Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4001,2,Mod(1,4001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4001.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(31.9481458487\) |
Analytic rank: | \(0\) |
Dimension: | \(184\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.163 | ||
Character | \(\chi\) | \(=\) | 4001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.45513 | 1.73604 | 0.868020 | − | 0.496530i | \(-0.165393\pi\) | ||||
0.868020 | + | 0.496530i | \(0.165393\pi\) | |||||||
\(3\) | −1.68371 | −0.972088 | −0.486044 | − | 0.873934i | \(-0.661561\pi\) | ||||
−0.486044 | + | 0.873934i | \(0.661561\pi\) | |||||||
\(4\) | 4.02766 | 2.01383 | ||||||||
\(5\) | −3.39190 | −1.51690 | −0.758452 | − | 0.651728i | \(-0.774044\pi\) | ||||
−0.758452 | + | 0.651728i | \(0.774044\pi\) | |||||||
\(6\) | −4.13372 | −1.68758 | ||||||||
\(7\) | 4.85354 | 1.83447 | 0.917233 | − | 0.398350i | \(-0.130417\pi\) | ||||
0.917233 | + | 0.398350i | \(0.130417\pi\) | |||||||
\(8\) | 4.97818 | 1.76005 | ||||||||
\(9\) | −0.165134 | −0.0550447 | ||||||||
\(10\) | −8.32756 | −2.63341 | ||||||||
\(11\) | −3.48051 | −1.04941 | −0.524706 | − | 0.851283i | \(-0.675825\pi\) | ||||
−0.524706 | + | 0.851283i | \(0.675825\pi\) | |||||||
\(12\) | −6.78140 | −1.95762 | ||||||||
\(13\) | −0.426081 | −0.118174 | −0.0590868 | − | 0.998253i | \(-0.518819\pi\) | ||||
−0.0590868 | + | 0.998253i | \(0.518819\pi\) | |||||||
\(14\) | 11.9161 | 3.18471 | ||||||||
\(15\) | 5.71097 | 1.47457 | ||||||||
\(16\) | 4.16675 | 1.04169 | ||||||||
\(17\) | −4.22969 | −1.02585 | −0.512926 | − | 0.858433i | \(-0.671438\pi\) | ||||
−0.512926 | + | 0.858433i | \(0.671438\pi\) | |||||||
\(18\) | −0.405426 | −0.0955598 | ||||||||
\(19\) | 7.37914 | 1.69289 | 0.846445 | − | 0.532476i | \(-0.178738\pi\) | ||||
0.846445 | + | 0.532476i | \(0.178738\pi\) | |||||||
\(20\) | −13.6614 | −3.05479 | ||||||||
\(21\) | −8.17194 | −1.78326 | ||||||||
\(22\) | −8.54510 | −1.82182 | ||||||||
\(23\) | 5.74129 | 1.19714 | 0.598571 | − | 0.801070i | \(-0.295735\pi\) | ||||
0.598571 | + | 0.801070i | \(0.295735\pi\) | |||||||
\(24\) | −8.38179 | −1.71093 | ||||||||
\(25\) | 6.50500 | 1.30100 | ||||||||
\(26\) | −1.04608 | −0.205154 | ||||||||
\(27\) | 5.32916 | 1.02560 | ||||||||
\(28\) | 19.5484 | 3.69431 | ||||||||
\(29\) | −1.35939 | −0.252433 | −0.126216 | − | 0.992003i | \(-0.540283\pi\) | ||||
−0.126216 | + | 0.992003i | \(0.540283\pi\) | |||||||
\(30\) | 14.0212 | 2.55990 | ||||||||
\(31\) | 1.93786 | 0.348049 | 0.174025 | − | 0.984741i | \(-0.444323\pi\) | ||||
0.174025 | + | 0.984741i | \(0.444323\pi\) | |||||||
\(32\) | 0.273552 | 0.0483576 | ||||||||
\(33\) | 5.86015 | 1.02012 | ||||||||
\(34\) | −10.3844 | −1.78092 | ||||||||
\(35\) | −16.4627 | −2.78271 | ||||||||
\(36\) | −0.665105 | −0.110851 | ||||||||
\(37\) | 5.57311 | 0.916214 | 0.458107 | − | 0.888897i | \(-0.348528\pi\) | ||||
0.458107 | + | 0.888897i | \(0.348528\pi\) | |||||||
\(38\) | 18.1167 | 2.93892 | ||||||||
\(39\) | 0.717395 | 0.114875 | ||||||||
\(40\) | −16.8855 | −2.66983 | ||||||||
\(41\) | −3.32289 | −0.518949 | −0.259474 | − | 0.965750i | \(-0.583549\pi\) | ||||
−0.259474 | + | 0.965750i | \(0.583549\pi\) | |||||||
\(42\) | −20.0632 | −3.09581 | ||||||||
\(43\) | −3.08418 | −0.470333 | −0.235167 | − | 0.971955i | \(-0.575564\pi\) | ||||
−0.235167 | + | 0.971955i | \(0.575564\pi\) | |||||||
\(44\) | −14.0183 | −2.11334 | ||||||||
\(45\) | 0.560119 | 0.0834976 | ||||||||
\(46\) | 14.0956 | 2.07829 | ||||||||
\(47\) | 13.0313 | 1.90081 | 0.950406 | − | 0.311013i | \(-0.100668\pi\) | ||||
0.950406 | + | 0.311013i | \(0.100668\pi\) | |||||||
\(48\) | −7.01558 | −1.01261 | ||||||||
\(49\) | 16.5569 | 2.36527 | ||||||||
\(50\) | 15.9706 | 2.25859 | ||||||||
\(51\) | 7.12156 | 0.997218 | ||||||||
\(52\) | −1.71611 | −0.237982 | ||||||||
\(53\) | 2.68870 | 0.369321 | 0.184661 | − | 0.982802i | \(-0.440881\pi\) | ||||
0.184661 | + | 0.982802i | \(0.440881\pi\) | |||||||
\(54\) | 13.0838 | 1.78048 | ||||||||
\(55\) | 11.8055 | 1.59186 | ||||||||
\(56\) | 24.1618 | 3.22876 | ||||||||
\(57\) | −12.4243 | −1.64564 | ||||||||
\(58\) | −3.33748 | −0.438233 | ||||||||
\(59\) | −7.51492 | −0.978359 | −0.489180 | − | 0.872183i | \(-0.662704\pi\) | ||||
−0.489180 | + | 0.872183i | \(0.662704\pi\) | |||||||
\(60\) | 23.0019 | 2.96953 | ||||||||
\(61\) | 13.7021 | 1.75437 | 0.877186 | − | 0.480150i | \(-0.159418\pi\) | ||||
0.877186 | + | 0.480150i | \(0.159418\pi\) | |||||||
\(62\) | 4.75769 | 0.604227 | ||||||||
\(63\) | −0.801486 | −0.100978 | ||||||||
\(64\) | −7.66189 | −0.957736 | ||||||||
\(65\) | 1.44522 | 0.179258 | ||||||||
\(66\) | 14.3874 | 1.77097 | ||||||||
\(67\) | −4.51784 | −0.551941 | −0.275971 | − | 0.961166i | \(-0.588999\pi\) | ||||
−0.275971 | + | 0.961166i | \(0.588999\pi\) | |||||||
\(68\) | −17.0358 | −2.06589 | ||||||||
\(69\) | −9.66665 | −1.16373 | ||||||||
\(70\) | −40.4182 | −4.83090 | ||||||||
\(71\) | −2.97385 | −0.352931 | −0.176466 | − | 0.984307i | \(-0.556466\pi\) | ||||
−0.176466 | + | 0.984307i | \(0.556466\pi\) | |||||||
\(72\) | −0.822067 | −0.0968815 | ||||||||
\(73\) | 13.5805 | 1.58948 | 0.794740 | − | 0.606950i | \(-0.207607\pi\) | ||||
0.794740 | + | 0.606950i | \(0.207607\pi\) | |||||||
\(74\) | 13.6827 | 1.59058 | ||||||||
\(75\) | −10.9525 | −1.26469 | ||||||||
\(76\) | 29.7207 | 3.40920 | ||||||||
\(77\) | −16.8928 | −1.92511 | ||||||||
\(78\) | 1.76130 | 0.199428 | ||||||||
\(79\) | −11.0053 | −1.23819 | −0.619095 | − | 0.785316i | \(-0.712500\pi\) | ||||
−0.619095 | + | 0.785316i | \(0.712500\pi\) | |||||||
\(80\) | −14.1332 | −1.58014 | ||||||||
\(81\) | −8.47733 | −0.941925 | ||||||||
\(82\) | −8.15813 | −0.900915 | ||||||||
\(83\) | 10.2706 | 1.12735 | 0.563675 | − | 0.825997i | \(-0.309387\pi\) | ||||
0.563675 | + | 0.825997i | \(0.309387\pi\) | |||||||
\(84\) | −32.9138 | −3.59119 | ||||||||
\(85\) | 14.3467 | 1.55612 | ||||||||
\(86\) | −7.57207 | −0.816517 | ||||||||
\(87\) | 2.28882 | 0.245387 | ||||||||
\(88\) | −17.3266 | −1.84702 | ||||||||
\(89\) | 3.18827 | 0.337956 | 0.168978 | − | 0.985620i | \(-0.445953\pi\) | ||||
0.168978 | + | 0.985620i | \(0.445953\pi\) | |||||||
\(90\) | 1.37516 | 0.144955 | ||||||||
\(91\) | −2.06800 | −0.216785 | ||||||||
\(92\) | 23.1240 | 2.41084 | ||||||||
\(93\) | −3.26278 | −0.338334 | ||||||||
\(94\) | 31.9936 | 3.29988 | ||||||||
\(95\) | −25.0293 | −2.56795 | ||||||||
\(96\) | −0.460581 | −0.0470078 | ||||||||
\(97\) | 10.7849 | 1.09504 | 0.547519 | − | 0.836793i | \(-0.315572\pi\) | ||||
0.547519 | + | 0.836793i | \(0.315572\pi\) | |||||||
\(98\) | 40.6493 | 4.10620 | ||||||||
\(99\) | 0.574750 | 0.0577646 | ||||||||
\(100\) | 26.2000 | 2.62000 | ||||||||
\(101\) | −4.99720 | −0.497240 | −0.248620 | − | 0.968601i | \(-0.579977\pi\) | ||||
−0.248620 | + | 0.968601i | \(0.579977\pi\) | |||||||
\(102\) | 17.4844 | 1.73121 | ||||||||
\(103\) | 17.8445 | 1.75827 | 0.879135 | − | 0.476572i | \(-0.158121\pi\) | ||||
0.879135 | + | 0.476572i | \(0.158121\pi\) | |||||||
\(104\) | −2.12111 | −0.207992 | ||||||||
\(105\) | 27.7184 | 2.70504 | ||||||||
\(106\) | 6.60110 | 0.641156 | ||||||||
