.745356i | ||||
\(10\) | −1.41421 | + | 1.73205i | −0.447214 | + | 0.547723i | ||||
\(11\) | − | 0.213422i | − | 0.0643491i | −0.999482 | − | 0.0321745i | \(-0.989757\pi\) | ||
0.999482 | − | 0.0321745i | \(-0.0102432\pi\) | |||||||
\(12\) | 0.707107 | + | 1.58114i | 0.204124 | + | 0.456435i | ||||
\(13\) | 6.70141 | 1.85864 | 0.929318 | − | 0.369279i | \(-0.120395\pi\) | ||||
0.929318 | + | 0.369279i | \(0.120395\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.73861 | − | 1.01132i | −0.965306 | − | 0.261123i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.16228i | 0.766965i | 0.923548 | + | 0.383482i | \(0.125275\pi\) | ||||
−0.923548 | + | 0.383482i | \(0.874725\pi\) | |||||||
\(18\) | −2.00000 | + | 2.23607i | −0.471405 | + | 0.527046i | ||||
\(19\) | 4.89433i | 1.12284i | 0.827532 | + | 0.561418i | \(0.189744\pi\) | ||||
−0.827532 | + | 0.561418i | \(0.810256\pi\) | |||||||
\(20\) | −1.41421 | + | 1.73205i | −0.316228 | + | 0.387298i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 0.213422i | − | 0.0455017i | ||||||
\(23\) | −6.47723 | −1.35059 | −0.675297 | − | 0.737545i | \(-0.735985\pi\) | ||||
−0.675297 | + | 0.737545i | \(0.735985\pi\) | |||||||
\(24\) | 0.707107 | + | 1.58114i | 0.144338 | + | 0.322749i | ||||
\(25\) | −1.00000 | − | 4.89898i | −0.200000 | − | 0.979796i | ||||
\(26\) | 6.70141 | 1.31425 | ||||||||
\(27\) | −4.94975 | − | 1.58114i | −0.952579 | − | 0.304290i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.02265i | 0.375596i | 0.982208 | + | 0.187798i | \(0.0601350\pi\) | ||||
−0.982208 | + | 0.187798i | \(0.939865\pi\) | |||||||
\(30\) | −3.73861 | − | 1.01132i | −0.682574 | − | 0.184641i | ||||
\(31\) | 0.301824i | 0.0542092i | 0.999633 | + | 0.0271046i | \(0.00862872\pi\) | ||||
−0.999633 | + | 0.0271046i | \(0.991371\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.337449 | − | 0.150912i | 0.0587424 | − | 0.0262704i | ||||
\(34\) | 3.16228i | 0.542326i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.00000 | + | 2.23607i | −0.333333 | + | 0.372678i | ||||
\(37\) | − | 7.13505i | − | 1.17299i | −0.809951 | − | 0.586497i | \(-0.800506\pi\) | ||
0.809951 | − | 0.586497i | \(-0.199494\pi\) | |||||||
\(38\) | 4.89433i | 0.793965i | ||||||||
\(39\) | 4.73861 | + | 10.5959i | 0.758785 | + | 1.69670i | ||||
\(40\) | −1.41421 | + | 1.73205i | −0.223607 | + | 0.273861i | ||||
\(41\) | −6.70141 | −1.04658 | −0.523292 | − | 0.852153i | \(-0.675296\pi\) | ||||
−0.523292 | + | 0.852153i | \(0.675296\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.02265i | 0.308451i | 0.988036 | + | 0.154225i | \(0.0492882\pi\) | ||||
−0.988036 | + | 0.154225i | \(0.950712\pi\) | |||||||
\(44\) | − | 0.213422i | − | 0.0321745i | ||||||
\(45\) | −1.04456 | − | 6.62638i | −0.155713 | − | 0.987802i | ||||
\(46\) | −6.47723 | −0.955015 | ||||||||
\(47\) | 7.75478i | 1.13115i | 0.824696 | + | 0.565576i | \(0.191346\pi\) | ||||
−0.824696 | + | 0.565576i | \(0.808654\pi\) | |||||||
\(48\) | 0.707107 | + | 1.58114i | 0.102062 | + | 0.228218i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.00000 | − | 4.89898i | −0.141421 | − | 0.692820i | ||||
\(51\) | −5.00000 | + | 2.23607i | −0.700140 | + | 0.313112i | ||||
\(52\) | 6.70141 | 0.929318 | ||||||||
\(53\) | 5.00000 | 0.686803 | 0.343401 | − | 0.939189i | \(-0.388421\pi\) | ||||
0.343401 | + | 0.939189i | \(0.388421\pi\) | |||||||
\(54\) | −4.94975 | − | 1.58114i | −0.673575 | − | 0.215166i | ||||
\(55\) | 0.369657 | + | 0.301824i | 0.0498446 | + | 0.0406979i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.73861 | + | 3.46081i | −1.02500 | + | 0.458396i | ||||
\(58\) | 2.02265i | 0.265586i | ||||||||
\(59\) | 4.91754 | 0.640209 | 0.320105 | − | 0.947382i | \(-0.396282\pi\) | ||||
0.320105 | + | 0.947382i | \(0.396282\pi\) | |||||||
\(60\) | −3.73861 | − | 1.01132i | −0.482653 | − | 0.130561i | ||||
\(61\) | 3.46410i | 0.443533i | 0.975100 | + | 0.221766i | \(0.0711822\pi\) | ||||
−0.975100 | + | 0.221766i | \(0.928818\pi\) | |||||||
\(62\) | 0.301824i | 0.0383317i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −9.47723 | + | 11.6072i | −1.17551 | + | 1.43969i | ||||
\(66\) | 0.337449 | − | 0.150912i | 0.0415372 | − | 0.0185760i | ||||
\(67\) | 5.32582i | 0.650653i | 0.945602 | + | 0.325326i | \(0.105474\pi\) | ||||
−0.945602 | + | 0.325326i | \(0.894526\pi\) | |||||||
\(68\) | 3.16228i | 0.383482i | ||||||||
\(69\) | −4.58009 | − | 10.2414i | −0.551378 | − | 1.23292i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.02265i | − | 0.240044i | −0.992771 | − | 0.120022i | \(-0.961703\pi\) | ||
0.992771 | − | 0.120022i | \(-0.0382965\pi\) | |||||||
\(72\) | −2.00000 | + | 2.23607i | −0.235702 | + | 0.263523i | ||||
\(73\) | −11.9886 | −1.40316 | −0.701580 | − | 0.712591i | \(-0.747522\pi\) | ||||
−0.701580 | + | 0.712591i | \(0.747522\pi\) | |||||||
\(74\) | − | 7.13505i | − | 0.829432i | ||||||
\(75\) | 7.03886 | − | 5.04524i | 0.812778 | − | 0.582574i | ||||
\(76\) | 4.89433i | 0.561418i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.73861 | + | 10.5959i | 0.536542 | + | 1.19974i | ||||
\(79\) | 0.522774 | 0.0588167 | 0.0294084 | − | 0.999567i | \(-0.490638\pi\) | ||||
0.0294084 | + | 0.999567i | \(0.490638\pi\) | |||||||
\(80\) | −1.41421 | + | 1.73205i | −0.158114 | + | 0.193649i | ||||
\(81\) | −1.00000 | − | 8.94427i | −0.111111 | − | 0.993808i | ||||
\(82\) | −6.70141 | −0.740047 | ||||||||
\(83\) | − | 16.7169i | − | 1.83491i | −0.397835 | − | 0.917457i | \(-0.630238\pi\) | ||
0.397835 | − | 0.917457i | \(-0.369762\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.47723 | − | 4.47214i | −0.594089 | − | 0.485071i | ||||
\(86\) | 2.02265i | 0.218108i | ||||||||
\(87\) | −3.19808 | + | 1.43023i | −0.342871 | + | 0.153336i | ||||
\(88\) | − | 0.213422i | − | 0.0227508i | ||||||
\(89\) | 10.5744 | 1.12088 | 0.560442 | − | 0.828194i | \(-0.310631\pi\) | ||||
0.560442 | + | 0.828194i | \(0.310631\pi\) | |||||||
\(90\) | −1.04456 | − | 6.62638i | −0.110106 | − | 0.698482i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.47723 | −0.675297 | ||||||||
\(93\) | −0.477226 | + | 0.213422i | −0.0494860 | + | 0.0221308i | ||||
\(94\) | 7.75478i | 0.799845i | ||||||||
\(95\) | −8.47723 | − | 6.92163i | −0.869745 | − | 0.710144i | ||||
\(96\) | 0.707107 | + | 1.58114i | 0.0721688 | + | 0.161374i | ||||
\(97\) | −3.50333 | −0.355709 | −0.177854 | − | 0.984057i | \(-0.556916\pi\) | ||||
−0.177854 | + | 0.984057i | \(0.556916\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.477226 | + | 0.426844i | 0.0479630 | + | 0.0428994i | ||||
\(100\) | −1.00000 | − | 4.89898i | −0.100000 | − | 0.489898i | ||||
\(101\) | 11.3137 | 1.12576 | 0.562878 | − | 0.826540i | \(-0.309694\pi\) | ||||
0.562878 | + | 0.826540i | \(0.309694\pi\) | |||||||
\(102\) | −5.00000 | + | 2.23607i | −0.495074 | + | 0.221404i | ||||
\(103\) | 10.5744 | 1.04193 | 0.520963 | − | 0.853579i | \(-0.325573\pi\) | ||||
0.520963 | + | 0.853579i | \(0.325573\pi\) | |||||||
\(104\) | 6.70141 | 0.657127 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.00000 | 0.485643 | ||||||||
\(107\) | 5.47723 | 0.529503 | 0.264752 | − | 0.964317i | \(-0.414710\pi\) | ||||
0.264752 | + | 0.964317i | \(0.414710\pi\) | |||||||
\(108\) | −4.94975 | − | 1.58114i | −0.476290 | − | 0.152145i | ||||
\(109\) | 12.4317 | 1.19074 | 0.595369 | − | 0.803452i | \(-0.297006\pi\) | ||||
0.595369 | + | 0.803452i | \(0.297006\pi\) | |||||||
\(110\) | 0.369657 | + | 0.301824i | 0.0352454 | + | 0.0287778i | ||||
\(111\) | 11.2815 | − | 5.04524i | 1.07079 | − | 0.478873i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.52277 | 0.613611 | 0.306806 | − | 0.951772i | \(-0.400740\pi\) | ||||
0.306806 | + | 0.951772i | \(0.400740\pi\) | |||||||
\(114\) | −7.73861 | + | 3.46081i | −0.724787 | + | 0.324135i | ||||
\(115\) | 9.16018 | − | 11.2189i | 0.854191 | − | 1.04617i | ||||
\(116\) | 2.02265i | 0.187798i | ||||||||
\(117\) | −13.4028 | + | 14.9848i | −1.23909 | + | 1.38535i | ||||
\(118\) | 4.91754 | 0.452696 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.73861 | − | 1.01132i | −0.341287 | − | 0.0923207i | ||||
\(121\) | 10.9545 | 0.995859 | ||||||||
\(122\) | 3.46410i | 0.313625i | ||||||||
\(123\) | −4.73861 | − | 10.5959i | −0.427266 | − | 0.955397i | ||||
\(124\) | 0.301824i | 0.0271046i | ||||||||
\(125\) | 9.89949 | + | 5.19615i | 0.885438 | + | 0.464758i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 13.6298i | − | 1.20945i | −0.796434 | − | 0.604726i | \(-0.793283\pi\) | ||
0.796434 | − | 0.604726i | \(-0.206717\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −3.19808 | + | 1.43023i | −0.281576 | + | 0.125924i | ||||
