Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [287,3,Mod(286,287)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(287, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("287.286");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 287 = 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 287.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.82018358714\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 286.8 | ||
Character | \(\chi\) | \(=\) | 287.286 |
Dual form | 287.3.d.d.286.7 |
$q$-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 \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).
\(n\) | \(206\) | \(211\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.67431 | −1.33716 | −0.668578 | − | 0.743642i | \(-0.733097\pi\) | ||||
−0.668578 | + | 0.743642i | \(0.733097\pi\) | |||||||
\(3\) | 2.89735 | 0.965782 | 0.482891 | − | 0.875680i | \(-0.339587\pi\) | ||||
0.482891 | + | 0.875680i | \(0.339587\pi\) | |||||||
\(4\) | 3.15194 | 0.787985 | ||||||||
\(5\) | 3.34396i | 0.668793i | 0.942433 | + | 0.334396i | \(0.108532\pi\) | ||||
−0.942433 | + | 0.334396i | \(0.891468\pi\) | |||||||
\(6\) | −7.74841 | −1.29140 | ||||||||
\(7\) | −4.11915 | − | 5.65974i | −0.588450 | − | 0.808534i | ||||
\(8\) | 2.26798 | 0.283498 | ||||||||
\(9\) | −0.605380 | −0.0672645 | ||||||||
\(10\) | − | 8.94280i | − | 0.894280i | ||||||
\(11\) | 15.3848i | 1.39862i | 0.714819 | + | 0.699309i | \(0.246509\pi\) | ||||
−0.714819 | + | 0.699309i | \(0.753491\pi\) | |||||||
\(12\) | 9.13226 | 0.761022 | ||||||||
\(13\) | −7.80554 | −0.600426 | −0.300213 | − | 0.953872i | \(-0.597058\pi\) | ||||
−0.300213 | + | 0.953872i | \(0.597058\pi\) | |||||||
\(14\) | 11.0159 | + | 15.1359i | 0.786849 | + | 1.08114i | ||||
\(15\) | 9.68862i | 0.645908i | ||||||||
\(16\) | −18.6730 | −1.16706 | ||||||||
\(17\) | −8.48488 | −0.499111 | −0.249555 | − | 0.968361i | \(-0.580284\pi\) | ||||
−0.249555 | + | 0.968361i | \(0.580284\pi\) | |||||||
\(18\) | 1.61897 | 0.0899430 | ||||||||
\(19\) | −0.826108 | −0.0434793 | −0.0217397 | − | 0.999764i | \(-0.506920\pi\) | ||||
−0.0217397 | + | 0.999764i | \(0.506920\pi\) | |||||||
\(20\) | 10.5400i | 0.526998i | ||||||||
\(21\) | −11.9346 | − | 16.3982i | −0.568315 | − | 0.780868i | ||||
\(22\) | − | 41.1438i | − | 1.87017i | ||||||
\(23\) | −2.74675 | −0.119424 | −0.0597119 | − | 0.998216i | \(-0.519018\pi\) | ||||
−0.0597119 | + | 0.998216i | \(0.519018\pi\) | |||||||
\(24\) | 6.57113 | 0.273797 | ||||||||
\(25\) | 13.8179 | 0.552716 | ||||||||
\(26\) | 20.8744 | 0.802863 | ||||||||
\(27\) | −27.8301 | −1.03075 | ||||||||
\(28\) | −12.9833 | − | 17.8391i | −0.463689 | − | 0.637112i | ||||
\(29\) | − | 15.8500i | − | 0.546553i | −0.961936 | − | 0.273276i | \(-0.911893\pi\) | ||
0.961936 | − | 0.273276i | \(-0.0881074\pi\) | |||||||
\(30\) | − | 25.9104i | − | 0.863680i | ||||||
\(31\) | 52.1405i | 1.68195i | 0.541073 | + | 0.840975i | \(0.318018\pi\) | ||||
−0.541073 | + | 0.840975i | \(0.681982\pi\) | |||||||
\(32\) | 40.8656 | 1.27705 | ||||||||
\(33\) | 44.5751i | 1.35076i | ||||||||
\(34\) | 22.6912 | 0.667389 | ||||||||
\(35\) | 18.9260 | − | 13.7743i | 0.540741 | − | 0.393551i | ||||
\(36\) | −1.90812 | −0.0530034 | ||||||||
\(37\) | −39.7168 | −1.07343 | −0.536714 | − | 0.843764i | \(-0.680335\pi\) | ||||
−0.536714 | + | 0.843764i | \(0.680335\pi\) | |||||||
\(38\) | 2.20927 | 0.0581386 | ||||||||
\(39\) | −22.6154 | −0.579881 | ||||||||
\(40\) | 7.58404i | 0.189601i | ||||||||
\(41\) | −38.1158 | + | 15.1057i | −0.929655 | + | 0.368432i | ||||
\(42\) | 31.9168 | + | 43.8539i | 0.759925 | + | 1.04414i | ||||
\(43\) | −71.9168 | −1.67248 | −0.836242 | − | 0.548361i | \(-0.815252\pi\) | ||||
−0.836242 | + | 0.548361i | \(0.815252\pi\) | |||||||
\(44\) | 48.4920i | 1.10209i | ||||||||
\(45\) | − | 2.02437i | − | 0.0449860i | ||||||
\(46\) | 7.34566 | 0.159688 | ||||||||
\(47\) | 0.994000 | 0.0211489 | 0.0105745 | − | 0.999944i | \(-0.496634\pi\) | ||||
0.0105745 | + | 0.999944i | \(0.496634\pi\) | |||||||
\(48\) | −54.1023 | −1.12713 | ||||||||
\(49\) | −15.0652 | + | 46.6266i | −0.307453 | + | 0.951563i | ||||
\(50\) | −36.9534 | −0.739068 | ||||||||
\(51\) | −24.5837 | −0.482032 | ||||||||
\(52\) | −24.6026 | −0.473127 | ||||||||
\(53\) | − | 10.7924i | − | 0.203630i | −0.994803 | − | 0.101815i | \(-0.967535\pi\) | ||
0.994803 | − | 0.101815i | \(-0.0324650\pi\) | |||||||
\(54\) | 74.4264 | 1.37827 | ||||||||
\(55\) | −51.4462 | −0.935386 | ||||||||
\(56\) | −9.34215 | − | 12.8362i | −0.166824 | − | 0.229217i | ||||
\(57\) | −2.39352 | −0.0419916 | ||||||||
\(58\) | 42.3879i | 0.730826i | ||||||||
\(59\) | 24.7187i | 0.418961i | 0.977813 | + | 0.209480i | \(0.0671772\pi\) | ||||
−0.977813 | + | 0.209480i | \(0.932823\pi\) | |||||||
\(60\) | 30.5379i | 0.508966i | ||||||||
\(61\) | 59.3552i | 0.973036i | 0.873671 | + | 0.486518i | \(0.161733\pi\) | ||||
−0.873671 | + | 0.486518i | \(0.838267\pi\) | |||||||
\(62\) | − | 139.440i | − | 2.24903i | ||||||
\(63\) | 2.49365 | + | 3.42629i | 0.0395818 | + | 0.0543856i | ||||
\(64\) | −34.5951 | −0.540549 | ||||||||
\(65\) | − | 26.1014i | − | 0.401561i | ||||||
\(66\) | − | 119.208i | − | 1.80618i | ||||||
\(67\) | 3.55600i | 0.0530747i | 0.999648 | + | 0.0265373i | \(0.00844809\pi\) | ||||
−0.999648 | + | 0.0265373i | \(0.991552\pi\) | |||||||
\(68\) | −26.7438 | −0.393292 | ||||||||
\(69\) | −7.95829 | −0.115337 | ||||||||
\(70\) | −50.6139 | + | 36.8367i | −0.723055 | + | 0.526239i | ||||
\(71\) | 49.0576i | 0.690952i | 0.938428 | + | 0.345476i | \(0.112283\pi\) | ||||
−0.938428 | + | 0.345476i | \(0.887717\pi\) | |||||||
\(72\) | −1.37299 | −0.0190693 | ||||||||
\(73\) | 106.882i | 1.46414i | 0.681232 | + | 0.732068i | \(0.261445\pi\) | ||||
−0.681232 | + | 0.732068i | \(0.738555\pi\) | |||||||
\(74\) | 106.215 | 1.43534 | ||||||||
\(75\) | 40.0353 | 0.533804 | ||||||||
\(76\) | −2.60384 | −0.0342611 | ||||||||
\(77\) | 87.0739 | − | 63.3723i | 1.13083 | − | 0.823017i | ||||
\(78\) | 60.4805 | 0.775391 | ||||||||
\(79\) | − | 109.832i | − | 1.39028i | −0.718874 | − | 0.695140i | \(-0.755342\pi\) | ||
0.718874 | − | 0.695140i | \(-0.244658\pi\) | |||||||
\(80\) | − | 62.4420i | − | 0.780525i | ||||||
\(81\) | −75.1851 | −0.928211 | ||||||||
\(82\) | 101.934 | − | 40.3974i | 1.24309 | − | 0.492651i | ||||
\(83\) | − | 117.729i | − | 1.41842i | −0.704996 | − | 0.709211i | \(-0.749051\pi\) | ||
0.704996 | − | 0.709211i | \(-0.250949\pi\) | |||||||
\(84\) | −37.6171 | − | 51.6862i | −0.447823 | − | 0.615312i | ||||
\(85\) | − | 28.3731i | − | 0.333802i | ||||||
\(86\) | 192.328 | 2.23637 | ||||||||
\(87\) | − | 45.9231i | − | 0.527851i | ||||||
\(88\) | 34.8924i | 0.396505i | ||||||||
\(89\) | 171.753 | 1.92981 | 0.964905 | − | 0.262598i | \(-0.0845792\pi\) | ||||
0.964905 | + | 0.262598i | \(0.0845792\pi\) | |||||||
\(90\) | 5.41379i | 0.0601532i | ||||||||
\(91\) | 32.1522 | + | 44.1773i | 0.353321 | + | 0.485465i | ||||
\(92\) | −8.65759 | −0.0941042 | ||||||||
\(93\) | 151.069i | 1.62440i | ||||||||
\(94\) | −2.65826 | −0.0282794 | ||||||||
\(95\) | − | 2.76247i | − | 0.0290787i | ||||||
\(96\) | 118.402 | 1.23335 | ||||||||
\(97\) | −41.4772 | −0.427600 | −0.213800 | − | 0.976878i | \(-0.568584\pi\) | ||||
−0.213800 | + | 0.976878i | \(0.568584\pi\) | |||||||
\(98\) | 40.2891 | − | 124.694i | 0.411113 | − | 1.27239i | ||||
\(99\) | − | 9.31366i | − | 0.0940773i | ||||||
\(100\) | 43.5532 | 0.435532 | ||||||||
\(101\) | 40.4210 | 0.400208 | 0.200104 | − | 0.979775i | \(-0.435872\pi\) | ||||
0.200104 | + | 0.979775i | \(0.435872\pi\) | |||||||
\(102\) | 65.7443 | 0.644552 | ||||||||
\(103\) | − | 105.805i | − | 1.02723i | −0.858019 | − | 0.513617i | \(-0.828305\pi\) | ||
0.858019 | − | 0.513617i | \(-0.171695\pi\) | |||||||
\(104\) | −17.7028 | −0.170219 | ||||||||
\(105\) | 54.8350 | − | 39.9089i | 0.522239 | − | 0.380085i | ||||
\(106\) | 28.8623i | 0.272286i | ||||||||
\(107\) | 53.1045 | 0.496304 | 0.248152 | − | 0.968721i | \(-0.420177\pi\) | ||||
