Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2671,2,Mod(1,2671)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2671, 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("2671.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2671 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2671.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: | \(21.3280423799\) |
Analytic rank: | \(0\) |
Dimension: | \(122\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.80 | ||
Character | \(\chi\) | \(=\) | 2671.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.22085 | 0.863271 | 0.431635 | − | 0.902048i | \(-0.357937\pi\) | ||||
0.431635 | + | 0.902048i | \(0.357937\pi\) | |||||||
\(3\) | −3.14093 | −1.81342 | −0.906709 | − | 0.421757i | \(-0.861413\pi\) | ||||
−0.906709 | + | 0.421757i | \(0.861413\pi\) | |||||||
\(4\) | −0.509528 | −0.254764 | ||||||||
\(5\) | −0.946195 | −0.423151 | −0.211576 | − | 0.977362i | \(-0.567859\pi\) | ||||
−0.211576 | + | 0.977362i | \(0.567859\pi\) | |||||||
\(6\) | −3.83460 | −1.56547 | ||||||||
\(7\) | −0.0224945 | −0.00850212 | −0.00425106 | − | 0.999991i | \(-0.501353\pi\) | ||||
−0.00425106 | + | 0.999991i | \(0.501353\pi\) | |||||||
\(8\) | −3.06375 | −1.08320 | ||||||||
\(9\) | 6.86545 | 2.28848 | ||||||||
\(10\) | −1.15516 | −0.365294 | ||||||||
\(11\) | −6.33640 | −1.91050 | −0.955248 | − | 0.295806i | \(-0.904412\pi\) | ||||
−0.955248 | + | 0.295806i | \(0.904412\pi\) | |||||||
\(12\) | 1.60039 | 0.461993 | ||||||||
\(13\) | 0.358954 | 0.0995561 | 0.0497780 | − | 0.998760i | \(-0.484149\pi\) | ||||
0.0497780 | + | 0.998760i | \(0.484149\pi\) | |||||||
\(14\) | −0.0274624 | −0.00733963 | ||||||||
\(15\) | 2.97193 | 0.767350 | ||||||||
\(16\) | −2.72133 | −0.680331 | ||||||||
\(17\) | −0.0188727 | −0.00457730 | −0.00228865 | − | 0.999997i | \(-0.500728\pi\) | ||||
−0.00228865 | + | 0.999997i | \(0.500728\pi\) | |||||||
\(18\) | 8.38168 | 1.97558 | ||||||||
\(19\) | −6.65643 | −1.52709 | −0.763545 | − | 0.645755i | \(-0.776543\pi\) | ||||
−0.763545 | + | 0.645755i | \(0.776543\pi\) | |||||||
\(20\) | 0.482113 | 0.107804 | ||||||||
\(21\) | 0.0706537 | 0.0154179 | ||||||||
\(22\) | −7.73579 | −1.64928 | ||||||||
\(23\) | 1.13749 | 0.237183 | 0.118591 | − | 0.992943i | \(-0.462162\pi\) | ||||
0.118591 | + | 0.992943i | \(0.462162\pi\) | |||||||
\(24\) | 9.62304 | 1.96430 | ||||||||
\(25\) | −4.10472 | −0.820943 | ||||||||
\(26\) | 0.438229 | 0.0859438 | ||||||||
\(27\) | −12.1411 | −2.33656 | ||||||||
\(28\) | 0.0114616 | 0.00216603 | ||||||||
\(29\) | −7.65975 | −1.42238 | −0.711190 | − | 0.703000i | \(-0.751843\pi\) | ||||
−0.711190 | + | 0.703000i | \(0.751843\pi\) | |||||||
\(30\) | 3.62828 | 0.662431 | ||||||||
\(31\) | −8.09110 | −1.45320 | −0.726602 | − | 0.687058i | \(-0.758902\pi\) | ||||
−0.726602 | + | 0.687058i | \(0.758902\pi\) | |||||||
\(32\) | 2.80518 | 0.495891 | ||||||||
\(33\) | 19.9022 | 3.46453 | ||||||||
\(34\) | −0.0230407 | −0.00395144 | ||||||||
\(35\) | 0.0212842 | 0.00359768 | ||||||||
\(36\) | −3.49814 | −0.583023 | ||||||||
\(37\) | 0.639087 | 0.105065 | 0.0525326 | − | 0.998619i | \(-0.483271\pi\) | ||||
0.0525326 | + | 0.998619i | \(0.483271\pi\) | |||||||
\(38\) | −8.12650 | −1.31829 | ||||||||
\(39\) | −1.12745 | −0.180537 | ||||||||
\(40\) | 2.89891 | 0.458358 | ||||||||
\(41\) | −2.68215 | −0.418881 | −0.209441 | − | 0.977821i | \(-0.567164\pi\) | ||||
−0.209441 | + | 0.977821i | \(0.567164\pi\) | |||||||
\(42\) | 0.0862575 | 0.0133098 | ||||||||
\(43\) | 10.9076 | 1.66339 | 0.831697 | − | 0.555230i | \(-0.187370\pi\) | ||||
0.831697 | + | 0.555230i | \(0.187370\pi\) | |||||||
\(44\) | 3.22857 | 0.486725 | ||||||||
\(45\) | −6.49605 | −0.968375 | ||||||||
\(46\) | 1.38870 | 0.204753 | ||||||||
\(47\) | 7.99169 | 1.16571 | 0.582854 | − | 0.812577i | \(-0.301936\pi\) | ||||
0.582854 | + | 0.812577i | \(0.301936\pi\) | |||||||
\(48\) | 8.54750 | 1.23373 | ||||||||
\(49\) | −6.99949 | −0.999928 | ||||||||
\(50\) | −5.01124 | −0.708696 | ||||||||
\(51\) | 0.0592778 | 0.00830055 | ||||||||
\(52\) | −0.182897 | −0.0253633 | ||||||||
\(53\) | −5.97511 | −0.820744 | −0.410372 | − | 0.911918i | \(-0.634601\pi\) | ||||
−0.410372 | + | 0.911918i | \(0.634601\pi\) | |||||||
\(54\) | −14.8225 | −2.01708 | ||||||||
\(55\) | 5.99547 | 0.808429 | ||||||||
\(56\) | 0.0689176 | 0.00920951 | ||||||||
\(57\) | 20.9074 | 2.76925 | ||||||||
\(58\) | −9.35140 | −1.22790 | ||||||||
\(59\) | −9.74596 | −1.26882 | −0.634408 | − | 0.772999i | \(-0.718756\pi\) | ||||
−0.634408 | + | 0.772999i | \(0.718756\pi\) | |||||||
\(60\) | −1.51428 | −0.195493 | ||||||||
\(61\) | 9.04821 | 1.15850 | 0.579252 | − | 0.815148i | \(-0.303345\pi\) | ||||
0.579252 | + | 0.815148i | \(0.303345\pi\) | |||||||
\(62\) | −9.87801 | −1.25451 | ||||||||
\(63\) | −0.154435 | −0.0194570 | ||||||||
\(64\) | 8.86735 | 1.10842 | ||||||||
\(65\) | −0.339641 | −0.0421273 | ||||||||
\(66\) | 24.2976 | 2.99082 | ||||||||
\(67\) | −6.76683 | −0.826700 | −0.413350 | − | 0.910572i | \(-0.635641\pi\) | ||||
−0.413350 | + | 0.910572i | \(0.635641\pi\) | |||||||
\(68\) | 0.00961615 | 0.00116613 | ||||||||
\(69\) | −3.57277 | −0.430111 | ||||||||
\(70\) | 0.0259848 | 0.00310577 | ||||||||
\(71\) | 5.84470 | 0.693638 | 0.346819 | − | 0.937932i | \(-0.387262\pi\) | ||||
0.346819 | + | 0.937932i | \(0.387262\pi\) | |||||||
\(72\) | −21.0341 | −2.47889 | ||||||||
\(73\) | −4.58304 | −0.536404 | −0.268202 | − | 0.963363i | \(-0.586430\pi\) | ||||
−0.268202 | + | 0.963363i | \(0.586430\pi\) | |||||||
\(74\) | 0.780229 | 0.0906997 | ||||||||
\(75\) | 12.8926 | 1.48871 | ||||||||
\(76\) | 3.39164 | 0.389047 | ||||||||
\(77\) | 0.142534 | 0.0162433 | ||||||||
\(78\) | −1.37645 | −0.155852 | ||||||||
\(79\) | −15.1903 | −1.70905 | −0.854523 | − | 0.519414i | \(-0.826150\pi\) | ||||
−0.854523 | + | 0.519414i | \(0.826150\pi\) | |||||||
\(80\) | 2.57490 | 0.287883 | ||||||||
\(81\) | 17.5381 | 1.94867 | ||||||||
\(82\) | −3.27450 | −0.361608 | ||||||||
\(83\) | −2.35275 | −0.258248 | −0.129124 | − | 0.991628i | \(-0.541216\pi\) | ||||
−0.129124 | + | 0.991628i | \(0.541216\pi\) | |||||||
\(84\) | −0.0360000 | −0.00392792 | ||||||||
\(85\) | 0.0178572 | 0.00193689 | ||||||||
\(86\) | 13.3165 | 1.43596 | ||||||||
\(87\) | 24.0587 | 2.57937 | ||||||||
\(88\) | 19.4132 | 2.06945 | ||||||||
\(89\) | 15.1594 | 1.60689 | 0.803446 | − | 0.595378i | \(-0.202998\pi\) | ||||
0.803446 | + | 0.595378i | \(0.202998\pi\) | |||||||
\(90\) | −7.93070 | −0.835969 | ||||||||
\(91\) | −0.00807450 | −0.000846438 0 | ||||||||
\(92\) | −0.579582 | −0.0604256 | ||||||||
\(93\) | 25.4136 | 2.63527 | ||||||||
\(94\) | 9.75664 | 1.00632 | ||||||||
\(95\) | 6.29828 | 0.646190 | ||||||||
\(96\) | −8.81088 | −0.899257 | ||||||||
\(97\) | 12.9716 | 1.31707 | 0.658534 | − | 0.752551i | \(-0.271177\pi\) | ||||
0.658534 | + | 0.752551i | \(0.271177\pi\) | |||||||
\(98\) | −8.54532 | −0.863208 | ||||||||
\(99\) | −43.5022 | −4.37214 | ||||||||
\(100\) | 2.09147 | 0.209147 | ||||||||
\(101\) | 16.4512 | 1.63695 | 0.818476 | − | 0.574540i | \(-0.194819\pi\) | ||||
0.818476 | + | 0.574540i | \(0.194819\pi\) | |||||||
\(102\) | 0.0723692 | 0.00716562 | ||||||||
\(103\) | −2.78791 | −0.274701 | −0.137350 | − | 0.990523i | \(-0.543859\pi\) | ||||
−0.137350 | + | 0.990523i | \(0.543859\pi\) | |||||||
