Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(289,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.bo (of order \(9\), degree \(6\), not 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: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 228) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 289.1 | ||
Root | \(-0.173648 - 0.984808i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.289 |
Dual form | 912.2.bo.e.385.1 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{1}{9}\right)\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.173648 | − | 0.984808i | −0.100256 | − | 0.568579i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.93969 | − | 1.62760i | 0.867457 | − | 0.727883i | −0.0961041 | − | 0.995371i | \(-0.530638\pi\) |
0.963561 | + | 0.267489i | \(0.0861937\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.61334 | + | 2.79439i | −0.609786 | + | 1.05618i | 0.381490 | + | 0.924373i | \(0.375411\pi\) |
−0.991275 | + | 0.131806i | \(0.957922\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.939693 | + | 0.342020i | −0.313231 | + | 0.114007i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.55303 | + | 2.68993i | 0.468257 | + | 0.811045i | 0.999342 | − | 0.0362735i | \(-0.0115487\pi\) |
−0.531085 | + | 0.847319i | \(0.678215\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.05303 | + | 5.97205i | −0.292059 | + | 1.65635i | 0.386862 | + | 0.922137i | \(0.373559\pi\) |
−0.678921 | + | 0.734211i | \(0.737552\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.93969 | − | 1.62760i | −0.500826 | − | 0.420243i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.58512 | + | 2.03282i | 1.35459 | + | 0.493031i | 0.914378 | − | 0.404862i | \(-0.132681\pi\) |
0.440213 | + | 0.897893i | \(0.354903\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.34002 | + | 0.405223i | −0.995669 | + | 0.0929645i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.03209 | + | 1.10359i | 0.661656 | + | 0.240823i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.14543 | + | 4.31753i | 1.07290 | + | 0.900267i | 0.995312 | − | 0.0967189i | \(-0.0308348\pi\) |
0.0775845 | + | 0.996986i | \(0.475279\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.245100 | − | 1.39003i | 0.0490200 | − | 0.278006i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.500000 | + | 0.866025i | 0.0962250 | + | 0.166667i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.69846 | + | 2.43804i | −1.24387 | + | 0.452733i | −0.878327 | − | 0.478060i | \(-0.841340\pi\) |
−0.365546 | + | 0.930793i | \(0.619118\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.81908 | − | 6.61484i | 0.685927 | − | 1.18806i | −0.287218 | − | 0.957865i | \(-0.592730\pi\) |
0.973145 | − | 0.230195i | \(-0.0739363\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.37939 | − | 1.99654i | 0.414198 | − | 0.347553i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.41875 | + | 8.04612i | 0.239812 | + | 1.36004i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.10607 | 0.346235 | 0.173118 | − | 0.984901i | \(-0.444616\pi\) | ||||
0.173118 | + | 0.984901i | \(0.444616\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.06418 | 0.971046 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.22281 | − | 6.93491i | −0.190971 | − | 1.08305i | −0.918041 | − | 0.396487i | \(-0.870229\pi\) |
0.727069 | − | 0.686564i | \(-0.240882\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.17752 | − | 6.02265i | 1.09456 | − | 0.918446i | 0.0975139 | − | 0.995234i | \(-0.468911\pi\) |
0.997047 | + | 0.0767882i | \(0.0244665\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.26604 | + | 2.19285i | −0.188731 | + | 0.326891i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.37211 | + | 1.59132i | −0.637738 | + | 0.232118i | −0.640596 | − | 0.767878i | \(-0.721313\pi\) |
0.00285780 | + | 0.999996i | \(0.499090\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.70574 | − | 2.95442i | −0.243677 | − | 0.422060i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.03209 | − | 5.85327i | 0.144521 | − | 0.819621i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.86824 | − | 4.08494i | −0.668704 | − | 0.561110i | 0.243977 | − | 0.969781i | \(-0.421548\pi\) |
−0.912682 | + | 0.408671i | \(0.865992\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.39053 | + | 2.68993i | 0.996539 | + | 0.362710i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.15270 | + | 4.20372i | 0.152679 | + | 0.556797i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.252374 | − | 0.0918566i | −0.0328563 | − | 0.0119587i | 0.325540 | − | 0.945528i | \(-0.394454\pi\) |
−0.358396 | + | 0.933570i | \(0.616676\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.21688 | + | 1.02108i | 0.155806 | + | 0.130737i | 0.717358 | − | 0.696705i | \(-0.245351\pi\) |
−0.561552 | + | 0.827441i | \(0.689796\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.560307 | − | 3.17766i | 0.0705921 | − | 0.400348i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.67752 | + | 13.2979i | 0.952279 | + | 1.64940i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.22668 | + | 0.446476i | −0.149863 | + | 0.0545457i | −0.415863 | − | 0.909427i | \(-0.636520\pi\) |
0.266000 | + | 0.963973i | \(0.414298\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.35844 | − | 5.81699i | 0.404309 | − | 0.700283i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.34002 | − | 5.31991i | 0.752422 | − | 0.631357i | −0.183720 | − | 0.982979i | \(-0.558814\pi\) |
0.936142 | + | 0.351621i | \(0.114370\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.159978 | + | 0.907278i | 0.0187240 | + | 0.106189i | 0.992737 | − | 0.120301i | \(-0.0383860\pi\) |
−0.974013 | + | 0.226490i | \(0.927275\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.41147 | −0.162983 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.0223 | −1.14215 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.09492 | + | 11.8809i | 0.235697 | + | 1.33671i | 0.841140 | + | 0.540817i | \(0.181885\pi\) |
−0.605443 | + | 0.795888i | \(0.707004\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.766044 | − | 0.642788i | 0.0851160 | − | 0.0714208i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.0432332 | − | 0.0748822i | 0.00474546 | − | 0.00821939i | −0.863643 | − | 0.504104i | \(-0.831823\pi\) |
0.868388 | + | 0.495885i | \(0.165156\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.1420 | − | 5.14728i | 1.53392 | − | 0.558301i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.56418 | + | 6.17334i | 0.382120 | + | 0.661851i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.22803 | + | 6.96448i | −0.130170 | + | 0.738233i | 0.847931 | + | 0.530106i | \(0.177848\pi\) |
−0.978102 | + | 0.208127i | \(0.933263\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.9893 | − | 12.5775i | −1.57131 | − | 1.31848i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.17752 | − | 2.61240i | −0.744274 | − | 0.270894i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.75877 | + | 7.84981i | −0.796033 | + | 0.805373i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.12701 | − | 1.13814i | −0.317500 | − | 0.115561i | 0.178354 | − | 0.983966i | \(-0.442923\pi\) |
−0.495854 | + | 0.868406i | \(0.665145\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.37939 | − | 1.99654i | −0.239137 | − | 0.200660i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.86824 | + | 10.5953i | −0.185897 | + | 1.05427i | 0.738901 | + | 0.673814i | \(0.235345\pi\) |
−0.924798 | + | 0.380459i | \(0.875766\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.96451 | + | 5.13468i | 0.292102 | + | 0.505935i | 0.974306 | − | 0.225226i | \(-0.0723121\pi\) |
−0.682205 | + | 0.731161i | \(0.738979\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.67752 | − | 2.79439i | 0.749249 | − | 0.272704i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.29086 | − | 2.23583i | 0.124792 | − | 0.216146i | −0.796860 | − | 0.604165i | \(-0.793507\pi\) |
0.921652 | + | 0.388018i | \(0.126840\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.66250 | − | 3.07321i | 0.350804 | − | 0.294360i | −0.450309 | − | 0.892873i | \(-0.648686\pi\) |
