Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2394,2,Mod(1709,2394)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2394, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2394.1709");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2394.b (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: | \(19.1161862439\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.2803712.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 6x^{4} + 8x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1709.5 | ||
Root | \(-2.05288i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2394.1709 |
Dual form | 2394.2.b.h.1709.2 |
$q$-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 \(\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times\).
\(n\) | \(533\) | \(1009\) | \(1711\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.69155i | 1.20370i | 0.798610 | + | 0.601848i | \(0.205569\pi\) | ||||
−0.798610 | + | 0.601848i | \(0.794431\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.69155i | 0.851142i | ||||||||
\(11\) | 4.10576i | 1.23793i | 0.785417 | + | 0.618967i | \(0.212448\pi\) | ||||
−0.785417 | + | 0.618967i | \(0.787552\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.15728i | 0.598322i | 0.954203 | + | 0.299161i | \(0.0967068\pi\) | ||||
−0.954203 | + | 0.299161i | \(0.903293\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 6.93419i | − | 1.68179i | −0.541200 | − | 0.840894i | \(-0.682030\pi\) | ||
0.541200 | − | 0.840894i | \(-0.317970\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.42864 | + | 2.69155i | 0.786584 | + | 0.617483i | ||||
\(20\) | 2.69155i | 0.601848i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.10576i | 0.875351i | ||||||||
\(23\) | − | 6.39992i | − | 1.33448i | −0.744845 | − | 0.667238i | \(-0.767476\pi\) | ||
0.744845 | − | 0.667238i | \(-0.232524\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.24443 | −0.448886 | ||||||||
\(26\) | 2.15728i | 0.423077i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 4.00000 | 0.742781 | 0.371391 | − | 0.928477i | \(-0.378881\pi\) | ||||
0.371391 | + | 0.928477i | \(0.378881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.55720i | 1.53692i | 0.639899 | + | 0.768459i | \(0.278976\pi\) | ||||
−0.639899 | + | 0.768459i | \(0.721024\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 6.93419i | − | 1.18920i | ||||||
\(35\) | 2.69155i | 0.454955i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.5057i | 1.72712i | 0.504243 | + | 0.863562i | \(0.331772\pi\) | ||||
−0.504243 | + | 0.863562i | \(0.668228\pi\) | |||||||
\(38\) | 3.42864 | + | 2.69155i | 0.556199 | + | 0.436627i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.69155i | 0.425571i | ||||||||
\(41\) | −7.05086 | −1.10116 | −0.550579 | − | 0.834783i | \(-0.685593\pi\) | ||||
−0.550579 | + | 0.834783i | \(0.685593\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.05086 | 0.465251 | 0.232626 | − | 0.972566i | \(-0.425268\pi\) | ||||
0.232626 | + | 0.972566i | \(0.425268\pi\) | |||||||
\(44\) | 4.10576i | 0.618967i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 6.39992i | − | 0.943617i | ||||||
\(47\) | 6.26304i | 0.913559i | 0.889580 | + | 0.456779i | \(0.150997\pi\) | ||||
−0.889580 | + | 0.456779i | \(0.849003\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.24443 | −0.317411 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.15728i | 0.299161i | ||||||||
\(53\) | −10.8573 | −1.49136 | −0.745681 | − | 0.666303i | \(-0.767876\pi\) | ||||
−0.745681 | + | 0.666303i | \(0.767876\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.0509 | −1.49010 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.00000 | 0.525226 | ||||||||
\(59\) | 2.75557 | 0.358744 | 0.179372 | − | 0.983781i | \(-0.442593\pi\) | ||||
0.179372 | + | 0.983781i | \(0.442593\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.80642 | −0.743436 | −0.371718 | − | 0.928346i | \(-0.621231\pi\) | ||||
−0.371718 | + | 0.928346i | \(0.621231\pi\) | |||||||
\(62\) | 8.55720i | 1.08677i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.80642 | −0.720198 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 0.136879i | − | 0.0167224i | −0.999965 | − | 0.00836122i | \(-0.997339\pi\) | ||
0.999965 | − | 0.00836122i | \(-0.00266149\pi\) | |||||||
\(68\) | − | 6.93419i | − | 0.840894i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.69155i | 0.321702i | ||||||||
\(71\) | −10.3684 | −1.23050 | −0.615252 | − | 0.788330i | \(-0.710946\pi\) | ||||
−0.615252 | + | 0.788330i | \(0.710946\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.56199 | 0.299859 | 0.149929 | − | 0.988697i | \(-0.452095\pi\) | ||||
0.149929 | + | 0.988697i | \(0.452095\pi\) | |||||||
\(74\) | 10.5057i | 1.22126i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.42864 | + | 2.69155i | 0.393292 | + | 0.308742i | ||||
\(77\) | 4.10576i | 0.467895i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 7.54038i | − | 0.848359i | −0.905578 | − | 0.424179i | \(-0.860563\pi\) | ||
0.905578 | − | 0.424179i | \(-0.139437\pi\) | |||||||
\(80\) | 2.69155i | 0.300924i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.05086 | −0.778637 | ||||||||
\(83\) | − | 4.84883i | − | 0.532228i | −0.963942 | − | 0.266114i | \(-0.914260\pi\) | ||
0.963942 | − | 0.266114i | \(-0.0857398\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.6637 | 2.02436 | ||||||||
\(86\) | 3.05086 | 0.328982 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.10576i | 0.437676i | ||||||||
\(89\) | −3.05086 | −0.323390 | −0.161695 | − | 0.986841i | \(-0.551696\pi\) | ||||
−0.161695 | + | 0.986841i | \(0.551696\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.15728i | 0.226144i | ||||||||
\(92\) | − | 6.39992i | − | 0.667238i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.26304i | 0.645983i | ||||||||
\(95\) | −7.24443 | + | 9.22835i | −0.743263 | + | 0.946809i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.19470i | 0.730511i | 0.930907 | + | 0.365255i | \(0.119018\pi\) | ||||
−0.930907 | + | 0.365255i | \(0.880982\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.24443 | −0.224443 | ||||||||
\(101\) | 9.41694i | 0.937020i | 0.883458 | + | 0.468510i | \(0.155209\pi\) | ||||
−0.883458 | + | 0.468510i | \(0.844791\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.72877i | 0.564473i | 0.959345 | + | 0.282236i | \(0.0910763\pi\) | ||||
−0.959345 | + | 0.282236i | \(0.908924\pi\) | |||||||
\(104\) | 2.15728i | 0.211539i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.8573 | −1.05455 | ||||||||
\(107\) | 15.4193 | 1.49064 | 0.745319 | − | 0.666708i | \(-0.232297\pi\) | ||||
0.745319 | + | 0.666708i | \(0.232297\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 16.1625i | − | 1.54809i | −0.633130 | − | 0.774045i | \(-0.718230\pi\) | ||
0.633130 | − | 0.774045i | \(-0.281770\pi\) | |||||||
