Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(277,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.277");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.k (of order \(4\), degree \(2\), 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: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 277.10 | ||
Character | \(\chi\) | \(=\) | 690.277 |
Dual form | 690.3.k.a.553.10 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.00000i | 0.500000 | + | 0.500000i | ||||
\(3\) | −1.22474 | + | 1.22474i | −0.408248 | + | 0.408248i | ||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | −4.92281 | + | 0.875159i | −0.984563 | + | 0.175032i | ||||
\(6\) | −2.44949 | −0.408248 | ||||||||
\(7\) | −4.77467 | − | 4.77467i | −0.682095 | − | 0.682095i | 0.278377 | − | 0.960472i | \(-0.410204\pi\) |
−0.960472 | + | 0.278377i | \(0.910204\pi\) | |||||||
\(8\) | −2.00000 | + | 2.00000i | −0.250000 | + | 0.250000i | ||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | −5.79797 | − | 4.04766i | −0.579797 | − | 0.404766i | ||||
\(11\) | 6.21921 | 0.565383 | 0.282692 | − | 0.959211i | \(-0.408773\pi\) | ||||
0.282692 | + | 0.959211i | \(0.408773\pi\) | |||||||
\(12\) | −2.44949 | − | 2.44949i | −0.204124 | − | 0.204124i | ||||
\(13\) | −0.0977897 | + | 0.0977897i | −0.00752229 | + | 0.00752229i | −0.710858 | − | 0.703336i | \(-0.751693\pi\) |
0.703336 | + | 0.710858i | \(0.251693\pi\) | |||||||
\(14\) | − | 9.54934i | − | 0.682095i | ||||||
\(15\) | 4.95735 | − | 7.10104i | 0.330490 | − | 0.473402i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −3.54869 | − | 3.54869i | −0.208746 | − | 0.208746i | 0.594988 | − | 0.803734i | \(-0.297157\pi\) |
−0.803734 | + | 0.594988i | \(0.797157\pi\) | |||||||
\(18\) | 3.00000 | − | 3.00000i | 0.166667 | − | 0.166667i | ||||
\(19\) | 5.38855i | 0.283608i | 0.989895 | + | 0.141804i | \(0.0452902\pi\) | ||||
−0.989895 | + | 0.141804i | \(0.954710\pi\) | |||||||
\(20\) | −1.75032 | − | 9.84563i | −0.0875159 | − | 0.492281i | ||||
\(21\) | 11.6955 | 0.556929 | ||||||||
\(22\) | 6.21921 | + | 6.21921i | 0.282692 | + | 0.282692i | ||||
\(23\) | 3.39116 | − | 3.39116i | 0.147442 | − | 0.147442i | ||||
\(24\) | − | 4.89898i | − | 0.204124i | ||||||
\(25\) | 23.4682 | − | 8.61649i | 0.938728 | − | 0.344659i | ||||
\(26\) | −0.195579 | −0.00752229 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | 9.54934 | − | 9.54934i | 0.341048 | − | 0.341048i | ||||
\(29\) | − | 55.0596i | − | 1.89861i | −0.314362 | − | 0.949303i | \(-0.601791\pi\) | ||
0.314362 | − | 0.949303i | \(-0.398209\pi\) | |||||||
\(30\) | 12.0584 | − | 2.14369i | 0.401946 | − | 0.0714564i | ||||
\(31\) | 14.2966 | 0.461182 | 0.230591 | − | 0.973051i | \(-0.425934\pi\) | ||||
0.230591 | + | 0.973051i | \(0.425934\pi\) | |||||||
\(32\) | −4.00000 | − | 4.00000i | −0.125000 | − | 0.125000i | ||||
\(33\) | −7.61695 | + | 7.61695i | −0.230817 | + | 0.230817i | ||||
\(34\) | − | 7.09737i | − | 0.208746i | ||||||
\(35\) | 27.6834 | + | 19.3262i | 0.790954 | + | 0.552177i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 41.5964 | + | 41.5964i | 1.12423 | + | 1.12423i | 0.991099 | + | 0.133128i | \(0.0425022\pi\) |
0.133128 | + | 0.991099i | \(0.457498\pi\) | |||||||
\(38\) | −5.38855 | + | 5.38855i | −0.141804 | + | 0.141804i | ||||
\(39\) | − | 0.239535i | − | 0.00614192i | ||||||
\(40\) | 8.09531 | − | 11.5959i | 0.202383 | − | 0.289899i | ||||
\(41\) | 15.3764 | 0.375034 | 0.187517 | − | 0.982261i | \(-0.439956\pi\) | ||||
0.187517 | + | 0.982261i | \(0.439956\pi\) | |||||||
\(42\) | 11.6955 | + | 11.6955i | 0.278464 | + | 0.278464i | ||||
\(43\) | 40.4973 | − | 40.4973i | 0.941797 | − | 0.941797i | −0.0566003 | − | 0.998397i | \(-0.518026\pi\) |
0.998397 | + | 0.0566003i | \(0.0180261\pi\) | |||||||
\(44\) | 12.4384i | 0.282692i | ||||||||
\(45\) | 2.62548 | + | 14.7684i | 0.0583439 | + | 0.328188i | ||||
\(46\) | 6.78233 | 0.147442 | ||||||||
\(47\) | 18.5795 | + | 18.5795i | 0.395309 | + | 0.395309i | 0.876575 | − | 0.481266i | \(-0.159823\pi\) |
−0.481266 | + | 0.876575i | \(0.659823\pi\) | |||||||
\(48\) | 4.89898 | − | 4.89898i | 0.102062 | − | 0.102062i | ||||
\(49\) | − | 3.40508i | − | 0.0694915i | ||||||
\(50\) | 32.0847 | + | 14.8517i | 0.641694 | + | 0.297034i | ||||
\(51\) | 8.69247 | 0.170441 | ||||||||
\(52\) | −0.195579 | − | 0.195579i | −0.00376114 | − | 0.00376114i | ||||
\(53\) | −30.0791 | + | 30.0791i | −0.567530 | + | 0.567530i | −0.931436 | − | 0.363906i | \(-0.881443\pi\) |
0.363906 | + | 0.931436i | \(0.381443\pi\) | |||||||
\(54\) | 7.34847i | 0.136083i | ||||||||
\(55\) | −30.6160 | + | 5.44280i | −0.556655 | + | 0.0989600i | ||||
\(56\) | 19.0987 | 0.341048 | ||||||||
\(57\) | −6.59960 | − | 6.59960i | −0.115782 | − | 0.115782i | ||||
\(58\) | 55.0596 | − | 55.0596i | 0.949303 | − | 0.949303i | ||||
\(59\) | − | 17.7359i | − | 0.300609i | −0.988640 | − | 0.150304i | \(-0.951975\pi\) | ||
0.988640 | − | 0.150304i | \(-0.0480254\pi\) | |||||||
\(60\) | 14.2021 | + | 9.91469i | 0.236701 | + | 0.165245i | ||||
\(61\) | 104.425 | 1.71189 | 0.855944 | − | 0.517068i | \(-0.172977\pi\) | ||||
0.855944 | + | 0.517068i | \(0.172977\pi\) | |||||||
\(62\) | 14.2966 | + | 14.2966i | 0.230591 | + | 0.230591i | ||||
\(63\) | −14.3240 | + | 14.3240i | −0.227365 | + | 0.227365i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 0.395819 | − | 0.566982i | 0.00608953 | − | 0.00872280i | ||||
\(66\) | −15.2339 | −0.230817 | ||||||||
\(67\) | −50.0903 | − | 50.0903i | −0.747616 | − | 0.747616i | 0.226415 | − | 0.974031i | \(-0.427299\pi\) |
−0.974031 | + | 0.226415i | \(0.927299\pi\) | |||||||
\(68\) | 7.09737 | − | 7.09737i | 0.104373 | − | 0.104373i | ||||
\(69\) | 8.30662i | 0.120386i | ||||||||
\(70\) | 8.35718 | + | 47.0096i | 0.119388 | + | 0.671566i | ||||
\(71\) | −39.0537 | −0.550052 | −0.275026 | − | 0.961437i | \(-0.588687\pi\) | ||||
−0.275026 | + | 0.961437i | \(0.588687\pi\) | |||||||
\(72\) | 6.00000 | + | 6.00000i | 0.0833333 | + | 0.0833333i | ||||
\(73\) | −39.1111 | + | 39.1111i | −0.535768 | + | 0.535768i | −0.922283 | − | 0.386515i | \(-0.873679\pi\) |
0.386515 | + | 0.922283i | \(0.373679\pi\) | |||||||
\(74\) | 83.1928i | 1.12423i | ||||||||
\(75\) | −18.1896 | + | 39.2955i | −0.242527 | + | 0.523941i | ||||
\(76\) | −10.7771 | −0.141804 | ||||||||
\(77\) | −29.6947 | − | 29.6947i | −0.385645 | − | 0.385645i | ||||
\(78\) | 0.239535 | − | 0.239535i | 0.00307096 | − | 0.00307096i | ||||
\(79\) | − | 71.7211i | − | 0.907862i | −0.891037 | − | 0.453931i | \(-0.850021\pi\) | ||
0.891037 | − | 0.453931i | \(-0.149979\pi\) | |||||||
\(80\) | 19.6913 | − | 3.50063i | 0.246141 | − | 0.0437579i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 15.3764 | + | 15.3764i | 0.187517 | + | 0.187517i | ||||
\(83\) | −38.3908 | + | 38.3908i | −0.462540 | + | 0.462540i | −0.899487 | − | 0.436947i | \(-0.856060\pi\) |
0.436947 | + | 0.899487i | \(0.356060\pi\) | |||||||
\(84\) | 23.3910i | 0.278464i | ||||||||
\(85\) | 20.5752 | + | 14.3639i | 0.242061 | + | 0.168987i | ||||
\(86\) | 80.9945 | 0.941797 | ||||||||
\(87\) | 67.4339 | + | 67.4339i | 0.775103 | + | 0.775103i | ||||
\(88\) | −12.4384 | + | 12.4384i | −0.141346 | + | 0.141346i | ||||
\(89\) | − | 20.0099i | − | 0.224830i | −0.993661 | − | 0.112415i | \(-0.964141\pi\) | ||
0.993661 | − | 0.112415i | \(-0.0358586\pi\) | |||||||
\(90\) | −12.1430 | + | 17.3939i | −0.134922 | + | 0.193266i | ||||
\(91\) | 0.933827 | 0.0102618 | ||||||||
\(92\) | 6.78233 | + | 6.78233i | 0.0737210 | + | 0.0737210i | ||||
\(93\) | −17.5097 | + | 17.5097i | −0.188277 | + | 0.188277i | ||||
\(94\) | 37.1591i | 0.395309i | ||||||||
\(95\) | −4.71583 | − | 26.5268i | −0.0496404 | − | 0.279230i | ||||
\(96\) | 9.79796 | 0.102062 | ||||||||
\(97\) | −22.7167 | − | 22.7167i | −0.234193 | − | 0.234193i | 0.580247 | − | 0.814440i | \(-0.302956\pi\) |
−0.814440 | + | 0.580247i | \(0.802956\pi\) | |||||||
\(98\) | 3.40508 | − | 3.40508i | 0.0347458 | − | 0.0347458i | ||||
\(99\) | − | 18.6576i | − | 0.188461i | ||||||
\(100\) | 17.2330 | + | 46.9364i | 0.172330 | + | 0.469364i | ||||
\(101\) | 82.8175 | 0.819975 | 0.409988 | − | 0.912091i | \(-0.365533\pi\) | ||||
0.409988 | + | 0.912091i | \(0.365533\pi\) | |||||||
\(102\) | 8.69247 | + | 8.69247i | 0.0852203 | + | 0.0852203i | ||||
\(103\) | 104.995 | − | 104.995i | 1.01937 | − | 1.01937i | 0.0195589 | − | 0.999809i | \(-0.493774\pi\) |
0.999809 | − | 0.0195589i | \(-0.00622620\pi\) | |||||||
\(104\) | − | 0.391159i | − | 0.00376114i | ||||||
\(105\) | −57.5748 | + | 10.2354i | −0.548331 | + | 0.0974802i | ||||
\(106\) | −60.1581 | −0.567530 | ||||||||
\(107\) | −121.033 | − | 121.033i | −1.13115 | − | 1.13115i | −0.989986 | − | 0.141168i | \(-0.954914\pi\) |
−0.141168 | − | 0.989986i | \(-0.545086\pi\) | |||||||
\(108\) | −7.34847 | + | 7.34847i | −0.0680414 | + | 0.0680414i | ||||
\(109\) | − | 178.570i | − | 1.63826i | −0.573610 | − | 0.819128i | \(-0.694458\pi\) | ||
0.573610 | − | 0.819128i | \(-0.305542\pi\) | |||||||
\(110\) | −36.0588 | − | 25.1732i | −0.327808 | − | 0.228848i | ||||
\(111\) | −101.890 | −0.917927 | ||||||||
\(112\) | 19.0987 | + | 19.0987i | 0.170524 | + | 0.170524i | ||||
\(113\) | 25.4462 | − | 25.4462i | 0.225188 | − | 0.225188i | −0.585491 | − | 0.810679i | \(-0.699098\pi\) |
0.810679 | + | 0.585491i | \(0.199098\pi\) | |||||||
