Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4235,2,Mod(1,4235)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4235, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4235.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4235 = 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4235.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(33.8166452560\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 14x^{8} + 26x^{7} + 67x^{6} - 110x^{5} - 132x^{4} + 168x^{3} + 94x^{2} - 54x - 11 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.09068\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4235.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.09068 | −1.47834 | −0.739168 | − | 0.673521i | \(-0.764781\pi\) | ||||
−0.739168 | + | 0.673521i | \(0.764781\pi\) | |||||||
\(3\) | −1.17179 | −0.676531 | −0.338266 | − | 0.941051i | \(-0.609840\pi\) | ||||
−0.338266 | + | 0.941051i | \(0.609840\pi\) | |||||||
\(4\) | 2.37096 | 1.18548 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 2.44983 | 1.00014 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −0.775558 | −0.274201 | ||||||||
\(9\) | −1.62692 | −0.542306 | ||||||||
\(10\) | −2.09068 | −0.661132 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −2.77826 | −0.802014 | ||||||||
\(13\) | −1.06949 | −0.296623 | −0.148311 | − | 0.988941i | \(-0.547384\pi\) | ||||
−0.148311 | + | 0.988941i | \(0.547384\pi\) | |||||||
\(14\) | −2.09068 | −0.558759 | ||||||||
\(15\) | −1.17179 | −0.302554 | ||||||||
\(16\) | −3.12047 | −0.780118 | ||||||||
\(17\) | −5.01686 | −1.21677 | −0.608383 | − | 0.793643i | \(-0.708182\pi\) | ||||
−0.608383 | + | 0.793643i | \(0.708182\pi\) | |||||||
\(18\) | 3.40137 | 0.801710 | ||||||||
\(19\) | −1.36590 | −0.313359 | −0.156679 | − | 0.987650i | \(-0.550079\pi\) | ||||
−0.156679 | + | 0.987650i | \(0.550079\pi\) | |||||||
\(20\) | 2.37096 | 0.530163 | ||||||||
\(21\) | −1.17179 | −0.255705 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.12817 | 0.860783 | 0.430391 | − | 0.902642i | \(-0.358376\pi\) | ||||
0.430391 | + | 0.902642i | \(0.358376\pi\) | |||||||
\(24\) | 0.908789 | 0.185506 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.23596 | 0.438509 | ||||||||
\(27\) | 5.42176 | 1.04342 | ||||||||
\(28\) | 2.37096 | 0.448069 | ||||||||
\(29\) | 6.92308 | 1.28558 | 0.642792 | − | 0.766041i | \(-0.277776\pi\) | ||||
0.642792 | + | 0.766041i | \(0.277776\pi\) | |||||||
\(30\) | 2.44983 | 0.447277 | ||||||||
\(31\) | 1.54746 | 0.277932 | 0.138966 | − | 0.990297i | \(-0.455622\pi\) | ||||
0.138966 | + | 0.990297i | \(0.455622\pi\) | |||||||
\(32\) | 8.07504 | 1.42748 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.4887 | 1.79879 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −3.85735 | −0.642892 | ||||||||
\(37\) | 10.1396 | 1.66694 | 0.833472 | − | 0.552561i | \(-0.186350\pi\) | ||||
0.833472 | + | 0.552561i | \(0.186350\pi\) | |||||||
\(38\) | 2.85566 | 0.463249 | ||||||||
\(39\) | 1.25321 | 0.200675 | ||||||||
\(40\) | −0.775558 | −0.122627 | ||||||||
\(41\) | −3.70892 | −0.579235 | −0.289618 | − | 0.957142i | \(-0.593528\pi\) | ||||
−0.289618 | + | 0.957142i | \(0.593528\pi\) | |||||||
\(42\) | 2.44983 | 0.378018 | ||||||||
\(43\) | −7.68270 | −1.17160 | −0.585801 | − | 0.810455i | \(-0.699220\pi\) | ||||
−0.585801 | + | 0.810455i | \(0.699220\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.62692 | −0.242526 | ||||||||
\(46\) | −8.63070 | −1.27253 | ||||||||
\(47\) | −12.0349 | −1.75548 | −0.877738 | − | 0.479141i | \(-0.840948\pi\) | ||||
−0.877738 | + | 0.479141i | \(0.840948\pi\) | |||||||
\(48\) | 3.65652 | 0.527774 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.09068 | −0.295667 | ||||||||
\(51\) | 5.87868 | 0.823180 | ||||||||
\(52\) | −2.53572 | −0.351640 | ||||||||
\(53\) | 3.81239 | 0.523672 | 0.261836 | − | 0.965112i | \(-0.415672\pi\) | ||||
0.261836 | + | 0.965112i | \(0.415672\pi\) | |||||||
\(54\) | −11.3352 | −1.54252 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.775558 | −0.103638 | ||||||||
\(57\) | 1.60054 | 0.211997 | ||||||||
\(58\) | −14.4740 | −1.90052 | ||||||||
\(59\) | −8.72837 | −1.13634 | −0.568168 | − | 0.822912i | \(-0.692348\pi\) | ||||
−0.568168 | + | 0.822912i | \(0.692348\pi\) | |||||||
\(60\) | −2.77826 | −0.358671 | ||||||||
\(61\) | −12.4241 | −1.59074 | −0.795372 | − | 0.606122i | \(-0.792724\pi\) | ||||
−0.795372 | + | 0.606122i | \(0.792724\pi\) | |||||||
\(62\) | −3.23525 | −0.410877 | ||||||||
\(63\) | −1.62692 | −0.204972 | ||||||||
\(64\) | −10.6414 | −1.33018 | ||||||||
\(65\) | −1.06949 | −0.132654 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.2819 | 1.50047 | 0.750237 | − | 0.661169i | \(-0.229939\pi\) | ||||
0.750237 | + | 0.661169i | \(0.229939\pi\) | |||||||
\(68\) | −11.8948 | −1.44245 | ||||||||
\(69\) | −4.83733 | −0.582346 | ||||||||
\(70\) | −2.09068 | −0.249885 | ||||||||
\(71\) | 7.29340 | 0.865567 | 0.432784 | − | 0.901498i | \(-0.357531\pi\) | ||||
0.432784 | + | 0.901498i | \(0.357531\pi\) | |||||||
\(72\) | 1.26177 | 0.148701 | ||||||||
\(73\) | −7.32603 | −0.857447 | −0.428723 | − | 0.903436i | \(-0.641037\pi\) | ||||
−0.428723 | + | 0.903436i | \(0.641037\pi\) | |||||||
\(74\) | −21.1988 | −2.46431 | ||||||||
\(75\) | −1.17179 | −0.135306 | ||||||||
\(76\) | −3.23849 | −0.371480 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.62007 | −0.296665 | ||||||||
\(79\) | −5.41792 | −0.609564 | −0.304782 | − | 0.952422i | \(-0.598584\pi\) | ||||
−0.304782 | + | 0.952422i | \(0.598584\pi\) | |||||||
\(80\) | −3.12047 | −0.348879 | ||||||||
\(81\) | −1.47239 | −0.163599 | ||||||||