\(107\) | −3.43821 | −0.332384 | −0.166192 | − | 0.986093i | \(-0.553147\pi\) | ||||
−0.166192 | + | 0.986093i | \(0.553147\pi\) | |||||||
\(108\) | 21.4640 | 2.06538 | ||||||||
\(109\) | −2.21934 | −0.212574 | −0.106287 | − | 0.994335i | \(-0.533896\pi\) | ||||
−0.106287 | + | 0.994335i | \(0.533896\pi\) | |||||||
\(110\) | 28.9841 | 2.76353 | ||||||||
\(111\) | −9.38348 | −0.890641 | ||||||||
\(112\) | 20.2235 | 1.91094 | ||||||||
\(113\) | 12.8825 | 1.21188 | 0.605940 | − | 0.795510i | \(-0.292797\pi\) | ||||
0.605940 | + | 0.795510i | \(0.292797\pi\) | |||||||
\(114\) | −30.5033 | −2.85689 | ||||||||
\(115\) | −19.4739 | −1.81595 | ||||||||
\(116\) | −5.47517 | −0.508357 | ||||||||
\(117\) | 0.0703605 | 0.00650483 | ||||||||
\(118\) | −18.4501 | −1.69847 | ||||||||
\(119\) | −20.5290 | −1.88189 | ||||||||
\(120\) | 28.4302 | 2.59531 | ||||||||
\(121\) | 1.11393 | 0.101266 | ||||||||
\(122\) | 33.6404 | 3.04566 | ||||||||
\(123\) | 5.59477 | 0.504464 | ||||||||
\(124\) | 7.80503 | 0.700912 | ||||||||
\(125\) | −5.10481 | −0.456588 | ||||||||
\(126\) | −1.96775 | −0.175301 | ||||||||
\(127\) | −17.4405 | −1.54759 | −0.773796 | − | 0.633434i | \(-0.781645\pi\) | ||||
−0.773796 | + | 0.633434i | \(0.781645\pi\) | |||||||
\(128\) | −19.3580 | −1.71103 | ||||||||
\(129\) | 5.19286 | 0.457206 | ||||||||
\(130\) | 3.54821 | 0.311199 | ||||||||
\(131\) | −13.9412 | −1.21804 | −0.609022 | − | 0.793153i | \(-0.708438\pi\) | ||||
−0.609022 | + | 0.793153i | \(0.708438\pi\) | |||||||
\(132\) | 23.6027 | 2.05435 | ||||||||
\(133\) | 35.8150 | 3.10555 | ||||||||
\(134\) | −11.0919 | −0.958192 | ||||||||
\(135\) | −18.0760 | −1.55573 | ||||||||
\(136\) | −21.0562 | −1.80555 | ||||||||
\(137\) | 17.4345 | 1.48953 | 0.744764 | − | 0.667328i | \(-0.232562\pi\) | ||||
0.744764 | + | 0.667328i | \(0.232562\pi\) | |||||||
\(138\) | −23.7329 | −2.02028 | ||||||||
\(139\) | 20.6453 | 1.75111 | 0.875554 | − | 0.483120i | \(-0.160497\pi\) | ||||
0.875554 | + | 0.483120i | \(0.160497\pi\) | |||||||
\(140\) | −66.3064 | −5.60391 | ||||||||
\(141\) | −21.9409 | −1.84776 | ||||||||
\(142\) | −7.30120 | −0.612703 | ||||||||
\(143\) | 1.48298 | 0.124013 | ||||||||
\(144\) | −0.688072 | −0.0573394 | ||||||||
\(145\) | 4.61092 | 0.382916 | ||||||||
\(146\) | 33.3419 | 2.75940 | ||||||||
\(147\) | −27.8769 | −2.29925 | ||||||||
\(148\) | 22.4466 | 1.84510 | ||||||||
\(149\) | 11.0111 | 0.902062 | 0.451031 | − | 0.892508i | \(-0.351056\pi\) | ||||
0.451031 | + | 0.892508i | \(0.351056\pi\) | |||||||
\(150\) | −26.8898 | −2.19555 | ||||||||
\(151\) | 21.9063 | 1.78271 | 0.891356 | − | 0.453304i | \(-0.149755\pi\) | ||||
0.891356 | + | 0.453304i | \(0.149755\pi\) | |||||||
\(152\) | 36.7347 | 2.97958 | ||||||||
\(153\) | 0.698467 | 0.0564677 | ||||||||
\(154\) | −41.4740 | −3.34207 | ||||||||
\(155\) | −6.57302 | −0.527957 | ||||||||
\(156\) | 2.88943 | 0.231339 | ||||||||
\(157\) | −12.5918 | −1.00494 | −0.502468 | − | 0.864596i | \(-0.667574\pi\) | ||||
−0.502468 | + | 0.864596i | \(0.667574\pi\) | |||||||
\(158\) | −27.0194 | −2.14955 | ||||||||
\(159\) | −4.52698 | −0.359013 | ||||||||
\(160\) | −0.927861 | −0.0733538 | ||||||||
\(161\) | 27.8656 | 2.19612 | ||||||||
\(162\) | −20.8129 | −1.63522 | ||||||||
\(163\) | −3.86920 | −0.303059 | −0.151529 | − | 0.988453i | \(-0.548420\pi\) | ||||
−0.151529 | + | 0.988453i | \(0.548420\pi\) | |||||||
\(164\) | −13.3835 | −1.04508 | ||||||||
\(165\) | −19.8771 | −1.54743 | ||||||||
\(166\) | 25.2158 | 1.95712 | ||||||||
\(167\) | −12.6164 | −0.976289 | −0.488144 | − | 0.872763i | \(-0.662326\pi\) | ||||
−0.488144 | + | 0.872763i | \(0.662326\pi\) | |||||||
\(168\) | −40.6814 | −3.13864 | ||||||||
\(169\) | −12.8185 | −0.986035 | ||||||||
\(170\) | 35.2230 | 2.70148 | ||||||||
\(171\) | −1.21855 | −0.0931847 | ||||||||
\(172\) | −12.4221 | −0.947173 | ||||||||
\(173\) | 8.33232 | 0.633495 | 0.316747 | − | 0.948510i | \(-0.397409\pi\) | ||||
0.316747 | + | 0.948510i | \(0.397409\pi\) | |||||||
\(174\) | 5.61934 | 0.426001 | ||||||||
\(175\) | 31.5723 | 2.38664 | ||||||||
\(176\) | −14.5024 | −1.09316 | ||||||||
\(177\) | 12.6529 | 0.951052 | ||||||||
\(178\) | 7.82762 | 0.586705 | ||||||||
\(179\) | −15.9978 | −1.19573 | −0.597866 | − | 0.801596i | \(-0.703985\pi\) | ||||
−0.597866 | + | 0.801596i | \(0.703985\pi\) | |||||||
\(180\) | 2.25597 | 0.168150 | ||||||||
\(181\) | 11.9696 | 0.889696 | 0.444848 | − | 0.895606i | \(-0.353258\pi\) | ||||
0.444848 | + | 0.895606i | \(0.353258\pi\) | |||||||
\(182\) | −5.07721 | −0.376348 | ||||||||
\(183\) | −23.0703 | −1.70540 | ||||||||
\(184\) | 28.5812 | 2.10703 | ||||||||
\(185\) | −18.9034 | −1.38981 | ||||||||
\(186\) | −8.01055 | −0.587362 | ||||||||
\(187\) | 14.7215 | 1.07654 | ||||||||
\(188\) | 52.4857 | 3.82791 | ||||||||
\(189\) | 25.8653 | 1.88142 | ||||||||
\(190\) | −61.4502 | −4.45807 | ||||||||
\(191\) | −2.60164 | −0.188248 | −0.0941241 | − | 0.995560i | \(-0.530005\pi\) | ||||
−0.0941241 | + | 0.995560i | \(0.530005\pi\) | |||||||
\(192\) | 12.9004 | 0.931004 | ||||||||
\(193\) | −7.91810 | −0.569957 | −0.284979 | − | 0.958534i | \(-0.591987\pi\) | ||||
−0.284979 | + | 0.958534i | \(0.591987\pi\) | |||||||
\(194\) | 26.4783 | 1.90103 | ||||||||
\(195\) | −2.43333 | −0.174255 | ||||||||
\(196\) | 66.6855 | 4.76325 | ||||||||
\(197\) | 4.88564 | 0.348087 | 0.174044 | − | 0.984738i | \(-0.444317\pi\) | ||||
0.174044 | + | 0.984738i | \(0.444317\pi\) | |||||||
\(198\) | 1.41109 | 0.100282 | ||||||||
\(199\) | 13.8846 | 0.984255 | 0.492127 | − | 0.870523i | \(-0.336219\pi\) | ||||
0.492127 | + | 0.870523i | \(0.336219\pi\) | |||||||
\(200\) | 32.3831 | 2.28983 | ||||||||
\(201\) | 7.60671 | 0.536536 | ||||||||
\(202\) | −12.2688 | −0.863227 | ||||||||
\(203\) | −6.59787 | −0.463079 | ||||||||
\(204\) | 28.6833 | 2.00823 | ||||||||
\(205\) | 11.2709 | 0.787196 | ||||||||
\(206\) | 43.8106 | 3.05243 | ||||||||
\(207\) | −0.948083 | −0.0658963 | ||||||||
\(208\) | −1.77537 | −0.123100 | ||||||||
\(209\) | −25.6831 | −1.77654 | ||||||||
\(210\) | 68.0523 | 4.69606 | ||||||||
\(211\) | 10.7942 | 0.743100 | 0.371550 | − | 0.928413i | \(-0.378826\pi\) | ||||
0.371550 | + | 0.928413i | \(0.378826\pi\) | |||||||
\(212\) | 10.8292 | 0.743751 | ||||||||
\(213\) | 5.00709 | 0.343080 | ||||||||
\(214\) | −8.44126 | −0.577032 | ||||||||
\(215\) | 10.4612 | 0.713451 | ||||||||
\(216\) | 26.5295 | 1.80510 | ||||||||
\(217\) | 9.40546 | 0.638484 | ||||||||
\(218\) | −5.44877 | −0.369037 | ||||||||
\(219\) | −22.8656 | −1.54511 | ||||||||
\(220\) | 47.5487 | 3.20574 | ||||||||
\(221\) | 1.80219 | 0.121229 | ||||||||
\(222\) | −23.0377 | −1.54619 | ||||||||
\(223\) | −8.45603 | −0.566258 | −0.283129 | − | 0.959082i | \(-0.591372\pi\) | ||||
−0.283129 | + | 0.959082i | \(0.591372\pi\) | |||||||
\(224\) | 1.32769 | 0.0887103 | ||||||||
\(225\) | −1.07420 | −0.0716132 | ||||||||
\(226\) | 31.6281 | 2.10387 | ||||||||
\(227\) | −8.41642 | −0.558617 | −0.279309 | − | 0.960201i | \(-0.590105\pi\) | ||||
−0.279309 | + | 0.960201i | \(0.590105\pi\) | |||||||
\(228\) | −50.0409 | −3.31404 | ||||||||
\(229\) | −19.3500 | −1.27869 | −0.639343 | − | 0.768921i | \(-0.720794\pi\) | ||||