\(104\) | −1.09975 | −0.107839 | ||||||||
\(105\) | −0.0668522 | −0.00652410 | ||||||||
\(106\) | −7.29470 | −0.708524 | ||||||||
\(107\) | 3.75751 | 0.363252 | 0.181626 | − | 0.983368i | \(-0.441864\pi\) | ||||
0.181626 | + | 0.983368i | \(0.441864\pi\) | |||||||
\(108\) | 6.18624 | 0.595271 | ||||||||
\(109\) | 3.69023 | 0.353460 | 0.176730 | − | 0.984259i | \(-0.443448\pi\) | ||||
0.176730 | + | 0.984259i | \(0.443448\pi\) | |||||||
\(110\) | 7.31956 | 0.697893 | ||||||||
\(111\) | −2.00733 | −0.190527 | ||||||||
\(112\) | 0.0612149 | 0.00578426 | ||||||||
\(113\) | 0.0599889 | 0.00564329 | 0.00282164 | − | 0.999996i | \(-0.499102\pi\) | ||||
0.00282164 | + | 0.999996i | \(0.499102\pi\) | |||||||
\(114\) | 25.5248 | 2.39061 | ||||||||
\(115\) | −1.07629 | −0.100364 | ||||||||
\(116\) | 3.90285 | 0.362371 | ||||||||
\(117\) | 2.46438 | 0.227832 | ||||||||
\(118\) | −11.8983 | −1.09533 | ||||||||
\(119\) | 0.000424531 0 | 3.89167e−5 0 | ||||||||
\(120\) | −9.10527 | −0.831194 | ||||||||
\(121\) | 29.1500 | 2.65000 | ||||||||
\(122\) | 11.0465 | 1.00010 | ||||||||
\(123\) | 8.42445 | 0.759607 | ||||||||
\(124\) | 4.12264 | 0.370224 | ||||||||
\(125\) | 8.61483 | 0.770534 | ||||||||
\(126\) | −0.188542 | −0.0167966 | ||||||||
\(127\) | 10.4771 | 0.929692 | 0.464846 | − | 0.885392i | \(-0.346110\pi\) | ||||
0.464846 | + | 0.885392i | \(0.346110\pi\) | |||||||
\(128\) | 5.21534 | 0.460975 | ||||||||
\(129\) | −34.2600 | −3.01643 | ||||||||
\(130\) | −0.414650 | −0.0363672 | ||||||||
\(131\) | −5.26636 | −0.460124 | −0.230062 | − | 0.973176i | \(-0.573893\pi\) | ||||
−0.230062 | + | 0.973176i | \(0.573893\pi\) | |||||||
\(132\) | −10.1407 | −0.882637 | ||||||||
\(133\) | 0.149733 | 0.0129835 | ||||||||
\(134\) | −8.26128 | −0.713666 | ||||||||
\(135\) | 11.4879 | 0.988718 | ||||||||
\(136\) | 0.0578212 | 0.00495813 | ||||||||
\(137\) | −3.92989 | −0.335753 | −0.167877 | − | 0.985808i | \(-0.553691\pi\) | ||||
−0.167877 | + | 0.985808i | \(0.553691\pi\) | |||||||
\(138\) | −4.36182 | −0.371302 | ||||||||
\(139\) | 1.53103 | 0.129860 | 0.0649299 | − | 0.997890i | \(-0.479318\pi\) | ||||
0.0649299 | + | 0.997890i | \(0.479318\pi\) | |||||||
\(140\) | −0.0108449 | −0.000916560 0 | ||||||||
\(141\) | −25.1013 | −2.11391 | ||||||||
\(142\) | 7.13549 | 0.598797 | ||||||||
\(143\) | −2.27448 | −0.190201 | ||||||||
\(144\) | −18.6831 | −1.55693 | ||||||||
\(145\) | 7.24761 | 0.601882 | ||||||||
\(146\) | −5.59520 | −0.463062 | ||||||||
\(147\) | 21.9849 | 1.81329 | ||||||||
\(148\) | −0.325633 | −0.0267668 | ||||||||
\(149\) | 7.53174 | 0.617024 | 0.308512 | − | 0.951220i | \(-0.400169\pi\) | ||||
0.308512 | + | 0.951220i | \(0.400169\pi\) | |||||||
\(150\) | 15.7400 | 1.28516 | ||||||||
\(151\) | 18.0198 | 1.46643 | 0.733215 | − | 0.679997i | \(-0.238019\pi\) | ||||
0.733215 | + | 0.679997i | \(0.238019\pi\) | |||||||
\(152\) | 20.3937 | 1.65414 | ||||||||
\(153\) | −0.129569 | −0.0104751 | ||||||||
\(154\) | 0.174013 | 0.0140223 | ||||||||
\(155\) | 7.65576 | 0.614925 | ||||||||
\(156\) | 0.574468 | 0.0459942 | ||||||||
\(157\) | −3.27134 | −0.261082 | −0.130541 | − | 0.991443i | \(-0.541671\pi\) | ||||
−0.130541 | + | 0.991443i | \(0.541671\pi\) | |||||||
\(158\) | −18.5451 | −1.47537 | ||||||||
\(159\) | 18.7674 | 1.48835 | ||||||||
\(160\) | −2.65425 | −0.209837 | ||||||||
\(161\) | −0.0255872 | −0.00201656 | ||||||||
\(162\) | 21.4113 | 1.68223 | ||||||||
\(163\) | −24.3816 | −1.90971 | −0.954856 | − | 0.297068i | \(-0.903991\pi\) | ||||
−0.954856 | + | 0.297068i | \(0.903991\pi\) | |||||||
\(164\) | 1.36663 | 0.106716 | ||||||||
\(165\) | −18.8314 | −1.46602 | ||||||||
\(166\) | −2.87235 | −0.222938 | ||||||||
\(167\) | 12.9593 | 1.00282 | 0.501411 | − | 0.865209i | \(-0.332814\pi\) | ||||
0.501411 | + | 0.865209i | \(0.332814\pi\) | |||||||
\(168\) | −0.216466 | −0.0167007 | ||||||||
\(169\) | −12.8712 | −0.990089 | ||||||||
\(170\) | 0.0218010 | 0.00167206 | ||||||||
\(171\) | −45.6994 | −3.49472 | ||||||||
\(172\) | −5.55773 | −0.423773 | ||||||||
\(173\) | −2.28681 | −0.173863 | −0.0869314 | − | 0.996214i | \(-0.527706\pi\) | ||||
−0.0869314 | + | 0.996214i | \(0.527706\pi\) | |||||||
\(174\) | 29.3721 | 2.22669 | ||||||||
\(175\) | 0.0923335 | 0.00697976 | ||||||||
\(176\) | 17.2434 | 1.29977 | ||||||||
\(177\) | 30.6114 | 2.30089 | ||||||||
\(178\) | 18.5073 | 1.38718 | ||||||||
\(179\) | −12.8359 | −0.959399 | −0.479700 | − | 0.877433i | \(-0.659254\pi\) | ||||
−0.479700 | + | 0.877433i | \(0.659254\pi\) | |||||||
\(180\) | 3.30992 | 0.246707 | ||||||||
\(181\) | 0.576179 | 0.0428271 | 0.0214135 | − | 0.999771i | \(-0.493183\pi\) | ||||
0.0214135 | + | 0.999771i | \(0.493183\pi\) | |||||||
\(182\) | −0.00985775 | −0.000730705 0 | ||||||||
\(183\) | −28.4198 | −2.10085 | ||||||||
\(184\) | −3.48498 | −0.256916 | ||||||||
\(185\) | −0.604701 | −0.0444585 | ||||||||
\(186\) | 31.0262 | 2.27495 | ||||||||
\(187\) | 0.119585 | 0.00874491 | ||||||||
\(188\) | −4.07199 | −0.296980 | ||||||||
\(189\) | 0.273108 | 0.0198657 | ||||||||
\(190\) | 7.68925 | 0.557837 | ||||||||
\(191\) | −14.3322 | −1.03704 | −0.518520 | − | 0.855065i | \(-0.673517\pi\) | ||||
−0.518520 | + | 0.855065i | \(0.673517\pi\) | |||||||
\(192\) | −27.8518 | −2.01003 | ||||||||
\(193\) | −6.85980 | −0.493779 | −0.246890 | − | 0.969044i | \(-0.579409\pi\) | ||||
−0.246890 | + | 0.969044i | \(0.579409\pi\) | |||||||
\(194\) | 15.8364 | 1.13699 | ||||||||
\(195\) | 1.06679 | 0.0763943 | ||||||||
\(196\) | 3.56644 | 0.254745 | ||||||||
\(197\) | 11.3893 | 0.811457 | 0.405728 | − | 0.913994i | \(-0.367018\pi\) | ||||
0.405728 | + | 0.913994i | \(0.367018\pi\) | |||||||
\(198\) | −53.1097 | −3.77434 | ||||||||
\(199\) | −25.2042 | −1.78668 | −0.893339 | − | 0.449383i | \(-0.851644\pi\) | ||||
−0.893339 | + | 0.449383i | \(0.851644\pi\) | |||||||
\(200\) | 12.5758 | 0.889246 | ||||||||
\(201\) | 21.2541 | 1.49915 | ||||||||
\(202\) | 20.0844 | 1.41313 | ||||||||
\(203\) | 0.172302 | 0.0120932 | ||||||||
\(204\) | −0.0302037 | −0.00211468 | ||||||||
\(205\) | 2.53784 | 0.177250 | ||||||||
\(206\) | −3.40362 | −0.237141 | ||||||||
\(207\) | 7.80937 | 0.542789 | ||||||||
\(208\) | −0.976832 | −0.0677311 | ||||||||
\(209\) | 42.1778 | 2.91750 | ||||||||
\(210\) | −0.0816164 | −0.00563207 | ||||||||
\(211\) | −8.73149 | −0.601101 | −0.300550 | − | 0.953766i | \(-0.597170\pi\) | ||||
−0.300550 | + | 0.953766i | \(0.597170\pi\) | |||||||
\(212\) | 3.04448 | 0.209096 | ||||||||
\(213\) | −18.3578 | −1.25786 | ||||||||
\(214\) | 4.58735 | 0.313585 | ||||||||
\(215\) | −10.3207 | −0.703867 | ||||||||
\(216\) | 37.1974 | 2.53096 | ||||||||
\(217\) | 0.182005 | 0.0123553 | ||||||||
\(218\) | 4.50522 | 0.305132 | ||||||||
\(219\) | 14.3950 | 0.972725 | ||||||||
\(220\) | −3.05486 | −0.205958 | ||||||||
\(221\) | −0.00677443 | −0.000455698 0 | ||||||||
\(222\) | −2.45064 | −0.164476 | ||||||||
\(223\) | −15.0962 | −1.01092 | −0.505459 | − | 0.862851i | \(-0.668677\pi\) | ||||
−0.505459 | + | 0.862851i | \(0.668677\pi\) | |||||||
\(224\) | −0.0631011 | −0.00421612 | ||||||||
\(225\) | −28.1807 | −1.87871 | ||||||||
\(226\) | 0.0732374 | 0.00487168 | ||||||||
\(227\) | −6.50073 | −0.431468 | −0.215734 | − | 0.976452i | \(-0.569214\pi\) | ||||
−0.215734 | + | 0.976452i | \(0.569214\pi\) | |||||||