0.248152 | + | 0.968721i | \(0.420177\pi\) | |||||||
\(108\) | −87.7188 | −0.812211 | ||||||||
\(109\) | − | 113.233i | − | 1.03883i | −0.854522 | − | 0.519416i | \(-0.826150\pi\) | ||
0.854522 | − | 0.519416i | \(-0.173850\pi\) | |||||||
\(110\) | 137.583 | 1.25076 | ||||||||
\(111\) | −115.073 | −1.03670 | ||||||||
\(112\) | 76.9170 | + | 105.684i | 0.686759 | + | 0.943611i | ||||
\(113\) | 25.9757 | 0.229873 | 0.114937 | − | 0.993373i | \(-0.463333\pi\) | ||||
0.114937 | + | 0.993373i | \(0.463333\pi\) | |||||||
\(114\) | 6.40102 | 0.0561493 | ||||||||
\(115\) | − | 9.18503i | − | 0.0798698i | ||||||
\(116\) | − | 49.9583i | − | 0.430675i | ||||||
\(117\) | 4.72532 | 0.0403873 | ||||||||
\(118\) | − | 66.1054i | − | 0.560215i | ||||||
\(119\) | 34.9505 | + | 48.0222i | 0.293702 | + | 0.403548i | ||||
\(120\) | 21.9736i | 0.183113i | ||||||||
\(121\) | −115.692 | −0.956134 | ||||||||
\(122\) | − | 158.734i | − | 1.30110i | ||||||
\(123\) | −110.435 | + | 43.7665i | −0.897844 | + | 0.355825i | ||||
\(124\) | 164.344i | 1.32535i | ||||||||
\(125\) | 129.806i | 1.03845i | ||||||||
\(126\) | −6.66880 | − | 9.16297i | −0.0529270 | − | 0.0727220i | ||||
\(127\) | 122.410 | 0.963855 | 0.481927 | − | 0.876211i | \(-0.339937\pi\) | ||||
0.481927 | + | 0.876211i | \(0.339937\pi\) | |||||||
\(128\) | −70.9442 | −0.554252 | ||||||||
\(129\) | −208.368 | −1.61525 | ||||||||
\(130\) | 69.8034i | 0.536949i | ||||||||
\(131\) | 48.9887i | 0.373959i | 0.982364 | + | 0.186980i | \(0.0598699\pi\) | ||||
−0.982364 | + | 0.186980i | \(0.940130\pi\) | |||||||
\(132\) | 140.498i | 1.06438i | ||||||||
\(133\) | 3.40286 | + | 4.67555i | 0.0255854 | + | 0.0351545i | ||||
\(134\) | − | 9.50985i | − | 0.0709691i | ||||||
\(135\) | − | 93.0629i | − | 0.689355i | ||||||
\(136\) | −19.2436 | −0.141497 | ||||||||
\(137\) | − | 51.3949i | − | 0.375145i | −0.982251 | − | 0.187573i | \(-0.939938\pi\) | ||
0.982251 | − | 0.187573i | \(-0.0600620\pi\) | |||||||
\(138\) | 21.2829 | 0.154224 | ||||||||
\(139\) | 121.729i | 0.875746i | 0.899037 | + | 0.437873i | \(0.144268\pi\) | ||||
−0.899037 | + | 0.437873i | \(0.855732\pi\) | |||||||
\(140\) | 59.6534 | − | 43.4157i | 0.426096 | − | 0.310112i | ||||
\(141\) | 2.87996 | 0.0204253 | ||||||||
\(142\) | − | 131.195i | − | 0.923911i | ||||||
\(143\) | − | 120.087i | − | 0.839767i | ||||||
\(144\) | 11.3043 | 0.0785020 | ||||||||
\(145\) | 53.0019 | 0.365531 | ||||||||
\(146\) | − | 285.835i | − | 1.95778i | ||||||
\(147\) | −43.6492 | + | 135.093i | −0.296933 | + | 0.919003i | ||||
\(148\) | −125.185 | −0.845844 | ||||||||
\(149\) | − | 147.905i | − | 0.992652i | −0.868136 | − | 0.496326i | \(-0.834682\pi\) | ||
0.868136 | − | 0.496326i | \(-0.165318\pi\) | |||||||
\(150\) | −107.067 | −0.713778 | ||||||||
\(151\) | − | 198.902i | − | 1.31723i | −0.752479 | − | 0.658616i | \(-0.771142\pi\) | ||
0.752479 | − | 0.658616i | \(-0.228858\pi\) | |||||||
\(152\) | −1.87360 | −0.0123263 | ||||||||
\(153\) | 5.13658 | 0.0335724 | ||||||||
\(154\) | −232.863 | + | 169.477i | −1.51210 | + | 1.10050i | ||||
\(155\) | −174.356 | −1.12488 | ||||||||
\(156\) | −71.2822 | −0.456937 | ||||||||
\(157\) | 153.292 | 0.976381 | 0.488190 | − | 0.872737i | \(-0.337657\pi\) | ||||
0.488190 | + | 0.872737i | \(0.337657\pi\) | |||||||
\(158\) | 293.725i | 1.85902i | ||||||||
\(159\) | − | 31.2694i | − | 0.196663i | ||||||
\(160\) | 136.653i | 0.854081i | ||||||||
\(161\) | 11.3143 | + | 15.5459i | 0.0702750 | + | 0.0965582i | ||||
\(162\) | 201.068 | 1.24116 | ||||||||
\(163\) | 177.866 | 1.09120 | 0.545600 | − | 0.838046i | \(-0.316302\pi\) | ||||
0.545600 | + | 0.838046i | \(0.316302\pi\) | |||||||
\(164\) | −120.139 | + | 47.6123i | −0.732553 | + | 0.290319i | ||||
\(165\) | −149.058 | −0.903379 | ||||||||
\(166\) | 314.844i | 1.89665i | ||||||||
\(167\) | 123.493 | 0.739479 | 0.369739 | − | 0.929136i | \(-0.379447\pi\) | ||||
0.369739 | + | 0.929136i | \(0.379447\pi\) | |||||||
\(168\) | −27.0675 | − | 37.1908i | −0.161116 | − | 0.221374i | ||||
\(169\) | −108.074 | −0.639488 | ||||||||
\(170\) | 75.8786i | 0.446345i | ||||||||
\(171\) | 0.500109 | 0.00292461 | ||||||||
\(172\) | −226.677 | −1.31789 | ||||||||
\(173\) | 335.378i | 1.93860i | 0.245875 | + | 0.969301i | \(0.420925\pi\) | ||||
−0.245875 | + | 0.969301i | \(0.579075\pi\) | |||||||
\(174\) | 122.813i | 0.705819i | ||||||||
\(175\) | −56.9180 | − | 78.2057i | −0.325246 | − | 0.446890i | ||||
\(176\) | − | 287.281i | − | 1.63228i | ||||||
\(177\) | 71.6186i | 0.404625i | ||||||||
\(178\) | −459.321 | −2.58046 | ||||||||
\(179\) | 262.625i | 1.46718i | 0.679593 | + | 0.733590i | \(0.262157\pi\) | ||||
−0.679593 | + | 0.733590i | \(0.737843\pi\) | |||||||
\(180\) | − | 6.38069i | − | 0.0354483i | ||||||
\(181\) | −28.4415 | −0.157135 | −0.0785677 | − | 0.996909i | \(-0.525035\pi\) | ||||
−0.0785677 | + | 0.996909i | \(0.525035\pi\) | |||||||
\(182\) | −85.9850 | − | 118.144i | −0.472445 | − | 0.649142i | ||||
\(183\) | 171.973i | 0.939741i | ||||||||
\(184\) | −6.22958 | −0.0338564 | ||||||||
\(185\) | − | 132.812i | − | 0.717901i | ||||||
\(186\) | − | 404.006i | − | 2.17207i | ||||||
\(187\) | − | 130.538i | − | 0.698066i | ||||||
\(188\) | 3.13303 | 0.0166650 | ||||||||
\(189\) | 114.636 | + | 157.511i | 0.606542 | + | 0.833392i | ||||
\(190\) | 7.38771i | 0.0388827i | ||||||||
\(191\) | 220.420i | 1.15403i | 0.816733 | + | 0.577016i | \(0.195783\pi\) | ||||
−0.816733 | + | 0.577016i | \(0.804217\pi\) | |||||||
\(192\) | −100.234 | −0.522052 | ||||||||
\(193\) | − | 19.7965i | − | 0.102572i | −0.998684 | − | 0.0512862i | \(-0.983668\pi\) | ||
0.998684 | − | 0.0512862i | \(-0.0163321\pi\) | |||||||
\(194\) | 110.923 | 0.571767 | ||||||||
\(195\) | − | 75.6250i | − | 0.387820i | ||||||
\(196\) | −47.4846 | + | 146.964i | −0.242269 | + | 0.749817i | ||||
\(197\) | 249.634 | 1.26718 | 0.633589 | − | 0.773670i | \(-0.281581\pi\) | ||||
0.633589 | + | 0.773670i | \(0.281581\pi\) | |||||||
\(198\) | 24.9076i | 0.125796i | ||||||||
\(199\) | −207.110 | −1.04075 | −0.520376 | − | 0.853937i | \(-0.674208\pi\) | ||||
−0.520376 | + | 0.853937i | \(0.674208\pi\) | |||||||
\(200\) | 31.3387 | 0.156694 | ||||||||
\(201\) | 10.3030i | 0.0512586i | ||||||||
\(202\) | −108.098 | −0.535140 | ||||||||
\(203\) | −89.7070 | + | 65.2887i | −0.441906 | + | 0.321619i | ||||
\(204\) | −77.4862 | −0.379834 | ||||||||
\(205\) | −50.5130 | − | 127.458i | −0.246405 | − | 0.621746i | ||||
\(206\) | 282.956i | 1.37357i | ||||||||
\(207\) | 1.66283 | 0.00803298 | ||||||||
\(208\) | 145.753 | 0.700736 | ||||||||
\(209\) | − | 12.7095i | − | 0.0608110i | ||||||
\(210\) | −146.646 | + | 106.729i | −0.698314 | + | 0.508232i | ||||
\(211\) | 342.458i | 1.62302i | 0.584337 | + | 0.811511i | \(0.301355\pi\) | ||||
−0.584337 | + | 0.811511i | \(0.698645\pi\) | |||||||
\(212\) | − | 34.0170i | − | 0.160458i | ||||||
\(213\) | 142.137i | 0.667310i | ||||||||
\(214\) | −142.018 | −0.663635 | ||||||||
\(215\) | − | 240.487i | − | 1.11854i | ||||||
\(216\) | −63.1182 | −0.292214 | ||||||||
\(217\) | 295.101 | − | 214.774i | 1.35991 | − | 0.989744i | ||||
\(218\) | 302.819i | 1.38908i | ||||||||
\(219\) | 309.674i | 1.41404i | ||||||||
\(220\) | −162.155 | −0.737070 | ||||||||
\(221\) | 66.2291 | 0.299679 | ||||||||
\(222\) | 307.742 | 1.38623 | ||||||||
\(223\) | 89.7556i | 0.402491i | 0.979541 | + | 0.201246i | \(0.0644990\pi\) | ||||
−0.979541 | + | 0.201246i | \(0.935501\pi\) | |||||||
\(224\) | −168.331 | − | 231.288i | −0.751480 | − | 1.03254i | ||||
\(225\) | −8.36509 | −0.0371782 | ||||||||
\(226\) | −69.4671 | −0.307376 | ||||||||
\(227\) | 54.6292 | 0.240657 | 0.120329 | − | 0.992734i | \(-0.461605\pi\) | ||||
0.120329 | + | 0.992734i | \(0.461605\pi\) | |||||||
\(228\) | −7.54423 | −0.0330887 | ||||||||
\(229\) | −245.368 | −1.07148 | −0.535739 | − | 0.844384i | \(-0.679967\pi\) | ||||
−0.535739 | + | 0.844384i | \(0.679967\pi\) | |||||||
\(230\) | 24.5636i | 0.106798i | ||||||||
\(231\) | 252.283 | − | 183.612i | 1.09214 | − | 0.794855i | ||||
