Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [170,2,Mod(69,170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(170, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("170.69");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 170 = 2 \cdot 5 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 170.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.35745683436\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.5161984.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 4x^{3} + 25x^{2} - 20x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 69.4 | ||
Root | \(-1.75233 + 1.75233i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 170.69 |
Dual form | 170.2.c.b.69.3 |
$q$-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 \(\left(\mathbb{Z}/170\mathbb{Z}\right)^\times\).
\(n\) | \(71\) | \(137\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | − | 3.14134i | − | 1.81365i | −0.421506 | − | 0.906826i | \(-0.638498\pi\) | ||
0.421506 | − | 0.906826i | \(-0.361502\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.38900 | + | 1.75233i | 0.621181 | + | 0.783667i | ||||
\(6\) | 3.14134 | 1.28245 | ||||||||
\(7\) | − | 3.50466i | − | 1.32464i | −0.749222 | − | 0.662319i | \(-0.769572\pi\) | ||
0.749222 | − | 0.662319i | \(-0.230428\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −6.86799 | −2.28933 | ||||||||
\(10\) | −1.75233 | + | 1.38900i | −0.554136 | + | 0.439242i | ||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 3.14134i | 0.906826i | ||||||||
\(13\) | − | 3.14134i | − | 0.871250i | −0.900128 | − | 0.435625i | \(-0.856527\pi\) | ||
0.900128 | − | 0.435625i | \(-0.143473\pi\) | |||||||
\(14\) | 3.50466 | 0.936661 | ||||||||
\(15\) | 5.50466 | − | 4.36333i | 1.42130 | − | 1.12661i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000i | 0.242536i | ||||||||
\(18\) | − | 6.86799i | − | 1.61880i | ||||||
\(19\) | 3.86799 | 0.887378 | 0.443689 | − | 0.896181i | \(-0.353669\pi\) | ||||
0.443689 | + | 0.896181i | \(0.353669\pi\) | |||||||
\(20\) | −1.38900 | − | 1.75233i | −0.310591 | − | 0.391833i | ||||
\(21\) | −11.0093 | −2.40243 | ||||||||
\(22\) | 2.00000i | 0.426401i | ||||||||
\(23\) | 7.50466i | 1.56483i | 0.622757 | + | 0.782415i | \(0.286013\pi\) | ||||
−0.622757 | + | 0.782415i | \(0.713987\pi\) | |||||||
\(24\) | −3.14134 | −0.641223 | ||||||||
\(25\) | −1.14134 | + | 4.86799i | −0.228267 | + | 0.973599i | ||||
\(26\) | 3.14134 | 0.616067 | ||||||||
\(27\) | 12.1507i | 2.33840i | ||||||||
\(28\) | 3.50466i | 0.662319i | ||||||||
\(29\) | 0.646000 | 0.119959 | 0.0599796 | − | 0.998200i | \(-0.480896\pi\) | ||||
0.0599796 | + | 0.998200i | \(0.480896\pi\) | |||||||
\(30\) | 4.36333 | + | 5.50466i | 0.796631 | + | 1.00501i | ||||
\(31\) | −3.91934 | −0.703935 | −0.351967 | − | 0.936012i | \(-0.614487\pi\) | ||||
−0.351967 | + | 0.936012i | \(0.614487\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − | 6.28267i | − | 1.09367i | ||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | 6.14134 | − | 4.86799i | 1.03808 | − | 0.822841i | ||||
\(36\) | 6.86799 | 1.14467 | ||||||||
\(37\) | 8.95798i | 1.47268i | 0.676610 | + | 0.736341i | \(0.263448\pi\) | ||||
−0.676610 | + | 0.736341i | \(0.736552\pi\) | |||||||
\(38\) | 3.86799i | 0.627471i | ||||||||
\(39\) | −9.86799 | −1.58014 | ||||||||
\(40\) | 1.75233 | − | 1.38900i | 0.277068 | − | 0.219621i | ||||
\(41\) | 6.72666 | 1.05053 | 0.525264 | − | 0.850940i | \(-0.323967\pi\) | ||||
0.525264 | + | 0.850940i | \(0.323967\pi\) | |||||||
\(42\) | − | 11.0093i | − | 1.69878i | ||||||
\(43\) | 4.28267i | 0.653101i | 0.945180 | + | 0.326551i | \(0.105886\pi\) | ||||
−0.945180 | + | 0.326551i | \(0.894114\pi\) | |||||||
\(44\) | −2.00000 | −0.301511 | ||||||||
\(45\) | −9.53967 | − | 12.0350i | −1.42209 | − | 1.79407i | ||||
\(46\) | −7.50466 | −1.10650 | ||||||||
\(47\) | − | 10.5946i | − | 1.54539i | −0.634778 | − | 0.772694i | \(-0.718909\pi\) | ||
0.634778 | − | 0.772694i | \(-0.281091\pi\) | |||||||
\(48\) | − | 3.14134i | − | 0.453413i | ||||||
\(49\) | −5.28267 | −0.754667 | ||||||||
\(50\) | −4.86799 | − | 1.14134i | −0.688438 | − | 0.161409i | ||||
\(51\) | 3.14134 | 0.439875 | ||||||||
\(52\) | 3.14134i | 0.435625i | ||||||||
\(53\) | 8.69735i | 1.19467i | 0.801991 | + | 0.597337i | \(0.203774\pi\) | ||||
−0.801991 | + | 0.597337i | \(0.796226\pi\) | |||||||
\(54\) | −12.1507 | −1.65350 | ||||||||
\(55\) | 2.77801 | + | 3.50466i | 0.374587 | + | 0.472569i | ||||
\(56\) | −3.50466 | −0.468330 | ||||||||
\(57\) | − | 12.1507i | − | 1.60939i | ||||||
\(58\) | 0.646000i | 0.0848240i | ||||||||
\(59\) | −4.41468 | −0.574742 | −0.287371 | − | 0.957819i | \(-0.592781\pi\) | ||||
−0.287371 | + | 0.957819i | \(0.592781\pi\) | |||||||
\(60\) | −5.50466 | + | 4.36333i | −0.710649 | + | 0.563303i | ||||
\(61\) | −0.910015 | −0.116516 | −0.0582578 | − | 0.998302i | \(-0.518555\pi\) | ||||
−0.0582578 | + | 0.998302i | \(0.518555\pi\) | |||||||
\(62\) | − | 3.91934i | − | 0.497757i | ||||||
\(63\) | 24.0700i | 3.03254i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 5.50466 | − | 4.36333i | 0.682770 | − | 0.541204i | ||||
\(66\) | 6.28267 | 0.773343 | ||||||||
\(67\) | − | 10.2827i | − | 1.25623i | −0.778121 | − | 0.628114i | \(-0.783827\pi\) | ||
0.778121 | − | 0.628114i | \(-0.216173\pi\) | |||||||
\(68\) | − | 1.00000i | − | 0.121268i | ||||||
\(69\) | 23.5747 | 2.83806 | ||||||||
\(70\) | 4.86799 | + | 6.14134i | 0.581836 | + | 0.734030i | ||||
\(71\) | 3.19269 | 0.378902 | 0.189451 | − | 0.981890i | \(-0.439329\pi\) | ||||
0.189451 | + | 0.981890i | \(0.439329\pi\) | |||||||
\(72\) | 6.86799i | 0.809401i | ||||||||
\(73\) | − | 3.14134i | − | 0.367666i | −0.982958 | − | 0.183833i | \(-0.941150\pi\) | ||
0.982958 | − | 0.183833i | \(-0.0588505\pi\) | |||||||
\(74\) | −8.95798 | −1.04134 | ||||||||
\(75\) | 15.2920 | + | 3.58532i | 1.76577 | + | 0.413997i | ||||
\(76\) | −3.86799 | −0.443689 | ||||||||
\(77\) | − | 7.00933i | − | 0.798787i | ||||||
\(78\) | − | 9.86799i | − | 1.11733i | ||||||
\(79\) | −2.05135 | −0.230795 | −0.115398 | − | 0.993319i | \(-0.536814\pi\) | ||||
−0.115398 | + | 0.993319i | \(0.536814\pi\) | |||||||
\(80\) | 1.38900 | + | 1.75233i | 0.155295 | + | 0.195917i | ||||
\(81\) | 17.5653 | 1.95170 | ||||||||
\(82\) | 6.72666i | 0.742835i | ||||||||
\(83\) | − | 1.73599i | − | 0.190549i | −0.995451 | − | 0.0952746i | \(-0.969627\pi\) | ||
0.995451 | − | 0.0952746i | \(-0.0303729\pi\) | |||||||
\(84\) | 11.0093 | 1.20122 | ||||||||
\(85\) | −1.75233 | + | 1.38900i | −0.190067 | + | 0.150659i | ||||
\(86\) | −4.28267 | −0.461812 | ||||||||
\(87\) | − | 2.02930i | − | 0.217564i | ||||||
\(88\) | − | 2.00000i | − | 0.213201i | ||||||
\(89\) | 4.41468 | 0.467955 | 0.233978 | − | 0.972242i | \(-0.424826\pi\) | ||||
0.233978 | + | 0.972242i | \(0.424826\pi\) | |||||||
\(90\) | 12.0350 | − | 9.53967i | 1.26860 | − | 1.00557i | ||||
\(91\) | −11.0093 | −1.15409 | ||||||||
\(92\) | − | 7.50466i | − | 0.782415i | ||||||
\(93\) | 12.3120i | 1.27669i | ||||||||
\(94\) | 10.5946 | 1.09275 | ||||||||
\(95\) | 5.37266 | + | 6.77801i | 0.551223 | + | 0.695409i | ||||
\(96\) | 3.14134 | 0.320611 | ||||||||
\(97\) | 2.41468i | 0.245174i | 0.992458 | + | 0.122587i | \(0.0391190\pi\) | ||||
−0.992458 | + | 0.122587i | \(0.960881\pi\) | |||||||
\(98\) | − | 5.28267i | − | 0.533630i | ||||||
\(99\) | −13.7360 | −1.38052 | ||||||||
\(100\) | 1.14134 | − | 4.86799i | 0.114134 | − | 0.486799i | ||||
\(101\) | −5.73599 | −0.570752 | −0.285376 | − | 0.958416i | \(-0.592118\pi\) | ||||
−0.285376 | + | 0.958416i | \(0.592118\pi\) | |||||||
\(102\) | 3.14134i | 0.311039i | ||||||||
\(103\) | 9.55602i | 0.941582i | 0.882245 | + | 0.470791i | \(0.156031\pi\) | ||||
−0.882245 | + | 0.470791i | \(0.843969\pi\) | |||||||
\(104\) | −3.14134 | −0.308033 | ||||||||
\(105\) | −15.2920 | − | 19.2920i | −1.49235 | − | 1.88271i | ||||
\(106\) | −8.69735 | −0.844761 | ||||||||
\(107\) | − | 10.8294i | − | 1.04691i | −0.852052 | − | 0.523457i | \(-0.824642\pi\) | ||
0.852052 | − | 0.523457i | \(-0.175358\pi\) | |||||||
\(108\) | − | 12.1507i | − | 1.16920i | ||||||
\(109\) | −10.0993 | −0.967339 | −0.483669 | − | 0.875251i | \(-0.660696\pi\) | ||||