\(110\) | −11.0509 | −1.05366 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 18.8573 | 1.77394 | 0.886972 | − | 0.461824i | \(-0.152805\pi\) | ||||
0.886972 | + | 0.461824i | \(0.152805\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 17.2257 | 1.60630 | ||||||||
\(116\) | 4.00000 | 0.371391 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.75557 | 0.253671 | ||||||||
\(119\) | − | 6.93419i | − | 0.635656i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.85728 | −0.532480 | ||||||||
\(122\) | −5.80642 | −0.525689 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.55720i | 0.768459i | ||||||||
\(125\) | 7.41675i | 0.663374i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 11.7111i | − | 1.03919i | −0.854412 | − | 0.519596i | \(-0.826082\pi\) | ||
0.854412 | − | 0.519596i | \(-0.173918\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.80642 | −0.509257 | ||||||||
\(131\) | − | 5.12259i | − | 0.447562i | −0.974639 | − | 0.223781i | \(-0.928160\pi\) | ||
0.974639 | − | 0.223781i | \(-0.0718401\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.42864 | + | 2.69155i | 0.297301 | + | 0.233387i | ||||
\(134\) | − | 0.136879i | − | 0.0118245i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 6.93419i | − | 0.594602i | ||||||
\(137\) | − | 2.20899i | − | 0.188727i | −0.995538 | − | 0.0943634i | \(-0.969918\pi\) | ||
0.995538 | − | 0.0943634i | \(-0.0300816\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.61285 | 0.645713 | 0.322857 | − | 0.946448i | \(-0.395357\pi\) | ||||
0.322857 | + | 0.946448i | \(0.395357\pi\) | |||||||
\(140\) | 2.69155i | 0.227477i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.3684 | −0.870098 | ||||||||
\(143\) | −8.85728 | −0.740683 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.7662i | 0.894084i | ||||||||
\(146\) | 2.56199 | 0.212032 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.5057i | 0.863562i | ||||||||
\(149\) | 3.43461i | 0.281375i | 0.990054 | + | 0.140687i | \(0.0449312\pi\) | ||||
−0.990054 | + | 0.140687i | \(0.955069\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.43104i | 0.197835i | 0.995096 | + | 0.0989175i | \(0.0315380\pi\) | ||||
−0.995096 | + | 0.0989175i | \(0.968462\pi\) | |||||||
\(152\) | 3.42864 | + | 2.69155i | 0.278099 | + | 0.218313i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.10576i | 0.330852i | ||||||||
\(155\) | −23.0321 | −1.84998 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.10171 | 0.646587 | 0.323293 | − | 0.946299i | \(-0.395210\pi\) | ||||
0.323293 | + | 0.946299i | \(0.395210\pi\) | |||||||
\(158\) | − | 7.54038i | − | 0.599880i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.69155i | 0.212786i | ||||||||
\(161\) | − | 6.39992i | − | 0.504384i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.29529 | 0.336433 | 0.168216 | − | 0.985750i | \(-0.446199\pi\) | ||||
0.168216 | + | 0.985750i | \(0.446199\pi\) | |||||||
\(164\) | −7.05086 | −0.550579 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 4.84883i | − | 0.376342i | ||||||
\(167\) | −14.3684 | −1.11186 | −0.555931 | − | 0.831229i | \(-0.687638\pi\) | ||||
−0.555931 | + | 0.831229i | \(0.687638\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.34614 | 0.642011 | ||||||||
\(170\) | 18.6637 | 1.43144 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.05086 | 0.232626 | ||||||||
\(173\) | 21.0509 | 1.60047 | 0.800233 | − | 0.599689i | \(-0.204709\pi\) | ||||
0.800233 | + | 0.599689i | \(0.204709\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.24443 | −0.169663 | ||||||||
\(176\) | 4.10576i | 0.309483i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.05086 | −0.228671 | ||||||||
\(179\) | −7.61285 | −0.569011 | −0.284505 | − | 0.958674i | \(-0.591829\pi\) | ||||
−0.284505 | + | 0.958674i | \(0.591829\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 15.2309i | − | 1.13210i | −0.824370 | − | 0.566051i | \(-0.808470\pi\) | ||
0.824370 | − | 0.566051i | \(-0.191530\pi\) | |||||||
\(182\) | 2.15728i | 0.159908i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 6.39992i | − | 0.471808i | ||||||
\(185\) | −28.2766 | −2.07893 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 28.4701 | 2.08194 | ||||||||
\(188\) | 6.26304i | 0.456779i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.24443 | + | 9.22835i | −0.525566 | + | 0.669495i | ||||
\(191\) | − | 8.95459i | − | 0.647931i | −0.946069 | − | 0.323966i | \(-0.894984\pi\) | ||
0.946069 | − | 0.323966i | \(-0.105016\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.7998i | 0.921353i | 0.887568 | + | 0.460676i | \(0.152393\pi\) | ||||
−0.887568 | + | 0.460676i | \(0.847607\pi\) | |||||||
\(194\) | 7.19470i | 0.516549i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | − | 4.12597i | − | 0.293963i | −0.989139 | − | 0.146982i | \(-0.953044\pi\) | ||
0.989139 | − | 0.146982i | \(-0.0469558\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.0509 | −1.35048 | −0.675240 | − | 0.737598i | \(-0.735960\pi\) | ||||
−0.675240 | + | 0.737598i | \(0.735960\pi\) | |||||||
\(200\) | −2.24443 | −0.158705 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.41694i | 0.662573i | ||||||||
\(203\) | 4.00000 | 0.280745 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 18.9777i | − | 1.32546i | ||||||
\(206\) | 5.72877i | 0.399143i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.15728i | 0.149580i | ||||||||
\(209\) | −11.0509 | + | 14.0772i | −0.764404 | + | 0.973739i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 2.69155i | − | 0.185294i | −0.995699 | − | 0.0926469i | \(-0.970467\pi\) | ||
0.995699 | − | 0.0926469i | \(-0.0295328\pi\) | |||||||
\(212\) | −10.8573 | −0.745681 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 15.4193 | 1.05404 | ||||||||
\(215\) | 8.21152i | 0.560021i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.55720i | 0.580901i | ||||||||
\(218\) | − | 16.1625i | − | 1.09467i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −11.0509 | −0.745049 | ||||||||
\(221\) | 14.9590 | 1.00625 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.76242i | 0.519810i | 0.965634 | + | 0.259905i | \(0.0836913\pi\) | ||||
−0.965634 | + | 0.259905i | \(0.916309\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 18.8573 | 1.25437 | ||||||||
\(227\) | −24.3783 | −1.61804 | −0.809021 | − | 0.587780i | \(-0.800002\pi\) | ||||
−0.809021 | + | 0.587780i | \(0.800002\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.7146 | −1.03845 | −0.519224 | − | 0.854638i | \(-0.673779\pi\) | ||||
−0.519224 | + | 0.854638i | \(0.673779\pi\) | |||||||
\(230\) | 17.2257 | 1.13583 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.00000 | 0.262613 | ||||||||
\(233\) | − | 17.0425i | − | 1.11649i | −0.829676 | − | 0.558245i | \(-0.811475\pi\) | ||
0.829676 | − | 0.558245i | \(-0.188525\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.8573 | −1.09965 | ||||||||