\(82\) | 7.75417 | 0.856305 | ||||||||
\(83\) | 0.0466470 | 0.00512017 | 0.00256009 | − | 0.999997i | \(-0.499185\pi\) | ||||
0.00256009 | + | 0.999997i | \(0.499185\pi\) | |||||||
\(84\) | −2.77826 | −0.303133 | ||||||||
\(85\) | −5.01686 | −0.544154 | ||||||||
\(86\) | 16.0621 | 1.73202 | ||||||||
\(87\) | −8.11237 | −0.869737 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.14060 | −0.332903 | −0.166452 | − | 0.986050i | \(-0.553231\pi\) | ||||
−0.166452 | + | 0.986050i | \(0.553231\pi\) | |||||||
\(90\) | 3.40137 | 0.358536 | ||||||||
\(91\) | −1.06949 | −0.112113 | ||||||||
\(92\) | 9.78772 | 1.02044 | ||||||||
\(93\) | −1.81329 | −0.188030 | ||||||||
\(94\) | 25.1612 | 2.59518 | ||||||||
\(95\) | −1.36590 | −0.140138 | ||||||||
\(96\) | −9.46222 | −0.965733 | ||||||||
\(97\) | 12.8210 | 1.30178 | 0.650889 | − | 0.759173i | \(-0.274396\pi\) | ||||
0.650889 | + | 0.759173i | \(0.274396\pi\) | |||||||
\(98\) | −2.09068 | −0.211191 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.37096 | 0.237096 | ||||||||
\(101\) | 6.58237 | 0.654970 | 0.327485 | − | 0.944856i | \(-0.393799\pi\) | ||||
0.327485 | + | 0.944856i | \(0.393799\pi\) | |||||||
\(102\) | −12.2905 | −1.21694 | ||||||||
\(103\) | 1.42092 | 0.140007 | 0.0700036 | − | 0.997547i | \(-0.477699\pi\) | ||||
0.0700036 | + | 0.997547i | \(0.477699\pi\) | |||||||
\(104\) | 0.829451 | 0.0813344 | ||||||||
\(105\) | −1.17179 | −0.114355 | ||||||||
\(106\) | −7.97050 | −0.774163 | ||||||||
\(107\) | 10.5639 | 1.02125 | 0.510623 | − | 0.859805i | \(-0.329415\pi\) | ||||
0.510623 | + | 0.859805i | \(0.329415\pi\) | |||||||
\(108\) | 12.8548 | 1.23695 | ||||||||
\(109\) | −8.32464 | −0.797356 | −0.398678 | − | 0.917091i | \(-0.630531\pi\) | ||||
−0.398678 | + | 0.917091i | \(0.630531\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.8815 | −1.12774 | ||||||||
\(112\) | −3.12047 | −0.294857 | ||||||||
\(113\) | 11.9777 | 1.12677 | 0.563383 | − | 0.826196i | \(-0.309500\pi\) | ||||
0.563383 | + | 0.826196i | \(0.309500\pi\) | |||||||
\(114\) | −3.34622 | −0.313403 | ||||||||
\(115\) | 4.12817 | 0.384954 | ||||||||
\(116\) | 16.4143 | 1.52403 | ||||||||
\(117\) | 1.73997 | 0.160860 | ||||||||
\(118\) | 18.2483 | 1.67989 | ||||||||
\(119\) | −5.01686 | −0.459894 | ||||||||
\(120\) | 0.908789 | 0.0829607 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 25.9749 | 2.35165 | ||||||||
\(123\) | 4.34606 | 0.391871 | ||||||||
\(124\) | 3.66896 | 0.329483 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 3.40137 | 0.303018 | ||||||||
\(127\) | 1.16924 | 0.103753 | 0.0518767 | − | 0.998653i | \(-0.483480\pi\) | ||||
0.0518767 | + | 0.998653i | \(0.483480\pi\) | |||||||
\(128\) | 6.09774 | 0.538969 | ||||||||
\(129\) | 9.00249 | 0.792625 | ||||||||
\(130\) | 2.23596 | 0.196107 | ||||||||
\(131\) | −0.200825 | −0.0175462 | −0.00877310 | − | 0.999962i | \(-0.502793\pi\) | ||||
−0.00877310 | + | 0.999962i | \(0.502793\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.36590 | −0.118438 | ||||||||
\(134\) | −25.6776 | −2.21821 | ||||||||
\(135\) | 5.42176 | 0.466631 | ||||||||
\(136\) | 3.89086 | 0.333639 | ||||||||
\(137\) | −5.42631 | −0.463601 | −0.231801 | − | 0.972763i | \(-0.574462\pi\) | ||||
−0.231801 | + | 0.972763i | \(0.574462\pi\) | |||||||
\(138\) | 10.1133 | 0.860904 | ||||||||
\(139\) | 3.01028 | 0.255329 | 0.127664 | − | 0.991817i | \(-0.459252\pi\) | ||||
0.127664 | + | 0.991817i | \(0.459252\pi\) | |||||||
\(140\) | 2.37096 | 0.200383 | ||||||||
\(141\) | 14.1024 | 1.18763 | ||||||||
\(142\) | −15.2482 | −1.27960 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 5.07675 | 0.423062 | ||||||||
\(145\) | 6.92308 | 0.574930 | ||||||||
\(146\) | 15.3164 | 1.26760 | ||||||||
\(147\) | −1.17179 | −0.0966473 | ||||||||
\(148\) | 24.0406 | 1.97613 | ||||||||
\(149\) | −5.65447 | −0.463233 | −0.231616 | − | 0.972807i | \(-0.574401\pi\) | ||||
−0.231616 | + | 0.972807i | \(0.574401\pi\) | |||||||
\(150\) | 2.44983 | 0.200028 | ||||||||
\(151\) | −18.1008 | −1.47302 | −0.736512 | − | 0.676425i | \(-0.763528\pi\) | ||||
−0.736512 | + | 0.676425i | \(0.763528\pi\) | |||||||
\(152\) | 1.05933 | 0.0859233 | ||||||||
\(153\) | 8.16201 | 0.659859 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.54746 | 0.124295 | ||||||||
\(156\) | 2.97132 | 0.237896 | ||||||||
\(157\) | −14.4299 | −1.15164 | −0.575818 | − | 0.817578i | \(-0.695316\pi\) | ||||
−0.575818 | + | 0.817578i | \(0.695316\pi\) | |||||||
\(158\) | 11.3272 | 0.901140 | ||||||||
\(159\) | −4.46730 | −0.354280 | ||||||||
\(160\) | 8.07504 | 0.638388 | ||||||||
\(161\) | 4.12817 | 0.325345 | ||||||||
\(162\) | 3.07830 | 0.241854 | ||||||||
\(163\) | 7.53849 | 0.590460 | 0.295230 | − | 0.955426i | \(-0.404604\pi\) | ||||
0.295230 | + | 0.955426i | \(0.404604\pi\) | |||||||
\(164\) | −8.79369 | −0.686672 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.0975241 | −0.00756934 | ||||||||
\(167\) | 11.5314 | 0.892325 | 0.446162 | − | 0.894952i | \(-0.352790\pi\) | ||||
0.446162 | + | 0.894952i | \(0.352790\pi\) | |||||||
\(168\) | 0.908789 | 0.0701146 | ||||||||
\(169\) | −11.8562 | −0.912015 | ||||||||
\(170\) | 10.4887 | 0.804443 | ||||||||
\(171\) | 2.22220 | 0.169936 | ||||||||
\(172\) | −18.2154 | −1.38891 | ||||||||
\(173\) | −10.0459 | −0.763779 | −0.381889 | − | 0.924208i | \(-0.624727\pi\) | ||||
−0.381889 | + | 0.924208i | \(0.624727\pi\) | |||||||
\(174\) | 16.9604 | 1.28576 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.2278 | 0.768767 | ||||||||
\(178\) | 6.56601 | 0.492143 | ||||||||
\(179\) | −16.3072 | −1.21886 | −0.609428 | − | 0.792842i | \(-0.708601\pi\) | ||||