\(130\) | −9.47723 | + | 11.6072i | −0.831208 | + | 1.01802i | ||||
\(131\) | −6.02651 | −0.526539 | −0.263269 | − | 0.964722i | \(-0.584801\pi\) | ||||
−0.263269 | + | 0.964722i | \(0.584801\pi\) | |||||||
\(132\) | 0.337449 | − | 0.150912i | 0.0293712 | − | 0.0131352i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 5.32582i | 0.460081i | ||||||||
\(135\) | 9.73861 | − | 6.33715i | 0.838166 | − | 0.545415i | ||||
\(136\) | 3.16228i | 0.271163i | ||||||||
\(137\) | 7.47723 | 0.638822 | 0.319411 | − | 0.947616i | \(-0.396515\pi\) | ||||
0.319411 | + | 0.947616i | \(0.396515\pi\) | |||||||
\(138\) | −4.58009 | − | 10.2414i | −0.389883 | − | 0.871805i | ||||
\(139\) | 7.53185i | 0.638843i | 0.947613 | + | 0.319422i | \(0.103489\pi\) | ||||
−0.947613 | + | 0.319422i | \(0.896511\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.2614 | + | 5.48346i | −1.03260 | + | 0.461791i | ||||
\(142\) | − | 2.02265i | − | 0.169737i | ||||||
\(143\) | − | 1.43023i | − | 0.119602i | ||||||
\(144\) | −2.00000 | + | 2.23607i | −0.166667 | + | 0.186339i | ||||
\(145\) | −3.50333 | − | 2.86045i | −0.290935 | − | 0.237548i | ||||
\(146\) | −11.9886 | −0.992184 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 7.13505i | − | 0.586497i | ||||||
\(149\) | 2.44949i | 0.200670i | 0.994954 | + | 0.100335i | \(0.0319915\pi\) | ||||
−0.994954 | + | 0.100335i | \(0.968009\pi\) | |||||||
\(150\) | 7.03886 | − | 5.04524i | 0.574721 | − | 0.411942i | ||||
\(151\) | −2.00000 | −0.162758 | −0.0813788 | − | 0.996683i | \(-0.525932\pi\) | ||||
−0.0813788 | + | 0.996683i | \(0.525932\pi\) | |||||||
\(152\) | 4.89433i | 0.396982i | ||||||||
\(153\) | −7.07107 | − | 6.32456i | −0.571662 | − | 0.511310i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.522774 | − | 0.426844i | −0.0419903 | − | 0.0342849i | ||||
\(156\) | 4.73861 | + | 10.5959i | 0.379393 | + | 0.848348i | ||||
\(157\) | −8.79052 | −0.701560 | −0.350780 | − | 0.936458i | \(-0.614084\pi\) | ||||
−0.350780 | + | 0.936458i | \(0.614084\pi\) | |||||||
\(158\) | 0.522774 | 0.0415897 | ||||||||
\(159\) | 3.53553 | + | 7.90569i | 0.280386 | + | 0.626962i | ||||
\(160\) | −1.41421 | + | 1.73205i | −0.111803 | + | 0.136931i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | − | 8.94427i | −0.0785674 | − | 0.702728i | ||||
\(163\) | − | 14.6969i | − | 1.15115i | −0.817748 | − | 0.575577i | \(-0.804778\pi\) | ||
0.817748 | − | 0.575577i | \(-0.195222\pi\) | |||||||
\(164\) | −6.70141 | −0.523292 | ||||||||
\(165\) | −0.215838 | + | 0.797901i | −0.0168030 | + | 0.0621165i | ||||
\(166\) | − | 16.7169i | − | 1.29748i | ||||||
\(167\) | 14.6830i | 1.13620i | 0.822958 | + | 0.568102i | \(0.192322\pi\) | ||||
−0.822958 | + | 0.568102i | \(0.807678\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 31.9089 | 2.45453 | ||||||||
\(170\) | −5.47723 | − | 4.47214i | −0.420084 | − | 0.342997i | ||||
\(171\) | −10.9441 | − | 9.78866i | −0.836913 | − | 0.748557i | ||||
\(172\) | 2.02265i | 0.154225i | ||||||||
\(173\) | − | 11.5207i | − | 0.875903i | −0.898999 | − | 0.437952i | \(-0.855704\pi\) | ||
0.898999 | − | 0.437952i | \(-0.144296\pi\) | |||||||
\(174\) | −3.19808 | + | 1.43023i | −0.242446 | + | 0.108425i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 0.213422i | − | 0.0160873i | ||||||
\(177\) | 3.47723 | + | 7.77531i | 0.261364 | + | 0.584428i | ||||
\(178\) | 10.5744 | 0.792584 | ||||||||
\(179\) | 14.9104i | 1.11445i | 0.830361 | + | 0.557226i | \(0.188134\pi\) | ||||
−0.830361 | + | 0.557226i | \(0.811866\pi\) | |||||||
\(180\) | −1.04456 | − | 6.62638i | −0.0778566 | − | 0.493901i | ||||
\(181\) | − | 3.16228i | − | 0.235050i | −0.993070 | − | 0.117525i | \(-0.962504\pi\) | ||
0.993070 | − | 0.117525i | \(-0.0374961\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.47723 | + | 2.44949i | −0.404888 | + | 0.181071i | ||||
\(184\) | −6.47723 | −0.477507 | ||||||||
\(185\) | 12.3583 | + | 10.0905i | 0.908598 | + | 0.741867i | ||||
\(186\) | −0.477226 | + | 0.213422i | −0.0349919 | + | 0.0156488i | ||||
\(187\) | 0.674899 | 0.0493535 | ||||||||
\(188\) | 7.75478i | 0.565576i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.47723 | − | 6.92163i | −0.615003 | − | 0.502148i | ||||
\(191\) | − | 1.59580i | − | 0.115468i | −0.998332 | − | 0.0577341i | \(-0.981612\pi\) | ||
0.998332 | − | 0.0577341i | \(-0.0183876\pi\) | |||||||
\(192\) | 0.707107 | + | 1.58114i | 0.0510310 | + | 0.114109i | ||||
\(193\) | 7.34847i | 0.528954i | 0.964392 | + | 0.264477i | \(0.0851994\pi\) | ||||
−0.964392 | + | 0.264477i | \(0.914801\pi\) | |||||||
\(194\) | −3.50333 | −0.251524 | ||||||||
\(195\) | −25.0540 | − | 6.77729i | −1.79415 | − | 0.485332i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.00000 | 0.641223 | 0.320612 | − | 0.947211i | \(-0.396112\pi\) | ||||
0.320612 | + | 0.947211i | \(0.396112\pi\) | |||||||
\(198\) | 0.477226 | + | 0.426844i | 0.0339149 | + | 0.0303344i | ||||
\(199\) | 22.4378i | 1.59057i | 0.606235 | + | 0.795286i | \(0.292679\pi\) | ||||
−0.606235 | + | 0.795286i | \(0.707321\pi\) | |||||||
\(200\) | −1.00000 | − | 4.89898i | −0.0707107 | − | 0.346410i | ||||
\(201\) | −8.42087 | + | 3.76593i | −0.593962 | + | 0.265628i | ||||
\(202\) | 11.3137 | 0.796030 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −5.00000 | + | 2.23607i | −0.350070 | + | 0.156556i | ||||
\(205\) | 9.47723 | − | 11.6072i | 0.661918 | − | 0.810681i | ||||
\(206\) | 10.5744 | 0.736753 | ||||||||
\(207\) | 12.9545 | − | 14.4835i | 0.900397 | − | 1.00667i | ||||
\(208\) | 6.70141 | 0.464659 | ||||||||
\(209\) | 1.04456 | 0.0722535 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.5228 | 0.930946 | 0.465473 | − | 0.885062i | \(-0.345884\pi\) | ||||
0.465473 | + | 0.885062i | \(0.345884\pi\) | |||||||
\(212\) | 5.00000 | 0.343401 | ||||||||
\(213\) | 3.19808 | − | 1.43023i | 0.219129 | − | 0.0979975i | ||||
\(214\) | 5.47723 | 0.374415 | ||||||||
\(215\) | −3.50333 | − | 2.86045i | −0.238925 | − | 0.195081i | ||||
\(216\) | −4.94975 | − | 1.58114i | −0.336788 | − | 0.107583i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 12.4317 | 0.841979 | ||||||||
\(219\) | −8.47723 | − | 18.9557i | −0.572838 | − | 1.28090i | ||||
\(220\) | 0.369657 | + | 0.301824i | 0.0249223 | + | 0.0203490i | ||||
\(221\) | 21.1917i | 1.42551i | ||||||||
\(222\) | 11.2815 | − | 5.04524i | 0.757165 | − | 0.338614i | ||||
\(223\) | 6.39617 | 0.428319 | 0.214160 | − | 0.976799i | \(-0.431299\pi\) | ||||
0.214160 | + | 0.976799i | \(0.431299\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.9545 | + | 7.56189i | 0.863630 | + | 0.504126i | ||||
\(226\) | 6.52277 | 0.433889 | ||||||||
\(227\) | − | 10.3923i | − | 0.689761i | −0.938647 | − | 0.344881i | \(-0.887919\pi\) | ||
0.938647 | − | 0.344881i | \(-0.112081\pi\) | |||||||
\(228\) | −7.73861 | + | 3.46081i | −0.512502 | + | 0.229198i | ||||
\(229\) | − | 7.23003i | − | 0.477774i | −0.971047 | − | 0.238887i | \(-0.923218\pi\) | ||
0.971047 | − | 0.238887i | \(-0.0767825\pi\) | |||||||
\(230\) | 9.16018 | − | 11.2189i | 0.604004 | − | 0.739751i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.02265i | 0.132793i | ||||||||
\(233\) | −4.00000 | −0.262049 | −0.131024 | − | 0.991379i | \(-0.541827\pi\) | ||||
−0.131024 | + | 0.991379i | \(0.541827\pi\) | |||||||
\(234\) | −13.4028 | + | 14.9848i | −0.876170 | + | 0.979588i | ||||
\(235\) | −13.4317 | − | 10.9669i | −0.876186 | − | 0.715403i | ||||
\(236\) | 4.91754 | 0.320105 | ||||||||
\(237\) | 0.369657 | + | 0.826579i | 0.0240118 | + | 0.0536921i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | −3.73861 | − | 1.01132i | −0.241326 | − | 0.0652806i | ||||
\(241\) | − | 3.98886i | − | 0.256945i | −0.991713 | − | 0.128472i | \(-0.958993\pi\) | ||
0.991713 | − | 0.128472i | \(-0.0410074\pi\) | |||||||
\(242\) | 10.9545 | 0.704179 | ||||||||
\(243\) | 13.4350 | − | 7.90569i | 0.861858 | − | 0.507151i | ||||
\(244\) | 3.46410i | 0.221766i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.73861 | − | 10.5959i | −0.302123 | − | 0.675567i | ||||
\(247\) | 32.7989i | 2.08694i | ||||||||
\(248\) | 0.301824i | 0.0191658i | ||||||||
\(249\) | 26.4317 | − | 11.8206i | 1.67504 | − | 0.749100i | ||||
\(250\) | 9.89949 | + | 5.19615i | 0.626099 | + | 0.328634i | ||||
\(251\) | 16.6009 | 1.04784 | 0.523920 | − | 0.851768i | \(-0.324469\pi\) | ||||
0.523920 | + | 0.851768i | \(0.324469\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.38238i | 0.0869095i | ||||||||
\(254\) | − | 13.6298i | − | 0.855212i | ||||||