\(114\) | − | 13.1992i | − | 0.115782i | ||||||
\(115\) | −13.7263 | + | 19.6619i | −0.119359 | + | 0.170973i | ||||
\(116\) | 110.119 | 0.949303 | ||||||||
\(117\) | 0.293369 | + | 0.293369i | 0.00250743 | + | 0.00250743i | ||||
\(118\) | 17.7359 | − | 17.7359i | 0.150304 | − | 0.150304i | ||||
\(119\) | 33.8876i | 0.284770i | ||||||||
\(120\) | 4.28738 | + | 24.1168i | 0.0357282 | + | 0.200973i | ||||
\(121\) | −82.3214 | −0.680342 | ||||||||
\(122\) | 104.425 | + | 104.425i | 0.855944 | + | 0.855944i | ||||
\(123\) | −18.8322 | + | 18.8322i | −0.153107 | + | 0.153107i | ||||
\(124\) | 28.5933i | 0.230591i | ||||||||
\(125\) | −107.989 | + | 62.9557i | −0.863910 | + | 0.503646i | ||||
\(126\) | −28.6480 | −0.227365 | ||||||||
\(127\) | 83.0337 | + | 83.0337i | 0.653809 | + | 0.653809i | 0.953908 | − | 0.300099i | \(-0.0970198\pi\) |
−0.300099 | + | 0.953908i | \(0.597020\pi\) | |||||||
\(128\) | 8.00000 | − | 8.00000i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 99.1976i | 0.768974i | ||||||||
\(130\) | 0.962801 | − | 0.171163i | 0.00740616 | − | 0.00131664i | ||||
\(131\) | 133.089 | 1.01595 | 0.507973 | − | 0.861373i | \(-0.330395\pi\) | ||||
0.507973 | + | 0.861373i | \(0.330395\pi\) | |||||||
\(132\) | −15.2339 | − | 15.2339i | −0.115408 | − | 0.115408i | ||||
\(133\) | 25.7285 | − | 25.7285i | 0.193448 | − | 0.193448i | ||||
\(134\) | − | 100.181i | − | 0.747616i | ||||||
\(135\) | −21.3031 | − | 14.8720i | −0.157801 | − | 0.110163i | ||||
\(136\) | 14.1947 | 0.104373 | ||||||||
\(137\) | −185.185 | − | 185.185i | −1.35172 | − | 1.35172i | −0.883741 | − | 0.467977i | \(-0.844983\pi\) |
−0.467977 | − | 0.883741i | \(-0.655017\pi\) | |||||||
\(138\) | −8.30662 | + | 8.30662i | −0.0601929 | + | 0.0601929i | ||||
\(139\) | − | 31.5467i | − | 0.226954i | −0.993541 | − | 0.113477i | \(-0.963801\pi\) | ||
0.993541 | − | 0.113477i | \(-0.0361989\pi\) | |||||||
\(140\) | −38.6524 | + | 55.3668i | −0.276089 | + | 0.395477i | ||||
\(141\) | −45.5104 | −0.322769 | ||||||||
\(142\) | −39.0537 | − | 39.0537i | −0.275026 | − | 0.275026i | ||||
\(143\) | −0.608175 | + | 0.608175i | −0.00425297 | + | 0.00425297i | ||||
\(144\) | 12.0000i | 0.0833333i | ||||||||
\(145\) | 48.1859 | + | 271.048i | 0.332316 | + | 1.86930i | ||||
\(146\) | −78.2222 | −0.535768 | ||||||||
\(147\) | 4.17036 | + | 4.17036i | 0.0283698 | + | 0.0283698i | ||||
\(148\) | −83.1928 | + | 83.1928i | −0.562113 | + | 0.562113i | ||||
\(149\) | − | 112.726i | − | 0.756550i | −0.925693 | − | 0.378275i | \(-0.876517\pi\) | ||
0.925693 | − | 0.378275i | \(-0.123483\pi\) | |||||||
\(150\) | −57.4851 | + | 21.1060i | −0.383234 | + | 0.140707i | ||||
\(151\) | 185.114 | 1.22592 | 0.612961 | − | 0.790113i | \(-0.289978\pi\) | ||||
0.612961 | + | 0.790113i | \(0.289978\pi\) | |||||||
\(152\) | −10.7771 | − | 10.7771i | −0.0709020 | − | 0.0709020i | ||||
\(153\) | −10.6461 | + | 10.6461i | −0.0695821 | + | 0.0695821i | ||||
\(154\) | − | 59.3894i | − | 0.385645i | ||||||
\(155\) | −70.3796 | + | 12.5118i | −0.454062 | + | 0.0807214i | ||||
\(156\) | 0.479070 | 0.00307096 | ||||||||
\(157\) | −139.491 | − | 139.491i | −0.888479 | − | 0.888479i | 0.105898 | − | 0.994377i | \(-0.466228\pi\) |
−0.994377 | + | 0.105898i | \(0.966228\pi\) | |||||||
\(158\) | 71.7211 | − | 71.7211i | 0.453931 | − | 0.453931i | ||||
\(159\) | − | 73.6784i | − | 0.463386i | ||||||
\(160\) | 23.1919 | + | 16.1906i | 0.144949 | + | 0.101191i | ||||
\(161\) | −32.3834 | −0.201139 | ||||||||
\(162\) | −9.00000 | − | 9.00000i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | 211.002 | − | 211.002i | 1.29449 | − | 1.29449i | 0.362515 | − | 0.931978i | \(-0.381918\pi\) |
0.931978 | − | 0.362515i | \(-0.118082\pi\) | |||||||
\(164\) | 30.7528i | 0.187517i | ||||||||
\(165\) | 30.8308 | − | 44.1629i | 0.186853 | − | 0.267654i | ||||
\(166\) | −76.7817 | −0.462540 | ||||||||
\(167\) | 50.5748 | + | 50.5748i | 0.302843 | + | 0.302843i | 0.842125 | − | 0.539282i | \(-0.181304\pi\) |
−0.539282 | + | 0.842125i | \(0.681304\pi\) | |||||||
\(168\) | −23.3910 | + | 23.3910i | −0.139232 | + | 0.139232i | ||||
\(169\) | 168.981i | 0.999887i | ||||||||
\(170\) | 6.21133 | + | 34.9390i | 0.0365372 | + | 0.205524i | ||||
\(171\) | 16.1656 | 0.0945359 | ||||||||
\(172\) | 80.9945 | + | 80.9945i | 0.470898 | + | 0.470898i | ||||
\(173\) | −194.213 | + | 194.213i | −1.12262 | + | 1.12262i | −0.131271 | + | 0.991347i | \(0.541906\pi\) |
−0.991347 | + | 0.131271i | \(0.958094\pi\) | |||||||
\(174\) | 134.868i | 0.775103i | ||||||||
\(175\) | −153.194 | − | 70.9120i | −0.875393 | − | 0.405211i | ||||
\(176\) | −24.8769 | −0.141346 | ||||||||
\(177\) | 21.7220 | + | 21.7220i | 0.122723 | + | 0.122723i | ||||
\(178\) | 20.0099 | − | 20.0099i | 0.112415 | − | 0.112415i | ||||
\(179\) | − | 111.660i | − | 0.623800i | −0.950115 | − | 0.311900i | \(-0.899035\pi\) | ||
0.950115 | − | 0.311900i | \(-0.100965\pi\) | |||||||
\(180\) | −29.5369 | + | 5.25095i | −0.164094 | + | 0.0291720i | ||||
\(181\) | 192.806 | 1.06523 | 0.532614 | − | 0.846358i | \(-0.321210\pi\) | ||||
0.532614 | + | 0.846358i | \(0.321210\pi\) | |||||||
\(182\) | 0.933827 | + | 0.933827i | 0.00513092 | + | 0.00513092i | ||||
\(183\) | −127.894 | + | 127.894i | −0.698875 | + | 0.698875i | ||||
\(184\) | 13.5647i | 0.0737210i | ||||||||
\(185\) | −241.175 | − | 168.368i | −1.30365 | − | 0.910097i | ||||
\(186\) | −35.0194 | −0.188277 | ||||||||
\(187\) | −22.0700 | − | 22.0700i | −0.118022 | − | 0.118022i | ||||
\(188\) | −37.1591 | + | 37.1591i | −0.197655 | + | 0.197655i | ||||
\(189\) | − | 35.0865i | − | 0.185643i | ||||||
\(190\) | 21.8110 | − | 31.2427i | 0.114795 | − | 0.164435i | ||||
\(191\) | 99.0271 | 0.518467 | 0.259233 | − | 0.965815i | \(-0.416530\pi\) | ||||
0.259233 | + | 0.965815i | \(0.416530\pi\) | |||||||
\(192\) | 9.79796 | + | 9.79796i | 0.0510310 | + | 0.0510310i | ||||
\(193\) | −179.344 | + | 179.344i | −0.929242 | + | 0.929242i | −0.997657 | − | 0.0684148i | \(-0.978206\pi\) |
0.0684148 | + | 0.997657i | \(0.478206\pi\) | |||||||
\(194\) | − | 45.4334i | − | 0.234193i | ||||||
\(195\) | 0.209631 | + | 1.17919i | 0.00107503 | + | 0.00604711i | ||||
\(196\) | 6.81017 | 0.0347458 | ||||||||
\(197\) | −62.4550 | − | 62.4550i | −0.317030 | − | 0.317030i | 0.530595 | − | 0.847625i | \(-0.321968\pi\) |
−0.847625 | + | 0.530595i | \(0.821968\pi\) | |||||||
\(198\) | 18.6576 | − | 18.6576i | 0.0942305 | − | 0.0942305i | ||||
\(199\) | − | 204.645i | − | 1.02837i | −0.857680 | − | 0.514183i | \(-0.828095\pi\) | ||
0.857680 | − | 0.514183i | \(-0.171905\pi\) | |||||||
\(200\) | −29.7034 | + | 64.1694i | −0.148517 | + | 0.320847i | ||||
\(201\) | 122.696 | 0.610426 | ||||||||
\(202\) | 82.8175 | + | 82.8175i | 0.409988 | + | 0.409988i | ||||
\(203\) | −262.891 | + | 262.891i | −1.29503 | + | 1.29503i | ||||
\(204\) | 17.3849i | 0.0852203i | ||||||||
\(205\) | −75.6951 | + | 13.4568i | −0.369245 | + | 0.0656428i | ||||
\(206\) | 209.990 | 1.01937 | ||||||||
\(207\) | −10.1735 | − | 10.1735i | −0.0491473 | − | 0.0491473i | ||||
\(208\) | 0.391159 | − | 0.391159i | 0.00188057 | − | 0.00188057i | ||||
\(209\) | 33.5125i | 0.160347i | ||||||||
\(210\) | −67.8102 | − | 47.3394i | −0.322906 | − | 0.225426i | ||||
\(211\) | 7.31007 | 0.0346449 | 0.0173224 | − | 0.999850i | \(-0.494486\pi\) | ||||
0.0173224 | + | 0.999850i | \(0.494486\pi\) | |||||||
\(212\) | −60.1581 | − | 60.1581i | −0.283765 | − | 0.283765i | ||||
\(213\) | 47.8308 | − | 47.8308i | 0.224558 | − | 0.224558i | ||||
\(214\) | − | 242.067i | − | 1.13115i | ||||||
\(215\) | −163.919 | + | 234.802i | −0.762414 | + | 1.09210i | ||||
\(216\) | −14.6969 | −0.0680414 | ||||||||
\(217\) | −68.2617 | − | 68.2617i | −0.314570 | − | 0.314570i | ||||
\(218\) | 178.570 | − | 178.570i | 0.819128 | − | 0.819128i | ||||
\(219\) | − | 95.8022i | − | 0.437453i | ||||||
\(220\) | −10.8856 | − | 61.2321i | −0.0494800 | − | 0.278328i | ||||
\(221\) | 0.694050 | 0.00314050 | ||||||||
\(222\) | −101.890 | − | 101.890i | −0.458964 | − | 0.458964i | ||||
\(223\) | 26.6273 | − | 26.6273i | 0.119405 | − | 0.119405i | −0.644879 | − | 0.764284i | \(-0.723092\pi\) |
0.764284 | + | 0.644879i | \(0.223092\pi\) | |||||||
\(224\) | 38.1973i | 0.170524i | ||||||||
\(225\) | −25.8495 | − | 70.4046i | −0.114886 | − | 0.312909i | ||||
\(226\) | 50.8924 | 0.225188 | ||||||||
\(227\) | −114.877 | − | 114.877i | −0.506068 | − | 0.506068i | 0.407249 | − | 0.913317i | \(-0.366488\pi\) |
−0.913317 | + | 0.407249i | \(0.866488\pi\) | |||||||
\(228\) | 13.1992 | − | 13.1992i | 0.0578912 | − | 0.0578912i | ||||
\(229\) | − | 56.2198i | − | 0.245501i | −0.992438 | − | 0.122751i | \(-0.960828\pi\) | ||
0.992438 | − | 0.122751i | \(-0.0391715\pi\) | |||||||
\(230\) | −33.3881 | + | 5.93561i | −0.145166 | + | 0.0258070i | ||||
\(231\) | 72.7368 | 0.314878 | ||||||||
\(232\) | 110.119 | + | 110.119i | 0.474652 | + | 0.474652i | ||||
\(233\) | −170.729 | + | 170.729i | −0.732742 | + | 0.732742i | −0.971162 | − | 0.238420i | \(-0.923371\pi\) |
0.238420 | + | 0.971162i | \(0.423371\pi\) | |||||||
\(234\) | 0.586738i | 0.00250743i | ||||||||
\(235\) | −107.724 | − | 75.2036i | −0.458399 | − | 0.320015i | ||||
\(236\) | 35.4719 | 0.150304 | ||||||||
\(237\) | 87.8401 | + | 87.8401i | 0.370633 | + | 0.370633i | ||||
\(238\) | −33.8876 | + | 33.8876i | −0.142385 | + | 0.142385i | ||||