\(236\) | 2.75557 | 0.179372 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 6.93419i | − | 0.449477i | ||||||
\(239\) | − | 25.7952i | − | 1.66856i | −0.551345 | − | 0.834278i | \(-0.685885\pi\) | ||
0.551345 | − | 0.834278i | \(-0.314115\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.3377i | 0.923572i | 0.886991 | + | 0.461786i | \(0.152791\pi\) | ||||
−0.886991 | + | 0.461786i | \(0.847209\pi\) | |||||||
\(242\) | −5.85728 | −0.376520 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.80642 | −0.371718 | ||||||||
\(245\) | 2.69155i | 0.171957i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.80642 | + | 7.39654i | −0.369454 | + | 0.470630i | ||||
\(248\) | 8.55720i | 0.543383i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.41675i | 0.469076i | ||||||||
\(251\) | 2.15032i | 0.135727i | 0.997695 | + | 0.0678635i | \(0.0216182\pi\) | ||||
−0.997695 | + | 0.0678635i | \(0.978382\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 26.2766 | 1.65199 | ||||||||
\(254\) | − | 11.7111i | − | 0.734820i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.6637 | 0.914697 | 0.457348 | − | 0.889288i | \(-0.348799\pi\) | ||||
0.457348 | + | 0.889288i | \(0.348799\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.5057i | 0.652791i | ||||||||
\(260\) | −5.80642 | −0.360099 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 5.12259i | − | 0.316474i | ||||||
\(263\) | − | 20.9597i | − | 1.29243i | −0.763156 | − | 0.646214i | \(-0.776351\pi\) | ||
0.763156 | − | 0.646214i | \(-0.223649\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 29.2229i | − | 1.79515i | ||||||
\(266\) | 3.42864 | + | 2.69155i | 0.210223 | + | 0.165029i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 0.136879i | − | 0.00836122i | ||||||
\(269\) | −11.4193 | −0.696245 | −0.348123 | − | 0.937449i | \(-0.613181\pi\) | ||||
−0.348123 | + | 0.937449i | \(0.613181\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.75557 | 0.410372 | 0.205186 | − | 0.978723i | \(-0.434220\pi\) | ||||
0.205186 | + | 0.978723i | \(0.434220\pi\) | |||||||
\(272\) | − | 6.93419i | − | 0.420447i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 2.20899i | − | 0.133450i | ||||||
\(275\) | − | 9.21510i | − | 0.555691i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.9590 | 1.01897 | 0.509483 | − | 0.860480i | \(-0.329837\pi\) | ||||
0.509483 | + | 0.860480i | \(0.329837\pi\) | |||||||
\(278\) | 7.61285 | 0.456588 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.69155i | 0.160851i | ||||||||
\(281\) | 12.7556 | 0.760933 | 0.380467 | − | 0.924795i | \(-0.375763\pi\) | ||||
0.380467 | + | 0.924795i | \(0.375763\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.9590 | 1.48366 | 0.741829 | − | 0.670589i | \(-0.233959\pi\) | ||||
0.741829 | + | 0.670589i | \(0.233959\pi\) | |||||||
\(284\) | −10.3684 | −0.615252 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.85728 | −0.523742 | ||||||||
\(287\) | −7.05086 | −0.416199 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −31.0830 | −1.82841 | ||||||||
\(290\) | 10.7662i | 0.632213i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.56199 | 0.149929 | ||||||||
\(293\) | 10.2953 | 0.601457 | 0.300729 | − | 0.953710i | \(-0.402770\pi\) | ||||
0.300729 | + | 0.953710i | \(0.402770\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.41675i | 0.431820i | ||||||||
\(296\) | 10.5057i | 0.610630i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.43461i | 0.198962i | ||||||||
\(299\) | 13.8064 | 0.798446 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.05086 | 0.175848 | ||||||||
\(302\) | 2.43104i | 0.139891i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.42864 | + | 2.69155i | 0.196646 | + | 0.154371i | ||||
\(305\) | − | 15.6283i | − | 0.894872i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7.66401i | − | 0.437408i | −0.975791 | − | 0.218704i | \(-0.929817\pi\) | ||
0.975791 | − | 0.218704i | \(-0.0701829\pi\) | |||||||
\(308\) | 4.10576i | 0.233947i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −23.0321 | −1.30814 | ||||||||
\(311\) | − | 28.0692i | − | 1.59166i | −0.605522 | − | 0.795829i | \(-0.707036\pi\) | ||
0.605522 | − | 0.795829i | \(-0.292964\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.9590 | 1.86295 | 0.931476 | − | 0.363803i | \(-0.118522\pi\) | ||||
0.931476 | + | 0.363803i | \(0.118522\pi\) | |||||||
\(314\) | 8.10171 | 0.457206 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 7.54038i | − | 0.424179i | ||||||
\(317\) | 25.4479 | 1.42929 | 0.714647 | − | 0.699485i | \(-0.246587\pi\) | ||||
0.714647 | + | 0.699485i | \(0.246587\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.4230i | 0.919514i | ||||||||
\(320\) | 2.69155i | 0.150462i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 6.39992i | − | 0.356654i | ||||||
\(323\) | 18.6637 | − | 23.7748i | 1.03848 | − | 1.32287i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 4.84187i | − | 0.268578i | ||||||
\(326\) | 4.29529 | 0.237894 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7.05086 | −0.389318 | ||||||||
\(329\) | 6.26304i | 0.345293i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 32.8531i | − | 1.80577i | −0.429885 | − | 0.902884i | \(-0.641446\pi\) | ||
0.429885 | − | 0.902884i | \(-0.358554\pi\) | |||||||
\(332\) | − | 4.84883i | − | 0.266114i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −14.3684 | −0.786205 | ||||||||
\(335\) | 0.368416 | 0.0201287 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 22.0799i | − | 1.20277i | −0.798960 | − | 0.601384i | \(-0.794616\pi\) | ||
0.798960 | − | 0.601384i | \(-0.205384\pi\) | |||||||
\(338\) | 8.34614 | 0.453970 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 18.6637 | 1.01218 | ||||||||
\(341\) | −35.1338 | −1.90260 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 3.05086 | 0.164491 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 21.0509 | 1.13170 | ||||||||
\(347\) | − | 11.2487i | − | 0.603865i | −0.953329 | − | 0.301932i | \(-0.902368\pi\) | ||
0.953329 | − | 0.301932i | \(-0.0976316\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.9081 | 1.70800 | 0.854002 | − | 0.520270i | \(-0.174169\pi\) | ||||
0.854002 | + | 0.520270i | \(0.174169\pi\) | |||||||
\(350\) | −2.24443 | −0.119970 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.10576i | 0.218838i | ||||||||
\(353\) | 33.1848i | 1.76625i | 0.469138 | + | 0.883125i | \(0.344565\pi\) | ||||
−0.469138 | + | 0.883125i | \(0.655435\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 27.9071i | − | 1.48115i | ||||||
\(356\) | −3.05086 | −0.161695 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.61285 | −0.402352 | ||||||||
\(359\) | − | 13.1253i | − | 0.692727i | −0.938100 | − | 0.346364i | \(-0.887416\pi\) | ||
0.938100 | − | 0.346364i | \(-0.112584\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.51114 | + | 18.4567i | 0.237428 | + | 0.971405i | ||||