0.801113 | + | 0.598513i | \(0.204242\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.365715 | − | 2.07407i | −0.0347121 | − | 0.196862i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.6655 | 1.56776 | 0.783879 | − | 0.620914i | \(-0.213238\pi\) | ||||
0.783879 | + | 0.620914i | \(0.213238\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 17.0077 | 1.58598 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.05303 | − | 5.97205i | −0.0973530 | − | 0.552116i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.6912 | + | 12.3274i | −1.34674 | + | 1.13005i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.676174 | − | 1.17117i | 0.0614704 | − | 0.106470i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.61721 | + | 2.40847i | −0.596654 | + | 0.217164i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.54323 | + | 7.86911i | 0.406359 | + | 0.703835i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.906260 | + | 5.13965i | −0.0804175 | + | 0.456070i | 0.917834 | + | 0.396964i | \(0.129936\pi\) |
−0.998252 | + | 0.0591064i | \(0.981175\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.17752 | − | 6.02265i | −0.631945 | − | 0.530265i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.13563 | − | 2.96113i | −0.710813 | − | 0.258715i | −0.0387926 | − | 0.999247i | \(-0.512351\pi\) |
−0.672021 | + | 0.740532i | \(0.734573\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.86959 | − | 12.7815i | 0.508958 | − | 1.10829i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.37939 | + | 0.866025i | 0.204785 | + | 0.0745356i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.4684 | − | 8.78401i | −0.894374 | − | 0.750469i | 0.0747087 | − | 0.997205i | \(-0.476197\pi\) |
−0.969083 | + | 0.246737i | \(0.920642\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.37551 | − | 13.4722i | 0.201489 | − | 1.14270i | −0.701382 | − | 0.712786i | \(-0.747433\pi\) |
0.902870 | − | 0.429913i | \(-0.141456\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.32635 | + | 4.02936i | 0.195914 | + | 0.339333i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −17.6998 | + | 6.44220i | −1.48013 | + | 0.538724i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.02481 | + | 15.6314i | −0.749470 | + | 1.29812i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.61334 | + | 2.19285i | −0.215545 | + | 0.180863i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.12314 | + | 23.3835i | 0.337781 | + | 1.91565i | 0.397838 | + | 0.917456i | \(0.369761\pi\) |
−0.0600574 | + | 0.998195i | \(0.519128\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.33544 | −0.678328 | −0.339164 | − | 0.940727i | \(-0.610144\pi\) | ||||
−0.339164 | + | 0.940727i | \(0.610144\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.94356 | −0.480509 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.35844 | − | 19.0467i | −0.269756 | − | 1.52986i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.6197 | − | 13.9456i | 1.32640 | − | 1.11298i | 0.341495 | − | 0.939884i | \(-0.389067\pi\) |
0.984905 | − | 0.173098i | \(-0.0553776\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.17752 | + | 5.50362i | −0.251994 | + | 0.436466i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.3662 | + | 7.41268i | −1.60508 | + | 0.584201i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.4927 | − | 19.9060i | −0.900180 | − | 1.55916i | −0.827260 | − | 0.561819i | \(-0.810102\pi\) |
−0.0729198 | − | 0.997338i | \(-0.523232\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.36571 | − | 7.74535i | 0.106321 | − | 0.602975i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.85710 | + | 4.91469i | 0.453236 | + | 0.380310i | 0.840635 | − | 0.541602i | \(-0.182182\pi\) |
−0.387399 | + | 0.921912i | \(0.626626\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −22.3405 | − | 8.13127i | −1.71850 | − | 0.625483i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.93969 | − | 1.86516i | 0.301276 | − | 0.142632i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.0360 | − | 4.01676i | −0.839048 | − | 0.305389i | −0.113481 | − | 0.993540i | \(-0.536200\pi\) |
−0.725567 | + | 0.688151i | \(0.758422\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.48886 | + | 2.92750i | 0.263733 | + | 0.221298i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.0466368 | + | 0.264490i | −0.00350544 | + | 0.0198803i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.09879 | − | 3.63522i | −0.156871 | − | 0.271709i | 0.776868 | − | 0.629664i | \(-0.216807\pi\) |
−0.933739 | + | 0.357955i | \(0.883474\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.5842 | + | 4.21632i | −0.861050 | + | 0.313397i | −0.734537 | − | 0.678568i | \(-0.762601\pi\) |
−0.126513 | + | 0.991965i | \(0.540379\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.794263 | − | 1.37570i | 0.0587136 | − | 0.101695i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.08512 | − | 3.42782i | 0.300344 | − | 0.252019i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.20574 | + | 18.1806i | 0.234427 | + | 1.32950i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.22668 | −0.234707 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.2044 | 0.738364 | 0.369182 | − | 0.929357i | \(-0.379638\pi\) | ||||
0.369182 | + | 0.929357i | \(0.379638\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.76945 | − | 21.3776i | −0.271331 | − | 1.53879i | −0.750381 | − | 0.661006i | \(-0.770130\pi\) |
0.479050 | − | 0.877788i | \(-0.340981\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 11.7626 | − | 9.87003i | 0.842340 | − | 0.706807i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.34255 | − | 14.4497i | 0.594382 | − | 1.02950i | −0.399252 | − | 0.916841i | \(-0.630730\pi\) |
0.993634 | − | 0.112658i | \(-0.0359366\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.31180 | + | 0.841428i | −0.163879 | + | 0.0596472i | −0.422657 | − | 0.906290i | \(-0.638903\pi\) |
0.258778 | + | 0.965937i | \(0.416680\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.652704 | + | 1.13052i | 0.0460382 | + | 0.0797404i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.99407 | − | 22.6515i | 0.280329 | − | 1.58982i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.6591 | − | 11.4613i | −0.953993 | − | 0.800495i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.31180 | − | 2.29731i | −0.438701 | − | 0.159674i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.83022 | − | 11.0450i | −0.541628 | − | 0.764002i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.15745 | − | 0.421278i | −0.0796822 | − | 0.0290020i | 0.301871 | − | 0.953349i | \(-0.402389\pi\) |
−0.381554 | + | 0.924347i | \(0.624611\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.34002 | − | 5.31991i | −0.434411 | − | 0.364514i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.11974 | − | 23.3642i | 0.280964 | − | 1.59342i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.3229 | + | 21.3440i | 0.836536 | + | 1.44892i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.865715 | − | 0.315094i | 0.0584996 | − | 0.0212921i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.0214 | + | 31.2140i | −1.21225 | + | 2.09968i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.03983 | + | 4.22892i | −0.337492 | + | 0.283189i | −0.795744 | − | 0.605633i | \(-0.792920\pi\) |
0.458252 | + | 0.888822i | \(0.348476\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.245100 | + | 1.39003i | 0.0163400 | + | 0.0926687i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.72967 | −0.645781 | −0.322891 | − | 0.946436i | \(-0.604655\pi\) | ||||
−0.322891 | + | 0.946436i | \(0.604655\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.86753 | −0.652064 | −0.326032 | − | 0.945359i | \(-0.605712\pi\) | ||||
−0.326032 | + | 0.945359i | \(0.605712\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.74035 | + | 9.87003i | 0.114507 | + | 0.649400i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.7121 | − | 14.0231i | 1.09485 | − | 0.918687i | 0.0977803 | − | 0.995208i | \(-0.468826\pi\) |