\(255\) | 3.19808 | − | 11.8225i | 0.200272 | − | 0.740356i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 23.6451i | − | 1.47494i | −0.675381 | − | 0.737469i | \(-0.736021\pi\) | ||
0.675381 | − | 0.737469i | \(-0.263979\pi\) | |||||||
\(258\) | −3.19808 | + | 1.43023i | −0.199104 | + | 0.0890420i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −9.47723 | + | 11.6072i | −0.587753 | + | 0.719847i | ||||
\(261\) | −4.52277 | − | 4.04529i | −0.279953 | − | 0.250397i | ||||
\(262\) | −6.02651 | −0.372319 | ||||||||
\(263\) | −2.00000 | −0.123325 | −0.0616626 | − | 0.998097i | \(-0.519640\pi\) | ||||
−0.0616626 | + | 0.998097i | \(0.519640\pi\) | |||||||
\(264\) | 0.337449 | − | 0.150912i | 0.0207686 | − | 0.00928799i | ||||
\(265\) | −7.07107 | + | 8.66025i | −0.434372 | + | 0.531995i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.47723 | + | 16.7196i | 0.457599 | + | 1.02322i | ||||
\(268\) | 5.32582i | 0.325326i | ||||||||
\(269\) | −28.8948 | −1.76174 | −0.880872 | − | 0.473354i | \(-0.843043\pi\) | ||||
−0.880872 | + | 0.473354i | \(0.843043\pi\) | |||||||
\(270\) | 9.73861 | − | 6.33715i | 0.592673 | − | 0.385666i | ||||
\(271\) | 6.32456i | 0.384189i | 0.981376 | + | 0.192095i | \(0.0615281\pi\) | ||||
−0.981376 | + | 0.192095i | \(0.938472\pi\) | |||||||
\(272\) | 3.16228i | 0.191741i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.47723 | 0.451716 | ||||||||
\(275\) | −1.04555 | + | 0.213422i | −0.0630490 | + | 0.0128698i | ||||
\(276\) | −4.58009 | − | 10.2414i | −0.275689 | − | 0.616459i | ||||
\(277\) | − | 9.79796i | − | 0.588702i | −0.955697 | − | 0.294351i | \(-0.904896\pi\) | ||
0.955697 | − | 0.294351i | \(-0.0951035\pi\) | |||||||
\(278\) | 7.53185i | 0.451730i | ||||||||
\(279\) | −0.674899 | − | 0.603648i | −0.0404051 | − | 0.0361395i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 11.6072i | − | 0.692427i | −0.938156 | − | 0.346213i | \(-0.887467\pi\) | ||
0.938156 | − | 0.346213i | \(-0.112533\pi\) | |||||||
\(282\) | −12.2614 | + | 5.48346i | −0.730155 | + | 0.326535i | ||||
\(283\) | 24.7165 | 1.46925 | 0.734623 | − | 0.678476i | \(-0.237359\pi\) | ||||
0.734623 | + | 0.678476i | \(0.237359\pi\) | |||||||
\(284\) | − | 2.02265i | − | 0.120022i | ||||||
\(285\) | 4.94975 | − | 18.2980i | 0.293198 | − | 1.08388i | ||||
\(286\) | − | 1.43023i | − | 0.0845711i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.00000 | + | 2.23607i | −0.117851 | + | 0.131762i | ||||
\(289\) | 7.00000 | 0.411765 | ||||||||
\(290\) | −3.50333 | − | 2.86045i | −0.205722 | − | 0.167972i | ||||
\(291\) | −2.47723 | − | 5.53924i | −0.145218 | − | 0.324716i | ||||
\(292\) | −11.9886 | −0.701580 | ||||||||
\(293\) | − | 4.59250i | − | 0.268297i | −0.990961 | − | 0.134148i | \(-0.957170\pi\) | ||
0.990961 | − | 0.134148i | \(-0.0428299\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.95445 | + | 8.51743i | −0.404904 | + | 0.495904i | ||||
\(296\) | − | 7.13505i | − | 0.414716i | ||||||
\(297\) | −0.337449 | + | 1.05638i | −0.0195808 | + | 0.0612976i | ||||
\(298\) | 2.44949i | 0.141895i | ||||||||
\(299\) | −43.4065 | −2.51027 | ||||||||
\(300\) | 7.03886 | − | 5.04524i | 0.406389 | − | 0.291287i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.00000 | −0.115087 | ||||||||
\(303\) | 8.00000 | + | 17.8885i | 0.459588 | + | 1.02767i | ||||
\(304\) | 4.89433i | 0.280709i | ||||||||
\(305\) | −6.00000 | − | 4.89898i | −0.343559 | − | 0.280515i | ||||
\(306\) | −7.07107 | − | 6.32456i | −0.404226 | − | 0.361551i | ||||
\(307\) | 3.50333 | 0.199945 | 0.0999727 | − | 0.994990i | \(-0.468124\pi\) | ||||
0.0999727 | + | 0.994990i | \(0.468124\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.47723 | + | 16.7196i | 0.425365 | + | 0.951144i | ||||
\(310\) | −0.522774 | − | 0.426844i | −0.0296916 | − | 0.0242431i | ||||
\(311\) | −28.8948 | −1.63847 | −0.819236 | − | 0.573457i | \(-0.805602\pi\) | ||||
−0.819236 | + | 0.573457i | \(0.805602\pi\) | |||||||
\(312\) | 4.73861 | + | 10.5959i | 0.268271 | + | 0.599872i | ||||
\(313\) | −23.2379 | −1.31348 | −0.656742 | − | 0.754115i | \(-0.728066\pi\) | ||||
−0.656742 | + | 0.754115i | \(0.728066\pi\) | |||||||
\(314\) | −8.79052 | −0.496078 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.522774 | 0.0294084 | ||||||||
\(317\) | 33.9089 | 1.90451 | 0.952257 | − | 0.305298i | \(-0.0987561\pi\) | ||||
0.952257 | + | 0.305298i | \(0.0987561\pi\) | |||||||
\(318\) | 3.53553 | + | 7.90569i | 0.198263 | + | 0.443329i | ||||
\(319\) | 0.431677 | 0.0241693 | ||||||||
\(320\) | −1.41421 | + | 1.73205i | −0.0790569 | + | 0.0968246i | ||||
\(321\) | 3.87298 | + | 8.66025i | 0.216169 | + | 0.483368i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.4772 | −0.861176 | ||||||||
\(324\) | −1.00000 | − | 8.94427i | −0.0555556 | − | 0.496904i | ||||
\(325\) | −6.70141 | − | 32.8301i | −0.371727 | − | 1.82108i | ||||
\(326\) | − | 14.6969i | − | 0.813988i | ||||||
\(327\) | 8.79052 | + | 19.6562i | 0.486117 | + | 1.08699i | ||||
\(328\) | −6.70141 | −0.370023 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.215838 | + | 0.797901i | −0.0118815 | + | 0.0439230i | ||||
\(331\) | −11.4317 | −0.628342 | −0.314171 | − | 0.949366i | \(-0.601726\pi\) | ||||
−0.314171 | + | 0.949366i | \(0.601726\pi\) | |||||||
\(332\) | − | 16.7169i | − | 0.917457i | ||||||
\(333\) | 15.9545 | + | 14.2701i | 0.874299 | + | 0.781996i | ||||
\(334\) | 14.6830i | 0.803417i | ||||||||
\(335\) | −9.22460 | − | 7.53185i | −0.503994 | − | 0.411509i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 17.1464i | − | 0.934025i | −0.884251 | − | 0.467013i | \(-0.845330\pi\) | ||
0.884251 | − | 0.467013i | \(-0.154670\pi\) | |||||||
\(338\) | 31.9089 | 1.73562 | ||||||||
\(339\) | 4.61230 | + | 10.3134i | 0.250506 | + | 0.560148i | ||||
\(340\) | −5.47723 | − | 4.47214i | −0.297044 | − | 0.242536i | ||||
\(341\) | 0.0644158 | 0.00348831 | ||||||||
\(342\) | −10.9441 | − | 9.78866i | −0.591787 | − | 0.529310i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.02265i | 0.109054i | ||||||||
\(345\) | 24.2158 | + | 6.55057i | 1.30374 | + | 0.352671i | ||||
\(346\) | − | 11.5207i | − | 0.619357i | ||||||
\(347\) | −6.52277 | −0.350161 | −0.175080 | − | 0.984554i | \(-0.556019\pi\) | ||||
−0.175080 | + | 0.984554i | \(0.556019\pi\) | |||||||
\(348\) | −3.19808 | + | 1.43023i | −0.171435 | + | 0.0766682i | ||||
\(349\) | 32.5282i | 1.74120i | 0.491994 | + | 0.870599i | \(0.336268\pi\) | ||||
−0.491994 | + | 0.870599i | \(0.663732\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −33.1703 | − | 10.5959i | −1.77050 | − | 0.565565i | ||||
\(352\) | − | 0.213422i | − | 0.0113754i | ||||||
\(353\) | − | 13.2528i | − | 0.705373i | −0.935742 | − | 0.352687i | \(-0.885268\pi\) | ||
0.935742 | − | 0.352687i | \(-0.114732\pi\) | |||||||
\(354\) | 3.47723 | + | 7.77531i | 0.184812 | + | 0.413253i | ||||
\(355\) | 3.50333 | + | 2.86045i | 0.185937 | + | 0.151817i | ||||
\(356\) | 10.5744 | 0.560442 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.9104i | 0.788037i | ||||||||
\(359\) | 6.49478i | 0.342781i | 0.985203 | + | 0.171391i | \(0.0548261\pi\) | ||||
−0.985203 | + | 0.171391i | \(0.945174\pi\) | |||||||
\(360\) | −1.04456 | − | 6.62638i | −0.0550529 | − | 0.349241i | ||||
\(361\) | −4.95445 | −0.260761 | ||||||||
\(362\) | − | 3.16228i | − | 0.166206i | ||||||
\(363\) | 7.74597 | + | 17.3205i | 0.406558 | + | 0.909091i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.9545 | − | 20.7649i | 0.887437 | − | 1.08688i | ||||
\(366\) | −5.47723 | + | 2.44949i | −0.286299 | + | 0.128037i | ||||
\(367\) | 8.11562 | 0.423632 | 0.211816 | − | 0.977310i | \(-0.432062\pi\) | ||||
0.211816 | + | 0.977310i | \(0.432062\pi\) | |||||||
\(368\) | −6.47723 | −0.337649 | ||||||||
\(369\) | 13.4028 | − | 14.9848i | 0.697723 | − | 0.780078i | ||||
\(370\) | 12.3583 | + | 10.0905i | 0.642476 | + | 0.524579i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.477226 | + | 0.213422i | −0.0247430 | + | 0.0110654i | ||||
\(373\) | − | 3.61845i | − | 0.187356i | −0.995603 | − | 0.0936781i | \(-0.970138\pi\) | ||
0.995603 | − | 0.0936781i | \(-0.0298624\pi\) | |||||||
\(374\) | 0.674899 | 0.0348982 | ||||||||
\(375\) | −1.21584 | + | 19.3267i | −0.0627856 | + | 0.998027i | ||||
\(376\) | 7.75478i | 0.399922i | ||||||||
\(377\) | 13.5546i | 0.698097i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.52277 | −0.489152 | −0.244576 | − | 0.969630i | \(-0.578649\pi\) | ||||
−0.244576 | + | 0.969630i | \(0.578649\pi\) | |||||||
\(380\) | −8.47723 | − | 6.92163i | −0.434872 | − | 0.355072i | ||||
\(381\) | 21.5507 | − | 9.63774i | 1.10407 | − | 0.493757i | ||||
\(382\) | − | 1.59580i | − | 0.0816484i | ||||||