−0.609428 | + | 0.792842i | \(0.708601\pi\) | |||||||
\(180\) | −3.85735 | −0.287510 | ||||||||
\(181\) | −11.7382 | −0.872492 | −0.436246 | − | 0.899827i | \(-0.643692\pi\) | ||||
−0.436246 | + | 0.899827i | \(0.643692\pi\) | |||||||
\(182\) | 2.23596 | 0.165741 | ||||||||
\(183\) | 14.5584 | 1.07619 | ||||||||
\(184\) | −3.20164 | −0.236028 | ||||||||
\(185\) | 10.1396 | 0.745480 | ||||||||
\(186\) | 3.79102 | 0.277971 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −28.5343 | −2.08108 | ||||||||
\(189\) | 5.42176 | 0.394375 | ||||||||
\(190\) | 2.85566 | 0.207171 | ||||||||
\(191\) | 11.5859 | 0.838329 | 0.419164 | − | 0.907910i | \(-0.362323\pi\) | ||||
0.419164 | + | 0.907910i | \(0.362323\pi\) | |||||||
\(192\) | 12.4695 | 0.899905 | ||||||||
\(193\) | 11.0124 | 0.792687 | 0.396344 | − | 0.918102i | \(-0.370279\pi\) | ||||
0.396344 | + | 0.918102i | \(0.370279\pi\) | |||||||
\(194\) | −26.8047 | −1.92447 | ||||||||
\(195\) | 1.25321 | 0.0897444 | ||||||||
\(196\) | 2.37096 | 0.169354 | ||||||||
\(197\) | 12.3315 | 0.878585 | 0.439293 | − | 0.898344i | \(-0.355229\pi\) | ||||
0.439293 | + | 0.898344i | \(0.355229\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.46213 | −0.670752 | −0.335376 | − | 0.942084i | \(-0.608863\pi\) | ||||
−0.335376 | + | 0.942084i | \(0.608863\pi\) | |||||||
\(200\) | −0.775558 | −0.0548403 | ||||||||
\(201\) | −14.3918 | −1.01512 | ||||||||
\(202\) | −13.7616 | −0.968266 | ||||||||
\(203\) | 6.92308 | 0.485905 | ||||||||
\(204\) | 13.9381 | 0.975863 | ||||||||
\(205\) | −3.70892 | −0.259042 | ||||||||
\(206\) | −2.97069 | −0.206978 | ||||||||
\(207\) | −6.71619 | −0.466807 | ||||||||
\(208\) | 3.33731 | 0.231401 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.44983 | 0.169055 | ||||||||
\(211\) | −10.4327 | −0.718218 | −0.359109 | − | 0.933296i | \(-0.616919\pi\) | ||||
−0.359109 | + | 0.933296i | \(0.616919\pi\) | |||||||
\(212\) | 9.03902 | 0.620802 | ||||||||
\(213\) | −8.54630 | −0.585583 | ||||||||
\(214\) | −22.0857 | −1.50975 | ||||||||
\(215\) | −7.68270 | −0.523956 | ||||||||
\(216\) | −4.20489 | −0.286107 | ||||||||
\(217\) | 1.54746 | 0.105048 | ||||||||
\(218\) | 17.4042 | 1.17876 | ||||||||
\(219\) | 8.58454 | 0.580090 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.36547 | 0.360921 | ||||||||
\(222\) | 24.8404 | 1.66718 | ||||||||
\(223\) | −3.36259 | −0.225176 | −0.112588 | − | 0.993642i | \(-0.535914\pi\) | ||||
−0.112588 | + | 0.993642i | \(0.535914\pi\) | |||||||
\(224\) | 8.07504 | 0.539536 | ||||||||
\(225\) | −1.62692 | −0.108461 | ||||||||
\(226\) | −25.0415 | −1.66574 | ||||||||
\(227\) | 4.82165 | 0.320024 | 0.160012 | − | 0.987115i | \(-0.448847\pi\) | ||||
0.160012 | + | 0.987115i | \(0.448847\pi\) | |||||||
\(228\) | 3.79482 | 0.251318 | ||||||||
\(229\) | −13.2867 | −0.878011 | −0.439005 | − | 0.898484i | \(-0.644669\pi\) | ||||
−0.439005 | + | 0.898484i | \(0.644669\pi\) | |||||||
\(230\) | −8.63070 | −0.569091 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.36925 | −0.352509 | ||||||||
\(233\) | −22.6748 | −1.48548 | −0.742738 | − | 0.669582i | \(-0.766473\pi\) | ||||
−0.742738 | + | 0.669582i | \(0.766473\pi\) | |||||||
\(234\) | −3.63773 | −0.237806 | ||||||||
\(235\) | −12.0349 | −0.785073 | ||||||||
\(236\) | −20.6946 | −1.34710 | ||||||||
\(237\) | 6.34864 | 0.412389 | ||||||||
\(238\) | 10.4887 | 0.679879 | ||||||||
\(239\) | −7.21013 | −0.466385 | −0.233192 | − | 0.972431i | \(-0.574917\pi\) | ||||
−0.233192 | + | 0.972431i | \(0.574917\pi\) | |||||||
\(240\) | 3.65652 | 0.236028 | ||||||||
\(241\) | 13.2512 | 0.853587 | 0.426793 | − | 0.904349i | \(-0.359643\pi\) | ||||
0.426793 | + | 0.904349i | \(0.359643\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.5399 | −0.932738 | ||||||||
\(244\) | −29.4570 | −1.88579 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −9.08623 | −0.579317 | ||||||||
\(247\) | 1.46081 | 0.0929493 | ||||||||
\(248\) | −1.20015 | −0.0762093 | ||||||||
\(249\) | −0.0546603 | −0.00346395 | ||||||||
\(250\) | −2.09068 | −0.132226 | ||||||||
\(251\) | 25.5786 | 1.61451 | 0.807253 | − | 0.590206i | \(-0.200953\pi\) | ||||
0.807253 | + | 0.590206i | \(0.200953\pi\) | |||||||
\(252\) | −3.85735 | −0.242990 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −2.44452 | −0.153383 | ||||||||
\(255\) | 5.87868 | 0.368137 | ||||||||
\(256\) | 8.53436 | 0.533397 | ||||||||
\(257\) | −6.44721 | −0.402166 | −0.201083 | − | 0.979574i | \(-0.564446\pi\) | ||||
−0.201083 | + | 0.979574i | \(0.564446\pi\) | |||||||
\(258\) | −18.8214 | −1.17177 | ||||||||
\(259\) | 10.1396 | 0.630046 | ||||||||
\(260\) | −2.53572 | −0.157258 | ||||||||
\(261\) | −11.2633 | −0.697179 | ||||||||
\(262\) | 0.419862 | 0.0259392 | ||||||||
\(263\) | 17.7885 | 1.09688 | 0.548442 | − | 0.836189i | \(-0.315221\pi\) | ||||
0.548442 | + | 0.836189i | \(0.315221\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.81239 | 0.234193 | ||||||||
\(266\) | 2.85566 | 0.175092 | ||||||||
\(267\) | 3.68012 | 0.225220 | ||||||||
\(268\) | 29.1199 | 1.77878 | ||||||||
\(269\) | 14.8592 | 0.905984 | 0.452992 | − | 0.891515i | \(-0.350357\pi\) | ||||
0.452992 | + | 0.891515i | \(0.350357\pi\) | |||||||
\(270\) | −11.3352 | −0.689837 | ||||||||
\(271\) | −13.1746 | −0.800303 | −0.400151 | − | 0.916449i | \(-0.631042\pi\) | ||||
−0.400151 | + | 0.916449i | \(0.631042\pi\) | |||||||
\(272\) | 15.6550 | 0.949221 | ||||||||
\(273\) | 1.25321 | 0.0758479 | ||||||||
\(274\) | 11.3447 | 0.685359 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −11.4691 | −0.690360 | ||||||||
\(277\) | 4.92847 | 0.296123 | 0.148061 | − | 0.988978i | \(-0.452697\pi\) | ||||