−0.483669 | + | 0.875251i | \(0.660696\pi\) | |||||||
\(110\) | −3.50466 | + | 2.77801i | −0.334157 | + | 0.264873i | ||||
\(111\) | 28.1400 | 2.67093 | ||||||||
\(112\) | − | 3.50466i | − | 0.331160i | ||||||
\(113\) | − | 4.85866i | − | 0.457065i | −0.973536 | − | 0.228532i | \(-0.926607\pi\) | ||
0.973536 | − | 0.228532i | \(-0.0733927\pi\) | |||||||
\(114\) | 12.1507 | 1.13801 | ||||||||
\(115\) | −13.1507 | + | 10.4240i | −1.22631 | + | 0.972044i | ||||
\(116\) | −0.646000 | −0.0599796 | ||||||||
\(117\) | 21.5747i | 1.99458i | ||||||||
\(118\) | − | 4.41468i | − | 0.406404i | ||||||
\(119\) | 3.50466 | 0.321272 | ||||||||
\(120\) | −4.36333 | − | 5.50466i | −0.398316 | − | 0.502505i | ||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | − | 0.910015i | − | 0.0823889i | ||||||
\(123\) | − | 21.1307i | − | 1.90529i | ||||||
\(124\) | 3.91934 | 0.351967 | ||||||||
\(125\) | −10.1157 | + | 4.76166i | −0.904772 | + | 0.425896i | ||||
\(126\) | −24.0700 | −2.14433 | ||||||||
\(127\) | 0.150665i | 0.0133693i | 0.999978 | + | 0.00668467i | \(0.00212781\pi\) | ||||
−0.999978 | + | 0.00668467i | \(0.997872\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 13.4533 | 1.18450 | ||||||||
\(130\) | 4.36333 | + | 5.50466i | 0.382689 | + | 0.482791i | ||||
\(131\) | 11.4533 | 1.00068 | 0.500340 | − | 0.865829i | \(-0.333208\pi\) | ||||
0.500340 | + | 0.865829i | \(0.333208\pi\) | |||||||
\(132\) | 6.28267i | 0.546836i | ||||||||
\(133\) | − | 13.5560i | − | 1.17546i | ||||||
\(134\) | 10.2827 | 0.888288 | ||||||||
\(135\) | −21.2920 | + | 16.8773i | −1.83252 | + | 1.45257i | ||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | − | 8.56534i | − | 0.731787i | −0.930657 | − | 0.365893i | \(-0.880763\pi\) | ||
0.930657 | − | 0.365893i | \(-0.119237\pi\) | |||||||
\(138\) | 23.5747i | 2.00681i | ||||||||
\(139\) | −14.3013 | −1.21302 | −0.606511 | − | 0.795075i | \(-0.707432\pi\) | ||||
−0.606511 | + | 0.795075i | \(0.707432\pi\) | |||||||
\(140\) | −6.14134 | + | 4.86799i | −0.519038 | + | 0.411420i | ||||
\(141\) | −33.2814 | −2.80280 | ||||||||
\(142\) | 3.19269i | 0.267924i | ||||||||
\(143\) | − | 6.28267i | − | 0.525383i | ||||||
\(144\) | −6.86799 | −0.572333 | ||||||||
\(145\) | 0.897297 | + | 1.13201i | 0.0745165 | + | 0.0940081i | ||||
\(146\) | 3.14134 | 0.259979 | ||||||||
\(147\) | 16.5946i | 1.36870i | ||||||||
\(148\) | − | 8.95798i | − | 0.736341i | ||||||
\(149\) | −10.0000 | −0.819232 | −0.409616 | − | 0.912258i | \(-0.634337\pi\) | ||||
−0.409616 | + | 0.912258i | \(0.634337\pi\) | |||||||
\(150\) | −3.58532 | + | 15.2920i | −0.292740 | + | 1.24859i | ||||
\(151\) | 21.0280 | 1.71123 | 0.855617 | − | 0.517610i | \(-0.173178\pi\) | ||||
0.855617 | + | 0.517610i | \(0.173178\pi\) | |||||||
\(152\) | − | 3.86799i | − | 0.313736i | ||||||
\(153\) | − | 6.86799i | − | 0.555244i | ||||||
\(154\) | 7.00933 | 0.564828 | ||||||||
\(155\) | −5.44398 | − | 6.86799i | −0.437271 | − | 0.551650i | ||||
\(156\) | 9.86799 | 0.790072 | ||||||||
\(157\) | − | 21.5747i | − | 1.72185i | −0.508735 | − | 0.860923i | \(-0.669887\pi\) | ||
0.508735 | − | 0.860923i | \(-0.330113\pi\) | |||||||
\(158\) | − | 2.05135i | − | 0.163197i | ||||||
\(159\) | 27.3213 | 2.16672 | ||||||||
\(160\) | −1.75233 | + | 1.38900i | −0.138534 | + | 0.109810i | ||||
\(161\) | 26.3013 | 2.07284 | ||||||||
\(162\) | 17.5653i | 1.38006i | ||||||||
\(163\) | − | 9.27334i | − | 0.726344i | −0.931722 | − | 0.363172i | \(-0.881694\pi\) | ||
0.931722 | − | 0.363172i | \(-0.118306\pi\) | |||||||
\(164\) | −6.72666 | −0.525264 | ||||||||
\(165\) | 11.0093 | − | 8.72666i | 0.857075 | − | 0.679369i | ||||
\(166\) | 1.73599 | 0.134739 | ||||||||
\(167\) | 20.7967i | 1.60929i | 0.593753 | + | 0.804647i | \(0.297646\pi\) | ||||
−0.593753 | + | 0.804647i | \(0.702354\pi\) | |||||||
\(168\) | 11.0093i | 0.849388i | ||||||||
\(169\) | 3.13201 | 0.240924 | ||||||||
\(170\) | −1.38900 | − | 1.75233i | −0.106532 | − | 0.134398i | ||||
\(171\) | −26.5653 | −2.03150 | ||||||||
\(172\) | − | 4.28267i | − | 0.326551i | ||||||
\(173\) | 13.9486i | 1.06050i | 0.847843 | + | 0.530248i | \(0.177901\pi\) | ||||
−0.847843 | + | 0.530248i | \(0.822099\pi\) | |||||||
\(174\) | 2.02930 | 0.153841 | ||||||||
\(175\) | 17.0607 | + | 4.00000i | 1.28967 | + | 0.302372i | ||||
\(176\) | 2.00000 | 0.150756 | ||||||||
\(177\) | 13.8680i | 1.04238i | ||||||||
\(178\) | 4.41468i | 0.330894i | ||||||||
\(179\) | −14.3013 | −1.06893 | −0.534466 | − | 0.845190i | \(-0.679487\pi\) | ||||
−0.534466 | + | 0.845190i | \(0.679487\pi\) | |||||||
\(180\) | 9.53967 | + | 12.0350i | 0.711045 | + | 0.897036i | ||||
\(181\) | −10.6753 | −0.793489 | −0.396745 | − | 0.917929i | \(-0.629860\pi\) | ||||
−0.396745 | + | 0.917929i | \(0.629860\pi\) | |||||||
\(182\) | − | 11.0093i | − | 0.816066i | ||||||
\(183\) | 2.85866i | 0.211319i | ||||||||
\(184\) | 7.50466 | 0.553251 | ||||||||
\(185\) | −15.6974 | + | 12.4427i | −1.15409 | + | 0.914803i | ||||
\(186\) | −12.3120 | −0.902758 | ||||||||
\(187\) | 2.00000i | 0.146254i | ||||||||
\(188\) | 10.5946i | 0.772694i | ||||||||
\(189\) | 42.5840 | 3.09753 | ||||||||
\(190\) | −6.77801 | + | 5.37266i | −0.491728 | + | 0.389774i | ||||
\(191\) | −4.56534 | −0.330337 | −0.165168 | − | 0.986265i | \(-0.552817\pi\) | ||||
−0.165168 | + | 0.986265i | \(0.552817\pi\) | |||||||
\(192\) | 3.14134i | 0.226706i | ||||||||
\(193\) | 12.0187i | 0.865122i | 0.901605 | + | 0.432561i | \(0.142390\pi\) | ||||
−0.901605 | + | 0.432561i | \(0.857610\pi\) | |||||||
\(194\) | −2.41468 | −0.173364 | ||||||||
\(195\) | −13.7067 | − | 17.2920i | −0.981556 | − | 1.23831i | ||||
\(196\) | 5.28267 | 0.377334 | ||||||||
\(197\) | 21.8900i | 1.55960i | 0.626028 | + | 0.779800i | \(0.284679\pi\) | ||||
−0.626028 | + | 0.779800i | \(0.715321\pi\) | |||||||
\(198\) | − | 13.7360i | − | 0.976174i | ||||||
\(199\) | 7.08998 | 0.502596 | 0.251298 | − | 0.967910i | \(-0.419143\pi\) | ||||
0.251298 | + | 0.967910i | \(0.419143\pi\) | |||||||
\(200\) | 4.86799 | + | 1.14134i | 0.344219 | + | 0.0807047i | ||||
\(201\) | −32.3013 | −2.27836 | ||||||||
\(202\) | − | 5.73599i | − | 0.403583i | ||||||
\(203\) | − | 2.26401i | − | 0.158903i | ||||||
\(204\) | −3.14134 | −0.219938 | ||||||||
\(205\) | 9.34335 | + | 11.7873i | 0.652568 | + | 0.823263i | ||||
\(206\) | −9.55602 | −0.665799 | ||||||||
\(207\) | − | 51.5420i | − | 3.58242i | ||||||
\(208\) | − | 3.14134i | − | 0.217812i | ||||||
\(209\) | 7.73599 | 0.535109 | ||||||||
\(210\) | 19.2920 | − | 15.2920i | 1.33127 | − | 1.05525i | ||||
\(211\) | −15.1893 | −1.04567 | −0.522837 | − | 0.852433i | \(-0.675126\pi\) | ||||
−0.522837 | + | 0.852433i | \(0.675126\pi\) | |||||||
\(212\) | − | 8.69735i | − | 0.597337i | ||||||
\(213\) | − | 10.0293i | − | 0.687197i | ||||||
\(214\) | 10.8294 | 0.740280 | ||||||||
\(215\) | −7.50466 | + | 5.94865i | −0.511814 | + | 0.405694i | ||||
\(216\) | 12.1507 | 0.826748 | ||||||||
\(217\) | 13.7360i | 0.932459i | ||||||||
\(218\) | − | 10.0993i | − | 0.684012i | ||||||
\(219\) | −9.86799 | −0.666817 | ||||||||
\(220\) | −2.77801 | − | 3.50466i | −0.187293 | − | 0.236284i | ||||
\(221\) | 3.14134 | 0.211309 | ||||||||
\(222\) | 28.1400i | 1.88863i | ||||||||
\(223\) | − | 5.60398i | − | 0.375270i | −0.982239 | − | 0.187635i | \(-0.939918\pi\) | ||
0.982239 | − | 0.187635i | \(-0.0600822\pi\) | |||||||
\(224\) | 3.50466 | 0.234165 | ||||||||
\(225\) | 7.83869 | − | 33.4333i | 0.522579 | − | 2.22889i | ||||
\(226\) | 4.85866 | 0.323194 | ||||||||
\(227\) | 7.76529i | 0.515400i | 0.966225 | + | 0.257700i | \(0.0829647\pi\) | ||||
−0.966225 | + | 0.257700i | \(0.917035\pi\) | |||||||
\(228\) | 12.1507i | 0.804697i | ||||||||
\(229\) | −13.0093 | −0.859681 | −0.429840 | − | 0.902905i | \(-0.641430\pi\) | ||||
−0.429840 | + | 0.902905i | \(0.641430\pi\) | |||||||
\(230\) | −10.4240 | − | 13.1507i | −0.687339 | − | 0.867129i | ||||
\(231\) | −22.0187 | −1.44872 | ||||||||
\(232\) | − | 0.646000i | − | 0.0424120i | ||||||
\(233\) | − | 10.8773i | − | 0.712597i | −0.934372 | − | 0.356299i | \(-0.884039\pi\) | ||
0.934372 | − | 0.356299i | \(-0.115961\pi\) | |||||||