0.997068 | + | 0.0765212i | \(0.0243813\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.89053 | + | 10.2027i | −0.384256 | + | 0.665551i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.3366 | − | 4.12619i | 0.736393 | − | 0.268025i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.6557 | + | 18.4562i | 0.689260 | + | 1.19383i | 0.972078 | + | 0.234659i | \(0.0753974\pi\) |
−0.282818 | + | 0.959174i | \(0.591269\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.71688 | − | 15.4082i | 0.175010 | − | 0.992529i | −0.763123 | − | 0.646253i | \(-0.776335\pi\) |
0.938133 | − | 0.346276i | \(-0.112554\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.766044 | − | 0.642788i | −0.0491418 | − | 0.0412348i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.11721 | − | 2.95442i | −0.518590 | − | 0.188751i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.15018 | − | 26.3455i | 0.136813 | − | 1.67633i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.0812519 | − | 0.0295733i | −0.00514913 | − | 0.00187413i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.75356 | + | 6.50601i | 0.489400 | + | 0.410655i | 0.853811 | − | 0.520583i | \(-0.174285\pi\) |
−0.364411 | + | 0.931238i | \(0.618730\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.62284 | + | 20.5461i | −0.227766 | + | 1.29172i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.52481 | − | 13.0334i | −0.471222 | − | 0.816181i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.49020 | − | 1.63430i | 0.280091 | − | 0.101945i | −0.198155 | − | 0.980171i | \(-0.563495\pi\) |
0.478246 | + | 0.878226i | \(0.341273\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.39780 | + | 5.88517i | −0.211129 | + | 0.365687i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.46064 | − | 4.58202i | 0.338005 | − | 0.283620i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.76651 | + | 21.3609i | 0.232253 | + | 1.31717i | 0.848322 | + | 0.529480i | \(0.177613\pi\) |
−0.616069 | + | 0.787692i | \(0.711276\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.0915 | −0.988494 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.07192 | 0.432794 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.561185 | − | 3.18264i | −0.0342160 | − | 0.194049i | 0.962909 | − | 0.269828i | \(-0.0869668\pi\) |
−0.997125 | + | 0.0757790i | \(0.975856\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.97952 | − | 7.53471i | 0.545467 | − | 0.457701i | −0.327935 | − | 0.944700i | \(-0.606353\pi\) |
0.873403 | + | 0.486999i | \(0.161908\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.78359 | + | 16.9457i | −0.592130 | + | 1.02560i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.11974 | − | 1.49946i | 0.248430 | − | 0.0904209i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.38666 | − | 7.59792i | −0.263569 | − | 0.456515i | 0.703619 | − | 0.710578i | \(-0.251566\pi\) |
−0.967188 | + | 0.254063i | \(0.918233\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.32635 | + | 7.52211i | −0.0794066 | + | 0.450337i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.4702 | + | 16.3374i | 1.16149 | + | 0.974609i | 0.999925 | − | 0.0122521i | \(-0.00390007\pi\) |
0.161569 | + | 0.986861i | \(0.448345\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.51114 | − | 0.913982i | −0.149272 | − | 0.0543306i | 0.266304 | − | 0.963889i | \(-0.414198\pi\) |
−0.415576 | + | 0.909559i | \(0.636420\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.07785 | + | 6.27779i | 0.537725 | + | 0.371864i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.3516 | + | 7.77136i | 1.26035 | + | 0.458729i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.0385 | + | 11.7797i | 0.825793 | + | 0.692923i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.577848 | + | 3.27714i | −0.0338741 | + | 0.192109i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.97683 | − | 17.2804i | −0.582853 | − | 1.00953i | −0.995139 | − | 0.0984765i | \(-0.968603\pi\) |
0.412287 | − | 0.911054i | \(-0.364730\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.639033 | + | 0.232589i | −0.0372059 | + | 0.0135419i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.55303 | + | 2.68993i | −0.0901161 | + | 0.156086i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −31.2028 | + | 26.1823i | −1.80450 | + | 1.51416i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.24985 | + | 29.7734i | 0.302596 | + | 1.71611i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.7588 | 0.618075 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.02229 | 0.230316 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.16431 | + | 23.6170i | 0.237670 | + | 1.34789i | 0.836917 | + | 0.547330i | \(0.184356\pi\) |
−0.599247 | + | 0.800564i | \(0.704533\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.54189 | − | 3.81110i | 0.258379 | − | 0.216806i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.0812519 | + | 0.140732i | −0.00460737 | + | 0.00798020i | −0.868320 | − | 0.496005i | \(-0.834800\pi\) |
0.863713 | + | 0.503985i | \(0.168133\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.31655 | + | 2.29904i | −0.357033 | + | 0.129949i | −0.514308 | − | 0.857606i | \(-0.671951\pi\) |
0.157275 | + | 0.987555i | \(0.449729\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.08512 | − | 7.07564i | −0.230171 | − | 0.398667i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.48024 | − | 14.0661i | 0.139304 | − | 0.790032i | −0.832461 | − | 0.554083i | \(-0.813069\pi\) |
0.971765 | − | 0.235949i | \(-0.0758199\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.9611 | − | 14.2321i | −0.949640 | − | 0.796842i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.42602 | − | 0.883000i | −0.135407 | − | 0.0492842i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −25.0633 | − | 6.55926i | −1.39456 | − | 0.364967i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.04323 | + | 2.92750i | 0.446158 | + | 0.162388i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.66250 | − | 3.07321i | −0.202537 | − | 0.169949i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.60694 | − | 14.7847i | 0.143725 | − | 0.815108i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.6532 | − | 28.8441i | −0.915341 | − | 1.58542i | −0.806401 | − | 0.591369i | \(-0.798588\pi\) |
−0.108940 | − | 0.994048i | \(-0.534746\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.97906 | + | 0.720317i | −0.108452 | + | 0.0394731i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.65270 | + | 2.86257i | −0.0902968 | + | 0.156399i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.41669 | + | 1.18874i | −0.0771720 | + | 0.0647550i | −0.680558 | − | 0.732695i | \(-0.738262\pi\) |
0.603386 | + | 0.797450i | \(0.293818\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.89393 | − | 16.4123i | −0.157177 | − | 0.891394i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 23.7246 | 1.28476 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.5790 | −0.625209 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.95336 | − | 16.7494i | −0.159004 | − | 0.901755i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.28493 | − | 4.43458i | 0.283710 | − | 0.238061i | −0.489816 | − | 0.871826i | \(-0.662936\pi\) |
0.773525 | + | 0.633765i | \(0.218491\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.61081 | − | 9.71822i | 0.300340 | − | 0.520204i | −0.675873 | − | 0.737018i | \(-0.736233\pi\) |
0.976213 | + | 0.216814i | \(0.0695665\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.69846 | + | 2.07407i | −0.304161 | + | 0.110706i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.954241 | + | 1.65279i | 0.0507891 | + | 0.0879693i | 0.890302 | − | 0.455370i | \(-0.150493\pi\) |
−0.839513 | + | 0.543339i | \(0.817160\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.63903 | − | 20.6380i | 0.193140 | − | 1.09535i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 14.6912 | + | 12.3274i | 0.777540 | + | 0.652434i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.95558 | + | 3.25957i | 0.472658 | + | 0.172033i | 0.567356 | − | 0.823473i | \(-0.307966\pi\) |