\(239\) | 143.495i | 0.600397i | 0.953877 | + | 0.300199i | \(0.0970530\pi\) | ||||
−0.953877 | + | 0.300199i | \(0.902947\pi\) | |||||||
\(240\) | −19.8294 | + | 28.4041i | −0.0826224 | + | 0.118351i | ||||
\(241\) | −97.6832 | −0.405325 | −0.202662 | − | 0.979249i | \(-0.564959\pi\) | ||||
−0.202662 | + | 0.979249i | \(0.564959\pi\) | |||||||
\(242\) | −82.3214 | − | 82.3214i | −0.340171 | − | 0.340171i | ||||
\(243\) | 11.0227 | − | 11.0227i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 208.850i | 0.855944i | ||||||||
\(245\) | 2.97999 | + | 16.7626i | 0.0121632 | + | 0.0684188i | ||||
\(246\) | −37.6643 | −0.153107 | ||||||||
\(247\) | −0.526945 | − | 0.526945i | −0.00213338 | − | 0.00213338i | ||||
\(248\) | −28.5933 | + | 28.5933i | −0.115295 | + | 0.115295i | ||||
\(249\) | − | 94.0380i | − | 0.377663i | ||||||
\(250\) | −170.945 | − | 45.0330i | −0.683778 | − | 0.180132i | ||||
\(251\) | 16.2884 | 0.0648940 | 0.0324470 | − | 0.999473i | \(-0.489670\pi\) | ||||
0.0324470 | + | 0.999473i | \(0.489670\pi\) | |||||||
\(252\) | −28.6480 | − | 28.6480i | −0.113683 | − | 0.113683i | ||||
\(253\) | 21.0904 | − | 21.0904i | 0.0833612 | − | 0.0833612i | ||||
\(254\) | 166.067i | 0.653809i | ||||||||
\(255\) | −42.7914 | + | 7.60729i | −0.167809 | + | 0.0298325i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 65.4723 | + | 65.4723i | 0.254756 | + | 0.254756i | 0.822917 | − | 0.568161i | \(-0.192345\pi\) |
−0.568161 | + | 0.822917i | \(0.692345\pi\) | |||||||
\(258\) | −99.1976 | + | 99.1976i | −0.384487 | + | 0.384487i | ||||
\(259\) | − | 397.218i | − | 1.53366i | ||||||
\(260\) | 1.13396 | + | 0.791638i | 0.00436140 | + | 0.00304476i | ||||
\(261\) | −165.179 | −0.632869 | ||||||||
\(262\) | 133.089 | + | 133.089i | 0.507973 | + | 0.507973i | ||||
\(263\) | −116.481 | + | 116.481i | −0.442895 | + | 0.442895i | −0.892984 | − | 0.450089i | \(-0.851392\pi\) |
0.450089 | + | 0.892984i | \(0.351392\pi\) | |||||||
\(264\) | − | 30.4678i | − | 0.115408i | ||||||
\(265\) | 121.750 | − | 174.398i | 0.459433 | − | 0.658104i | ||||
\(266\) | 51.4571 | 0.193448 | ||||||||
\(267\) | 24.5070 | + | 24.5070i | 0.0917866 | + | 0.0917866i | ||||
\(268\) | 100.181 | − | 100.181i | 0.373808 | − | 0.373808i | ||||
\(269\) | 296.382i | 1.10179i | 0.834574 | + | 0.550897i | \(0.185714\pi\) | ||||
−0.834574 | + | 0.550897i | \(0.814286\pi\) | |||||||
\(270\) | −6.43108 | − | 36.1751i | −0.0238188 | − | 0.133982i | ||||
\(271\) | 227.220 | 0.838449 | 0.419224 | − | 0.907883i | \(-0.362302\pi\) | ||||
0.419224 | + | 0.907883i | \(0.362302\pi\) | |||||||
\(272\) | 14.1947 | + | 14.1947i | 0.0521866 | + | 0.0521866i | ||||
\(273\) | −1.14370 | + | 1.14370i | −0.00418938 | + | 0.00418938i | ||||
\(274\) | − | 370.371i | − | 1.35172i | ||||||
\(275\) | 145.954 | − | 53.5878i | 0.530741 | − | 0.194865i | ||||
\(276\) | −16.6132 | −0.0601929 | ||||||||
\(277\) | 280.325 | + | 280.325i | 1.01200 | + | 1.01200i | 0.999927 | + | 0.0120768i | \(0.00384425\pi\) |
0.0120768 | + | 0.999927i | \(0.496156\pi\) | |||||||
\(278\) | 31.5467 | − | 31.5467i | 0.113477 | − | 0.113477i | ||||
\(279\) | − | 42.8899i | − | 0.153727i | ||||||
\(280\) | −94.0192 | + | 16.7144i | −0.335783 | + | 0.0596942i | ||||
\(281\) | −135.612 | −0.482607 | −0.241303 | − | 0.970450i | \(-0.577575\pi\) | ||||
−0.241303 | + | 0.970450i | \(0.577575\pi\) | |||||||
\(282\) | −45.5104 | − | 45.5104i | −0.161384 | − | 0.161384i | ||||
\(283\) | 191.782 | − | 191.782i | 0.677675 | − | 0.677675i | −0.281799 | − | 0.959474i | \(-0.590931\pi\) |
0.959474 | + | 0.281799i | \(0.0909310\pi\) | |||||||
\(284\) | − | 78.1074i | − | 0.275026i | ||||||
\(285\) | 38.2643 | + | 26.7129i | 0.134261 | + | 0.0937295i | ||||
\(286\) | −1.21635 | −0.00425297 | ||||||||
\(287\) | −73.4172 | − | 73.4172i | −0.255809 | − | 0.255809i | ||||
\(288\) | −12.0000 | + | 12.0000i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | − | 263.814i | − | 0.912850i | ||||||
\(290\) | −222.862 | + | 319.234i | −0.768490 | + | 1.10081i | ||||
\(291\) | 55.6444 | 0.191218 | ||||||||
\(292\) | −78.2222 | − | 78.2222i | −0.267884 | − | 0.267884i | ||||
\(293\) | 28.7884 | − | 28.7884i | 0.0982538 | − | 0.0982538i | −0.656271 | − | 0.754525i | \(-0.727867\pi\) |
0.754525 | + | 0.656271i | \(0.227867\pi\) | |||||||
\(294\) | 8.34072i | 0.0283698i | ||||||||
\(295\) | 15.5218 | + | 87.3107i | 0.0526161 | + | 0.295968i | ||||
\(296\) | −166.386 | −0.562113 | ||||||||
\(297\) | 22.8509 | + | 22.8509i | 0.0769389 | + | 0.0769389i | ||||
\(298\) | 112.726 | − | 112.726i | 0.378275 | − | 0.378275i | ||||
\(299\) | 0.663242i | 0.00221820i | ||||||||
\(300\) | −78.5911 | − | 36.3791i | −0.261970 | − | 0.121264i | ||||
\(301\) | −386.722 | −1.28479 | ||||||||
\(302\) | 185.114 | + | 185.114i | 0.612961 | + | 0.612961i | ||||
\(303\) | −101.430 | + | 101.430i | −0.334753 | + | 0.334753i | ||||
\(304\) | − | 21.5542i | − | 0.0709020i | ||||||
\(305\) | −514.066 | + | 91.3886i | −1.68546 | + | 0.299635i | ||||
\(306\) | −21.2921 | −0.0695821 | ||||||||
\(307\) | 6.39515 | + | 6.39515i | 0.0208311 | + | 0.0208311i | 0.717446 | − | 0.696615i | \(-0.245311\pi\) |
−0.696615 | + | 0.717446i | \(0.745311\pi\) | |||||||
\(308\) | 59.3894 | − | 59.3894i | 0.192823 | − | 0.192823i | ||||
\(309\) | 257.184i | 0.832310i | ||||||||
\(310\) | −82.8915 | − | 57.8678i | −0.267392 | − | 0.186670i | ||||
\(311\) | 375.884 | 1.20863 | 0.604315 | − | 0.796745i | \(-0.293447\pi\) | ||||
0.604315 | + | 0.796745i | \(0.293447\pi\) | |||||||
\(312\) | 0.479070 | + | 0.479070i | 0.00153548 | + | 0.00153548i | ||||
\(313\) | 24.7214 | − | 24.7214i | 0.0789820 | − | 0.0789820i | −0.666512 | − | 0.745494i | \(-0.732214\pi\) |
0.745494 | + | 0.666512i | \(0.232214\pi\) | |||||||
\(314\) | − | 278.983i | − | 0.888479i | ||||||
\(315\) | 57.9786 | − | 83.0502i | 0.184059 | − | 0.263651i | ||||
\(316\) | 143.442 | 0.453931 | ||||||||
\(317\) | −113.695 | − | 113.695i | −0.358661 | − | 0.358661i | 0.504658 | − | 0.863319i | \(-0.331618\pi\) |
−0.863319 | + | 0.504658i | \(0.831618\pi\) | |||||||
\(318\) | 73.6784 | − | 73.6784i | 0.231693 | − | 0.231693i | ||||
\(319\) | − | 342.427i | − | 1.07344i | ||||||
\(320\) | 7.00127 | + | 39.3825i | 0.0218790 | + | 0.123070i | ||||
\(321\) | 296.470 | 0.923583 | ||||||||
\(322\) | −32.3834 | − | 32.3834i | −0.100569 | − | 0.100569i | ||||
\(323\) | 19.1223 | − | 19.1223i | 0.0592021 | − | 0.0592021i | ||||
\(324\) | − | 18.0000i | − | 0.0555556i | ||||||
\(325\) | −1.45234 | + | 3.13755i | −0.00446875 | + | 0.00965401i | ||||
\(326\) | 422.005 | 1.29449 | ||||||||
\(327\) | 218.703 | + | 218.703i | 0.668816 | + | 0.668816i | ||||
\(328\) | −30.7528 | + | 30.7528i | −0.0937585 | + | 0.0937585i | ||||
\(329\) | − | 177.422i | − | 0.539277i | ||||||
\(330\) | 74.9937 | − | 13.3321i | 0.227254 | − | 0.0404002i | ||||
\(331\) | −299.118 | −0.903681 | −0.451840 | − | 0.892099i | \(-0.649232\pi\) | ||||
−0.451840 | + | 0.892099i | \(0.649232\pi\) | |||||||
\(332\) | −76.7817 | − | 76.7817i | −0.231270 | − | 0.231270i | ||||
\(333\) | 124.789 | − | 124.789i | 0.374742 | − | 0.374742i | ||||
\(334\) | 101.150i | 0.302843i | ||||||||
\(335\) | 290.422 | + | 202.748i | 0.866931 | + | 0.605218i | ||||
\(336\) | −46.7820 | −0.139232 | ||||||||
\(337\) | −43.0548 | − | 43.0548i | −0.127759 | − | 0.127759i | 0.640336 | − | 0.768095i | \(-0.278795\pi\) |
−0.768095 | + | 0.640336i | \(0.778795\pi\) | |||||||
\(338\) | −168.981 | + | 168.981i | −0.499943 | + | 0.499943i | ||||
\(339\) | 62.3302i | 0.183865i | ||||||||
\(340\) | −28.7277 | + | 41.1504i | −0.0844933 | + | 0.121031i | ||||
\(341\) | 88.9138 | 0.260744 | ||||||||
\(342\) | 16.1656 | + | 16.1656i | 0.0472680 | + | 0.0472680i | ||||
\(343\) | −250.217 | + | 250.217i | −0.729495 | + | 0.729495i | ||||
\(344\) | 161.989i | 0.470898i | ||||||||
\(345\) | −7.26961 | − | 40.8920i | −0.0210713 | − | 0.118527i | ||||
\(346\) | −388.426 | −1.12262 | ||||||||
\(347\) | 180.407 | + | 180.407i | 0.519904 | + | 0.519904i | 0.917542 | − | 0.397639i | \(-0.130170\pi\) |
−0.397639 | + | 0.917542i | \(0.630170\pi\) | |||||||
\(348\) | −134.868 | + | 134.868i | −0.387551 | + | 0.387551i | ||||
\(349\) | 76.9282i | 0.220425i | 0.993908 | + | 0.110212i | \(0.0351531\pi\) | ||||
−0.993908 | + | 0.110212i | \(0.964847\pi\) | |||||||
\(350\) | −82.2817 | − | 224.106i | −0.235091 | − | 0.640302i | ||||
\(351\) | −0.718605 | −0.00204731 | ||||||||
\(352\) | −24.8769 | − | 24.8769i | −0.0706729 | − | 0.0706729i | ||||
\(353\) | −411.334 | + | 411.334i | −1.16525 | + | 1.16525i | −0.181943 | + | 0.983309i | \(0.558239\pi\) |
−0.983309 | + | 0.181943i | \(0.941761\pi\) | |||||||
\(354\) | 43.4440i | 0.122723i | ||||||||
\(355\) | 192.254 | − | 34.1782i | 0.541561 | − | 0.0962766i | ||||
\(356\) | 40.0198 | 0.112415 | ||||||||
\(357\) | −41.5037 | − | 41.5037i | −0.116257 | − | 0.116257i | ||||
\(358\) | 111.660 | − | 111.660i | 0.311900 | − | 0.311900i | ||||
\(359\) | 112.879i | 0.314426i | 0.987565 | + | 0.157213i | \(0.0502509\pi\) | ||||
−0.987565 | + | 0.157213i | \(0.949749\pi\) | |||||||
\(360\) | −34.7878 | − | 24.2859i | −0.0966329 | − | 0.0674609i | ||||
\(361\) | 331.964 | 0.919567 | ||||||||
\(362\) | 192.806 | + | 192.806i | 0.532614 | + | 0.532614i | ||||
\(363\) | 100.823 | − | 100.823i | 0.277748 | − | 0.277748i | ||||