\(228\) | −10.6529 | −0.705505 | ||||||||
\(229\) | −13.3493 | −0.882146 | −0.441073 | − | 0.897471i | \(-0.645402\pi\) | ||||
−0.441073 | + | 0.897471i | \(0.645402\pi\) | |||||||
\(230\) | −1.31398 | −0.0866414 | ||||||||
\(231\) | −0.447690 | −0.0294558 | ||||||||
\(232\) | 23.4676 | 1.54072 | ||||||||
\(233\) | 27.3005 | 1.78852 | 0.894258 | − | 0.447551i | \(-0.147704\pi\) | ||||
0.894258 | + | 0.447551i | \(0.147704\pi\) | |||||||
\(234\) | 3.00864 | 0.196681 | ||||||||
\(235\) | −7.56169 | −0.493270 | ||||||||
\(236\) | 4.96584 | 0.323248 | ||||||||
\(237\) | 47.7118 | 3.09921 | ||||||||
\(238\) | 0.000518289 0 | 3.35957e−5 0 | ||||||||
\(239\) | −12.4180 | −0.803251 | −0.401625 | − | 0.915804i | \(-0.631555\pi\) | ||||
−0.401625 | + | 0.915804i | \(0.631555\pi\) | |||||||
\(240\) | −8.08760 | −0.522052 | ||||||||
\(241\) | −3.98664 | −0.256802 | −0.128401 | − | 0.991722i | \(-0.540984\pi\) | ||||
−0.128401 | + | 0.991722i | \(0.540984\pi\) | |||||||
\(242\) | 35.5877 | 2.28766 | ||||||||
\(243\) | −18.6625 | −1.19720 | ||||||||
\(244\) | −4.61032 | −0.295145 | ||||||||
\(245\) | 6.62289 | 0.423121 | ||||||||
\(246\) | 10.2850 | 0.655746 | ||||||||
\(247\) | −2.38936 | −0.152031 | ||||||||
\(248\) | 24.7891 | 1.57411 | ||||||||
\(249\) | 7.38982 | 0.468311 | ||||||||
\(250\) | 10.5174 | 0.665180 | ||||||||
\(251\) | −10.2676 | −0.648084 | −0.324042 | − | 0.946043i | \(-0.605042\pi\) | ||||
−0.324042 | + | 0.946043i | \(0.605042\pi\) | |||||||
\(252\) | 0.0786889 | 0.00495693 | ||||||||
\(253\) | −7.20758 | −0.453137 | ||||||||
\(254\) | 12.7909 | 0.802576 | ||||||||
\(255\) | −0.0560883 | −0.00351239 | ||||||||
\(256\) | −11.3676 | −0.710473 | ||||||||
\(257\) | 9.95019 | 0.620676 | 0.310338 | − | 0.950626i | \(-0.399558\pi\) | ||||
0.310338 | + | 0.950626i | \(0.399558\pi\) | |||||||
\(258\) | −41.8263 | −2.60399 | ||||||||
\(259\) | −0.0143759 | −0.000893278 0 | ||||||||
\(260\) | 0.173056 | 0.0107325 | ||||||||
\(261\) | −52.5876 | −3.25509 | ||||||||
\(262\) | −6.42943 | −0.397212 | ||||||||
\(263\) | −4.10482 | −0.253114 | −0.126557 | − | 0.991959i | \(-0.540393\pi\) | ||||
−0.126557 | + | 0.991959i | \(0.540393\pi\) | |||||||
\(264\) | −60.9754 | −3.75278 | ||||||||
\(265\) | 5.65362 | 0.347299 | ||||||||
\(266\) | 0.182801 | 0.0112083 | ||||||||
\(267\) | −47.6146 | −2.91397 | ||||||||
\(268\) | 3.44789 | 0.210613 | ||||||||
\(269\) | −3.11361 | −0.189840 | −0.0949200 | − | 0.995485i | \(-0.530260\pi\) | ||||
−0.0949200 | + | 0.995485i | \(0.530260\pi\) | |||||||
\(270\) | 14.0249 | 0.853531 | ||||||||
\(271\) | 6.43569 | 0.390941 | 0.195470 | − | 0.980710i | \(-0.437377\pi\) | ||||
0.195470 | + | 0.980710i | \(0.437377\pi\) | |||||||
\(272\) | 0.0513587 | 0.00311408 | ||||||||
\(273\) | 0.0253615 | 0.00153495 | ||||||||
\(274\) | −4.79781 | −0.289846 | ||||||||
\(275\) | 26.0091 | 1.56841 | ||||||||
\(276\) | 1.82043 | 0.109577 | ||||||||
\(277\) | −12.8651 | −0.772991 | −0.386496 | − | 0.922291i | \(-0.626315\pi\) | ||||
−0.386496 | + | 0.922291i | \(0.626315\pi\) | |||||||
\(278\) | 1.86915 | 0.112104 | ||||||||
\(279\) | −55.5490 | −3.32563 | ||||||||
\(280\) | −0.0652095 | −0.00389701 | ||||||||
\(281\) | 7.36315 | 0.439249 | 0.219624 | − | 0.975585i | \(-0.429517\pi\) | ||||
0.219624 | + | 0.975585i | \(0.429517\pi\) | |||||||
\(282\) | −30.6449 | −1.82488 | ||||||||
\(283\) | 9.49154 | 0.564214 | 0.282107 | − | 0.959383i | \(-0.408967\pi\) | ||||
0.282107 | + | 0.959383i | \(0.408967\pi\) | |||||||
\(284\) | −2.97804 | −0.176714 | ||||||||
\(285\) | −19.7825 | −1.17181 | ||||||||
\(286\) | −2.77680 | −0.164195 | ||||||||
\(287\) | 0.0603336 | 0.00356138 | ||||||||
\(288\) | 19.2588 | 1.13484 | ||||||||
\(289\) | −16.9996 | −0.999979 | ||||||||
\(290\) | 8.84824 | 0.519587 | ||||||||
\(291\) | −40.7429 | −2.38839 | ||||||||
\(292\) | 2.33519 | 0.136656 | ||||||||
\(293\) | 11.5436 | 0.674385 | 0.337193 | − | 0.941436i | \(-0.390523\pi\) | ||||
0.337193 | + | 0.941436i | \(0.390523\pi\) | |||||||
\(294\) | 26.8403 | 1.56536 | ||||||||
\(295\) | 9.22157 | 0.536901 | ||||||||
\(296\) | −1.95801 | −0.113807 | ||||||||
\(297\) | 76.9310 | 4.46399 | ||||||||
\(298\) | 9.19511 | 0.532659 | ||||||||
\(299\) | 0.408306 | 0.0236130 | ||||||||
\(300\) | −6.56915 | −0.379270 | ||||||||
\(301\) | −0.245361 | −0.0141424 | ||||||||
\(302\) | 21.9994 | 1.26593 | ||||||||
\(303\) | −51.6720 | −2.96848 | ||||||||
\(304\) | 18.1143 | 1.03893 | ||||||||
\(305\) | −8.56137 | −0.490223 | ||||||||
\(306\) | −0.158185 | −0.00904282 | ||||||||
\(307\) | −13.2120 | −0.754049 | −0.377025 | − | 0.926203i | \(-0.623053\pi\) | ||||
−0.377025 | + | 0.926203i | \(0.623053\pi\) | |||||||
\(308\) | −0.0726251 | −0.00413820 | ||||||||
\(309\) | 8.75663 | 0.498147 | ||||||||
\(310\) | 9.34652 | 0.530847 | ||||||||
\(311\) | 21.2986 | 1.20773 | 0.603867 | − | 0.797085i | \(-0.293626\pi\) | ||||
0.603867 | + | 0.797085i | \(0.293626\pi\) | |||||||
\(312\) | 3.45423 | 0.195558 | ||||||||
\(313\) | −14.1808 | −0.801547 | −0.400774 | − | 0.916177i | \(-0.631259\pi\) | ||||
−0.400774 | + | 0.916177i | \(0.631259\pi\) | |||||||
\(314\) | −3.99382 | −0.225384 | ||||||||
\(315\) | 0.146125 | 0.00823324 | ||||||||
\(316\) | 7.73989 | 0.435403 | ||||||||
\(317\) | −28.8514 | −1.62046 | −0.810229 | − | 0.586113i | \(-0.800657\pi\) | ||||
−0.810229 | + | 0.586113i | \(0.800657\pi\) | |||||||
\(318\) | 22.9122 | 1.28485 | ||||||||
\(319\) | 48.5352 | 2.71745 | ||||||||
\(320\) | −8.39024 | −0.469029 | ||||||||
\(321\) | −11.8021 | −0.658727 | ||||||||
\(322\) | −0.0312381 | −0.00174083 | ||||||||
\(323\) | 0.125625 | 0.00698994 | ||||||||
\(324\) | −8.93613 | −0.496452 | ||||||||
\(325\) | −1.47341 | −0.0817299 | ||||||||
\(326\) | −29.7662 | −1.64860 | ||||||||
\(327\) | −11.5908 | −0.640971 | ||||||||
\(328\) | 8.21745 | 0.453733 | ||||||||
\(329\) | −0.179769 | −0.00991099 | ||||||||
\(330\) | −22.9902 | −1.26557 | ||||||||
\(331\) | 29.5040 | 1.62169 | 0.810843 | − | 0.585264i | \(-0.199009\pi\) | ||||
0.810843 | + | 0.585264i | \(0.199009\pi\) | |||||||
\(332\) | 1.19879 | 0.0657922 | ||||||||
\(333\) | 4.38762 | 0.240440 | ||||||||
\(334\) | 15.8214 | 0.865707 | ||||||||
\(335\) | 6.40274 | 0.349819 | ||||||||
\(336\) | −0.192272 | −0.0104893 | ||||||||
\(337\) | −30.9951 | −1.68841 | −0.844205 | − | 0.536021i | \(-0.819927\pi\) | ||||
−0.844205 | + | 0.536021i | \(0.819927\pi\) | |||||||
\(338\) | −15.7137 | −0.854714 | ||||||||
\(339\) | −0.188421 | −0.0102336 | ||||||||
\(340\) | −0.00909875 | −0.000493449 0 | ||||||||
\(341\) | 51.2684 | 2.77634 | ||||||||
\(342\) | −55.7921 | −3.01689 | ||||||||
\(343\) | 0.314912 | 0.0170036 | ||||||||
\(344\) | −33.4182 | −1.80179 | ||||||||
\(345\) | 3.38054 | 0.182002 | ||||||||
\(346\) | −2.79185 | −0.150091 | ||||||||
\(347\) | −30.5123 | −1.63799 | −0.818993 | − | 0.573804i | \(-0.805467\pi\) | ||||
−0.818993 | + | 0.573804i | \(0.805467\pi\) | |||||||
\(348\) | −12.2586 | −0.657130 | ||||||||
\(349\) | −18.7502 | −1.00367 | −0.501837 | − | 0.864962i | \(-0.667342\pi\) | ||||
−0.501837 | + | 0.864962i | \(0.667342\pi\) | |||||||
\(350\) | 0.112725 | 0.00602542 | ||||||||
\(351\) | −4.35811 | −0.232619 | ||||||||
\(352\) | −17.7747 | −0.947397 | ||||||||
\(353\) | 3.35416 | 0.178524 | 0.0892621 | − | 0.996008i | \(-0.471549\pi\) | ||||