−0.639343 | + | 0.768921i | \(0.720794\pi\) | |||||||
\(230\) | −47.8110 | −3.15256 | ||||||||
\(231\) | 28.4425 | 1.87138 | ||||||||
\(232\) | −6.76729 | −0.444295 | ||||||||
\(233\) | −1.72695 | −0.113136 | −0.0565681 | − | 0.998399i | \(-0.518016\pi\) | ||||
−0.0565681 | + | 0.998399i | \(0.518016\pi\) | |||||||
\(234\) | 0.172744 | 0.0112926 | ||||||||
\(235\) | −44.2009 | −2.88335 | ||||||||
\(236\) | −30.2676 | −1.97025 | ||||||||
\(237\) | 18.5296 | 1.20363 | ||||||||
\(238\) | −50.4014 | −3.26704 | ||||||||
\(239\) | 0.851466 | 0.0550767 | 0.0275384 | − | 0.999621i | \(-0.491233\pi\) | ||||
0.0275384 | + | 0.999621i | \(0.491233\pi\) | |||||||
\(240\) | 23.7962 | 1.53604 | ||||||||
\(241\) | −29.7887 | −1.91886 | −0.959429 | − | 0.281949i | \(-0.909019\pi\) | ||||
−0.959429 | + | 0.281949i | \(0.909019\pi\) | |||||||
\(242\) | 2.73483 | 0.175802 | ||||||||
\(243\) | −1.71414 | −0.109962 | ||||||||
\(244\) | 55.1874 | 3.53301 | ||||||||
\(245\) | −56.1593 | −3.58789 | ||||||||
\(246\) | 13.7359 | 0.875769 | ||||||||
\(247\) | −3.14411 | −0.200055 | ||||||||
\(248\) | 9.64699 | 0.612584 | ||||||||
\(249\) | −17.2928 | −1.09588 | ||||||||
\(250\) | −12.5330 | −0.792655 | ||||||||
\(251\) | 24.9382 | 1.57408 | 0.787042 | − | 0.616899i | \(-0.211611\pi\) | ||||
0.787042 | + | 0.616899i | \(0.211611\pi\) | |||||||
\(252\) | −3.22811 | −0.203352 | ||||||||
\(253\) | −19.9826 | −1.25630 | ||||||||
\(254\) | −42.8187 | −2.68668 | ||||||||
\(255\) | −24.1556 | −1.51268 | ||||||||
\(256\) | −32.2027 | −2.01267 | ||||||||
\(257\) | 10.6895 | 0.666794 | 0.333397 | − | 0.942787i | \(-0.391805\pi\) | ||||
0.333397 | + | 0.942787i | \(0.391805\pi\) | |||||||
\(258\) | 12.7491 | 0.793727 | ||||||||
\(259\) | 27.0493 | 1.68076 | ||||||||
\(260\) | 5.82088 | 0.360996 | ||||||||
\(261\) | 0.224482 | 0.0138951 | ||||||||
\(262\) | −34.2274 | −2.11457 | ||||||||
\(263\) | 17.7317 | 1.09339 | 0.546693 | − | 0.837333i | \(-0.315886\pi\) | ||||
0.546693 | + | 0.837333i | \(0.315886\pi\) | |||||||
\(264\) | 29.1729 | 1.79547 | ||||||||
\(265\) | −9.11980 | −0.560225 | ||||||||
\(266\) | 87.9304 | 5.39136 | ||||||||
\(267\) | −5.36811 | −0.328523 | ||||||||
\(268\) | −18.1963 | −1.11152 | ||||||||
\(269\) | −11.0867 | −0.675967 | −0.337984 | − | 0.941152i | \(-0.609745\pi\) | ||||
−0.337984 | + | 0.941152i | \(0.609745\pi\) | |||||||
\(270\) | −44.3789 | −2.70081 | ||||||||
\(271\) | −7.62285 | −0.463055 | −0.231527 | − | 0.972828i | \(-0.574372\pi\) | ||||
−0.231527 | + | 0.972828i | \(0.574372\pi\) | |||||||
\(272\) | −17.6241 | −1.06862 | ||||||||
\(273\) | 3.48191 | 0.210735 | ||||||||
\(274\) | 42.8039 | 2.58588 | ||||||||
\(275\) | −22.6407 | −1.36529 | ||||||||
\(276\) | −38.9340 | −2.34355 | ||||||||
\(277\) | −10.5790 | −0.635628 | −0.317814 | − | 0.948153i | \(-0.602949\pi\) | ||||
−0.317814 | + | 0.948153i | \(0.602949\pi\) | |||||||
\(278\) | 50.6868 | 3.03999 | ||||||||
\(279\) | −0.320006 | −0.0191583 | ||||||||
\(280\) | −81.9545 | −4.89772 | ||||||||
\(281\) | 0.907789 | 0.0541542 | 0.0270771 | − | 0.999633i | \(-0.491380\pi\) | ||||
0.0270771 | + | 0.999633i | \(0.491380\pi\) | |||||||
\(282\) | −53.8677 | −3.20778 | ||||||||
\(283\) | −26.3679 | −1.56741 | −0.783704 | − | 0.621135i | \(-0.786672\pi\) | ||||
−0.783704 | + | 0.621135i | \(0.786672\pi\) | |||||||
\(284\) | −11.9777 | −0.710744 | ||||||||
\(285\) | 42.1420 | 2.49628 | ||||||||
\(286\) | 3.64090 | 0.215291 | ||||||||
\(287\) | −16.1278 | −0.951994 | ||||||||
\(288\) | −0.0451727 | −0.00266183 | ||||||||
\(289\) | 0.890314 | 0.0523714 | ||||||||
\(290\) | 11.3204 | 0.664758 | ||||||||
\(291\) | −18.1586 | −1.06447 | ||||||||
\(292\) | 54.6978 | 3.20095 | ||||||||
\(293\) | −10.9282 | −0.638432 | −0.319216 | − | 0.947682i | \(-0.603420\pi\) | ||||
−0.319216 | + | 0.947682i | \(0.603420\pi\) | |||||||
\(294\) | −68.4414 | −3.99159 | ||||||||
\(295\) | 25.4899 | 1.48408 | ||||||||
\(296\) | 27.7439 | 1.61258 | ||||||||
\(297\) | −18.5482 | −1.07627 | ||||||||
\(298\) | 27.0336 | 1.56601 | ||||||||
\(299\) | −2.44625 | −0.141471 | ||||||||
\(300\) | −44.1130 | −2.54687 | ||||||||
\(301\) | −14.9692 | −0.862811 | ||||||||
\(302\) | 53.7829 | 3.09486 | ||||||||
\(303\) | 8.41381 | 0.483361 | ||||||||
\(304\) | 30.7470 | 1.76346 | ||||||||
\(305\) | −46.4761 | −2.66122 | ||||||||
\(306\) | 1.71483 | 0.0980301 | ||||||||
\(307\) | 17.2644 | 0.985330 | 0.492665 | − | 0.870219i | \(-0.336023\pi\) | ||||
0.492665 | + | 0.870219i | \(0.336023\pi\) | |||||||
\(308\) | −68.0385 | −3.87685 | ||||||||
\(309\) | −30.0449 | −1.70919 | ||||||||
\(310\) | −16.1376 | −0.916555 | ||||||||
\(311\) | −5.26031 | −0.298285 | −0.149142 | − | 0.988816i | \(-0.547651\pi\) | ||||
−0.149142 | + | 0.988816i | \(0.547651\pi\) | |||||||
\(312\) | 3.57132 | 0.202186 | ||||||||
\(313\) | 12.2534 | 0.692602 | 0.346301 | − | 0.938123i | \(-0.387438\pi\) | ||||
0.346301 | + | 0.938123i | \(0.387438\pi\) | |||||||
\(314\) | −30.9145 | −1.74461 | ||||||||
\(315\) | 2.71856 | 0.153174 | ||||||||
\(316\) | −44.3255 | −2.49351 | ||||||||
\(317\) | 26.1884 | 1.47088 | 0.735442 | − | 0.677587i | \(-0.236974\pi\) | ||||
0.735442 | + | 0.677587i | \(0.236974\pi\) | |||||||
\(318\) | −11.1143 | −0.623260 | ||||||||
\(319\) | 4.73137 | 0.264906 | ||||||||
\(320\) | 25.9884 | 1.45279 | ||||||||
\(321\) | 5.78894 | 0.323107 | ||||||||
\(322\) | 68.4137 | 3.81255 | ||||||||
\(323\) | −31.2115 | −1.73665 | ||||||||
\(324\) | −34.1438 | −1.89688 | ||||||||
\(325\) | −2.77166 | −0.153744 | ||||||||
\(326\) | −9.49938 | −0.526122 | ||||||||
\(327\) | 3.73671 | 0.206641 | ||||||||
\(328\) | −16.5420 | −0.913377 | ||||||||
\(329\) | 63.2480 | 3.48698 | ||||||||
\(330\) | −48.8008 | −2.68639 | ||||||||
\(331\) | −26.3473 | −1.44818 | −0.724089 | − | 0.689706i | \(-0.757740\pi\) | ||||
−0.724089 | + | 0.689706i | \(0.757740\pi\) | |||||||
\(332\) | 41.3667 | 2.27029 | ||||||||
\(333\) | −0.920311 | −0.0504327 | ||||||||
\(334\) | −30.9750 | −1.69488 | ||||||||
\(335\) | 15.3241 | 0.837243 | ||||||||
\(336\) | −34.0504 | −1.85760 | ||||||||
\(337\) | 17.1357 | 0.933442 | 0.466721 | − | 0.884405i | \(-0.345435\pi\) | ||||
0.466721 | + | 0.884405i | \(0.345435\pi\) | |||||||
\(338\) | −31.4710 | −1.71180 | ||||||||
\(339\) | −21.6903 | −1.17805 | ||||||||
\(340\) | 57.7837 | 3.13376 | ||||||||
\(341\) | −6.74472 | −0.365247 | ||||||||
\(342\) | −2.99169 | −0.161772 | ||||||||
\(343\) | 46.3847 | 2.50454 | ||||||||
\(344\) | −15.3536 | −0.827811 | ||||||||
\(345\) | 32.7883 | 1.76526 | ||||||||
\(346\) | 20.4569 | 1.09977 | ||||||||
\(347\) | 17.7415 | 0.952416 | 0.476208 | − | 0.879333i | \(-0.342011\pi\) | ||||
0.476208 | + | 0.879333i | \(0.342011\pi\) | |||||||
\(348\) | 9.21858 | 0.494168 | ||||||||
\(349\) | −29.8296 | −1.59674 | −0.798372 | − | 0.602164i | \(-0.794305\pi\) | ||||
−0.798372 | + | 0.602164i | \(0.794305\pi\) | |||||||
\(350\) | 77.5141 | 4.14330 | ||||||||
\(351\) | −2.27065 | −0.121198 | ||||||||
\(352\) | −0.952098 | −0.0507470 | ||||||||
\(353\) | 3.33018 | 0.177248 | 0.0886239 | − | 0.996065i | \(-0.471753\pi\) | ||||
0.0886239 | + | 0.996065i | \(0.471753\pi\) | |||||||
\(354\) | 31.0646 | 1.65106 | ||||||||