\(364\) | 1.86765i | 0.00513092i | ||||||||
\(365\) | 158.308 | − | 226.765i | 0.433721 | − | 0.621274i | ||||
\(366\) | −255.788 | −0.698875 | ||||||||
\(367\) | 405.857 | + | 405.857i | 1.10588 | + | 1.10588i | 0.993687 | + | 0.112192i | \(0.0357871\pi\) |
0.112192 | + | 0.993687i | \(0.464213\pi\) | |||||||
\(368\) | −13.5647 | + | 13.5647i | −0.0368605 | + | 0.0368605i | ||||
\(369\) | − | 46.1292i | − | 0.125011i | ||||||
\(370\) | −72.8069 | − | 409.543i | −0.196775 | − | 1.10687i | ||||
\(371\) | 287.235 | 0.774219 | ||||||||
\(372\) | −35.0194 | − | 35.0194i | −0.0941383 | − | 0.0941383i | ||||
\(373\) | −96.2819 | + | 96.2819i | −0.258128 | + | 0.258128i | −0.824293 | − | 0.566164i | \(-0.808427\pi\) |
0.566164 | + | 0.824293i | \(0.308427\pi\) | |||||||
\(374\) | − | 44.1401i | − | 0.118022i | ||||||
\(375\) | 55.1540 | − | 209.363i | 0.147077 | − | 0.558302i | ||||
\(376\) | −74.3182 | −0.197655 | ||||||||
\(377\) | 5.38426 | + | 5.38426i | 0.0142819 | + | 0.0142819i | ||||
\(378\) | 35.0865 | − | 35.0865i | 0.0928214 | − | 0.0928214i | ||||
\(379\) | − | 200.497i | − | 0.529017i | −0.964383 | − | 0.264509i | \(-0.914790\pi\) | ||
0.964383 | − | 0.264509i | \(-0.0852097\pi\) | |||||||
\(380\) | 53.0536 | − | 9.43167i | 0.139615 | − | 0.0248202i | ||||
\(381\) | −203.390 | −0.533833 | ||||||||
\(382\) | 99.0271 | + | 99.0271i | 0.259233 | + | 0.259233i | ||||
\(383\) | 63.0994 | − | 63.0994i | 0.164750 | − | 0.164750i | −0.619917 | − | 0.784667i | \(-0.712834\pi\) |
0.784667 | + | 0.619917i | \(0.212834\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 172.169 | + | 120.194i | 0.447192 | + | 0.312192i | ||||
\(386\) | −358.687 | −0.929242 | ||||||||
\(387\) | −121.492 | − | 121.492i | −0.313932 | − | 0.313932i | ||||
\(388\) | 45.4334 | − | 45.4334i | 0.117096 | − | 0.117096i | ||||
\(389\) | 346.298i | 0.890227i | 0.895474 | + | 0.445113i | \(0.146837\pi\) | ||||
−0.895474 | + | 0.445113i | \(0.853163\pi\) | |||||||
\(390\) | −0.969555 | + | 1.38882i | −0.00248604 | + | 0.00356107i | ||||
\(391\) | −24.0684 | −0.0615559 | ||||||||
\(392\) | 6.81017 | + | 6.81017i | 0.0173729 | + | 0.0173729i | ||||
\(393\) | −163.000 | + | 163.000i | −0.414759 | + | 0.414759i | ||||
\(394\) | − | 124.910i | − | 0.317030i | ||||||
\(395\) | 62.7673 | + | 353.070i | 0.158905 | + | 0.893847i | ||||
\(396\) | 37.3153 | 0.0942305 | ||||||||
\(397\) | 16.2056 | + | 16.2056i | 0.0408202 | + | 0.0408202i | 0.727222 | − | 0.686402i | \(-0.240811\pi\) |
−0.686402 | + | 0.727222i | \(0.740811\pi\) | |||||||
\(398\) | 204.645 | − | 204.645i | 0.514183 | − | 0.514183i | ||||
\(399\) | 63.0218i | 0.157949i | ||||||||
\(400\) | −93.8728 | + | 34.4659i | −0.234682 | + | 0.0861649i | ||||
\(401\) | −252.470 | −0.629602 | −0.314801 | − | 0.949158i | \(-0.601938\pi\) | ||||
−0.314801 | + | 0.949158i | \(0.601938\pi\) | |||||||
\(402\) | 122.696 | + | 122.696i | 0.305213 | + | 0.305213i | ||||
\(403\) | −1.39806 | + | 1.39806i | −0.00346914 | + | 0.00346914i | ||||
\(404\) | 165.635i | 0.409988i | ||||||||
\(405\) | 44.3053 | − | 7.87643i | 0.109396 | − | 0.0194480i | ||||
\(406\) | −525.782 | −1.29503 | ||||||||
\(407\) | 258.697 | + | 258.697i | 0.635619 | + | 0.635619i | ||||
\(408\) | −17.3849 | + | 17.3849i | −0.0426102 | + | 0.0426102i | ||||
\(409\) | 448.966i | 1.09772i | 0.835915 | + | 0.548858i | \(0.184937\pi\) | ||||
−0.835915 | + | 0.548858i | \(0.815063\pi\) | |||||||
\(410\) | −89.1519 | − | 62.2384i | −0.217444 | − | 0.151801i | ||||
\(411\) | 453.610 | 1.10367 | ||||||||
\(412\) | 209.990 | + | 209.990i | 0.509684 | + | 0.509684i | ||||
\(413\) | −84.6832 | + | 84.6832i | −0.205044 | + | 0.205044i | ||||
\(414\) | − | 20.3470i | − | 0.0491473i | ||||||
\(415\) | 155.393 | − | 222.589i | 0.374441 | − | 0.536359i | ||||
\(416\) | 0.782318 | 0.00188057 | ||||||||
\(417\) | 38.6366 | + | 38.6366i | 0.0926538 | + | 0.0926538i | ||||
\(418\) | −33.5125 | + | 33.5125i | −0.0801735 | + | 0.0801735i | ||||
\(419\) | − | 56.1614i | − | 0.134037i | −0.997752 | − | 0.0670184i | \(-0.978651\pi\) | ||
0.997752 | − | 0.0670184i | \(-0.0213486\pi\) | |||||||
\(420\) | −20.4708 | − | 115.150i | −0.0487401 | − | 0.274166i | ||||
\(421\) | 302.461 | 0.718436 | 0.359218 | − | 0.933254i | \(-0.383044\pi\) | ||||
0.359218 | + | 0.933254i | \(0.383044\pi\) | |||||||
\(422\) | 7.31007 | + | 7.31007i | 0.0173224 | + | 0.0173224i | ||||
\(423\) | 55.7386 | − | 55.7386i | 0.131770 | − | 0.131770i | ||||
\(424\) | − | 120.316i | − | 0.283765i | ||||||
\(425\) | −113.858 | − | 52.7041i | −0.267902 | − | 0.124010i | ||||
\(426\) | 95.6617 | 0.224558 | ||||||||
\(427\) | −498.596 | − | 498.596i | −1.16767 | − | 1.16767i | ||||
\(428\) | 242.067 | − | 242.067i | 0.565577 | − | 0.565577i | ||||
\(429\) | − | 1.48972i | − | 0.00347254i | ||||||
\(430\) | −398.721 | + | 70.8830i | −0.927258 | + | 0.164844i | ||||
\(431\) | −294.456 | −0.683192 | −0.341596 | − | 0.939847i | \(-0.610967\pi\) | ||||
−0.341596 | + | 0.939847i | \(0.610967\pi\) | |||||||
\(432\) | −14.6969 | − | 14.6969i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | −510.866 | + | 510.866i | −1.17983 | + | 1.17983i | −0.200042 | + | 0.979787i | \(0.564108\pi\) |
−0.979787 | + | 0.200042i | \(0.935892\pi\) | |||||||
\(434\) | − | 136.523i | − | 0.314570i | ||||||
\(435\) | −390.980 | − | 272.949i | −0.898805 | − | 0.627470i | ||||
\(436\) | 357.140 | 0.819128 | ||||||||
\(437\) | 18.2735 | + | 18.2735i | 0.0418157 | + | 0.0418157i | ||||
\(438\) | 95.8022 | − | 95.8022i | 0.218726 | − | 0.218726i | ||||
\(439\) | − | 71.7873i | − | 0.163525i | −0.996652 | − | 0.0817623i | \(-0.973945\pi\) | ||
0.996652 | − | 0.0817623i | \(-0.0260548\pi\) | |||||||
\(440\) | 50.3465 | − | 72.1177i | 0.114424 | − | 0.163904i | ||||
\(441\) | −10.2153 | −0.0231638 | ||||||||
\(442\) | 0.694050 | + | 0.694050i | 0.00157025 | + | 0.00157025i | ||||
\(443\) | 271.317 | − | 271.317i | 0.612455 | − | 0.612455i | −0.331130 | − | 0.943585i | \(-0.607430\pi\) |
0.943585 | + | 0.331130i | \(0.107430\pi\) | |||||||
\(444\) | − | 203.780i | − | 0.458964i | ||||||
\(445\) | 17.5118 | + | 98.5050i | 0.0393524 | + | 0.221359i | ||||
\(446\) | 53.2546 | 0.119405 | ||||||||
\(447\) | 138.060 | + | 138.060i | 0.308860 | + | 0.308860i | ||||
\(448\) | −38.1973 | + | 38.1973i | −0.0852619 | + | 0.0852619i | ||||
\(449\) | 27.0296i | 0.0601996i | 0.999547 | + | 0.0300998i | \(0.00958251\pi\) | ||||
−0.999547 | + | 0.0300998i | \(0.990417\pi\) | |||||||
\(450\) | 44.5551 | − | 96.2540i | 0.0990114 | − | 0.213898i | ||||
\(451\) | 95.6291 | 0.212038 | ||||||||
\(452\) | 50.8924 | + | 50.8924i | 0.112594 | + | 0.112594i | ||||
\(453\) | −226.718 | + | 226.718i | −0.500481 | + | 0.500481i | ||||
\(454\) | − | 229.755i | − | 0.506068i | ||||||
\(455\) | −4.59706 | + | 0.817247i | −0.0101034 | + | 0.00179615i | ||||
\(456\) | 26.3984 | 0.0578912 | ||||||||
\(457\) | 325.157 | + | 325.157i | 0.711504 | + | 0.711504i | 0.966850 | − | 0.255346i | \(-0.0821893\pi\) |
−0.255346 | + | 0.966850i | \(0.582189\pi\) | |||||||
\(458\) | 56.2198 | − | 56.2198i | 0.122751 | − | 0.122751i | ||||
\(459\) | − | 26.0774i | − | 0.0568135i | ||||||
\(460\) | −39.3238 | − | 27.4525i | −0.0854864 | − | 0.0596794i | ||||
\(461\) | 362.643 | 0.786645 | 0.393323 | − | 0.919401i | \(-0.371326\pi\) | ||||
0.393323 | + | 0.919401i | \(0.371326\pi\) | |||||||
\(462\) | 72.7368 | + | 72.7368i | 0.157439 | + | 0.157439i | ||||
\(463\) | 489.243 | − | 489.243i | 1.05668 | − | 1.05668i | 0.0583859 | − | 0.998294i | \(-0.481405\pi\) |
0.998294 | − | 0.0583859i | \(-0.0185954\pi\) | |||||||
\(464\) | 220.238i | 0.474652i | ||||||||
\(465\) | 70.8733 | − | 101.521i | 0.152416 | − | 0.218324i | ||||
\(466\) | −341.458 | −0.732742 | ||||||||
\(467\) | −102.330 | − | 102.330i | −0.219122 | − | 0.219122i | 0.589006 | − | 0.808128i | \(-0.299519\pi\) |
−0.808128 | + | 0.589006i | \(0.799519\pi\) | |||||||
\(468\) | −0.586738 | + | 0.586738i | −0.00125371 | + | 0.00125371i | ||||
\(469\) | 478.329i | 1.01989i | ||||||||
\(470\) | −32.5201 | − | 182.927i | −0.0691917 | − | 0.389207i | ||||
\(471\) | 341.682 | 0.725440 | ||||||||
\(472\) | 35.4719 | + | 35.4719i | 0.0751522 | + | 0.0751522i | ||||
\(473\) | 251.861 | − | 251.861i | 0.532476 | − | 0.532476i | ||||
\(474\) | 175.680i | 0.370633i | ||||||||
\(475\) | 46.4304 | + | 126.460i | 0.0977481 | + | 0.266231i | ||||
\(476\) | −67.7752 | −0.142385 | ||||||||
\(477\) | 90.2372 | + | 90.2372i | 0.189177 | + | 0.189177i | ||||
\(478\) | −143.495 | + | 143.495i | −0.300199 | + | 0.300199i | ||||
\(479\) | − | 543.454i | − | 1.13456i | −0.823525 | − | 0.567280i | \(-0.807996\pi\) | ||
0.823525 | − | 0.567280i | \(-0.192004\pi\) | |||||||
\(480\) | −48.2335 | + | 8.57477i | −0.100487 | + | 0.0178641i | ||||
\(481\) | −8.13540 | −0.0169135 | ||||||||
\(482\) | −97.6832 | − | 97.6832i | −0.202662 | − | 0.202662i | ||||
\(483\) | 39.6614 | − | 39.6614i | 0.0821146 | − | 0.0821146i | ||||
\(484\) | − | 164.643i | − | 0.340171i | ||||||
\(485\) | 131.711 | + | 91.9494i | 0.271569 | + | 0.189586i | ||||
\(486\) | 22.0454 | 0.0453609 | ||||||||
\(487\) | 423.656 | + | 423.656i | 0.869931 | + | 0.869931i | 0.992464 | − | 0.122533i | \(-0.0391018\pi\) |
−0.122533 | + | 0.992464i | \(0.539102\pi\) | |||||||
\(488\) | −208.850 | + | 208.850i | −0.427972 | + | 0.427972i | ||||