0.0892621 | + | 0.996008i | \(0.471549\pi\) | |||||||
\(354\) | 37.3719 | 1.98629 | ||||||||
\(355\) | −5.53022 | −0.293514 | ||||||||
\(356\) | −7.72413 | −0.409378 | ||||||||
\(357\) | −0.00133342 | −7.05723e−5 0 | ||||||||
\(358\) | −15.6707 | −0.828221 | ||||||||
\(359\) | 1.98616 | 0.104826 | 0.0524128 | − | 0.998626i | \(-0.483309\pi\) | ||||
0.0524128 | + | 0.998626i | \(0.483309\pi\) | |||||||
\(360\) | 19.9023 | 1.04894 | ||||||||
\(361\) | 25.3081 | 1.33200 | ||||||||
\(362\) | 0.703428 | 0.0369713 | ||||||||
\(363\) | −91.5580 | −4.80555 | ||||||||
\(364\) | 0.00411418 | 0.000215642 0 | ||||||||
\(365\) | 4.33645 | 0.226980 | ||||||||
\(366\) | −34.6963 | −1.81360 | ||||||||
\(367\) | 20.9339 | 1.09274 | 0.546369 | − | 0.837544i | \(-0.316010\pi\) | ||||
0.546369 | + | 0.837544i | \(0.316010\pi\) | |||||||
\(368\) | −3.09548 | −0.161363 | ||||||||
\(369\) | −18.4142 | −0.958603 | ||||||||
\(370\) | −0.738248 | −0.0383797 | ||||||||
\(371\) | 0.134407 | 0.00697807 | ||||||||
\(372\) | −12.9489 | −0.671371 | ||||||||
\(373\) | −7.22722 | −0.374211 | −0.187106 | − | 0.982340i | \(-0.559911\pi\) | ||||
−0.187106 | + | 0.982340i | \(0.559911\pi\) | |||||||
\(374\) | 0.145995 | 0.00754922 | ||||||||
\(375\) | −27.0586 | −1.39730 | ||||||||
\(376\) | −24.4846 | −1.26270 | ||||||||
\(377\) | −2.74950 | −0.141607 | ||||||||
\(378\) | 0.333424 | 0.0171495 | ||||||||
\(379\) | 14.5494 | 0.747352 | 0.373676 | − | 0.927559i | \(-0.378097\pi\) | ||||
0.373676 | + | 0.927559i | \(0.378097\pi\) | |||||||
\(380\) | −3.20915 | −0.164626 | ||||||||
\(381\) | −32.9078 | −1.68592 | ||||||||
\(382\) | −17.4974 | −0.895247 | ||||||||
\(383\) | 33.4698 | 1.71023 | 0.855114 | − | 0.518439i | \(-0.173487\pi\) | ||||
0.855114 | + | 0.518439i | \(0.173487\pi\) | |||||||
\(384\) | −16.3810 | −0.835940 | ||||||||
\(385\) | −0.134865 | −0.00687336 | ||||||||
\(386\) | −8.37478 | −0.426265 | ||||||||
\(387\) | 74.8856 | 3.80665 | ||||||||
\(388\) | −6.60940 | −0.335541 | ||||||||
\(389\) | 0.947467 | 0.0480385 | 0.0240192 | − | 0.999711i | \(-0.492354\pi\) | ||||
0.0240192 | + | 0.999711i | \(0.492354\pi\) | |||||||
\(390\) | 1.30239 | 0.0659490 | ||||||||
\(391\) | −0.0214674 | −0.00108566 | ||||||||
\(392\) | 21.4447 | 1.08312 | ||||||||
\(393\) | 16.5413 | 0.834397 | ||||||||
\(394\) | 13.9047 | 0.700507 | ||||||||
\(395\) | 14.3730 | 0.723184 | ||||||||
\(396\) | 22.1656 | 1.11386 | ||||||||
\(397\) | −24.8447 | −1.24692 | −0.623460 | − | 0.781855i | \(-0.714274\pi\) | ||||
−0.623460 | + | 0.781855i | \(0.714274\pi\) | |||||||
\(398\) | −30.7705 | −1.54239 | ||||||||
\(399\) | −0.470301 | −0.0235445 | ||||||||
\(400\) | 11.1703 | 0.558513 | ||||||||
\(401\) | 15.9321 | 0.795613 | 0.397807 | − | 0.917469i | \(-0.369771\pi\) | ||||
0.397807 | + | 0.917469i | \(0.369771\pi\) | |||||||
\(402\) | 25.9481 | 1.29417 | ||||||||
\(403\) | −2.90434 | −0.144675 | ||||||||
\(404\) | −8.38233 | −0.417036 | ||||||||
\(405\) | −16.5944 | −0.824583 | ||||||||
\(406\) | 0.210355 | 0.0104397 | ||||||||
\(407\) | −4.04951 | −0.200727 | ||||||||
\(408\) | −0.181613 | −0.00899116 | ||||||||
\(409\) | 6.85730 | 0.339071 | 0.169536 | − | 0.985524i | \(-0.445773\pi\) | ||||
0.169536 | + | 0.985524i | \(0.445773\pi\) | |||||||
\(410\) | 3.09831 | 0.153015 | ||||||||
\(411\) | 12.3435 | 0.608861 | ||||||||
\(412\) | 1.42052 | 0.0699838 | ||||||||
\(413\) | 0.219230 | 0.0107876 | ||||||||
\(414\) | 9.53406 | 0.468573 | ||||||||
\(415\) | 2.22616 | 0.109278 | ||||||||
\(416\) | 1.00693 | 0.0493689 | ||||||||
\(417\) | −4.80885 | −0.235490 | ||||||||
\(418\) | 51.4927 | 2.51859 | ||||||||
\(419\) | 25.8878 | 1.26470 | 0.632352 | − | 0.774681i | \(-0.282090\pi\) | ||||
0.632352 | + | 0.774681i | \(0.282090\pi\) | |||||||
\(420\) | 0.0340630 | 0.00166211 | ||||||||
\(421\) | 40.0558 | 1.95220 | 0.976100 | − | 0.217322i | \(-0.0697320\pi\) | ||||
0.976100 | + | 0.217322i | \(0.0697320\pi\) | |||||||
\(422\) | −10.6598 | −0.518913 | ||||||||
\(423\) | 54.8665 | 2.66770 | ||||||||
\(424\) | 18.3063 | 0.889031 | ||||||||
\(425\) | 0.0774670 | 0.00375770 | ||||||||
\(426\) | −22.4121 | −1.08587 | ||||||||
\(427\) | −0.203535 | −0.00984975 | ||||||||
\(428\) | −1.91455 | −0.0925434 | ||||||||
\(429\) | 7.14398 | 0.344915 | ||||||||
\(430\) | −12.6000 | −0.607628 | ||||||||
\(431\) | −16.3544 | −0.787762 | −0.393881 | − | 0.919161i | \(-0.628868\pi\) | ||||
−0.393881 | + | 0.919161i | \(0.628868\pi\) | |||||||
\(432\) | 33.0399 | 1.58963 | ||||||||
\(433\) | −0.620336 | −0.0298114 | −0.0149057 | − | 0.999889i | \(-0.504745\pi\) | ||||
−0.0149057 | + | 0.999889i | \(0.504745\pi\) | |||||||
\(434\) | 0.222201 | 0.0106660 | ||||||||
\(435\) | −22.7643 | −1.09146 | ||||||||
\(436\) | −1.88028 | −0.0900489 | ||||||||
\(437\) | −7.57161 | −0.362199 | ||||||||
\(438\) | 17.5741 | 0.839725 | ||||||||
\(439\) | 26.1015 | 1.24575 | 0.622877 | − | 0.782319i | \(-0.285964\pi\) | ||||
0.622877 | + | 0.782319i | \(0.285964\pi\) | |||||||
\(440\) | −18.3686 | −0.875691 | ||||||||
\(441\) | −48.0547 | −2.28832 | ||||||||
\(442\) | −0.00827056 | −0.000393390 0 | ||||||||
\(443\) | −17.1496 | −0.814800 | −0.407400 | − | 0.913250i | \(-0.633564\pi\) | ||||
−0.407400 | + | 0.913250i | \(0.633564\pi\) | |||||||
\(444\) | 1.02279 | 0.0485394 | ||||||||
\(445\) | −14.3437 | −0.679958 | ||||||||
\(446\) | −18.4302 | −0.872695 | ||||||||
\(447\) | −23.6567 | −1.11892 | ||||||||
\(448\) | −0.199467 | −0.00942392 | ||||||||
\(449\) | 17.4659 | 0.824265 | 0.412132 | − | 0.911124i | \(-0.364784\pi\) | ||||
0.412132 | + | 0.911124i | \(0.364784\pi\) | |||||||
\(450\) | −34.4044 | −1.62184 | ||||||||
\(451\) | 16.9952 | 0.800271 | ||||||||
\(452\) | −0.0305660 | −0.00143771 | ||||||||
\(453\) | −56.5989 | −2.65925 | ||||||||
\(454\) | −7.93641 | −0.372474 | ||||||||
\(455\) | 0.00764005 | 0.000358171 0 | ||||||||
\(456\) | −64.0551 | −2.99966 | ||||||||
\(457\) | 17.3283 | 0.810583 | 0.405291 | − | 0.914188i | \(-0.367170\pi\) | ||||
0.405291 | + | 0.914188i | \(0.367170\pi\) | |||||||
\(458\) | −16.2975 | −0.761531 | ||||||||
\(459\) | 0.229135 | 0.0106951 | ||||||||
\(460\) | 0.548397 | 0.0255692 | ||||||||
\(461\) | −4.65508 | −0.216809 | −0.108404 | − | 0.994107i | \(-0.534574\pi\) | ||||
−0.108404 | + | 0.994107i | \(0.534574\pi\) | |||||||
\(462\) | −0.546562 | −0.0254284 | ||||||||
\(463\) | 11.5407 | 0.536343 | 0.268171 | − | 0.963371i | \(-0.413581\pi\) | ||||
0.268171 | + | 0.963371i | \(0.413581\pi\) | |||||||
\(464\) | 20.8447 | 0.967690 | ||||||||
\(465\) | −24.0462 | −1.11512 | ||||||||
\(466\) | 33.3298 | 1.54397 | ||||||||
\(467\) | 12.1981 | 0.564460 | 0.282230 | − | 0.959347i | \(-0.408926\pi\) | ||||
0.282230 | + | 0.959347i | \(0.408926\pi\) | |||||||
\(468\) | −1.25567 | −0.0580435 | ||||||||
\(469\) | 0.152216 | 0.00702870 | ||||||||
\(470\) | −9.23168 | −0.425826 | ||||||||
\(471\) | 10.2751 | 0.473450 | ||||||||
\(472\) | 29.8592 | 1.37438 | ||||||||
\(473\) | −69.1149 | −3.17791 | ||||||||
\(474\) | 58.2489 | 2.67546 | ||||||||
\(475\) | 27.3228 | 1.25365 | ||||||||
\(476\) | −0.000216311 0 | −9.91458e−6 0 | ||||||||
\(477\) | −41.0218 | −1.87826 | ||||||||
\(478\) | −15.1605 | −0.693423 | ||||||||
\(479\) | 9.03674 | 0.412899 | 0.206450 | − | 0.978457i | \(-0.433809\pi\) | ||||