\(383\) | − | 0.826579i | − | 0.0422362i | −0.999777 | − | 0.0211181i | \(-0.993277\pi\) | ||
0.999777 | − | 0.0211181i | \(-0.00672260\pi\) | |||||||
\(384\) | 0.707107 | + | 1.58114i | 0.0360844 | + | 0.0806872i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.34847i | 0.374027i | ||||||||
\(387\) | −4.52277 | − | 4.04529i | −0.229906 | − | 0.205634i | ||||
\(388\) | −3.50333 | −0.177854 | ||||||||
\(389\) | 7.34847i | 0.372582i | 0.982495 | + | 0.186291i | \(0.0596468\pi\) | ||||
−0.982495 | + | 0.186291i | \(0.940353\pi\) | |||||||
\(390\) | −25.0540 | − | 6.77729i | −1.26866 | − | 0.343181i | ||||
\(391\) | − | 20.4828i | − | 1.03586i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.26139 | − | 9.52875i | −0.214959 | − | 0.480662i | ||||
\(394\) | 9.00000 | 0.453413 | ||||||||
\(395\) | −0.739315 | + | 0.905472i | −0.0371990 | + | 0.0455592i | ||||
\(396\) | 0.477226 | + | 0.426844i | 0.0239815 | + | 0.0214497i | ||||
\(397\) | 30.3734 | 1.52440 | 0.762198 | − | 0.647344i | \(-0.224120\pi\) | ||||
0.762198 | + | 0.647344i | \(0.224120\pi\) | |||||||
\(398\) | 22.4378i | 1.12470i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.00000 | − | 4.89898i | −0.0500000 | − | 0.244949i | ||||
\(401\) | − | 30.3494i | − | 1.51558i | −0.652500 | − | 0.757789i | \(-0.726280\pi\) | ||
0.652500 | − | 0.757789i | \(-0.273720\pi\) | |||||||
\(402\) | −8.42087 | + | 3.76593i | −0.419995 | + | 0.187827i | ||||
\(403\) | 2.02265i | 0.100755i | ||||||||
\(404\) | 11.3137 | 0.562878 | ||||||||
\(405\) | 16.9061 | + | 10.9171i | 0.840073 | + | 0.542473i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.52277 | −0.0754811 | ||||||||
\(408\) | −5.00000 | + | 2.23607i | −0.247537 | + | 0.110702i | ||||
\(409\) | 22.4378i | 1.10948i | 0.832025 | + | 0.554738i | \(0.187182\pi\) | ||||
−0.832025 | + | 0.554738i | \(0.812818\pi\) | |||||||
\(410\) | 9.47723 | − | 11.6072i | 0.468047 | − | 0.573238i | ||||
\(411\) | 5.28720 | + | 11.8225i | 0.260798 | + | 0.583162i | ||||
\(412\) | 10.5744 | 0.520963 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 12.9545 | − | 14.4835i | 0.636677 | − | 0.711826i | ||||
\(415\) | 28.9545 | + | 23.6412i | 1.42132 | + | 1.16050i | ||||
\(416\) | 6.70141 | 0.328564 | ||||||||
\(417\) | −11.9089 | + | 5.32582i | −0.583181 | + | 0.260807i | ||||
\(418\) | 1.04456 | 0.0510909 | ||||||||
\(419\) | −16.6009 | −0.811007 | −0.405504 | − | 0.914093i | \(-0.632904\pi\) | ||||
−0.405504 | + | 0.914093i | \(0.632904\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.95445 | −0.143991 | −0.0719956 | − | 0.997405i | \(-0.522937\pi\) | ||||
−0.0719956 | + | 0.997405i | \(0.522937\pi\) | |||||||
\(422\) | 13.5228 | 0.658278 | ||||||||
\(423\) | −17.3402 | − | 15.5096i | −0.843110 | − | 0.754101i | ||||
\(424\) | 5.00000 | 0.242821 | ||||||||
\(425\) | 15.4919 | − | 3.16228i | 0.751469 | − | 0.153393i | ||||
\(426\) | 3.19808 | − | 1.43023i | 0.154948 | − | 0.0692947i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5.47723 | 0.264752 | ||||||||
\(429\) | 2.26139 | − | 1.01132i | 0.109181 | − | 0.0488271i | ||||
\(430\) | −3.50333 | − | 2.86045i | −0.168945 | − | 0.137943i | ||||
\(431\) | − | 37.0576i | − | 1.78500i | −0.451045 | − | 0.892501i | \(-0.648949\pi\) | ||
0.451045 | − | 0.892501i | \(-0.351051\pi\) | |||||||
\(432\) | −4.94975 | − | 1.58114i | −0.238145 | − | 0.0760726i | ||||
\(433\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.04555 | − | 7.56189i | 0.0980766 | − | 0.362565i | ||||
\(436\) | 12.4317 | 0.595369 | ||||||||
\(437\) | − | 31.7017i | − | 1.51650i | ||||||
\(438\) | −8.47723 | − | 18.9557i | −0.405058 | − | 0.905736i | ||||
\(439\) | 22.7396i | 1.08530i | 0.839958 | + | 0.542651i | \(0.182579\pi\) | ||||
−0.839958 | + | 0.542651i | \(0.817421\pi\) | |||||||
\(440\) | 0.369657 | + | 0.301824i | 0.0176227 | + | 0.0143889i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 21.1917i | 1.00799i | ||||||||
\(443\) | −36.9545 | −1.75576 | −0.877879 | − | 0.478882i | \(-0.841042\pi\) | ||||
−0.877879 | + | 0.478882i | \(0.841042\pi\) | |||||||
\(444\) | 11.2815 | − | 5.04524i | 0.535396 | − | 0.239437i | ||||
\(445\) | −14.9545 | + | 18.3154i | −0.708909 | + | 0.868233i | ||||
\(446\) | 6.39617 | 0.302867 | ||||||||
\(447\) | −3.87298 | + | 1.73205i | −0.183186 | + | 0.0819232i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.51660i | 0.165959i | 0.996551 | + | 0.0829793i | \(0.0264435\pi\) | ||||
−0.996551 | + | 0.0829793i | \(0.973556\pi\) | |||||||
\(450\) | 12.9545 | + | 7.56189i | 0.610679 | + | 0.356471i | ||||
\(451\) | 1.43023i | 0.0673468i | ||||||||
\(452\) | 6.52277 | 0.306806 | ||||||||
\(453\) | −1.41421 | − | 3.16228i | −0.0664455 | − | 0.148577i | ||||
\(454\) | − | 10.3923i | − | 0.487735i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.73861 | + | 3.46081i | −0.362394 | + | 0.162067i | ||||
\(457\) | − | 37.9113i | − | 1.77342i | −0.462330 | − | 0.886708i | \(-0.652986\pi\) | ||
0.462330 | − | 0.886708i | \(-0.347014\pi\) | |||||||
\(458\) | − | 7.23003i | − | 0.337837i | ||||||
\(459\) | 5.00000 | − | 15.6525i | 0.233380 | − | 0.730595i | ||||
\(460\) | 9.16018 | − | 11.2189i | 0.427096 | − | 0.523083i | ||||
\(461\) | −16.2957 | −0.758965 | −0.379482 | − | 0.925199i | \(-0.623898\pi\) | ||||
−0.379482 | + | 0.925199i | \(0.623898\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 17.6751i | − | 0.821433i | −0.911763 | − | 0.410716i | \(-0.865279\pi\) | ||
0.911763 | − | 0.410716i | \(-0.134721\pi\) | |||||||
\(464\) | 2.02265i | 0.0938990i | ||||||||
\(465\) | 0.305242 | − | 1.12840i | 0.0141552 | − | 0.0523284i | ||||
\(466\) | −4.00000 | −0.185296 | ||||||||
\(467\) | − | 34.3392i | − | 1.58903i | −0.607246 | − | 0.794514i | \(-0.707726\pi\) | ||
0.607246 | − | 0.794514i | \(-0.292274\pi\) | |||||||
\(468\) | −13.4028 | + | 14.9848i | −0.619546 | + | 0.692673i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −13.4317 | − | 10.9669i | −0.619557 | − | 0.505866i | ||||
\(471\) | −6.21584 | − | 13.8990i | −0.286411 | − | 0.640434i | ||||
\(472\) | 4.91754 | 0.226348 | ||||||||
\(473\) | 0.431677 | 0.0198485 | ||||||||
\(474\) | 0.369657 | + | 0.826579i | 0.0169789 | + | 0.0379660i | ||||
\(475\) | 23.9772 | − | 4.89433i | 1.10015 | − | 0.224567i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.0000 | + | 11.1803i | −0.457869 | + | 0.511913i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.3781 | −0.519880 | −0.259940 | − | 0.965625i | \(-0.583703\pi\) | ||||
−0.259940 | + | 0.965625i | \(0.583703\pi\) | |||||||
\(480\) | −3.73861 | − | 1.01132i | −0.170644 | − | 0.0461604i | ||||
\(481\) | − | 47.8149i | − | 2.18017i | ||||||
\(482\) | − | 3.98886i | − | 0.181687i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.9545 | 0.497930 | ||||||||
\(485\) | 4.95445 | − | 6.06794i | 0.224970 | − | 0.275531i | ||||
\(486\) | 13.4350 | − | 7.90569i | 0.609425 | − | 0.358610i | ||||
\(487\) | 36.6308i | 1.65990i | 0.557839 | + | 0.829949i | \(0.311631\pi\) | ||||
−0.557839 | + | 0.829949i | \(0.688369\pi\) | |||||||
\(488\) | 3.46410i | 0.156813i | ||||||||
\(489\) | 23.2379 | − | 10.3923i | 1.05085 | − | 0.469956i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.04529i | 0.182561i | 0.995825 | + | 0.0912807i | \(0.0290961\pi\) | ||||
−0.995825 | + | 0.0912807i | \(0.970904\pi\) | |||||||
\(492\) | −4.73861 | − | 10.5959i | −0.213633 | − | 0.477698i | ||||
\(493\) | −6.39617 | −0.288069 | ||||||||
\(494\) | 32.7989i | 1.47569i | ||||||||
\(495\) | −1.41421 | + | 0.222931i | −0.0635642 | + | 0.0100200i | ||||
\(496\) | 0.301824i | 0.0135523i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 26.4317 | − | 11.8206i | 1.18443 | − | 0.529694i | ||||
\(499\) | −41.9089 | −1.87610 | −0.938050 | − | 0.346500i | \(-0.887370\pi\) | ||||
−0.938050 | + | 0.346500i | \(0.887370\pi\) | |||||||
\(500\) | 9.89949 | + | 5.19615i | 0.442719 | + | 0.232379i | ||||
\(501\) | −23.2158 | + | 10.3824i | −1.03721 | + | 0.463853i | ||||
\(502\) | 16.6009 | 0.740935 | ||||||||
\(503\) | − | 22.4378i | − | 1.00045i | −0.865895 | − | 0.500225i | \(-0.833251\pi\) | ||
0.865895 | − | 0.500225i | \(-0.166749\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.0000 | + | 19.5959i | −0.711991 | + | 0.872007i | ||||
\(506\) | 1.38238i | 0.0614543i | ||||||||
\(507\) | 22.5630 | + | 50.4524i | 1.00206 | + | 2.24067i | ||||
\(508\) | − | 13.6298i | − | 0.604726i | ||||||
\(509\) | −9.22460 | −0.408873 | −0.204437 | − | 0.978880i | \(-0.565536\pi\) | ||||
−0.204437 | + | 0.978880i | \(0.565536\pi\) | |||||||