\(232\) | − | 35.9476i | − | 0.154946i | ||||||
\(233\) | − | 237.177i | − | 1.01793i | −0.860788 | − | 0.508963i | \(-0.830029\pi\) | ||
0.860788 | − | 0.508963i | \(-0.169971\pi\) | |||||||
\(234\) | −12.6370 | −0.0540042 | ||||||||
\(235\) | 3.32390i | 0.0141443i | ||||||||
\(236\) | 77.9117i | 0.330134i | ||||||||
\(237\) | − | 318.222i | − | 1.34271i | ||||||
\(238\) | −93.4685 | − | 128.426i | −0.392725 | − | 0.539606i | ||||
\(239\) | − | 348.003i | − | 1.45608i | −0.685535 | − | 0.728040i | \(-0.740432\pi\) | ||
0.685535 | − | 0.728040i | \(-0.259568\pi\) | |||||||
\(240\) | − | 180.916i | − | 0.753817i | ||||||
\(241\) | 48.8897i | 0.202862i | 0.994843 | + | 0.101431i | \(0.0323421\pi\) | ||||
−0.994843 | + | 0.101431i | \(0.967658\pi\) | |||||||
\(242\) | 309.397 | 1.27850 | ||||||||
\(243\) | 32.6338 | 0.134295 | ||||||||
\(244\) | 187.084i | 0.766737i | ||||||||
\(245\) | −155.918 | − | 50.3775i | −0.636399 | − | 0.205623i | ||||
\(246\) | 295.337 | − | 117.045i | 1.20056 | − | 0.475794i | ||||
\(247\) | 6.44822 | 0.0261061 | ||||||||
\(248\) | 118.254i | 0.476829i | ||||||||
\(249\) | − | 341.102i | − | 1.36989i | ||||||
\(250\) | − | 347.141i | − | 1.38856i | ||||||
\(251\) | − | 129.340i | − | 0.515299i | −0.966238 | − | 0.257650i | \(-0.917052\pi\) | ||
0.966238 | − | 0.257650i | \(-0.0829480\pi\) | |||||||
\(252\) | 7.85983 | + | 10.7995i | 0.0311898 | + | 0.0428550i | ||||
\(253\) | − | 42.2582i | − | 0.167029i | ||||||
\(254\) | −327.361 | −1.28882 | ||||||||
\(255\) | − | 82.2068i | − | 0.322380i | ||||||
\(256\) | 328.107 | 1.28167 | ||||||||
\(257\) | −364.713 | −1.41912 | −0.709558 | − | 0.704647i | \(-0.751106\pi\) | ||||
−0.709558 | + | 0.704647i | \(0.751106\pi\) | |||||||
\(258\) | 557.240 | 2.15985 | ||||||||
\(259\) | 163.600 | + | 224.787i | 0.631658 | + | 0.867902i | ||||
\(260\) | − | 82.2701i | − | 0.316424i | ||||||
\(261\) | 9.59530i | 0.0367636i | ||||||||
\(262\) | − | 131.011i | − | 0.500042i | ||||||
\(263\) | − | 48.9787i | − | 0.186231i | −0.995655 | − | 0.0931153i | \(-0.970317\pi\) | ||
0.995655 | − | 0.0931153i | \(-0.0296825\pi\) | |||||||
\(264\) | 101.096i | 0.382938i | ||||||||
\(265\) | 36.0894 | 0.136187 | ||||||||
\(266\) | −9.10031 | − | 12.5039i | −0.0342117 | − | 0.0470070i | ||||
\(267\) | 497.629 | 1.86378 | ||||||||
\(268\) | 11.2083i | 0.0418220i | ||||||||
\(269\) | − | 116.578i | − | 0.433374i | −0.976241 | − | 0.216687i | \(-0.930475\pi\) | ||
0.976241 | − | 0.216687i | \(-0.0695252\pi\) | |||||||
\(270\) | 248.879i | 0.921775i | ||||||||
\(271\) | − | 23.3593i | − | 0.0861967i | −0.999071 | − | 0.0430983i | \(-0.986277\pi\) | ||
0.999071 | − | 0.0430983i | \(-0.0137229\pi\) | |||||||
\(272\) | 158.439 | 0.582495 | ||||||||
\(273\) | 93.1561 | + | 127.997i | 0.341231 | + | 0.468853i | ||||
\(274\) | 137.446i | 0.501627i | ||||||||
\(275\) | 212.586i | 0.773039i | ||||||||
\(276\) | −25.0840 | −0.0908842 | ||||||||
\(277\) | 199.356 | 0.719696 | 0.359848 | − | 0.933011i | \(-0.382829\pi\) | ||||
0.359848 | + | 0.933011i | \(0.382829\pi\) | |||||||
\(278\) | − | 325.540i | − | 1.17101i | ||||||
\(279\) | − | 31.5648i | − | 0.113136i | ||||||
\(280\) | 42.9237 | − | 31.2398i | 0.153299 | − | 0.111571i | ||||
\(281\) | 192.518i | 0.685119i | 0.939496 | + | 0.342559i | \(0.111294\pi\) | ||||
−0.939496 | + | 0.342559i | \(0.888706\pi\) | |||||||
\(282\) | −7.70192 | −0.0273118 | ||||||||
\(283\) | − | 258.377i | − | 0.912994i | −0.889725 | − | 0.456497i | \(-0.849104\pi\) | ||
0.889725 | − | 0.456497i | \(-0.150896\pi\) | |||||||
\(284\) | 154.627i | 0.544460i | ||||||||
\(285\) | − | 8.00384i | − | 0.0280837i | ||||||
\(286\) | 321.149i | 1.12290i | ||||||||
\(287\) | 242.499 | + | 153.503i | 0.844945 | + | 0.534853i | ||||
\(288\) | −24.7392 | −0.0859000 | ||||||||
\(289\) | −217.007 | −0.750888 | ||||||||
\(290\) | −141.744 | −0.488771 | ||||||||
\(291\) | −120.174 | −0.412968 | ||||||||
\(292\) | 336.885i | 1.15372i | ||||||||
\(293\) | −203.782 | −0.695503 | −0.347751 | − | 0.937587i | \(-0.613055\pi\) | ||||
−0.347751 | + | 0.937587i | \(0.613055\pi\) | |||||||
\(294\) | 116.731 | − | 361.282i | 0.397046 | − | 1.22885i | ||||
\(295\) | −82.6583 | −0.280198 | ||||||||
\(296\) | −90.0770 | −0.304314 | ||||||||
\(297\) | − | 428.161i | − | 1.44162i | ||||||
\(298\) | 395.544i | 1.32733i | ||||||||
\(299\) | 21.4399 | 0.0717052 | ||||||||
\(300\) | 126.189 | 0.420629 | ||||||||
\(301\) | 296.236 | + | 407.030i | 0.984173 | + | 1.35226i | ||||
\(302\) | 531.926i | 1.76134i | ||||||||
\(303\) | 117.114 | 0.386514 | ||||||||
\(304\) | 15.4259 | 0.0507432 | ||||||||
\(305\) | −198.482 | −0.650759 | ||||||||
\(306\) | −13.7368 | −0.0448915 | ||||||||
\(307\) | − | 395.521i | − | 1.28834i | −0.764881 | − | 0.644171i | \(-0.777202\pi\) | ||
0.764881 | − | 0.644171i | \(-0.222798\pi\) | |||||||
\(308\) | 274.452 | − | 199.746i | 0.891077 | − | 0.648525i | ||||
\(309\) | − | 306.554i | − | 0.992085i | ||||||
\(310\) | 466.282 | 1.50413 | ||||||||
\(311\) | 237.771 | 0.764537 | 0.382269 | − | 0.924051i | \(-0.375143\pi\) | ||||
0.382269 | + | 0.924051i | \(0.375143\pi\) | |||||||
\(312\) | −51.2912 | −0.164395 | ||||||||
\(313\) | −435.532 | −1.39148 | −0.695738 | − | 0.718295i | \(-0.744923\pi\) | ||||
−0.695738 | + | 0.718295i | \(0.744923\pi\) | |||||||
\(314\) | −409.950 | −1.30557 | ||||||||
\(315\) | −11.4574 | + | 8.33868i | −0.0363727 | + | 0.0264720i | ||||
\(316\) | − | 346.184i | − | 1.09552i | ||||||
\(317\) | 169.230i | 0.533849i | 0.963717 | + | 0.266925i | \(0.0860075\pi\) | ||||
−0.963717 | + | 0.266925i | \(0.913993\pi\) | |||||||
\(318\) | 83.6240i | 0.262969i | ||||||||
\(319\) | 243.850 | 0.764419 | ||||||||
\(320\) | − | 115.685i | − | 0.361515i | ||||||
\(321\) | 153.862 | 0.479321 | ||||||||
\(322\) | −30.2579 | − | 41.5745i | −0.0939686 | − | 0.129113i | ||||
\(323\) | 7.00943 | 0.0217010 | ||||||||
\(324\) | −236.979 | −0.731416 | ||||||||
\(325\) | −107.856 | −0.331865 | ||||||||
\(326\) | −475.668 | −1.45910 | ||||||||
\(327\) | − | 328.074i | − | 1.00329i | ||||||
\(328\) | −86.4460 | + | 34.2595i | −0.263555 | + | 0.104450i | ||||
\(329\) | −4.09443 | − | 5.62578i | −0.0124451 | − | 0.0170996i | ||||
\(330\) | 398.626 | 1.20796 | ||||||||
\(331\) | 86.5093i | 0.261358i | 0.991425 | + | 0.130679i | \(0.0417157\pi\) | ||||
−0.991425 | + | 0.130679i | \(0.958284\pi\) | |||||||
\(332\) | − | 371.075i | − | 1.11769i | ||||||
\(333\) | 24.0438 | 0.0722035 | ||||||||
\(334\) | −330.258 | −0.988798 | ||||||||
\(335\) | −11.8911 | −0.0354959 | ||||||||
\(336\) | 222.855 | + | 306.205i | 0.663260 | + | 0.911323i | ||||
\(337\) | −380.320 | −1.12855 | −0.564273 | − | 0.825588i | \(-0.690844\pi\) | ||||
−0.564273 | + | 0.825588i | \(0.690844\pi\) | |||||||
\(338\) | 289.022 | 0.855095 | ||||||||
\(339\) | 75.2606 | 0.222008 | ||||||||
\(340\) | − | 89.4304i | − | 0.263031i | ||||||
\(341\) | −802.171 | −2.35241 | ||||||||
\(342\) | −1.33745 | −0.00391066 | ||||||||
\(343\) | 325.950 | − | 106.797i | 0.950292 | − | 0.311361i | ||||
\(344\) | −163.106 | −0.474145 | ||||||||
\(345\) | − | 26.6122i | − | 0.0771369i | ||||||
\(346\) | − | 896.906i | − | 2.59221i | ||||||
\(347\) | 82.6726i | 0.238250i | 0.992879 | + | 0.119125i | \(0.0380089\pi\) | ||||
−0.992879 | + | 0.119125i | \(0.961991\pi\) | |||||||
\(348\) | − | 144.747i | − | 0.415939i | ||||||
\(349\) | 315.374i | 0.903651i | 0.892106 | + | 0.451826i | \(0.149227\pi\) | ||||
−0.892106 | + | 0.451826i | \(0.850773\pi\) | |||||||
\(350\) | 152.216 | + | 209.146i | 0.434904 | + | 0.597561i | ||||
\(351\) | 217.229 | 0.618886 | ||||||||
\(352\) | 628.709i | 1.78611i | ||||||||
\(353\) | 584.610i | 1.65612i | 0.560640 | + | 0.828060i | \(0.310555\pi\) | ||||
−0.560640 | + | 0.828060i | \(0.689445\pi\) | |||||||
\(354\) | − | 191.530i | − | 0.541046i | ||||||
\(355\) | −164.047 | −0.462104 | ||||||||
\(356\) | 541.355 | 1.52066 | ||||||||
\(357\) | 101.264 | + | 139.137i | 0.283652 | + | 0.389739i | ||||
\(358\) | − | 702.341i | − | 1.96185i | ||||||