0.206450 | + | 0.978457i | \(0.433809\pi\) | |||||||
\(480\) | 8.33681 | 0.380522 | ||||||||
\(481\) | 0.229403 | 0.0104599 | ||||||||
\(482\) | −4.86708 | −0.221690 | ||||||||
\(483\) | 0.0803677 | 0.00365686 | ||||||||
\(484\) | −14.8527 | −0.675123 | ||||||||
\(485\) | −12.2737 | −0.557319 | ||||||||
\(486\) | −22.7841 | −1.03351 | ||||||||
\(487\) | −3.89191 | −0.176359 | −0.0881796 | − | 0.996105i | \(-0.528105\pi\) | ||||
−0.0881796 | + | 0.996105i | \(0.528105\pi\) | |||||||
\(488\) | −27.7215 | −1.25489 | ||||||||
\(489\) | 76.5809 | 3.46311 | ||||||||
\(490\) | 8.08554 | 0.365268 | ||||||||
\(491\) | −39.6501 | −1.78938 | −0.894691 | − | 0.446686i | \(-0.852604\pi\) | ||||
−0.894691 | + | 0.446686i | \(0.852604\pi\) | |||||||
\(492\) | −4.29249 | −0.193520 | ||||||||
\(493\) | 0.144560 | 0.00651065 | ||||||||
\(494\) | −2.91704 | −0.131244 | ||||||||
\(495\) | 41.1616 | 1.85008 | ||||||||
\(496\) | 22.0185 | 0.988661 | ||||||||
\(497\) | −0.131474 | −0.00589739 | ||||||||
\(498\) | 9.02185 | 0.404279 | ||||||||
\(499\) | −5.98204 | −0.267793 | −0.133896 | − | 0.990995i | \(-0.542749\pi\) | ||||
−0.133896 | + | 0.990995i | \(0.542749\pi\) | |||||||
\(500\) | −4.38950 | −0.196304 | ||||||||
\(501\) | −40.7043 | −1.81854 | ||||||||
\(502\) | −12.5352 | −0.559472 | ||||||||
\(503\) | −30.5397 | −1.36170 | −0.680849 | − | 0.732424i | \(-0.738389\pi\) | ||||
−0.680849 | + | 0.732424i | \(0.738389\pi\) | |||||||
\(504\) | 0.473151 | 0.0210758 | ||||||||
\(505\) | −15.5660 | −0.692678 | ||||||||
\(506\) | −8.79936 | −0.391179 | ||||||||
\(507\) | 40.4274 | 1.79544 | ||||||||
\(508\) | −5.33837 | −0.236852 | ||||||||
\(509\) | 34.8350 | 1.54404 | 0.772018 | − | 0.635601i | \(-0.219248\pi\) | ||||
0.772018 | + | 0.635601i | \(0.219248\pi\) | |||||||
\(510\) | −0.0684754 | −0.00303214 | ||||||||
\(511\) | 0.103093 | 0.00456058 | ||||||||
\(512\) | −24.3088 | −1.07431 | ||||||||
\(513\) | 80.8165 | 3.56814 | ||||||||
\(514\) | 12.1477 | 0.535811 | ||||||||
\(515\) | 2.63790 | 0.116240 | ||||||||
\(516\) | 17.4564 | 0.768477 | ||||||||
\(517\) | −50.6385 | −2.22708 | ||||||||
\(518\) | −0.0175509 | −0.000771140 0 | ||||||||
\(519\) | 7.18271 | 0.315286 | ||||||||
\(520\) | 1.04058 | 0.0456323 | ||||||||
\(521\) | −12.7551 | −0.558810 | −0.279405 | − | 0.960173i | \(-0.590137\pi\) | ||||
−0.279405 | + | 0.960173i | \(0.590137\pi\) | |||||||
\(522\) | −64.2015 | −2.81003 | ||||||||
\(523\) | −29.5165 | −1.29066 | −0.645332 | − | 0.763902i | \(-0.723281\pi\) | ||||
−0.645332 | + | 0.763902i | \(0.723281\pi\) | |||||||
\(524\) | 2.68336 | 0.117223 | ||||||||
\(525\) | −0.290013 | −0.0126572 | ||||||||
\(526\) | −5.01137 | −0.218506 | ||||||||
\(527\) | 0.152701 | 0.00665175 | ||||||||
\(528\) | −54.1604 | −2.35703 | ||||||||
\(529\) | −21.7061 | −0.943744 | ||||||||
\(530\) | 6.90221 | 0.299813 | ||||||||
\(531\) | −66.9104 | −2.90366 | ||||||||
\(532\) | −0.0762932 | −0.00330773 | ||||||||
\(533\) | −0.962770 | −0.0417022 | ||||||||
\(534\) | −58.1302 | −2.51554 | ||||||||
\(535\) | −3.55533 | −0.153710 | ||||||||
\(536\) | 20.7319 | 0.895482 | ||||||||
\(537\) | 40.3166 | 1.73979 | ||||||||
\(538\) | −3.80124 | −0.163883 | ||||||||
\(539\) | 44.3516 | 1.91036 | ||||||||
\(540\) | −5.85338 | −0.251890 | ||||||||
\(541\) | 20.4901 | 0.880940 | 0.440470 | − | 0.897767i | \(-0.354812\pi\) | ||||
0.440470 | + | 0.897767i | \(0.354812\pi\) | |||||||
\(542\) | 7.85701 | 0.337488 | ||||||||
\(543\) | −1.80974 | −0.0776633 | ||||||||
\(544\) | −0.0529413 | −0.00226984 | ||||||||
\(545\) | −3.49168 | −0.149567 | ||||||||
\(546\) | 0.0309625 | 0.00132507 | ||||||||
\(547\) | −36.3056 | −1.55231 | −0.776157 | − | 0.630540i | \(-0.782834\pi\) | ||||
−0.776157 | + | 0.630540i | \(0.782834\pi\) | |||||||
\(548\) | 2.00239 | 0.0855378 | ||||||||
\(549\) | 62.1201 | 2.65122 | ||||||||
\(550\) | 31.7532 | 1.35396 | ||||||||
\(551\) | 50.9866 | 2.17210 | ||||||||
\(552\) | 10.9461 | 0.465897 | ||||||||
\(553\) | 0.341699 | 0.0145305 | ||||||||
\(554\) | −15.7064 | −0.667301 | ||||||||
\(555\) | 1.89932 | 0.0806218 | ||||||||
\(556\) | −0.780100 | −0.0330836 | ||||||||
\(557\) | −18.1871 | −0.770614 | −0.385307 | − | 0.922788i | \(-0.625904\pi\) | ||||
−0.385307 | + | 0.922788i | \(0.625904\pi\) | |||||||
\(558\) | −67.8170 | −2.87092 | ||||||||
\(559\) | 3.91533 | 0.165601 | ||||||||
\(560\) | −0.0579212 | −0.00244762 | ||||||||
\(561\) | −0.375608 | −0.0158582 | ||||||||
\(562\) | 8.98929 | 0.379191 | ||||||||
\(563\) | 11.2207 | 0.472895 | 0.236448 | − | 0.971644i | \(-0.424017\pi\) | ||||
0.236448 | + | 0.971644i | \(0.424017\pi\) | |||||||
\(564\) | 12.7898 | 0.538549 | ||||||||
\(565\) | −0.0567612 | −0.00238796 | ||||||||
\(566\) | 11.5877 | 0.487069 | ||||||||
\(567\) | −0.394510 | −0.0165679 | ||||||||
\(568\) | −17.9067 | −0.751349 | ||||||||
\(569\) | 41.0440 | 1.72066 | 0.860328 | − | 0.509741i | \(-0.170259\pi\) | ||||
0.860328 | + | 0.509741i | \(0.170259\pi\) | |||||||
\(570\) | −24.1514 | −1.01159 | ||||||||
\(571\) | −25.4279 | −1.06412 | −0.532062 | − | 0.846705i | \(-0.678583\pi\) | ||||
−0.532062 | + | 0.846705i | \(0.678583\pi\) | |||||||
\(572\) | 1.15891 | 0.0484565 | ||||||||
\(573\) | 45.0164 | 1.88059 | ||||||||
\(574\) | 0.0736582 | 0.00307444 | ||||||||
\(575\) | −4.66906 | −0.194713 | ||||||||
\(576\) | 60.8784 | 2.53660 | ||||||||
\(577\) | 27.6682 | 1.15184 | 0.575922 | − | 0.817505i | \(-0.304643\pi\) | ||||
0.575922 | + | 0.817505i | \(0.304643\pi\) | |||||||
\(578\) | −20.7540 | −0.863252 | ||||||||
\(579\) | 21.5462 | 0.895428 | ||||||||
\(580\) | −3.69286 | −0.153338 | ||||||||
\(581\) | 0.0529239 | 0.00219565 | ||||||||
\(582\) | −49.7410 | −2.06183 | ||||||||
\(583\) | 37.8607 | 1.56803 | ||||||||
\(584\) | 14.0413 | 0.581034 | ||||||||
\(585\) | −2.33179 | −0.0964076 | ||||||||
\(586\) | 14.0930 | 0.582177 | ||||||||
\(587\) | 34.0275 | 1.40447 | 0.702234 | − | 0.711947i | \(-0.252186\pi\) | ||||
0.702234 | + | 0.711947i | \(0.252186\pi\) | |||||||
\(588\) | −11.2019 | −0.461960 | ||||||||
\(589\) | 53.8578 | 2.21917 | ||||||||
\(590\) | 11.2581 | 0.463491 | ||||||||
\(591\) | −35.7731 | −1.47151 | ||||||||
\(592\) | −1.73916 | −0.0714792 | ||||||||
\(593\) | −48.2166 | −1.98002 | −0.990009 | − | 0.141003i | \(-0.954967\pi\) | ||||
−0.990009 | + | 0.141003i | \(0.954967\pi\) | |||||||
\(594\) | 93.9211 | 3.85363 | ||||||||
\(595\) | −0.000401689 0 | −1.64677e−5 0 | ||||||||
\(596\) | −3.83763 | −0.157195 | ||||||||
\(597\) | 79.1647 | 3.23999 | ||||||||
\(598\) | 0.498480 | 0.0203844 | ||||||||
\(599\) | −30.8669 | −1.26119 | −0.630593 | − | 0.776113i | \(-0.717188\pi\) | ||||
−0.630593 | + | 0.776113i | \(0.717188\pi\) | |||||||
\(600\) | −39.4999 | −1.61257 | ||||||||
\(601\) | 24.3388 | 0.992801 | 0.496400 | − | 0.868094i | \(-0.334655\pi\) | ||||
0.496400 | + | 0.868094i | \(0.334655\pi\) | |||||||
\(602\) | −0.299549 | −0.0122087 | ||||||||
\(603\) | −46.4573 | −1.89189 | ||||||||
\(604\) | −9.18159 | −0.373593 | ||||||||
\(605\) | −27.5815 | −1.12135 | ||||||||
\(606\) | −63.0837 | −2.56260 | ||||||||
\(607\) | 28.5189 | 1.15755 | 0.578773 | − | 0.815488i | \(-0.303532\pi\) | ||||
0.578773 | + | 0.815488i | \(0.303532\pi\) | |||||||
\(608\) | −18.6725 | −0.757270 | ||||||||
\(609\) | −0.541189 | −0.0219301 | ||||||||