−0.0946982 | + | 0.995506i | \(0.530189\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.6716 | − | 3.51735i | 0.982715 | − | 0.185124i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.27079 | − | 0.462531i | −0.0666993 | − | 0.0242766i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.78699 | + | 1.49946i | 0.0935353 | + | 0.0784854i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.11216 | + | 17.6499i | −0.162453 | + | 0.921319i | 0.789198 | + | 0.614139i | \(0.210496\pi\) |
−0.951651 | + | 0.307180i | \(0.900615\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.52094 | + | 6.09845i | 0.183293 | + | 0.317473i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.2690 | − | 7.01336i | 1.00040 | − | 0.364115i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.2344 | − | 26.3868i | 0.788808 | − | 1.36626i | −0.137889 | − | 0.990448i | \(-0.544032\pi\) |
0.926697 | − | 0.375809i | \(-0.122635\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.96064 | − | 5.84067i | 0.359446 | − | 0.301611i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.50640 | − | 42.5709i | −0.386599 | − | 2.19251i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.57903 | −0.337942 | −0.168971 | − | 0.985621i | \(-0.554044\pi\) | ||||
−0.168971 | + | 0.985621i | \(0.554044\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.21894 | 0.267374 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.99525 | − | 22.6582i | −0.204148 | − | 1.15778i | −0.898775 | − | 0.438410i | \(-0.855542\pi\) |
0.694627 | − | 0.719370i | \(-0.255569\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −19.4402 | + | 16.3122i | −0.990762 | + | 0.831348i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.68479 | + | 8.11430i | −0.238141 | + | 0.412473i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.6587 | + | 9.33900i | −1.30095 | + | 0.473506i | −0.897305 | − | 0.441411i | \(-0.854478\pi\) |
−0.403642 | + | 0.914917i | \(0.632256\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.9611 | + | 34.5736i | 1.00948 | + | 1.74846i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.50340 | + | 8.52623i | −0.0758367 | + | 0.430091i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 23.4008 | + | 19.6356i | 1.17742 | + | 0.987974i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.52734 | + | 2.01179i | 0.277409 | + | 0.100969i | 0.476978 | − | 0.878915i | \(-0.341732\pi\) |
−0.199569 | + | 0.979884i | \(0.563954\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13.6065 | − | 3.56093i | −0.681179 | − | 0.178270i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.02987 | + | 1.46675i | 0.201242 | + | 0.0732461i | 0.440675 | − | 0.897667i | \(-0.354739\pi\) |
−0.239433 | + | 0.970913i | \(0.576961\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 35.4825 | + | 29.7734i | 1.76751 | + | 1.48312i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.439693 | − | 2.49362i | 0.0218485 | − | 0.123909i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.27079 | + | 5.66518i | 0.162127 | + | 0.280812i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.4714 | − | 11.0907i | 1.50671 | − | 0.548398i | 0.548924 | − | 0.835872i | \(-0.315038\pi\) |
0.957788 | + | 0.287474i | \(0.0928155\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.83275 | + | 11.8347i | −0.337035 | + | 0.583761i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.663848 | − | 0.557035i | 0.0326658 | − | 0.0274099i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.0380187 | − | 0.215615i | −0.00186626 | − | 0.0105841i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.6800 | −0.669915 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.86577 | −0.481974 | −0.240987 | − | 0.970528i | \(-0.577471\pi\) | ||||
−0.240987 | + | 0.970528i | \(0.577471\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.83884 | + | 21.7711i | 0.187094 | + | 1.06106i | 0.923236 | + | 0.384234i | \(0.125534\pi\) |
−0.736142 | + | 0.676827i | \(0.763355\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.56418 | − | 2.99070i | 0.173296 | − | 0.145413i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.19459 | − | 7.26525i | 0.203468 | − | 0.352416i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.81655 | + | 1.75308i | −0.233089 | + | 0.0848376i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.41787 | + | 16.3122i | 0.454699 | + | 0.787562i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.39693 | − | 24.9362i | 0.211792 | − | 1.20113i | −0.674594 | − | 0.738189i | \(-0.735681\pi\) |
0.886387 | − | 0.462946i | \(-0.153208\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.81702 | + | 8.23746i | 0.471776 | + | 0.395867i | 0.847442 | − | 0.530888i | \(-0.178142\pi\) |
−0.375666 | + | 0.926755i | \(0.622586\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.9611 | + | 6.17334i | 0.813223 | + | 0.295989i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −24.0808 | − | 16.6531i | −1.15194 | − | 0.796627i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.90895 | − | 1.78671i | −0.234291 | − | 0.0852751i | 0.222206 | − | 0.975000i | \(-0.428674\pi\) |
−0.456498 | + | 0.889725i | \(0.650896\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.61334 | + | 2.19285i | 0.124445 | + | 0.104422i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.02141 | − | 17.1353i | 0.143552 | − | 0.814121i | −0.824967 | − | 0.565181i | \(-0.808806\pi\) |
0.968519 | − | 0.248941i | \(-0.0800825\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.95336 | + | 15.5077i | 0.424430 | + | 0.735135i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.3123 | − | 8.12100i | 1.05533 | − | 0.384110i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.8255 | + | 20.4823i | −0.558079 | + | 0.966621i | 0.439578 | + | 0.898204i | \(0.355128\pi\) |
−0.997657 | + | 0.0684163i | \(0.978205\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.7554 | − | 14.0594i | 0.788979 | − | 0.662032i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.44743 | + | 8.20880i | 0.0680064 | + | 0.385683i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −49.5458 | −2.32274 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.2695 | −1.13528 | −0.567640 | − | 0.823277i | \(-0.692143\pi\) | ||||
−0.567640 | + | 0.823277i | \(0.692143\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.03209 | + | 5.85327i | 0.0481738 | + | 0.273207i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.34318 | − | 4.48346i | 0.248857 | − | 0.208815i | −0.509823 | − | 0.860279i | \(-0.670289\pi\) |
0.758680 | + | 0.651464i | \(0.225845\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.0385 | − | 24.3154i | 0.652424 | − | 1.13003i | −0.330109 | − | 0.943943i | \(-0.607086\pi\) |
0.982533 | − | 0.186088i | \(-0.0595811\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −18.1741 | + | 6.61484i | −0.842804 | + | 0.306756i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.91147 | + | 3.31077i | 0.0884525 | + | 0.153204i | 0.906857 | − | 0.421438i | \(-0.138475\pi\) |
−0.818405 | + | 0.574642i | \(0.805141\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.731429 | − | 4.14814i | 0.0337743 | − | 0.191543i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.6197 | − | 13.9456i | −0.765797 | − | 0.642580i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 27.3475 | + | 9.95366i | 1.25744 | + | 0.457670i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.500467 | + | 6.13208i | −0.0229630 | + | 0.281359i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.97178 | + | 2.17355i | 0.273429 | + | 0.0995201i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.7010 | + | 19.8875i | 1.08293 | + | 0.908683i | 0.996160 | − | 0.0875461i | \(-0.0279025\pi\) |
0.0867654 | + | 0.996229i | \(0.472347\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.21776 | + | 12.5775i | −0.101121 | + | 0.573486i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.8366 | + | 18.7696i | 0.493083 | + | 0.854045i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.91787 | + | 2.88187i | −0.359532 | + | 0.130859i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.43242 | + | 2.48102i | −0.0649091 | + | 0.112426i | −0.896654 | − | 0.442733i | \(-0.854009\pi\) |
0.831745 | + | 0.555159i | \(0.187342\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.6079 | + | 14.7748i | −0.796256 | + | 0.668138i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.24985 | + | 41.1159i | 0.327181 | + | 1.85554i | 0.493883 | + | 0.869529i | \(0.335577\pi\) |