\(359\) | 479.495 | 1.33564 | 0.667821 | − | 0.744322i | \(-0.267227\pi\) | ||||
0.667821 | + | 0.744322i | \(0.267227\pi\) | |||||||
\(360\) | − | 4.59123i | − | 0.0127534i | ||||||
\(361\) | −360.318 | −0.998110 | ||||||||
\(362\) | 76.0614 | 0.210114 | ||||||||
\(363\) | −335.201 | −0.923418 | ||||||||
\(364\) | 101.342 | + | 139.244i | 0.278411 | + | 0.382539i | ||||
\(365\) | −357.409 | −0.979203 | ||||||||
\(366\) | − | 459.908i | − | 1.25658i | ||||||
\(367\) | 273.041i | 0.743982i | 0.928236 | + | 0.371991i | \(0.121325\pi\) | ||||
−0.928236 | + | 0.371991i | \(0.878675\pi\) | |||||||
\(368\) | 51.2902 | 0.139375 | ||||||||
\(369\) | 23.0746 | − | 9.14471i | 0.0625327 | − | 0.0247824i | ||||
\(370\) | 355.180i | 0.959945i | ||||||||
\(371\) | −61.0822 | + | 44.4556i | −0.164642 | + | 0.119826i | ||||
\(372\) | 476.160i | 1.28000i | ||||||||
\(373\) | 1.89956 | 0.00509264 | 0.00254632 | − | 0.999997i | \(-0.499189\pi\) | ||||
0.00254632 | + | 0.999997i | \(0.499189\pi\) | |||||||
\(374\) | 349.100i | 0.933422i | ||||||||
\(375\) | 376.092i | 1.00291i | ||||||||
\(376\) | 2.25437 | 0.00599567 | ||||||||
\(377\) | 123.718i | 0.328165i | ||||||||
\(378\) | −306.573 | − | 421.234i | −0.811041 | − | 1.11437i | ||||
\(379\) | −418.879 | −1.10522 | −0.552611 | − | 0.833439i | \(-0.686368\pi\) | ||||
−0.552611 | + | 0.833439i | \(0.686368\pi\) | |||||||
\(380\) | − | 8.70715i | − | 0.0229135i | ||||||
\(381\) | 354.663 | 0.930874 | ||||||||
\(382\) | − | 589.472i | − | 1.54312i | ||||||
\(383\) | −184.199 | −0.480936 | −0.240468 | − | 0.970657i | \(-0.577301\pi\) | ||||
−0.240468 | + | 0.970657i | \(0.577301\pi\) | |||||||
\(384\) | −205.550 | −0.535287 | ||||||||
\(385\) | 211.915 | + | 291.172i | 0.550428 | + | 0.756291i | ||||
\(386\) | 52.9419i | 0.137155i | ||||||||
\(387\) | 43.5370 | 0.112499 | ||||||||
\(388\) | −130.733 | −0.336942 | ||||||||
\(389\) | −145.229 | −0.373339 | −0.186670 | − | 0.982423i | \(-0.559769\pi\) | ||||
−0.186670 | + | 0.982423i | \(0.559769\pi\) | |||||||
\(390\) | 202.245i | 0.518576i | ||||||||
\(391\) | 23.3059 | 0.0596058 | ||||||||
\(392\) | −34.1676 | + | 105.748i | −0.0871623 | + | 0.269766i | ||||
\(393\) | 141.937i | 0.361163i | ||||||||
\(394\) | −667.599 | −1.69441 | ||||||||
\(395\) | 367.275 | 0.929810 | ||||||||
\(396\) | − | 29.3561i | − | 0.0741315i | ||||||
\(397\) | 498.076 | 1.25460 | 0.627300 | − | 0.778778i | \(-0.284160\pi\) | ||||
0.627300 | + | 0.778778i | \(0.284160\pi\) | |||||||
\(398\) | 553.875 | 1.39165 | ||||||||
\(399\) | 9.85927 | + | 13.5467i | 0.0247099 | + | 0.0339516i | ||||
\(400\) | −258.022 | −0.645056 | ||||||||
\(401\) | 165.137 | 0.411812 | 0.205906 | − | 0.978572i | \(-0.433986\pi\) | ||||
0.205906 | + | 0.978572i | \(0.433986\pi\) | |||||||
\(402\) | − | 27.5533i | − | 0.0685407i | ||||||
\(403\) | − | 406.985i | − | 1.00989i | ||||||
\(404\) | 127.404 | 0.315358 | ||||||||
\(405\) | − | 251.416i | − | 0.620781i | ||||||
\(406\) | 239.904 | − | 174.602i | 0.590898 | − | 0.430055i | ||||
\(407\) | − | 611.036i | − | 1.50132i | ||||||
\(408\) | −55.7552 | −0.136655 | ||||||||
\(409\) | 643.763i | 1.57399i | 0.616958 | + | 0.786996i | \(0.288365\pi\) | ||||
−0.616958 | + | 0.786996i | \(0.711635\pi\) | |||||||
\(410\) | 135.087 | + | 340.862i | 0.329482 | + | 0.831371i | ||||
\(411\) | − | 148.909i | − | 0.362309i | ||||||
\(412\) | − | 333.491i | − | 0.809445i | ||||||
\(413\) | 139.901 | − | 101.820i | 0.338744 | − | 0.246537i | ||||
\(414\) | −4.44692 | −0.0107413 | ||||||||
\(415\) | 393.682 | 0.948630 | ||||||||
\(416\) | −318.978 | −0.766774 | ||||||||
\(417\) | 352.690i | 0.845780i | ||||||||
\(418\) | 33.9892i | 0.0813138i | ||||||||
\(419\) | 755.940i | 1.80415i | 0.431576 | + | 0.902077i | \(0.357958\pi\) | ||||
−0.431576 | + | 0.902077i | \(0.642042\pi\) | |||||||
\(420\) | 172.837 | − | 125.790i | 0.411516 | − | 0.299501i | ||||
\(421\) | 231.259i | 0.549308i | 0.961543 | + | 0.274654i | \(0.0885633\pi\) | ||||
−0.961543 | + | 0.274654i | \(0.911437\pi\) | |||||||
\(422\) | − | 915.839i | − | 2.17023i | ||||||
\(423\) | −0.601748 | −0.00142257 | ||||||||
\(424\) | − | 24.4770i | − | 0.0577287i | ||||||
\(425\) | −117.243 | −0.275867 | ||||||||
\(426\) | − | 380.118i | − | 0.892297i | ||||||
\(427\) | 335.935 | − | 244.493i | 0.786732 | − | 0.572583i | ||||
\(428\) | 167.382 | 0.391080 | ||||||||
\(429\) | − | 347.933i | − | 0.811033i | ||||||
\(430\) | 643.137i | 1.49567i | ||||||||
\(431\) | −90.1501 | −0.209165 | −0.104582 | − | 0.994516i | \(-0.533351\pi\) | ||||
−0.104582 | + | 0.994516i | \(0.533351\pi\) | |||||||
\(432\) | 519.673 | 1.20295 | ||||||||
\(433\) | − | 391.594i | − | 0.904373i | −0.891923 | − | 0.452187i | \(-0.850644\pi\) | ||
0.891923 | − | 0.452187i | \(-0.149356\pi\) | |||||||
\(434\) | −789.193 | + | 574.374i | −1.81842 | + | 1.32344i | ||||
\(435\) | 153.565 | 0.353023 | ||||||||
\(436\) | − | 356.902i | − | 0.818583i | ||||||
\(437\) | 2.26911 | 0.00519247 | ||||||||
\(438\) | − | 828.164i | − | 1.89079i | ||||||
\(439\) | −610.875 | −1.39151 | −0.695757 | − | 0.718277i | \(-0.744931\pi\) | ||||
−0.695757 | + | 0.718277i | \(0.744931\pi\) | |||||||
\(440\) | −116.679 | −0.265180 | ||||||||
\(441\) | 9.12018 | − | 28.2268i | 0.0206807 | − | 0.0640064i | ||||
\(442\) | −177.117 | −0.400718 | ||||||||
\(443\) | 293.107 | 0.661640 | 0.330820 | − | 0.943694i | \(-0.392675\pi\) | ||||
0.330820 | + | 0.943694i | \(0.392675\pi\) | |||||||
\(444\) | −362.704 | −0.816902 | ||||||||
\(445\) | 574.336i | 1.29064i | ||||||||
\(446\) | − | 240.034i | − | 0.538194i | ||||||
\(447\) | − | 428.532i | − | 0.958686i | ||||||
\(448\) | 142.502 | + | 195.799i | 0.318086 | + | 0.437052i | ||||
\(449\) | −317.488 | −0.707101 | −0.353551 | − | 0.935415i | \(-0.615026\pi\) | ||||
−0.353551 | + | 0.935415i | \(0.615026\pi\) | |||||||
\(450\) | 22.3708 | 0.0497130 | ||||||||
\(451\) | −232.399 | − | 586.405i | −0.515296 | − | 1.30023i | ||||
\(452\) | 81.8738 | 0.181137 | ||||||||
\(453\) | − | 576.288i | − | 1.27216i | ||||||
\(454\) | −146.095 | −0.321796 | ||||||||
\(455\) | −147.727 | + | 107.516i | −0.324675 | + | 0.236298i | ||||
\(456\) | −5.42846 | −0.0119045 | ||||||||
\(457\) | 816.773i | 1.78725i | 0.448814 | + | 0.893625i | \(0.351846\pi\) | ||||
−0.448814 | + | 0.893625i | \(0.648154\pi\) | |||||||
\(458\) | 656.191 | 1.43273 | ||||||||
\(459\) | 236.135 | 0.514456 | ||||||||
\(460\) | − | 28.9507i | − | 0.0629362i | ||||||
\(461\) | 554.338i | 1.20247i | 0.799073 | + | 0.601235i | \(0.205324\pi\) | ||||
−0.799073 | + | 0.601235i | \(0.794676\pi\) | |||||||
\(462\) | −674.684 | + | 491.034i | −1.46036 | + | 1.06285i | ||||
\(463\) | − | 735.278i | − | 1.58807i | −0.607870 | − | 0.794036i | \(-0.707976\pi\) | ||
0.607870 | − | 0.794036i | \(-0.292024\pi\) | |||||||
\(464\) | 295.968i | 0.637863i | ||||||||
\(465\) | −505.169 | −1.08639 | ||||||||
\(466\) | 634.285i | 1.36113i | ||||||||
\(467\) | − | 387.715i | − | 0.830225i | −0.909770 | − | 0.415113i | \(-0.863742\pi\) | ||
0.909770 | − | 0.415113i | \(-0.136258\pi\) | |||||||
\(468\) | 14.8939 | 0.0318246 | ||||||||
\(469\) | 20.1260 | − | 14.6477i | 0.0429126 | − | 0.0312318i | ||||
\(470\) | − | 8.88914i | − | 0.0189131i | ||||||
\(471\) | 444.139 | 0.942971 | ||||||||
\(472\) | 56.0615i | 0.118774i | ||||||||
\(473\) | − | 1106.43i | − | 2.33917i | ||||||
\(474\) | 851.024i | 1.79541i | ||||||||
\(475\) | −11.4151 | −0.0240317 | ||||||||
\(476\) | 110.162 | + | 151.363i | 0.231432 | + | 0.317989i | ||||
\(477\) | 6.53351i | 0.0136971i | ||||||||
\(478\) | 930.668i | 1.94700i | ||||||||
\(479\) | 930.051 | 1.94165 | 0.970826 | − | 0.239785i | \(-0.0770770\pi\) | ||||
0.970826 | + | 0.239785i | \(0.0770770\pi\) | |||||||
\(480\) | 395.931i | 0.824857i | ||||||||
\(481\) | 310.011 | 0.644514 | ||||||||
\(482\) | − | 130.746i | − | 0.271258i | ||||||
\(483\) | 32.7814 | + | 45.0418i | 0.0678703 | + | 0.0932542i | ||||
\(484\) | −364.655 | −0.753419 | ||||||||
\(485\) | − | 138.698i | − | 0.285975i | ||||||