\(234\) | −21.5747 | −1.41038 | ||||||||
\(235\) | 18.5653 | − | 14.7160i | 1.21107 | − | 0.959967i | ||||
\(236\) | 4.41468 | 0.287371 | ||||||||
\(237\) | 6.44398i | 0.418582i | ||||||||
\(238\) | 3.50466i | 0.227174i | ||||||||
\(239\) | −24.3013 | −1.57192 | −0.785961 | − | 0.618276i | \(-0.787831\pi\) | ||||
−0.785961 | + | 0.618276i | \(0.787831\pi\) | |||||||
\(240\) | 5.50466 | − | 4.36333i | 0.355325 | − | 0.281652i | ||||
\(241\) | 19.8573 | 1.27912 | 0.639562 | − | 0.768739i | \(-0.279116\pi\) | ||||
0.639562 | + | 0.768739i | \(0.279116\pi\) | |||||||
\(242\) | − | 7.00000i | − | 0.449977i | ||||||
\(243\) | − | 18.7267i | − | 1.20132i | ||||||
\(244\) | 0.910015 | 0.0582578 | ||||||||
\(245\) | −7.33765 | − | 9.25700i | −0.468785 | − | 0.591408i | ||||
\(246\) | 21.1307 | 1.34724 | ||||||||
\(247\) | − | 12.1507i | − | 0.773128i | ||||||
\(248\) | 3.91934i | 0.248879i | ||||||||
\(249\) | −5.45331 | −0.345590 | ||||||||
\(250\) | −4.76166 | − | 10.1157i | −0.301154 | − | 0.639771i | ||||
\(251\) | 10.8294 | 0.683543 | 0.341772 | − | 0.939783i | \(-0.388973\pi\) | ||||
0.341772 | + | 0.939783i | \(0.388973\pi\) | |||||||
\(252\) | − | 24.0700i | − | 1.51627i | ||||||
\(253\) | 15.0093i | 0.943628i | ||||||||
\(254\) | −0.150665 | −0.00945355 | ||||||||
\(255\) | 4.36333 | + | 5.50466i | 0.273242 | + | 0.344715i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 24.5653i | 1.53234i | 0.642636 | + | 0.766172i | \(0.277841\pi\) | ||||
−0.642636 | + | 0.766172i | \(0.722159\pi\) | |||||||
\(258\) | 13.4533i | 0.837567i | ||||||||
\(259\) | 31.3947 | 1.95077 | ||||||||
\(260\) | −5.50466 | + | 4.36333i | −0.341385 | + | 0.270602i | ||||
\(261\) | −4.43673 | −0.274626 | ||||||||
\(262\) | 11.4533i | 0.707588i | ||||||||
\(263\) | − | 7.32131i | − | 0.451451i | −0.974191 | − | 0.225726i | \(-0.927525\pi\) | ||
0.974191 | − | 0.225726i | \(-0.0724752\pi\) | |||||||
\(264\) | −6.28267 | −0.386672 | ||||||||
\(265\) | −15.2406 | + | 12.0807i | −0.936226 | + | 0.742109i | ||||
\(266\) | 13.5560 | 0.831173 | ||||||||
\(267\) | − | 13.8680i | − | 0.848707i | ||||||
\(268\) | 10.2827i | 0.628114i | ||||||||
\(269\) | 5.37266 | 0.327577 | 0.163788 | − | 0.986496i | \(-0.447629\pi\) | ||||
0.163788 | + | 0.986496i | \(0.447629\pi\) | |||||||
\(270\) | −16.8773 | − | 21.2920i | −1.02712 | − | 1.29579i | ||||
\(271\) | 9.18930 | 0.558210 | 0.279105 | − | 0.960261i | \(-0.409962\pi\) | ||||
0.279105 | + | 0.960261i | \(0.409962\pi\) | |||||||
\(272\) | 1.00000i | 0.0606339i | ||||||||
\(273\) | 34.5840i | 2.09312i | ||||||||
\(274\) | 8.56534 | 0.517451 | ||||||||
\(275\) | −2.28267 | + | 9.73599i | −0.137650 | + | 0.587102i | ||||
\(276\) | −23.5747 | −1.41903 | ||||||||
\(277\) | − | 4.79667i | − | 0.288204i | −0.989563 | − | 0.144102i | \(-0.953971\pi\) | ||
0.989563 | − | 0.144102i | \(-0.0460293\pi\) | |||||||
\(278\) | − | 14.3013i | − | 0.857737i | ||||||
\(279\) | 26.9180 | 1.61154 | ||||||||
\(280\) | −4.86799 | − | 6.14134i | −0.290918 | − | 0.367015i | ||||
\(281\) | 31.2627 | 1.86498 | 0.932488 | − | 0.361201i | \(-0.117633\pi\) | ||||
0.932488 | + | 0.361201i | \(0.117633\pi\) | |||||||
\(282\) | − | 33.2814i | − | 1.98188i | ||||||
\(283\) | 17.0573i | 1.01395i | 0.861961 | + | 0.506975i | \(0.169236\pi\) | ||||
−0.861961 | + | 0.506975i | \(0.830764\pi\) | |||||||
\(284\) | −3.19269 | −0.189451 | ||||||||
\(285\) | 21.2920 | − | 16.8773i | 1.26123 | − | 0.999726i | ||||
\(286\) | 6.28267 | 0.371502 | ||||||||
\(287\) | − | 23.5747i | − | 1.39157i | ||||||
\(288\) | − | 6.86799i | − | 0.404700i | ||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | −1.13201 | + | 0.897297i | −0.0664738 | + | 0.0526911i | ||||
\(291\) | 7.58532 | 0.444659 | ||||||||
\(292\) | 3.14134i | 0.183833i | ||||||||
\(293\) | 22.2534i | 1.30006i | 0.759910 | + | 0.650028i | \(0.225243\pi\) | ||||
−0.759910 | + | 0.650028i | \(0.774757\pi\) | |||||||
\(294\) | −16.5946 | −0.967820 | ||||||||
\(295\) | −6.13201 | − | 7.73599i | −0.357019 | − | 0.450406i | ||||
\(296\) | 8.95798 | 0.520672 | ||||||||
\(297\) | 24.3013i | 1.41011i | ||||||||
\(298\) | − | 10.0000i | − | 0.579284i | ||||||
\(299\) | 23.5747 | 1.36336 | ||||||||
\(300\) | −15.2920 | − | 3.58532i | −0.882884 | − | 0.206999i | ||||
\(301\) | 15.0093 | 0.865123 | ||||||||
\(302\) | 21.0280i | 1.21002i | ||||||||
\(303\) | 18.0187i | 1.03514i | ||||||||
\(304\) | 3.86799 | 0.221845 | ||||||||
\(305\) | −1.26401 | − | 1.59465i | −0.0723773 | − | 0.0913093i | ||||
\(306\) | 6.86799 | 0.392617 | ||||||||
\(307\) | − | 29.7360i | − | 1.69712i | −0.529097 | − | 0.848561i | \(-0.677469\pi\) | ||
0.529097 | − | 0.848561i | \(-0.322531\pi\) | |||||||
\(308\) | 7.00933i | 0.399394i | ||||||||
\(309\) | 30.0187 | 1.70770 | ||||||||
\(310\) | 6.86799 | − | 5.44398i | 0.390076 | − | 0.309198i | ||||
\(311\) | −23.1820 | −1.31453 | −0.657266 | − | 0.753658i | \(-0.728287\pi\) | ||||
−0.657266 | + | 0.753658i | \(0.728287\pi\) | |||||||
\(312\) | 9.86799i | 0.558665i | ||||||||
\(313\) | − | 23.4533i | − | 1.32566i | −0.748770 | − | 0.662830i | \(-0.769355\pi\) | ||
0.748770 | − | 0.662830i | \(-0.230645\pi\) | |||||||
\(314\) | 21.5747 | 1.21753 | ||||||||
\(315\) | −42.1787 | + | 33.4333i | −2.37650 | + | 1.88376i | ||||
\(316\) | 2.05135 | 0.115398 | ||||||||
\(317\) | 3.60737i | 0.202610i | 0.994855 | + | 0.101305i | \(0.0323018\pi\) | ||||
−0.994855 | + | 0.101305i | \(0.967698\pi\) | |||||||
\(318\) | 27.3213i | 1.53210i | ||||||||
\(319\) | 1.29200 | 0.0723382 | ||||||||
\(320\) | −1.38900 | − | 1.75233i | −0.0776477 | − | 0.0979583i | ||||
\(321\) | −34.0187 | −1.89874 | ||||||||
\(322\) | 26.3013i | 1.46572i | ||||||||
\(323\) | 3.86799i | 0.215221i | ||||||||
\(324\) | −17.5653 | −0.975852 | ||||||||
\(325\) | 15.2920 | + | 3.58532i | 0.848248 | + | 0.198878i | ||||
\(326\) | 9.27334 | 0.513603 | ||||||||
\(327\) | 31.7253i | 1.75442i | ||||||||
\(328\) | − | 6.72666i | − | 0.371417i | ||||||
\(329\) | −37.1307 | −2.04708 | ||||||||
\(330\) | 8.72666 | + | 11.0093i | 0.480387 | + | 0.606044i | ||||
\(331\) | −33.9053 | −1.86360 | −0.931802 | − | 0.362967i | \(-0.881764\pi\) | ||||
−0.931802 | + | 0.362967i | \(0.881764\pi\) | |||||||
\(332\) | 1.73599i | 0.0952746i | ||||||||
\(333\) | − | 61.5233i | − | 3.37146i | ||||||
\(334\) | −20.7967 | −1.13794 | ||||||||
\(335\) | 18.0187 | − | 14.2827i | 0.984464 | − | 0.780346i | ||||
\(336\) | −11.0093 | −0.600608 | ||||||||
\(337\) | − | 8.33063i | − | 0.453799i | −0.973918 | − | 0.226899i | \(-0.927141\pi\) | ||
0.973918 | − | 0.226899i | \(-0.0728588\pi\) | |||||||
\(338\) | 3.13201i | 0.170359i | ||||||||
\(339\) | −15.2627 | −0.828956 | ||||||||
\(340\) | 1.75233 | − | 1.38900i | 0.0950336 | − | 0.0753293i | ||||
\(341\) | −7.83869 | −0.424489 | ||||||||
\(342\) | − | 26.5653i | − | 1.43649i | ||||||
\(343\) | − | 6.01866i | − | 0.324977i | ||||||
\(344\) | 4.28267 | 0.230906 | ||||||||
\(345\) | 32.7453 | + | 41.3107i | 1.76295 | + | 2.22409i | ||||
\(346\) | −13.9486 | −0.749884 | ||||||||
\(347\) | 7.14134i | 0.383367i | 0.981457 | + | 0.191684i | \(0.0613947\pi\) | ||||
−0.981457 | + | 0.191684i | \(0.938605\pi\) | |||||||
\(348\) | 2.02930i | 0.108782i | ||||||||
\(349\) | −4.64939 | −0.248876 | −0.124438 | − | 0.992227i | \(-0.539713\pi\) | ||||
−0.124438 | + | 0.992227i | \(0.539713\pi\) | |||||||
\(350\) | −4.00000 | + | 17.0607i | −0.213809 | + | 0.911932i | ||||
\(351\) | 38.1693 | 2.03733 | ||||||||
\(352\) | 2.00000i | 0.106600i | ||||||||
\(353\) | 20.8480i | 1.10963i | 0.831974 | + | 0.554814i | \(0.187211\pi\) | ||||
−0.831974 | + | 0.554814i | \(0.812789\pi\) | |||||||
\(354\) | −13.8680 | −0.737075 | ||||||||
\(355\) | 4.43466 | + | 5.59465i | 0.235367 | + | 0.296933i | ||||
\(356\) | −4.41468 | −0.233978 | ||||||||
\(357\) | − | 11.0093i | − | 0.582675i | ||||||
\(358\) | − | 14.3013i | − | 0.755849i | ||||||
\(359\) | −12.4626 | −0.657753 | −0.328877 | − | 0.944373i | \(-0.606670\pi\) | ||||
−0.328877 | + | 0.944373i | \(0.606670\pi\) | |||||||
\(360\) | −12.0350 | + | 9.53967i | −0.634300 | + | 0.502785i | ||||
\(361\) | −4.03863 | −0.212560 | ||||||||
\(362\) | − | 10.6753i | − | 0.561082i | ||||||