\(510\) | 3.19808 | − | 11.8225i | 0.141614 | − | 0.523511i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 7.73861 | − | 24.2257i | 0.341668 | − | 1.06959i | ||||
\(514\) | − | 23.6451i | − | 1.04294i | ||||||
\(515\) | −14.9545 | + | 18.3154i | −0.658972 | + | 0.807072i | ||||
\(516\) | −3.19808 | + | 1.43023i | −0.140788 | + | 0.0629622i | ||||
\(517\) | 1.65504 | 0.0727885 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.2158 | − | 8.14637i | 0.799587 | − | 0.357586i | ||||
\(520\) | −9.47723 | + | 11.6072i | −0.415604 | + | 0.509009i | ||||
\(521\) | 18.6256 | 0.816002 | 0.408001 | − | 0.912981i | \(-0.366226\pi\) | ||||
0.408001 | + | 0.912981i | \(0.366226\pi\) | |||||||
\(522\) | −4.52277 | − | 4.04529i | −0.197956 | − | 0.177058i | ||||
\(523\) | 14.0777 | 0.615576 | 0.307788 | − | 0.951455i | \(-0.400411\pi\) | ||||
0.307788 | + | 0.951455i | \(0.400411\pi\) | |||||||
\(524\) | −6.02651 | −0.263269 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.00000 | −0.0872041 | ||||||||
\(527\) | −0.954451 | −0.0415765 | ||||||||
\(528\) | 0.337449 | − | 0.150912i | 0.0146856 | − | 0.00656760i | ||||
\(529\) | 18.9545 | 0.824107 | ||||||||
\(530\) | −7.07107 | + | 8.66025i | −0.307148 | + | 0.376177i | ||||
\(531\) | −9.83508 | + | 10.9960i | −0.426806 | + | 0.477184i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −44.9089 | −1.94522 | ||||||||
\(534\) | 7.47723 | + | 16.7196i | 0.323571 | + | 0.723527i | ||||
\(535\) | −7.74597 | + | 9.48683i | −0.334887 | + | 0.410152i | ||||
\(536\) | 5.32582i | 0.230041i | ||||||||
\(537\) | −23.5753 | + | 10.5432i | −1.01735 | + | 0.454973i | ||||
\(538\) | −28.8948 | −1.24574 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 9.73861 | − | 6.33715i | 0.419083 | − | 0.272707i | ||||
\(541\) | 19.4772 | 0.837391 | 0.418696 | − | 0.908127i | \(-0.362487\pi\) | ||||
0.418696 | + | 0.908127i | \(0.362487\pi\) | |||||||
\(542\) | 6.32456i | 0.271663i | ||||||||
\(543\) | 5.00000 | − | 2.23607i | 0.214571 | − | 0.0959589i | ||||
\(544\) | 3.16228i | 0.135582i | ||||||||
\(545\) | −17.5810 | + | 21.5323i | −0.753089 | + | 0.922342i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.2144i | 0.992575i | 0.868158 | + | 0.496287i | \(0.165304\pi\) | ||||
−0.868158 | + | 0.496287i | \(0.834696\pi\) | |||||||
\(548\) | 7.47723 | 0.319411 | ||||||||
\(549\) | −7.74597 | − | 6.92820i | −0.330590 | − | 0.295689i | ||||
\(550\) | −1.04555 | + | 0.213422i | −0.0445824 | + | 0.00910033i | ||||
\(551\) | −9.89949 | −0.421733 | ||||||||
\(552\) | −4.58009 | − | 10.2414i | −0.194942 | − | 0.435903i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 9.79796i | − | 0.416275i | ||||||
\(555\) | −7.21584 | + | 26.6752i | −0.306295 | + | 1.13230i | ||||
\(556\) | 7.53185i | 0.319422i | ||||||||
\(557\) | −37.8634 | −1.60432 | −0.802161 | − | 0.597108i | \(-0.796316\pi\) | ||||
−0.802161 | + | 0.597108i | \(0.796316\pi\) | |||||||
\(558\) | −0.674899 | − | 0.603648i | −0.0285707 | − | 0.0255545i | ||||
\(559\) | 13.5546i | 0.573298i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.477226 | + | 1.06711i | 0.0201485 | + | 0.0450534i | ||||
\(562\) | − | 11.6072i | − | 0.489619i | ||||||
\(563\) | − | 10.3923i | − | 0.437983i | −0.975727 | − | 0.218992i | \(-0.929723\pi\) | ||
0.975727 | − | 0.218992i | \(-0.0702768\pi\) | |||||||
\(564\) | −12.2614 | + | 5.48346i | −0.516298 | + | 0.230895i | ||||
\(565\) | −9.22460 | + | 11.2978i | −0.388082 | + | 0.475301i | ||||
\(566\) | 24.7165 | 1.03891 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 2.02265i | − | 0.0848683i | ||||||
\(569\) | 12.0340i | 0.504493i | 0.967663 | + | 0.252246i | \(0.0811693\pi\) | ||||
−0.967663 | + | 0.252246i | \(0.918831\pi\) | |||||||
\(570\) | 4.94975 | − | 18.2980i | 0.207322 | − | 0.766419i | ||||
\(571\) | −6.95445 | −0.291035 | −0.145517 | − | 0.989356i | \(-0.546485\pi\) | ||||
−0.145517 | + | 0.989356i | \(0.546485\pi\) | |||||||
\(572\) | − | 1.43023i | − | 0.0598008i | ||||||
\(573\) | 2.52319 | − | 1.12840i | 0.105408 | − | 0.0471397i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.47723 | + | 31.7318i | 0.270119 | + | 1.32331i | ||||
\(576\) | −2.00000 | + | 2.23607i | −0.0833333 | + | 0.0931695i | ||||
\(577\) | 14.8170 | 0.616841 | 0.308421 | − | 0.951250i | \(-0.400200\pi\) | ||||
0.308421 | + | 0.951250i | \(0.400200\pi\) | |||||||
\(578\) | 7.00000 | 0.291162 | ||||||||
\(579\) | −11.6190 | + | 5.19615i | −0.482867 | + | 0.215945i | ||||
\(580\) | −3.50333 | − | 2.86045i | −0.145468 | − | 0.118774i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2.47723 | − | 5.53924i | −0.102684 | − | 0.229609i | ||||
\(583\) | − | 1.06711i | − | 0.0441951i | ||||||
\(584\) | −11.9886 | −0.496092 | ||||||||
\(585\) | −7.00000 | − | 44.4061i | −0.289414 | − | 1.83597i | ||||
\(586\) | − | 4.59250i | − | 0.189715i | ||||||
\(587\) | − | 27.4110i | − | 1.13137i | −0.824621 | − | 0.565686i | \(-0.808611\pi\) | ||
0.824621 | − | 0.565686i | \(-0.191389\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.47723 | −0.0608680 | ||||||||
\(590\) | −6.95445 | + | 8.51743i | −0.286310 | + | 0.350657i | ||||
\(591\) | 6.36396 | + | 14.2302i | 0.261778 | + | 0.585354i | ||||
\(592\) | − | 7.13505i | − | 0.293249i | ||||||
\(593\) | 36.2942i | 1.49042i | 0.666828 | + | 0.745212i | \(0.267652\pi\) | ||||
−0.666828 | + | 0.745212i | \(0.732348\pi\) | |||||||
\(594\) | −0.337449 | + | 1.05638i | −0.0138457 | + | 0.0433440i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.44949i | 0.100335i | ||||||||
\(597\) | −35.4772 | + | 15.8659i | −1.45199 | + | 0.649348i | ||||
\(598\) | −43.4065 | −1.77503 | ||||||||
\(599\) | − | 5.75267i | − | 0.235048i | −0.993070 | − | 0.117524i | \(-0.962504\pi\) | ||
0.993070 | − | 0.117524i | \(-0.0374956\pi\) | |||||||
\(600\) | 7.03886 | − | 5.04524i | 0.287360 | − | 0.205971i | ||||
\(601\) | − | 16.7169i | − | 0.681895i | −0.940082 | − | 0.340947i | \(-0.889252\pi\) | ||
0.940082 | − | 0.340947i | \(-0.110748\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.9089 | − | 10.6516i | −0.484968 | − | 0.433769i | ||||
\(604\) | −2.00000 | −0.0813788 | ||||||||
\(605\) | −15.4919 | + | 18.9737i | −0.629837 | + | 0.771389i | ||||
\(606\) | 8.00000 | + | 17.8885i | 0.324978 | + | 0.726672i | ||||
\(607\) | −26.4360 | −1.07300 | −0.536502 | − | 0.843899i | \(-0.680255\pi\) | ||||
−0.536502 | + | 0.843899i | \(0.680255\pi\) | |||||||
\(608\) | 4.89433i | 0.198491i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.00000 | − | 4.89898i | −0.242933 | − | 0.198354i | ||||
\(611\) | 51.9680i | 2.10240i | ||||||||
\(612\) | −7.07107 | − | 6.32456i | −0.285831 | − | 0.255655i | ||||
\(613\) | − | 25.4504i | − | 1.02793i | −0.857810 | − | 0.513967i | \(-0.828175\pi\) | ||
0.857810 | − | 0.513967i | \(-0.171825\pi\) | |||||||
\(614\) | 3.50333 | 0.141383 | ||||||||
\(615\) | 25.0540 | + | 6.77729i | 1.01027 | + | 0.273287i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.4772 | 1.02567 | 0.512837 | − | 0.858486i | \(-0.328594\pi\) | ||||
0.512837 | + | 0.858486i | \(0.328594\pi\) | |||||||
\(618\) | 7.47723 | + | 16.7196i | 0.300778 | + | 0.672560i | ||||
\(619\) | 26.7284i | 1.07431i | 0.843484 | + | 0.537154i | \(0.180500\pi\) | ||||
−0.843484 | + | 0.537154i | \(0.819500\pi\) | |||||||
\(620\) | −0.522774 | − | 0.426844i | −0.0209951 | − | 0.0171424i | ||||
\(621\) | 32.0606 | + | 10.2414i | 1.28655 | + | 0.410973i | ||||
\(622\) | −28.8948 | −1.15857 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.73861 | + | 10.5959i | 0.189696 | + | 0.424174i | ||||
\(625\) | −23.0000 | + | 9.79796i | −0.920000 | + | 0.391918i | ||||
\(626\) | −23.2379 | −0.928773 | ||||||||
\(627\) | 0.738613 | + | 1.65159i | 0.0294974 | + | 0.0659581i | ||||
\(628\) | −8.79052 | −0.350780 | ||||||||
\(629\) | 22.5630 | 0.899646 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.47723 | −0.297664 | −0.148832 | − | 0.988863i | \(-0.547551\pi\) | ||||
−0.148832 | + | 0.988863i | \(0.547551\pi\) | |||||||
\(632\) | 0.522774 | 0.0207949 | ||||||||
\(633\) | 9.56205 | + | 21.3814i | 0.380057 | + | 0.849834i | ||||
\(634\) | 33.9089 | 1.34669 | ||||||||
\(635\) | 23.6076 | + | 19.2755i | 0.936837 | + | 0.764924i | ||||
\(636\) | 3.53553 | + | 7.90569i | 0.140193 | + | 0.313481i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.431677 | 0.0170902 | ||||||||
\(639\) | 4.52277 | + | 4.04529i | 0.178918 | + | 0.160029i | ||||
\(640\) | −1.41421 | + | 1.73205i | −0.0559017 | + | 0.0684653i | ||||
\(641\) | − | 6.28136i | − | 0.248099i | −0.992276 | − | 0.124049i | \(-0.960412\pi\) | ||
0.992276 | − | 0.124049i | \(-0.0395881\pi\) | |||||||