\(355\) | 10.0870 | 0.535363 | ||||||||
\(356\) | 12.8413 | 0.680586 | ||||||||
\(357\) | 34.5648 | 1.82936 | ||||||||
\(358\) | −39.2767 | −2.07584 | ||||||||
\(359\) | 12.3715 | 0.652941 | 0.326470 | − | 0.945207i | \(-0.394141\pi\) | ||||
0.326470 | + | 0.945207i | \(0.394141\pi\) | |||||||
\(360\) | 2.78837 | 0.146960 | ||||||||
\(361\) | 35.4517 | 1.86588 | ||||||||
\(362\) | 29.3870 | 1.54455 | ||||||||
\(363\) | −1.87552 | −0.0984394 | ||||||||
\(364\) | −8.32922 | −0.436570 | ||||||||
\(365\) | −46.0638 | −2.41109 | ||||||||
\(366\) | −56.6406 | −2.96065 | ||||||||
\(367\) | 1.46809 | 0.0766338 | 0.0383169 | − | 0.999266i | \(-0.487800\pi\) | ||||
0.0383169 | + | 0.999266i | \(0.487800\pi\) | |||||||
\(368\) | 23.9225 | 1.24705 | ||||||||
\(369\) | 0.548723 | 0.0285654 | ||||||||
\(370\) | −46.4104 | −2.41276 | ||||||||
\(371\) | 13.0497 | 0.677507 | ||||||||
\(372\) | −13.1414 | −0.681349 | ||||||||
\(373\) | 2.17868 | 0.112808 | 0.0564040 | − | 0.998408i | \(-0.482037\pi\) | ||||
0.0564040 | + | 0.998408i | \(0.482037\pi\) | |||||||
\(374\) | 36.1431 | 1.86892 | ||||||||
\(375\) | 8.59500 | 0.443844 | ||||||||
\(376\) | 64.8722 | 3.34553 | ||||||||
\(377\) | 0.579211 | 0.0298309 | ||||||||
\(378\) | 63.5026 | 3.26622 | ||||||||
\(379\) | −33.9374 | −1.74325 | −0.871623 | − | 0.490178i | \(-0.836932\pi\) | ||||
−0.871623 | + | 0.490178i | \(0.836932\pi\) | |||||||
\(380\) | −100.810 | −5.17143 | ||||||||
\(381\) | 29.3646 | 1.50440 | ||||||||
\(382\) | −6.38737 | −0.326806 | ||||||||
\(383\) | 14.0581 | 0.718337 | 0.359169 | − | 0.933273i | \(-0.383060\pi\) | ||||
0.359169 | + | 0.933273i | \(0.383060\pi\) | |||||||
\(384\) | 32.5933 | 1.66327 | ||||||||
\(385\) | 57.2987 | 2.92021 | ||||||||
\(386\) | −19.4400 | −0.989468 | ||||||||
\(387\) | 0.509304 | 0.0258894 | ||||||||
\(388\) | 43.4378 | 2.20522 | ||||||||
\(389\) | −22.7645 | −1.15420 | −0.577102 | − | 0.816672i | \(-0.695817\pi\) | ||||
−0.577102 | + | 0.816672i | \(0.695817\pi\) | |||||||
\(390\) | −5.97415 | −0.302513 | ||||||||
\(391\) | −24.2839 | −1.22809 | ||||||||
\(392\) | 82.4231 | 4.16299 | ||||||||
\(393\) | 23.4728 | 1.18405 | ||||||||
\(394\) | 11.9949 | 0.604293 | ||||||||
\(395\) | 37.3288 | 1.87822 | ||||||||
\(396\) | 2.31490 | 0.116328 | ||||||||
\(397\) | −21.7040 | −1.08929 | −0.544646 | − | 0.838666i | \(-0.683336\pi\) | ||||
−0.544646 | + | 0.838666i | \(0.683336\pi\) | |||||||
\(398\) | 34.0886 | 1.70870 | ||||||||
\(399\) | −60.3019 | −3.01887 | ||||||||
\(400\) | 27.1047 | 1.35523 | ||||||||
\(401\) | 21.6302 | 1.08016 | 0.540080 | − | 0.841614i | \(-0.318394\pi\) | ||||
0.540080 | + | 0.841614i | \(0.318394\pi\) | |||||||
\(402\) | 18.6755 | 0.931447 | ||||||||
\(403\) | −0.825683 | −0.0411302 | ||||||||
\(404\) | −20.1270 | −1.00136 | ||||||||
\(405\) | 28.7543 | 1.42881 | ||||||||
\(406\) | −16.1986 | −0.803924 | ||||||||
\(407\) | −19.3973 | −0.961486 | ||||||||
\(408\) | 35.4524 | 1.75516 | ||||||||
\(409\) | 16.2837 | 0.805177 | 0.402588 | − | 0.915381i | \(-0.368111\pi\) | ||||
0.402588 | + | 0.915381i | \(0.368111\pi\) | |||||||
\(410\) | 27.6716 | 1.36660 | ||||||||
\(411\) | −29.3545 | −1.44795 | ||||||||
\(412\) | 71.8716 | 3.54086 | ||||||||
\(413\) | −36.4740 | −1.79477 | ||||||||
\(414\) | −2.32767 | −0.114399 | ||||||||
\(415\) | −34.8370 | −1.71008 | ||||||||
\(416\) | −0.116555 | −0.00571459 | ||||||||
\(417\) | −34.7605 | −1.70223 | ||||||||
\(418\) | −63.0555 | −3.08414 | ||||||||
\(419\) | −22.5997 | −1.10407 | −0.552034 | − | 0.833821i | \(-0.686148\pi\) | ||||
−0.552034 | + | 0.833821i | \(0.686148\pi\) | |||||||
\(420\) | 111.640 | 5.44750 | ||||||||
\(421\) | −10.7229 | −0.522601 | −0.261301 | − | 0.965257i | \(-0.584151\pi\) | ||||
−0.261301 | + | 0.965257i | \(0.584151\pi\) | |||||||
\(422\) | 26.5010 | 1.29005 | ||||||||
\(423\) | −2.15191 | −0.104630 | ||||||||
\(424\) | 13.3848 | 0.650024 | ||||||||
\(425\) | −27.5142 | −1.33463 | ||||||||
\(426\) | 12.2931 | 0.595601 | ||||||||
\(427\) | 66.5037 | 3.21834 | ||||||||
\(428\) | −13.8480 | −0.669366 | ||||||||
\(429\) | −2.49690 | −0.120551 | ||||||||
\(430\) | 25.6837 | 1.23858 | ||||||||
\(431\) | 10.5556 | 0.508448 | 0.254224 | − | 0.967145i | \(-0.418180\pi\) | ||||
0.254224 | + | 0.967145i | \(0.418180\pi\) | |||||||
\(432\) | 22.2052 | 1.06835 | ||||||||
\(433\) | −9.28043 | −0.445989 | −0.222994 | − | 0.974820i | \(-0.571583\pi\) | ||||
−0.222994 | + | 0.974820i | \(0.571583\pi\) | |||||||
\(434\) | 23.0916 | 1.10843 | ||||||||
\(435\) | −7.76344 | −0.372228 | ||||||||
\(436\) | −8.93875 | −0.428089 | ||||||||
\(437\) | 42.3658 | 2.02663 | ||||||||
\(438\) | −56.1380 | −2.68238 | ||||||||
\(439\) | −2.40958 | −0.115003 | −0.0575014 | − | 0.998345i | \(-0.518313\pi\) | ||||
−0.0575014 | + | 0.998345i | \(0.518313\pi\) | |||||||
\(440\) | 58.7701 | 2.80175 | ||||||||
\(441\) | −2.73411 | −0.130195 | ||||||||
\(442\) | 4.42462 | 0.210458 | ||||||||
\(443\) | 4.00274 | 0.190176 | 0.0950879 | − | 0.995469i | \(-0.469687\pi\) | ||||
0.0950879 | + | 0.995469i | \(0.469687\pi\) | |||||||
\(444\) | −37.7935 | −1.79360 | ||||||||
\(445\) | −10.8143 | −0.512647 | ||||||||
\(446\) | −20.7607 | −0.983046 | ||||||||
\(447\) | −18.5394 | −0.876883 | ||||||||
\(448\) | −37.1873 | −1.75694 | ||||||||
\(449\) | 22.6782 | 1.07025 | 0.535125 | − | 0.844773i | \(-0.320265\pi\) | ||||
0.535125 | + | 0.844773i | \(0.320265\pi\) | |||||||
\(450\) | −2.63729 | −0.124323 | ||||||||
\(451\) | 11.5653 | 0.544591 | ||||||||
\(452\) | 51.8862 | 2.44052 | ||||||||
\(453\) | −36.8838 | −1.73295 | ||||||||
\(454\) | −20.6634 | −0.969781 | ||||||||
\(455\) | 7.01446 | 0.328843 | ||||||||
\(456\) | −61.8504 | −2.89641 | ||||||||
\(457\) | 4.48023 | 0.209576 | 0.104788 | − | 0.994495i | \(-0.466584\pi\) | ||||
0.104788 | + | 0.994495i | \(0.466584\pi\) | |||||||
\(458\) | −47.5069 | −2.21985 | ||||||||
\(459\) | −22.5407 | −1.05211 | ||||||||
\(460\) | −78.4343 | −3.65702 | ||||||||
\(461\) | −13.5759 | −0.632292 | −0.316146 | − | 0.948710i | \(-0.602389\pi\) | ||||
−0.316146 | + | 0.948710i | \(0.602389\pi\) | |||||||
\(462\) | 69.8300 | 3.24879 | ||||||||
\(463\) | −39.1044 | −1.81734 | −0.908668 | − | 0.417520i | \(-0.862899\pi\) | ||||
−0.908668 | + | 0.417520i | \(0.862899\pi\) | |||||||
\(464\) | −5.66424 | −0.262956 | ||||||||
\(465\) | 11.0670 | 0.513221 | ||||||||
\(466\) | −4.23989 | −0.196409 | ||||||||
\(467\) | 36.9311 | 1.70897 | 0.854483 | − | 0.519479i | \(-0.173874\pi\) | ||||
0.854483 | + | 0.519479i | \(0.173874\pi\) | |||||||
\(468\) | 0.283388 | 0.0130996 | ||||||||
\(469\) | −21.9275 | −1.01252 | ||||||||
\(470\) | −108.519 | −5.00561 | ||||||||
\(471\) | 21.2009 | 0.976885 | ||||||||
\(472\) | −37.4106 | −1.72196 | ||||||||
\(473\) | 10.7345 | 0.493574 | ||||||||
\(474\) | 45.4927 | 2.08955 | ||||||||
\(475\) | 48.0013 | 2.20245 | ||||||||
\(476\) | −82.6839 | −3.78981 | ||||||||
\(477\) | −0.443996 | −0.0203292 | ||||||||
\(478\) | 2.09046 | 0.0956154 | ||||||||
\(479\) | −9.60238 | −0.438744 | −0.219372 | − | 0.975641i | \(-0.570401\pi\) | ||||
−0.219372 | + | 0.975641i | \(0.570401\pi\) | |||||||
\(480\) | 1.56224 | 0.0713064 | ||||||||