\(362\) | − | 15.2309i | − | 0.800517i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.15728i | 0.113072i | ||||||||
\(365\) | 6.89573i | 0.360939i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.5718 | 0.760644 | 0.380322 | − | 0.924854i | \(-0.375813\pi\) | ||||
0.380322 | + | 0.924854i | \(0.375813\pi\) | |||||||
\(368\) | − | 6.39992i | − | 0.333619i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −28.2766 | −1.47003 | ||||||||
\(371\) | −10.8573 | −0.563682 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.5734i | 0.961692i | 0.876805 | + | 0.480846i | \(0.159670\pi\) | ||||
−0.876805 | + | 0.480846i | \(0.840330\pi\) | |||||||
\(374\) | 28.4701 | 1.47216 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.26304i | 0.322992i | ||||||||
\(377\) | 8.62912i | 0.444422i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 2.04061i | − | 0.104819i | −0.998626 | − | 0.0524096i | \(-0.983310\pi\) | ||
0.998626 | − | 0.0524096i | \(-0.0166901\pi\) | |||||||
\(380\) | −7.24443 | + | 9.22835i | −0.371631 | + | 0.473404i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 8.95459i | − | 0.458157i | ||||||
\(383\) | −23.1240 | −1.18158 | −0.590790 | − | 0.806825i | \(-0.701184\pi\) | ||||
−0.590790 | + | 0.806825i | \(0.701184\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.0509 | −0.563204 | ||||||||
\(386\) | 12.7998i | 0.651495i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.19470i | 0.365255i | ||||||||
\(389\) | 23.1037i | 1.17140i | 0.810527 | + | 0.585702i | \(0.199181\pi\) | ||||
−0.810527 | + | 0.585702i | \(0.800819\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −44.3783 | −2.24431 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 4.12597i | − | 0.207863i | ||||||
\(395\) | 20.2953 | 1.02117 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.5906 | −0.531526 | −0.265763 | − | 0.964038i | \(-0.585624\pi\) | ||||
−0.265763 | + | 0.964038i | \(0.585624\pi\) | |||||||
\(398\) | −19.0509 | −0.954933 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.24443 | −0.112222 | ||||||||
\(401\) | 17.1338 | 0.855623 | 0.427811 | − | 0.903868i | \(-0.359285\pi\) | ||||
0.427811 | + | 0.903868i | \(0.359285\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.4603 | −0.919572 | ||||||||
\(404\) | 9.41694i | 0.468510i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.00000 | 0.198517 | ||||||||
\(407\) | −43.1338 | −2.13806 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 7.46846i | − | 0.369291i | −0.982805 | − | 0.184646i | \(-0.940886\pi\) | ||
0.982805 | − | 0.184646i | \(-0.0591138\pi\) | |||||||
\(410\) | − | 18.9777i | − | 0.937243i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.72877i | 0.282236i | ||||||||
\(413\) | 2.75557 | 0.135593 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.0509 | 0.640641 | ||||||||
\(416\) | 2.15728i | 0.105769i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −11.0509 | + | 14.0772i | −0.540515 | + | 0.688537i | ||||
\(419\) | − | 16.9573i | − | 0.828419i | −0.910182 | − | 0.414210i | \(-0.864058\pi\) | ||
0.910182 | − | 0.414210i | \(-0.135942\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 23.9704i | − | 1.16825i | −0.811665 | − | 0.584123i | \(-0.801439\pi\) | ||
0.811665 | − | 0.584123i | \(-0.198561\pi\) | |||||||
\(422\) | − | 2.69155i | − | 0.131023i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10.8573 | −0.527276 | ||||||||
\(425\) | 15.5633i | 0.754931i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.80642 | −0.280993 | ||||||||
\(428\) | 15.4193 | 0.745319 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.21152i | 0.395995i | ||||||||
\(431\) | 21.6860 | 1.04458 | 0.522288 | − | 0.852769i | \(-0.325078\pi\) | ||||
0.522288 | + | 0.852769i | \(0.325078\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 28.1026i | − | 1.35053i | −0.737577 | − | 0.675263i | \(-0.764030\pi\) | ||
0.737577 | − | 0.675263i | \(-0.235970\pi\) | |||||||
\(434\) | 8.55720i | 0.410759i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 16.1625i | − | 0.774045i | ||||||
\(437\) | 17.2257 | − | 21.9430i | 0.824017 | − | 1.04968i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.83181i | 0.0874276i | 0.999044 | + | 0.0437138i | \(0.0139190\pi\) | ||||
−0.999044 | + | 0.0437138i | \(0.986081\pi\) | |||||||
\(440\) | −11.0509 | −0.526829 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 14.9590 | 0.711527 | ||||||||
\(443\) | 14.6247i | 0.694840i | 0.937710 | + | 0.347420i | \(0.112942\pi\) | ||||
−0.937710 | + | 0.347420i | \(0.887058\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 8.21152i | − | 0.389264i | ||||||
\(446\) | 7.76242i | 0.367561i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 28.9491i | − | 1.36316i | ||||||
\(452\) | 18.8573 | 0.886972 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −24.3783 | −1.14413 | ||||||||
\(455\) | −5.80642 | −0.272209 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −39.6958 | −1.85689 | −0.928446 | − | 0.371467i | \(-0.878855\pi\) | ||||
−0.928446 | + | 0.371467i | \(0.878855\pi\) | |||||||
\(458\) | −15.7146 | −0.734293 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 17.2257 | 0.803152 | ||||||||
\(461\) | − | 1.20541i | − | 0.0561418i | −0.999606 | − | 0.0280709i | \(-0.991064\pi\) | ||
0.999606 | − | 0.0280709i | \(-0.00893641\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.6637 | −0.960324 | −0.480162 | − | 0.877180i | \(-0.659422\pi\) | ||||
−0.480162 | + | 0.877180i | \(0.659422\pi\) | |||||||
\(464\) | 4.00000 | 0.185695 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 17.0425i | − | 0.789478i | ||||||
\(467\) | 41.7622i | 1.93253i | 0.257559 | + | 0.966263i | \(0.417082\pi\) | ||||
−0.257559 | + | 0.966263i | \(0.582918\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 0.136879i | − | 0.00632049i | ||||||
\(470\) | −16.8573 | −0.777568 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.75557 | 0.126835 | ||||||||
\(473\) | 12.5261i | 0.575950i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.69535 | − | 6.04099i | −0.353087 | − | 0.277180i | ||||
\(476\) | − | 6.93419i | − | 0.317828i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 25.7952i | − | 1.17985i | ||||||
\(479\) | − | 15.1659i | − | 0.692949i | −0.938059 | − | 0.346474i | \(-0.887379\pi\) | ||
0.938059 | − | 0.346474i | \(-0.112621\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.6637 | −1.03338 | ||||||||
\(482\) | 14.3377i | 0.653064i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.85728 | −0.266240 | ||||||||
\(485\) | −19.3649 | −0.879314 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.6426i | 0.482261i | 0.970493 | + | 0.241130i | \(0.0775181\pi\) | ||||
−0.970493 | + | 0.241130i | \(0.922482\pi\) | |||||||
\(488\) | −5.80642 | −0.262844 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.69155i | 0.121592i | ||||||||
\(491\) | − | 21.7412i | − | 0.981166i | −0.871394 | − | 0.490583i | \(-0.836784\pi\) | ||