−0.166702 | + | 0.986007i | \(0.553312\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −42.3678 | −1.90815 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.86484 | −0.353498 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.63728 | + | 26.2993i | 0.208010 | + | 1.17969i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.26991 | + | 6.10018i | −0.325446 | + | 0.273082i | −0.790841 | − | 0.612021i | \(-0.790357\pi\) |
0.465395 | + | 0.885103i | \(0.345912\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.82295 | − | 6.62154i | 0.170797 | − | 0.295829i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.8785 | + | 4.32342i | −0.529636 | + | 0.192772i | −0.592976 | − | 0.805220i | \(-0.702047\pi\) |
0.0633395 | + | 0.997992i | \(0.479825\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.6211 | + | 23.5924i | 0.606130 | + | 1.04985i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.12836 | + | 23.4131i | −0.183347 | + | 1.03981i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.9349 | − | 12.5319i | −0.661980 | − | 0.555467i | 0.248700 | − | 0.968581i | \(-0.419997\pi\) |
−0.910679 | + | 0.413114i | \(0.864441\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.79339 | − | 1.01671i | −0.123572 | − | 0.0449766i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.52094 | − | 3.55596i | −0.111302 | − | 0.156999i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.1074 | + | 5.13468i | 0.621647 | + | 0.226261i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.0706 | − | 9.28931i | −0.486883 | − | 0.408544i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.03936 | + | 11.5658i | −0.0895181 | + | 0.507682i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.1416 | − | 17.5657i | −0.444310 | − | 0.769567i | 0.553694 | − | 0.832720i | \(-0.313218\pi\) |
−0.998004 | + | 0.0631531i | \(0.979884\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.3461 | − | 5.22156i | 0.627312 | − | 0.228323i | −0.00874906 | − | 0.999962i | \(-0.502785\pi\) |
0.636061 | + | 0.771639i | \(0.280563\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.27719 | − | 3.94421i | 0.0993847 | − | 0.172139i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 34.7768 | − | 29.1812i | 1.51490 | − | 1.27115i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.84049 | + | 21.7805i | 0.166978 | + | 0.946978i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.268571 | 0.0116550 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 42.7033 | 1.84968 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.13516 | − | 6.43783i | −0.0490774 | − | 0.278332i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.21554 | + | 2.69816i | −0.138761 | + | 0.116434i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.29813 | − | 9.17664i | 0.228207 | − | 0.395266i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.3726 | − | 7.05104i | 0.832892 | − | 0.303148i | 0.109847 | − | 0.993949i | \(-0.464964\pi\) |
0.723045 | + | 0.690801i | \(0.242742\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.16385 | + | 10.6761i | 0.264516 | + | 0.458155i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.10220 | − | 11.9221i | 0.0900482 | − | 0.510689i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.7645 | + | 18.2625i | 0.930581 | + | 0.780850i | 0.975922 | − | 0.218122i | \(-0.0699929\pi\) |
−0.0453408 | + | 0.998972i | \(0.514437\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.49273 | − | 0.543308i | −0.0637080 | − | 0.0231878i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 28.0835 | − | 13.2955i | 1.19640 | − | 0.566408i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −36.5797 | − | 13.3139i | −1.55553 | − | 0.566165i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.08512 | − | 3.42782i | −0.173404 | − | 0.145503i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.56717 | + | 37.2443i | −0.278260 | + | 1.57809i | 0.450152 | + | 0.892952i | \(0.351370\pi\) |
−0.728412 | + | 0.685139i | \(0.759741\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 28.4094 | + | 49.2065i | 1.20159 | + | 2.08122i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.3478 | − | 6.31407i | 0.732423 | − | 0.266580i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.82042 | − | 8.34922i | 0.203157 | − | 0.351877i | −0.746387 | − | 0.665512i | \(-0.768213\pi\) |
0.949544 | + | 0.313634i | \(0.101547\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 32.3259 | − | 27.1247i | 1.35996 | − | 1.14114i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.560307 | + | 3.17766i | 0.0235307 | + | 0.133449i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.1129 | 0.885098 | 0.442549 | − | 0.896744i | \(-0.354074\pi\) | ||||
0.442549 | + | 0.896744i | \(0.354074\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.11112 | 0.0883476 | 0.0441738 | − | 0.999024i | \(-0.485934\pi\) | ||||
0.0441738 | + | 0.999024i | \(0.485934\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.77197 | − | 10.0494i | −0.0740253 | − | 0.419818i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.26264 | − | 6.09408i | 0.302873 | − | 0.254141i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.5715 | + | 20.0423i | −0.481726 | + | 0.834374i | −0.999780 | − | 0.0209742i | \(-0.993323\pi\) |
0.518054 | + | 0.855348i | \(0.326657\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −20.3983 | + | 7.42436i | −0.847723 | + | 0.308546i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.139500 | + | 0.241621i | 0.00578743 | + | 0.0100241i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.42767 | − | 19.4393i | 0.141960 | − | 0.805093i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −11.7626 | − | 9.87003i | −0.486325 | − | 0.408075i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.0052 | − | 6.55336i | −0.743155 | − | 0.270486i | −0.0574324 | − | 0.998349i | \(-0.518291\pi\) |
−0.685722 | + | 0.727863i | \(0.740514\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.8944 | + | 30.2561i | −0.572509 | + | 1.24668i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.6789 | − | 5.70664i | −0.644942 | − | 0.234740i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 28.4978 | + | 23.9125i | 1.17026 | + | 0.981968i | 0.999994 | − | 0.00342988i | \(-0.00109177\pi\) |
0.170269 | + | 0.985398i | \(0.445536\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.43242 | + | 47.8226i | −0.345695 | + | 1.96054i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.23009 | + | 2.13057i | 0.0503440 | + | 0.0871984i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.0412 | − | 10.5701i | 1.18659 | − | 0.431884i | 0.328065 | − | 0.944655i | \(-0.393603\pi\) |
0.858525 | + | 0.512772i | \(0.171381\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.7802 | − | 37.7244i | 0.888432 | − | 1.53881i | 0.0467035 | − | 0.998909i | \(-0.485128\pi\) |
0.841729 | − | 0.539901i | \(-0.181538\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.00000 | − | 0.839100i | 0.0407231 | − | 0.0341708i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.594618 | − | 3.37225i | −0.0241747 | − | 0.137101i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.9659 | −0.850978 | −0.425489 | − | 0.904964i | \(-0.639898\pi\) | ||||
−0.425489 | + | 0.904964i | \(0.639898\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −23.0009 | −0.932045 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.89945 | − | 27.7862i | −0.198211 | − | 1.12411i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.82951 | − | 4.05244i | 0.195062 | − | 0.163676i | −0.540026 | − | 0.841649i | \(-0.681585\pi\) |
0.735088 | + | 0.677972i | \(0.237141\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.91534 | + | 15.4418i | −0.359501 | + | 0.622675i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 36.1241 | − | 13.1481i | 1.45430 | − | 0.529322i | 0.510512 | − | 0.859871i | \(-0.329456\pi\) |
0.943789 | + | 0.330549i | \(0.107234\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.31908 | − | 16.1411i | −0.374565 | − | 0.648766i | 0.615697 | − | 0.787983i | \(-0.288875\pi\) |