\(481\) | −2.37460 | −0.108272 | ||||||||
\(482\) | −73.1351 | −3.33121 | ||||||||
\(483\) | −46.9175 | −2.13482 | ||||||||
\(484\) | 4.48652 | 0.203933 | ||||||||
\(485\) | −36.5812 | −1.66107 | ||||||||
\(486\) | −4.20843 | −0.190898 | ||||||||
\(487\) | −7.82233 | −0.354464 | −0.177232 | − | 0.984169i | \(-0.556714\pi\) | ||||
−0.177232 | + | 0.984169i | \(0.556714\pi\) | |||||||
\(488\) | 68.2114 | 3.08779 | ||||||||
\(489\) | 6.51459 | 0.294600 | ||||||||
\(490\) | −137.878 | −6.22871 | ||||||||
\(491\) | −31.0270 | −1.40023 | −0.700114 | − | 0.714031i | \(-0.746867\pi\) | ||||
−0.700114 | + | 0.714031i | \(0.746867\pi\) | |||||||
\(492\) | 22.5339 | 1.01591 | ||||||||
\(493\) | 5.74981 | 0.258958 | ||||||||
\(494\) | −7.71920 | −0.347303 | ||||||||
\(495\) | −1.94950 | −0.0876234 | ||||||||
\(496\) | 8.07456 | 0.362558 | ||||||||
\(497\) | −14.4337 | −0.647441 | ||||||||
\(498\) | −42.4560 | −1.90250 | ||||||||
\(499\) | −38.2468 | −1.71216 | −0.856080 | − | 0.516843i | \(-0.827107\pi\) | ||||
−0.856080 | + | 0.516843i | \(0.827107\pi\) | |||||||
\(500\) | −20.5605 | −0.919492 | ||||||||
\(501\) | 21.2424 | 0.949039 | ||||||||
\(502\) | 61.2265 | 2.73267 | ||||||||
\(503\) | 4.97067 | 0.221631 | 0.110816 | − | 0.993841i | \(-0.464654\pi\) | ||||
0.110816 | + | 0.993841i | \(0.464654\pi\) | |||||||
\(504\) | −3.98994 | −0.177726 | ||||||||
\(505\) | 16.9500 | 0.754265 | ||||||||
\(506\) | −49.0599 | −2.18098 | ||||||||
\(507\) | 21.5825 | 0.958513 | ||||||||
\(508\) | −70.2444 | −3.11659 | ||||||||
\(509\) | −18.1195 | −0.803134 | −0.401567 | − | 0.915830i | \(-0.631534\pi\) | ||||
−0.401567 | + | 0.915830i | \(0.631534\pi\) | |||||||
\(510\) | −59.3052 | −2.62608 | ||||||||
\(511\) | 65.9136 | 2.91585 | ||||||||
\(512\) | −40.3458 | −1.78305 | ||||||||
\(513\) | 39.3246 | 1.73622 | ||||||||
\(514\) | 26.2442 | 1.15758 | ||||||||
\(515\) | −60.5268 | −2.66713 | ||||||||
\(516\) | 20.9151 | 0.920735 | ||||||||
\(517\) | −45.3555 | −1.99473 | ||||||||
\(518\) | 66.4096 | 2.91787 | ||||||||
\(519\) | −14.0292 | −0.615813 | ||||||||
\(520\) | 7.19459 | 0.315503 | ||||||||
\(521\) | −41.9498 | −1.83786 | −0.918928 | − | 0.394426i | \(-0.870943\pi\) | ||||
−0.918928 | + | 0.394426i | \(0.870943\pi\) | |||||||
\(522\) | 0.551132 | 0.0241224 | ||||||||
\(523\) | 25.5330 | 1.11648 | 0.558239 | − | 0.829680i | \(-0.311477\pi\) | ||||
0.558239 | + | 0.829680i | \(0.311477\pi\) | |||||||
\(524\) | −56.1503 | −2.45294 | ||||||||
\(525\) | −53.1585 | −2.32003 | ||||||||
\(526\) | 43.5337 | 1.89816 | ||||||||
\(527\) | −8.19654 | −0.357047 | ||||||||
\(528\) | 24.4178 | 1.06265 | ||||||||
\(529\) | 9.96243 | 0.433149 | ||||||||
\(530\) | −22.3903 | −0.972573 | ||||||||
\(531\) | 1.24097 | 0.0538535 | ||||||||
\(532\) | 144.251 | 6.25406 | ||||||||
\(533\) | 1.41582 | 0.0613260 | ||||||||
\(534\) | −13.1794 | −0.570329 | ||||||||
\(535\) | 11.6621 | 0.504195 | ||||||||
\(536\) | −22.4906 | −0.971446 | ||||||||
\(537\) | 26.9356 | 1.16236 | ||||||||
\(538\) | −27.2193 | −1.17351 | ||||||||
\(539\) | −57.6263 | −2.48214 | ||||||||
\(540\) | −72.8039 | −3.13298 | ||||||||
\(541\) | 39.2494 | 1.68746 | 0.843732 | − | 0.536764i | \(-0.180354\pi\) | ||||
0.843732 | + | 0.536764i | \(0.180354\pi\) | |||||||
\(542\) | −18.7151 | −0.803881 | ||||||||
\(543\) | −20.1533 | −0.864863 | ||||||||
\(544\) | −1.15704 | −0.0496077 | ||||||||
\(545\) | 7.52778 | 0.322455 | ||||||||
\(546\) | 8.54853 | 0.365844 | ||||||||
\(547\) | 9.71122 | 0.415222 | 0.207611 | − | 0.978211i | \(-0.433431\pi\) | ||||
0.207611 | + | 0.978211i | \(0.433431\pi\) | |||||||
\(548\) | 70.2202 | 2.99966 | ||||||||
\(549\) | −2.26268 | −0.0965689 | ||||||||
\(550\) | −55.5859 | −2.37019 | ||||||||
\(551\) | −10.0311 | −0.427341 | ||||||||
\(552\) | −48.1223 | −2.04822 | ||||||||
\(553\) | −53.4146 | −2.27142 | ||||||||
\(554\) | −25.9727 | −1.10347 | ||||||||
\(555\) | 31.8278 | 1.35102 | ||||||||
\(556\) | 83.1522 | 3.52644 | ||||||||
\(557\) | −21.9292 | −0.929169 | −0.464584 | − | 0.885529i | \(-0.653796\pi\) | ||||
−0.464584 | + | 0.885529i | \(0.653796\pi\) | |||||||
\(558\) | −0.785657 | −0.0332595 | ||||||||
\(559\) | 1.31411 | 0.0555810 | ||||||||
\(560\) | −68.5961 | −2.89871 | ||||||||
\(561\) | −24.7866 | −1.04649 | ||||||||
\(562\) | 2.22874 | 0.0940138 | ||||||||
\(563\) | −20.3681 | −0.858413 | −0.429207 | − | 0.903206i | \(-0.641207\pi\) | ||||
−0.429207 | + | 0.903206i | \(0.641207\pi\) | |||||||
\(564\) | −88.3705 | −3.72107 | ||||||||
\(565\) | −43.6961 | −1.83831 | ||||||||
\(566\) | −64.7366 | −2.72108 | ||||||||
\(567\) | −41.1451 | −1.72793 | ||||||||
\(568\) | −14.8044 | −0.621178 | ||||||||
\(569\) | 10.1505 | 0.425530 | 0.212765 | − | 0.977103i | \(-0.431753\pi\) | ||||
0.212765 | + | 0.977103i | \(0.431753\pi\) | |||||||
\(570\) | 103.464 | 4.33364 | ||||||||
\(571\) | −22.4729 | −0.940462 | −0.470231 | − | 0.882543i | \(-0.655829\pi\) | ||||
−0.470231 | + | 0.882543i | \(0.655829\pi\) | |||||||
\(572\) | 5.97293 | 0.249741 | ||||||||
\(573\) | 4.38040 | 0.182994 | ||||||||
\(574\) | −39.5959 | −1.65270 | ||||||||
\(575\) | 37.3471 | 1.55748 | ||||||||
\(576\) | 1.26524 | 0.0527183 | ||||||||
\(577\) | 4.10618 | 0.170943 | 0.0854713 | − | 0.996341i | \(-0.472760\pi\) | ||||
0.0854713 | + | 0.996341i | \(0.472760\pi\) | |||||||
\(578\) | 2.18584 | 0.0909188 | ||||||||
\(579\) | 13.3318 | 0.554049 | ||||||||
\(580\) | 18.5713 | 0.771129 | ||||||||
\(581\) | 49.8490 | 2.06809 | ||||||||
\(582\) | −44.5816 | −1.84797 | ||||||||
\(583\) | −9.35803 | −0.387570 | ||||||||
\(584\) | 67.6063 | 2.79757 | ||||||||
\(585\) | −0.238656 | −0.00986721 | ||||||||
\(586\) | −26.8301 | −1.10834 | ||||||||
\(587\) | 22.9876 | 0.948798 | 0.474399 | − | 0.880310i | \(-0.342665\pi\) | ||||
0.474399 | + | 0.880310i | \(0.342665\pi\) | |||||||
\(588\) | −112.279 | −4.63030 | ||||||||
\(589\) | 14.2997 | 0.589209 | ||||||||
\(590\) | 62.5810 | 2.57642 | ||||||||
\(591\) | −8.22598 | −0.338371 | ||||||||
\(592\) | 23.2218 | 0.954408 | ||||||||
\(593\) | 1.78019 | 0.0731037 | 0.0365518 | − | 0.999332i | \(-0.488363\pi\) | ||||
0.0365518 | + | 0.999332i | \(0.488363\pi\) | |||||||
\(594\) | −45.5381 | −1.86845 | ||||||||
\(595\) | 69.6324 | 2.85465 | ||||||||
\(596\) | 44.3489 | 1.81660 | ||||||||
\(597\) | −23.3776 | −0.956782 | ||||||||
\(598\) | −6.00587 | −0.245598 | ||||||||
\(599\) | −9.79284 | −0.400124 | −0.200062 | − | 0.979783i | \(-0.564114\pi\) | ||||
−0.200062 | + | 0.979783i | \(0.564114\pi\) | |||||||
\(600\) | −54.5235 | −2.22591 | ||||||||
\(601\) | 38.0291 | 1.55124 | 0.775619 | − | 0.631201i | \(-0.217438\pi\) | ||||
0.775619 | + | 0.631201i | \(0.217438\pi\) | |||||||
\(602\) | −36.7514 | −1.49787 | ||||||||
\(603\) | 0.746049 | 0.0303815 | ||||||||
\(604\) | 88.2313 | 3.59008 | ||||||||
\(605\) | −3.77833 | −0.153611 | ||||||||
\(606\) | 20.6570 | 0.839133 | ||||||||
\(607\) | −8.30354 | −0.337030 | −0.168515 | − | 0.985699i | \(-0.553897\pi\) | ||||
−0.168515 | + | 0.985699i | \(0.553897\pi\) | |||||||
\(608\) | 2.01858 | 0.0818641 | ||||||||
\(609\) | 11.1089 | 0.450154 | ||||||||
\(610\) | −114.105 | −4.61998 | ||||||||