\(610\) | −10.4521 | −0.423195 | ||||||||
\(611\) | 2.86865 | 0.116053 | ||||||||
\(612\) | 0.0660192 | 0.00266867 | ||||||||
\(613\) | −14.2204 | −0.574358 | −0.287179 | − | 0.957877i | \(-0.592717\pi\) | ||||
−0.287179 | + | 0.957877i | \(0.592717\pi\) | |||||||
\(614\) | −16.1299 | −0.650949 | ||||||||
\(615\) | −7.97117 | −0.321429 | ||||||||
\(616\) | −0.436690 | −0.0175947 | ||||||||
\(617\) | −37.4279 | −1.50679 | −0.753395 | − | 0.657568i | \(-0.771585\pi\) | ||||
−0.753395 | + | 0.657568i | \(0.771585\pi\) | |||||||
\(618\) | 10.6905 | 0.430036 | ||||||||
\(619\) | −30.1790 | −1.21300 | −0.606498 | − | 0.795085i | \(-0.707426\pi\) | ||||
−0.606498 | + | 0.795085i | \(0.707426\pi\) | |||||||
\(620\) | −3.90082 | −0.156661 | ||||||||
\(621\) | −13.8104 | −0.554191 | ||||||||
\(622\) | 26.0024 | 1.04260 | ||||||||
\(623\) | −0.341003 | −0.0136620 | ||||||||
\(624\) | 3.06816 | 0.122825 | ||||||||
\(625\) | 12.3723 | 0.494891 | ||||||||
\(626\) | −17.3126 | −0.691952 | ||||||||
\(627\) | −132.478 | −5.29064 | ||||||||
\(628\) | 1.66684 | 0.0665142 | ||||||||
\(629\) | −0.0120613 | −0.000480915 0 | ||||||||
\(630\) | 0.178397 | 0.00710751 | ||||||||
\(631\) | −11.3900 | −0.453429 | −0.226715 | − | 0.973961i | \(-0.572798\pi\) | ||||
−0.226715 | + | 0.973961i | \(0.572798\pi\) | |||||||
\(632\) | 46.5394 | 1.85124 | ||||||||
\(633\) | 27.4250 | 1.09005 | ||||||||
\(634\) | −35.2233 | −1.39889 | ||||||||
\(635\) | −9.91337 | −0.393400 | ||||||||
\(636\) | −9.56251 | −0.379178 | ||||||||
\(637\) | −2.51250 | −0.0995489 | ||||||||
\(638\) | 59.2542 | 2.34590 | ||||||||
\(639\) | 40.1265 | 1.58738 | ||||||||
\(640\) | −4.93473 | −0.195062 | ||||||||
\(641\) | −35.9168 | −1.41863 | −0.709315 | − | 0.704892i | \(-0.750996\pi\) | ||||
−0.709315 | + | 0.704892i | \(0.750996\pi\) | |||||||
\(642\) | −14.4085 | −0.568660 | ||||||||
\(643\) | −11.7899 | −0.464947 | −0.232474 | − | 0.972603i | \(-0.574682\pi\) | ||||
−0.232474 | + | 0.972603i | \(0.574682\pi\) | |||||||
\(644\) | 0.0130374 | 0.000513746 0 | ||||||||
\(645\) | 32.4167 | 1.27641 | ||||||||
\(646\) | 0.153369 | 0.00603421 | ||||||||
\(647\) | −8.51966 | −0.334942 | −0.167471 | − | 0.985877i | \(-0.553560\pi\) | ||||
−0.167471 | + | 0.985877i | \(0.553560\pi\) | |||||||
\(648\) | −53.7323 | −2.11080 | ||||||||
\(649\) | 61.7543 | 2.42407 | ||||||||
\(650\) | −1.79881 | −0.0705550 | ||||||||
\(651\) | −0.571666 | −0.0224054 | ||||||||
\(652\) | 12.4231 | 0.486526 | ||||||||
\(653\) | 11.9568 | 0.467905 | 0.233952 | − | 0.972248i | \(-0.424834\pi\) | ||||
0.233952 | + | 0.972248i | \(0.424834\pi\) | |||||||
\(654\) | −14.1506 | −0.553331 | ||||||||
\(655\) | 4.98300 | 0.194702 | ||||||||
\(656\) | 7.29900 | 0.284978 | ||||||||
\(657\) | −31.4646 | −1.22755 | ||||||||
\(658\) | −0.219471 | −0.00855586 | ||||||||
\(659\) | −9.67627 | −0.376934 | −0.188467 | − | 0.982080i | \(-0.560352\pi\) | ||||
−0.188467 | + | 0.982080i | \(0.560352\pi\) | |||||||
\(660\) | 9.59510 | 0.373489 | ||||||||
\(661\) | 10.2307 | 0.397926 | 0.198963 | − | 0.980007i | \(-0.436243\pi\) | ||||
0.198963 | + | 0.980007i | \(0.436243\pi\) | |||||||
\(662\) | 36.0199 | 1.39995 | ||||||||
\(663\) | 0.0212780 | 0.000826370 0 | ||||||||
\(664\) | 7.20824 | 0.279734 | ||||||||
\(665\) | −0.141677 | −0.00549399 | ||||||||
\(666\) | 5.35662 | 0.207565 | ||||||||
\(667\) | −8.71287 | −0.337364 | ||||||||
\(668\) | −6.60314 | −0.255483 | ||||||||
\(669\) | 47.4162 | 1.83322 | ||||||||
\(670\) | 7.81678 | 0.301988 | ||||||||
\(671\) | −57.3331 | −2.21332 | ||||||||
\(672\) | 0.198196 | 0.00764559 | ||||||||
\(673\) | −21.1798 | −0.816422 | −0.408211 | − | 0.912888i | \(-0.633847\pi\) | ||||
−0.408211 | + | 0.912888i | \(0.633847\pi\) | |||||||
\(674\) | −37.8403 | −1.45755 | ||||||||
\(675\) | 49.8358 | 1.91818 | ||||||||
\(676\) | 6.55821 | 0.252239 | ||||||||
\(677\) | −48.9082 | −1.87969 | −0.939847 | − | 0.341596i | \(-0.889032\pi\) | ||||
−0.939847 | + | 0.341596i | \(0.889032\pi\) | |||||||
\(678\) | −0.230034 | −0.00883439 | ||||||||
\(679\) | −0.291790 | −0.0111979 | ||||||||
\(680\) | −0.0547102 | −0.00209804 | ||||||||
\(681\) | 20.4183 | 0.782432 | ||||||||
\(682\) | 62.5910 | 2.39673 | ||||||||
\(683\) | 31.5927 | 1.20886 | 0.604430 | − | 0.796658i | \(-0.293401\pi\) | ||||
0.604430 | + | 0.796658i | \(0.293401\pi\) | |||||||
\(684\) | 23.2851 | 0.890329 | ||||||||
\(685\) | 3.71844 | 0.142074 | ||||||||
\(686\) | 0.384460 | 0.0146787 | ||||||||
\(687\) | 41.9292 | 1.59970 | ||||||||
\(688\) | −29.6831 | −1.13166 | ||||||||
\(689\) | −2.14479 | −0.0817100 | ||||||||
\(690\) | 4.12713 | 0.157117 | ||||||||
\(691\) | −15.7644 | −0.599708 | −0.299854 | − | 0.953985i | \(-0.596938\pi\) | ||||
−0.299854 | + | 0.953985i | \(0.596938\pi\) | |||||||
\(692\) | 1.16519 | 0.0442940 | ||||||||
\(693\) | 0.978561 | 0.0371725 | ||||||||
\(694\) | −37.2509 | −1.41402 | ||||||||
\(695\) | −1.44865 | −0.0549504 | ||||||||
\(696\) | −73.7101 | −2.79397 | ||||||||
\(697\) | 0.0506193 | 0.00191734 | ||||||||
\(698\) | −22.8911 | −0.866442 | ||||||||
\(699\) | −85.7491 | −3.24333 | ||||||||
\(700\) | −0.0470465 | −0.00177819 | ||||||||
\(701\) | 11.1194 | 0.419972 | 0.209986 | − | 0.977704i | \(-0.432658\pi\) | ||||
0.209986 | + | 0.977704i | \(0.432658\pi\) | |||||||
\(702\) | −5.32059 | −0.200813 | ||||||||
\(703\) | −4.25404 | −0.160444 | ||||||||
\(704\) | −56.1871 | −2.11763 | ||||||||
\(705\) | 23.7508 | 0.894505 | ||||||||
\(706\) | 4.09493 | 0.154115 | ||||||||
\(707\) | −0.370061 | −0.0139176 | ||||||||
\(708\) | −15.5974 | −0.586184 | ||||||||
\(709\) | −31.4261 | −1.18023 | −0.590116 | − | 0.807319i | \(-0.700918\pi\) | ||||
−0.590116 | + | 0.807319i | \(0.700918\pi\) | |||||||
\(710\) | −6.75156 | −0.253382 | ||||||||
\(711\) | −104.288 | −3.91112 | ||||||||
\(712\) | −46.4446 | −1.74059 | ||||||||
\(713\) | −9.20353 | −0.344675 | ||||||||
\(714\) | −0.00162791 | −6.09230e−5 0 | ||||||||
\(715\) | 2.15210 | 0.0804840 | ||||||||
\(716\) | 6.54024 | 0.244420 | ||||||||
\(717\) | 39.0040 | 1.45663 | ||||||||
\(718\) | 2.42481 | 0.0904929 | ||||||||
\(719\) | 48.6905 | 1.81585 | 0.907925 | − | 0.419133i | \(-0.137666\pi\) | ||||
0.907925 | + | 0.419133i | \(0.137666\pi\) | |||||||
\(720\) | 17.6779 | 0.658816 | ||||||||
\(721\) | 0.0627126 | 0.00233554 | ||||||||
\(722\) | 30.8973 | 1.14988 | ||||||||
\(723\) | 12.5218 | 0.465689 | ||||||||
\(724\) | −0.293579 | −0.0109108 | ||||||||
\(725\) | 31.4411 | 1.16769 | ||||||||
\(726\) | −111.779 | −4.14849 | ||||||||
\(727\) | 44.7373 | 1.65921 | 0.829607 | − | 0.558348i | \(-0.188565\pi\) | ||||
0.829607 | + | 0.558348i | \(0.188565\pi\) | |||||||
\(728\) | 0.0247383 | 0.000916862 0 | ||||||||
\(729\) | 6.00345 | 0.222350 | ||||||||
\(730\) | 5.29415 | 0.195945 | ||||||||
\(731\) | −0.205856 | −0.00761385 | ||||||||
\(732\) | 14.4807 | 0.535222 | ||||||||
\(733\) | −4.39845 | −0.162460 | −0.0812302 | − | 0.996695i | \(-0.525885\pi\) | ||||
−0.0812302 | + | 0.996695i | \(0.525885\pi\) | |||||||
\(734\) | 25.5571 | 0.943329 | ||||||||
\(735\) | −20.8020 | −0.767294 | ||||||||
\(736\) | 3.19086 | 0.117617 | ||||||||
\(737\) | 42.8773 | 1.57941 | ||||||||
\(738\) | −22.4809 | −0.827534 | ||||||||
\(739\) | −29.7684 | −1.09505 | −0.547523 | − | 0.836790i | \(-0.684429\pi\) | ||||