0.871394 | − | 0.490583i | \(-0.163216\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 27.7368i | − | 1.24920i | ||||||
\(494\) | −5.80642 | + | 7.39654i | −0.261243 | + | 0.332786i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.55720i | 0.384230i | ||||||||
\(497\) | −10.3684 | −0.465087 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.0830 | −0.540908 | −0.270454 | − | 0.962733i | \(-0.587174\pi\) | ||||
−0.270454 | + | 0.962733i | \(0.587174\pi\) | |||||||
\(500\) | 7.41675i | 0.331687i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.15032i | 0.0959734i | ||||||||
\(503\) | − | 13.6798i | − | 0.609952i | −0.952360 | − | 0.304976i | \(-0.901352\pi\) | ||
0.952360 | − | 0.304976i | \(-0.0986484\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −25.3461 | −1.12789 | ||||||||
\(506\) | 26.2766 | 1.16814 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 11.7111i | − | 0.519596i | ||||||
\(509\) | 5.87955 | 0.260607 | 0.130303 | − | 0.991474i | \(-0.458405\pi\) | ||||
0.130303 | + | 0.991474i | \(0.458405\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.56199 | 0.113336 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14.6637 | 0.646788 | ||||||||
\(515\) | −15.4193 | −0.679454 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −25.7146 | −1.13092 | ||||||||
\(518\) | 10.5057i | 0.461593i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.80642 | −0.254629 | ||||||||
\(521\) | −3.51114 | −0.153826 | −0.0769129 | − | 0.997038i | \(-0.524506\pi\) | ||||
−0.0769129 | + | 0.997038i | \(0.524506\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.1207i | 1.14218i | 0.820888 | + | 0.571089i | \(0.193479\pi\) | ||||
−0.820888 | + | 0.571089i | \(0.806521\pi\) | |||||||
\(524\) | − | 5.12259i | − | 0.223781i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 20.9597i | − | 0.913884i | ||||||
\(527\) | 59.3372 | 2.58477 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.9590 | −0.780826 | ||||||||
\(530\) | − | 29.2229i | − | 1.26936i | ||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.42864 | + | 2.69155i | 0.148650 | + | 0.116693i | ||||
\(533\) | − | 15.2107i | − | 0.658847i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 41.5017i | 1.79428i | ||||||||
\(536\) | − | 0.136879i | − | 0.00591227i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −11.4193 | −0.492320 | ||||||||
\(539\) | 4.10576i | 0.176848i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.5210 | −0.753286 | −0.376643 | − | 0.926359i | \(-0.622922\pi\) | ||||
−0.376643 | + | 0.926359i | \(0.622922\pi\) | |||||||
\(542\) | 6.75557 | 0.290177 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 6.93419i | − | 0.297301i | ||||||
\(545\) | 43.5022 | 1.86343 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 30.1545i | − | 1.28932i | −0.764471 | − | 0.644658i | \(-0.777000\pi\) | ||
0.764471 | − | 0.644658i | \(-0.223000\pi\) | |||||||
\(548\) | − | 2.20899i | − | 0.0943634i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | − | 9.21510i | − | 0.392933i | ||||||
\(551\) | 13.7146 | + | 10.7662i | 0.584260 | + | 0.458655i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 7.54038i | − | 0.320649i | ||||||
\(554\) | 16.9590 | 0.720518 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.61285 | 0.322857 | ||||||||
\(557\) | 12.4409i | 0.527139i | 0.964640 | + | 0.263569i | \(0.0848998\pi\) | ||||
−0.964640 | + | 0.263569i | \(0.915100\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.58155i | 0.278370i | ||||||||
\(560\) | 2.69155i | 0.113739i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12.7556 | 0.538061 | ||||||||
\(563\) | −27.8796 | −1.17498 | −0.587492 | − | 0.809230i | \(-0.699884\pi\) | ||||
−0.587492 | + | 0.809230i | \(0.699884\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 50.7553i | 2.13529i | ||||||||
\(566\) | 24.9590 | 1.04910 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.3684 | −0.435049 | ||||||||
\(569\) | 29.9911 | 1.25729 | 0.628646 | − | 0.777691i | \(-0.283609\pi\) | ||||
0.628646 | + | 0.777691i | \(0.283609\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.6637 | 1.45063 | 0.725315 | − | 0.688417i | \(-0.241694\pi\) | ||||
0.725315 | + | 0.688417i | \(0.241694\pi\) | |||||||
\(572\) | −8.85728 | −0.370341 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7.05086 | −0.294297 | ||||||||
\(575\) | 14.3642i | 0.599028i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.8064 | 0.824552 | 0.412276 | − | 0.911059i | \(-0.364734\pi\) | ||||
0.412276 | + | 0.911059i | \(0.364734\pi\) | |||||||
\(578\) | −31.0830 | −1.29288 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 10.7662i | 0.447042i | ||||||||
\(581\) | − | 4.84883i | − | 0.201163i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 44.5774i | − | 1.84621i | ||||||
\(584\) | 2.56199 | 0.106016 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.2953 | 0.425294 | ||||||||
\(587\) | − | 38.9338i | − | 1.60697i | −0.595325 | − | 0.803485i | \(-0.702977\pi\) | ||
0.595325 | − | 0.803485i | \(-0.297023\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.0321 | + | 29.3396i | −0.949022 | + | 1.20892i | ||||
\(590\) | 7.41675i | 0.305343i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.5057i | 0.431781i | ||||||||
\(593\) | − | 8.55024i | − | 0.351116i | −0.984469 | − | 0.175558i | \(-0.943827\pi\) | ||
0.984469 | − | 0.175558i | \(-0.0561730\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.6637 | 0.765137 | ||||||||
\(596\) | 3.43461i | 0.140687i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 13.8064 | 0.564587 | ||||||||
\(599\) | 26.8385 | 1.09659 | 0.548297 | − | 0.836284i | \(-0.315277\pi\) | ||||
0.548297 | + | 0.836284i | \(0.315277\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.1530i | 0.414151i | 0.978325 | + | 0.207076i | \(0.0663946\pi\) | ||||
−0.978325 | + | 0.207076i | \(0.933605\pi\) | |||||||
\(602\) | 3.05086 | 0.124344 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.43104i | 0.0989175i | ||||||||
\(605\) | − | 15.7651i | − | 0.640944i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 45.5740i | − | 1.84979i | −0.380220 | − | 0.924896i | \(-0.624152\pi\) | ||
0.380220 | − | 0.924896i | \(-0.375848\pi\) | |||||||
\(608\) | 3.42864 | + | 2.69155i | 0.139050 | + | 0.109157i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 15.6283i | − | 0.632770i | ||||||
\(611\) | −13.5111 | −0.546602 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −45.8992 | −1.85385 | −0.926926 | − | 0.375243i | \(-0.877559\pi\) | ||||
−0.926926 | + | 0.375243i | \(0.877559\pi\) | |||||||
\(614\) | − | 7.66401i | − | 0.309294i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.10576i | 0.165426i | ||||||||
\(617\) | 8.93438i | 0.359685i | 0.983695 | + | 0.179842i | \(0.0575588\pi\) | ||||
−0.983695 | + | 0.179842i | \(0.942441\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.4924 | 0.783466 | 0.391733 | − | 0.920079i | \(-0.371876\pi\) | ||||