−0.990262 | + | 0.139217i | \(0.955541\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.16637 | + | 6.61484i | −0.0468050 | + | 0.265444i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.4802 | − | 14.6677i | −0.700331 | − | 0.587647i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 28.2520 | + | 10.2829i | 1.13008 | + | 0.411315i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.51754 | + | 9.62922i | −0.380094 | + | 0.384554i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.7626 | + | 4.28125i | 0.469007 | + | 0.170705i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.8407 | − | 9.93556i | −0.471372 | − | 0.395528i | 0.375923 | − | 0.926651i | \(-0.377326\pi\) |
−0.847295 | + | 0.531123i | \(0.821770\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.213888 | + | 1.21302i | −0.00850130 | + | 0.0482133i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.60741 | + | 11.4444i | 0.262207 | + | 0.454156i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.4402 | − | 7.07564i | 0.770247 | − | 0.280347i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.13816 | + | 7.16750i | −0.163703 | + | 0.283542i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.1630 | + | 16.0796i | −0.756892 | + | 0.635108i | −0.937316 | − | 0.348481i | \(-0.886697\pi\) |
0.180424 | + | 0.983589i | \(0.442253\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.96333 | − | 22.4771i | −0.156298 | − | 0.886412i | −0.957589 | − | 0.288137i | \(-0.906964\pi\) |
0.801291 | − | 0.598275i | \(-0.204147\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −23.7246 | −0.934156 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −46.1252 | −1.81337 | −0.906684 | − | 0.421811i | \(-0.861395\pi\) | ||||
−0.906684 | + | 0.421811i | \(0.861395\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.144857 | − | 0.821525i | −0.00568614 | − | 0.0322477i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 18.8799 | − | 15.8421i | 0.739960 | − | 0.620900i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.33868 | − | 12.7110i | 0.287185 | − | 0.497418i | −0.685952 | − | 0.727647i | \(-0.740614\pi\) |
0.973137 | + | 0.230228i | \(0.0739473\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.6001 | + | 7.49784i | −0.804914 | + | 0.292965i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.460637 | − | 0.797847i | −0.0179712 | − | 0.0311270i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.73648 | − | 21.1906i | 0.145553 | − | 0.825470i | −0.821369 | − | 0.570397i | \(-0.806789\pi\) |
0.966922 | − | 0.255073i | \(-0.0820995\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.0494 | − | 20.1798i | −0.935413 | − | 0.784904i | 0.0413686 | − | 0.999144i | \(-0.486828\pi\) |
−0.976781 | + | 0.214240i | \(0.931273\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 33.8692 | + | 12.3274i | 1.31537 | + | 0.478755i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.41787 | − | 34.3454i | −0.365209 | − | 1.33186i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −44.9928 | − | 16.3760i | −1.74213 | − | 0.634083i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.03983 | + | 4.22892i | 0.194851 | + | 0.163499i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.856792 | + | 4.85911i | −0.0330761 | + | 0.187584i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.83662 | − | 10.1093i | −0.224985 | − | 0.389686i | 0.731330 | − | 0.682024i | \(-0.238900\pi\) |
−0.956315 | + | 0.292338i | \(0.905567\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.32635 | − | 0.482753i | 0.0510513 | − | 0.0185812i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.6866 | + | 35.8302i | −0.795051 | + | 1.37707i | 0.127756 | + | 0.991806i | \(0.459223\pi\) |
−0.922807 | + | 0.385263i | \(0.874111\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.22534 | − | 6.90188i | 0.315659 | − | 0.264870i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.68954 | + | 9.58186i | 0.0647433 | + | 0.367178i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.5117 | 1.12923 | 0.564616 | − | 0.825354i | \(-0.309024\pi\) | ||||
0.564616 | + | 0.825354i | \(0.309024\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −34.6023 | −1.32208 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.71348 | + | 9.71762i | 0.0653733 | + | 0.370750i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 29.5219 | − | 24.7718i | 1.12469 | − | 0.943730i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.23917 | + | 3.87836i | −0.0851820 | + | 0.147540i | −0.905469 | − | 0.424413i | \(-0.860481\pi\) |
0.820287 | + | 0.571953i | \(0.193814\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.41787 | − | 3.42782i | 0.357755 | − | 0.130212i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.3195 | − | 29.9983i | −0.656968 | − | 1.13790i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.26786 | − | 41.2181i | 0.275290 | − | 1.56125i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16.7121 | − | 14.0231i | −0.632111 | − | 0.530404i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.55690 | − | 2.02255i | −0.209881 | − | 0.0763906i | 0.234940 | − | 0.972010i | \(-0.424511\pi\) |
−0.444821 | + | 0.895619i | \(0.646733\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.14038 | + | 0.853427i | −0.344736 | + | 0.0321876i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.0706 | + | 4.02936i | 0.416942 | + | 0.151754i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −26.5933 | − | 22.3145i | −1.00015 | − | 0.839221i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.19830 | − | 29.4810i | 0.195226 | − | 1.10718i | −0.716870 | − | 0.697207i | \(-0.754426\pi\) |
0.912096 | − | 0.409976i | \(-0.134463\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.03209 | − | 10.4479i | −0.226221 | − | 0.391826i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 48.2105 | − | 17.5472i | 1.80550 | − | 0.657148i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −23.8469 | + | 41.3040i | −0.891823 | + | 1.54468i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.3255 | − | 13.6987i | 0.609686 | − | 0.511587i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.29709 | − | 47.0552i | −0.309429 | − | 1.75486i | −0.601886 | − | 0.798582i | \(-0.705584\pi\) |
0.292456 | − | 0.956279i | \(-0.405527\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.1310 | −0.712477 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −15.6459 | −0.581877 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.74716 | + | 9.90863i | 0.0648879 | + | 0.367997i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.0933 | − | 26.9295i | 1.19028 | − | 0.998760i | 0.190421 | − | 0.981702i | \(-0.439015\pi\) |
0.999855 | − | 0.0170574i | \(-0.00542981\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.500000 | + | 0.866025i | −0.0185185 | + | 0.0320750i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 52.3303 | − | 19.0467i | 1.93551 | − | 0.704466i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.8068 | − | 18.7178i | −0.399156 | − | 0.691359i | 0.594466 | − | 0.804121i | \(-0.297364\pi\) |
−0.993622 | + | 0.112762i | \(0.964030\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.50000 | + | 8.50692i | −0.0553283 | + | 0.313783i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.10607 | − | 2.60630i | −0.114413 | − | 0.0960043i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.4688 | + | 11.0898i | 1.12081 | + | 0.407943i | 0.834949 | − | 0.550327i | \(-0.185497\pi\) |
0.285865 | + | 0.958270i | \(0.407719\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −26.3187 | + | 2.45734i | −0.966840 | + | 0.0902728i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.2754 | − | 9.19951i | −0.927266 | − | 0.337497i | −0.166141 | − | 0.986102i | \(-0.553131\pi\) |
−0.761125 | + | 0.648605i | \(0.775353\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 46.0565 | + | 38.6460i | 1.68738 | + | 1.41588i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.0150147 | + | 0.0851529i | −0.000549361 | + | 0.00311558i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.16519 | + | 7.21432i | 0.152193 | + | 0.263606i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.38103 | + | 1.95854i | −0.196357 | + | 0.0714680i | −0.438327 | − | 0.898816i | \(-0.644429\pi\) |