\(642\) | 3.87298 | + | 8.66025i | 0.152854 | + | 0.341793i | ||||
\(643\) | −20.4095 | −0.804871 | −0.402436 | − | 0.915448i | \(-0.631836\pi\) | ||||
−0.402436 | + | 0.915448i | \(0.631836\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.04555 | − | 7.56189i | 0.0805434 | − | 0.297749i | ||||
\(646\) | −15.4772 | −0.608943 | ||||||||
\(647\) | 23.8680i | 0.938348i | 0.883106 | + | 0.469174i | \(0.155448\pi\) | ||||
−0.883106 | + | 0.469174i | \(0.844552\pi\) | |||||||
\(648\) | −1.00000 | − | 8.94427i | −0.0392837 | − | 0.351364i | ||||
\(649\) | − | 1.04951i | − | 0.0411969i | ||||||
\(650\) | −6.70141 | − | 32.8301i | −0.262851 | − | 1.28770i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 14.6969i | − | 0.575577i | ||||||
\(653\) | −25.8634 | −1.01211 | −0.506056 | − | 0.862501i | \(-0.668897\pi\) | ||||
−0.506056 | + | 0.862501i | \(0.668897\pi\) | |||||||
\(654\) | 8.79052 | + | 19.6562i | 0.343737 | + | 0.768619i | ||||
\(655\) | 8.52277 | − | 10.4382i | 0.333012 | − | 0.407855i | ||||
\(656\) | −6.70141 | −0.261646 | ||||||||
\(657\) | 23.9772 | − | 26.8073i | 0.935440 | − | 1.04585i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 34.2929i | 1.33586i | 0.744224 | + | 0.667930i | \(0.232819\pi\) | ||||
−0.744224 | + | 0.667930i | \(0.767181\pi\) | |||||||
\(660\) | −0.215838 | + | 0.797901i | −0.00840150 | + | 0.0310583i | ||||
\(661\) | − | 13.2528i | − | 0.515473i | −0.966215 | − | 0.257736i | \(-0.917023\pi\) | ||
0.966215 | − | 0.257736i | \(-0.0829766\pi\) | |||||||
\(662\) | −11.4317 | −0.444305 | ||||||||
\(663\) | −33.5071 | + | 14.9848i | −1.30131 | + | 0.581962i | ||||
\(664\) | − | 16.7169i | − | 0.648740i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 15.9545 | + | 14.2701i | 0.618222 | + | 0.552955i | ||||
\(667\) | − | 13.1011i | − | 0.507278i | ||||||
\(668\) | 14.6830i | 0.568102i | ||||||||
\(669\) | 4.52277 | + | 10.1132i | 0.174861 | + | 0.391000i | ||||
\(670\) | −9.22460 | − | 7.53185i | −0.356377 | − | 0.290981i | ||||
\(671\) | 0.739315 | 0.0285409 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 48.4514i | − | 1.86766i | −0.357713 | − | 0.933832i | \(-0.616443\pi\) | ||
0.357713 | − | 0.933832i | \(-0.383557\pi\) | |||||||
\(674\) | − | 17.1464i | − | 0.660456i | ||||||
\(675\) | −2.79622 | + | 25.8299i | −0.107627 | + | 0.994191i | ||||
\(676\) | 31.9089 | 1.22727 | ||||||||
\(677\) | − | 32.9090i | − | 1.26479i | −0.774644 | − | 0.632397i | \(-0.782071\pi\) | ||
0.774644 | − | 0.632397i | \(-0.217929\pi\) | |||||||
\(678\) | 4.61230 | + | 10.3134i | 0.177134 | + | 0.396084i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −5.47723 | − | 4.47214i | −0.210042 | − | 0.171499i | ||||
\(681\) | 16.4317 | − | 7.34847i | 0.629663 | − | 0.281594i | ||||
\(682\) | 0.0644158 | 0.00246661 | ||||||||
\(683\) | 2.95445 | 0.113049 | 0.0565245 | − | 0.998401i | \(-0.481998\pi\) | ||||
0.0565245 | + | 0.998401i | \(0.481998\pi\) | |||||||
\(684\) | −10.9441 | − | 9.78866i | −0.418456 | − | 0.374279i | ||||
\(685\) | −10.5744 | + | 12.9509i | −0.404027 | + | 0.494830i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.4317 | − | 5.11240i | 0.436146 | − | 0.195050i | ||||
\(688\) | 2.02265i | 0.0771127i | ||||||||
\(689\) | 33.5071 | 1.27652 | ||||||||
\(690\) | 24.2158 | + | 6.55057i | 0.921881 | + | 0.249376i | ||||
\(691\) | 3.46410i | 0.131781i | 0.997827 | + | 0.0658903i | \(0.0209887\pi\) | ||||
−0.997827 | + | 0.0658903i | \(0.979011\pi\) | |||||||
\(692\) | − | 11.5207i | − | 0.437952i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.52277 | −0.247601 | ||||||||
\(695\) | −13.0455 | − | 10.6516i | −0.494846 | − | 0.404040i | ||||
\(696\) | −3.19808 | + | 1.43023i | −0.121223 | + | 0.0542126i | ||||
\(697\) | − | 21.1917i | − | 0.802694i | ||||||
\(698\) | 32.5282i | 1.23121i | ||||||||
\(699\) | −2.82843 | − | 6.32456i | −0.106981 | − | 0.239217i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 7.03320i | − | 0.265640i | −0.991140 | − | 0.132820i | \(-0.957597\pi\) | ||
0.991140 | − | 0.132820i | \(-0.0424033\pi\) | |||||||
\(702\) | −33.1703 | − | 10.5959i | −1.25193 | − | 0.399915i | ||||
\(703\) | 34.9213 | 1.31708 | ||||||||
\(704\) | − | 0.213422i | − | 0.00804364i | ||||||
\(705\) | 7.84259 | − | 28.9921i | 0.295369 | − | 1.09191i | ||||
\(706\) | − | 13.2528i | − | 0.498774i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 3.47723 | + | 7.77531i | 0.130682 | + | 0.292214i | ||||
\(709\) | 10.4317 | 0.391770 | 0.195885 | − | 0.980627i | \(-0.437242\pi\) | ||||
0.195885 | + | 0.980627i | \(0.437242\pi\) | |||||||
\(710\) | 3.50333 | + | 2.86045i | 0.131477 | + | 0.107351i | ||||
\(711\) | −1.04555 | + | 1.16896i | −0.0392111 | + | 0.0438394i | ||||
\(712\) | 10.5744 | 0.396292 | ||||||||
\(713\) | − | 1.95498i | − | 0.0732146i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.47723 | + | 2.02265i | 0.0926430 | + | 0.0756427i | ||||
\(716\) | 14.9104i | 0.557226i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.49478i | 0.242383i | ||||||||
\(719\) | 47.2795 | 1.76323 | 0.881614 | − | 0.471970i | \(-0.156457\pi\) | ||||
0.881614 | + | 0.471970i | \(0.156457\pi\) | |||||||
\(720\) | −1.04456 | − | 6.62638i | −0.0389283 | − | 0.246951i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −4.95445 | −0.184386 | ||||||||
\(723\) | 6.30694 | − | 2.82055i | 0.234557 | − | 0.104897i | ||||
\(724\) | − | 3.16228i | − | 0.117525i | ||||||
\(725\) | 9.90890 | − | 2.02265i | 0.368007 | − | 0.0751192i | ||||
\(726\) | 7.74597 | + | 17.3205i | 0.287480 | + | 0.642824i | ||||
\(727\) | −23.6076 | −0.875556 | −0.437778 | − | 0.899083i | \(-0.644234\pi\) | ||||
−0.437778 | + | 0.899083i | \(0.644234\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.0000 | + | 15.6525i | 0.814815 | + | 0.579721i | ||||
\(730\) | 16.9545 | − | 20.7649i | 0.627512 | − | 0.768543i | ||||
\(731\) | −6.39617 | −0.236571 | ||||||||
\(732\) | −5.47723 | + | 2.44949i | −0.202444 | + | 0.0905357i | ||||
\(733\) | −36.3355 | −1.34208 | −0.671041 | − | 0.741420i | \(-0.734152\pi\) | ||||
−0.671041 | + | 0.741420i | \(0.734152\pi\) | |||||||
\(734\) | 8.11562 | 0.299553 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.47723 | −0.238754 | ||||||||
\(737\) | 1.13665 | 0.0418689 | ||||||||
\(738\) | 13.4028 | − | 14.9848i | 0.493365 | − | 0.551598i | ||||
\(739\) | −4.47723 | −0.164697 | −0.0823487 | − | 0.996604i | \(-0.526242\pi\) | ||||
−0.0823487 | + | 0.996604i | \(0.526242\pi\) | |||||||
\(740\) | 12.3583 | + | 10.0905i | 0.454299 | + | 0.370933i | ||||
\(741\) | −51.8596 | + | 23.1923i | −1.90511 | + | 0.851991i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.4317 | −0.712879 | −0.356440 | − | 0.934318i | \(-0.616009\pi\) | ||||
−0.356440 | + | 0.934318i | \(0.616009\pi\) | |||||||
\(744\) | −0.477226 | + | 0.213422i | −0.0174959 | + | 0.00782442i | ||||
\(745\) | −4.24264 | − | 3.46410i | −0.155438 | − | 0.126915i | ||||
\(746\) | − | 3.61845i | − | 0.132481i | ||||||
\(747\) | 37.3800 | + | 33.4337i | 1.36766 | + | 1.22328i | ||||
\(748\) | 0.674899 | 0.0246767 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.21584 | + | 19.3267i | −0.0443961 | + | 0.705712i | ||||
\(751\) | −32.0000 | −1.16770 | −0.583848 | − | 0.811863i | \(-0.698454\pi\) | ||||
−0.583848 | + | 0.811863i | \(0.698454\pi\) | |||||||
\(752\) | 7.75478i | 0.282788i | ||||||||
\(753\) | 11.7386 | + | 26.2483i | 0.427779 | + | 0.956543i | ||||
\(754\) | 13.5546i | 0.493629i | ||||||||
\(755\) | 2.82843 | − | 3.46410i | 0.102937 | − | 0.126072i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.2476i | 1.09937i | 0.835373 | + | 0.549683i | \(0.185252\pi\) | ||||
−0.835373 | + | 0.549683i | \(0.814748\pi\) | |||||||
\(758\) | −9.52277 | −0.345883 | ||||||||
\(759\) | −2.18574 | + | 0.977491i | −0.0793372 | + | 0.0354807i | ||||
\(760\) | −8.47723 | − | 6.92163i | −0.307501 | − | 0.251074i | ||||
\(761\) | −9.52984 | −0.345456 | −0.172728 | − | 0.984970i | \(-0.555258\pi\) | ||||
−0.172728 | + | 0.984970i | \(0.555258\pi\) | |||||||
\(762\) | 21.5507 | − | 9.63774i | 0.780698 | − | 0.349139i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 1.59580i | − | 0.0577341i | ||||||
\(765\) | 20.9545 | − | 3.30318i | 0.757610 | − | 0.119427i | ||||
\(766\) | − | 0.826579i | − | 0.0298655i | ||||||
\(767\) | 32.9545 | 1.18992 | ||||||||
\(768\) | 0.707107 | + | 1.58114i | 0.0255155 | + | 0.0570544i | ||||
\(769\) | − | 28.8412i | − | 1.04004i | −0.854154 | − | 0.520020i | \(-0.825924\pi\) | ||
0.854154 | − | 0.520020i | \(-0.174076\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 37.3861 | − | 16.7196i | 1.34643 | − | 0.602141i | ||||