\(486\) | −87.2728 | −0.179574 | ||||||||
\(487\) | 290.975 | 0.597485 | 0.298743 | − | 0.954334i | \(-0.403433\pi\) | ||||
0.298743 | + | 0.954334i | \(0.403433\pi\) | |||||||
\(488\) | 134.616i | 0.275853i | ||||||||
\(489\) | 515.338 | 1.05386 | ||||||||
\(490\) | 416.972 | + | 134.725i | 0.850964 | + | 0.274949i | ||||
\(491\) | −410.398 | −0.835840 | −0.417920 | − | 0.908484i | \(-0.637241\pi\) | ||||
−0.417920 | + | 0.908484i | \(0.637241\pi\) | |||||||
\(492\) | −348.084 | + | 137.949i | −0.707487 | + | 0.280385i | ||||
\(493\) | 134.486i | 0.272790i | ||||||||
\(494\) | −17.2445 | −0.0349080 | ||||||||
\(495\) | 31.1445 | 0.0629182 | ||||||||
\(496\) | − | 973.621i | − | 1.96295i | ||||||
\(497\) | 277.653 | − | 202.076i | 0.558658 | − | 0.406591i | ||||
\(498\) | 912.212i | 1.83175i | ||||||||
\(499\) | − | 588.240i | − | 1.17884i | −0.807828 | − | 0.589419i | \(-0.799357\pi\) | ||
0.807828 | − | 0.589419i | \(-0.200643\pi\) | |||||||
\(500\) | 409.139i | 0.818279i | ||||||||
\(501\) | 357.802 | 0.714175 | ||||||||
\(502\) | 345.896i | 0.689035i | ||||||||
\(503\) | −126.971 | −0.252428 | −0.126214 | − | 0.992003i | \(-0.540283\pi\) | ||||
−0.126214 | + | 0.992003i | \(0.540283\pi\) | |||||||
\(504\) | 5.65555 | + | 7.77076i | 0.0112213 | + | 0.0154182i | ||||
\(505\) | 135.166i | 0.267656i | ||||||||
\(506\) | 113.012i | 0.223343i | ||||||||
\(507\) | −313.126 | −0.617607 | ||||||||
\(508\) | 385.827 | 0.759502 | ||||||||
\(509\) | −580.463 | −1.14040 | −0.570199 | − | 0.821506i | \(-0.693134\pi\) | ||||
−0.570199 | + | 0.821506i | \(0.693134\pi\) | |||||||
\(510\) | 219.847i | 0.431072i | ||||||||
\(511\) | 604.923 | − | 440.262i | 1.18380 | − | 0.861570i | ||||
\(512\) | −593.684 | −1.15954 | ||||||||
\(513\) | 22.9907 | 0.0448161 | ||||||||
\(514\) | 975.356 | 1.89758 | ||||||||
\(515\) | 353.809 | 0.687007 | ||||||||
\(516\) | −656.763 | −1.27280 | ||||||||
\(517\) | 15.2925i | 0.0295793i | ||||||||
\(518\) | −437.516 | − | 601.150i | −0.844625 | − | 1.16052i | ||||
\(519\) | 971.707i | 1.87227i | ||||||||
\(520\) | − | 59.1976i | − | 0.113841i | ||||||
\(521\) | 104.630 | 0.200825 | 0.100412 | − | 0.994946i | \(-0.467984\pi\) | ||||
0.100412 | + | 0.994946i | \(0.467984\pi\) | |||||||
\(522\) | − | 25.6608i | − | 0.0491586i | ||||||
\(523\) | − | 822.767i | − | 1.57317i | −0.617483 | − | 0.786584i | \(-0.711848\pi\) | ||
0.617483 | − | 0.786584i | \(-0.288152\pi\) | |||||||
\(524\) | 154.409i | 0.294674i | ||||||||
\(525\) | −164.911 | − | 226.589i | −0.314117 | − | 0.431598i | ||||
\(526\) | 130.984i | 0.249019i | ||||||||
\(527\) | − | 442.406i | − | 0.839480i | ||||||
\(528\) | − | 832.353i | − | 1.57643i | ||||||
\(529\) | −521.455 | −0.985738 | ||||||||
\(530\) | −96.5144 | −0.182103 | ||||||||
\(531\) | − | 14.9642i | − | 0.0281812i | ||||||
\(532\) | 10.7256 | + | 14.7370i | 0.0201609 | + | 0.0277012i | ||||
\(533\) | 297.515 | − | 117.908i | 0.558189 | − | 0.221216i | ||||
\(534\) | −1330.81 | −2.49216 | ||||||||
\(535\) | 177.579i | 0.331924i | ||||||||
\(536\) | 8.06494i | 0.0150465i | ||||||||
\(537\) | 760.916i | 1.41698i | ||||||||
\(538\) | 311.765i | 0.579489i | ||||||||
\(539\) | −717.341 | − | 231.775i | −1.33087 | − | 0.430010i | ||||
\(540\) | − | 293.329i | − | 0.543201i | ||||||
\(541\) | 135.498 | 0.250459 | 0.125230 | − | 0.992128i | \(-0.460033\pi\) | ||||
0.125230 | + | 0.992128i | \(0.460033\pi\) | |||||||
\(542\) | 62.4700i | 0.115258i | ||||||||
\(543\) | −82.4049 | −0.151759 | ||||||||
\(544\) | −346.740 | −0.637389 | ||||||||
\(545\) | 378.646 | 0.694763 | ||||||||
\(546\) | −249.128 | − | 342.304i | −0.456279 | − | 0.626930i | ||||
\(547\) | 73.5580i | 0.134475i | 0.997737 | + | 0.0672376i | \(0.0214186\pi\) | ||||
−0.997737 | + | 0.0672376i | \(0.978581\pi\) | |||||||
\(548\) | − | 161.994i | − | 0.295609i | ||||||
\(549\) | − | 35.9324i | − | 0.0654507i | ||||||
\(550\) | − | 568.521i | − | 1.03367i | ||||||
\(551\) | 13.0938i | 0.0237638i | ||||||||
\(552\) | −18.0492 | −0.0326979 | ||||||||
\(553\) | −621.621 | + | 452.415i | −1.12409 | + | 0.818111i | ||||
\(554\) | −533.139 | −0.962346 | ||||||||
\(555\) | − | 384.801i | − | 0.693336i | ||||||
\(556\) | 383.681i | 0.690074i | ||||||||
\(557\) | 806.927i | 1.44870i | 0.689431 | + | 0.724351i | \(0.257861\pi\) | ||||
−0.689431 | + | 0.724351i | \(0.742139\pi\) | |||||||
\(558\) | 84.4141i | 0.151280i | ||||||||
\(559\) | 561.349 | 1.00420 | ||||||||
\(560\) | −353.405 | + | 257.208i | −0.631080 | + | 0.459300i | ||||
\(561\) | − | 378.215i | − | 0.674180i | ||||||
\(562\) | − | 514.854i | − | 0.916110i | ||||||
\(563\) | 310.513 | 0.551532 | 0.275766 | − | 0.961225i | \(-0.411068\pi\) | ||||
0.275766 | + | 0.961225i | \(0.411068\pi\) | |||||||
\(564\) | 9.07746 | 0.0160948 | ||||||||
\(565\) | 86.8618i | 0.153738i | ||||||||
\(566\) | 690.981i | 1.22082i | ||||||||
\(567\) | 309.699 | + | 425.528i | 0.546206 | + | 0.750490i | ||||
\(568\) | 111.262i | 0.195883i | ||||||||
\(569\) | −1064.91 | −1.87155 | −0.935777 | − | 0.352594i | \(-0.885300\pi\) | ||||
−0.935777 | + | 0.352594i | \(0.885300\pi\) | |||||||
\(570\) | 21.4048i | 0.0375522i | ||||||||
\(571\) | 571.145i | 1.00025i | 0.865952 | + | 0.500127i | \(0.166713\pi\) | ||||
−0.865952 | + | 0.500127i | \(0.833287\pi\) | |||||||
\(572\) | − | 378.506i | − | 0.661724i | ||||||
\(573\) | 638.633i | 1.11454i | ||||||||
\(574\) | −648.518 | − | 410.514i | −1.12982 | − | 0.715182i | ||||
\(575\) | −37.9543 | −0.0660075 | ||||||||
\(576\) | 20.9432 | 0.0363597 | ||||||||
\(577\) | −937.964 | −1.62559 | −0.812793 | − | 0.582552i | \(-0.802054\pi\) | ||||
−0.812793 | + | 0.582552i | \(0.802054\pi\) | |||||||
\(578\) | 580.344 | 1.00405 | ||||||||
\(579\) | − | 57.3572i | − | 0.0990625i | ||||||
\(580\) | 167.059 | 0.288032 | ||||||||
\(581\) | −666.315 | + | 484.943i | −1.14684 | + | 0.834670i | ||||
\(582\) | 321.382 | 0.552203 | ||||||||
\(583\) | 166.039 | 0.284801 | ||||||||
\(584\) | 242.406i | 0.415079i | ||||||||
\(585\) | 15.8013i | 0.0270108i | ||||||||
\(586\) | 544.977 | 0.929996 | ||||||||
\(587\) | −186.707 | −0.318070 | −0.159035 | − | 0.987273i | \(-0.550838\pi\) | ||||
−0.159035 | + | 0.987273i | \(0.550838\pi\) | |||||||
\(588\) | −137.579 | + | 425.806i | −0.233979 | + | 0.724160i | ||||
\(589\) | − | 43.0736i | − | 0.0731301i | ||||||
\(590\) | 221.054 | 0.374668 | ||||||||
\(591\) | 723.276 | 1.22382 | ||||||||
\(592\) | 741.634 | 1.25276 | ||||||||
\(593\) | 363.034 | 0.612199 | 0.306099 | − | 0.952000i | \(-0.400976\pi\) | ||||
0.306099 | + | 0.952000i | \(0.400976\pi\) | |||||||
\(594\) | 1145.04i | 1.92767i | ||||||||
\(595\) | −160.584 | + | 116.873i | −0.269890 | + | 0.196426i | ||||
\(596\) | − | 466.188i | − | 0.782194i | ||||||
\(597\) | −600.068 | −1.00514 | ||||||||
\(598\) | −57.3369 | −0.0958811 | ||||||||
\(599\) | −720.720 | −1.20321 | −0.601603 | − | 0.798795i | \(-0.705471\pi\) | ||||
−0.601603 | + | 0.798795i | \(0.705471\pi\) | |||||||
\(600\) | 90.7992 | 0.151332 | ||||||||
\(601\) | −769.330 | −1.28008 | −0.640042 | − | 0.768340i | \(-0.721083\pi\) | ||||
−0.640042 | + | 0.768340i | \(0.721083\pi\) | |||||||
\(602\) | −792.227 | − | 1088.52i | −1.31599 | − | 1.80818i | ||||
\(603\) | − | 2.15273i | − | 0.00357004i | ||||||
\(604\) | − | 626.927i | − | 1.03796i | ||||||
\(605\) | − | 386.871i | − | 0.639456i | ||||||
\(606\) | −313.198 | −0.516829 | ||||||||
\(607\) | 89.4029i | 0.147286i | 0.997285 | + | 0.0736432i | \(0.0234626\pi\) | ||||
−0.997285 | + | 0.0736432i | \(0.976537\pi\) | |||||||
\(608\) | −33.7594 | −0.0555253 | ||||||||
\(609\) | −259.912 | + | 189.164i | −0.426785 | + | 0.310614i | ||||
\(610\) | 530.801 | 0.870166 | ||||||||
\(611\) | −7.75871 | −0.0126984 | ||||||||
\(612\) | 16.1902 | 0.0264545 | ||||||||
\(613\) | 909.661 | 1.48395 | 0.741974 | − | 0.670428i | \(-0.233890\pi\) | ||||
0.741974 | + | 0.670428i | \(0.233890\pi\) | |||||||
\(614\) | 1057.75i | 1.72271i | ||||||||
\(615\) | −146.354 | − | 369.290i | −0.237973 | − | 0.600472i | ||||