0.391733 | + | 0.920079i | \(0.371876\pi\) | |||||||
\(620\) | −23.0321 | −0.924992 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 28.0692i | − | 1.12547i | ||||||
\(623\) | −3.05086 | −0.122230 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1847 | −1.24739 | ||||||||
\(626\) | 32.9590 | 1.31731 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.10171 | 0.323293 | ||||||||
\(629\) | 72.8484 | 2.90466 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.63512 | −0.264140 | −0.132070 | − | 0.991240i | \(-0.542162\pi\) | ||||
−0.132070 | + | 0.991240i | \(0.542162\pi\) | |||||||
\(632\) | − | 7.54038i | − | 0.299940i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 25.4479 | 1.01066 | ||||||||
\(635\) | 31.5210 | 1.25087 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.15728i | 0.0854746i | ||||||||
\(638\) | 16.4230i | 0.650195i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.69155i | 0.106393i | ||||||||
\(641\) | −0.488863 | −0.0193089 | −0.00965445 | − | 0.999953i | \(-0.503073\pi\) | ||||
−0.00965445 | + | 0.999953i | \(0.503073\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.9590 | 1.06316 | 0.531579 | − | 0.847008i | \(-0.321599\pi\) | ||||
0.531579 | + | 0.847008i | \(0.321599\pi\) | |||||||
\(644\) | − | 6.39992i | − | 0.252192i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 18.6637 | − | 23.7748i | 0.734314 | − | 0.935408i | ||||
\(647\) | 29.1377i | 1.14552i | 0.819722 | + | 0.572761i | \(0.194128\pi\) | ||||
−0.819722 | + | 0.572761i | \(0.805872\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.3137i | 0.444102i | ||||||||
\(650\) | − | 4.84187i | − | 0.189914i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.29529 | 0.168216 | ||||||||
\(653\) | 8.44053i | 0.330304i | 0.986268 | + | 0.165152i | \(0.0528114\pi\) | ||||
−0.986268 | + | 0.165152i | \(0.947189\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.7877 | 0.538730 | ||||||||
\(656\) | −7.05086 | −0.275290 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.26304i | 0.244159i | ||||||||
\(659\) | −0.930409 | −0.0362436 | −0.0181218 | − | 0.999836i | \(-0.505769\pi\) | ||||
−0.0181218 | + | 0.999836i | \(0.505769\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.3171i | 1.80153i | 0.434311 | + | 0.900763i | \(0.356992\pi\) | ||||
−0.434311 | + | 0.900763i | \(0.643008\pi\) | |||||||
\(662\) | − | 32.8531i | − | 1.27687i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 4.84883i | − | 0.188171i | ||||||
\(665\) | −7.24443 | + | 9.22835i | −0.280927 | + | 0.357860i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 25.5997i | − | 0.991224i | ||||||
\(668\) | −14.3684 | −0.555931 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.368416 | 0.0142332 | ||||||||
\(671\) | − | 23.8398i | − | 0.920325i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 5.90412i | − | 0.227587i | −0.993504 | − | 0.113793i | \(-0.963700\pi\) | ||
0.993504 | − | 0.113793i | \(-0.0363002\pi\) | |||||||
\(674\) | − | 22.0799i | − | 0.850486i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.34614 | 0.321005 | ||||||||
\(677\) | −14.0286 | −0.539162 | −0.269581 | − | 0.962978i | \(-0.586885\pi\) | ||||
−0.269581 | + | 0.962978i | \(0.586885\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.19470i | 0.276107i | ||||||||
\(680\) | 18.6637 | 0.715720 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −35.1338 | −1.34534 | ||||||||
\(683\) | −20.7467 | −0.793850 | −0.396925 | − | 0.917851i | \(-0.629923\pi\) | ||||
−0.396925 | + | 0.917851i | \(0.629923\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.94561 | 0.227170 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.05086 | 0.116313 | ||||||||
\(689\) | − | 23.4222i | − | 0.892315i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.2480 | −0.846353 | −0.423176 | − | 0.906047i | \(-0.639085\pi\) | ||||
−0.423176 | + | 0.906047i | \(0.639085\pi\) | |||||||
\(692\) | 21.0509 | 0.800233 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 11.2487i | − | 0.426997i | ||||||
\(695\) | 20.4903i | 0.777243i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 48.8920i | 1.85192i | ||||||||
\(698\) | 31.9081 | 1.20774 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.24443 | −0.0848315 | ||||||||
\(701\) | − | 40.7252i | − | 1.53817i | −0.639147 | − | 0.769085i | \(-0.720712\pi\) | ||
0.639147 | − | 0.769085i | \(-0.279288\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −28.2766 | + | 36.0202i | −1.06647 | + | 1.35853i | ||||
\(704\) | 4.10576i | 0.154742i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 33.1848i | 1.24893i | ||||||||
\(707\) | 9.41694i | 0.354160i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −40.0098 | −1.50260 | −0.751301 | − | 0.659960i | \(-0.770573\pi\) | ||||
−0.751301 | + | 0.659960i | \(0.770573\pi\) | |||||||
\(710\) | − | 27.9071i | − | 1.04733i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.05086 | −0.114336 | ||||||||
\(713\) | 54.7654 | 2.05098 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 23.8398i | − | 0.891558i | ||||||
\(716\) | −7.61285 | −0.284505 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 13.1253i | − | 0.489832i | ||||||
\(719\) | 46.1222i | 1.72007i | 0.510237 | + | 0.860034i | \(0.329558\pi\) | ||||
−0.510237 | + | 0.860034i | \(0.670442\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.72877i | 0.213351i | ||||||||
\(722\) | 4.51114 | + | 18.4567i | 0.167887 | + | 0.686887i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 15.2309i | − | 0.566051i | ||||||
\(725\) | −8.97773 | −0.333424 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.266706 | −0.00989159 | −0.00494579 | − | 0.999988i | \(-0.501574\pi\) | ||||
−0.00494579 | + | 0.999988i | \(0.501574\pi\) | |||||||
\(728\) | 2.15728i | 0.0799541i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.89573i | 0.255222i | ||||||||
\(731\) | − | 21.1552i | − | 0.782454i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.13383 | 0.263494 | 0.131747 | − | 0.991283i | \(-0.457941\pi\) | ||||
0.131747 | + | 0.991283i | \(0.457941\pi\) | |||||||
\(734\) | 14.5718 | 0.537856 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 6.39992i | − | 0.235904i | ||||||
\(737\) | 0.561993 | 0.0207013 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.1936 | 0.963546 | 0.481773 | − | 0.876296i | \(-0.339993\pi\) | ||||
0.481773 | + | 0.876296i | \(0.339993\pi\) | |||||||
\(740\) | −28.2766 | −1.03947 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10.8573 | −0.398583 | ||||||||
\(743\) | −27.3176 | −1.00218 | −0.501092 | − | 0.865394i | \(-0.667068\pi\) | ||||
−0.501092 | + | 0.865394i | \(0.667068\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.24443 | −0.338690 | ||||||||
\(746\) | 18.5734i | 0.680019i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 28.4701 | 1.04097 | ||||||||