\(489\) | 516.848i | 1.05695i | ||||||||
\(490\) | −13.7826 | + | 19.7426i | −0.0281278 | + | 0.0402910i | ||||
\(491\) | −366.712 | −0.746868 | −0.373434 | − | 0.927657i | \(-0.621820\pi\) | ||||
−0.373434 | + | 0.927657i | \(0.621820\pi\) | |||||||
\(492\) | −37.6643 | − | 37.6643i | −0.0765535 | − | 0.0765535i | ||||
\(493\) | −195.389 | + | 195.389i | −0.396327 | + | 0.396327i | ||||
\(494\) | − | 1.05389i | − | 0.00213338i | ||||||
\(495\) | 16.3284 | + | 91.8481i | 0.0329867 | + | 0.185552i | ||||
\(496\) | −57.1865 | −0.115295 | ||||||||
\(497\) | 186.469 | + | 186.469i | 0.375188 | + | 0.375188i | ||||
\(498\) | 94.0380 | − | 94.0380i | 0.188831 | − | 0.188831i | ||||
\(499\) | − | 500.886i | − | 1.00378i | −0.864932 | − | 0.501890i | \(-0.832638\pi\) | ||
0.864932 | − | 0.501890i | \(-0.167362\pi\) | |||||||
\(500\) | −125.911 | − | 215.978i | −0.251823 | − | 0.431955i | ||||
\(501\) | −123.882 | −0.247270 | ||||||||
\(502\) | 16.2884 | + | 16.2884i | 0.0324470 | + | 0.0324470i | ||||
\(503\) | 449.857 | − | 449.857i | 0.894348 | − | 0.894348i | −0.100581 | − | 0.994929i | \(-0.532070\pi\) |
0.994929 | + | 0.100581i | \(0.0320701\pi\) | |||||||
\(504\) | − | 57.2960i | − | 0.113683i | ||||||
\(505\) | −407.695 | + | 72.4784i | −0.807317 | + | 0.143522i | ||||
\(506\) | 42.1808 | 0.0833612 | ||||||||
\(507\) | −206.958 | − | 206.958i | −0.408202 | − | 0.408202i | ||||
\(508\) | −166.067 | + | 166.067i | −0.326904 | + | 0.326904i | ||||
\(509\) | − | 851.790i | − | 1.67346i | −0.547618 | − | 0.836728i | \(-0.684465\pi\) | ||
0.547618 | − | 0.836728i | \(-0.315535\pi\) | |||||||
\(510\) | −50.3987 | − | 35.1841i | −0.0988210 | − | 0.0689885i | ||||
\(511\) | 373.485 | 0.730890 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −19.7988 | + | 19.7988i | −0.0385941 | + | 0.0385941i | ||||
\(514\) | 130.945i | 0.254756i | ||||||||
\(515\) | −424.983 | + | 608.757i | −0.825210 | + | 1.18205i | ||||
\(516\) | −198.395 | −0.384487 | ||||||||
\(517\) | 115.550 | + | 115.550i | 0.223501 | + | 0.223501i | ||||
\(518\) | 397.218 | − | 397.218i | 0.766830 | − | 0.766830i | ||||
\(519\) | − | 475.722i | − | 0.916613i | ||||||
\(520\) | 0.342326 | + | 1.92560i | 0.000658319 | + | 0.00370308i | ||||
\(521\) | 701.483 | 1.34642 | 0.673208 | − | 0.739453i | \(-0.264916\pi\) | ||||
0.673208 | + | 0.739453i | \(0.264916\pi\) | |||||||
\(522\) | −165.179 | − | 165.179i | −0.316434 | − | 0.316434i | ||||
\(523\) | 402.773 | − | 402.773i | 0.770121 | − | 0.770121i | −0.208007 | − | 0.978127i | \(-0.566698\pi\) |
0.978127 | + | 0.208007i | \(0.0666975\pi\) | |||||||
\(524\) | 266.178i | 0.507973i | ||||||||
\(525\) | 274.472 | − | 100.774i | 0.522804 | − | 0.191951i | ||||
\(526\) | −232.963 | −0.442895 | ||||||||
\(527\) | −50.7343 | − | 50.7343i | −0.0962699 | − | 0.0962699i | ||||
\(528\) | 30.4678 | − | 30.4678i | 0.0577042 | − | 0.0577042i | ||||
\(529\) | − | 23.0000i | − | 0.0434783i | ||||||
\(530\) | 296.147 | − | 52.6479i | 0.558769 | − | 0.0993357i | ||||
\(531\) | −53.2078 | −0.100203 | ||||||||
\(532\) | 51.4571 | + | 51.4571i | 0.0967238 | + | 0.0967238i | ||||
\(533\) | −1.50365 | + | 1.50365i | −0.00282111 | + | 0.00282111i | ||||
\(534\) | 49.0140i | 0.0917866i | ||||||||
\(535\) | 701.749 | + | 489.902i | 1.31168 | + | 0.915704i | ||||
\(536\) | 200.361 | 0.373808 | ||||||||
\(537\) | 136.755 | + | 136.755i | 0.254665 | + | 0.254665i | ||||
\(538\) | −296.382 | + | 296.382i | −0.550897 | + | 0.550897i | ||||
\(539\) | − | 21.1769i | − | 0.0392893i | ||||||
\(540\) | 29.7441 | − | 42.6062i | 0.0550816 | − | 0.0789004i | ||||
\(541\) | 37.5641 | 0.0694345 | 0.0347172 | − | 0.999397i | \(-0.488947\pi\) | ||||
0.0347172 | + | 0.999397i | \(0.488947\pi\) | |||||||
\(542\) | 227.220 | + | 227.220i | 0.419224 | + | 0.419224i | ||||
\(543\) | −236.138 | + | 236.138i | −0.434877 | + | 0.434877i | ||||
\(544\) | 28.3895i | 0.0521866i | ||||||||
\(545\) | 156.277 | + | 879.067i | 0.286747 | + | 1.61297i | ||||
\(546\) | −2.28740 | −0.00418938 | ||||||||
\(547\) | 592.447 | + | 592.447i | 1.08308 | + | 1.08308i | 0.996220 | + | 0.0868632i | \(0.0276843\pi\) |
0.0868632 | + | 0.996220i | \(0.472316\pi\) | |||||||
\(548\) | 370.371 | − | 370.371i | 0.675859 | − | 0.675859i | ||||
\(549\) | − | 313.276i | − | 0.570629i | ||||||
\(550\) | 199.542 | + | 92.3660i | 0.362803 | + | 0.167938i | ||||
\(551\) | 296.691 | 0.538460 | ||||||||
\(552\) | −16.6132 | − | 16.6132i | −0.0300965 | − | 0.0300965i | ||||
\(553\) | −342.445 | + | 342.445i | −0.619249 | + | 0.619249i | ||||
\(554\) | 560.650i | 1.01200i | ||||||||
\(555\) | 501.585 | − | 89.1699i | 0.903757 | − | 0.160666i | ||||
\(556\) | 63.0933 | 0.113477 | ||||||||
\(557\) | −260.273 | − | 260.273i | −0.467277 | − | 0.467277i | 0.433754 | − | 0.901031i | \(-0.357189\pi\) |
−0.901031 | + | 0.433754i | \(0.857189\pi\) | |||||||
\(558\) | 42.8899 | − | 42.8899i | 0.0768636 | − | 0.0768636i | ||||
\(559\) | 7.92043i | 0.0141689i | ||||||||
\(560\) | −110.734 | − | 77.3048i | −0.197739 | − | 0.138044i | ||||
\(561\) | 54.0603 | 0.0963642 | ||||||||
\(562\) | −135.612 | − | 135.612i | −0.241303 | − | 0.241303i | ||||
\(563\) | −188.827 | + | 188.827i | −0.335394 | + | 0.335394i | −0.854631 | − | 0.519236i | \(-0.826216\pi\) |
0.519236 | + | 0.854631i | \(0.326216\pi\) | |||||||
\(564\) | − | 91.0208i | − | 0.161384i | ||||||
\(565\) | −102.997 | + | 147.536i | −0.182296 | + | 0.261126i | ||||
\(566\) | 383.564 | 0.677675 | ||||||||
\(567\) | 42.9720 | + | 42.9720i | 0.0757884 | + | 0.0757884i | ||||
\(568\) | 78.1074 | − | 78.1074i | 0.137513 | − | 0.137513i | ||||
\(569\) | − | 181.407i | − | 0.318817i | −0.987213 | − | 0.159409i | \(-0.949041\pi\) | ||
0.987213 | − | 0.159409i | \(-0.0509587\pi\) | |||||||
\(570\) | 11.5514 | + | 64.9772i | 0.0202656 | + | 0.113995i | ||||
\(571\) | −700.274 | −1.22640 | −0.613200 | − | 0.789928i | \(-0.710118\pi\) | ||||
−0.613200 | + | 0.789928i | \(0.710118\pi\) | |||||||
\(572\) | −1.21635 | − | 1.21635i | −0.00212649 | − | 0.00212649i | ||||
\(573\) | −121.283 | + | 121.283i | −0.211663 | + | 0.211663i | ||||
\(574\) | − | 146.834i | − | 0.255809i | ||||||
\(575\) | 50.3646 | − | 108.804i | 0.0875906 | − | 0.189225i | ||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 435.694 | + | 435.694i | 0.755102 | + | 0.755102i | 0.975427 | − | 0.220325i | \(-0.0707117\pi\) |
−0.220325 | + | 0.975427i | \(0.570712\pi\) | |||||||
\(578\) | 263.814 | − | 263.814i | 0.456425 | − | 0.456425i | ||||
\(579\) | − | 439.301i | − | 0.758723i | ||||||
\(580\) | −542.096 | + | 96.3717i | −0.934649 | + | 0.166158i | ||||
\(581\) | 366.607 | 0.630993 | ||||||||
\(582\) | 55.6444 | + | 55.6444i | 0.0956089 | + | 0.0956089i | ||||
\(583\) | −187.068 | + | 187.068i | −0.320872 | + | 0.320872i | ||||
\(584\) | − | 156.444i | − | 0.267884i | ||||||
\(585\) | −1.70095 | − | 1.18746i | −0.00290760 | − | 0.00202984i | ||||
\(586\) | 57.5767 | 0.0982538 | ||||||||
\(587\) | −123.516 | − | 123.516i | −0.210419 | − | 0.210419i | 0.594027 | − | 0.804445i | \(-0.297537\pi\) |
−0.804445 | + | 0.594027i | \(0.797537\pi\) | |||||||
\(588\) | −8.34072 | + | 8.34072i | −0.0141849 | + | 0.0141849i | ||||
\(589\) | 77.0381i | 0.130795i | ||||||||
\(590\) | −71.7889 | + | 102.832i | −0.121676 | + | 0.174292i | ||||
\(591\) | 152.983 | 0.258854 | ||||||||
\(592\) | −166.386 | − | 166.386i | −0.281057 | − | 0.281057i | ||||
\(593\) | 131.838 | − | 131.838i | 0.222323 | − | 0.222323i | −0.587153 | − | 0.809476i | \(-0.699751\pi\) |
0.809476 | + | 0.587153i | \(0.199751\pi\) | |||||||
\(594\) | 45.7017i | 0.0769389i | ||||||||
\(595\) | −29.6570 | − | 166.822i | −0.0498437 | − | 0.280374i | ||||
\(596\) | 225.452 | 0.378275 | ||||||||
\(597\) | 250.638 | + | 250.638i | 0.419829 | + | 0.419829i | ||||
\(598\) | −0.663242 | + | 0.663242i | −0.00110910 | + | 0.00110910i | ||||
\(599\) | − | 933.159i | − | 1.55786i | −0.627110 | − | 0.778931i | \(-0.715762\pi\) | ||
0.627110 | − | 0.778931i | \(-0.284238\pi\) | |||||||
\(600\) | −42.2120 | − | 114.970i | −0.0703533 | − | 0.191617i | ||||
\(601\) | −355.783 | −0.591986 | −0.295993 | − | 0.955190i | \(-0.595650\pi\) | ||||
−0.295993 | + | 0.955190i | \(0.595650\pi\) | |||||||
\(602\) | −386.722 | − | 386.722i | −0.642395 | − | 0.642395i | ||||
\(603\) | −150.271 | + | 150.271i | −0.249205 | + | 0.249205i | ||||
\(604\) | 370.228i | 0.612961i | ||||||||
\(605\) | 405.253 | − | 72.0443i | 0.669839 | − | 0.119081i | ||||
\(606\) | −202.861 | −0.334753 | ||||||||
\(607\) | 238.085 | + | 238.085i | 0.392232 | + | 0.392232i | 0.875482 | − | 0.483250i | \(-0.160544\pi\) |
−0.483250 | + | 0.875482i | \(0.660544\pi\) | |||||||
\(608\) | 21.5542 | − | 21.5542i | 0.0354510 | − | 0.0354510i | ||||
\(609\) | − | 643.949i | − | 1.05739i | ||||||
\(610\) | −605.454 | − | 422.677i | −0.992548 | − | 0.692913i | ||||
\(611\) | −3.63378 | −0.00594726 | ||||||||
\(612\) | −21.2921 | − | 21.2921i | −0.0347910 | − | 0.0347910i | ||||
\(613\) | 411.262 | − | 411.262i | 0.670900 | − | 0.670900i | −0.287023 | − | 0.957924i | \(-0.592666\pi\) |
0.957924 | + | 0.287023i | \(0.0926658\pi\) | |||||||
\(614\) | 12.7903i | 0.0208311i | ||||||||
\(615\) | 76.2261 | − | 109.188i | 0.123945 | − | 0.177542i | ||||
\(616\) | 118.779 | 0.192823 | ||||||||