0.241970 | + | 0.970284i | \(0.422206\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.06077 | − | 8.76552i | 0.184425 | − | 0.319433i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.1682 | + | 13.5667i | −0.588421 | + | 0.493743i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.50269 | + | 8.52217i | 0.0546161 | + | 0.309744i | 0.999862 | − | 0.0166157i | \(-0.00528920\pi\) |
−0.945246 | + | 0.326359i | \(0.894178\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.8631 | 0.757282 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.7279 | −1.36764 | −0.683818 | − | 0.729653i | \(-0.739682\pi\) | ||||
−0.683818 | + | 0.729653i | \(0.739682\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.67886 | + | 15.1926i | 0.0969813 | + | 0.550009i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −11.5287 | + | 9.67372i | −0.416820 | + | 0.349754i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.814330 | − | 1.41046i | 0.0294038 | − | 0.0509288i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.5724 | + | 12.5833i | −1.24671 | + | 0.453766i | −0.879289 | − | 0.476288i | \(-0.841982\pi\) |
−0.367423 | + | 0.930054i | \(0.619760\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.38919 | − | 4.13819i | −0.0860444 | − | 0.149033i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.46750 | − | 19.6652i | 0.124717 | − | 0.707307i | −0.856758 | − | 0.515719i | \(-0.827525\pi\) |
0.981475 | − | 0.191588i | \(-0.0613639\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.25877 | − | 6.92993i | −0.296664 | − | 0.248930i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.38578 | + | 2.32423i | 0.229089 | + | 0.0833814i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.11721 | + | 29.6021i | 0.290829 | + | 1.06061i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.1565 | + | 8.79224i | 0.864386 | + | 0.314611i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.46064 | − | 4.58202i | −0.195147 | − | 0.163748i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.53936 | − | 54.1004i | 0.340474 | − | 1.93093i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.18392 | + | 7.24675i | 0.149140 | + | 0.258319i | 0.930910 | − | 0.365249i | \(-0.119016\pi\) |
−0.781770 | + | 0.623567i | \(0.785683\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20.3824 | − | 7.41858i | 0.725632 | − | 0.264108i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −26.8871 | + | 46.5699i | −0.955996 | + | 1.65583i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.37939 | + | 6.19204i | −0.262050 | + | 0.219886i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.79426 | + | 15.8471i | 0.0991023 | + | 0.562037i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42.1729 | −1.49384 | −0.746921 | − | 0.664913i | \(-0.768469\pi\) | ||||
−0.746921 | + | 0.664913i | \(0.768469\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27.6536 | −0.978315 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.22803 | − | 6.96448i | −0.0433902 | − | 0.246078i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.19207 | + | 1.83936i | −0.0773563 | + | 0.0649097i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −27.4393 | + | 47.5262i | −0.967108 | + | 1.67508i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.03684 | + | 1.10532i | −0.106902 | + | 0.0389090i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.03121 | + | 5.25021i | 0.106572 | + | 0.184588i | 0.914379 | − | 0.404859i | \(-0.132679\pi\) |
−0.807808 | + | 0.589446i | \(0.799346\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.46168 | + | 25.3034i | −0.156671 | + | 0.888523i | 0.800572 | + | 0.599237i | \(0.204529\pi\) |
−0.957243 | + | 0.289287i | \(0.906582\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.97952 | − | 7.53471i | −0.314926 | − | 0.264254i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −54.6912 | − | 19.9060i | −1.91575 | − | 0.697276i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28.7101 | + | 29.0469i | −1.00444 | + | 1.01622i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 18.3871 | + | 6.69237i | 0.642498 | + | 0.233850i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.192533 | − | 0.161555i | −0.00671946 | − | 0.00563830i | 0.639422 | − | 0.768856i | \(-0.279174\pi\) |
−0.646141 | + | 0.763218i | \(0.723618\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.83497 | + | 16.0779i | −0.0988208 | + | 0.560441i | 0.894689 | + | 0.446691i | \(0.147397\pi\) |
−0.993509 | + | 0.113750i | \(0.963714\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.19207 | − | 3.79677i | −0.0763180 | − | 0.132187i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.9008 | − | 9.06315i | 0.865886 | − | 0.315157i | 0.129386 | − | 0.991594i | \(-0.458699\pi\) |
0.736500 | + | 0.676438i | \(0.236477\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.8148 | + | 36.0523i | −0.722928 | + | 1.25215i | 0.236894 | + | 0.971536i | \(0.423871\pi\) |
−0.959821 | + | 0.280612i | \(0.909463\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.72075 | + | 5.63938i | −0.233140 | + | 0.195628i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.52094 | − | 19.9683i | −0.121993 | − | 0.691860i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.3601 | 0.669984 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.63816 | 0.264013 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.93289 | − | 27.9758i | −0.170302 | − | 0.965831i | −0.943428 | − | 0.331578i | \(-0.892419\pi\) |
0.773126 | − | 0.634253i | \(-0.218692\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.7101 | − | 14.0214i | 0.576209 | − | 0.483497i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.7083 | − | 22.0114i | 0.437696 | − | 0.758111i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −56.5681 | + | 20.5891i | −1.94600 | + | 0.708287i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.18180 | + | 3.77899i | 0.0749675 | + | 0.129848i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.464041 | + | 2.63171i | −0.0159258 | + | 0.0903199i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.8366 | + | 9.09300i | 0.371475 | + | 0.311704i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.5535 | + | 9.30071i | 0.874935 | + | 0.318450i | 0.740164 | − | 0.672426i | \(-0.234748\pi\) |
0.134771 | + | 0.990877i | \(0.456970\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.60607 | − | 10.0301i | 0.157524 | − | 0.343021i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −39.4381 | − | 14.3543i | −1.34718 | − | 0.490333i | −0.435113 | − | 0.900376i | \(-0.643292\pi\) |
−0.912066 | + | 0.410042i | \(0.865514\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27.0519 | − | 22.6992i | −0.922999 | − | 0.774488i | 0.0515481 | − | 0.998671i | \(-0.483584\pi\) |
−0.974547 | + | 0.224182i | \(0.928029\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.94562 | − | 22.3767i | 0.134466 | − | 0.762597i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.00521 | + | 10.4013i | 0.204420 | + | 0.354066i | 0.949948 | − | 0.312409i | \(-0.101136\pi\) |
−0.745528 | + | 0.666474i | \(0.767803\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −27.9440 | + | 10.1708i | −0.950126 | + | 0.345817i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.16297 | − | 15.8707i | 0.311191 | − | 0.538998i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28.7053 | + | 24.0866i | −0.973762 | + | 0.817083i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.37464 | − | 7.79596i | −0.0465778 | − | 0.264156i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.32770 | 0.112625 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −29.3191 | −0.991168 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.13145 | − | 17.7594i | −0.105742 | − | 0.599691i | −0.990921 | − | 0.134442i | \(-0.957076\pi\) |
0.885180 | − | 0.465249i | \(-0.154035\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.2854 | + | 12.8260i | −0.515564 | + | 0.432609i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.9101 | + | 20.6290i | −0.401262 | + | 0.695007i | −0.993879 | − | 0.110478i | \(-0.964762\pi\) |