\(363\) | 21.9894i | 1.15414i | ||||||||
\(364\) | 11.0093 | 0.577046 | ||||||||
\(365\) | 5.50466 | − | 4.36333i | 0.288127 | − | 0.228387i | ||||
\(366\) | −2.85866 | −0.149425 | ||||||||
\(367\) | − | 5.22199i | − | 0.272586i | −0.990669 | − | 0.136293i | \(-0.956481\pi\) | ||
0.990669 | − | 0.136293i | \(-0.0435188\pi\) | |||||||
\(368\) | 7.50466i | 0.391208i | ||||||||
\(369\) | −46.1986 | −2.40500 | ||||||||
\(370\) | −12.4427 | − | 15.6974i | −0.646863 | − | 0.816066i | ||||
\(371\) | 30.4813 | 1.58251 | ||||||||
\(372\) | − | 12.3120i | − | 0.638346i | ||||||
\(373\) | − | 26.4626i | − | 1.37018i | −0.728457 | − | 0.685092i | \(-0.759762\pi\) | ||
0.728457 | − | 0.685092i | \(-0.240238\pi\) | |||||||
\(374\) | −2.00000 | −0.103418 | ||||||||
\(375\) | 14.9580 | + | 31.7767i | 0.772427 | + | 1.64094i | ||||
\(376\) | −10.5946 | −0.546377 | ||||||||
\(377\) | − | 2.02930i | − | 0.104515i | ||||||
\(378\) | 42.5840i | 2.19028i | ||||||||
\(379\) | −8.70800 | −0.447300 | −0.223650 | − | 0.974670i | \(-0.571797\pi\) | ||||
−0.223650 | + | 0.974670i | \(0.571797\pi\) | |||||||
\(380\) | −5.37266 | − | 6.77801i | −0.275611 | − | 0.347704i | ||||
\(381\) | 0.473289 | 0.0242473 | ||||||||
\(382\) | − | 4.56534i | − | 0.233583i | ||||||
\(383\) | − | 33.8094i | − | 1.72758i | −0.503853 | − | 0.863789i | \(-0.668085\pi\) | ||
0.503853 | − | 0.863789i | \(-0.331915\pi\) | |||||||
\(384\) | −3.14134 | −0.160306 | ||||||||
\(385\) | 12.2827 | − | 9.73599i | 0.625983 | − | 0.496192i | ||||
\(386\) | −12.0187 | −0.611734 | ||||||||
\(387\) | − | 29.4134i | − | 1.49517i | ||||||
\(388\) | − | 2.41468i | − | 0.122587i | ||||||
\(389\) | 22.4626 | 1.13890 | 0.569451 | − | 0.822026i | \(-0.307156\pi\) | ||||
0.569451 | + | 0.822026i | \(0.307156\pi\) | |||||||
\(390\) | 17.2920 | − | 13.7067i | 0.875615 | − | 0.694065i | ||||
\(391\) | −7.50466 | −0.379527 | ||||||||
\(392\) | 5.28267i | 0.266815i | ||||||||
\(393\) | − | 35.9787i | − | 1.81489i | ||||||
\(394\) | −21.8900 | −1.10280 | ||||||||
\(395\) | −2.84934 | − | 3.59465i | −0.143366 | − | 0.180866i | ||||
\(396\) | 13.7360 | 0.690259 | ||||||||
\(397\) | 23.8060i | 1.19479i | 0.801948 | + | 0.597394i | \(0.203797\pi\) | ||||
−0.801948 | + | 0.597394i | \(0.796203\pi\) | |||||||
\(398\) | 7.08998i | 0.355389i | ||||||||
\(399\) | −42.5840 | −2.13187 | ||||||||
\(400\) | −1.14134 | + | 4.86799i | −0.0570668 | + | 0.243400i | ||||
\(401\) | 14.4626 | 0.722230 | 0.361115 | − | 0.932521i | \(-0.382396\pi\) | ||||
0.361115 | + | 0.932521i | \(0.382396\pi\) | |||||||
\(402\) | − | 32.3013i | − | 1.61104i | ||||||
\(403\) | 12.3120i | 0.613303i | ||||||||
\(404\) | 5.73599 | 0.285376 | ||||||||
\(405\) | 24.3983 | + | 30.7803i | 1.21236 | + | 1.52949i | ||||
\(406\) | 2.26401 | 0.112361 | ||||||||
\(407\) | 17.9160i | 0.888061i | ||||||||
\(408\) | − | 3.14134i | − | 0.155519i | ||||||
\(409\) | 6.13201 | 0.303208 | 0.151604 | − | 0.988441i | \(-0.451556\pi\) | ||||
0.151604 | + | 0.988441i | \(0.451556\pi\) | |||||||
\(410\) | −11.7873 | + | 9.34335i | −0.582135 | + | 0.461435i | ||||
\(411\) | −26.9066 | −1.32721 | ||||||||
\(412\) | − | 9.55602i | − | 0.470791i | ||||||
\(413\) | 15.4720i | 0.761326i | ||||||||
\(414\) | 51.5420 | 2.53315 | ||||||||
\(415\) | 3.04202 | − | 2.41129i | 0.149327 | − | 0.118366i | ||||
\(416\) | 3.14134 | 0.154017 | ||||||||
\(417\) | 44.9253i | 2.20000i | ||||||||
\(418\) | 7.73599i | 0.378379i | ||||||||
\(419\) | −21.8387 | −1.06689 | −0.533445 | − | 0.845835i | \(-0.679103\pi\) | ||||
−0.533445 | + | 0.845835i | \(0.679103\pi\) | |||||||
\(420\) | 15.2920 | + | 19.2920i | 0.746173 | + | 0.941353i | ||||
\(421\) | 3.71733 | 0.181171 | 0.0905857 | − | 0.995889i | \(-0.471126\pi\) | ||||
0.0905857 | + | 0.995889i | \(0.471126\pi\) | |||||||
\(422\) | − | 15.1893i | − | 0.739403i | ||||||
\(423\) | 72.7640i | 3.53791i | ||||||||
\(424\) | 8.69735 | 0.422381 | ||||||||
\(425\) | −4.86799 | − | 1.14134i | −0.236132 | − | 0.0553629i | ||||
\(426\) | 10.0293 | 0.485921 | ||||||||
\(427\) | 3.18930i | 0.154341i | ||||||||
\(428\) | 10.8294i | 0.523457i | ||||||||
\(429\) | −19.7360 | −0.952862 | ||||||||
\(430\) | −5.94865 | − | 7.50466i | −0.286869 | − | 0.361907i | ||||
\(431\) | −11.9673 | −0.576445 | −0.288222 | − | 0.957563i | \(-0.593064\pi\) | ||||
−0.288222 | + | 0.957563i | \(0.593064\pi\) | |||||||
\(432\) | 12.1507i | 0.584599i | ||||||||
\(433\) | − | 18.3013i | − | 0.879506i | −0.898119 | − | 0.439753i | \(-0.855066\pi\) | ||
0.898119 | − | 0.439753i | \(-0.144934\pi\) | |||||||
\(434\) | −13.7360 | −0.659348 | ||||||||
\(435\) | 3.55602 | − | 2.81871i | 0.170498 | − | 0.135147i | ||||
\(436\) | 10.0993 | 0.483669 | ||||||||
\(437\) | 29.0280i | 1.38860i | ||||||||
\(438\) | − | 9.86799i | − | 0.471511i | ||||||
\(439\) | 31.0793 | 1.48334 | 0.741668 | − | 0.670767i | \(-0.234035\pi\) | ||||
0.741668 | + | 0.670767i | \(0.234035\pi\) | |||||||
\(440\) | 3.50466 | − | 2.77801i | 0.167078 | − | 0.132436i | ||||
\(441\) | 36.2814 | 1.72768 | ||||||||
\(442\) | 3.14134i | 0.149418i | ||||||||
\(443\) | − | 29.3947i | − | 1.39658i | −0.715813 | − | 0.698292i | \(-0.753944\pi\) | ||
0.715813 | − | 0.698292i | \(-0.246056\pi\) | |||||||
\(444\) | −28.1400 | −1.33547 | ||||||||
\(445\) | 6.13201 | + | 7.73599i | 0.290685 | + | 0.366721i | ||||
\(446\) | 5.60398 | 0.265356 | ||||||||
\(447\) | 31.4134i | 1.48580i | ||||||||
\(448\) | 3.50466i | 0.165580i | ||||||||
\(449\) | −14.1027 | −0.665548 | −0.332774 | − | 0.943007i | \(-0.607985\pi\) | ||||
−0.332774 | + | 0.943007i | \(0.607985\pi\) | |||||||
\(450\) | 33.4333 | + | 7.83869i | 1.57606 | + | 0.369519i | ||||
\(451\) | 13.4533 | 0.633492 | ||||||||
\(452\) | 4.85866i | 0.228532i | ||||||||
\(453\) | − | 66.0560i | − | 3.10358i | ||||||
\(454\) | −7.76529 | −0.364443 | ||||||||
\(455\) | −15.2920 | − | 19.2920i | −0.716900 | − | 0.904423i | ||||
\(456\) | −12.1507 | −0.569007 | ||||||||
\(457\) | − | 30.8294i | − | 1.44214i | −0.692864 | − | 0.721068i | \(-0.743651\pi\) | ||
0.692864 | − | 0.721068i | \(-0.256349\pi\) | |||||||
\(458\) | − | 13.0093i | − | 0.607886i | ||||||
\(459\) | −12.1507 | −0.567144 | ||||||||
\(460\) | 13.1507 | − | 10.4240i | 0.613153 | − | 0.486022i | ||||
\(461\) | 4.38538 | 0.204247 | 0.102124 | − | 0.994772i | \(-0.467436\pi\) | ||||
0.102124 | + | 0.994772i | \(0.467436\pi\) | |||||||
\(462\) | − | 22.0187i | − | 1.02440i | ||||||
\(463\) | 2.55733i | 0.118849i | 0.998233 | + | 0.0594247i | \(0.0189266\pi\) | ||||
−0.998233 | + | 0.0594247i | \(0.981073\pi\) | |||||||
\(464\) | 0.646000 | 0.0299898 | ||||||||
\(465\) | −21.5747 | + | 17.1014i | −1.00050 | + | 0.793058i | ||||
\(466\) | 10.8773 | 0.503882 | ||||||||
\(467\) | − | 12.6240i | − | 0.584167i | −0.956393 | − | 0.292083i | \(-0.905651\pi\) | ||
0.956393 | − | 0.292083i | \(-0.0943485\pi\) | |||||||
\(468\) | − | 21.5747i | − | 0.997290i | ||||||
\(469\) | −36.0373 | −1.66405 | ||||||||
\(470\) | 14.7160 | + | 18.5653i | 0.678799 | + | 0.856355i | ||||
\(471\) | −67.7733 | −3.12283 | ||||||||
\(472\) | 4.41468i | 0.203202i | ||||||||
\(473\) | 8.56534i | 0.393835i | ||||||||
\(474\) | −6.44398 | −0.295982 | ||||||||
\(475\) | −4.41468 | + | 18.8294i | −0.202559 | + | 0.863950i | ||||
\(476\) | −3.50466 | −0.160636 | ||||||||
\(477\) | − | 59.7333i | − | 2.73500i | ||||||
\(478\) | − | 24.3013i | − | 1.11152i | ||||||
\(479\) | 7.75803 | 0.354474 | 0.177237 | − | 0.984168i | \(-0.443284\pi\) | ||||
0.177237 | + | 0.984168i | \(0.443284\pi\) | |||||||
\(480\) | 4.36333 | + | 5.50466i | 0.199158 | + | 0.251252i | ||||
\(481\) | 28.1400 | 1.28307 | ||||||||
\(482\) | 19.8573i | 0.904477i | ||||||||
\(483\) | − | 82.6213i | − | 3.75940i | ||||||
\(484\) | 7.00000 | 0.318182 | ||||||||
\(485\) | −4.23132 | + | 3.35400i | −0.192134 | + | 0.152297i | ||||
\(486\) | 18.7267 | 0.849458 | ||||||||
\(487\) | 8.33402i | 0.377651i | 0.982011 | + | 0.188825i | \(0.0604680\pi\) | ||||
−0.982011 | + | 0.188825i | \(0.939532\pi\) | |||||||
\(488\) | 0.910015i | 0.0411945i | ||||||||
\(489\) | −29.1307 | −1.31734 | ||||||||
\(490\) | 9.25700 | − | 7.33765i | 0.418188 | − | 0.331481i | ||||