\(617\) | 9.19782 | + | 9.19782i | 0.0149073 | + | 0.0149073i | 0.714521 | − | 0.699614i | \(-0.246645\pi\) |
−0.699614 | + | 0.714521i | \(0.746645\pi\) | |||||||
\(618\) | −257.184 | + | 257.184i | −0.416155 | + | 0.416155i | ||||
\(619\) | 821.926i | 1.32783i | 0.747809 | + | 0.663914i | \(0.231106\pi\) | ||||
−0.747809 | + | 0.663914i | \(0.768894\pi\) | |||||||
\(620\) | −25.0236 | − | 140.759i | −0.0403607 | − | 0.227031i | ||||
\(621\) | 24.9199 | 0.0401286 | ||||||||
\(622\) | 375.884 | + | 375.884i | 0.604315 | + | 0.604315i | ||||
\(623\) | −95.5406 | + | 95.5406i | −0.153356 | + | 0.153356i | ||||
\(624\) | 0.958140i | 0.00153548i | ||||||||
\(625\) | 476.512 | − | 404.427i | 0.762420 | − | 0.647083i | ||||
\(626\) | 49.4427 | 0.0789820 | ||||||||
\(627\) | −41.0443 | − | 41.0443i | −0.0654614 | − | 0.0654614i | ||||
\(628\) | 278.983 | − | 278.983i | 0.444240 | − | 0.444240i | ||||
\(629\) | − | 295.225i | − | 0.469356i | ||||||
\(630\) | 141.029 | − | 25.0716i | 0.223855 | − | 0.0397961i | ||||
\(631\) | 17.9920 | 0.0285135 | 0.0142568 | − | 0.999898i | \(-0.495462\pi\) | ||||
0.0142568 | + | 0.999898i | \(0.495462\pi\) | |||||||
\(632\) | 143.442 | + | 143.442i | 0.226966 | + | 0.226966i | ||||
\(633\) | −8.95297 | + | 8.95297i | −0.0141437 | + | 0.0141437i | ||||
\(634\) | − | 227.391i | − | 0.358661i | ||||||
\(635\) | −481.427 | − | 336.092i | −0.758153 | − | 0.529278i | ||||
\(636\) | 147.357 | 0.231693 | ||||||||
\(637\) | 0.332982 | + | 0.332982i | 0.000522735 | + | 0.000522735i | ||||
\(638\) | 342.427 | − | 342.427i | 0.536720 | − | 0.536720i | ||||
\(639\) | 117.161i | 0.183351i | ||||||||
\(640\) | −32.3812 | + | 46.3838i | −0.0505957 | + | 0.0724747i | ||||
\(641\) | 411.466 | 0.641912 | 0.320956 | − | 0.947094i | \(-0.395996\pi\) | ||||
0.320956 | + | 0.947094i | \(0.395996\pi\) | |||||||
\(642\) | 296.470 | + | 296.470i | 0.461792 | + | 0.461792i | ||||
\(643\) | 118.655 | − | 118.655i | 0.184534 | − | 0.184534i | −0.608794 | − | 0.793328i | \(-0.708347\pi\) |
0.793328 | + | 0.608794i | \(0.208347\pi\) | |||||||
\(644\) | − | 64.7668i | − | 0.100569i | ||||||
\(645\) | −86.8136 | − | 488.331i | −0.134595 | − | 0.757103i | ||||
\(646\) | 38.2445 | 0.0592021 | ||||||||
\(647\) | 183.932 | + | 183.932i | 0.284285 | + | 0.284285i | 0.834815 | − | 0.550531i | \(-0.185575\pi\) |
−0.550531 | + | 0.834815i | \(0.685575\pi\) | |||||||
\(648\) | 18.0000 | − | 18.0000i | 0.0277778 | − | 0.0277778i | ||||
\(649\) | − | 110.304i | − | 0.169959i | ||||||
\(650\) | −4.58990 | + | 1.68521i | −0.00706138 | + | 0.00259263i | ||||
\(651\) | 167.206 | 0.256845 | ||||||||
\(652\) | 422.005 | + | 422.005i | 0.647247 | + | 0.647247i | ||||
\(653\) | 116.529 | − | 116.529i | 0.178452 | − | 0.178452i | −0.612229 | − | 0.790681i | \(-0.709727\pi\) |
0.790681 | + | 0.612229i | \(0.209727\pi\) | |||||||
\(654\) | 437.405i | 0.668816i | ||||||||
\(655\) | −655.173 | + | 116.474i | −1.00026 | + | 0.177823i | ||||
\(656\) | −61.5056 | −0.0937585 | ||||||||
\(657\) | 117.333 | + | 117.333i | 0.178589 | + | 0.178589i | ||||
\(658\) | 177.422 | − | 177.422i | 0.269639 | − | 0.269639i | ||||
\(659\) | − | 612.241i | − | 0.929045i | −0.885561 | − | 0.464523i | \(-0.846226\pi\) | ||
0.885561 | − | 0.464523i | \(-0.153774\pi\) | |||||||
\(660\) | 88.3257 | + | 61.6616i | 0.133827 | + | 0.0934266i | ||||
\(661\) | −455.394 | −0.688947 | −0.344473 | − | 0.938796i | \(-0.611943\pi\) | ||||
−0.344473 | + | 0.938796i | \(0.611943\pi\) | |||||||
\(662\) | −299.118 | − | 299.118i | −0.451840 | − | 0.451840i | ||||
\(663\) | −0.850034 | + | 0.850034i | −0.00128210 | + | 0.00128210i | ||||
\(664\) | − | 153.563i | − | 0.231270i | ||||||
\(665\) | −104.140 | + | 149.173i | −0.156602 | + | 0.224321i | ||||
\(666\) | 249.578 | 0.374742 | ||||||||
\(667\) | −186.716 | − | 186.716i | −0.279934 | − | 0.279934i | ||||
\(668\) | −101.150 | + | 101.150i | −0.151422 | + | 0.151422i | ||||
\(669\) | 65.2233i | 0.0974937i | ||||||||
\(670\) | 87.6738 | + | 493.170i | 0.130856 | + | 0.736075i | ||||
\(671\) | 649.443 | 0.967873 | ||||||||
\(672\) | −46.7820 | − | 46.7820i | −0.0696161 | − | 0.0696161i | ||||
\(673\) | 101.805 | − | 101.805i | 0.151271 | − | 0.151271i | −0.627415 | − | 0.778685i | \(-0.715887\pi\) |
0.778685 | + | 0.627415i | \(0.215887\pi\) | |||||||
\(674\) | − | 86.1096i | − | 0.127759i | ||||||
\(675\) | 117.887 | + | 54.5687i | 0.174647 | + | 0.0808425i | ||||
\(676\) | −337.962 | −0.499943 | ||||||||
\(677\) | −590.792 | − | 590.792i | −0.872662 | − | 0.872662i | 0.120099 | − | 0.992762i | \(-0.461679\pi\) |
−0.992762 | + | 0.120099i | \(0.961679\pi\) | |||||||
\(678\) | −62.3302 | + | 62.3302i | −0.0919324 | + | 0.0919324i | ||||
\(679\) | 216.930i | 0.319484i | ||||||||
\(680\) | −69.8781 | + | 12.4227i | −0.102762 | + | 0.0182686i | ||||
\(681\) | 281.391 | 0.413203 | ||||||||
\(682\) | 88.9138 | + | 88.9138i | 0.130372 | + | 0.130372i | ||||
\(683\) | −50.6235 | + | 50.6235i | −0.0741194 | + | 0.0741194i | −0.743195 | − | 0.669075i | \(-0.766690\pi\) |
0.669075 | + | 0.743195i | \(0.266690\pi\) | |||||||
\(684\) | 32.3313i | 0.0472680i | ||||||||
\(685\) | 1073.70 | + | 749.566i | 1.56744 | + | 1.09426i | ||||
\(686\) | −500.434 | −0.729495 | ||||||||
\(687\) | 68.8549 | + | 68.8549i | 0.100225 | + | 0.100225i | ||||
\(688\) | −161.989 | + | 161.989i | −0.235449 | + | 0.235449i | ||||
\(689\) | − | 5.88285i | − | 0.00853824i | ||||||
\(690\) | 33.6224 | − | 48.1616i | 0.0487280 | − | 0.0697994i | ||||
\(691\) | 293.780 | 0.425152 | 0.212576 | − | 0.977145i | \(-0.431815\pi\) | ||||
0.212576 | + | 0.977145i | \(0.431815\pi\) | |||||||
\(692\) | −388.426 | − | 388.426i | −0.561309 | − | 0.561309i | ||||
\(693\) | −89.0841 | + | 89.0841i | −0.128548 | + | 0.128548i | ||||
\(694\) | 360.813i | 0.519904i | ||||||||
\(695\) | 27.6083 | + | 155.298i | 0.0397242 | + | 0.223451i | ||||
\(696\) | −269.736 | −0.387551 | ||||||||
\(697\) | −54.5660 | − | 54.5660i | −0.0782870 | − | 0.0782870i | ||||
\(698\) | −76.9282 | + | 76.9282i | −0.110212 | + | 0.110212i | ||||
\(699\) | − | 418.199i | − | 0.598282i | ||||||
\(700\) | 141.824 | − | 306.387i | 0.202606 | − | 0.437696i | ||||
\(701\) | −880.820 | −1.25652 | −0.628259 | − | 0.778004i | \(-0.716232\pi\) | ||||
−0.628259 | + | 0.778004i | \(0.716232\pi\) | |||||||
\(702\) | −0.718605 | − | 0.718605i | −0.00102365 | − | 0.00102365i | ||||
\(703\) | −224.144 | + | 224.144i | −0.318840 | + | 0.318840i | ||||
\(704\) | − | 49.7537i | − | 0.0706729i | ||||||
\(705\) | 224.039 | − | 39.8288i | 0.317786 | − | 0.0564948i | ||||
\(706\) | −822.668 | −1.16525 | ||||||||
\(707\) | −395.426 | − | 395.426i | −0.559301 | − | 0.559301i | ||||
\(708\) | −43.4440 | + | 43.4440i | −0.0613616 | + | 0.0613616i | ||||
\(709\) | 347.660i | 0.490353i | 0.969478 | + | 0.245176i | \(0.0788459\pi\) | ||||
−0.969478 | + | 0.245176i | \(0.921154\pi\) | |||||||
\(710\) | 226.432 | + | 158.076i | 0.318919 | + | 0.222642i | ||||
\(711\) | −215.163 | −0.302621 | ||||||||
\(712\) | 40.0198 | + | 40.0198i | 0.0562076 | + | 0.0562076i | ||||
\(713\) | 48.4822 | − | 48.4822i | 0.0679975 | − | 0.0679975i | ||||
\(714\) | − | 83.0073i | − | 0.116257i | ||||||
\(715\) | 2.46168 | − | 3.52618i | 0.00344291 | − | 0.00493173i | ||||
\(716\) | 223.320 | 0.311900 | ||||||||
\(717\) | −175.745 | − | 175.745i | −0.245111 | − | 0.245111i | ||||
\(718\) | −112.879 | + | 112.879i | −0.157213 | + | 0.157213i | ||||
\(719\) | − | 99.3256i | − | 0.138144i | −0.997612 | − | 0.0690721i | \(-0.977996\pi\) | ||
0.997612 | − | 0.0690721i | \(-0.0220038\pi\) | |||||||
\(720\) | −10.5019 | − | 59.0738i | −0.0145860 | − | 0.0820469i | ||||
\(721\) | −1002.63 | −1.39061 | ||||||||
\(722\) | 331.964 | + | 331.964i | 0.459783 | + | 0.459783i | ||||
\(723\) | 119.637 | − | 119.637i | 0.165473 | − | 0.165473i | ||||
\(724\) | 385.613i | 0.532614i | ||||||||
\(725\) | −474.420 | − | 1292.15i | −0.654372 | − | 1.78227i | ||||
\(726\) | 201.645 | 0.277748 | ||||||||
\(727\) | −786.876 | − | 786.876i | −1.08236 | − | 1.08236i | −0.996289 | − | 0.0860721i | \(-0.972568\pi\) |
−0.0860721 | − | 0.996289i | \(-0.527432\pi\) | |||||||
\(728\) | −1.86765 | + | 1.86765i | −0.00256546 | + | 0.00256546i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | 385.073 | − | 68.4568i | 0.527497 | − | 0.0937764i | ||||
\(731\) | −287.424 | −0.393193 | ||||||||
\(732\) | −255.788 | − | 255.788i | −0.349438 | − | 0.349438i | ||||
\(733\) | −969.091 | + | 969.091i | −1.32209 | + | 1.32209i | −0.410006 | + | 0.912083i | \(0.634473\pi\) |
−0.912083 | + | 0.410006i | \(0.865527\pi\) | |||||||
\(734\) | 811.715i | 1.10588i | ||||||||
\(735\) | −24.1796 | − | 16.8802i | −0.0328975 | − | 0.0229662i | ||||
\(736\) | −27.1293 | −0.0368605 | ||||||||
\(737\) | −311.522 | − | 311.522i | −0.422689 | − | 0.422689i | ||||
\(738\) | 46.1292 | − | 46.1292i | 0.0625057 | − | 0.0625057i | ||||
\(739\) | − | 1051.09i | − | 1.42232i | −0.703030 | − | 0.711160i | \(-0.748170\pi\) | ||
0.703030 | − | 0.711160i | \(-0.251830\pi\) | |||||||
\(740\) | 336.736 | − | 482.350i | 0.455048 | − | 0.651824i | ||||
\(741\) | 1.29075 | 0.00174190 | ||||||||
\(742\) | 287.235 | + | 287.235i | 0.387109 | + | 0.387109i | ||||
\(743\) | 205.793 | − | 205.793i | 0.276976 | − | 0.276976i | −0.554925 | − | 0.831901i | \(-0.687253\pi\) |
0.831901 | + | 0.554925i | \(0.187253\pi\) | |||||||