0.592616 | + | 0.805485i | \(0.298095\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.1197 | − | 4.04725i | 0.374209 | − | 0.136201i | −0.148067 | − | 0.988977i | \(-0.547305\pi\) |
0.522276 | + | 0.852776i | \(0.325083\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.340022 | + | 0.588936i | 0.0114297 | + | 0.0197969i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.37283 | − | 36.1421i | 0.213979 | − | 1.21353i | −0.668692 | − | 0.743540i | \(-0.733145\pi\) |
0.882670 | − | 0.469993i | \(-0.155744\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.9001 | − | 10.8245i | −0.432655 | − | 0.363041i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.91875 | + | 1.06234i | 0.0977817 | + | 0.0355896i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.3302 | − | 8.67804i | 0.613397 | − | 0.290399i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.98767 | − | 3.63522i | −0.333851 | − | 0.121512i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 31.2028 | + | 26.1823i | 1.04183 | + | 0.874200i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.45471 | + | 53.6203i | −0.315332 | + | 1.78834i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.8858 | − | 32.7111i | −0.629177 | − | 1.08977i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 28.4094 | − | 10.3402i | 0.945406 | − | 0.344100i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.6074 | + | 27.0328i | −0.518808 | + | 0.898602i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.3746 | − | 18.7746i | 0.742938 | − | 0.623399i | −0.190687 | − | 0.981651i | \(-0.561072\pi\) |
0.933625 | + | 0.358252i | \(0.116627\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.86824 | − | 10.5953i | −0.0619656 | − | 0.351425i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.12567 | −0.103558 | −0.0517790 | − | 0.998659i | \(-0.516489\pi\) | ||||
−0.0517790 | + | 0.998659i | \(0.516489\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.268571 | 0.00888839 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.698463 | − | 3.96118i | −0.0230905 | − | 0.130953i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.4001 | − | 17.9568i | 0.706693 | − | 0.592986i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.39322 | + | 7.60928i | −0.144919 | + | 0.251007i | −0.929343 | − | 0.369218i | \(-0.879625\pi\) |
0.784424 | + | 0.620225i | \(0.212959\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.5351 | − | 8.20210i | 0.742556 | − | 0.270268i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 25.0945 | + | 43.4650i | 0.825996 | + | 1.43067i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.516197 | − | 2.92750i | 0.0169724 | − | 0.0962555i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.54189 | − | 3.81110i | −0.149175 | − | 0.125173i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.6377 | − | 8.60344i | −0.775529 | − | 0.282270i | −0.0762221 | − | 0.997091i | \(-0.524286\pi\) |
−0.699307 | + | 0.714821i | \(0.746508\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.60014 | + | 12.1311i | 0.281858 | + | 0.397579i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.152704 | + | 0.0555796i | 0.00499929 | + | 0.00181959i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 35.8089 | + | 30.0472i | 1.17108 | + | 0.982649i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.59698 | + | 26.0708i | −0.150177 | + | 0.851695i | 0.812887 | + | 0.582422i | \(0.197895\pi\) |
−0.963064 | + | 0.269274i | \(0.913216\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.36097 | + | 5.82137i | 0.109681 | + | 0.189973i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.95171 | + | 1.80228i | −0.161421 | + | 0.0587525i | −0.421467 | − | 0.906844i | \(-0.638485\pi\) |
0.260046 | + | 0.965596i | \(0.416262\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.6498 | − | 40.9626i | 0.770142 | − | 1.33393i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.25877 | + | 5.25173i | −0.203598 | + | 0.170839i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.23324 | − | 24.0079i | −0.137562 | − | 0.780152i | −0.973041 | − | 0.230630i | \(-0.925921\pi\) |
0.835480 | − | 0.549521i | \(-0.185190\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.58677 | −0.181354 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.2831 | −0.463162 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.61633 | + | 48.8657i | 0.279110 | + | 1.58291i | 0.725595 | + | 0.688122i | \(0.241565\pi\) |
−0.446484 | + | 0.894792i | \(0.647324\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.7934 | − | 16.6086i | 0.640499 | − | 0.537442i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.0706 | + | 19.1748i | −0.357861 | + | 0.619833i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 41.4350 | − | 15.0811i | 1.33801 | − | 0.486994i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.6707 | − | 23.6784i | −0.440991 | − | 0.763818i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.448311 | + | 2.54250i | −0.0144466 | + | 0.0819308i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −42.1057 | − | 35.3308i | −1.35543 | − | 1.13734i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.3307 | − | 8.85565i | −0.782422 | − | 0.284778i | −0.0802399 | − | 0.996776i | \(-0.525569\pi\) |
−0.702182 | + | 0.711997i | \(0.747791\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.10741 | + | 25.8215i | −0.0676998 | + | 0.829507i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.8645 | + | 4.31834i | 0.380751 | + | 0.138582i | 0.525303 | − | 0.850915i | \(-0.323952\pi\) |
−0.144552 | + | 0.989497i | \(0.546174\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 33.8141 | + | 28.3734i | 1.08403 | + | 0.909609i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.48633 | − | 8.42939i | 0.0476006 | − | 0.269957i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.69072 | − | 2.92842i | −0.0540910 | − | 0.0936884i | 0.837712 | − | 0.546112i | \(-0.183893\pi\) |
−0.891803 | + | 0.452424i | \(0.850559\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −20.6411 | + | 7.51276i | −0.659694 | + | 0.240109i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.39053 | + | 4.14052i | −0.0763237 | + | 0.132197i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.170493 | − | 0.143061i | 0.00543788 | − | 0.00456293i | −0.640065 | − | 0.768321i | \(-0.721092\pi\) |
0.645503 | + | 0.763758i | \(0.276648\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.33631 | − | 41.6063i | −0.233754 | − | 1.32569i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −15.0128 | −0.477862 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 62.9344 | 2.00120 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.838536 | + | 4.75557i | 0.0266370 | + | 0.151066i | 0.995225 | − | 0.0976038i | \(-0.0311178\pi\) |
−0.968588 | + | 0.248670i | \(0.920007\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −25.5141 | + | 21.4089i | −0.809667 | + | 0.679391i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.11468 | + | 5.39479i | −0.0987422 | + | 0.171026i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.8794 | − | 4.32374i | 0.376224 | − | 0.136934i | −0.146985 | − | 0.989139i | \(-0.546957\pi\) |
0.523209 | + | 0.852204i | \(0.324735\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.05303 | + | 1.82391i | 0.0333165 | + | 0.0577059i |
(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 | 912.2.bo.e.289.1 | 6 | ||
4.3 | odd | 2 | 228.2.q.a.61.1 | ✓ | 6 | ||
12.11 | even | 2 | 684.2.bo.a.289.1 | 6 | |||
19.5 | even | 9 | inner | 912.2.bo.e.385.1 | 6 | ||
76.43 | odd | 18 | 228.2.q.a.157.1 | yes | 6 | ||
76.47 | odd | 18 | 4332.2.a.o.1.3 | 3 | |||
76.67 | even | 18 | 4332.2.a.n.1.3 | 3 | |||
228.119 | even | 18 | 684.2.bo.a.613.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
228.2.q.a.61.1 | ✓ | 6 | 4.3 | odd | 2 | ||
228.2.q.a.157.1 | yes | 6 | 76.43 | odd | 18 | ||
684.2.bo.a.289.1 | 6 | 12.11 | even | 2 | |||
684.2.bo.a.613.1 | 6 | 228.119 | even | 18 | |||
912.2.bo.e.289.1 | 6 | 1.1 | even | 1 | trivial | ||
912.2.bo.e.385.1 | 6 | 19.5 | even | 9 | inner | ||
4332.2.a.n.1.3 | 3 | 76.67 | even | 18 | |||
4332.2.a.o.1.3 | 3 | 76.47 | odd | 18 |