\(491\) | 9.84934 | 0.444494 | 0.222247 | − | 0.974990i | \(-0.428661\pi\) | ||||
0.222247 | + | 0.974990i | \(0.428661\pi\) | |||||||
\(492\) | 21.1307i | 0.952645i | ||||||||
\(493\) | 0.646000i | 0.0290944i | ||||||||
\(494\) | 12.1507 | 0.546684 | ||||||||
\(495\) | −19.0793 | − | 24.0700i | −0.857552 | − | 1.08187i | ||||
\(496\) | −3.91934 | −0.175984 | ||||||||
\(497\) | − | 11.1893i | − | 0.501909i | ||||||
\(498\) | − | 5.45331i | − | 0.244369i | ||||||
\(499\) | 21.4134 | 0.958594 | 0.479297 | − | 0.877653i | \(-0.340892\pi\) | ||||
0.479297 | + | 0.877653i | \(0.340892\pi\) | |||||||
\(500\) | 10.1157 | − | 4.76166i | 0.452386 | − | 0.212948i | ||||
\(501\) | 65.3293 | 2.91870 | ||||||||
\(502\) | 10.8294i | 0.483338i | ||||||||
\(503\) | 5.36201i | 0.239080i | 0.992829 | + | 0.119540i | \(0.0381420\pi\) | ||||
−0.992829 | + | 0.119540i | \(0.961858\pi\) | |||||||
\(504\) | 24.0700 | 1.07216 | ||||||||
\(505\) | −7.96731 | − | 10.0514i | −0.354540 | − | 0.447279i | ||||
\(506\) | −15.0093 | −0.667246 | ||||||||
\(507\) | − | 9.83869i | − | 0.436951i | ||||||
\(508\) | − | 0.150665i | − | 0.00668467i | ||||||
\(509\) | 18.8294 | 0.834597 | 0.417298 | − | 0.908770i | \(-0.362977\pi\) | ||||
0.417298 | + | 0.908770i | \(0.362977\pi\) | |||||||
\(510\) | −5.50466 | + | 4.36333i | −0.243751 | + | 0.193211i | ||||
\(511\) | −11.0093 | −0.487024 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 46.9987i | 2.07504i | ||||||||
\(514\) | −24.5653 | −1.08353 | ||||||||
\(515\) | −16.7453 | + | 13.2733i | −0.737887 | + | 0.584893i | ||||
\(516\) | −13.4533 | −0.592249 | ||||||||
\(517\) | − | 21.1893i | − | 0.931904i | ||||||
\(518\) | 31.3947i | 1.37940i | ||||||||
\(519\) | 43.8174 | 1.92337 | ||||||||
\(520\) | −4.36333 | − | 5.50466i | −0.191345 | − | 0.241396i | ||||
\(521\) | 23.2920 | 1.02044 | 0.510221 | − | 0.860044i | \(-0.329564\pi\) | ||||
0.510221 | + | 0.860044i | \(0.329564\pi\) | |||||||
\(522\) | − | 4.43673i | − | 0.194190i | ||||||
\(523\) | − | 11.7360i | − | 0.513179i | −0.966521 | − | 0.256589i | \(-0.917401\pi\) | ||
0.966521 | − | 0.256589i | \(-0.0825988\pi\) | |||||||
\(524\) | −11.4533 | −0.500340 | ||||||||
\(525\) | 12.5653 | − | 53.5933i | 0.548397 | − | 2.33900i | ||||
\(526\) | 7.32131 | 0.319224 | ||||||||
\(527\) | − | 3.91934i | − | 0.170729i | ||||||
\(528\) | − | 6.28267i | − | 0.273418i | ||||||
\(529\) | −33.3200 | −1.44870 | ||||||||
\(530\) | −12.0807 | − | 15.2406i | −0.524750 | − | 0.662012i | ||||
\(531\) | 30.3200 | 1.31578 | ||||||||
\(532\) | 13.5560i | 0.587728i | ||||||||
\(533\) | − | 21.1307i | − | 0.915272i | ||||||
\(534\) | 13.8680 | 0.600127 | ||||||||
\(535\) | 18.9766 | − | 15.0420i | 0.820431 | − | 0.650323i | ||||
\(536\) | −10.2827 | −0.444144 | ||||||||
\(537\) | 44.9253i | 1.93867i | ||||||||
\(538\) | 5.37266i | 0.231632i | ||||||||
\(539\) | −10.5653 | −0.455082 | ||||||||
\(540\) | 21.2920 | − | 16.8773i | 0.916262 | − | 0.726284i | ||||
\(541\) | −36.2686 | −1.55931 | −0.779655 | − | 0.626209i | \(-0.784606\pi\) | ||||
−0.779655 | + | 0.626209i | \(0.784606\pi\) | |||||||
\(542\) | 9.18930i | 0.394714i | ||||||||
\(543\) | 33.5347i | 1.43911i | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | −14.0280 | − | 17.6974i | −0.600893 | − | 0.758071i | ||||
\(546\) | −34.5840 | −1.48006 | ||||||||
\(547\) | 33.8280i | 1.44638i | 0.690648 | + | 0.723191i | \(0.257326\pi\) | ||||
−0.690648 | + | 0.723191i | \(0.742674\pi\) | |||||||
\(548\) | 8.56534i | 0.365893i | ||||||||
\(549\) | 6.24998 | 0.266743 | ||||||||
\(550\) | −9.73599 | − | 2.28267i | −0.415144 | − | 0.0973335i | ||||
\(551\) | 2.49873 | 0.106449 | ||||||||
\(552\) | − | 23.5747i | − | 1.00340i | ||||||
\(553\) | 7.18930i | 0.305720i | ||||||||
\(554\) | 4.79667 | 0.203791 | ||||||||
\(555\) | 39.0866 | + | 49.3107i | 1.65913 | + | 2.09312i | ||||
\(556\) | 14.3013 | 0.606511 | ||||||||
\(557\) | 0.0293046i | 0.00124168i | 1.00000 | 0.000620838i | \(0.000197619\pi\) | |||||
−1.00000 | 0.000620838i | \(0.999802\pi\) | ||||||||
\(558\) | 26.9180i | 1.13953i | ||||||||
\(559\) | 13.4533 | 0.569015 | ||||||||
\(560\) | 6.14134 | − | 4.86799i | 0.259519 | − | 0.205710i | ||||
\(561\) | 6.28267 | 0.265255 | ||||||||
\(562\) | 31.2627i | 1.31874i | ||||||||
\(563\) | 12.6426i | 0.532823i | 0.963859 | + | 0.266411i | \(0.0858379\pi\) | ||||
−0.963859 | + | 0.266411i | \(0.914162\pi\) | |||||||
\(564\) | 33.2814 | 1.40140 | ||||||||
\(565\) | 8.51399 | − | 6.74870i | 0.358186 | − | 0.283920i | ||||
\(566\) | −17.0573 | −0.716971 | ||||||||
\(567\) | − | 61.5606i | − | 2.58530i | ||||||
\(568\) | − | 3.19269i | − | 0.133962i | ||||||
\(569\) | 2.15066 | 0.0901606 | 0.0450803 | − | 0.998983i | \(-0.485646\pi\) | ||||
0.0450803 | + | 0.998983i | \(0.485646\pi\) | |||||||
\(570\) | 16.8773 | + | 21.2920i | 0.706913 | + | 0.891824i | ||||
\(571\) | −30.4626 | −1.27482 | −0.637411 | − | 0.770524i | \(-0.719995\pi\) | ||||
−0.637411 | + | 0.770524i | \(0.719995\pi\) | |||||||
\(572\) | 6.28267i | 0.262692i | ||||||||
\(573\) | 14.3413i | 0.599116i | ||||||||
\(574\) | 23.5747 | 0.983988 | ||||||||
\(575\) | −36.5327 | − | 8.56534i | −1.52352 | − | 0.357200i | ||||
\(576\) | 6.86799 | 0.286166 | ||||||||
\(577\) | − | 16.9253i | − | 0.704609i | −0.935885 | − | 0.352304i | \(-0.885398\pi\) | ||
0.935885 | − | 0.352304i | \(-0.114602\pi\) | |||||||
\(578\) | − | 1.00000i | − | 0.0415945i | ||||||
\(579\) | 37.7546 | 1.56903 | ||||||||
\(580\) | −0.897297 | − | 1.13201i | −0.0372582 | − | 0.0470040i | ||||
\(581\) | −6.08405 | −0.252409 | ||||||||
\(582\) | 7.58532i | 0.314422i | ||||||||
\(583\) | 17.3947i | 0.720415i | ||||||||
\(584\) | −3.14134 | −0.129989 | ||||||||
\(585\) | −37.8060 | + | 29.9673i | −1.56309 | + | 1.23900i | ||||
\(586\) | −22.2534 | −0.919278 | ||||||||
\(587\) | − | 30.0560i | − | 1.24054i | −0.784387 | − | 0.620271i | \(-0.787022\pi\) | ||
0.784387 | − | 0.620271i | \(-0.212978\pi\) | |||||||
\(588\) | − | 16.5946i | − | 0.684352i | ||||||
\(589\) | −15.1600 | −0.624657 | ||||||||
\(590\) | 7.73599 | − | 6.13201i | 0.318485 | − | 0.252451i | ||||
\(591\) | 68.7640 | 2.82857 | ||||||||
\(592\) | 8.95798i | 0.368171i | ||||||||
\(593\) | − | 34.3200i | − | 1.40935i | −0.709529 | − | 0.704676i | \(-0.751092\pi\) | ||
0.709529 | − | 0.704676i | \(-0.248908\pi\) | |||||||
\(594\) | −24.3013 | −0.997096 | ||||||||
\(595\) | 4.86799 | + | 6.14134i | 0.199568 | + | 0.251770i | ||||
\(596\) | 10.0000 | 0.409616 | ||||||||
\(597\) | − | 22.2720i | − | 0.911533i | ||||||
\(598\) | 23.5747i | 0.964040i | ||||||||
\(599\) | 8.35994 | 0.341578 | 0.170789 | − | 0.985308i | \(-0.445368\pi\) | ||||
0.170789 | + | 0.985308i | \(0.445368\pi\) | |||||||
\(600\) | 3.58532 | − | 15.2920i | 0.146370 | − | 0.624293i | ||||
\(601\) | 18.5653 | 0.757296 | 0.378648 | − | 0.925541i | \(-0.376389\pi\) | ||||
0.378648 | + | 0.925541i | \(0.376389\pi\) | |||||||
\(602\) | 15.0093i | 0.611735i | ||||||||
\(603\) | 70.6213i | 2.87592i | ||||||||
\(604\) | −21.0280 | −0.855617 | ||||||||
\(605\) | −9.72303 | − | 12.2663i | −0.395297 | − | 0.498697i | ||||
\(606\) | −18.0187 | −0.731958 | ||||||||
\(607\) | 17.9860i | 0.730028i | 0.931002 | + | 0.365014i | \(0.118936\pi\) | ||||
−0.931002 | + | 0.365014i | \(0.881064\pi\) | |||||||
\(608\) | 3.86799i | 0.156868i | ||||||||
\(609\) | −7.11203 | −0.288194 | ||||||||
\(610\) | 1.59465 | − | 1.26401i | 0.0645655 | − | 0.0511785i | ||||
\(611\) | −33.2814 | −1.34642 | ||||||||
\(612\) | 6.86799i | 0.277622i | ||||||||
\(613\) | − | 2.04796i | − | 0.0827164i | −0.999144 | − | 0.0413582i | \(-0.986832\pi\) | ||
0.999144 | − | 0.0413582i | \(-0.0131685\pi\) | |||||||
\(614\) | 29.7360 | 1.20005 | ||||||||
\(615\) | 37.0280 | − | 29.3506i | 1.49311 | − | 1.18353i | ||||
\(616\) | −7.00933 | −0.282414 | ||||||||
\(617\) | 1.74663i | 0.0703168i | 0.999382 | + | 0.0351584i | \(0.0111936\pi\) | ||||
−0.999382 | + | 0.0351584i | \(0.988806\pi\) | |||||||
\(618\) | 30.0187i | 1.20753i | ||||||||
\(619\) | 13.0093 | 0.522889 | 0.261445 | − | 0.965219i | \(-0.415801\pi\) | ||||
0.261445 | + | 0.965219i | \(0.415801\pi\) | |||||||
\(620\) | 5.44398 | + | 6.86799i | 0.218636 | + | 0.275825i | ||||