0.148061 | + | 0.988978i | \(0.452697\pi\) | |||||||
\(278\) | −6.29355 | −0.377462 | ||||||||
\(279\) | −2.51759 | −0.150724 | ||||||||
\(280\) | −0.775558 | −0.0463485 | ||||||||
\(281\) | −25.6183 | −1.52826 | −0.764130 | − | 0.645062i | \(-0.776832\pi\) | ||||
−0.764130 | + | 0.645062i | \(0.776832\pi\) | |||||||
\(282\) | −29.4836 | −1.75572 | ||||||||
\(283\) | −25.2779 | −1.50262 | −0.751309 | − | 0.659951i | \(-0.770577\pi\) | ||||
−0.751309 | + | 0.659951i | \(0.770577\pi\) | |||||||
\(284\) | 17.2923 | 1.02611 | ||||||||
\(285\) | 1.60054 | 0.0948078 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.70892 | −0.218930 | ||||||||
\(288\) | −13.1374 | −0.774129 | ||||||||
\(289\) | 8.16884 | 0.480520 | ||||||||
\(290\) | −14.4740 | −0.849941 | ||||||||
\(291\) | −15.0235 | −0.880694 | ||||||||
\(292\) | −17.3697 | −1.01649 | ||||||||
\(293\) | 23.8860 | 1.39543 | 0.697716 | − | 0.716374i | \(-0.254200\pi\) | ||||
0.697716 | + | 0.716374i | \(0.254200\pi\) | |||||||
\(294\) | 2.44983 | 0.142877 | ||||||||
\(295\) | −8.72837 | −0.508185 | ||||||||
\(296\) | −7.86387 | −0.457078 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 11.8217 | 0.684814 | ||||||||
\(299\) | −4.41503 | −0.255328 | ||||||||
\(300\) | −2.77826 | −0.160403 | ||||||||
\(301\) | −7.68270 | −0.442824 | ||||||||
\(302\) | 37.8431 | 2.17763 | ||||||||
\(303\) | −7.71313 | −0.443107 | ||||||||
\(304\) | 4.26225 | 0.244457 | ||||||||
\(305\) | −12.4241 | −0.711402 | ||||||||
\(306\) | −17.0642 | −0.975494 | ||||||||
\(307\) | 27.5818 | 1.57418 | 0.787088 | − | 0.616841i | \(-0.211588\pi\) | ||||
0.787088 | + | 0.616841i | \(0.211588\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.66501 | −0.0947193 | ||||||||
\(310\) | −3.23525 | −0.183750 | ||||||||
\(311\) | 12.7943 | 0.725501 | 0.362750 | − | 0.931886i | \(-0.381838\pi\) | ||||
0.362750 | + | 0.931886i | \(0.381838\pi\) | |||||||
\(312\) | −0.971940 | −0.0550253 | ||||||||
\(313\) | −3.66737 | −0.207292 | −0.103646 | − | 0.994614i | \(-0.533051\pi\) | ||||
−0.103646 | + | 0.994614i | \(0.533051\pi\) | |||||||
\(314\) | 30.1685 | 1.70250 | ||||||||
\(315\) | −1.62692 | −0.0916664 | ||||||||
\(316\) | −12.8457 | −0.722625 | ||||||||
\(317\) | 29.3633 | 1.64921 | 0.824603 | − | 0.565712i | \(-0.191399\pi\) | ||||
0.824603 | + | 0.565712i | \(0.191399\pi\) | |||||||
\(318\) | 9.33972 | 0.523746 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −10.6414 | −0.594873 | ||||||||
\(321\) | −12.3786 | −0.690905 | ||||||||
\(322\) | −8.63070 | −0.480970 | ||||||||
\(323\) | 6.85251 | 0.381284 | ||||||||
\(324\) | −3.49098 | −0.193943 | ||||||||
\(325\) | −1.06949 | −0.0593246 | ||||||||
\(326\) | −15.7606 | −0.872899 | ||||||||
\(327\) | 9.75470 | 0.539436 | ||||||||
\(328\) | 2.87648 | 0.158827 | ||||||||
\(329\) | −12.0349 | −0.663507 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.9178 | −1.31464 | −0.657321 | − | 0.753611i | \(-0.728310\pi\) | ||||
−0.657321 | + | 0.753611i | \(0.728310\pi\) | |||||||
\(332\) | 0.110598 | 0.00606986 | ||||||||
\(333\) | −16.4963 | −0.903993 | ||||||||
\(334\) | −24.1085 | −1.31916 | ||||||||
\(335\) | 12.2819 | 0.671033 | ||||||||
\(336\) | 3.65652 | 0.199480 | ||||||||
\(337\) | −25.3419 | −1.38046 | −0.690232 | − | 0.723588i | \(-0.742491\pi\) | ||||
−0.690232 | + | 0.723588i | \(0.742491\pi\) | |||||||
\(338\) | 24.7876 | 1.34827 | ||||||||
\(339\) | −14.0353 | −0.762292 | ||||||||
\(340\) | −11.8948 | −0.645084 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −4.64592 | −0.251223 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 5.95839 | 0.321255 | ||||||||
\(345\) | −4.83733 | −0.260433 | ||||||||
\(346\) | 21.0029 | 1.12912 | ||||||||
\(347\) | −34.8652 | −1.87166 | −0.935831 | − | 0.352449i | \(-0.885349\pi\) | ||||
−0.935831 | + | 0.352449i | \(0.885349\pi\) | |||||||
\(348\) | −19.2341 | −1.03106 | ||||||||
\(349\) | −0.759664 | −0.0406639 | −0.0203319 | − | 0.999793i | \(-0.506472\pi\) | ||||
−0.0203319 | + | 0.999793i | \(0.506472\pi\) | |||||||
\(350\) | −2.09068 | −0.111752 | ||||||||
\(351\) | −5.79851 | −0.309502 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −36.1431 | −1.92371 | −0.961853 | − | 0.273567i | \(-0.911796\pi\) | ||||
−0.961853 | + | 0.273567i | \(0.911796\pi\) | |||||||
\(354\) | −21.3831 | −1.13650 | ||||||||
\(355\) | 7.29340 | 0.387093 | ||||||||
\(356\) | −7.44625 | −0.394650 | ||||||||
\(357\) | 5.87868 | 0.311133 | ||||||||
\(358\) | 34.0931 | 1.80188 | ||||||||
\(359\) | 8.32590 | 0.439424 | 0.219712 | − | 0.975565i | \(-0.429488\pi\) | ||||
0.219712 | + | 0.975565i | \(0.429488\pi\) | |||||||
\(360\) | 1.26177 | 0.0665011 | ||||||||
\(361\) | −17.1343 | −0.901806 | ||||||||
\(362\) | 24.5408 | 1.28984 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.53572 | −0.132908 | ||||||||
\(365\) | −7.32603 | −0.383462 | ||||||||
\(366\) | −30.4370 | −1.59097 | ||||||||
\(367\) | −34.3230 | −1.79165 | −0.895823 | − | 0.444411i | \(-0.853413\pi\) | ||||
−0.895823 | + | 0.444411i | \(0.853413\pi\) | |||||||
\(368\) | −12.8818 | −0.671512 | ||||||||
\(369\) | 6.03410 | 0.314123 | ||||||||
\(370\) | −21.1988 | −1.10207 | ||||||||
\(371\) | 3.81239 | 0.197929 | ||||||||
\(372\) | −4.29924 | −0.222905 | ||||||||
\(373\) | 11.5541 | 0.598249 | 0.299125 | − | 0.954214i | \(-0.403305\pi\) | ||||
0.299125 | + | 0.954214i | \(0.403305\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.17179 | −0.0605108 | ||||||||
\(376\) | 9.33379 | 0.481354 | ||||||||
\(377\) | −7.40416 | −0.381333 | ||||||||
\(378\) | −11.3352 | −0.583019 | ||||||||