\(616\) | 197.482 | − | 143.727i | 0.320588 | − | 0.233323i | ||||
\(617\) | 164.383 | 0.266422 | 0.133211 | − | 0.991088i | \(-0.457471\pi\) | ||||
0.133211 | + | 0.991088i | \(0.457471\pi\) | |||||||
\(618\) | 819.821i | 1.32657i | ||||||||
\(619\) | 511.799i | 0.826816i | 0.910546 | + | 0.413408i | \(0.135662\pi\) | ||||
−0.910546 | + | 0.413408i | \(0.864338\pi\) | |||||||
\(620\) | −549.559 | −0.886385 | ||||||||
\(621\) | 76.4424 | 0.123096 | ||||||||
\(622\) | −635.874 | −1.02230 | ||||||||
\(623\) | −707.477 | − | 972.078i | −1.13560 | − | 1.56032i | ||||
\(624\) | 422.298 | 0.676759 | ||||||||
\(625\) | −88.6178 | −0.141788 | ||||||||
\(626\) | 1164.75 | 1.86062 | ||||||||
\(627\) | − | 36.8238i | − | 0.0587302i | ||||||
\(628\) | 483.166 | 0.769373 | ||||||||
\(629\) | 336.993 | 0.535759 | ||||||||
\(630\) | 30.6406 | − | 22.3002i | 0.0486359 | − | 0.0353972i | ||||
\(631\) | 738.033 | 1.16962 | 0.584812 | − | 0.811169i | \(-0.301168\pi\) | ||||
0.584812 | + | 0.811169i | \(0.301168\pi\) | |||||||
\(632\) | − | 249.097i | − | 0.394141i | ||||||
\(633\) | 992.219i | 1.56749i | ||||||||
\(634\) | − | 452.574i | − | 0.713839i | ||||||
\(635\) | 409.333i | 0.644619i | ||||||||
\(636\) | − | 98.5591i | − | 0.154967i | ||||||
\(637\) | 117.592 | − | 363.946i | 0.184603 | − | 0.571344i | ||||
\(638\) | −652.130 | −1.02215 | ||||||||
\(639\) | − | 29.6985i | − | 0.0464765i | ||||||
\(640\) | − | 237.235i | − | 0.370680i | ||||||
\(641\) | − | 255.387i | − | 0.398419i | −0.979957 | − | 0.199209i | \(-0.936163\pi\) | ||
0.979957 | − | 0.199209i | \(-0.0638374\pi\) | |||||||
\(642\) | −411.475 | −0.640927 | ||||||||
\(643\) | 44.4007 | 0.0690524 | 0.0345262 | − | 0.999404i | \(-0.489008\pi\) | ||||
0.0345262 | + | 0.999404i | \(0.489008\pi\) | |||||||
\(644\) | 35.6619 | + | 48.9996i | 0.0553756 | + | 0.0760864i | ||||
\(645\) | − | 696.775i | − | 1.08027i | ||||||
\(646\) | −18.7454 | −0.0290176 | ||||||||
\(647\) | 121.051i | 0.187097i | 0.995615 | + | 0.0935483i | \(0.0298209\pi\) | ||||
−0.995615 | + | 0.0935483i | \(0.970179\pi\) | |||||||
\(648\) | −170.518 | −0.263146 | ||||||||
\(649\) | −380.292 | −0.585966 | ||||||||
\(650\) | 288.441 | 0.443756 | ||||||||
\(651\) | 855.011 | − | 622.276i | 1.31338 | − | 0.955877i | ||||
\(652\) | 560.621 | 0.859848 | ||||||||
\(653\) | 815.923i | 1.24950i | 0.780825 | + | 0.624749i | \(0.214799\pi\) | ||||
−0.780825 | + | 0.624749i | \(0.785201\pi\) | |||||||
\(654\) | 877.373i | 1.34155i | ||||||||
\(655\) | −163.816 | −0.250101 | ||||||||
\(656\) | 711.738 | − | 282.070i | 1.08497 | − | 0.429984i | ||||
\(657\) | − | 64.7042i | − | 0.0984843i | ||||||
\(658\) | 10.9498 | + | 15.0451i | 0.0166410 | + | 0.0228649i | ||||
\(659\) | 23.2550i | 0.0352883i | 0.999844 | + | 0.0176442i | \(0.00561661\pi\) | ||||
−0.999844 | + | 0.0176442i | \(0.994383\pi\) | |||||||
\(660\) | −469.820 | −0.711849 | ||||||||
\(661\) | − | 600.186i | − | 0.907996i | −0.891003 | − | 0.453998i | \(-0.849997\pi\) | ||
0.891003 | − | 0.453998i | \(-0.150003\pi\) | |||||||
\(662\) | − | 231.353i | − | 0.349476i | ||||||
\(663\) | 191.889 | 0.289425 | ||||||||
\(664\) | − | 267.007i | − | 0.402119i | ||||||
\(665\) | −15.6349 | + | 11.3790i | −0.0235111 | + | 0.0171113i | ||||
\(666\) | −64.3005 | −0.0965473 | ||||||||
\(667\) | 43.5361i | 0.0652715i | ||||||||
\(668\) | 389.242 | 0.582698 | ||||||||
\(669\) | 260.053i | 0.388719i | ||||||||
\(670\) | 31.8006 | 0.0474636 | ||||||||
\(671\) | −913.168 | −1.36091 | ||||||||
\(672\) | −487.715 | − | 670.123i | −0.725766 | − | 0.997207i | ||||
\(673\) | − | 125.725i | − | 0.186813i | −0.995628 | − | 0.0934066i | \(-0.970224\pi\) | ||
0.995628 | − | 0.0934066i | \(-0.0297757\pi\) | |||||||
\(674\) | 1017.09 | 1.50904 | ||||||||
\(675\) | −384.554 | −0.569710 | ||||||||
\(676\) | −340.641 | −0.503907 | ||||||||
\(677\) | 218.443i | 0.322663i | 0.986900 | + | 0.161331i | \(0.0515788\pi\) | ||||
−0.986900 | + | 0.161331i | \(0.948421\pi\) | |||||||
\(678\) | −201.270 | −0.296859 | ||||||||
\(679\) | 170.851 | + | 234.750i | 0.251621 | + | 0.345729i | ||||
\(680\) | − | 64.3497i | − | 0.0946320i | ||||||
\(681\) | 158.280 | 0.232422 | ||||||||
\(682\) | 2145.25 | 3.14553 | ||||||||
\(683\) | 1038.31i | 1.52022i | 0.649797 | + | 0.760108i | \(0.274854\pi\) | ||||
−0.649797 | + | 0.760108i | \(0.725146\pi\) | |||||||
\(684\) | 1.57631 | 0.00230455 | ||||||||
\(685\) | 171.863 | 0.250894 | ||||||||
\(686\) | −871.692 | + | 285.608i | −1.27069 | + | 0.416338i | ||||
\(687\) | −710.917 | −1.03481 | ||||||||
\(688\) | 1342.90 | 1.95190 | ||||||||
\(689\) | 84.2406i | 0.122265i | ||||||||
\(690\) | 71.1694i | 0.103144i | ||||||||
\(691\) | −752.770 | −1.08939 | −0.544696 | − | 0.838634i | \(-0.683355\pi\) | ||||
−0.544696 | + | 0.838634i | \(0.683355\pi\) | |||||||
\(692\) | 1057.09i | 1.52759i | ||||||||
\(693\) | −52.7128 | + | 38.3643i | −0.0760647 | + | 0.0553598i | ||||
\(694\) | − | 221.092i | − | 0.318577i | ||||||
\(695\) | −407.056 | −0.585692 | ||||||||
\(696\) | − | 104.153i | − | 0.149645i | ||||||
\(697\) | 323.408 | − | 128.170i | 0.464001 | − | 0.183889i | ||||
\(698\) | − | 843.409i | − | 1.20832i | ||||||
\(699\) | − | 687.184i | − | 0.983096i | ||||||
\(700\) | −179.402 | − | 246.500i | −0.256289 | − | 0.352142i | ||||
\(701\) | 631.386 | 0.900693 | 0.450347 | − | 0.892854i | \(-0.351300\pi\) | ||||
0.450347 | + | 0.892854i | \(0.351300\pi\) | |||||||
\(702\) | −580.938 | −0.827547 | ||||||||
\(703\) | 32.8104 | 0.0466719 | ||||||||
\(704\) | − | 532.239i | − | 0.756022i | ||||||
\(705\) | 9.63049i | 0.0136603i | ||||||||
\(706\) | − | 1563.43i | − | 2.21449i | ||||||
\(707\) | −166.500 | − | 228.772i | −0.235502 | − | 0.323582i | ||||
\(708\) | 225.737i | 0.318838i | ||||||||
\(709\) | − | 270.461i | − | 0.381468i | −0.981642 | − | 0.190734i | \(-0.938913\pi\) | ||
0.981642 | − | 0.190734i | \(-0.0610868\pi\) | |||||||
\(710\) | 438.712 | 0.617905 | ||||||||
\(711\) | 66.4902i | 0.0935165i | ||||||||
\(712\) | 389.533 | 0.547097 | ||||||||
\(713\) | − | 143.217i | − | 0.200865i | ||||||
\(714\) | −270.811 | − | 372.096i | −0.379287 | − | 0.521142i | ||||
\(715\) | 401.566 | 0.561630 | ||||||||
\(716\) | 827.778i | 1.15611i | ||||||||
\(717\) | − | 1008.29i | − | 1.40626i | ||||||
\(718\) | −1282.32 | −1.78596 | ||||||||
\(719\) | 1057.01 | 1.47011 | 0.735055 | − | 0.678007i | \(-0.237156\pi\) | ||||
0.735055 | + | 0.678007i | \(0.237156\pi\) | |||||||
\(720\) | 37.8011i | 0.0525016i | ||||||||
\(721\) | −598.829 | + | 435.827i | −0.830554 | + | 0.604476i | ||||
\(722\) | 963.601 | 1.33463 | ||||||||
\(723\) | 141.650i | 0.195920i | ||||||||
\(724\) | −89.6458 | −0.123820 | ||||||||
\(725\) | − | 219.014i | − | 0.302089i | ||||||
\(726\) | 896.431 | 1.23475 | ||||||||
\(727\) | 504.265 | 0.693624 | 0.346812 | − | 0.937935i | \(-0.387264\pi\) | ||||
0.346812 | + | 0.937935i | \(0.387264\pi\) | |||||||
\(728\) | 72.9206 | + | 100.193i | 0.100166 | + | 0.137628i | ||||
\(729\) | 771.217 | 1.05791 | ||||||||
\(730\) | 955.823 | 1.30935 | ||||||||
\(731\) | 610.205 | 0.834754 | ||||||||
\(732\) | 542.047i | 0.740501i | ||||||||
\(733\) | − | 10.4157i | − | 0.0142097i | −0.999975 | − | 0.00710485i | \(-0.997738\pi\) | ||
0.999975 | − | 0.00710485i | \(-0.00226156\pi\) | |||||||
\(734\) | − | 730.197i | − | 0.994819i | ||||||
\(735\) | −451.747 | − | 145.961i | −0.614622 | − | 0.198587i | ||||
\(736\) | −112.248 | −0.152510 | ||||||||
\(737\) | −54.7084 | −0.0742312 | ||||||||
\(738\) | −61.7086 | + | 24.4558i | −0.0836159 | + | 0.0331379i | ||||
\(739\) | 855.658 | 1.15786 | 0.578929 | − | 0.815378i | \(-0.303471\pi\) | ||||
0.578929 | + | 0.815378i | \(0.303471\pi\) | |||||||
\(740\) | − | 418.614i | − | 0.565695i | ||||||
\(741\) | 18.6827 | 0.0252128 | ||||||||
\(742\) | 163.353 | − | 118.888i | 0.220152 | − | 0.160226i | ||||
\(743\) | −32.4259 | −0.0436419 | −0.0218209 | − | 0.999762i | \(-0.506946\pi\) | ||||
−0.0218209 | + | 0.999762i | \(0.506946\pi\) | |||||||
\(744\) | 342.622i | 0.460513i | ||||||||