−0.547523 | + | 0.836790i | \(0.684429\pi\) | |||||||
\(740\) | 0.308112 | 0.0113264 | ||||||||
\(741\) | 7.50480 | 0.275696 | ||||||||
\(742\) | 0.164091 | 0.00602396 | ||||||||
\(743\) | 0.325683 | 0.0119481 | 0.00597407 | − | 0.999982i | \(-0.498098\pi\) | ||||
0.00597407 | + | 0.999982i | \(0.498098\pi\) | |||||||
\(744\) | −77.8610 | −2.85452 | ||||||||
\(745\) | −7.12649 | −0.261094 | ||||||||
\(746\) | −8.82334 | −0.323045 | ||||||||
\(747\) | −16.1527 | −0.590995 | ||||||||
\(748\) | −0.0609318 | −0.00222789 | ||||||||
\(749\) | −0.0845232 | −0.00308841 | ||||||||
\(750\) | −33.0345 | −1.20625 | ||||||||
\(751\) | −6.81255 | −0.248593 | −0.124297 | − | 0.992245i | \(-0.539667\pi\) | ||||
−0.124297 | + | 0.992245i | \(0.539667\pi\) | |||||||
\(752\) | −21.7480 | −0.793067 | ||||||||
\(753\) | 32.2498 | 1.17525 | ||||||||
\(754\) | −3.35673 | −0.122245 | ||||||||
\(755\) | −17.0502 | −0.620522 | ||||||||
\(756\) | −0.139156 | −0.00506107 | ||||||||
\(757\) | 13.6442 | 0.495905 | 0.247953 | − | 0.968772i | \(-0.420242\pi\) | ||||
0.247953 | + | 0.968772i | \(0.420242\pi\) | |||||||
\(758\) | 17.7626 | 0.645167 | ||||||||
\(759\) | 22.6385 | 0.821726 | ||||||||
\(760\) | −19.2964 | −0.699953 | ||||||||
\(761\) | 0.601384 | 0.0218002 | 0.0109001 | − | 0.999941i | \(-0.496530\pi\) | ||||
0.0109001 | + | 0.999941i | \(0.496530\pi\) | |||||||
\(762\) | −40.1755 | −1.45540 | ||||||||
\(763\) | −0.0830099 | −0.00300516 | ||||||||
\(764\) | 7.30265 | 0.264200 | ||||||||
\(765\) | 0.122598 | 0.00443254 | ||||||||
\(766\) | 40.8616 | 1.47639 | ||||||||
\(767\) | −3.49835 | −0.126318 | ||||||||
\(768\) | 35.7048 | 1.28838 | ||||||||
\(769\) | −3.34733 | −0.120708 | −0.0603538 | − | 0.998177i | \(-0.519223\pi\) | ||||
−0.0603538 | + | 0.998177i | \(0.519223\pi\) | |||||||
\(770\) | −0.164650 | −0.00593357 | ||||||||
\(771\) | −31.2529 | −1.12554 | ||||||||
\(772\) | 3.49526 | 0.125797 | ||||||||
\(773\) | −9.87620 | −0.355222 | −0.177611 | − | 0.984101i | \(-0.556837\pi\) | ||||
−0.177611 | + | 0.984101i | \(0.556837\pi\) | |||||||
\(774\) | 91.4240 | 3.28617 | ||||||||
\(775\) | 33.2117 | 1.19300 | ||||||||
\(776\) | −39.7418 | −1.42665 | ||||||||
\(777\) | 0.0451538 | 0.00161989 | ||||||||
\(778\) | 1.15671 | 0.0414702 | ||||||||
\(779\) | 17.8535 | 0.639670 | ||||||||
\(780\) | −0.543559 | −0.0194625 | ||||||||
\(781\) | −37.0343 | −1.32519 | ||||||||
\(782\) | −0.0262085 | −0.000937214 0 | ||||||||
\(783\) | 92.9979 | 3.32347 | ||||||||
\(784\) | 19.0479 | 0.680282 | ||||||||
\(785\) | 3.09533 | 0.110477 | ||||||||
\(786\) | 20.1944 | 0.720311 | ||||||||
\(787\) | 15.9163 | 0.567355 | 0.283677 | − | 0.958920i | \(-0.408446\pi\) | ||||
0.283677 | + | 0.958920i | \(0.408446\pi\) | |||||||
\(788\) | −5.80318 | −0.206730 | ||||||||
\(789\) | 12.8930 | 0.459001 | ||||||||
\(790\) | 17.5473 | 0.624304 | ||||||||
\(791\) | −0.00134942 | −4.79799e−5 0 | ||||||||
\(792\) | 133.280 | 4.73590 | ||||||||
\(793\) | 3.24790 | 0.115336 | ||||||||
\(794\) | −30.3316 | −1.07643 | ||||||||
\(795\) | −17.7576 | −0.629798 | ||||||||
\(796\) | 12.8422 | 0.455181 | ||||||||
\(797\) | 38.7987 | 1.37432 | 0.687161 | − | 0.726505i | \(-0.258857\pi\) | ||||
0.687161 | + | 0.726505i | \(0.258857\pi\) | |||||||
\(798\) | −0.574167 | −0.0203253 | ||||||||
\(799\) | −0.150824 | −0.00533579 | ||||||||
\(800\) | −11.5145 | −0.407098 | ||||||||
\(801\) | 104.076 | 3.67735 | ||||||||
\(802\) | 19.4507 | 0.686830 | ||||||||
\(803\) | 29.0400 | 1.02480 | ||||||||
\(804\) | −10.8296 | −0.381930 | ||||||||
\(805\) | 0.0242105 | 0.000853308 0 | ||||||||
\(806\) | −3.54576 | −0.124894 | ||||||||
\(807\) | 9.77963 | 0.344259 | ||||||||
\(808\) | −50.4023 | −1.77315 | ||||||||
\(809\) | −0.684369 | −0.0240611 | −0.0120306 | − | 0.999928i | \(-0.503830\pi\) | ||||
−0.0120306 | + | 0.999928i | \(0.503830\pi\) | |||||||
\(810\) | −20.2593 | −0.711839 | ||||||||
\(811\) | 34.2689 | 1.20334 | 0.601672 | − | 0.798743i | \(-0.294502\pi\) | ||||
0.601672 | + | 0.798743i | \(0.294502\pi\) | |||||||
\(812\) | −0.0877928 | −0.00308092 | ||||||||
\(813\) | −20.2141 | −0.708939 | ||||||||
\(814\) | −4.94384 | −0.173282 | ||||||||
\(815\) | 23.0697 | 0.808097 | ||||||||
\(816\) | −0.161314 | −0.00564712 | ||||||||
\(817\) | −72.6057 | −2.54015 | ||||||||
\(818\) | 8.37172 | 0.292710 | ||||||||
\(819\) | −0.0554351 | −0.00193706 | ||||||||
\(820\) | −1.29310 | −0.0451569 | ||||||||
\(821\) | −16.1277 | −0.562861 | −0.281431 | − | 0.959582i | \(-0.590809\pi\) | ||||
−0.281431 | + | 0.959582i | \(0.590809\pi\) | |||||||
\(822\) | 15.0696 | 0.525612 | ||||||||
\(823\) | 26.7045 | 0.930861 | 0.465430 | − | 0.885084i | \(-0.345900\pi\) | ||||
0.465430 | + | 0.885084i | \(0.345900\pi\) | |||||||
\(824\) | 8.54147 | 0.297556 | ||||||||
\(825\) | −81.6928 | −2.84418 | ||||||||
\(826\) | 0.267647 | 0.00931264 | ||||||||
\(827\) | 1.68571 | 0.0586178 | 0.0293089 | − | 0.999570i | \(-0.490669\pi\) | ||||
0.0293089 | + | 0.999570i | \(0.490669\pi\) | |||||||
\(828\) | −3.97909 | −0.138283 | ||||||||
\(829\) | 47.5517 | 1.65154 | 0.825770 | − | 0.564007i | \(-0.190741\pi\) | ||||
0.825770 | + | 0.564007i | \(0.190741\pi\) | |||||||
\(830\) | 2.71780 | 0.0943363 | ||||||||
\(831\) | 40.4085 | 1.40176 | ||||||||
\(832\) | 3.18298 | 0.110350 | ||||||||
\(833\) | 0.132099 | 0.00457696 | ||||||||
\(834\) | −5.87087 | −0.203292 | ||||||||
\(835\) | −12.2620 | −0.424346 | ||||||||
\(836\) | −21.4908 | −0.743274 | ||||||||
\(837\) | 98.2350 | 3.39550 | ||||||||
\(838\) | 31.6051 | 1.09178 | ||||||||
\(839\) | 27.8988 | 0.963174 | 0.481587 | − | 0.876398i | \(-0.340061\pi\) | ||||
0.481587 | + | 0.876398i | \(0.340061\pi\) | |||||||
\(840\) | 0.204819 | 0.00706691 | ||||||||
\(841\) | 29.6717 | 1.02316 | ||||||||
\(842\) | 48.9021 | 1.68528 | ||||||||
\(843\) | −23.1272 | −0.796541 | ||||||||
\(844\) | 4.44894 | 0.153139 | ||||||||
\(845\) | 12.1786 | 0.418957 | ||||||||
\(846\) | 66.9837 | 2.30295 | ||||||||
\(847\) | −0.655714 | −0.0225306 | ||||||||
\(848\) | 16.2602 | 0.558378 | ||||||||
\(849\) | −29.8123 | −1.02316 | ||||||||
\(850\) | 0.0945754 | 0.00324391 | ||||||||
\(851\) | 0.726954 | 0.0249197 | ||||||||
\(852\) | 9.35380 | 0.320456 | ||||||||
\(853\) | 21.6002 | 0.739578 | 0.369789 | − | 0.929116i | \(-0.379430\pi\) | ||||
0.369789 | + | 0.929116i | \(0.379430\pi\) | |||||||
\(854\) | −0.248486 | −0.00850300 | ||||||||
\(855\) | 43.2405 | 1.47879 | ||||||||
\(856\) | −11.5121 | −0.393475 | ||||||||
\(857\) | 6.86410 | 0.234473 | 0.117237 | − | 0.993104i | \(-0.462596\pi\) | ||||
0.117237 | + | 0.993104i | \(0.462596\pi\) | |||||||
\(858\) | 8.72172 | 0.297755 | ||||||||
\(859\) | 24.6814 | 0.842119 | 0.421059 | − | 0.907033i | \(-0.361658\pi\) | ||||
0.421059 | + | 0.907033i | \(0.361658\pi\) | |||||||
\(860\) | 5.25869 | 0.179320 | ||||||||
\(861\) | −0.189504 | −0.00645827 | ||||||||
\(862\) | −19.9662 | −0.680052 | ||||||||
\(863\) | 50.3396 | 1.71358 | 0.856789 | − | 0.515667i | \(-0.172456\pi\) | ||||
0.856789 | + | 0.515667i | \(0.172456\pi\) | |||||||
\(864\) | −34.0580 | −1.15868 | ||||||||
\(865\) | 2.16377 | 0.0735703 | ||||||||
\(866\) | −0.757336 | −0.0257353 | ||||||||
\(867\) | 53.3947 | 1.81338 | ||||||||
\(868\) | −0.0927367 | −0.00314769 | ||||||||
\(869\) | 96.2520 | 3.26512 | ||||||||