\(611\) | −5.55239 | −0.224626 | ||||||||
\(612\) | 2.81319 | 0.113716 | ||||||||
\(613\) | −25.6858 | −1.03744 | −0.518720 | − | 0.854944i | \(-0.673591\pi\) | ||||
−0.518720 | + | 0.854944i | \(0.673591\pi\) | |||||||
\(614\) | 42.3863 | 1.71057 | ||||||||
\(615\) | −18.9769 | −0.765224 | ||||||||
\(616\) | −84.0953 | −3.38830 | ||||||||
\(617\) | 5.44989 | 0.219404 | 0.109702 | − | 0.993964i | \(-0.465010\pi\) | ||||
0.109702 | + | 0.993964i | \(0.465010\pi\) | |||||||
\(618\) | −73.7641 | −2.96723 | ||||||||
\(619\) | −3.76621 | −0.151377 | −0.0756885 | − | 0.997132i | \(-0.524115\pi\) | ||||
−0.0756885 | + | 0.997132i | \(0.524115\pi\) | |||||||
\(620\) | −26.4739 | −1.06322 | ||||||||
\(621\) | 30.5962 | 1.22778 | ||||||||
\(622\) | −12.9147 | −0.517834 | ||||||||
\(623\) | 15.4744 | 0.619969 | ||||||||
\(624\) | 2.98920 | 0.119664 | ||||||||
\(625\) | −15.2100 | −0.608399 | ||||||||
\(626\) | 30.0837 | 1.20238 | ||||||||
\(627\) | 43.2429 | 1.72695 | ||||||||
\(628\) | −50.7155 | −2.02377 | ||||||||
\(629\) | −23.5726 | −0.939899 | ||||||||
\(630\) | 6.67442 | 0.265915 | ||||||||
\(631\) | −42.3230 | −1.68485 | −0.842427 | − | 0.538810i | \(-0.818874\pi\) | ||||
−0.842427 | + | 0.538810i | \(0.818874\pi\) | |||||||
\(632\) | −54.7862 | −2.17928 | ||||||||
\(633\) | −18.1742 | −0.722359 | ||||||||
\(634\) | 64.2958 | 2.55351 | ||||||||
\(635\) | 59.1564 | 2.34755 | ||||||||
\(636\) | −18.2331 | −0.722991 | ||||||||
\(637\) | −7.05457 | −0.279512 | ||||||||
\(638\) | 11.6161 | 0.459887 | ||||||||
\(639\) | 0.491085 | 0.0194270 | ||||||||
\(640\) | 65.6606 | 2.59546 | ||||||||
\(641\) | −14.9924 | −0.592163 | −0.296082 | − | 0.955163i | \(-0.595680\pi\) | ||||
−0.296082 | + | 0.955163i | \(0.595680\pi\) | |||||||
\(642\) | 14.2126 | 0.560926 | ||||||||
\(643\) | −2.76592 | −0.109077 | −0.0545386 | − | 0.998512i | \(-0.517369\pi\) | ||||
−0.0545386 | + | 0.998512i | \(0.517369\pi\) | |||||||
\(644\) | 112.233 | 4.42261 | ||||||||
\(645\) | −17.6137 | −0.693537 | ||||||||
\(646\) | −76.6283 | −3.01490 | ||||||||
\(647\) | −23.5620 | −0.926319 | −0.463159 | − | 0.886275i | \(-0.653284\pi\) | ||||
−0.463159 | + | 0.886275i | \(0.653284\pi\) | |||||||
\(648\) | −42.2017 | −1.65784 | ||||||||
\(649\) | 26.1557 | 1.02670 | ||||||||
\(650\) | −6.80478 | −0.266905 | ||||||||
\(651\) | −15.8360 | −0.620663 | ||||||||
\(652\) | −15.5838 | −0.610309 | ||||||||
\(653\) | −11.5492 | −0.451957 | −0.225978 | − | 0.974132i | \(-0.572558\pi\) | ||||
−0.225978 | + | 0.974132i | \(0.572558\pi\) | |||||||
\(654\) | 9.17412 | 0.358737 | ||||||||
\(655\) | 47.2871 | 1.84766 | ||||||||
\(656\) | −13.8457 | −0.540582 | ||||||||
\(657\) | −2.24261 | −0.0874925 | ||||||||
\(658\) | 155.282 | 6.05353 | ||||||||
\(659\) | −23.0029 | −0.896065 | −0.448033 | − | 0.894017i | \(-0.647875\pi\) | ||||
−0.448033 | + | 0.894017i | \(0.647875\pi\) | |||||||
\(660\) | −80.0581 | −3.11626 | ||||||||
\(661\) | −38.7427 | −1.50692 | −0.753459 | − | 0.657495i | \(-0.771616\pi\) | ||||
−0.753459 | + | 0.657495i | \(0.771616\pi\) | |||||||
\(662\) | −64.6861 | −2.51410 | ||||||||
\(663\) | −3.03436 | −0.117845 | ||||||||
\(664\) | 51.1291 | 1.98419 | ||||||||
\(665\) | −121.481 | −4.71083 | ||||||||
\(666\) | −2.25948 | −0.0875532 | ||||||||
\(667\) | −7.80466 | −0.302198 | ||||||||
\(668\) | −50.8147 | −1.96608 | ||||||||
\(669\) | 14.2375 | 0.550453 | ||||||||
\(670\) | 37.6225 | 1.45349 | ||||||||
\(671\) | −47.6902 | −1.84106 | ||||||||
\(672\) | −2.23545 | −0.0862343 | ||||||||
\(673\) | 1.09656 | 0.0422692 | 0.0211346 | − | 0.999777i | \(-0.493272\pi\) | ||||
0.0211346 | + | 0.999777i | \(0.493272\pi\) | |||||||
\(674\) | 42.0704 | 1.62049 | ||||||||
\(675\) | 34.6662 | 1.33430 | ||||||||
\(676\) | −51.6284 | −1.98571 | ||||||||
\(677\) | 14.8640 | 0.571269 | 0.285634 | − | 0.958339i | \(-0.407796\pi\) | ||||
0.285634 | + | 0.958339i | \(0.407796\pi\) | |||||||
\(678\) | −53.2525 | −2.04515 | ||||||||
\(679\) | 52.3448 | 2.00881 | ||||||||
\(680\) | 71.4205 | 2.73885 | ||||||||
\(681\) | 14.1708 | 0.543025 | ||||||||
\(682\) | −16.5592 | −0.634083 | ||||||||
\(683\) | 7.91661 | 0.302921 | 0.151460 | − | 0.988463i | \(-0.451602\pi\) | ||||
0.151460 | + | 0.988463i | \(0.451602\pi\) | |||||||
\(684\) | −4.90790 | −0.187658 | ||||||||
\(685\) | −59.1360 | −2.25947 | ||||||||
\(686\) | 113.880 | 4.34798 | ||||||||
\(687\) | 32.5798 | 1.24300 | ||||||||
\(688\) | −12.8510 | −0.489940 | ||||||||
\(689\) | −1.14560 | −0.0436440 | ||||||||
\(690\) | 80.4996 | 3.06457 | ||||||||
\(691\) | 17.8706 | 0.679829 | 0.339914 | − | 0.940456i | \(-0.389602\pi\) | ||||
0.339914 | + | 0.940456i | \(0.389602\pi\) | |||||||
\(692\) | 33.5598 | 1.27575 | ||||||||
\(693\) | 2.78958 | 0.105967 | ||||||||
\(694\) | 43.5578 | 1.65343 | ||||||||
\(695\) | −70.0267 | −2.65626 | ||||||||
\(696\) | 11.3941 | 0.431894 | ||||||||
\(697\) | 14.0548 | 0.532364 | ||||||||
\(698\) | −73.2357 | −2.77201 | ||||||||
\(699\) | 2.90768 | 0.109978 | ||||||||
\(700\) | 127.163 | 4.80629 | ||||||||
\(701\) | 42.3565 | 1.59978 | 0.799892 | − | 0.600144i | \(-0.204890\pi\) | ||||
0.799892 | + | 0.600144i | \(0.204890\pi\) | |||||||
\(702\) | −5.57474 | −0.210405 | ||||||||
\(703\) | 41.1248 | 1.55105 | ||||||||
\(704\) | 26.6673 | 1.00506 | ||||||||
\(705\) | 74.4214 | 2.80287 | ||||||||
\(706\) | 8.17604 | 0.307709 | ||||||||
\(707\) | −24.2541 | −0.912169 | ||||||||
\(708\) | 50.9617 | 1.91526 | ||||||||
\(709\) | 24.1365 | 0.906467 | 0.453233 | − | 0.891392i | \(-0.350270\pi\) | ||||
0.453233 | + | 0.891392i | \(0.350270\pi\) | |||||||
\(710\) | 24.7649 | 0.929412 | ||||||||
\(711\) | 1.81735 | 0.0681558 | ||||||||
\(712\) | 15.8718 | 0.594820 | ||||||||
\(713\) | 11.1258 | 0.416664 | ||||||||
\(714\) | 84.8611 | 3.17585 | ||||||||
\(715\) | −5.03011 | −0.188116 | ||||||||
\(716\) | −64.4338 | −2.40800 | ||||||||
\(717\) | −1.43362 | −0.0535394 | ||||||||
\(718\) | 30.3736 | 1.13353 | ||||||||
\(719\) | −21.3950 | −0.797901 | −0.398950 | − | 0.916973i | \(-0.630625\pi\) | ||||
−0.398950 | + | 0.916973i | \(0.630625\pi\) | |||||||
\(720\) | 2.33387 | 0.0869784 | ||||||||
\(721\) | 86.6090 | 3.22549 | ||||||||
\(722\) | 87.0385 | 3.23924 | ||||||||
\(723\) | 50.1554 | 1.86530 | ||||||||
\(724\) | 48.2097 | 1.79170 | ||||||||
\(725\) | −8.84284 | −0.328415 | ||||||||
\(726\) | −4.60465 | −0.170895 | ||||||||
\(727\) | −3.36788 | −0.124908 | −0.0624538 | − | 0.998048i | \(-0.519893\pi\) | ||||
−0.0624538 | + | 0.998048i | \(0.519893\pi\) | |||||||
\(728\) | −10.2949 | −0.381554 | ||||||||
\(729\) | 28.3181 | 1.04882 | ||||||||
\(730\) | −113.093 | −4.18575 | ||||||||
\(731\) | 13.0452 | 0.482492 | ||||||||
\(732\) | −92.9194 | −3.43440 | ||||||||
\(733\) | 3.98604 | 0.147228 | 0.0736139 | − | 0.997287i | \(-0.476547\pi\) | ||||
0.0736139 | + | 0.997287i | \(0.476547\pi\) | |||||||
\(734\) | 3.60436 | 0.133039 | ||||||||
\(735\) | 94.5557 | 3.48774 | ||||||||
\(736\) | 1.57054 | 0.0578909 | ||||||||
\(737\) | 15.7244 | 0.579214 | ||||||||
\(738\) | 1.34719 | 0.0495906 | ||||||||
\(739\) | 49.4424 | 1.81877 | 0.909385 | − | 0.415956i | \(-0.136553\pi\) | ||||
0.909385 | + | 0.415956i | \(0.136553\pi\) | |||||||