\(745\) | 494.589 | 0.663878 | ||||||||
\(746\) | −5.08000 | −0.00680966 | ||||||||
\(747\) | 71.2708i | 0.0954094i | ||||||||
\(748\) | − | 411.449i | − | 0.550065i | ||||||
\(749\) | −218.745 | − | 300.557i | −0.292050 | − | 0.401278i | ||||
\(750\) | − | 1005.79i | − | 1.34105i | ||||||
\(751\) | 1167.73i | 1.55490i | 0.628947 | + | 0.777448i | \(0.283486\pi\) | ||||
−0.628947 | + | 0.777448i | \(0.716514\pi\) | |||||||
\(752\) | −18.5610 | −0.0246822 | ||||||||
\(753\) | − | 374.743i | − | 0.497667i | ||||||
\(754\) | − | 330.861i | − | 0.438807i | ||||||
\(755\) | 665.121 | 0.880955 | ||||||||
\(756\) | 361.327 | + | 496.465i | 0.477946 | + | 0.656700i | ||||
\(757\) | 757.594i | 1.00078i | 0.865799 | + | 0.500392i | \(0.166811\pi\) | ||||
−0.865799 | + | 0.500392i | \(0.833189\pi\) | |||||||
\(758\) | 1120.21 | 1.47785 | ||||||||
\(759\) | − | 122.437i | − | 0.161313i | ||||||
\(760\) | − | 6.26524i | − | 0.00824373i | ||||||
\(761\) | − | 1155.38i | − | 1.51823i | −0.650955 | − | 0.759117i | \(-0.725631\pi\) | ||
0.650955 | − | 0.759117i | \(-0.274369\pi\) | |||||||
\(762\) | −948.479 | −1.24472 | ||||||||
\(763\) | −640.867 | + | 466.422i | −0.839930 | + | 0.611300i | ||||
\(764\) | 694.750i | 0.909359i | ||||||||
\(765\) | 17.1765i | 0.0224530i | ||||||||
\(766\) | 492.604 | 0.643086 | ||||||||
\(767\) | − | 192.943i | − | 0.251555i | ||||||
\(768\) | 950.641 | 1.23781 | ||||||||
\(769\) | − | 425.981i | − | 0.553942i | −0.960878 | − | 0.276971i | \(-0.910669\pi\) | ||
0.960878 | − | 0.276971i | \(-0.0893306\pi\) | |||||||
\(770\) | −566.726 | − | 778.685i | −0.736008 | − | 1.01128i | ||||
\(771\) | −1056.70 | −1.37056 | ||||||||
\(772\) | − | 62.3972i | − | 0.0808254i | ||||||
\(773\) | 170.364 | 0.220393 | 0.110197 | − | 0.993910i | \(-0.464852\pi\) | ||||
0.110197 | + | 0.993910i | \(0.464852\pi\) | |||||||
\(774\) | −116.431 | −0.150428 | ||||||||
\(775\) | 720.472i | 0.929642i | ||||||||
\(776\) | −94.0694 | −0.121223 | ||||||||
\(777\) | 474.005 | + | 651.285i | 0.610045 | + | 0.838205i | ||||
\(778\) | 388.387 | 0.499212 | ||||||||
\(779\) | 31.4878 | − | 12.4790i | 0.0404208 | − | 0.0160192i | ||||
\(780\) | − | 238.365i | − | 0.305596i | ||||||
\(781\) | −754.742 | −0.966379 | ||||||||
\(782\) | −62.3271 | −0.0797022 | ||||||||
\(783\) | 441.108i | 0.563357i | ||||||||
\(784\) | 281.313 | − | 870.660i | 0.358818 | − | 1.11054i | ||||
\(785\) | 512.602i | 0.652996i | ||||||||
\(786\) | − | 379.584i | − | 0.482932i | ||||||
\(787\) | − | 644.912i | − | 0.819456i | −0.912208 | − | 0.409728i | \(-0.865624\pi\) | ||
0.912208 | − | 0.409728i | \(-0.134376\pi\) | |||||||
\(788\) | 786.831 | 0.998516 | ||||||||
\(789\) | − | 141.908i | − | 0.179858i | ||||||
\(790\) | −982.207 | −1.24330 | ||||||||
\(791\) | −106.998 | − | 147.016i | −0.135269 | − | 0.185860i | ||||
\(792\) | − | 21.1232i | − | 0.0266707i | ||||||
\(793\) | − | 463.299i | − | 0.584236i | ||||||
\(794\) | −1332.01 | −1.67759 | ||||||||
\(795\) | 104.564 | 0.131527 | ||||||||
\(796\) | −652.796 | −0.820096 | ||||||||
\(797\) | − | 22.0824i | − | 0.0277069i | −0.999904 | − | 0.0138535i | \(-0.995590\pi\) | ||
0.999904 | − | 0.0138535i | \(-0.00440984\pi\) | |||||||
\(798\) | −26.3667 | − | 36.2281i | −0.0330410 | − | 0.0453986i | ||||
\(799\) | −8.43397 | −0.0105557 | ||||||||
\(800\) | 564.677 | 0.705846 | ||||||||
\(801\) | −103.976 | −0.129808 | ||||||||
\(802\) | −441.626 | −0.550656 | ||||||||
\(803\) | −1644.36 | −2.04777 | ||||||||
\(804\) | 32.4743i | 0.0403910i | ||||||||
\(805\) | −51.9848 | + | 37.8345i | −0.0645775 | + | 0.0469994i | ||||
\(806\) | 1088.40i | 1.35038i | ||||||||
\(807\) | − | 337.766i | − | 0.418545i | ||||||
\(808\) | 91.6740 | 0.113458 | ||||||||
\(809\) | 164.851i | 0.203772i | 0.994796 | + | 0.101886i | \(0.0324876\pi\) | ||||
−0.994796 | + | 0.101886i | \(0.967512\pi\) | |||||||
\(810\) | 672.365i | 0.830080i | ||||||||
\(811\) | − | 851.489i | − | 1.04992i | −0.851125 | − | 0.524962i | \(-0.824079\pi\) | ||
0.851125 | − | 0.524962i | \(-0.175921\pi\) | |||||||
\(812\) | −282.751 | + | 205.786i | −0.348215 | + | 0.253431i | ||||
\(813\) | − | 67.6800i | − | 0.0832472i | ||||||
\(814\) | 1634.10i | 2.00749i | ||||||||
\(815\) | 594.776i | 0.729786i | ||||||||
\(816\) | 459.051 | 0.562563 | ||||||||
\(817\) | 59.4110 | 0.0727185 | ||||||||
\(818\) | − | 1721.62i | − | 2.10467i | ||||||
\(819\) | −19.4643 | − | 26.7441i | −0.0237659 | − | 0.0326545i | ||||
\(820\) | −159.214 | − | 401.740i | −0.194163 | − | 0.489926i | ||||
\(821\) | −439.368 | −0.535162 | −0.267581 | − | 0.963535i | \(-0.586224\pi\) | ||||
−0.267581 | + | 0.963535i | \(0.586224\pi\) | |||||||
\(822\) | 398.228i | 0.484463i | ||||||||
\(823\) | 502.881i | 0.611034i | 0.952187 | + | 0.305517i | \(0.0988292\pi\) | ||||
−0.952187 | + | 0.305517i | \(0.901171\pi\) | |||||||
\(824\) | − | 239.964i | − | 0.291218i | ||||||
\(825\) | 615.935i | 0.746588i | ||||||||
\(826\) | −374.139 | + | 272.298i | −0.452953 | + | 0.329659i | ||||
\(827\) | 920.174i | 1.11267i | 0.830960 | + | 0.556333i | \(0.187792\pi\) | ||||
−0.830960 | + | 0.556333i | \(0.812208\pi\) | |||||||
\(828\) | 5.24113 | 0.00632987 | ||||||||
\(829\) | − | 331.557i | − | 0.399948i | −0.979801 | − | 0.199974i | \(-0.935914\pi\) | ||
0.979801 | − | 0.199974i | \(-0.0640858\pi\) | |||||||
\(830\) | −1052.83 | −1.26847 | ||||||||
\(831\) | 577.603 | 0.695070 | ||||||||
\(832\) | 270.034 | 0.324560 | ||||||||
\(833\) | 127.827 | − | 395.621i | 0.153453 | − | 0.474935i | ||||
\(834\) | − | 943.203i | − | 1.13094i | ||||||
\(835\) | 412.956i | 0.494558i | ||||||||
\(836\) | − | 40.0596i | − | 0.0479181i | ||||||
\(837\) | − | 1451.08i | − | 1.73366i | ||||||
\(838\) | − | 2021.62i | − | 2.41243i | ||||||
\(839\) | 1249.10 | 1.48879 | 0.744397 | − | 0.667738i | \(-0.232737\pi\) | ||||
0.744397 | + | 0.667738i | \(0.232737\pi\) | |||||||
\(840\) | 124.365 | − | 90.5126i | 0.148053 | − | 0.107753i | ||||
\(841\) | 589.776 | 0.701280 | ||||||||
\(842\) | − | 618.457i | − | 0.734510i | ||||||
\(843\) | 557.793i | 0.661676i | ||||||||
\(844\) | 1079.41i | 1.27892i | ||||||||
\(845\) | − | 361.394i | − | 0.427685i | ||||||
\(846\) | 1.60926 | 0.00190220 | ||||||||
\(847\) | 476.554 | + | 654.788i | 0.562637 | + | 0.773067i | ||||
\(848\) | 201.527i | 0.237650i | ||||||||
\(849\) | − | 748.609i | − | 0.881754i | ||||||
\(850\) | 313.545 | 0.368877 | ||||||||
\(851\) | 109.092 | 0.128193 | ||||||||
\(852\) | 448.007i | 0.525830i | ||||||||
\(853\) | 318.424i | 0.373299i | 0.982427 | + | 0.186650i | \(0.0597629\pi\) | ||||
−0.982427 | + | 0.186650i | \(0.940237\pi\) | |||||||
\(854\) | −898.393 | + | 653.850i | −1.05198 | + | 0.765632i | ||||
\(855\) | 1.67235i | 0.00195596i | ||||||||
\(856\) | 120.440 | 0.140701 | ||||||||
\(857\) | 1484.46i | 1.73216i | 0.499902 | + | 0.866082i | \(0.333369\pi\) | ||||
−0.499902 | + | 0.866082i | \(0.666631\pi\) | |||||||
\(858\) | 930.481i | 1.08448i | ||||||||
\(859\) | 644.561i | 0.750362i | 0.926952 | + | 0.375181i | \(0.122419\pi\) | ||||
−0.926952 | + | 0.375181i | \(0.877581\pi\) | |||||||
\(860\) | − | 758.000i | − | 0.881396i | ||||||
\(861\) | 702.604 | + | 444.751i | 0.816033 | + | 0.516552i | ||||
\(862\) | 241.089 | 0.279686 | ||||||||
\(863\) | 421.677 | 0.488618 | 0.244309 | − | 0.969697i | \(-0.421439\pi\) | ||||
0.244309 | + | 0.969697i | \(0.421439\pi\) | |||||||
\(864\) | −1137.29 | −1.31631 | ||||||||
\(865\) | −1121.49 | −1.29652 | ||||||||
\(866\) | 1047.24i | 1.20929i | ||||||||
\(867\) | −628.744 | −0.725195 | ||||||||
\(868\) | 930.141 | − | 676.956i | 1.07159 | − | 0.779903i | ||||
\(869\) | 1689.75 | 1.94447 | ||||||||
\(870\) | −410.681 | −0.472047 | ||||||||
\(871\) | − | 27.7565i | − | 0.0318674i | ||||||
\(872\) | − | 256.809i | − | 0.294506i | ||||||
\(873\) | 25.1094 | 0.0287623 | ||||||||
\(874\) | −6.06831 | −0.00694314 | ||||||||
\(875\) | 734.666 | − | 534.689i | 0.839618 | − | 0.611073i | ||||
\(876\) | 976.073i | 1.11424i | ||||||||