\(379\) | −26.1411 | −1.34278 | −0.671390 | − | 0.741104i | \(-0.734302\pi\) | ||||
−0.671390 | + | 0.741104i | \(0.734302\pi\) | |||||||
\(380\) | −3.23849 | −0.166131 | ||||||||
\(381\) | −1.37010 | −0.0701924 | ||||||||
\(382\) | −24.2225 | −1.23933 | ||||||||
\(383\) | −13.0351 | −0.666064 | −0.333032 | − | 0.942916i | \(-0.608072\pi\) | ||||
−0.333032 | + | 0.942916i | \(0.608072\pi\) | |||||||
\(384\) | −7.14525 | −0.364630 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −23.0234 | −1.17186 | ||||||||
\(387\) | 12.4991 | 0.635366 | ||||||||
\(388\) | 30.3981 | 1.54323 | ||||||||
\(389\) | 19.3799 | 0.982602 | 0.491301 | − | 0.870990i | \(-0.336522\pi\) | ||||
0.491301 | + | 0.870990i | \(0.336522\pi\) | |||||||
\(390\) | −2.62007 | −0.132672 | ||||||||
\(391\) | −20.7104 | −1.04737 | ||||||||
\(392\) | −0.775558 | −0.0391716 | ||||||||
\(393\) | 0.235324 | 0.0118705 | ||||||||
\(394\) | −25.7813 | −1.29884 | ||||||||
\(395\) | −5.41792 | −0.272605 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.8036 | 1.39542 | 0.697712 | − | 0.716378i | \(-0.254202\pi\) | ||||
0.697712 | + | 0.716378i | \(0.254202\pi\) | |||||||
\(398\) | 19.7823 | 0.991598 | ||||||||
\(399\) | 1.60054 | 0.0801273 | ||||||||
\(400\) | −3.12047 | −0.156024 | ||||||||
\(401\) | −22.9886 | −1.14800 | −0.573998 | − | 0.818857i | \(-0.694608\pi\) | ||||
−0.573998 | + | 0.818857i | \(0.694608\pi\) | |||||||
\(402\) | 30.0887 | 1.50069 | ||||||||
\(403\) | −1.65499 | −0.0824410 | ||||||||
\(404\) | 15.6065 | 0.776453 | ||||||||
\(405\) | −1.47239 | −0.0731637 | ||||||||
\(406\) | −14.4740 | −0.718331 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −4.55926 | −0.225717 | ||||||||
\(409\) | −35.9430 | −1.77727 | −0.888634 | − | 0.458618i | \(-0.848345\pi\) | ||||
−0.888634 | + | 0.458618i | \(0.848345\pi\) | |||||||
\(410\) | 7.75417 | 0.382951 | ||||||||
\(411\) | 6.35848 | 0.313641 | ||||||||
\(412\) | 3.36894 | 0.165976 | ||||||||
\(413\) | −8.72837 | −0.429495 | ||||||||
\(414\) | 14.0414 | 0.690098 | ||||||||
\(415\) | 0.0466470 | 0.00228981 | ||||||||
\(416\) | −8.63616 | −0.423423 | ||||||||
\(417\) | −3.52741 | −0.172738 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.1444 | −0.935263 | −0.467632 | − | 0.883923i | \(-0.654893\pi\) | ||||
−0.467632 | + | 0.883923i | \(0.654893\pi\) | |||||||
\(420\) | −2.77826 | −0.135565 | ||||||||
\(421\) | 28.7275 | 1.40009 | 0.700046 | − | 0.714098i | \(-0.253163\pi\) | ||||
0.700046 | + | 0.714098i | \(0.253163\pi\) | |||||||
\(422\) | 21.8115 | 1.06177 | ||||||||
\(423\) | 19.5798 | 0.952004 | ||||||||
\(424\) | −2.95673 | −0.143591 | ||||||||
\(425\) | −5.01686 | −0.243353 | ||||||||
\(426\) | 17.8676 | 0.865689 | ||||||||
\(427\) | −12.4241 | −0.601245 | ||||||||
\(428\) | 25.0465 | 1.21067 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 16.0621 | 0.774584 | ||||||||
\(431\) | 12.9759 | 0.625025 | 0.312513 | − | 0.949914i | \(-0.398829\pi\) | ||||
0.312513 | + | 0.949914i | \(0.398829\pi\) | |||||||
\(432\) | −16.9184 | −0.813989 | ||||||||
\(433\) | −37.5382 | −1.80397 | −0.901985 | − | 0.431767i | \(-0.857890\pi\) | ||||
−0.901985 | + | 0.431767i | \(0.857890\pi\) | |||||||
\(434\) | −3.23525 | −0.155297 | ||||||||
\(435\) | −8.11237 | −0.388958 | ||||||||
\(436\) | −19.7374 | −0.945250 | ||||||||
\(437\) | −5.63866 | −0.269734 | ||||||||
\(438\) | −17.9476 | −0.857568 | ||||||||
\(439\) | −16.2174 | −0.774015 | −0.387007 | − | 0.922077i | \(-0.626491\pi\) | ||||
−0.387007 | + | 0.922077i | \(0.626491\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.62692 | −0.0774722 | ||||||||
\(442\) | −11.2175 | −0.533562 | ||||||||
\(443\) | −34.5866 | −1.64326 | −0.821629 | − | 0.570022i | \(-0.806935\pi\) | ||||
−0.821629 | + | 0.570022i | \(0.806935\pi\) | |||||||
\(444\) | −28.1705 | −1.33691 | ||||||||
\(445\) | −3.14060 | −0.148879 | ||||||||
\(446\) | 7.03012 | 0.332886 | ||||||||
\(447\) | 6.62584 | 0.313391 | ||||||||
\(448\) | −10.6414 | −0.502759 | ||||||||
\(449\) | −11.6118 | −0.547995 | −0.273998 | − | 0.961730i | \(-0.588346\pi\) | ||||
−0.273998 | + | 0.961730i | \(0.588346\pi\) | |||||||
\(450\) | 3.40137 | 0.160342 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 28.3986 | 1.33576 | ||||||||
\(453\) | 21.2103 | 0.996546 | ||||||||
\(454\) | −10.0805 | −0.473103 | ||||||||
\(455\) | −1.06949 | −0.0501384 | ||||||||
\(456\) | −1.24131 | −0.0581298 | ||||||||
\(457\) | −24.1449 | −1.12945 | −0.564726 | − | 0.825279i | \(-0.691018\pi\) | ||||
−0.564726 | + | 0.825279i | \(0.691018\pi\) | |||||||
\(458\) | 27.7783 | 1.29800 | ||||||||
\(459\) | −27.2002 | −1.26960 | ||||||||
\(460\) | 9.78772 | 0.456355 | ||||||||
\(461\) | 12.7118 | 0.592046 | 0.296023 | − | 0.955181i | \(-0.404340\pi\) | ||||
0.296023 | + | 0.955181i | \(0.404340\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.0814 | −0.933263 | −0.466632 | − | 0.884452i | \(-0.654533\pi\) | ||||
−0.466632 | + | 0.884452i | \(0.654533\pi\) | |||||||
\(464\) | −21.6033 | −1.00291 | ||||||||
\(465\) | −1.81329 | −0.0840894 | ||||||||
\(466\) | 47.4058 | 2.19603 | ||||||||
\(467\) | −19.9131 | −0.921467 | −0.460734 | − | 0.887538i | \(-0.652414\pi\) | ||||
−0.460734 | + | 0.887538i | \(0.652414\pi\) | |||||||
\(468\) | 4.12540 | 0.190697 | ||||||||
\(469\) | 12.2819 | 0.567126 | ||||||||
\(470\) | 25.1612 | 1.16060 | ||||||||
\(471\) | 16.9088 | 0.779117 | ||||||||
\(472\) | 6.76936 | 0.311585 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −13.2730 | −0.609649 | ||||||||
\(475\) | −1.36590 | −0.0626717 | ||||||||
\(476\) | −11.8948 | −0.545195 | ||||||||
\(477\) | −6.20244 | −0.283990 | ||||||||
\(478\) | 15.0741 | 0.689474 | ||||||||