\(870\) | −27.7917 | −0.942228 | ||||||||
\(871\) | −2.42898 | −0.0823030 | ||||||||
\(872\) | −11.3060 | −0.382868 | ||||||||
\(873\) | 89.0559 | 3.01409 | ||||||||
\(874\) | −9.24379 | −0.312676 | ||||||||
\(875\) | −0.193786 | −0.00655118 | ||||||||
\(876\) | −7.33466 | −0.247815 | ||||||||
\(877\) | −8.51355 | −0.287482 | −0.143741 | − | 0.989615i | \(-0.545913\pi\) | ||||
−0.143741 | + | 0.989615i | \(0.545913\pi\) | |||||||
\(878\) | 31.8659 | 1.07542 | ||||||||
\(879\) | −36.2577 | −1.22294 | ||||||||
\(880\) | −16.3156 | −0.550000 | ||||||||
\(881\) | −32.6365 | −1.09955 | −0.549776 | − | 0.835312i | \(-0.685287\pi\) | ||||
−0.549776 | + | 0.835312i | \(0.685287\pi\) | |||||||
\(882\) | −58.6675 | −1.97544 | ||||||||
\(883\) | 1.56632 | 0.0527108 | 0.0263554 | − | 0.999653i | \(-0.491610\pi\) | ||||
0.0263554 | + | 0.999653i | \(0.491610\pi\) | |||||||
\(884\) | 0.00345176 | 0.000116095 0 | ||||||||
\(885\) | −28.9643 | −0.973625 | ||||||||
\(886\) | −20.9370 | −0.703393 | ||||||||
\(887\) | −30.1670 | −1.01291 | −0.506454 | − | 0.862267i | \(-0.669044\pi\) | ||||
−0.506454 | + | 0.862267i | \(0.669044\pi\) | |||||||
\(888\) | 6.14996 | 0.206379 | ||||||||
\(889\) | −0.235677 | −0.00790435 | ||||||||
\(890\) | −17.5115 | −0.586988 | ||||||||
\(891\) | −111.128 | −3.72293 | ||||||||
\(892\) | 7.69194 | 0.257545 | ||||||||
\(893\) | −53.1961 | −1.78014 | ||||||||
\(894\) | −28.8812 | −0.965932 | ||||||||
\(895\) | 12.1452 | 0.405971 | ||||||||
\(896\) | −0.117316 | −0.00391927 | ||||||||
\(897\) | −1.28246 | −0.0428202 | ||||||||
\(898\) | 21.3232 | 0.711563 | ||||||||
\(899\) | 61.9758 | 2.06701 | ||||||||
\(900\) | 14.3589 | 0.478629 | ||||||||
\(901\) | 0.112766 | 0.00375679 | ||||||||
\(902\) | 20.7485 | 0.690851 | ||||||||
\(903\) | 0.770662 | 0.0256460 | ||||||||
\(904\) | −0.183791 | −0.00611281 | ||||||||
\(905\) | −0.545178 | −0.0181223 | ||||||||
\(906\) | −69.0987 | −2.29565 | ||||||||
\(907\) | 26.9452 | 0.894700 | 0.447350 | − | 0.894359i | \(-0.352368\pi\) | ||||
0.447350 | + | 0.894359i | \(0.352368\pi\) | |||||||
\(908\) | 3.31230 | 0.109923 | ||||||||
\(909\) | 112.945 | 3.74614 | ||||||||
\(910\) | 0.00932735 | 0.000309199 0 | ||||||||
\(911\) | 32.9757 | 1.09253 | 0.546266 | − | 0.837612i | \(-0.316049\pi\) | ||||
0.546266 | + | 0.837612i | \(0.316049\pi\) | |||||||
\(912\) | −56.8958 | −1.88401 | ||||||||
\(913\) | 14.9080 | 0.493381 | ||||||||
\(914\) | 21.1552 | 0.699752 | ||||||||
\(915\) | 26.8907 | 0.888979 | ||||||||
\(916\) | 6.80184 | 0.224739 | ||||||||
\(917\) | 0.118464 | 0.00391203 | ||||||||
\(918\) | 0.279740 | 0.00923278 | ||||||||
\(919\) | 45.6169 | 1.50476 | 0.752381 | − | 0.658728i | \(-0.228905\pi\) | ||||
0.752381 | + | 0.658728i | \(0.228905\pi\) | |||||||
\(920\) | 3.29747 | 0.108714 | ||||||||
\(921\) | 41.4980 | 1.36741 | ||||||||
\(922\) | −5.68315 | −0.187164 | ||||||||
\(923\) | 2.09798 | 0.0690558 | ||||||||
\(924\) | 0.228110 | 0.00750428 | ||||||||
\(925\) | −2.62327 | −0.0862526 | ||||||||
\(926\) | 14.0895 | 0.463009 | ||||||||
\(927\) | −19.1402 | −0.628648 | ||||||||
\(928\) | −21.4870 | −0.705345 | ||||||||
\(929\) | 20.3305 | 0.667023 | 0.333511 | − | 0.942746i | \(-0.391766\pi\) | ||||
0.333511 | + | 0.942746i | \(0.391766\pi\) | |||||||
\(930\) | −29.3568 | −0.962647 | ||||||||
\(931\) | 46.5916 | 1.52698 | ||||||||
\(932\) | −13.9104 | −0.455649 | ||||||||
\(933\) | −66.8975 | −2.19013 | ||||||||
\(934\) | 14.8920 | 0.487282 | ||||||||
\(935\) | −0.113151 | −0.00370042 | ||||||||
\(936\) | −7.55027 | −0.246788 | ||||||||
\(937\) | −15.7936 | −0.515953 | −0.257976 | − | 0.966151i | \(-0.583056\pi\) | ||||
−0.257976 | + | 0.966151i | \(0.583056\pi\) | |||||||
\(938\) | 0.185833 | 0.00606767 | ||||||||
\(939\) | 44.5410 | 1.45354 | ||||||||
\(940\) | 3.85289 | 0.125668 | ||||||||
\(941\) | −11.8889 | −0.387568 | −0.193784 | − | 0.981044i | \(-0.562076\pi\) | ||||
−0.193784 | + | 0.981044i | \(0.562076\pi\) | |||||||
\(942\) | 12.5443 | 0.408716 | ||||||||
\(943\) | −3.05091 | −0.0993514 | ||||||||
\(944\) | 26.5219 | 0.863215 | ||||||||
\(945\) | −0.258414 | −0.00840620 | ||||||||
\(946\) | −84.3789 | −2.74339 | ||||||||
\(947\) | 11.8570 | 0.385302 | 0.192651 | − | 0.981267i | \(-0.438291\pi\) | ||||
0.192651 | + | 0.981267i | \(0.438291\pi\) | |||||||
\(948\) | −24.3105 | −0.789567 | ||||||||
\(949\) | −1.64510 | −0.0534023 | ||||||||
\(950\) | 33.3570 | 1.08224 | ||||||||
\(951\) | 90.6204 | 2.93857 | ||||||||
\(952\) | −0.00130066 | −4.21546e−5 0 | ||||||||
\(953\) | −3.90429 | −0.126472 | −0.0632361 | − | 0.997999i | \(-0.520142\pi\) | ||||
−0.0632361 | + | 0.997999i | \(0.520142\pi\) | |||||||
\(954\) | −50.0814 | −1.62145 | ||||||||
\(955\) | 13.5610 | 0.438825 | ||||||||
\(956\) | 6.32729 | 0.204639 | ||||||||
\(957\) | −152.446 | −4.92787 | ||||||||
\(958\) | 11.0325 | 0.356444 | ||||||||
\(959\) | 0.0884010 | 0.00285462 | ||||||||
\(960\) | 26.3532 | 0.850545 | ||||||||
\(961\) | 34.4659 | 1.11180 | ||||||||
\(962\) | 0.280067 | 0.00902971 | ||||||||
\(963\) | 25.7970 | 0.831296 | ||||||||
\(964\) | 2.03130 | 0.0654239 | ||||||||
\(965\) | 6.49071 | 0.208943 | ||||||||
\(966\) | 0.0981169 | 0.00315686 | ||||||||
\(967\) | 11.9696 | 0.384916 | 0.192458 | − | 0.981305i | \(-0.438354\pi\) | ||||
0.192458 | + | 0.981305i | \(0.438354\pi\) | |||||||
\(968\) | −89.3083 | −2.87048 | ||||||||
\(969\) | −0.394578 | −0.0126757 | ||||||||
\(970\) | −14.9843 | −0.481117 | ||||||||
\(971\) | −43.3466 | −1.39106 | −0.695529 | − | 0.718498i | \(-0.744830\pi\) | ||||
−0.695529 | + | 0.718498i | \(0.744830\pi\) | |||||||
\(972\) | 9.50906 | 0.305003 | ||||||||
\(973\) | −0.0344396 | −0.00110408 | ||||||||
\(974\) | −4.75143 | −0.152246 | ||||||||
\(975\) | 4.62787 | 0.148210 | ||||||||
\(976\) | −24.6231 | −0.788167 | ||||||||
\(977\) | 54.7469 | 1.75151 | 0.875754 | − | 0.482757i | \(-0.160365\pi\) | ||||
0.875754 | + | 0.482757i | \(0.160365\pi\) | |||||||
\(978\) | 93.4937 | 2.98960 | ||||||||
\(979\) | −96.0559 | −3.06996 | ||||||||
\(980\) | −3.37454 | −0.107796 | ||||||||
\(981\) | 25.3351 | 0.808888 | ||||||||
\(982\) | −48.4067 | −1.54472 | ||||||||
\(983\) | −2.64257 | −0.0842847 | −0.0421424 | − | 0.999112i | \(-0.513418\pi\) | ||||
−0.0421424 | + | 0.999112i | \(0.513418\pi\) | |||||||
\(984\) | −25.8104 | −0.822807 | ||||||||
\(985\) | −10.7765 | −0.343369 | ||||||||
\(986\) | 0.176486 | 0.00562045 | ||||||||
\(987\) | 0.564642 | 0.0179728 | ||||||||
\(988\) | 1.21744 | 0.0387320 | ||||||||
\(989\) | 12.4073 | 0.394528 | ||||||||
\(990\) | 50.2521 | 1.59712 | ||||||||
\(991\) | 36.7064 | 1.16602 | 0.583009 | − | 0.812465i | \(-0.301875\pi\) | ||||
0.583009 | + | 0.812465i | \(0.301875\pi\) | |||||||
\(992\) | −22.6970 | −0.720630 | ||||||||
\(993\) | −92.6700 | −2.94079 | ||||||||
\(994\) | −0.160509 | −0.00509105 | ||||||||
\(995\) | 23.8481 | 0.756035 | ||||||||
\(996\) | −3.76532 | −0.119309 | ||||||||
\(997\) | 39.6303 | 1.25510 | 0.627552 | − | 0.778575i | \(-0.284057\pi\) | ||||
0.627552 | + | 0.778575i | \(0.284057\pi\) | |||||||
\(998\) | −7.30317 | −0.231178 | ||||||||
\(999\) | −7.75923 | −0.245491 |
(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 | 2671.2.a.b.1.80 | ✓ | 122 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2671.2.a.b.1.80 | ✓ | 122 | 1.1 | even | 1 | trivial |