\(749\) | 15.4193 | 0.563408 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 34.0787i | − | 1.24355i | −0.783196 | − | 0.621774i | \(-0.786412\pi\) | ||
0.783196 | − | 0.621774i | \(-0.213588\pi\) | |||||||
\(752\) | 6.26304i | 0.228390i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.62912i | 0.314254i | ||||||||
\(755\) | −6.54326 | −0.238133 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −51.7975 | −1.88261 | −0.941307 | − | 0.337553i | \(-0.890401\pi\) | ||||
−0.941307 | + | 0.337553i | \(0.890401\pi\) | |||||||
\(758\) | − | 2.04061i | − | 0.0741183i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.24443 | + | 9.22835i | −0.262783 | + | 0.334747i | ||||
\(761\) | − | 27.5280i | − | 0.997888i | −0.866634 | − | 0.498944i | \(-0.833721\pi\) | ||
0.866634 | − | 0.498944i | \(-0.166279\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 16.1625i | − | 0.585123i | ||||||
\(764\) | − | 8.95459i | − | 0.323966i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −23.1240 | −0.835504 | ||||||||
\(767\) | 5.94453i | 0.214645i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.5299 | 0.632143 | 0.316072 | − | 0.948735i | \(-0.397636\pi\) | ||||
0.316072 | + | 0.948735i | \(0.397636\pi\) | |||||||
\(770\) | −11.0509 | −0.398245 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 12.7998i | 0.460676i | ||||||||
\(773\) | −0.222156 | −0.00799041 | −0.00399520 | − | 0.999992i | \(-0.501272\pi\) | ||||
−0.00399520 | + | 0.999992i | \(0.501272\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 19.2061i | − | 0.689902i | ||||||
\(776\) | 7.19470i | 0.258275i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 23.1037i | 0.828307i | ||||||||
\(779\) | −24.1748 | − | 18.9777i | −0.866154 | − | 0.679947i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 42.5702i | − | 1.52328i | ||||||
\(782\) | −44.3783 | −1.58696 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 21.8061i | 0.778295i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 20.8675i | − | 0.743847i | −0.928263 | − | 0.371923i | \(-0.878698\pi\) | ||
0.928263 | − | 0.371923i | \(-0.121302\pi\) | |||||||
\(788\) | − | 4.12597i | − | 0.146982i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 20.2953 | 0.722074 | ||||||||
\(791\) | 18.8573 | 0.670488 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 12.5261i | − | 0.444814i | ||||||
\(794\) | −10.5906 | −0.375845 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −19.0509 | −0.675240 | ||||||||
\(797\) | −21.0223 | −0.744647 | −0.372324 | − | 0.928103i | \(-0.621439\pi\) | ||||
−0.372324 | + | 0.928103i | \(0.621439\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 43.4291 | 1.53641 | ||||||||
\(800\) | −2.24443 | −0.0793526 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 17.1338 | 0.605017 | ||||||||
\(803\) | 10.5189i | 0.371205i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.2257 | 0.607126 | ||||||||
\(806\) | −18.4603 | −0.650236 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.41694i | 0.331287i | ||||||||
\(809\) | 39.5135i | 1.38922i | 0.719386 | + | 0.694610i | \(0.244423\pi\) | ||||
−0.719386 | + | 0.694610i | \(0.755577\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.4895i | 0.965287i | 0.875817 | + | 0.482643i | \(0.160323\pi\) | ||||
−0.875817 | + | 0.482643i | \(0.839677\pi\) | |||||||
\(812\) | 4.00000 | 0.140372 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −43.1338 | −1.51184 | ||||||||
\(815\) | 11.5610i | 0.404963i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.4603 | + | 8.21152i | 0.365959 | + | 0.287285i | ||||
\(818\) | − | 7.46846i | − | 0.261128i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 18.9777i | − | 0.662731i | ||||||
\(821\) | 23.6512i | 0.825433i | 0.910860 | + | 0.412716i | \(0.135420\pi\) | ||||
−0.910860 | + | 0.412716i | \(0.864580\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.97142 | 0.208151 | 0.104075 | − | 0.994569i | \(-0.466812\pi\) | ||||
0.104075 | + | 0.994569i | \(0.466812\pi\) | |||||||
\(824\) | 5.72877i | 0.199571i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.75557 | 0.0958785 | ||||||||
\(827\) | 43.8163 | 1.52364 | 0.761820 | − | 0.647788i | \(-0.224306\pi\) | ||||
0.761820 | + | 0.647788i | \(0.224306\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.1623i | 0.491879i | 0.969285 | + | 0.245939i | \(0.0790964\pi\) | ||||
−0.969285 | + | 0.245939i | \(0.920904\pi\) | |||||||
\(830\) | 13.0509 | 0.453002 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.15728i | 0.0747902i | ||||||||
\(833\) | − | 6.93419i | − | 0.240255i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 38.6733i | − | 1.33834i | ||||||
\(836\) | −11.0509 | + | 14.0772i | −0.382202 | + | 0.486869i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 16.9573i | − | 0.585781i | ||||||
\(839\) | 43.7975 | 1.51206 | 0.756029 | − | 0.654538i | \(-0.227137\pi\) | ||||
0.756029 | + | 0.654538i | \(0.227137\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | − | 23.9704i | − | 0.826074i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 2.69155i | − | 0.0926469i | ||||||
\(845\) | 22.4640i | 0.772787i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.85728 | −0.201258 | ||||||||
\(848\) | −10.8573 | −0.372840 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 15.5633i | 0.533817i | ||||||||
\(851\) | 67.2355 | 2.30480 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.8385 | 1.12437 | 0.562185 | − | 0.827011i | \(-0.309961\pi\) | ||||
0.562185 | + | 0.827011i | \(0.309961\pi\) | |||||||
\(854\) | −5.80642 | −0.198692 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.4193 | 0.527020 | ||||||||
\(857\) | −27.6040 | −0.942933 | −0.471467 | − | 0.881884i | \(-0.656275\pi\) | ||||
−0.471467 | + | 0.881884i | \(0.656275\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.5941 | 0.600303 | 0.300152 | − | 0.953891i | \(-0.402963\pi\) | ||||
0.300152 | + | 0.953891i | \(0.402963\pi\) | |||||||
\(860\) | 8.21152i | 0.280011i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 21.6860 | 0.738627 | ||||||||
\(863\) | −48.8484 | −1.66282 | −0.831409 | − | 0.555661i | \(-0.812465\pi\) | ||||
−0.831409 | + | 0.555661i | \(0.812465\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 56.6594i | 1.92648i | ||||||||
\(866\) | − | 28.1026i | − | 0.954967i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.55720i | 0.290450i | ||||||||
\(869\) | 30.9590 | 1.05021 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.295286 | 0.0100054 | ||||||||
\(872\) | − | 16.1625i | − | 0.547333i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 17.2257 | − | 21.9430i | 0.582668 | − | 0.742234i | ||||
\(875\) | 7.41675i | 0.250732i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 39.1671i | 1.32258i | 0.750130 | + | 0.661290i | \(0.229991\pi\) | ||||
−0.750130 | + | 0.661290i | \(0.770009\pi\) | |||||||