\(479\) | −32.1313 | −1.46812 | −0.734058 | − | 0.679087i | \(-0.762376\pi\) | ||||
−0.734058 | + | 0.679087i | \(0.762376\pi\) | |||||||
\(480\) | −9.46222 | −0.431889 | ||||||||
\(481\) | −10.8442 | −0.494454 | ||||||||
\(482\) | −27.7041 | −1.26189 | ||||||||
\(483\) | −4.83733 | −0.220106 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.8210 | 0.582173 | ||||||||
\(486\) | 30.3984 | 1.37890 | ||||||||
\(487\) | 6.86275 | 0.310981 | 0.155490 | − | 0.987837i | \(-0.450304\pi\) | ||||
0.155490 | + | 0.987837i | \(0.450304\pi\) | |||||||
\(488\) | 9.63562 | 0.436184 | ||||||||
\(489\) | −8.83350 | −0.399465 | ||||||||
\(490\) | −2.09068 | −0.0944475 | ||||||||
\(491\) | 16.5239 | 0.745711 | 0.372856 | − | 0.927889i | \(-0.378379\pi\) | ||||
0.372856 | + | 0.927889i | \(0.378379\pi\) | |||||||
\(492\) | 10.3043 | 0.464555 | ||||||||
\(493\) | −34.7321 | −1.56425 | ||||||||
\(494\) | −3.05410 | −0.137410 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.82880 | −0.216820 | ||||||||
\(497\) | 7.29340 | 0.327154 | ||||||||
\(498\) | 0.114277 | 0.00512089 | ||||||||
\(499\) | 13.3608 | 0.598111 | 0.299056 | − | 0.954236i | \(-0.403328\pi\) | ||||
0.299056 | + | 0.954236i | \(0.403328\pi\) | |||||||
\(500\) | 2.37096 | 0.106033 | ||||||||
\(501\) | −13.5123 | −0.603685 | ||||||||
\(502\) | −53.4767 | −2.38678 | ||||||||
\(503\) | 41.5574 | 1.85295 | 0.926475 | − | 0.376355i | \(-0.122823\pi\) | ||||
0.926475 | + | 0.376355i | \(0.122823\pi\) | |||||||
\(504\) | 1.26177 | 0.0562037 | ||||||||
\(505\) | 6.58237 | 0.292911 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.8929 | 0.617006 | ||||||||
\(508\) | 2.77222 | 0.122998 | ||||||||
\(509\) | 20.1615 | 0.893644 | 0.446822 | − | 0.894623i | \(-0.352556\pi\) | ||||
0.446822 | + | 0.894623i | \(0.352556\pi\) | |||||||
\(510\) | −12.2905 | −0.544231 | ||||||||
\(511\) | −7.32603 | −0.324085 | ||||||||
\(512\) | −30.0381 | −1.32751 | ||||||||
\(513\) | −7.40557 | −0.326964 | ||||||||
\(514\) | 13.4791 | 0.594537 | ||||||||
\(515\) | 1.42092 | 0.0626132 | ||||||||
\(516\) | 21.3445 | 0.939641 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −21.1988 | −0.931420 | ||||||||
\(519\) | 11.7717 | 0.516720 | ||||||||
\(520\) | 0.829451 | 0.0363738 | ||||||||
\(521\) | 15.8795 | 0.695693 | 0.347846 | − | 0.937552i | \(-0.386913\pi\) | ||||
0.347846 | + | 0.937552i | \(0.386913\pi\) | |||||||
\(522\) | 23.5479 | 1.03067 | ||||||||
\(523\) | −19.5991 | −0.857007 | −0.428504 | − | 0.903540i | \(-0.640959\pi\) | ||||
−0.428504 | + | 0.903540i | \(0.640959\pi\) | |||||||
\(524\) | −0.476149 | −0.0208007 | ||||||||
\(525\) | −1.17179 | −0.0511409 | ||||||||
\(526\) | −37.1900 | −1.62156 | ||||||||
\(527\) | −7.76338 | −0.338178 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.95822 | −0.259053 | ||||||||
\(530\) | −7.97050 | −0.346216 | ||||||||
\(531\) | 14.2003 | 0.616242 | ||||||||
\(532\) | −3.23849 | −0.140406 | ||||||||
\(533\) | 3.96664 | 0.171814 | ||||||||
\(534\) | −7.69396 | −0.332950 | ||||||||
\(535\) | 10.5639 | 0.456715 | ||||||||
\(536\) | −9.52534 | −0.411432 | ||||||||
\(537\) | 19.1085 | 0.824593 | ||||||||
\(538\) | −31.0660 | −1.33935 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 12.8548 | 0.553181 | ||||||||
\(541\) | −22.2854 | −0.958124 | −0.479062 | − | 0.877781i | \(-0.659023\pi\) | ||||
−0.479062 | + | 0.877781i | \(0.659023\pi\) | |||||||
\(542\) | 27.5440 | 1.18312 | ||||||||
\(543\) | 13.7546 | 0.590268 | ||||||||
\(544\) | −40.5113 | −1.73691 | ||||||||
\(545\) | −8.32464 | −0.356589 | ||||||||
\(546\) | −2.62007 | −0.112129 | ||||||||
\(547\) | 38.5829 | 1.64969 | 0.824843 | − | 0.565361i | \(-0.191263\pi\) | ||||
0.824843 | + | 0.565361i | \(0.191263\pi\) | |||||||
\(548\) | −12.8656 | −0.549590 | ||||||||
\(549\) | 20.2130 | 0.862669 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.45622 | −0.402848 | ||||||||
\(552\) | 3.75163 | 0.159680 | ||||||||
\(553\) | −5.41792 | −0.230393 | ||||||||
\(554\) | −10.3039 | −0.437769 | ||||||||
\(555\) | −11.8815 | −0.504341 | ||||||||
\(556\) | 7.13725 | 0.302687 | ||||||||
\(557\) | −22.8525 | −0.968292 | −0.484146 | − | 0.874987i | \(-0.660870\pi\) | ||||
−0.484146 | + | 0.874987i | \(0.660870\pi\) | |||||||
\(558\) | 5.26348 | 0.222821 | ||||||||
\(559\) | 8.21657 | 0.347524 | ||||||||
\(560\) | −3.12047 | −0.131864 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 53.5598 | 2.25928 | ||||||||
\(563\) | 7.37512 | 0.310824 | 0.155412 | − | 0.987850i | \(-0.450329\pi\) | ||||
0.155412 | + | 0.987850i | \(0.450329\pi\) | |||||||
\(564\) | 33.4361 | 1.40792 | ||||||||
\(565\) | 11.9777 | 0.503905 | ||||||||
\(566\) | 52.8482 | 2.22137 | ||||||||
\(567\) | −1.47239 | −0.0618346 | ||||||||
\(568\) | −5.65646 | −0.237340 | ||||||||
\(569\) | 21.4100 | 0.897554 | 0.448777 | − | 0.893644i | \(-0.351860\pi\) | ||||
0.448777 | + | 0.893644i | \(0.351860\pi\) | |||||||
\(570\) | −3.34622 | −0.140158 | ||||||||
\(571\) | 11.6530 | 0.487661 | 0.243831 | − | 0.969818i | \(-0.421596\pi\) | ||||
0.243831 | + | 0.969818i | \(0.421596\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.5762 | −0.567156 | ||||||||
\(574\) | 7.75417 | 0.323653 | ||||||||
\(575\) | 4.12817 | 0.172157 | ||||||||
\(576\) | 17.3127 | 0.721362 | ||||||||
\(577\) | 32.0583 | 1.33460 | 0.667302 | − | 0.744788i | \(-0.267449\pi\) | ||||
0.667302 | + | 0.744788i | \(0.267449\pi\) | |||||||
\(578\) | −17.0785 | −0.710371 | ||||||||
\(579\) | −12.9041 | −0.536278 | ||||||||
\(580\) | 16.4143 | 0.681568 | ||||||||
\(581\) | 0.0466470 | 0.00193524 | ||||||||