\(744\) | − | 70.0389i | − | 0.0941383i | ||||||
\(745\) | 98.6530 | + | 554.929i | 0.132420 | + | 0.744871i | ||||
\(746\) | −192.564 | −0.258128 | ||||||||
\(747\) | 115.173 | + | 115.173i | 0.154180 | + | 0.154180i | ||||
\(748\) | 44.1401 | − | 44.1401i | 0.0590108 | − | 0.0590108i | ||||
\(749\) | 1155.79i | 1.54311i | ||||||||
\(750\) | 264.517 | − | 154.209i | 0.352690 | − | 0.205613i | ||||
\(751\) | 33.6100 | 0.0447537 | 0.0223768 | − | 0.999750i | \(-0.492877\pi\) | ||||
0.0223768 | + | 0.999750i | \(0.492877\pi\) | |||||||
\(752\) | −74.3182 | − | 74.3182i | −0.0988273 | − | 0.0988273i | ||||
\(753\) | −19.9491 | + | 19.9491i | −0.0264929 | + | 0.0264929i | ||||
\(754\) | 10.7685i | 0.0142819i | ||||||||
\(755\) | −911.283 | + | 162.004i | −1.20700 | + | 0.214575i | ||||
\(756\) | 70.1730 | 0.0928214 | ||||||||
\(757\) | −614.446 | − | 614.446i | −0.811685 | − | 0.811685i | 0.173201 | − | 0.984886i | \(-0.444589\pi\) |
−0.984886 | + | 0.173201i | \(0.944589\pi\) | |||||||
\(758\) | 200.497 | − | 200.497i | 0.264509 | − | 0.264509i | ||||
\(759\) | 51.6607i | 0.0680641i | ||||||||
\(760\) | 62.4853 | + | 43.6220i | 0.0822175 | + | 0.0573973i | ||||
\(761\) | −417.553 | −0.548690 | −0.274345 | − | 0.961631i | \(-0.588461\pi\) | ||||
−0.274345 | + | 0.961631i | \(0.588461\pi\) | |||||||
\(762\) | −203.390 | − | 203.390i | −0.266916 | − | 0.266916i | ||||
\(763\) | −852.612 | + | 852.612i | −1.11745 | + | 1.11745i | ||||
\(764\) | 198.054i | 0.259233i | ||||||||
\(765\) | 43.0916 | − | 61.7256i | 0.0563289 | − | 0.0806870i | ||||
\(766\) | 126.199 | 0.164750 | ||||||||
\(767\) | 1.73439 | + | 1.73439i | 0.00226127 | + | 0.00226127i | ||||
\(768\) | −19.5959 | + | 19.5959i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | − | 613.533i | − | 0.797833i | −0.916987 | − | 0.398916i | \(-0.869386\pi\) | ||
0.916987 | − | 0.398916i | \(-0.130614\pi\) | |||||||
\(770\) | 51.9751 | + | 292.363i | 0.0675001 | + | 0.379692i | ||||
\(771\) | −160.374 | −0.208007 | ||||||||
\(772\) | −358.687 | − | 358.687i | −0.464621 | − | 0.464621i | ||||
\(773\) | −804.283 | + | 804.283i | −1.04047 | + | 1.04047i | −0.0413235 | + | 0.999146i | \(0.513157\pi\) |
−0.999146 | + | 0.0413235i | \(0.986843\pi\) | |||||||
\(774\) | − | 242.984i | − | 0.313932i | ||||||
\(775\) | 335.516 | − | 123.187i | 0.432924 | − | 0.158951i | ||||
\(776\) | 90.8669 | 0.117096 | ||||||||
\(777\) | 486.491 | + | 486.491i | 0.626114 | + | 0.626114i | ||||
\(778\) | −346.298 | + | 346.298i | −0.445113 | + | 0.445113i | ||||
\(779\) | 82.8565i | 0.106363i | ||||||||
\(780\) | −2.35837 | + | 0.419262i | −0.00302355 | + | 0.000537515i | ||||
\(781\) | −242.883 | −0.310990 | ||||||||
\(782\) | −24.0684 | − | 24.0684i | −0.0307780 | − | 0.0307780i | ||||
\(783\) | 202.302 | − | 202.302i | 0.258368 | − | 0.258368i | ||||
\(784\) | 13.6203i | 0.0173729i | ||||||||
\(785\) | 808.767 | + | 564.613i | 1.03028 | + | 0.719252i | ||||
\(786\) | −326.000 | −0.414759 | ||||||||
\(787\) | −656.269 | − | 656.269i | −0.833887 | − | 0.833887i | 0.154159 | − | 0.988046i | \(-0.450733\pi\) |
−0.988046 | + | 0.154159i | \(0.950733\pi\) | |||||||
\(788\) | 124.910 | − | 124.910i | 0.158515 | − | 0.158515i | ||||
\(789\) | − | 285.320i | − | 0.361622i | ||||||
\(790\) | −290.302 | + | 415.837i | −0.367471 | + | 0.526376i | ||||
\(791\) | −242.994 | −0.307199 | ||||||||
\(792\) | 37.3153 | + | 37.3153i | 0.0471153 | + | 0.0471153i | ||||
\(793\) | −10.2117 | + | 10.2117i | −0.0128773 | + | 0.0128773i | ||||
\(794\) | 32.4112i | 0.0408202i | ||||||||
\(795\) | 64.4803 | + | 362.705i | 0.0811072 | + | 0.456233i | ||||
\(796\) | 409.290 | 0.514183 | ||||||||
\(797\) | −472.517 | − | 472.517i | −0.592870 | − | 0.592870i | 0.345536 | − | 0.938406i | \(-0.387697\pi\) |
−0.938406 | + | 0.345536i | \(0.887697\pi\) | |||||||
\(798\) | −63.0218 | + | 63.0218i | −0.0789747 | + | 0.0789747i | ||||
\(799\) | − | 131.866i | − | 0.165039i | ||||||
\(800\) | −128.339 | − | 59.4068i | −0.160423 | − | 0.0742585i | ||||
\(801\) | −60.0297 | −0.0749434 | ||||||||
\(802\) | −252.470 | − | 252.470i | −0.314801 | − | 0.314801i | ||||
\(803\) | −243.240 | + | 243.240i | −0.302914 | + | 0.302914i | ||||
\(804\) | 245.391i | 0.305213i | ||||||||
\(805\) | 159.417 | − | 28.3406i | 0.198034 | − | 0.0352057i | ||||
\(806\) | −2.79613 | −0.00346914 | ||||||||
\(807\) | −362.993 | − | 362.993i | −0.449805 | − | 0.449805i | ||||
\(808\) | −165.635 | + | 165.635i | −0.204994 | + | 0.204994i | ||||
\(809\) | 1160.79i | 1.43485i | 0.696637 | + | 0.717424i | \(0.254679\pi\) | ||||
−0.696637 | + | 0.717424i | \(0.745321\pi\) | |||||||
\(810\) | 52.1818 | + | 36.4289i | 0.0644219 | + | 0.0449739i | ||||
\(811\) | −1075.91 | −1.32665 | −0.663324 | − | 0.748333i | \(-0.730855\pi\) | ||||
−0.663324 | + | 0.748333i | \(0.730855\pi\) | |||||||
\(812\) | −525.782 | − | 525.782i | −0.647515 | − | 0.647515i | ||||
\(813\) | −278.286 | + | 278.286i | −0.342295 | + | 0.342295i | ||||
\(814\) | 517.394i | 0.635619i | ||||||||
\(815\) | −854.065 | + | 1223.39i | −1.04793 | + | 1.50109i | ||||
\(816\) | −34.7699 | −0.0426102 | ||||||||
\(817\) | 218.221 | + | 218.221i | 0.267101 | + | 0.267101i | ||||
\(818\) | −448.966 | + | 448.966i | −0.548858 | + | 0.548858i | ||||
\(819\) | − | 2.80148i | − | 0.00342061i | ||||||
\(820\) | −26.9136 | − | 151.390i | −0.0328214 | − | 0.184622i | ||||
\(821\) | 610.633 | 0.743767 | 0.371883 | − | 0.928279i | \(-0.378712\pi\) | ||||
0.371883 | + | 0.928279i | \(0.378712\pi\) | |||||||
\(822\) | 453.610 | + | 453.610i | 0.551836 | + | 0.551836i | ||||
\(823\) | −1047.06 | + | 1047.06i | −1.27224 | + | 1.27224i | −0.327335 | + | 0.944908i | \(0.606151\pi\) |
−0.944908 | + | 0.327335i | \(0.893849\pi\) | |||||||
\(824\) | 419.979i | 0.509684i | ||||||||
\(825\) | −113.125 | + | 244.387i | −0.137121 | + | 0.296227i | ||||
\(826\) | −169.366 | −0.205044 | ||||||||
\(827\) | −936.786 | − | 936.786i | −1.13275 | − | 1.13275i | −0.989718 | − | 0.143035i | \(-0.954314\pi\) |
−0.143035 | − | 0.989718i | \(-0.545686\pi\) | |||||||
\(828\) | 20.3470 | − | 20.3470i | 0.0245737 | − | 0.0245737i | ||||
\(829\) | − | 830.224i | − | 1.00148i | −0.865599 | − | 0.500738i | \(-0.833062\pi\) | ||
0.865599 | − | 0.500738i | \(-0.166938\pi\) | |||||||
\(830\) | 377.982 | − | 67.1961i | 0.455400 | − | 0.0809592i | ||||
\(831\) | −686.653 | −0.826298 | ||||||||
\(832\) | 0.782318 | + | 0.782318i | 0.000940286 | + | 0.000940286i | ||||
\(833\) | −12.0836 | + | 12.0836i | −0.0145061 | + | 0.0145061i | ||||
\(834\) | 77.2732i | 0.0926538i | ||||||||
\(835\) | −293.231 | − | 204.709i | −0.351175 | − | 0.245161i | ||||
\(836\) | −67.0251 | −0.0801735 | ||||||||
\(837\) | 52.5292 | + | 52.5292i | 0.0627589 | + | 0.0627589i | ||||
\(838\) | 56.1614 | − | 56.1614i | 0.0670184 | − | 0.0670184i | ||||
\(839\) | 1286.98i | 1.53394i | 0.641681 | + | 0.766971i | \(0.278237\pi\) | ||||
−0.641681 | + | 0.766971i | \(0.721763\pi\) | |||||||
\(840\) | 94.6787 | − | 135.620i | 0.112713 | − | 0.161453i | ||||
\(841\) | −2190.56 | −2.60471 | ||||||||
\(842\) | 302.461 | + | 302.461i | 0.359218 | + | 0.359218i | ||||
\(843\) | 166.091 | − | 166.091i | 0.197023 | − | 0.197023i | ||||
\(844\) | 14.6201i | 0.0173224i | ||||||||
\(845\) | −147.885 | − | 831.861i | −0.175012 | − | 0.984451i | ||||
\(846\) | 111.477 | 0.131770 | ||||||||
\(847\) | 393.057 | + | 393.057i | 0.464058 | + | 0.464058i | ||||
\(848\) | 120.316 | − | 120.316i | 0.141882 | − | 0.141882i | ||||
\(849\) | 469.768i | 0.553319i | ||||||||
\(850\) | −61.1544 | − | 166.563i | −0.0719464 | − | 0.195956i | ||||
\(851\) | 282.121 | 0.331516 | ||||||||
\(852\) | 95.6617 | + | 95.6617i | 0.112279 | + | 0.112279i | ||||
\(853\) | −272.712 | + | 272.712i | −0.319709 | + | 0.319709i | −0.848655 | − | 0.528946i | \(-0.822587\pi\) |
0.528946 | + | 0.848655i | \(0.322587\pi\) | |||||||
\(854\) | − | 997.191i | − | 1.16767i | ||||||
\(855\) | −79.5805 | + | 14.1475i | −0.0930766 | + | 0.0165468i | ||||
\(856\) | 484.134 | 0.565577 | ||||||||
\(857\) | 887.692 | + | 887.692i | 1.03581 | + | 1.03581i | 0.999334 | + | 0.0364794i | \(0.0116143\pi\) |
0.0364794 | + | 0.999334i | \(0.488386\pi\) | |||||||
\(858\) | 1.48972 | − | 1.48972i | 0.00173627 | − | 0.00173627i | ||||
\(859\) | 574.747i | 0.669089i | 0.942380 | + | 0.334544i | \(0.108582\pi\) | ||||
−0.942380 | + | 0.334544i | \(0.891418\pi\) | |||||||
\(860\) | −469.604 | − | 327.838i | −0.546051 | − | 0.381207i | ||||
\(861\) | 179.835 | 0.208867 | ||||||||
\(862\) | −294.456 | − | 294.456i | −0.341596 | − | 0.341596i | ||||
\(863\) | 145.359 | − | 145.359i | 0.168435 | − | 0.168435i | −0.617856 | − | 0.786291i | \(-0.711999\pi\) |
0.786291 | + | 0.617856i | \(0.211999\pi\) | |||||||
\(864\) | − | 29.3939i | − | 0.0340207i | ||||||
\(865\) | 786.107 | − | 1126.04i | 0.908794 | − | 1.30178i | ||||
\(866\) | −1021.73 | −1.17983 | ||||||||
\(867\) | 323.104 | + | 323.104i | 0.372669 | + | 0.372669i | ||||
\(868\) | 136.523 | − | 136.523i | 0.157285 | − | 0.157285i | ||||
\(869\) | − | 446.049i | − | 0.513290i | ||||||
\(870\) | −118.031 | − | 663.929i | −0.135668 | − | 0.763137i | ||||
\(871\) | 9.79663 | 0.0112476 | ||||||||
\(872\) | 357.140 | + | 357.140i | 0.409564 | + | 0.409564i | ||||
\(873\) | −68.1502 | + | 68.1502i | −0.0780643 | + | 0.0780643i | ||||
\(874\) | 36.5469i | 0.0418157i | ||||||||