\(772\) | 7.34847i | 0.264477i | ||||||||
\(773\) | 28.8412i | 1.03735i | 0.854973 | + | 0.518673i | \(0.173574\pi\) | ||||
−0.854973 | + | 0.518673i | \(0.826426\pi\) | |||||||
\(774\) | −4.52277 | − | 4.04529i | −0.162568 | − | 0.145405i | ||||
\(775\) | 1.47863 | − | 0.301824i | 0.0531139 | − | 0.0108418i | ||||
\(776\) | −3.50333 | −0.125762 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.34847i | 0.263455i | ||||||||
\(779\) | − | 32.7989i | − | 1.17514i | ||||||
\(780\) | −25.0540 | − | 6.77729i | −0.897076 | − | 0.242666i | ||||
\(781\) | −0.431677 | −0.0154466 | ||||||||
\(782\) | − | 20.4828i | − | 0.732463i | ||||||
\(783\) | 3.19808 | − | 10.0116i | 0.114290 | − | 0.357785i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.4317 | − | 15.2256i | 0.443706 | − | 0.543426i | ||||
\(786\) | −4.26139 | − | 9.52875i | −0.151999 | − | 0.339879i | ||||
\(787\) | −34.6804 | −1.23622 | −0.618112 | − | 0.786090i | \(-0.712102\pi\) | ||||
−0.618112 | + | 0.786090i | \(0.712102\pi\) | |||||||
\(788\) | 9.00000 | 0.320612 | ||||||||
\(789\) | −1.41421 | − | 3.16228i | −0.0503473 | − | 0.112580i | ||||
\(790\) | −0.739315 | + | 0.905472i | −0.0263036 | + | 0.0322152i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.477226 | + | 0.426844i | 0.0169575 | + | 0.0151672i | ||||
\(793\) | 23.2144i | 0.824366i | ||||||||
\(794\) | 30.3734 | 1.07791 | ||||||||
\(795\) | −18.6931 | − | 5.05662i | −0.662975 | − | 0.179340i | ||||
\(796\) | 22.4378i | 0.795286i | ||||||||
\(797\) | 28.9201i | 1.02440i | 0.858865 | + | 0.512201i | \(0.171170\pi\) | ||||
−0.858865 | + | 0.512201i | \(0.828830\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.5228 | −0.867553 | ||||||||
\(800\) | −1.00000 | − | 4.89898i | −0.0353553 | − | 0.173205i | ||||
\(801\) | −21.1488 | + | 23.6451i | −0.747256 | + | 0.835457i | ||||
\(802\) | − | 30.3494i | − | 1.07168i | ||||||
\(803\) | 2.55863i | 0.0902921i | ||||||||
\(804\) | −8.42087 | + | 3.76593i | −0.296981 | + | 0.132814i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.02265i | 0.0712447i | ||||||||
\(807\) | −20.4317 | − | 45.6866i | −0.719229 | − | 1.60825i | ||||
\(808\) | 11.3137 | 0.398015 | ||||||||
\(809\) | 40.1474i | 1.41151i | 0.708458 | + | 0.705753i | \(0.249391\pi\) | ||||
−0.708458 | + | 0.705753i | \(0.750609\pi\) | |||||||
\(810\) | 16.9061 | + | 10.9171i | 0.594021 | + | 0.383586i | ||||
\(811\) | − | 6.70527i | − | 0.235454i | −0.993046 | − | 0.117727i | \(-0.962439\pi\) | ||
0.993046 | − | 0.117727i | \(-0.0375608\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.0000 | + | 4.47214i | −0.350715 | + | 0.156845i | ||||
\(814\) | −1.52277 | −0.0533732 | ||||||||
\(815\) | 25.4558 | + | 20.7846i | 0.891679 | + | 0.728053i | ||||
\(816\) | −5.00000 | + | 2.23607i | −0.175035 | + | 0.0782780i | ||||
\(817\) | −9.89949 | −0.346339 | ||||||||
\(818\) | 22.4378i | 0.784518i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.47723 | − | 11.6072i | 0.330959 | − | 0.405340i | ||||
\(821\) | 50.9009i | 1.77645i | 0.459406 | + | 0.888226i | \(0.348062\pi\) | ||||
−0.459406 | + | 0.888226i | \(0.651938\pi\) | |||||||
\(822\) | 5.28720 | + | 11.8225i | 0.184412 | + | 0.412358i | ||||
\(823\) | 32.5855i | 1.13586i | 0.823077 | + | 0.567929i | \(0.192255\pi\) | ||||
−0.823077 | + | 0.567929i | \(0.807745\pi\) | |||||||
\(824\) | 10.5744 | 0.368376 | ||||||||
\(825\) | −1.07676 | − | 1.50225i | −0.0374881 | − | 0.0523015i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.9089 | 1.38777 | 0.693884 | − | 0.720087i | \(-0.255898\pi\) | ||||
0.693884 | + | 0.720087i | \(0.255898\pi\) | |||||||
\(828\) | 12.9545 | − | 14.4835i | 0.450198 | − | 0.503337i | ||||
\(829\) | 18.8296i | 0.653980i | 0.945028 | + | 0.326990i | \(0.106034\pi\) | ||||
−0.945028 | + | 0.326990i | \(0.893966\pi\) | |||||||
\(830\) | 28.9545 | + | 23.6412i | 1.00502 | + | 0.820598i | ||||
\(831\) | 15.4919 | − | 6.92820i | 0.537409 | − | 0.240337i | ||||
\(832\) | 6.70141 | 0.232330 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −11.9089 | + | 5.32582i | −0.412372 | + | 0.184418i | ||||
\(835\) | −25.4317 | − | 20.7649i | −0.880099 | − | 0.718598i | ||||
\(836\) | 1.04456 | 0.0361267 | ||||||||
\(837\) | 0.477226 | − | 1.49395i | 0.0164953 | − | 0.0516385i | ||||
\(838\) | −16.6009 | −0.573469 | ||||||||
\(839\) | −37.3156 | −1.28828 | −0.644139 | − | 0.764908i | \(-0.722784\pi\) | ||||
−0.644139 | + | 0.764908i | \(0.722784\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.9089 | 0.858928 | ||||||||
\(842\) | −2.95445 | −0.101817 | ||||||||
\(843\) | 18.3526 | − | 8.20752i | 0.632096 | − | 0.282682i | ||||
\(844\) | 13.5228 | 0.465473 | ||||||||
\(845\) | −45.1260 | + | 55.2678i | −1.55238 | + | 1.90127i | ||||
\(846\) | −17.3402 | − | 15.5096i | −0.596169 | − | 0.533230i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.00000 | 0.171701 | ||||||||
\(849\) | 17.4772 | + | 39.0803i | 0.599817 | + | 1.34123i | ||||
\(850\) | 15.4919 | − | 3.16228i | 0.531369 | − | 0.108465i | ||||
\(851\) | 46.2153i | 1.58424i | ||||||||
\(852\) | 3.19808 | − | 1.43023i | 0.109565 | − | 0.0489988i | ||||
\(853\) | 53.9165 | 1.84607 | 0.923033 | − | 0.384720i | \(-0.125702\pi\) | ||||
0.923033 | + | 0.384720i | \(0.125702\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 32.4317 | − | 5.11240i | 1.10914 | − | 0.174840i | ||||
\(856\) | 5.47723 | 0.187208 | ||||||||
\(857\) | − | 40.3619i | − | 1.37874i | −0.724411 | − | 0.689369i | \(-0.757888\pi\) | ||
0.724411 | − | 0.689369i | \(-0.242112\pi\) | |||||||
\(858\) | 2.26139 | − | 1.01132i | 0.0772025 | − | 0.0345260i | ||||
\(859\) | − | 17.9242i | − | 0.611564i | −0.952102 | − | 0.305782i | \(-0.901082\pi\) | ||
0.952102 | − | 0.305782i | \(-0.0989179\pi\) | |||||||
\(860\) | −3.50333 | − | 2.86045i | −0.119462 | − | 0.0975407i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 37.0576i | − | 1.26219i | ||||||
\(863\) | −15.5228 | −0.528401 | −0.264201 | − | 0.964468i | \(-0.585108\pi\) | ||||
−0.264201 | + | 0.964468i | \(0.585108\pi\) | |||||||
\(864\) | −4.94975 | − | 1.58114i | −0.168394 | − | 0.0537914i | ||||
\(865\) | 19.9545 | + | 16.2927i | 0.678472 | + | 0.553970i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.94975 | + | 11.0680i | 0.168102 | + | 0.375888i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 0.111571i | − | 0.00378480i | ||||||
\(870\) | 2.04555 | − | 7.56189i | 0.0693506 | − | 0.256372i | ||||
\(871\) | 35.6905i | 1.20933i | ||||||||
\(872\) | 12.4317 | 0.420990 | ||||||||
\(873\) | 7.00665 | − | 7.83368i | 0.237139 | − | 0.265130i | ||||
\(874\) | − | 31.7017i | − | 1.07232i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.47723 | − | 18.9557i | −0.286419 | − | 0.640452i | ||||
\(877\) | 42.2816i | 1.42775i | 0.700274 | + | 0.713874i | \(0.253061\pi\) | ||||
−0.700274 | + | 0.713874i | \(0.746939\pi\) | |||||||
\(878\) | 22.7396i | 0.767424i | ||||||||
\(879\) | 7.26139 | − | 3.24739i | 0.244921 | − | 0.109532i | ||||
\(880\) | 0.369657 | + | 0.301824i | 0.0124611 | + | 0.0101745i | ||||
\(881\) | 26.5004 | 0.892821 | 0.446411 | − | 0.894828i | \(-0.352702\pi\) | ||||
0.446411 | + | 0.894828i | \(0.352702\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.2823i | 0.985428i | 0.870191 | + | 0.492714i | \(0.163995\pi\) | ||||
−0.870191 | + | 0.492714i | \(0.836005\pi\) | |||||||
\(884\) | 21.1917i | 0.712755i | ||||||||
\(885\) | −18.3848 | − | 4.97322i | −0.617997 | − | 0.167173i | ||||
\(886\) | −36.9545 | −1.24151 | ||||||||
\(887\) | 3.46410i | 0.116313i | 0.998307 | + | 0.0581566i | \(0.0185223\pi\) | ||||
−0.998307 | + | 0.0581566i | \(0.981478\pi\) | |||||||
\(888\) | 11.2815 | − | 5.04524i | 0.378582 | − | 0.169307i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −14.9545 | + | 18.3154i | −0.501274 | + | 0.613933i | ||||
\(891\) | −1.90890 | + | 0.213422i | −0.0639506 | + | 0.00714990i | ||||
\(892\) | 6.39617 | 0.214160 | ||||||||
\(893\) | −37.9545 | −1.27010 | ||||||||
\(894\) | −3.87298 | + | 1.73205i | −0.129532 | + | 0.0579284i | ||||
\(895\) | −25.8255 | − | 21.0864i | −0.863251 | − | 0.704842i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −30.6931 | − | 68.6318i | −1.02481 | − | 2.29155i | ||||
\(898\) | 3.51660i | 0.117350i | ||||||||
\(899\) | −0.610483 | −0.0203608 | ||||||||
\(900\) | 12.9545 | + | 7.56189i | 0.431815 | + | 0.252063i | ||||
\(901\) | 15.8114i | 0.526754i | ||||||||
\(902\) | 1.43023i | 0.0476213i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.52277 | 0.216944 | ||||||||
\(905\) | 5.47723 | + | 4.47214i | 0.182069 | + | 0.148659i | ||||