\(582\) | 31.4094 | 1.30196 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 5.68176 | 0.235113 | ||||||||
\(585\) | 1.73997 | 0.0719389 | ||||||||
\(586\) | −49.9380 | −2.06292 | ||||||||
\(587\) | −8.23754 | −0.340000 | −0.170000 | − | 0.985444i | \(-0.554377\pi\) | ||||
−0.170000 | + | 0.985444i | \(0.554377\pi\) | |||||||
\(588\) | −2.77826 | −0.114573 | ||||||||
\(589\) | −2.11367 | −0.0870923 | ||||||||
\(590\) | 18.2483 | 0.751269 | ||||||||
\(591\) | −14.4499 | −0.594390 | ||||||||
\(592\) | −31.6404 | −1.30041 | ||||||||
\(593\) | 0.976706 | 0.0401085 | 0.0200543 | − | 0.999799i | \(-0.493616\pi\) | ||||
0.0200543 | + | 0.999799i | \(0.493616\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.01686 | −0.205671 | ||||||||
\(596\) | −13.4065 | −0.549153 | ||||||||
\(597\) | 11.0876 | 0.453785 | ||||||||
\(598\) | 9.23044 | 0.377461 | ||||||||
\(599\) | −12.9440 | −0.528876 | −0.264438 | − | 0.964403i | \(-0.585186\pi\) | ||||
−0.264438 | + | 0.964403i | \(0.585186\pi\) | |||||||
\(600\) | 0.908789 | 0.0371011 | ||||||||
\(601\) | 9.36714 | 0.382093 | 0.191047 | − | 0.981581i | \(-0.438812\pi\) | ||||
0.191047 | + | 0.981581i | \(0.438812\pi\) | |||||||
\(602\) | 16.0621 | 0.654643 | ||||||||
\(603\) | −19.9817 | −0.813716 | ||||||||
\(604\) | −42.9163 | −1.74624 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 16.1257 | 0.655062 | ||||||||
\(607\) | −3.92443 | −0.159288 | −0.0796439 | − | 0.996823i | \(-0.525378\pi\) | ||||
−0.0796439 | + | 0.996823i | \(0.525378\pi\) | |||||||
\(608\) | −11.0297 | −0.447312 | ||||||||
\(609\) | −8.11237 | −0.328730 | ||||||||
\(610\) | 25.9749 | 1.05169 | ||||||||
\(611\) | 12.8712 | 0.520714 | ||||||||
\(612\) | 19.3518 | 0.782250 | ||||||||
\(613\) | −47.1030 | −1.90247 | −0.951236 | − | 0.308463i | \(-0.900185\pi\) | ||||
−0.951236 | + | 0.308463i | \(0.900185\pi\) | |||||||
\(614\) | −57.6648 | −2.32716 | ||||||||
\(615\) | 4.34606 | 0.175250 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.1976 | −1.17545 | −0.587725 | − | 0.809061i | \(-0.699976\pi\) | ||||
−0.587725 | + | 0.809061i | \(0.699976\pi\) | |||||||
\(618\) | 3.48102 | 0.140027 | ||||||||
\(619\) | −14.4885 | −0.582342 | −0.291171 | − | 0.956671i | \(-0.594045\pi\) | ||||
−0.291171 | + | 0.956671i | \(0.594045\pi\) | |||||||
\(620\) | 3.66896 | 0.147349 | ||||||||
\(621\) | 22.3819 | 0.898156 | ||||||||
\(622\) | −26.7489 | −1.07253 | ||||||||
\(623\) | −3.14060 | −0.125826 | ||||||||
\(624\) | −3.91061 | −0.156550 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 7.66731 | 0.306447 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −34.2128 | −1.36524 | ||||||||
\(629\) | −50.8690 | −2.02828 | ||||||||
\(630\) | 3.40137 | 0.135514 | ||||||||
\(631\) | −4.24628 | −0.169042 | −0.0845209 | − | 0.996422i | \(-0.526936\pi\) | ||||
−0.0845209 | + | 0.996422i | \(0.526936\pi\) | |||||||
\(632\) | 4.20191 | 0.167143 | ||||||||
\(633\) | 12.2249 | 0.485897 | ||||||||
\(634\) | −61.3893 | −2.43808 | ||||||||
\(635\) | 1.16924 | 0.0463999 | ||||||||
\(636\) | −10.5918 | −0.419992 | ||||||||
\(637\) | −1.06949 | −0.0423747 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.8658 | −0.469402 | ||||||||
\(640\) | 6.09774 | 0.241034 | ||||||||
\(641\) | −5.47306 | −0.216173 | −0.108086 | − | 0.994142i | \(-0.534472\pi\) | ||||
−0.108086 | + | 0.994142i | \(0.534472\pi\) | |||||||
\(642\) | 25.8797 | 1.02139 | ||||||||
\(643\) | −4.59595 | −0.181247 | −0.0906233 | − | 0.995885i | \(-0.528886\pi\) | ||||
−0.0906233 | + | 0.995885i | \(0.528886\pi\) | |||||||
\(644\) | 9.78772 | 0.385690 | ||||||||
\(645\) | 9.00249 | 0.354473 | ||||||||
\(646\) | −14.3264 | −0.563666 | ||||||||
\(647\) | 46.8490 | 1.84183 | 0.920913 | − | 0.389769i | \(-0.127445\pi\) | ||||
0.920913 | + | 0.389769i | \(0.127445\pi\) | |||||||
\(648\) | 1.14192 | 0.0448590 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.23596 | 0.0877017 | ||||||||
\(651\) | −1.81329 | −0.0710685 | ||||||||
\(652\) | 17.8735 | 0.699979 | ||||||||
\(653\) | −19.7735 | −0.773798 | −0.386899 | − | 0.922122i | \(-0.626454\pi\) | ||||
−0.386899 | + | 0.922122i | \(0.626454\pi\) | |||||||
\(654\) | −20.3940 | −0.797469 | ||||||||
\(655\) | −0.200825 | −0.00784689 | ||||||||
\(656\) | 11.5736 | 0.451872 | ||||||||
\(657\) | 11.9188 | 0.464998 | ||||||||
\(658\) | 25.1612 | 0.980887 | ||||||||
\(659\) | −0.186499 | −0.00726498 | −0.00363249 | − | 0.999993i | \(-0.501156\pi\) | ||||
−0.00363249 | + | 0.999993i | \(0.501156\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.06632 | 0.197057 | 0.0985285 | − | 0.995134i | \(-0.468586\pi\) | ||||
0.0985285 | + | 0.995134i | \(0.468586\pi\) | |||||||
\(662\) | 50.0046 | 1.94348 | ||||||||
\(663\) | −6.28719 | −0.244174 | ||||||||
\(664\) | −0.0361775 | −0.00140396 | ||||||||
\(665\) | −1.36590 | −0.0529673 | ||||||||
\(666\) | 34.4886 | 1.33641 | ||||||||
\(667\) | 28.5796 | 1.10661 | ||||||||
\(668\) | 27.3404 | 1.05783 | ||||||||
\(669\) | 3.94024 | 0.152339 | ||||||||
\(670\) | −25.6776 | −0.992012 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −9.46222 | −0.365013 | ||||||||
\(673\) | −10.1700 | −0.392023 | −0.196012 | − | 0.980602i | \(-0.562799\pi\) | ||||
−0.196012 | + | 0.980602i | \(0.562799\pi\) | |||||||
\(674\) | 52.9820 | 2.04079 | ||||||||
\(675\) | 5.42176 | 0.208684 | ||||||||
\(676\) | −28.1105 | −1.08117 | ||||||||
\(677\) | 3.28103 | 0.126100 | 0.0630500 | − | 0.998010i | \(-0.479917\pi\) | ||||
0.0630500 | + | 0.998010i | \(0.479917\pi\) | |||||||
\(678\) | 29.3433 | 1.12692 | ||||||||
\(679\) | 12.8210 | 0.492026 | ||||||||
\(680\) | 3.89086 | 0.149208 | ||||||||