\(621\) | −91.1867 | −3.65919 | ||||||||
\(622\) | − | 23.1820i | − | 0.929515i | ||||||
\(623\) | − | 15.4720i | − | 0.619871i | ||||||
\(624\) | −9.86799 | −0.395036 | ||||||||
\(625\) | −22.3947 | − | 11.1120i | −0.895788 | − | 0.444481i | ||||
\(626\) | 23.4533 | 0.937383 | ||||||||
\(627\) | − | 24.3013i | − | 0.970502i | ||||||
\(628\) | 21.5747i | 0.860923i | ||||||||
\(629\) | −8.95798 | −0.357178 | ||||||||
\(630\) | −33.4333 | − | 42.1787i | −1.33202 | − | 1.68044i | ||||
\(631\) | 0.161312 | 0.00642173 | 0.00321086 | − | 0.999995i | \(-0.498978\pi\) | ||||
0.00321086 | + | 0.999995i | \(0.498978\pi\) | |||||||
\(632\) | 2.05135i | 0.0815984i | ||||||||
\(633\) | 47.7147i | 1.89649i | ||||||||
\(634\) | −3.60737 | −0.143267 | ||||||||
\(635\) | −0.264015 | + | 0.209274i | −0.0104771 | + | 0.00830479i | ||||
\(636\) | −27.3213 | −1.08336 | ||||||||
\(637\) | 16.5946i | 0.657504i | ||||||||
\(638\) | 1.29200i | 0.0511508i | ||||||||
\(639\) | −21.9274 | −0.867433 | ||||||||
\(640\) | 1.75233 | − | 1.38900i | 0.0692670 | − | 0.0549052i | ||||
\(641\) | 9.53736 | 0.376703 | 0.188352 | − | 0.982102i | \(-0.439686\pi\) | ||||
0.188352 | + | 0.982102i | \(0.439686\pi\) | |||||||
\(642\) | − | 34.0187i | − | 1.34261i | ||||||
\(643\) | − | 34.1986i | − | 1.34866i | −0.738429 | − | 0.674331i | \(-0.764432\pi\) | ||
0.738429 | − | 0.674331i | \(-0.235568\pi\) | |||||||
\(644\) | −26.3013 | −1.03642 | ||||||||
\(645\) | 18.6867 | + | 23.5747i | 0.735788 | + | 0.928252i | ||||
\(646\) | −3.86799 | −0.152184 | ||||||||
\(647\) | − | 1.61076i | − | 0.0633254i | −0.999499 | − | 0.0316627i | \(-0.989920\pi\) | ||
0.999499 | − | 0.0316627i | \(-0.0100802\pi\) | |||||||
\(648\) | − | 17.5653i | − | 0.690032i | ||||||
\(649\) | −8.82936 | −0.346583 | ||||||||
\(650\) | −3.58532 | + | 15.2920i | −0.140628 | + | 0.599802i | ||||
\(651\) | 43.1493 | 1.69116 | ||||||||
\(652\) | 9.27334i | 0.363172i | ||||||||
\(653\) | 37.3993i | 1.46355i | 0.681547 | + | 0.731774i | \(0.261307\pi\) | ||||
−0.681547 | + | 0.731774i | \(0.738693\pi\) | |||||||
\(654\) | −31.7253 | −1.24056 | ||||||||
\(655\) | 15.9087 | + | 20.0700i | 0.621604 | + | 0.784200i | ||||
\(656\) | 6.72666 | 0.262632 | ||||||||
\(657\) | 21.5747i | 0.841708i | ||||||||
\(658\) | − | 37.1307i | − | 1.44750i | ||||||
\(659\) | 2.07340 | 0.0807681 | 0.0403841 | − | 0.999184i | \(-0.487142\pi\) | ||||
0.0403841 | + | 0.999184i | \(0.487142\pi\) | |||||||
\(660\) | −11.0093 | + | 8.72666i | −0.428538 | + | 0.339685i | ||||
\(661\) | −46.4040 | −1.80491 | −0.902454 | − | 0.430787i | \(-0.858236\pi\) | ||||
−0.902454 | + | 0.430787i | \(0.858236\pi\) | |||||||
\(662\) | − | 33.9053i | − | 1.31777i | ||||||
\(663\) | − | 9.86799i | − | 0.383241i | ||||||
\(664\) | −1.73599 | −0.0673693 | ||||||||
\(665\) | 23.7546 | − | 18.8294i | 0.921166 | − | 0.730171i | ||||
\(666\) | 61.5233 | 2.38398 | ||||||||
\(667\) | 4.84802i | 0.187716i | ||||||||
\(668\) | − | 20.7967i | − | 0.804647i | ||||||
\(669\) | −17.6040 | −0.680609 | ||||||||
\(670\) | 14.2827 | + | 18.0187i | 0.551788 | + | 0.696121i | ||||
\(671\) | −1.82003 | −0.0702615 | ||||||||
\(672\) | − | 11.0093i | − | 0.424694i | ||||||
\(673\) | 17.6812i | 0.681562i | 0.940143 | + | 0.340781i | \(0.110691\pi\) | ||||
−0.940143 | + | 0.340781i | \(0.889309\pi\) | |||||||
\(674\) | 8.33063 | 0.320884 | ||||||||
\(675\) | −59.1493 | − | 13.8680i | −2.27666 | − | 0.533779i | ||||
\(676\) | −3.13201 | −0.120462 | ||||||||
\(677\) | 29.2007i | 1.12227i | 0.827723 | + | 0.561137i | \(0.189636\pi\) | ||||
−0.827723 | + | 0.561137i | \(0.810364\pi\) | |||||||
\(678\) | − | 15.2627i | − | 0.586160i | ||||||
\(679\) | 8.46264 | 0.324766 | ||||||||
\(680\) | 1.38900 | + | 1.75233i | 0.0532659 | + | 0.0671989i | ||||
\(681\) | 24.3934 | 0.934757 | ||||||||
\(682\) | − | 7.83869i | − | 0.300159i | ||||||
\(683\) | − | 2.04796i | − | 0.0783631i | −0.999232 | − | 0.0391815i | \(-0.987525\pi\) | ||
0.999232 | − | 0.0391815i | \(-0.0124751\pi\) | |||||||
\(684\) | 26.5653 | 1.01575 | ||||||||
\(685\) | 15.0093 | − | 11.8973i | 0.573477 | − | 0.454572i | ||||
\(686\) | 6.01866 | 0.229793 | ||||||||
\(687\) | 40.8667i | 1.55916i | ||||||||
\(688\) | 4.28267i | 0.163275i | ||||||||
\(689\) | 27.3213 | 1.04086 | ||||||||
\(690\) | −41.3107 | + | 32.7453i | −1.57267 | + | 1.24659i | ||||
\(691\) | −24.4881 | −0.931570 | −0.465785 | − | 0.884898i | \(-0.654228\pi\) | ||||
−0.465785 | + | 0.884898i | \(0.654228\pi\) | |||||||
\(692\) | − | 13.9486i | − | 0.530248i | ||||||
\(693\) | 48.1400i | 1.82869i | ||||||||
\(694\) | −7.14134 | −0.271081 | ||||||||
\(695\) | −19.8646 | − | 25.0607i | −0.753507 | − | 0.950606i | ||||
\(696\) | −2.02930 | −0.0769206 | ||||||||
\(697\) | 6.72666i | 0.254790i | ||||||||
\(698\) | − | 4.64939i | − | 0.175982i | ||||||
\(699\) | −34.1693 | −1.29240 | ||||||||
\(700\) | −17.0607 | − | 4.00000i | −0.644833 | − | 0.151186i | ||||
\(701\) | 29.7360 | 1.12311 | 0.561556 | − | 0.827439i | \(-0.310203\pi\) | ||||
0.561556 | + | 0.827439i | \(0.310203\pi\) | |||||||
\(702\) | 38.1693i | 1.44061i | ||||||||
\(703\) | 34.6494i | 1.30683i | ||||||||
\(704\) | −2.00000 | −0.0753778 | ||||||||
\(705\) | −46.2279 | − | 58.3200i | −1.74104 | − | 2.19646i | ||||
\(706\) | −20.8480 | −0.784625 | ||||||||
\(707\) | 20.1027i | 0.756040i | ||||||||
\(708\) | − | 13.8680i | − | 0.521191i | ||||||
\(709\) | 4.08066 | 0.153252 | 0.0766261 | − | 0.997060i | \(-0.475585\pi\) | ||||
0.0766261 | + | 0.997060i | \(0.475585\pi\) | |||||||
\(710\) | −5.59465 | + | 4.43466i | −0.209963 | + | 0.166430i | ||||
\(711\) | 14.0887 | 0.528366 | ||||||||
\(712\) | − | 4.41468i | − | 0.165447i | ||||||
\(713\) | − | 29.4134i | − | 1.10154i | ||||||
\(714\) | 11.0093 | 0.412014 | ||||||||
\(715\) | 11.0093 | − | 8.72666i | 0.411726 | − | 0.326358i | ||||
\(716\) | 14.3013 | 0.534466 | ||||||||
\(717\) | 76.3386i | 2.85092i | ||||||||
\(718\) | − | 12.4626i | − | 0.465102i | ||||||
\(719\) | −38.7020 | −1.44334 | −0.721670 | − | 0.692237i | \(-0.756625\pi\) | ||||
−0.721670 | + | 0.692237i | \(0.756625\pi\) | |||||||
\(720\) | −9.53967 | − | 12.0350i | −0.355522 | − | 0.448518i | ||||
\(721\) | 33.4906 | 1.24726 | ||||||||
\(722\) | − | 4.03863i | − | 0.150302i | ||||||
\(723\) | − | 62.3786i | − | 2.31988i | ||||||
\(724\) | 10.6753 | 0.396745 | ||||||||
\(725\) | −0.737304 | + | 3.14473i | −0.0273828 | + | 0.116792i | ||||
\(726\) | −21.9894 | −0.816101 | ||||||||
\(727\) | 11.9894i | 0.444660i | 0.974971 | + | 0.222330i | \(0.0713663\pi\) | ||||
−0.974971 | + | 0.222330i | \(0.928634\pi\) | |||||||
\(728\) | 11.0093i | 0.408033i | ||||||||
\(729\) | −6.13069 | −0.227063 | ||||||||
\(730\) | 4.36333 | + | 5.50466i | 0.161494 | + | 0.203737i | ||||
\(731\) | −4.28267 | −0.158400 | ||||||||
\(732\) | − | 2.85866i | − | 0.105659i | ||||||
\(733\) | 46.3973i | 1.71372i | 0.515548 | + | 0.856861i | \(0.327588\pi\) | ||||
−0.515548 | + | 0.856861i | \(0.672412\pi\) | |||||||
\(734\) | 5.22199 | 0.192747 | ||||||||
\(735\) | −29.0793 | + | 23.0500i | −1.07261 | + | 0.850213i | ||||
\(736\) | −7.50466 | −0.276626 | ||||||||
\(737\) | − | 20.5653i | − | 0.757534i | ||||||
\(738\) | − | 46.1986i | − | 1.70059i | ||||||
\(739\) | 43.6413 | 1.60537 | 0.802685 | − | 0.596403i | \(-0.203404\pi\) | ||||
0.802685 | + | 0.596403i | \(0.203404\pi\) | |||||||
\(740\) | 15.6974 | − | 12.4427i | 0.577046 | − | 0.457401i | ||||
\(741\) | −38.1693 | −1.40219 | ||||||||
\(742\) | 30.4813i | 1.11900i | ||||||||
\(743\) | − | 11.6447i | − | 0.427202i | −0.976921 | − | 0.213601i | \(-0.931481\pi\) | ||
0.976921 | − | 0.213601i | \(-0.0685192\pi\) | |||||||
\(744\) | 12.3120 | 0.451379 | ||||||||
\(745\) | −13.8900 | − | 17.5233i | −0.508892 | − | 0.642005i | ||||
\(746\) | 26.4626 | 0.968866 | ||||||||
\(747\) | 11.9227i | 0.436230i | ||||||||
\(748\) | − | 2.00000i | − | 0.0731272i | ||||||
\(749\) | −37.9533 | −1.38678 | ||||||||
\(750\) | −31.7767 | + | 14.9580i | −1.16032 | + | 0.546188i | ||||
\(751\) | −3.72072 | −0.135771 | −0.0678854 | − | 0.997693i | \(-0.521625\pi\) | ||||
−0.0678854 | + | 0.997693i | \(0.521625\pi\) | |||||||
\(752\) | − | 10.5946i | − | 0.386347i | ||||||