\(906\) | −1.41421 | − | 3.16228i | −0.0469841 | − | 0.105060i | ||||
\(907\) | − | 9.79796i | − | 0.325336i | −0.986681 | − | 0.162668i | \(-0.947990\pi\) | ||
0.986681 | − | 0.162668i | \(-0.0520099\pi\) | |||||||
\(908\) | − | 10.3923i | − | 0.344881i | ||||||
\(909\) | −22.6274 | + | 25.2982i | −0.750504 | + | 0.839089i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.1238i | 0.501073i | 0.968107 | + | 0.250537i | \(0.0806071\pi\) | ||||
−0.968107 | + | 0.250537i | \(0.919393\pi\) | |||||||
\(912\) | −7.73861 | + | 3.46081i | −0.256251 | + | 0.114599i | ||||
\(913\) | −3.56774 | −0.118075 | ||||||||
\(914\) | − | 37.9113i | − | 1.25399i | ||||||
\(915\) | 3.50333 | − | 12.9509i | 0.115816 | − | 0.428145i | ||||
\(916\) | − | 7.23003i | − | 0.238887i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.00000 | − | 15.6525i | 0.165025 | − | 0.516609i | ||||
\(919\) | −32.4317 | −1.06982 | −0.534911 | − | 0.844908i | \(-0.679655\pi\) | ||||
−0.534911 | + | 0.844908i | \(0.679655\pi\) | |||||||
\(920\) | 9.16018 | − | 11.2189i | 0.302002 | − | 0.369876i | ||||
\(921\) | 2.47723 | + | 5.53924i | 0.0816274 | + | 0.182524i | ||||
\(922\) | −16.2957 | −0.536669 | ||||||||
\(923\) | − | 13.5546i | − | 0.446155i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −34.9545 | + | 7.13505i | −1.14930 | + | 0.234599i | ||||
\(926\) | − | 17.6751i | − | 0.580841i | ||||||
\(927\) | −21.1488 | + | 23.6451i | −0.694617 | + | 0.776606i | ||||
\(928\) | 2.02265i | 0.0663966i | ||||||||
\(929\) | 23.6720 | 0.776652 | 0.388326 | − | 0.921522i | \(-0.373053\pi\) | ||||
0.388326 | + | 0.921522i | \(0.373053\pi\) | |||||||
\(930\) | 0.305242 | − | 1.12840i | 0.0100093 | − | 0.0370018i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −4.00000 | −0.131024 | ||||||||
\(933\) | −20.4317 | − | 45.6866i | −0.668903 | − | 1.49571i | ||||
\(934\) | − | 34.3392i | − | 1.12361i | ||||||
\(935\) | −0.954451 | + | 1.16896i | −0.0312139 | + | 0.0382291i | ||||
\(936\) | −13.4028 | + | 14.9848i | −0.438085 | + | 0.489794i | ||||
\(937\) | 22.6918 | 0.741310 | 0.370655 | − | 0.928771i | \(-0.379133\pi\) | ||||
0.370655 | + | 0.928771i | \(0.379133\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.4317 | − | 36.7423i | −0.536228 | − | 1.19904i | ||||
\(940\) | −13.4317 | − | 10.9669i | −0.438093 | − | 0.357701i | ||||
\(941\) | −4.98196 | −0.162407 | −0.0812036 | − | 0.996698i | \(-0.525876\pi\) | ||||
−0.0812036 | + | 0.996698i | \(0.525876\pi\) | |||||||
\(942\) | −6.21584 | − | 13.8990i | −0.202523 | − | 0.452855i | ||||
\(943\) | 43.4065 | 1.41351 | ||||||||
\(944\) | 4.91754 | 0.160052 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.431677 | 0.0140350 | ||||||||
\(947\) | −32.8634 | −1.06792 | −0.533958 | − | 0.845511i | \(-0.679296\pi\) | ||||
−0.533958 | + | 0.845511i | \(0.679296\pi\) | |||||||
\(948\) | 0.369657 | + | 0.826579i | 0.0120059 | + | 0.0268460i | ||||
\(949\) | −80.3406 | −2.60797 | ||||||||
\(950\) | 23.9772 | − | 4.89433i | 0.777924 | − | 0.158793i | ||||
\(951\) | 23.9772 | + | 53.6147i | 0.777514 | + | 1.73858i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.0455 | 0.811305 | 0.405652 | − | 0.914027i | \(-0.367044\pi\) | ||||
0.405652 | + | 0.914027i | \(0.367044\pi\) | |||||||
\(954\) | −10.0000 | + | 11.1803i | −0.323762 | + | 0.361977i | ||||
\(955\) | 2.76401 | + | 2.25681i | 0.0894413 | + | 0.0730285i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.305242 | + | 0.682541i | 0.00986706 | + | 0.0220634i | ||||
\(958\) | −11.3781 | −0.367611 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.73861 | − | 1.01132i | −0.120663 | − | 0.0326403i | ||||
\(961\) | 30.9089 | 0.997061 | ||||||||
\(962\) | − | 47.8149i | − | 1.54161i | ||||||
\(963\) | −10.9545 | + | 12.2474i | −0.353002 | + | 0.394669i | ||||
\(964\) | − | 3.98886i | − | 0.128472i | ||||||
\(965\) | −12.7279 | − | 10.3923i | −0.409726 | − | 0.334540i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46.4287i | 1.49305i | 0.665359 | + | 0.746524i | \(0.268279\pi\) | ||||
−0.665359 | + | 0.746524i | \(0.731721\pi\) | |||||||
\(968\) | 10.9545 | 0.352089 | ||||||||
\(969\) | −10.9441 | − | 24.4716i | −0.351574 | − | 0.786142i | ||||
\(970\) | 4.95445 | − | 6.06794i | 0.159078 | − | 0.194830i | ||||
\(971\) | 0.980140 | 0.0314542 | 0.0157271 | − | 0.999876i | \(-0.494994\pi\) | ||||
0.0157271 | + | 0.999876i | \(0.494994\pi\) | |||||||
\(972\) | 13.4350 | − | 7.90569i | 0.430929 | − | 0.253575i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 36.6308i | 1.17373i | ||||||||
\(975\) | 47.1703 | − | 33.8102i | 1.51066 | − | 1.08279i | ||||
\(976\) | 3.46410i | 0.110883i | ||||||||
\(977\) | −39.9089 | −1.27680 | −0.638399 | − | 0.769705i | \(-0.720403\pi\) | ||||
−0.638399 | + | 0.769705i | \(0.720403\pi\) | |||||||
\(978\) | 23.2379 | − | 10.3923i | 0.743066 | − | 0.332309i | ||||
\(979\) | − | 2.25681i | − | 0.0721278i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −24.8634 | + | 27.7981i | −0.793826 | + | 0.887524i | ||||
\(982\) | 4.04529i | 0.129090i | ||||||||
\(983\) | 33.8144i | 1.07851i | 0.842142 | + | 0.539257i | \(0.181295\pi\) | ||||
−0.842142 | + | 0.539257i | \(0.818705\pi\) | |||||||
\(984\) | −4.73861 | − | 10.5959i | −0.151061 | − | 0.337784i | ||||
\(985\) | −12.7279 | + | 15.5885i | −0.405545 | + | 0.496690i | ||||
\(986\) | −6.39617 | −0.203696 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 32.7989i | 1.04347i | ||||||||
\(989\) | − | 13.1011i | − | 0.416592i | ||||||
\(990\) | −1.41421 | + | 0.222931i | −0.0449467 | + | 0.00708521i | ||||
\(991\) | 21.4772 | 0.682247 | 0.341123 | − | 0.940019i | \(-0.389193\pi\) | ||||
0.341123 | + | 0.940019i | \(0.389193\pi\) | |||||||
\(992\) | 0.301824i | 0.00958292i | ||||||||
\(993\) | −8.08342 | − | 18.0751i | −0.256519 | − | 0.573595i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −38.8634 | − | 31.7318i | −1.23205 | − | 1.00597i | ||||
\(996\) | 26.4317 | − | 11.8206i | 0.837520 | − | 0.374550i | ||||
\(997\) | −15.4919 | −0.490634 | −0.245317 | − | 0.969443i | \(-0.578892\pi\) | ||||
−0.245317 | + | 0.969443i | \(0.578892\pi\) | |||||||
\(998\) | −41.9089 | −1.32660 | ||||||||
\(999\) | −11.2815 | + | 35.3167i | −0.356931 | + | 1.11737i |
(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 | 1470.2.d.f.1469.8 | 8 | ||
3.2 | odd | 2 | 1470.2.d.e.1469.5 | 8 | |||
5.4 | even | 2 | 1470.2.d.e.1469.1 | 8 | |||
7.2 | even | 3 | 210.2.t.e.59.1 | ✓ | 8 | ||
7.3 | odd | 6 | 210.2.t.e.89.2 | yes | 8 | ||
7.6 | odd | 2 | inner | 1470.2.d.f.1469.1 | 8 | ||
15.14 | odd | 2 | inner | 1470.2.d.f.1469.4 | 8 | ||
21.2 | odd | 6 | 210.2.t.f.59.3 | yes | 8 | ||
21.17 | even | 6 | 210.2.t.f.89.4 | yes | 8 | ||
21.20 | even | 2 | 1470.2.d.e.1469.4 | 8 | |||
35.2 | odd | 12 | 1050.2.s.i.101.6 | 16 | |||
35.3 | even | 12 | 1050.2.s.i.551.5 | 16 | |||
35.9 | even | 6 | 210.2.t.f.59.4 | yes | 8 | ||
35.17 | even | 12 | 1050.2.s.i.551.4 | 16 | |||
35.23 | odd | 12 | 1050.2.s.i.101.3 | 16 | |||
35.24 | odd | 6 | 210.2.t.f.89.3 | yes | 8 | ||
35.34 | odd | 2 | 1470.2.d.e.1469.8 | 8 | |||
105.2 | even | 12 | 1050.2.s.i.101.4 | 16 | |||
105.17 | odd | 12 | 1050.2.s.i.551.6 | 16 | |||
105.23 | even | 12 | 1050.2.s.i.101.5 | 16 | |||
105.38 | odd | 12 | 1050.2.s.i.551.3 | 16 | |||
105.44 | odd | 6 | 210.2.t.e.59.2 | yes | 8 | ||
105.59 | even | 6 | 210.2.t.e.89.1 | yes | 8 | ||
105.104 | even | 2 | inner | 1470.2.d.f.1469.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.t.e.59.1 | ✓ | 8 | 7.2 | even | 3 | ||
210.2.t.e.59.2 | yes | 8 | 105.44 | odd | 6 | ||
210.2.t.e.89.1 | yes | 8 | 105.59 | even | 6 | ||
210.2.t.e.89.2 | yes | 8 | 7.3 | odd | 6 | ||
210.2.t.f.59.3 | yes | 8 | 21.2 | odd | 6 | ||
210.2.t.f.59.4 | yes | 8 | 35.9 | even | 6 | ||
210.2.t.f.89.3 | yes | 8 | 35.24 | odd | 6 | ||
210.2.t.f.89.4 | yes | 8 | 21.17 | even | 6 | ||
1050.2.s.i.101.3 | 16 | 35.23 | odd | 12 | |||
1050.2.s.i.101.4 | 16 | 105.2 | even | 12 | |||
1050.2.s.i.101.5 | 16 | 105.23 | even | 12 | |||
1050.2.s.i.101.6 | 16 | 35.2 | odd | 12 | |||
1050.2.s.i.551.3 | 16 | 105.38 | odd | 12 | |||
1050.2.s.i.551.4 | 16 | 35.17 | even | 12 | |||
1050.2.s.i.551.5 | 16 | 35.3 | even | 12 | |||
1050.2.s.i.551.6 | 16 | 105.17 | odd | 12 | |||
1470.2.d.e.1469.1 | 8 | 5.4 | even | 2 | |||
1470.2.d.e.1469.4 | 8 | 21.20 | even | 2 | |||
1470.2.d.e.1469.5 | 8 | 3.2 | odd | 2 | |||
1470.2.d.e.1469.8 | 8 | 35.34 | odd | 2 | |||
1470.2.d.f.1469.1 | 8 | 7.6 | odd | 2 | inner | ||
1470.2.d.f.1469.4 | 8 | 15.14 | odd | 2 | inner | ||
1470.2.d.f.1469.5 | 8 | 105.104 | even | 2 | inner | ||
1470.2.d.f.1469.8 | 8 | 1.1 | even | 1 | trivial |