\(878\) | 1.83181i | 0.0618206i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −11.0509 | −0.372524 | ||||||||
\(881\) | 4.10576i | 0.138327i | 0.997605 | + | 0.0691633i | \(0.0220330\pi\) | ||||
−0.997605 | + | 0.0691633i | \(0.977967\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.1052 | 0.912164 | 0.456082 | − | 0.889938i | \(-0.349252\pi\) | ||||
0.456082 | + | 0.889938i | \(0.349252\pi\) | |||||||
\(884\) | 14.9590 | 0.503125 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14.6247i | 0.491326i | ||||||||
\(887\) | −24.6923 | −0.829086 | −0.414543 | − | 0.910030i | \(-0.636059\pi\) | ||||
−0.414543 | + | 0.910030i | \(0.636059\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 11.7111i | − | 0.392778i | ||||||
\(890\) | − | 8.21152i | − | 0.275251i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.76242i | 0.259905i | ||||||||
\(893\) | −16.8573 | + | 21.4737i | −0.564107 | + | 0.718590i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 20.4903i | − | 0.684917i | ||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −30.0000 | −1.00111 | ||||||||
\(899\) | 34.2288i | 1.14159i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 75.2864i | 2.50815i | ||||||||
\(902\) | − | 28.9491i | − | 0.963901i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18.8573 | 0.627184 | ||||||||
\(905\) | 40.9946 | 1.36271 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.3278i | 0.442543i | 0.975212 | + | 0.221272i | \(0.0710207\pi\) | ||||
−0.975212 | + | 0.221272i | \(0.928979\pi\) | |||||||
\(908\) | −24.3783 | −0.809021 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.80642 | −0.192481 | ||||||||
\(911\) | 44.3497 | 1.46937 | 0.734685 | − | 0.678408i | \(-0.237330\pi\) | ||||
0.734685 | + | 0.678408i | \(0.237330\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.9081 | 0.658863 | ||||||||
\(914\) | −39.6958 | −1.31302 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15.7146 | −0.519224 | ||||||||
\(917\) | − | 5.12259i | − | 0.169163i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.0286 | 0.330812 | 0.165406 | − | 0.986226i | \(-0.447106\pi\) | ||||
0.165406 | + | 0.986226i | \(0.447106\pi\) | |||||||
\(920\) | 17.2257 | 0.567914 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 1.20541i | − | 0.0396982i | ||||||
\(923\) | − | 22.3676i | − | 0.736238i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 23.5793i | − | 0.775282i | ||||||
\(926\) | −20.6637 | −0.679051 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.00000 | 0.131306 | ||||||||
\(929\) | 52.0326i | 1.70713i | 0.520983 | + | 0.853567i | \(0.325566\pi\) | ||||
−0.520983 | + | 0.853567i | \(0.674434\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.42864 | + | 2.69155i | 0.112369 | + | 0.0882119i | ||||
\(932\) | − | 17.0425i | − | 0.558245i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 41.7622i | 1.36650i | ||||||||
\(935\) | 76.6287i | 2.50603i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.1971 | −0.431131 | −0.215565 | − | 0.976489i | \(-0.569159\pi\) | ||||
−0.215565 | + | 0.976489i | \(0.569159\pi\) | |||||||
\(938\) | − | 0.136879i | − | 0.00446926i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −16.8573 | −0.549824 | ||||||||
\(941\) | −6.65386 | −0.216910 | −0.108455 | − | 0.994101i | \(-0.534590\pi\) | ||||
−0.108455 | + | 0.994101i | \(0.534590\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 45.1249i | 1.46947i | ||||||||
\(944\) | 2.75557 | 0.0896861 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.5261i | 0.407258i | ||||||||
\(947\) | − | 24.4662i | − | 0.795044i | −0.917593 | − | 0.397522i | \(-0.869870\pi\) | ||
0.917593 | − | 0.397522i | \(-0.130130\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.52694i | 0.179412i | ||||||||
\(950\) | −7.69535 | − | 6.04099i | −0.249670 | − | 0.195996i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 6.93419i | − | 0.224738i | ||||||
\(953\) | −33.9367 | −1.09932 | −0.549659 | − | 0.835389i | \(-0.685242\pi\) | ||||
−0.549659 | + | 0.835389i | \(0.685242\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.1017 | 0.779913 | ||||||||
\(956\) | − | 25.7952i | − | 0.834278i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 15.1659i | − | 0.489989i | ||||||
\(959\) | − | 2.20899i | − | 0.0713320i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −42.2257 | −1.36212 | ||||||||
\(962\) | −22.6637 | −0.730707 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 14.3377i | 0.461786i | ||||||||
\(965\) | −34.4514 | −1.10903 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.0731 | 1.03140 | 0.515701 | − | 0.856769i | \(-0.327531\pi\) | ||||
0.515701 | + | 0.856769i | \(0.327531\pi\) | |||||||
\(968\) | −5.85728 | −0.188260 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −19.3649 | −0.621769 | ||||||||
\(971\) | −43.2168 | −1.38689 | −0.693447 | − | 0.720508i | \(-0.743909\pi\) | ||||
−0.693447 | + | 0.720508i | \(0.743909\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.61285 | 0.244057 | ||||||||
\(974\) | 10.6426i | 0.341010i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.80642 | −0.185859 | ||||||||
\(977\) | 5.90813 | 0.189018 | 0.0945090 | − | 0.995524i | \(-0.469872\pi\) | ||||
0.0945090 | + | 0.995524i | \(0.469872\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 12.5261i | − | 0.400335i | ||||||
\(980\) | 2.69155i | 0.0859784i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 21.7412i | − | 0.693789i | ||||||
\(983\) | −23.0607 | −0.735522 | −0.367761 | − | 0.929920i | \(-0.619876\pi\) | ||||
−0.367761 | + | 0.929920i | \(0.619876\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.1052 | 0.353843 | ||||||||
\(986\) | − | 27.7368i | − | 0.883318i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.80642 | + | 7.39654i | −0.184727 | + | 0.235315i | ||||
\(989\) | − | 19.5252i | − | 0.620866i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.88267i | 0.282167i | 0.989998 | + | 0.141084i | \(0.0450587\pi\) | ||||
−0.989998 | + | 0.141084i | \(0.954941\pi\) | |||||||
\(992\) | 8.55720i | 0.271691i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −10.3684 | −0.328866 | ||||||||
\(995\) | − | 51.2763i | − | 1.62557i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42.5906 | −1.34886 | −0.674428 | − | 0.738340i | \(-0.735610\pi\) | ||||
−0.674428 | + | 0.738340i | \(0.735610\pi\) | |||||||
\(998\) | −12.0830 | −0.382480 | ||||||||
\(999\) | 0 | 0 |
(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 | 2394.2.b.h.1709.5 | yes | 6 | |
3.2 | odd | 2 | 2394.2.b.g.1709.2 | ✓ | 6 | ||
19.18 | odd | 2 | 2394.2.b.g.1709.5 | yes | 6 | ||
57.56 | even | 2 | inner | 2394.2.b.h.1709.2 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2394.2.b.g.1709.2 | ✓ | 6 | 3.2 | odd | 2 | ||
2394.2.b.g.1709.5 | yes | 6 | 19.18 | odd | 2 | ||
2394.2.b.h.1709.2 | yes | 6 | 57.56 | even | 2 | inner | |
2394.2.b.h.1709.5 | yes | 6 | 1.1 | even | 1 | trivial |