\(740\) | −76.1367 | −2.79884 | ||||||||
\(741\) | 5.29376 | 0.194471 | ||||||||
\(742\) | 32.0387 | 1.17618 | ||||||||
\(743\) | −18.2597 | −0.669884 | −0.334942 | − | 0.942239i | \(-0.608717\pi\) | ||||
−0.334942 | + | 0.942239i | \(0.608717\pi\) | |||||||
\(744\) | −16.2427 | −0.595486 | ||||||||
\(745\) | −37.3485 | −1.36834 | ||||||||
\(746\) | 5.34895 | 0.195839 | ||||||||
\(747\) | −1.69603 | −0.0620547 | ||||||||
\(748\) | 59.2932 | 2.16797 | ||||||||
\(749\) | −16.6875 | −0.609748 | ||||||||
\(750\) | 21.1019 | 0.770531 | ||||||||
\(751\) | 49.9351 | 1.82216 | 0.911079 | − | 0.412231i | \(-0.135250\pi\) | ||||
0.911079 | + | 0.412231i | \(0.135250\pi\) | |||||||
\(752\) | 54.2982 | 1.98005 | ||||||||
\(753\) | −41.9886 | −1.53015 | ||||||||
\(754\) | 1.42204 | 0.0517876 | ||||||||
\(755\) | −74.3041 | −2.70420 | ||||||||
\(756\) | 104.177 | 3.78887 | ||||||||
\(757\) | −27.7753 | −1.00951 | −0.504755 | − | 0.863263i | \(-0.668417\pi\) | ||||
−0.504755 | + | 0.863263i | \(0.668417\pi\) | |||||||
\(758\) | −83.3206 | −3.02634 | ||||||||
\(759\) | 33.6448 | 1.22123 | ||||||||
\(760\) | −124.600 | −4.51973 | ||||||||
\(761\) | 8.08376 | 0.293036 | 0.146518 | − | 0.989208i | \(-0.453193\pi\) | ||||
0.146518 | + | 0.989208i | \(0.453193\pi\) | |||||||
\(762\) | 72.0940 | 2.61169 | ||||||||
\(763\) | −10.7717 | −0.389960 | ||||||||
\(764\) | −10.4785 | −0.379100 | ||||||||
\(765\) | −2.36913 | −0.0856561 | ||||||||
\(766\) | 34.5146 | 1.24706 | ||||||||
\(767\) | 3.20196 | 0.115616 | ||||||||
\(768\) | 54.2199 | 1.95649 | ||||||||
\(769\) | 8.00443 | 0.288647 | 0.144324 | − | 0.989531i | \(-0.453899\pi\) | ||||
0.144324 | + | 0.989531i | \(0.453899\pi\) | |||||||
\(770\) | 140.676 | 5.06960 | ||||||||
\(771\) | −17.9980 | −0.648183 | ||||||||
\(772\) | −31.8915 | −1.14780 | ||||||||
\(773\) | 51.7562 | 1.86154 | 0.930771 | − | 0.365603i | \(-0.119137\pi\) | ||||
0.930771 | + | 0.365603i | \(0.119137\pi\) | |||||||
\(774\) | 1.25041 | 0.0449450 | ||||||||
\(775\) | 12.6058 | 0.452812 | ||||||||
\(776\) | 53.6890 | 1.92732 | ||||||||
\(777\) | −45.5431 | −1.63385 | ||||||||
\(778\) | −55.8897 | −2.00374 | ||||||||
\(779\) | −24.5201 | −0.878523 | ||||||||
\(780\) | −9.80065 | −0.350920 | ||||||||
\(781\) | 10.3505 | 0.370371 | ||||||||
\(782\) | −59.6202 | −2.13201 | ||||||||
\(783\) | −7.24441 | −0.258894 | ||||||||
\(784\) | 68.9883 | 2.46387 | ||||||||
\(785\) | 42.7102 | 1.52439 | ||||||||
\(786\) | 57.6288 | 2.05555 | ||||||||
\(787\) | 38.6301 | 1.37702 | 0.688508 | − | 0.725229i | \(-0.258266\pi\) | ||||
0.688508 | + | 0.725229i | \(0.258266\pi\) | |||||||
\(788\) | 19.6777 | 0.700989 | ||||||||
\(789\) | −29.8550 | −1.06287 | ||||||||
\(790\) | 91.6471 | 3.26066 | ||||||||
\(791\) | 62.5256 | 2.22315 | ||||||||
\(792\) | 2.86121 | 0.101669 | ||||||||
\(793\) | −5.83820 | −0.207321 | ||||||||
\(794\) | −53.2861 | −1.89105 | ||||||||
\(795\) | 15.3551 | 0.544588 | ||||||||
\(796\) | 55.9226 | 1.98212 | ||||||||
\(797\) | −46.6619 | −1.65285 | −0.826424 | − | 0.563048i | \(-0.809629\pi\) | ||||
−0.826424 | + | 0.563048i | \(0.809629\pi\) | |||||||
\(798\) | −148.049 | −5.24088 | ||||||||
\(799\) | −55.1184 | −1.94995 | ||||||||
\(800\) | 1.77945 | 0.0629132 | ||||||||
\(801\) | −0.526492 | −0.0186027 | ||||||||
\(802\) | 53.1049 | 1.87520 | ||||||||
\(803\) | −47.2671 | −1.66802 | ||||||||
\(804\) | 30.6373 | 1.08049 | ||||||||
\(805\) | −94.5174 | −3.33130 | ||||||||
\(806\) | −2.02716 | −0.0714037 | ||||||||
\(807\) | 18.6667 | 0.657100 | ||||||||
\(808\) | −24.8769 | −0.875167 | ||||||||
\(809\) | 26.5733 | 0.934267 | 0.467133 | − | 0.884187i | \(-0.345287\pi\) | ||||
0.467133 | + | 0.884187i | \(0.345287\pi\) | |||||||
\(810\) | 70.5955 | 2.48047 | ||||||||
\(811\) | 32.5016 | 1.14129 | 0.570644 | − | 0.821198i | \(-0.306694\pi\) | ||||
0.570644 | + | 0.821198i | \(0.306694\pi\) | |||||||
\(812\) | −26.5740 | −0.932564 | ||||||||
\(813\) | 12.8346 | 0.450130 | ||||||||
\(814\) | −47.6228 | −1.66918 | ||||||||
\(815\) | 13.1239 | 0.459711 | ||||||||
\(816\) | 29.6738 | 1.03879 | ||||||||
\(817\) | −22.7586 | −0.796223 | ||||||||
\(818\) | 39.9786 | 1.39782 | ||||||||
\(819\) | 0.341498 | 0.0119329 | ||||||||
\(820\) | 45.3955 | 1.58528 | ||||||||
\(821\) | −43.7002 | −1.52515 | −0.762573 | − | 0.646902i | \(-0.776064\pi\) | ||||
−0.762573 | + | 0.646902i | \(0.776064\pi\) | |||||||
\(822\) | −72.0692 | −2.51370 | ||||||||
\(823\) | 32.0137 | 1.11593 | 0.557964 | − | 0.829865i | \(-0.311583\pi\) | ||||
0.557964 | + | 0.829865i | \(0.311583\pi\) | |||||||
\(824\) | 88.8331 | 3.09465 | ||||||||
\(825\) | 38.1203 | 1.32718 | ||||||||
\(826\) | −89.5484 | −3.11579 | ||||||||
\(827\) | −24.0050 | −0.834735 | −0.417368 | − | 0.908738i | \(-0.637047\pi\) | ||||
−0.417368 | + | 0.908738i | \(0.637047\pi\) | |||||||
\(828\) | −3.81856 | −0.132704 | ||||||||
\(829\) | −46.8935 | −1.62868 | −0.814339 | − | 0.580390i | \(-0.802900\pi\) | ||||
−0.814339 | + | 0.580390i | \(0.802900\pi\) | |||||||
\(830\) | −85.5295 | −2.96877 | ||||||||
\(831\) | 17.8118 | 0.617886 | ||||||||
\(832\) | 3.26459 | 0.113179 | ||||||||
\(833\) | −70.0305 | −2.42641 | ||||||||
\(834\) | −85.3417 | −2.95514 | ||||||||
\(835\) | 42.7937 | 1.48094 | ||||||||
\(836\) | −103.443 | −3.57765 | ||||||||
\(837\) | 10.3271 | 0.356958 | ||||||||
\(838\) | −55.4853 | −1.91671 | ||||||||
\(839\) | 23.7493 | 0.819917 | 0.409958 | − | 0.912104i | \(-0.365543\pi\) | ||||
0.409958 | + | 0.912104i | \(0.365543\pi\) | |||||||
\(840\) | 137.987 | 4.76101 | ||||||||
\(841\) | −27.1521 | −0.936278 | ||||||||
\(842\) | −26.3261 | −0.907257 | ||||||||
\(843\) | −1.52845 | −0.0526426 | ||||||||
\(844\) | 43.4752 | 1.49648 | ||||||||
\(845\) | 43.4789 | 1.49572 | ||||||||
\(846\) | −5.28323 | −0.181641 | ||||||||
\(847\) | 5.40648 | 0.185769 | ||||||||
\(848\) | 11.2031 | 0.384717 | ||||||||
\(849\) | 44.3958 | 1.52366 | ||||||||
\(850\) | −67.5508 | −2.31697 | ||||||||
\(851\) | 31.9969 | 1.09684 | ||||||||
\(852\) | 20.1669 | 0.690906 | ||||||||
\(853\) | 42.5399 | 1.45654 | 0.728269 | − | 0.685292i | \(-0.240325\pi\) | ||||
0.728269 | + | 0.685292i | \(0.240325\pi\) | |||||||
\(854\) | 163.275 | 5.58716 | ||||||||
\(855\) | 4.13319 | 0.141352 | ||||||||
\(856\) | −17.1160 | −0.585014 | ||||||||
\(857\) | −3.36702 | −0.115015 | −0.0575076 | − | 0.998345i | \(-0.518315\pi\) | ||||
−0.0575076 | + | 0.998345i | \(0.518315\pi\) | |||||||
\(858\) | −6.13021 | −0.209282 | ||||||||
\(859\) | −15.4734 | −0.527945 | −0.263972 | − | 0.964530i | \(-0.585033\pi\) | ||||
−0.263972 | + | 0.964530i | \(0.585033\pi\) | |||||||
\(860\) | 42.1344 | 1.43677 | ||||||||
\(861\) | 27.1545 | 0.925422 | ||||||||
\(862\) | 25.9155 | 0.882685 | ||||||||
\(863\) | 41.0989 | 1.39902 | 0.699511 | − | 0.714622i | \(-0.253401\pi\) | ||||
0.699511 | + | 0.714622i | \(0.253401\pi\) | |||||||
\(864\) | 1.45780 | 0.0495953 | ||||||||
\(865\) | −28.2624 | −0.960951 | ||||||||
\(866\) | −22.7847 | −0.774254 | ||||||||
\(867\) | −1.49903 | −0.0509096 | ||||||||
\(868\) | 37.8820 | 1.28580 | ||||||||
\(869\) | 38.3039 | 1.29937 | ||||||||
\(870\) | −19.0603 | −0.646203 | ||||||||