\(753\) | − | 34.0187i | − | 1.23971i | ||||||
\(754\) | 2.02930 | 0.0739029 | ||||||||
\(755\) | 29.2080 | + | 36.8480i | 1.06299 | + | 1.34104i | ||||
\(756\) | −42.5840 | −1.54877 | ||||||||
\(757\) | 38.7533i | 1.40851i | 0.709945 | + | 0.704257i | \(0.248720\pi\) | ||||
−0.709945 | + | 0.704257i | \(0.751280\pi\) | |||||||
\(758\) | − | 8.70800i | − | 0.316289i | ||||||
\(759\) | 47.1493 | 1.71141 | ||||||||
\(760\) | 6.77801 | − | 5.37266i | 0.245864 | − | 0.194887i | ||||
\(761\) | −46.6027 | −1.68935 | −0.844673 | − | 0.535283i | \(-0.820205\pi\) | ||||
−0.844673 | + | 0.535283i | \(0.820205\pi\) | |||||||
\(762\) | 0.473289i | 0.0171454i | ||||||||
\(763\) | 35.3947i | 1.28137i | ||||||||
\(764\) | 4.56534 | 0.165168 | ||||||||
\(765\) | 12.0350 | − | 9.53967i | 0.435127 | − | 0.344907i | ||||
\(766\) | 33.8094 | 1.22158 | ||||||||
\(767\) | 13.8680i | 0.500744i | ||||||||
\(768\) | − | 3.14134i | − | 0.113353i | ||||||
\(769\) | 36.9987 | 1.33421 | 0.667103 | − | 0.744965i | \(-0.267534\pi\) | ||||
0.667103 | + | 0.744965i | \(0.267534\pi\) | |||||||
\(770\) | 9.73599 | + | 12.2827i | 0.350861 | + | 0.442637i | ||||
\(771\) | 77.1680 | 2.77914 | ||||||||
\(772\) | − | 12.0187i | − | 0.432561i | ||||||
\(773\) | 19.9813i | 0.718679i | 0.933207 | + | 0.359339i | \(0.116998\pi\) | ||||
−0.933207 | + | 0.359339i | \(0.883002\pi\) | |||||||
\(774\) | 29.4134 | 1.05724 | ||||||||
\(775\) | 4.47329 | − | 19.0793i | 0.160685 | − | 0.685350i | ||||
\(776\) | 2.41468 | 0.0866819 | ||||||||
\(777\) | − | 98.6213i | − | 3.53802i | ||||||
\(778\) | 22.4626i | 0.805325i | ||||||||
\(779\) | 26.0187 | 0.932215 | ||||||||
\(780\) | 13.7067 | + | 17.2920i | 0.490778 | + | 0.619153i | ||||
\(781\) | 6.38538 | 0.228487 | ||||||||
\(782\) | − | 7.50466i | − | 0.268366i | ||||||
\(783\) | 7.84934i | 0.280512i | ||||||||
\(784\) | −5.28267 | −0.188667 | ||||||||
\(785\) | 37.8060 | − | 29.9673i | 1.34935 | − | 1.06958i | ||||
\(786\) | 35.9787 | 1.28332 | ||||||||
\(787\) | − | 18.4520i | − | 0.657743i | −0.944375 | − | 0.328871i | \(-0.893332\pi\) | ||
0.944375 | − | 0.328871i | \(-0.106668\pi\) | |||||||
\(788\) | − | 21.8900i | − | 0.779800i | ||||||
\(789\) | −22.9987 | −0.818775 | ||||||||
\(790\) | 3.59465 | − | 2.84934i | 0.127892 | − | 0.101375i | ||||
\(791\) | −17.0280 | −0.605445 | ||||||||
\(792\) | 13.7360i | 0.488087i | ||||||||
\(793\) | 2.85866i | 0.101514i | ||||||||
\(794\) | −23.8060 | −0.844843 | ||||||||
\(795\) | 37.9494 | + | 47.8760i | 1.34593 | + | 1.69799i | ||||
\(796\) | −7.08998 | −0.251298 | ||||||||
\(797\) | − | 9.11203i | − | 0.322765i | −0.986892 | − | 0.161382i | \(-0.948405\pi\) | ||
0.986892 | − | 0.161382i | \(-0.0515952\pi\) | |||||||
\(798\) | − | 42.5840i | − | 1.50746i | ||||||
\(799\) | 10.5946 | 0.374812 | ||||||||
\(800\) | −4.86799 | − | 1.14134i | −0.172110 | − | 0.0403523i | ||||
\(801\) | −30.3200 | −1.07130 | ||||||||
\(802\) | 14.4626i | 0.510694i | ||||||||
\(803\) | − | 6.28267i | − | 0.221711i | ||||||
\(804\) | 32.3013 | 1.13918 | ||||||||
\(805\) | 36.5327 | + | 46.0887i | 1.28761 | + | 1.62441i | ||||
\(806\) | −12.3120 | −0.433671 | ||||||||
\(807\) | − | 16.8773i | − | 0.594110i | ||||||
\(808\) | 5.73599i | 0.201791i | ||||||||
\(809\) | 52.1587 | 1.83380 | 0.916901 | − | 0.399115i | \(-0.130683\pi\) | ||||
0.916901 | + | 0.399115i | \(0.130683\pi\) | |||||||
\(810\) | −30.7803 | + | 24.3983i | −1.08151 | + | 0.857270i | ||||
\(811\) | 31.6519 | 1.11145 | 0.555725 | − | 0.831366i | \(-0.312441\pi\) | ||||
0.555725 | + | 0.831366i | \(0.312441\pi\) | |||||||
\(812\) | 2.26401i | 0.0794513i | ||||||||
\(813\) | − | 28.8667i | − | 1.01240i | ||||||
\(814\) | −17.9160 | −0.627954 | ||||||||
\(815\) | 16.2500 | − | 12.8807i | 0.569212 | − | 0.451192i | ||||
\(816\) | 3.14134 | 0.109969 | ||||||||
\(817\) | 16.5653i | 0.579548i | ||||||||
\(818\) | 6.13201i | 0.214401i | ||||||||
\(819\) | 75.6120 | 2.64210 | ||||||||
\(820\) | −9.34335 | − | 11.7873i | −0.326284 | − | 0.411632i | ||||
\(821\) | 19.3327 | 0.674716 | 0.337358 | − | 0.941376i | \(-0.390467\pi\) | ||||
0.337358 | + | 0.941376i | \(0.390467\pi\) | |||||||
\(822\) | − | 26.9066i | − | 0.938476i | ||||||
\(823\) | 11.5633i | 0.403070i | 0.979481 | + | 0.201535i | \(0.0645930\pi\) | ||||
−0.979481 | + | 0.201535i | \(0.935407\pi\) | |||||||
\(824\) | 9.55602 | 0.332900 | ||||||||
\(825\) | 30.5840 | + | 7.17064i | 1.06480 | + | 0.249650i | ||||
\(826\) | −15.4720 | −0.538339 | ||||||||
\(827\) | 35.4320i | 1.23209i | 0.787710 | + | 0.616046i | \(0.211266\pi\) | ||||
−0.787710 | + | 0.616046i | \(0.788734\pi\) | |||||||
\(828\) | 51.5420i | 1.79121i | ||||||||
\(829\) | 23.1307 | 0.803362 | 0.401681 | − | 0.915780i | \(-0.368426\pi\) | ||||
0.401681 | + | 0.915780i | \(0.368426\pi\) | |||||||
\(830\) | 2.41129 | + | 3.04202i | 0.0836971 | + | 0.105590i | ||||
\(831\) | −15.0679 | −0.522701 | ||||||||
\(832\) | 3.14134i | 0.108906i | ||||||||
\(833\) | − | 5.28267i | − | 0.183034i | ||||||
\(834\) | −44.9253 | −1.55564 | ||||||||
\(835\) | −36.4427 | + | 28.8867i | −1.26115 | + | 0.999664i | ||||
\(836\) | −7.73599 | −0.267555 | ||||||||
\(837\) | − | 47.6226i | − | 1.64608i | ||||||
\(838\) | − | 21.8387i | − | 0.754405i | ||||||
\(839\) | −7.28861 | −0.251631 | −0.125815 | − | 0.992054i | \(-0.540155\pi\) | ||||
−0.125815 | + | 0.992054i | \(0.540155\pi\) | |||||||
\(840\) | −19.2920 | + | 15.2920i | −0.665637 | + | 0.527624i | ||||
\(841\) | −28.5827 | −0.985610 | ||||||||
\(842\) | 3.71733i | 0.128108i | ||||||||
\(843\) | − | 98.2066i | − | 3.38242i | ||||||
\(844\) | 15.1893 | 0.522837 | ||||||||
\(845\) | 4.35037 | + | 5.48832i | 0.149657 | + | 0.188804i | ||||
\(846\) | −72.7640 | −2.50168 | ||||||||
\(847\) | 24.5327i | 0.842952i | ||||||||
\(848\) | 8.69735i | 0.298668i | ||||||||
\(849\) | 53.5827 | 1.83895 | ||||||||
\(850\) | 1.14134 | − | 4.86799i | 0.0391475 | − | 0.166971i | ||||
\(851\) | −67.2266 | −2.30450 | ||||||||
\(852\) | 10.0293i | 0.343598i | ||||||||
\(853\) | − | 15.7033i | − | 0.537670i | −0.963186 | − | 0.268835i | \(-0.913361\pi\) | ||
0.963186 | − | 0.268835i | \(-0.0866387\pi\) | |||||||
\(854\) | −3.18930 | −0.109136 | ||||||||
\(855\) | −36.8994 | − | 46.5513i | −1.26193 | − | 1.59202i | ||||
\(856\) | −10.8294 | −0.370140 | ||||||||
\(857\) | − | 36.7347i | − | 1.25483i | −0.778684 | − | 0.627416i | \(-0.784113\pi\) | ||
0.778684 | − | 0.627416i | \(-0.215887\pi\) | |||||||
\(858\) | − | 19.7360i | − | 0.673775i | ||||||
\(859\) | −6.99868 | −0.238792 | −0.119396 | − | 0.992847i | \(-0.538096\pi\) | ||||
−0.119396 | + | 0.992847i | \(0.538096\pi\) | |||||||
\(860\) | 7.50466 | − | 5.94865i | 0.255907 | − | 0.202847i | ||||
\(861\) | −74.0560 | −2.52382 | ||||||||
\(862\) | − | 11.9673i | − | 0.407608i | ||||||
\(863\) | − | 21.2334i | − | 0.722793i | −0.932412 | − | 0.361397i | \(-0.882300\pi\) | ||
0.932412 | − | 0.361397i | \(-0.117700\pi\) | |||||||
\(864\) | −12.1507 | −0.413374 | ||||||||
\(865\) | −24.4427 | + | 19.3747i | −0.831076 | + | 0.658761i | ||||
\(866\) | 18.3013 | 0.621904 | ||||||||
\(867\) | 3.14134i | 0.106685i | ||||||||
\(868\) | − | 13.7360i | − | 0.466230i | ||||||
\(869\) | −4.10270 | −0.139175 | ||||||||
\(870\) | 2.81871 | + | 3.55602i | 0.0955633 | + | 0.120560i | ||||
\(871\) | −32.3013 | −1.09449 | ||||||||
\(872\) | 10.0993i | 0.342006i | ||||||||
\(873\) | − | 16.5840i | − | 0.561283i | ||||||
\(874\) | −29.0280 | −0.981886 | ||||||||
\(875\) | 16.6880 | + | 35.4520i | 0.564158 | + | 1.19850i | ||||
\(876\) | 9.86799 | 0.333409 | ||||||||
\(877\) | − | 6.31537i | − | 0.213255i | −0.994299 | − | 0.106627i | \(-0.965995\pi\) | ||
0.994299 | − | 0.106627i | \(-0.0340052\pi\) | |||||||
\(878\) | 31.0793i | 1.04888i | ||||||||
\(879\) | 69.9053 | 2.35785 | ||||||||
\(880\) | 2.77801 | + | 3.50466i | 0.0936466 | + | 0.118142i | ||||
\(881\) | 14.0373 | 0.472929 | 0.236465 | − | 0.971640i | \(-0.424011\pi\) | ||||
0.236465 | + | 0.971640i | \(0.424011\pi\) | |||||||
\(882\) | 36.2814i | 1.22166i | ||||||||
\(883\) | 42.8853i | 1.44321i | 0.692307 | + | 0.721603i | \(0.256594\pi\) | ||||
−0.692307 | + | 0.721603i | \(0.743406\pi\) | |||||||