\(875\) | 816.203 | + | 215.018i | 0.932804 | + | 0.245735i | ||||
\(876\) | 191.604 | 0.218726 | ||||||||
\(877\) | 43.7982 | + | 43.7982i | 0.0499409 | + | 0.0499409i | 0.731636 | − | 0.681695i | \(-0.238757\pi\) |
−0.681695 | + | 0.731636i | \(0.738757\pi\) | |||||||
\(878\) | 71.7873 | − | 71.7873i | 0.0817623 | − | 0.0817623i | ||||
\(879\) | 70.5168i | 0.0802239i | ||||||||
\(880\) | 122.464 | − | 21.7712i | 0.139164 | − | 0.0247400i | ||||
\(881\) | −150.385 | −0.170698 | −0.0853490 | − | 0.996351i | \(-0.527201\pi\) | ||||
−0.0853490 | + | 0.996351i | \(0.527201\pi\) | |||||||
\(882\) | −10.2153 | − | 10.2153i | −0.0115819 | − | 0.0115819i | ||||
\(883\) | 299.171 | − | 299.171i | 0.338812 | − | 0.338812i | −0.517108 | − | 0.855920i | \(-0.672991\pi\) |
0.855920 | + | 0.517108i | \(0.172991\pi\) | |||||||
\(884\) | 1.38810i | 0.00157025i | ||||||||
\(885\) | −125.944 | − | 87.9231i | −0.142309 | − | 0.0993482i | ||||
\(886\) | 542.635 | 0.612455 | ||||||||
\(887\) | −964.756 | − | 964.756i | −1.08766 | − | 1.08766i | −0.995769 | − | 0.0918932i | \(-0.970708\pi\) |
−0.0918932 | − | 0.995769i | \(-0.529292\pi\) | |||||||
\(888\) | 203.780 | − | 203.780i | 0.229482 | − | 0.229482i | ||||
\(889\) | − | 792.917i | − | 0.891920i | ||||||
\(890\) | −80.9931 | + | 116.017i | −0.0910035 | + | 0.130356i | ||||
\(891\) | −55.9729 | −0.0628203 | ||||||||
\(892\) | 53.2546 | + | 53.2546i | 0.0597024 | + | 0.0597024i | ||||
\(893\) | −100.117 | + | 100.117i | −0.112113 | + | 0.112113i | ||||
\(894\) | 276.121i | 0.308860i | ||||||||
\(895\) | 97.7204 | + | 549.683i | 0.109185 | + | 0.614171i | ||||
\(896\) | −76.3947 | −0.0852619 | ||||||||
\(897\) | −0.812302 | − | 0.812302i | −0.000905577 | − | 0.000905577i | ||||
\(898\) | −27.0296 | + | 27.0296i | −0.0300998 | + | 0.0300998i | ||||
\(899\) | − | 787.166i | − | 0.875602i | ||||||
\(900\) | 140.809 | − | 51.6989i | 0.156455 | − | 0.0574432i | ||||
\(901\) | 213.482 | 0.236939 | ||||||||
\(902\) | 95.6291 | + | 95.6291i | 0.106019 | + | 0.106019i | ||||
\(903\) | 473.636 | − | 473.636i | 0.524513 | − | 0.524513i | ||||
\(904\) | 101.785i | 0.112594i | ||||||||
\(905\) | −949.149 | + | 168.736i | −1.04878 | + | 0.186449i | ||||
\(906\) | −453.435 | −0.500481 | ||||||||
\(907\) | −166.682 | − | 166.682i | −0.183773 | − | 0.183773i | 0.609225 | − | 0.792998i | \(-0.291481\pi\) |
−0.792998 | + | 0.609225i | \(0.791481\pi\) | |||||||
\(908\) | 229.755 | − | 229.755i | 0.253034 | − | 0.253034i | ||||
\(909\) | − | 248.452i | − | 0.273325i | ||||||
\(910\) | −5.41430 | − | 3.77981i | −0.00594978 | − | 0.00415364i | ||||
\(911\) | 1103.14 | 1.21091 | 0.605454 | − | 0.795880i | \(-0.292992\pi\) | ||||
0.605454 | + | 0.795880i | \(0.292992\pi\) | |||||||
\(912\) | 26.3984 | + | 26.3984i | 0.0289456 | + | 0.0289456i | ||||
\(913\) | −238.761 | + | 238.761i | −0.261512 | + | 0.261512i | ||||
\(914\) | 650.315i | 0.711504i | ||||||||
\(915\) | 517.672 | − | 741.527i | 0.565761 | − | 0.810412i | ||||
\(916\) | 112.440 | 0.122751 | ||||||||
\(917\) | −635.456 | − | 635.456i | −0.692973 | − | 0.692973i | ||||
\(918\) | 26.0774 | − | 26.0774i | 0.0284068 | − | 0.0284068i | ||||
\(919\) | 1612.17i | 1.75426i | 0.480252 | + | 0.877130i | \(0.340545\pi\) | ||||
−0.480252 | + | 0.877130i | \(0.659455\pi\) | |||||||
\(920\) | −11.8712 | − | 66.7763i | −0.0129035 | − | 0.0725829i | ||||
\(921\) | −15.6648 | −0.0170085 | ||||||||
\(922\) | 362.643 | + | 362.643i | 0.393323 | + | 0.393323i | ||||
\(923\) | 3.81905 | − | 3.81905i | 0.00413765 | − | 0.00413765i | ||||
\(924\) | 145.474i | 0.157439i | ||||||||
\(925\) | 1334.61 | + | 617.778i | 1.44282 | + | 0.667868i | ||||
\(926\) | 978.486 | 1.05668 | ||||||||
\(927\) | −314.985 | − | 314.985i | −0.339789 | − | 0.339789i | ||||
\(928\) | −220.238 | + | 220.238i | −0.237326 | + | 0.237326i | ||||
\(929\) | − | 984.188i | − | 1.05941i | −0.848183 | − | 0.529703i | \(-0.822303\pi\) | ||
0.848183 | − | 0.529703i | \(-0.177697\pi\) | |||||||
\(930\) | 172.394 | − | 30.6476i | 0.185370 | − | 0.0329544i | ||||
\(931\) | 18.3485 | 0.0197083 | ||||||||
\(932\) | −341.458 | − | 341.458i | −0.366371 | − | 0.366371i | ||||
\(933\) | −460.362 | + | 460.362i | −0.493421 | + | 0.493421i | ||||
\(934\) | − | 204.660i | − | 0.219122i | ||||||
\(935\) | 127.962 | + | 89.3319i | 0.136857 | + | 0.0955422i | ||||
\(936\) | −1.17348 | −0.00125371 | ||||||||
\(937\) | 548.571 | + | 548.571i | 0.585454 | + | 0.585454i | 0.936397 | − | 0.350943i | \(-0.114139\pi\) |
−0.350943 | + | 0.936397i | \(0.614139\pi\) | |||||||
\(938\) | −478.329 | + | 478.329i | −0.509945 | + | 0.509945i | ||||
\(939\) | 60.5547i | 0.0644885i | ||||||||
\(940\) | 150.407 | − | 215.447i | 0.160008 | − | 0.229199i | ||||
\(941\) | −456.842 | −0.485485 | −0.242743 | − | 0.970091i | \(-0.578047\pi\) | ||||
−0.242743 | + | 0.970091i | \(0.578047\pi\) | |||||||
\(942\) | 341.682 | + | 341.682i | 0.362720 | + | 0.362720i | ||||
\(943\) | 52.1439 | − | 52.1439i | 0.0552958 | − | 0.0552958i | ||||
\(944\) | 70.9437i | 0.0751522i | ||||||||
\(945\) | 30.7063 | + | 172.724i | 0.0324934 | + | 0.182777i | ||||
\(946\) | 503.722 | 0.532476 | ||||||||
\(947\) | 409.447 | + | 409.447i | 0.432362 | + | 0.432362i | 0.889431 | − | 0.457069i | \(-0.151101\pi\) |
−0.457069 | + | 0.889431i | \(0.651101\pi\) | |||||||
\(948\) | −175.680 | + | 175.680i | −0.185317 | + | 0.185317i | ||||
\(949\) | − | 7.64932i | − | 0.00806040i | ||||||
\(950\) | −80.0292 | + | 172.890i | −0.0842412 | + | 0.181989i | ||||
\(951\) | 278.496 | 0.292845 | ||||||||
\(952\) | −67.7752 | − | 67.7752i | −0.0711924 | − | 0.0711924i | ||||
\(953\) | 1312.57 | − | 1312.57i | 1.37730 | − | 1.37730i | 0.528152 | − | 0.849150i | \(-0.322885\pi\) |
0.849150 | − | 0.528152i | \(-0.177115\pi\) | |||||||
\(954\) | 180.474i | 0.189177i | ||||||||
\(955\) | −487.492 | + | 86.6644i | −0.510463 | + | 0.0907481i | ||||
\(956\) | −286.990 | −0.300199 | ||||||||
\(957\) | 419.386 | + | 419.386i | 0.438230 | + | 0.438230i | ||||
\(958\) | 543.454 | − | 543.454i | 0.567280 | − | 0.567280i | ||||
\(959\) | 1768.40i | 1.84400i | ||||||||
\(960\) | −56.8083 | − | 39.6588i | −0.0591753 | − | 0.0413112i | ||||
\(961\) | −756.606 | −0.787312 | ||||||||
\(962\) | −8.13540 | − | 8.13540i | −0.00845676 | − | 0.00845676i | ||||
\(963\) | −363.100 | + | 363.100i | −0.377051 | + | 0.377051i | ||||
\(964\) | − | 195.366i | − | 0.202662i | ||||||
\(965\) | 725.922 | − | 1039.83i | 0.752250 | − | 1.07754i | ||||
\(966\) | 79.3227 | 0.0821146 | ||||||||
\(967\) | −663.105 | − | 663.105i | −0.685734 | − | 0.685734i | 0.275552 | − | 0.961286i | \(-0.411139\pi\) |
−0.961286 | + | 0.275552i | \(0.911139\pi\) | |||||||
\(968\) | 164.643 | − | 164.643i | 0.170085 | − | 0.170085i | ||||
\(969\) | 46.8398i | 0.0483383i | ||||||||
\(970\) | 39.7615 | + | 223.660i | 0.0409912 | + | 0.230578i | ||||
\(971\) | 567.405 | 0.584352 | 0.292176 | − | 0.956365i | \(-0.405621\pi\) | ||||
0.292176 | + | 0.956365i | \(0.405621\pi\) | |||||||
\(972\) | 22.0454 | + | 22.0454i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | −150.625 | + | 150.625i | −0.154805 | + | 0.154805i | ||||
\(974\) | 847.313i | 0.869931i | ||||||||
\(975\) | −2.06395 | − | 5.62145i | −0.00211687 | − | 0.00576559i | ||||
\(976\) | −417.701 | −0.427972 | ||||||||
\(977\) | −802.299 | − | 802.299i | −0.821186 | − | 0.821186i | 0.165092 | − | 0.986278i | \(-0.447208\pi\) |
−0.986278 | + | 0.165092i | \(0.947208\pi\) | |||||||
\(978\) | −516.848 | + | 516.848i | −0.528475 | + | 0.528475i | ||||
\(979\) | − | 124.446i | − | 0.127115i | ||||||
\(980\) | −33.5252 | + | 5.95998i | −0.0342094 | + | 0.00608161i | ||||
\(981\) | −535.710 | −0.546086 | ||||||||
\(982\) | −366.712 | − | 366.712i | −0.373434 | − | 0.373434i | ||||
\(983\) | −161.578 | + | 161.578i | −0.164372 | + | 0.164372i | −0.784500 | − | 0.620128i | \(-0.787081\pi\) |
0.620128 | + | 0.784500i | \(0.287081\pi\) | |||||||
\(984\) | − | 75.3286i | − | 0.0765535i | ||||||
\(985\) | 362.112 | + | 252.796i | 0.367627 | + | 0.256646i | ||||
\(986\) | −390.778 | −0.396327 | ||||||||
\(987\) | 217.297 | + | 217.297i | 0.220159 | + | 0.220159i | ||||
\(988\) | 1.05389 | − | 1.05389i | 0.00106669 | − | 0.00106669i | ||||
\(989\) | − | 274.666i | − | 0.277721i | ||||||
\(990\) | −75.5197 | + | 108.177i | −0.0762825 | + | 0.109269i | ||||
\(991\) | −917.892 | −0.926228 | −0.463114 | − | 0.886299i | \(-0.653268\pi\) | ||||
−0.463114 | + | 0.886299i | \(0.653268\pi\) | |||||||
\(992\) | −57.1865 | − | 57.1865i | −0.0576477 | − | 0.0576477i | ||||
\(993\) | 366.344 | − | 366.344i | 0.368926 | − | 0.368926i | ||||
\(994\) | 372.937i | 0.375188i | ||||||||
\(995\) | 179.097 | + | 1007.43i | 0.179997 | + | 1.01249i | ||||
\(996\) | 188.076 | 0.188831 | ||||||||
\(997\) | −327.573 | − | 327.573i | −0.328558 | − | 0.328558i | 0.523480 | − | 0.852038i | \(-0.324634\pi\) |
−0.852038 | + | 0.523480i | \(0.824634\pi\) | |||||||
\(998\) | 500.886 | − | 500.886i | 0.501890 | − | 0.501890i | ||||
\(999\) | 305.670i | 0.305976i |
(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 | 690.3.k.a.277.10 | ✓ | 40 | |
5.3 | odd | 4 | inner | 690.3.k.a.553.10 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.k.a.277.10 | ✓ | 40 | 1.1 | even | 1 | trivial | |
690.3.k.a.553.10 | yes | 40 | 5.3 | odd | 4 | inner |