\(871\) | 1.92496 | 0.0652249 | ||||||||
\(872\) | −11.0483 | −0.374142 | ||||||||
\(873\) | −1.78095 | −0.0602760 | ||||||||
\(874\) | 104.014 | 3.51831 | ||||||||
\(875\) | −24.7764 | −0.837596 | ||||||||
\(876\) | −92.0950 | −3.11160 | ||||||||
\(877\) | 42.0576 | 1.42018 | 0.710092 | − | 0.704109i | \(-0.248653\pi\) | ||||
0.710092 | + | 0.704109i | \(0.248653\pi\) | |||||||
\(878\) | −5.91582 | −0.199649 | ||||||||
\(879\) | 18.3999 | 0.620612 | ||||||||
\(880\) | 49.1907 | 1.65822 | ||||||||
\(881\) | 21.8530 | 0.736246 | 0.368123 | − | 0.929777i | \(-0.380001\pi\) | ||||
0.368123 | + | 0.929777i | \(0.380001\pi\) | |||||||
\(882\) | −6.71258 | −0.226024 | ||||||||
\(883\) | −4.84112 | −0.162917 | −0.0814583 | − | 0.996677i | \(-0.525958\pi\) | ||||
−0.0814583 | + | 0.996677i | \(0.525958\pi\) | |||||||
\(884\) | 7.25862 | 0.244134 | ||||||||
\(885\) | −42.9175 | −1.44265 | ||||||||
\(886\) | 9.82725 | 0.330153 | ||||||||
\(887\) | −7.88437 | −0.264731 | −0.132366 | − | 0.991201i | \(-0.542257\pi\) | ||||
−0.132366 | + | 0.991201i | \(0.542257\pi\) | |||||||
\(888\) | −46.7126 | −1.56757 | ||||||||
\(889\) | −84.6481 | −2.83901 | ||||||||
\(890\) | −26.5505 | −0.889975 | ||||||||
\(891\) | 29.5054 | 0.988468 | ||||||||
\(892\) | −34.0581 | −1.14035 | ||||||||
\(893\) | 96.1598 | 3.21787 | ||||||||
\(894\) | −45.5166 | −1.52230 | ||||||||
\(895\) | 54.2630 | 1.81381 | ||||||||
\(896\) | −93.9551 | −3.13882 | ||||||||
\(897\) | 4.11877 | 0.137522 | ||||||||
\(898\) | 55.6779 | 1.85800 | ||||||||
\(899\) | −2.63430 | −0.0878590 | ||||||||
\(900\) | −4.32651 | −0.144217 | ||||||||
\(901\) | −11.3724 | −0.378869 | ||||||||
\(902\) | 28.3944 | 0.945431 | ||||||||
\(903\) | 25.2038 | 0.838728 | ||||||||
\(904\) | 64.1312 | 2.13297 | ||||||||
\(905\) | −40.5998 | −1.34958 | ||||||||
\(906\) | −90.5546 | −3.00847 | ||||||||
\(907\) | 37.8701 | 1.25746 | 0.628728 | − | 0.777626i | \(-0.283576\pi\) | ||||
0.628728 | + | 0.777626i | \(0.283576\pi\) | |||||||
\(908\) | −33.8985 | −1.12496 | ||||||||
\(909\) | 0.825208 | 0.0273704 | ||||||||
\(910\) | 17.2214 | 0.570884 | ||||||||
\(911\) | 13.0667 | 0.432920 | 0.216460 | − | 0.976292i | \(-0.430549\pi\) | ||||
0.216460 | + | 0.976292i | \(0.430549\pi\) | |||||||
\(912\) | −51.7689 | −1.71424 | ||||||||
\(913\) | −35.7471 | −1.18306 | ||||||||
\(914\) | 10.9995 | 0.363833 | ||||||||
\(915\) | 78.2522 | 2.58694 | ||||||||
\(916\) | −77.9355 | −2.57506 | ||||||||
\(917\) | −67.6640 | −2.23446 | ||||||||
\(918\) | −55.3403 | −1.82650 | ||||||||
\(919\) | −31.9778 | −1.05485 | −0.527425 | − | 0.849601i | \(-0.676843\pi\) | ||||
−0.527425 | + | 0.849601i | \(0.676843\pi\) | |||||||
\(920\) | −96.9445 | −3.19617 | ||||||||
\(921\) | −29.0681 | −0.957827 | ||||||||
\(922\) | −33.3306 | −1.09768 | ||||||||
\(923\) | 1.26710 | 0.0417072 | ||||||||
\(924\) | 114.557 | 3.76864 | ||||||||
\(925\) | 36.2531 | 1.19199 | ||||||||
\(926\) | −96.0064 | −3.15497 | ||||||||
\(927\) | −2.94674 | −0.0967835 | ||||||||
\(928\) | −0.371864 | −0.0122070 | ||||||||
\(929\) | 33.6309 | 1.10340 | 0.551698 | − | 0.834044i | \(-0.313980\pi\) | ||||
0.551698 | + | 0.834044i | \(0.313980\pi\) | |||||||
\(930\) | 27.1710 | 0.890972 | ||||||||
\(931\) | 122.175 | 4.00414 | ||||||||
\(932\) | −6.95557 | −0.227837 | ||||||||
\(933\) | 8.85681 | 0.289959 | ||||||||
\(934\) | 90.6706 | 2.96683 | ||||||||
\(935\) | −49.9338 | −1.63301 | ||||||||
\(936\) | 0.350267 | 0.0114488 | ||||||||
\(937\) | −11.2217 | −0.366598 | −0.183299 | − | 0.983057i | \(-0.558678\pi\) | ||||
−0.183299 | + | 0.983057i | \(0.558678\pi\) | |||||||
\(938\) | −53.8349 | −1.75777 | ||||||||
\(939\) | −20.6311 | −0.673270 | ||||||||
\(940\) | −178.026 | −5.80658 | ||||||||
\(941\) | −40.1158 | −1.30774 | −0.653869 | − | 0.756608i | \(-0.726855\pi\) | ||||
−0.653869 | + | 0.756608i | \(0.726855\pi\) | |||||||
\(942\) | 52.0509 | 1.69591 | ||||||||
\(943\) | −19.0777 | −0.621255 | ||||||||
\(944\) | −31.3128 | −1.01914 | ||||||||
\(945\) | −87.7325 | −2.85394 | ||||||||
\(946\) | 26.3546 | 0.856863 | ||||||||
\(947\) | −22.4602 | −0.729857 | −0.364929 | − | 0.931035i | \(-0.618907\pi\) | ||||
−0.364929 | + | 0.931035i | \(0.618907\pi\) | |||||||
\(948\) | 74.6312 | 2.42391 | ||||||||
\(949\) | −5.78640 | −0.187835 | ||||||||
\(950\) | 117.849 | 3.82354 | ||||||||
\(951\) | −44.0935 | −1.42983 | ||||||||
\(952\) | −102.197 | −3.31222 | ||||||||
\(953\) | −13.5722 | −0.439648 | −0.219824 | − | 0.975540i | \(-0.570548\pi\) | ||||
−0.219824 | + | 0.975540i | \(0.570548\pi\) | |||||||
\(954\) | −1.09007 | −0.0352922 | ||||||||
\(955\) | 8.82451 | 0.285555 | ||||||||
\(956\) | 3.42942 | 0.110915 | ||||||||
\(957\) | −7.96624 | −0.257512 | ||||||||
\(958\) | −23.5751 | −0.761676 | ||||||||
\(959\) | 84.6189 | 2.73249 | ||||||||
\(960\) | −43.7568 | −1.41224 | ||||||||
\(961\) | −27.2447 | −0.878862 | ||||||||
\(962\) | −5.82994 | −0.187965 | ||||||||
\(963\) | 0.567766 | 0.0182960 | ||||||||
\(964\) | −119.979 | −3.86426 | ||||||||
\(965\) | 26.8574 | 0.864571 | ||||||||
\(966\) | −115.189 | −3.70613 | ||||||||
\(967\) | 7.77861 | 0.250143 | 0.125072 | − | 0.992148i | \(-0.460084\pi\) | ||||
0.125072 | + | 0.992148i | \(0.460084\pi\) | |||||||
\(968\) | 5.54532 | 0.178233 | ||||||||
\(969\) | 52.5510 | 1.68818 | ||||||||
\(970\) | −89.8117 | −2.88368 | ||||||||
\(971\) | 16.7610 | 0.537886 | 0.268943 | − | 0.963156i | \(-0.413326\pi\) | ||||
0.268943 | + | 0.963156i | \(0.413326\pi\) | |||||||
\(972\) | −6.90397 | −0.221445 | ||||||||
\(973\) | 100.203 | 3.21235 | ||||||||
\(974\) | −19.2048 | −0.615363 | ||||||||
\(975\) | 4.66665 | 0.149453 | ||||||||
\(976\) | 57.0932 | 1.82751 | ||||||||
\(977\) | 23.5536 | 0.753546 | 0.376773 | − | 0.926306i | \(-0.377034\pi\) | ||||
0.376773 | + | 0.926306i | \(0.377034\pi\) | |||||||
\(978\) | 15.9942 | 0.511437 | ||||||||
\(979\) | −11.0968 | −0.354655 | ||||||||
\(980\) | −226.191 | −7.22540 | ||||||||
\(981\) | 0.366489 | 0.0117011 | ||||||||
\(982\) | −76.1752 | −2.43085 | ||||||||
\(983\) | 47.0503 | 1.50067 | 0.750336 | − | 0.661057i | \(-0.229892\pi\) | ||||
0.750336 | + | 0.661057i | \(0.229892\pi\) | |||||||
\(984\) | 27.8518 | 0.887882 | ||||||||
\(985\) | −16.5716 | −0.528015 | ||||||||
\(986\) | 14.1165 | 0.449562 | ||||||||
\(987\) | −106.491 | −3.38965 | ||||||||
\(988\) | −12.6634 | −0.402877 | ||||||||
\(989\) | −17.7072 | −0.563056 | ||||||||
\(990\) | −4.78627 | −0.152118 | ||||||||
\(991\) | 30.7486 | 0.976761 | 0.488380 | − | 0.872631i | \(-0.337588\pi\) | ||||
0.488380 | + | 0.872631i | \(0.337588\pi\) | |||||||
\(992\) | 0.530104 | 0.0168308 | ||||||||
\(993\) | 44.3611 | 1.40776 | ||||||||
\(994\) | −35.4367 | −1.12398 | ||||||||
\(995\) | −47.0953 | −1.49302 | ||||||||
\(996\) | −69.6494 | −2.20693 | ||||||||
\(997\) | 42.3465 | 1.34113 | 0.670563 | − | 0.741852i | \(-0.266052\pi\) | ||||
0.670563 | + | 0.741852i | \(0.266052\pi\) | |||||||
\(998\) | −93.9008 | −2.97238 | ||||||||
\(999\) | 29.7000 | 0.939666 |
(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 | 4001.2.a.b.1.163 | ✓ | 184 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4001.2.a.b.1.163 | ✓ | 184 | 1.1 | even | 1 | trivial |