\(884\) | −3.14134 | −0.105655 | ||||||||
\(885\) | −24.3013 | + | 19.2627i | −0.816880 | + | 0.647508i | ||||
\(886\) | 29.3947 | 0.987534 | ||||||||
\(887\) | 7.66598i | 0.257398i | 0.991684 | + | 0.128699i | \(0.0410802\pi\) | ||||
−0.991684 | + | 0.128699i | \(0.958920\pi\) | |||||||
\(888\) | − | 28.1400i | − | 0.944317i | ||||||
\(889\) | 0.528030 | 0.0177095 | ||||||||
\(890\) | −7.73599 | + | 6.13201i | −0.259311 | + | 0.205545i | ||||
\(891\) | 35.1307 | 1.17692 | ||||||||
\(892\) | 5.60398i | 0.187635i | ||||||||
\(893\) | − | 40.9800i | − | 1.37134i | ||||||
\(894\) | −31.4134 | −1.05062 | ||||||||
\(895\) | −19.8646 | − | 25.0607i | −0.664000 | − | 0.837686i | ||||
\(896\) | −3.50466 | −0.117083 | ||||||||
\(897\) | − | 74.0560i | − | 2.47266i | ||||||
\(898\) | − | 14.1027i | − | 0.470613i | ||||||
\(899\) | −2.53190 | −0.0844435 | ||||||||
\(900\) | −7.83869 | + | 33.4333i | −0.261290 | + | 1.11444i | ||||
\(901\) | −8.69735 | −0.289751 | ||||||||
\(902\) | 13.4533i | 0.447946i | ||||||||
\(903\) | − | 47.1493i | − | 1.56903i | ||||||
\(904\) | −4.85866 | −0.161597 | ||||||||
\(905\) | −14.8280 | − | 18.7067i | −0.492901 | − | 0.621831i | ||||
\(906\) | 66.0560 | 2.19456 | ||||||||
\(907\) | − | 49.6226i | − | 1.64769i | −0.566813 | − | 0.823846i | \(-0.691824\pi\) | ||
0.566813 | − | 0.823846i | \(-0.308176\pi\) | |||||||
\(908\) | − | 7.76529i | − | 0.257700i | ||||||
\(909\) | 39.3947 | 1.30664 | ||||||||
\(910\) | 19.2920 | − | 15.2920i | 0.639524 | − | 0.506925i | ||||
\(911\) | −16.4953 | −0.546515 | −0.273257 | − | 0.961941i | \(-0.588101\pi\) | ||||
−0.273257 | + | 0.961941i | \(0.588101\pi\) | |||||||
\(912\) | − | 12.1507i | − | 0.402349i | ||||||
\(913\) | − | 3.47197i | − | 0.114905i | ||||||
\(914\) | 30.8294 | 1.01974 | ||||||||
\(915\) | −5.00933 | + | 3.97070i | −0.165603 | + | 0.131267i | ||||
\(916\) | 13.0093 | 0.429840 | ||||||||
\(917\) | − | 40.1400i | − | 1.32554i | ||||||
\(918\) | − | 12.1507i | − | 0.401032i | ||||||
\(919\) | −12.2640 | −0.404553 | −0.202276 | − | 0.979329i | \(-0.564834\pi\) | ||||
−0.202276 | + | 0.979329i | \(0.564834\pi\) | |||||||
\(920\) | 10.4240 | + | 13.1507i | 0.343669 | + | 0.433565i | ||||
\(921\) | −93.4107 | −3.07799 | ||||||||
\(922\) | 4.38538i | 0.144425i | ||||||||
\(923\) | − | 10.0293i | − | 0.330119i | ||||||
\(924\) | 22.0187 | 0.724361 | ||||||||
\(925\) | −43.6074 | − | 10.2241i | −1.43380 | − | 0.336165i | ||||
\(926\) | −2.55733 | −0.0840392 | ||||||||
\(927\) | − | 65.6306i | − | 2.15559i | ||||||
\(928\) | 0.646000i | 0.0212060i | ||||||||
\(929\) | 20.1214 | 0.660160 | 0.330080 | − | 0.943953i | \(-0.392924\pi\) | ||||
0.330080 | + | 0.943953i | \(0.392924\pi\) | |||||||
\(930\) | −17.1014 | − | 21.5747i | −0.560776 | − | 0.707461i | ||||
\(931\) | −20.4333 | −0.669676 | ||||||||
\(932\) | 10.8773i | 0.356299i | ||||||||
\(933\) | 72.8226i | 2.38410i | ||||||||
\(934\) | 12.6240 | 0.413068 | ||||||||
\(935\) | −3.50466 | + | 2.77801i | −0.114615 | + | 0.0908506i | ||||
\(936\) | 21.5747 | 0.705190 | ||||||||
\(937\) | − | 33.1706i | − | 1.08364i | −0.840495 | − | 0.541819i | \(-0.817736\pi\) | ||
0.840495 | − | 0.541819i | \(-0.182264\pi\) | |||||||
\(938\) | − | 36.0373i | − | 1.17666i | ||||||
\(939\) | −73.6747 | −2.40428 | ||||||||
\(940\) | −18.5653 | + | 14.7160i | −0.605535 | + | 0.479983i | ||||
\(941\) | 24.9100 | 0.812043 | 0.406022 | − | 0.913863i | \(-0.366916\pi\) | ||||
0.406022 | + | 0.913863i | \(0.366916\pi\) | |||||||
\(942\) | − | 67.7733i | − | 2.20817i | ||||||
\(943\) | 50.4813i | 1.64390i | ||||||||
\(944\) | −4.41468 | −0.143686 | ||||||||
\(945\) | 59.1493 | + | 74.6213i | 1.92413 | + | 2.42743i | ||||
\(946\) | −8.56534 | −0.278483 | ||||||||
\(947\) | 11.8680i | 0.385658i | 0.981232 | + | 0.192829i | \(0.0617663\pi\) | ||||
−0.981232 | + | 0.192829i | \(0.938234\pi\) | |||||||
\(948\) | − | 6.44398i | − | 0.209291i | ||||||
\(949\) | −9.86799 | −0.320329 | ||||||||
\(950\) | −18.8294 | − | 4.41468i | −0.610905 | − | 0.143231i | ||||
\(951\) | 11.3320 | 0.367464 | ||||||||
\(952\) | − | 3.50466i | − | 0.113587i | ||||||
\(953\) | − | 34.8667i | − | 1.12944i | −0.825282 | − | 0.564721i | \(-0.808984\pi\) | ||
0.825282 | − | 0.564721i | \(-0.191016\pi\) | |||||||
\(954\) | 59.7333 | 1.93394 | ||||||||
\(955\) | −6.34128 | − | 8.00000i | −0.205199 | − | 0.258874i | ||||
\(956\) | 24.3013 | 0.785961 | ||||||||
\(957\) | − | 4.05861i | − | 0.131196i | ||||||
\(958\) | 7.75803i | 0.250651i | ||||||||
\(959\) | −30.0187 | −0.969353 | ||||||||
\(960\) | −5.50466 | + | 4.36333i | −0.177662 | + | 0.140826i | ||||
\(961\) | −15.6387 | −0.504476 | ||||||||
\(962\) | 28.1400i | 0.907271i | ||||||||
\(963\) | 74.3760i | 2.39673i | ||||||||
\(964\) | −19.8573 | −0.639562 | ||||||||
\(965\) | −21.0607 | + | 16.6940i | −0.677967 | + | 0.537398i | ||||
\(966\) | 82.6213 | 2.65830 | ||||||||
\(967\) | − | 13.0934i | − | 0.421055i | −0.977588 | − | 0.210527i | \(-0.932482\pi\) | ||
0.977588 | − | 0.210527i | \(-0.0675181\pi\) | |||||||
\(968\) | 7.00000i | 0.224989i | ||||||||
\(969\) | 12.1507 | 0.390336 | ||||||||
\(970\) | −3.35400 | − | 4.23132i | −0.107690 | − | 0.135860i | ||||
\(971\) | 27.3586 | 0.877980 | 0.438990 | − | 0.898492i | \(-0.355336\pi\) | ||||
0.438990 | + | 0.898492i | \(0.355336\pi\) | |||||||
\(972\) | 18.7267i | 0.600658i | ||||||||
\(973\) | 50.1214i | 1.60682i | ||||||||
\(974\) | −8.33402 | −0.267039 | ||||||||
\(975\) | 11.2627 | − | 48.0373i | 0.360695 | − | 1.53843i | ||||
\(976\) | −0.910015 | −0.0291289 | ||||||||
\(977\) | 52.5441i | 1.68103i | 0.541786 | + | 0.840517i | \(0.317748\pi\) | ||||
−0.541786 | + | 0.840517i | \(0.682252\pi\) | |||||||
\(978\) | − | 29.1307i | − | 0.931497i | ||||||
\(979\) | 8.82936 | 0.282188 | ||||||||
\(980\) | 7.33765 | + | 9.25700i | 0.234393 | + | 0.295704i | ||||
\(981\) | 69.3620 | 2.21456 | ||||||||
\(982\) | 9.84934i | 0.314305i | ||||||||
\(983\) | 25.7873i | 0.822488i | 0.911525 | + | 0.411244i | \(0.134906\pi\) | ||||
−0.911525 | + | 0.411244i | \(0.865094\pi\) | |||||||
\(984\) | −21.1307 | −0.673622 | ||||||||
\(985\) | −38.3586 | + | 30.4054i | −1.22221 | + | 0.968795i | ||||
\(986\) | −0.646000 | −0.0205728 | ||||||||
\(987\) | 116.640i | 3.71269i | ||||||||
\(988\) | 12.1507i | 0.386564i | ||||||||
\(989\) | −32.1400 | −1.02199 | ||||||||
\(990\) | 24.0700 | − | 19.0793i | 0.764995 | − | 0.606381i | ||||
\(991\) | 55.8980 | 1.77566 | 0.887830 | − | 0.460172i | \(-0.152212\pi\) | ||||
0.887830 | + | 0.460172i | \(0.152212\pi\) | |||||||
\(992\) | − | 3.91934i | − | 0.124439i | ||||||
\(993\) | 106.508i | 3.37993i | ||||||||
\(994\) | 11.1893 | 0.354903 | ||||||||
\(995\) | 9.84802 | + | 12.4240i | 0.312203 | + | 0.393868i | ||||
\(996\) | 5.45331 | 0.172795 | ||||||||
\(997\) | − | 33.6260i | − | 1.06495i | −0.846447 | − | 0.532473i | \(-0.821263\pi\) | ||
0.846447 | − | 0.532473i | \(-0.178737\pi\) | |||||||
\(998\) | 21.4134i | 0.677828i | ||||||||
\(999\) | −108.845 | −3.44372 |
(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 | 170.2.c.b.69.4 | yes | 6 | |
3.2 | odd | 2 | 1530.2.d.g.919.2 | 6 | |||
4.3 | odd | 2 | 1360.2.e.c.1089.6 | 6 | |||
5.2 | odd | 4 | 850.2.a.p.1.1 | 3 | |||
5.3 | odd | 4 | 850.2.a.q.1.3 | 3 | |||
5.4 | even | 2 | inner | 170.2.c.b.69.3 | ✓ | 6 | |
15.2 | even | 4 | 7650.2.a.do.1.3 | 3 | |||
15.8 | even | 4 | 7650.2.a.dj.1.1 | 3 | |||
15.14 | odd | 2 | 1530.2.d.g.919.5 | 6 | |||
20.3 | even | 4 | 6800.2.a.bk.1.1 | 3 | |||
20.7 | even | 4 | 6800.2.a.bp.1.3 | 3 | |||
20.19 | odd | 2 | 1360.2.e.c.1089.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
170.2.c.b.69.3 | ✓ | 6 | 5.4 | even | 2 | inner | |
170.2.c.b.69.4 | yes | 6 | 1.1 | even | 1 | trivial | |
850.2.a.p.1.1 | 3 | 5.2 | odd | 4 | |||
850.2.a.q.1.3 | 3 | 5.3 | odd | 4 | |||
1360.2.e.c.1089.1 | 6 | 20.19 | odd | 2 | |||
1360.2.e.c.1089.6 | 6 | 4.3 | odd | 2 | |||
1530.2.d.g.919.2 | 6 | 3.2 | odd | 2 | |||
1530.2.d.g.919.5 | 6 | 15.14 | odd | 2 | |||
6800.2.a.bk.1.1 | 3 | 20.3 | even | 4 | |||
6800.2.a.bp.1.3 | 3 | 20.7 | even | 4 | |||
7650.2.a.dj.1.1 | 3 | 15.8 | even | 4 | |||
7650.2.a.do.1.3 | 3 | 15.2 | even | 4 |