\(877\) | −1393.92 | −1.58942 | −0.794711 | − | 0.606988i | \(-0.792378\pi\) | ||||
−0.794711 | + | 0.606988i | \(0.792378\pi\) | |||||||
\(878\) | 1633.67 | 1.86067 | ||||||||
\(879\) | −590.428 | −0.671704 | ||||||||
\(880\) | 960.657 | 1.09166 | ||||||||
\(881\) | 1208.12i | 1.37131i | 0.727928 | + | 0.685654i | \(0.240484\pi\) | ||||
−0.727928 | + | 0.685654i | \(0.759516\pi\) | |||||||
\(882\) | −24.3902 | + | 75.4873i | −0.0276533 | + | 0.0855865i | ||||
\(883\) | − | 474.857i | − | 0.537777i | −0.963171 | − | 0.268889i | \(-0.913344\pi\) | ||
0.963171 | − | 0.268889i | \(-0.0866563\pi\) | |||||||
\(884\) | 208.750 | 0.236143 | ||||||||
\(885\) | −239.490 | −0.270610 | ||||||||
\(886\) | −783.858 | −0.884716 | ||||||||
\(887\) | −1313.75 | −1.48111 | −0.740556 | − | 0.671995i | \(-0.765438\pi\) | ||||
−0.740556 | + | 0.671995i | \(0.765438\pi\) | |||||||
\(888\) | −260.984 | −0.293901 | ||||||||
\(889\) | −504.223 | − | 692.806i | −0.567180 | − | 0.779309i | ||||
\(890\) | − | 1535.95i | − | 1.72579i | ||||||
\(891\) | − | 1156.71i | − | 1.29821i | ||||||
\(892\) | 282.904i | 0.317157i | ||||||||
\(893\) | −0.821151 | −0.000919542 | ||||||||
\(894\) | 1146.03i | 1.28191i | ||||||||
\(895\) | −878.209 | −0.981239 | ||||||||
\(896\) | 292.230 | + | 401.526i | 0.326149 | + | 0.448131i | ||||
\(897\) | 62.1187 | 0.0692517 | ||||||||
\(898\) | 849.063 | 0.945504 | ||||||||
\(899\) | 826.428 | 0.919275 | ||||||||
\(900\) | −26.3662 | −0.0292958 | ||||||||
\(901\) | 91.5724i | 0.101634i | ||||||||
\(902\) | 621.506 | + | 1568.23i | 0.689031 | + | 1.73861i | ||||
\(903\) | 858.298 | + | 1179.31i | 0.950496 | + | 1.30599i | ||||
\(904\) | 58.9124 | 0.0651685 | ||||||||
\(905\) | − | 95.1073i | − | 0.105091i | ||||||
\(906\) | 1541.17i | 1.70107i | ||||||||
\(907\) | 902.223 | 0.994733 | 0.497366 | − | 0.867541i | \(-0.334300\pi\) | ||||
0.497366 | + | 0.867541i | \(0.334300\pi\) | |||||||
\(908\) | 172.188 | 0.189634 | ||||||||
\(909\) | −24.4701 | −0.0269198 | ||||||||
\(910\) | 395.069 | − | 287.531i | 0.434141 | − | 0.315968i | ||||
\(911\) | 188.927 | 0.207385 | 0.103692 | − | 0.994609i | \(-0.466934\pi\) | ||||
0.103692 | + | 0.994609i | \(0.466934\pi\) | |||||||
\(912\) | 44.6943 | 0.0490069 | ||||||||
\(913\) | 1811.24 | 1.98383 | ||||||||
\(914\) | − | 2184.31i | − | 2.38983i | ||||||
\(915\) | −575.070 | −0.628492 | ||||||||
\(916\) | −773.386 | −0.844308 | ||||||||
\(917\) | 277.263 | − | 201.792i | 0.302359 | − | 0.220056i | ||||
\(918\) | −631.499 | −0.687908 | ||||||||
\(919\) | − | 936.432i | − | 1.01897i | −0.860480 | − | 0.509484i | \(-0.829836\pi\) | ||
0.860480 | − | 0.509484i | \(-0.170164\pi\) | |||||||
\(920\) | − | 20.8315i | − | 0.0226429i | ||||||
\(921\) | − | 1145.96i | − | 1.24426i | ||||||
\(922\) | − | 1482.47i | − | 1.60789i | ||||||
\(923\) | − | 382.921i | − | 0.414866i | ||||||
\(924\) | 795.182 | − | 578.732i | 0.860586 | − | 0.626334i | ||||
\(925\) | −548.803 | −0.593301 | ||||||||
\(926\) | 1966.36i | 2.12350i | ||||||||
\(927\) | 64.0523i | 0.0690964i | ||||||||
\(928\) | − | 647.721i | − | 0.697975i | ||||||
\(929\) | −1398.53 | −1.50541 | −0.752705 | − | 0.658357i | \(-0.771252\pi\) | ||||
−0.752705 | + | 0.658357i | \(0.771252\pi\) | |||||||
\(930\) | 1350.98 | 1.45267 | ||||||||
\(931\) | 12.4455 | − | 38.5186i | 0.0133679 | − | 0.0413733i | ||||
\(932\) | − | 747.567i | − | 0.802111i | ||||||
\(933\) | 688.905 | 0.738376 | ||||||||
\(934\) | 1036.87i | 1.11014i | ||||||||
\(935\) | 436.515 | 0.466861 | ||||||||
\(936\) | 10.7169 | 0.0114497 | ||||||||
\(937\) | −609.901 | −0.650908 | −0.325454 | − | 0.945558i | \(-0.605517\pi\) | ||||
−0.325454 | + | 0.945558i | \(0.605517\pi\) | |||||||
\(938\) | −53.8233 | + | 39.1725i | −0.0573809 | + | 0.0417617i | ||||
\(939\) | −1261.89 | −1.34386 | ||||||||
\(940\) | 10.4767i | 0.0111455i | ||||||||
\(941\) | − | 475.722i | − | 0.505549i | −0.967525 | − | 0.252775i | \(-0.918657\pi\) | ||
0.967525 | − | 0.252775i | \(-0.0813432\pi\) | |||||||
\(942\) | −1187.77 | −1.26090 | ||||||||
\(943\) | 104.695 | − | 41.4916i | 0.111023 | − | 0.0439996i | ||||
\(944\) | − | 461.573i | − | 0.488954i | ||||||
\(945\) | −526.711 | + | 383.340i | −0.557367 | + | 0.405651i | ||||
\(946\) | 2958.93i | 3.12783i | ||||||||
\(947\) | −1018.93 | −1.07596 | −0.537978 | − | 0.842959i | \(-0.680812\pi\) | ||||
−0.537978 | + | 0.842959i | \(0.680812\pi\) | |||||||
\(948\) | − | 1003.02i | − | 1.05803i | ||||||
\(949\) | − | 834.271i | − | 0.879105i | ||||||
\(950\) | 30.5275 | 0.0321342 | ||||||||
\(951\) | 490.319i | 0.515582i | ||||||||
\(952\) | 79.2671 | + | 108.913i | 0.0832637 | + | 0.114405i | ||||
\(953\) | −141.741 | −0.148732 | −0.0743658 | − | 0.997231i | \(-0.523693\pi\) | ||||
−0.0743658 | + | 0.997231i | \(0.523693\pi\) | |||||||
\(954\) | − | 17.4726i | − | 0.0183151i | ||||||
\(955\) | −737.076 | −0.771808 | ||||||||
\(956\) | − | 1096.88i | − | 1.14737i | ||||||
\(957\) | 706.517 | 0.738263 | ||||||||
\(958\) | −2487.25 | −2.59629 | ||||||||
\(959\) | −290.881 | + | 211.703i | −0.303318 | + | 0.220754i | ||||
\(960\) | − | 335.179i | − | 0.349145i | ||||||
\(961\) | −1757.63 | −1.82896 | ||||||||
\(962\) | −829.067 | −0.861816 | ||||||||
\(963\) | −32.1484 | −0.0333836 | ||||||||
\(964\) | 154.097i | 0.159852i | ||||||||
\(965\) | 66.1986 | 0.0685996 | ||||||||
\(966\) | −87.6676 | − | 120.456i | −0.0907532 | − | 0.124695i | ||||
\(967\) | 210.263i | 0.217439i | 0.994072 | + | 0.108719i | \(0.0346750\pi\) | ||||
−0.994072 | + | 0.108719i | \(0.965325\pi\) | |||||||
\(968\) | −262.388 | −0.271062 | ||||||||
\(969\) | 20.3087 | 0.0209585 | ||||||||
\(970\) | 370.922i | 0.382394i | ||||||||
\(971\) | −386.037 | −0.397566 | −0.198783 | − | 0.980043i | \(-0.563699\pi\) | ||||
−0.198783 | + | 0.980043i | \(0.563699\pi\) | |||||||
\(972\) | 102.860 | 0.105823 | ||||||||
\(973\) | 688.952 | − | 501.419i | 0.708070 | − | 0.515333i | ||||
\(974\) | −778.159 | −0.798931 | ||||||||
\(975\) | −312.497 | −0.320510 | ||||||||
\(976\) | − | 1108.34i | − | 1.13560i | ||||||
\(977\) | 991.983i | 1.01534i | 0.861553 | + | 0.507668i | \(0.169492\pi\) | ||||
−0.861553 | + | 0.507668i | \(0.830508\pi\) | |||||||
\(978\) | −1378.17 | −1.40918 | ||||||||
\(979\) | 2642.39i | 2.69907i | ||||||||
\(980\) | −491.443 | − | 158.787i | −0.501472 | − | 0.162027i | ||||
\(981\) | 68.5488i | 0.0698764i | ||||||||
\(982\) | 1097.53 | 1.11765 | ||||||||
\(983\) | − | 1043.79i | − | 1.06185i | −0.847420 | − | 0.530923i | \(-0.821845\pi\) | ||
0.847420 | − | 0.530923i | \(-0.178155\pi\) | |||||||
\(984\) | −250.464 | + | 99.2616i | −0.254537 | + | 0.100876i | ||||
\(985\) | 834.767i | 0.847479i | ||||||||
\(986\) | − | 359.657i | − | 0.364763i | ||||||
\(987\) | −11.8630 | − | 16.2998i | −0.0120192 | − | 0.0165145i | ||||
\(988\) | 20.3244 | 0.0205712 | ||||||||
\(989\) | 197.537 | 0.199734 | ||||||||
\(990\) | −83.2901 | −0.0841315 | ||||||||
\(991\) | − | 1131.06i | − | 1.14134i | −0.821181 | − | 0.570668i | \(-0.806684\pi\) | ||
0.821181 | − | 0.570668i | \(-0.193316\pi\) | |||||||
\(992\) | 2130.75i | 2.14793i | ||||||||
\(993\) | 250.648i | 0.252415i | ||||||||
\(994\) | −742.531 | + | 540.413i | −0.747013 | + | 0.543675i | ||||
\(995\) | − | 692.567i | − | 0.696047i | ||||||
\(996\) | − | 1075.13i | − | 1.07945i | ||||||
\(997\) | −1647.10 | −1.65205 | −0.826026 | − | 0.563632i | \(-0.809404\pi\) | ||||
−0.826026 | + | 0.563632i | \(0.809404\pi\) | |||||||
\(998\) | 1573.14i | 1.57629i | ||||||||
\(999\) | 1105.32 | 1.10643 |
(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 | 287.3.d.d.286.8 | yes | 32 | |
7.6 | odd | 2 | inner | 287.3.d.d.286.5 | ✓ | 32 | |
41.40 | even | 2 | inner | 287.3.d.d.286.6 | yes | 32 | |
287.286 | odd | 2 | inner | 287.3.d.d.286.7 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.3.d.d.286.5 | ✓ | 32 | 7.6 | odd | 2 | inner | |
287.3.d.d.286.6 | yes | 32 | 41.40 | even | 2 | inner | |
287.3.d.d.286.7 | yes | 32 | 287.286 | odd | 2 | inner | |
287.3.d.d.286.8 | yes | 32 | 1.1 | even | 1 | trivial |