\(681\) | −5.64994 | −0.216506 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.11730 | −0.0427523 | −0.0213762 | − | 0.999772i | \(-0.506805\pi\) | ||||
−0.0213762 | + | 0.999772i | \(0.506805\pi\) | |||||||
\(684\) | 5.26875 | 0.201456 | ||||||||
\(685\) | −5.42631 | −0.207329 | ||||||||
\(686\) | −2.09068 | −0.0798227 | ||||||||
\(687\) | 15.5692 | 0.594002 | ||||||||
\(688\) | 23.9737 | 0.913987 | ||||||||
\(689\) | −4.07731 | −0.155333 | ||||||||
\(690\) | 10.1133 | 0.385008 | ||||||||
\(691\) | −40.3162 | −1.53370 | −0.766850 | − | 0.641826i | \(-0.778177\pi\) | ||||
−0.766850 | + | 0.641826i | \(0.778177\pi\) | |||||||
\(692\) | −23.8185 | −0.905444 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 72.8921 | 2.76695 | ||||||||
\(695\) | 3.01028 | 0.114186 | ||||||||
\(696\) | 6.29161 | 0.238483 | ||||||||
\(697\) | 18.6071 | 0.704794 | ||||||||
\(698\) | 1.58822 | 0.0601149 | ||||||||
\(699\) | 26.5700 | 1.00497 | ||||||||
\(700\) | 2.37096 | 0.0896138 | ||||||||
\(701\) | 4.75394 | 0.179554 | 0.0897769 | − | 0.995962i | \(-0.471385\pi\) | ||||
0.0897769 | + | 0.995962i | \(0.471385\pi\) | |||||||
\(702\) | 12.1229 | 0.457548 | ||||||||
\(703\) | −13.8497 | −0.522351 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14.1024 | 0.531126 | ||||||||
\(706\) | 75.5639 | 2.84388 | ||||||||
\(707\) | 6.58237 | 0.247555 | ||||||||
\(708\) | 24.2497 | 0.911358 | ||||||||
\(709\) | −47.5235 | −1.78478 | −0.892392 | − | 0.451261i | \(-0.850974\pi\) | ||||
−0.892392 | + | 0.451261i | \(0.850974\pi\) | |||||||
\(710\) | −15.2482 | −0.572254 | ||||||||
\(711\) | 8.81450 | 0.330570 | ||||||||
\(712\) | 2.43572 | 0.0912826 | ||||||||
\(713\) | 6.38817 | 0.239239 | ||||||||
\(714\) | −12.2905 | −0.459959 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −38.6636 | −1.44493 | ||||||||
\(717\) | 8.44874 | 0.315524 | ||||||||
\(718\) | −17.4068 | −0.649617 | ||||||||
\(719\) | 15.6866 | 0.585011 | 0.292506 | − | 0.956264i | \(-0.405511\pi\) | ||||
0.292506 | + | 0.956264i | \(0.405511\pi\) | |||||||
\(720\) | 5.07675 | 0.189199 | ||||||||
\(721\) | 1.42092 | 0.0529178 | ||||||||
\(722\) | 35.8225 | 1.33317 | ||||||||
\(723\) | −15.5276 | −0.577478 | ||||||||
\(724\) | −27.8307 | −1.03432 | ||||||||
\(725\) | 6.92308 | 0.257117 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.7434 | −1.32565 | −0.662824 | − | 0.748775i | \(-0.730642\pi\) | ||||
−0.662824 | + | 0.748775i | \(0.730642\pi\) | |||||||
\(728\) | 0.829451 | 0.0307415 | ||||||||
\(729\) | 21.4549 | 0.794625 | ||||||||
\(730\) | 15.3164 | 0.566886 | ||||||||
\(731\) | 38.5430 | 1.42557 | ||||||||
\(732\) | 34.5174 | 1.27580 | ||||||||
\(733\) | −28.5664 | −1.05512 | −0.527562 | − | 0.849517i | \(-0.676894\pi\) | ||||
−0.527562 | + | 0.849517i | \(0.676894\pi\) | |||||||
\(734\) | 71.7585 | 2.64866 | ||||||||
\(735\) | −1.17179 | −0.0432220 | ||||||||
\(736\) | 33.3351 | 1.22875 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −12.6154 | −0.464379 | ||||||||
\(739\) | −7.97795 | −0.293474 | −0.146737 | − | 0.989176i | \(-0.546877\pi\) | ||||
−0.146737 | + | 0.989176i | \(0.546877\pi\) | |||||||
\(740\) | 24.0406 | 0.883752 | ||||||||
\(741\) | −1.71176 | −0.0628831 | ||||||||
\(742\) | −7.97050 | −0.292606 | ||||||||
\(743\) | 44.8508 | 1.64542 | 0.822708 | − | 0.568464i | \(-0.192462\pi\) | ||||
0.822708 | + | 0.568464i | \(0.192462\pi\) | |||||||
\(744\) | 1.40631 | 0.0515580 | ||||||||
\(745\) | −5.65447 | −0.207164 | ||||||||
\(746\) | −24.1560 | −0.884414 | ||||||||
\(747\) | −0.0758908 | −0.00277670 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.5639 | 0.385995 | ||||||||
\(750\) | 2.44983 | 0.0894553 | ||||||||
\(751\) | 49.7175 | 1.81422 | 0.907108 | − | 0.420897i | \(-0.138285\pi\) | ||||
0.907108 | + | 0.420897i | \(0.138285\pi\) | |||||||
\(752\) | 37.5547 | 1.36948 | ||||||||
\(753\) | −29.9726 | −1.09226 | ||||||||
\(754\) | 15.4797 | 0.563739 | ||||||||
\(755\) | −18.1008 | −0.658756 | ||||||||
\(756\) | 12.8548 | 0.467523 | ||||||||
\(757\) | 0.797363 | 0.0289807 | 0.0144903 | − | 0.999895i | \(-0.495387\pi\) | ||||
0.0144903 | + | 0.999895i | \(0.495387\pi\) | |||||||
\(758\) | 54.6528 | 1.98508 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.05933 | 0.0384261 | ||||||||
\(761\) | −38.6346 | −1.40050 | −0.700251 | − | 0.713897i | \(-0.746929\pi\) | ||||
−0.700251 | + | 0.713897i | \(0.746929\pi\) | |||||||
\(762\) | 2.86445 | 0.103768 | ||||||||
\(763\) | −8.32464 | −0.301372 | ||||||||
\(764\) | 27.4698 | 0.993822 | ||||||||
\(765\) | 8.16201 | 0.295098 | ||||||||
\(766\) | 27.2523 | 0.984667 | ||||||||
\(767\) | 9.33490 | 0.337064 | ||||||||
\(768\) | −10.0004 | −0.360860 | ||||||||
\(769\) | −37.9357 | −1.36800 | −0.683999 | − | 0.729483i | \(-0.739761\pi\) | ||||
−0.683999 | + | 0.729483i | \(0.739761\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.55475 | 0.272078 | ||||||||
\(772\) | 26.1099 | 0.939715 | ||||||||
\(773\) | 1.46474 | 0.0526830 | 0.0263415 | − | 0.999653i | \(-0.491614\pi\) | ||||
0.0263415 | + | 0.999653i | \(0.491614\pi\) | |||||||
\(774\) | −26.1317 | −0.939285 | ||||||||
\(775\) | 1.54746 | 0.0555864 | ||||||||
\(776\) | −9.94346 | −0.356949 | ||||||||
\(777\) | −11.8815 | −0.426246 | ||||||||
\(778\) | −40.5173 | −1.45262 | ||||||||
\(779\) | 5.06600 | 0.181508 | ||||||||
\(780\) | 2.97132 | 0.106390 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 43.2990 | 1.54837 | ||||||||
\(783\) | 37.5352 | 1.34140 | ||||||||
\(784\) | −3.12047 | −0.111445 | ||||||||
\(785\) | −14.4299 | −0.515027 | ||||||||
\(786\) | −0.491989 | −0.0175487 | ||||||||
\(787\) | −12.2969 | −0.438339 | −0.219169 | − | 0.975687i | \(-0.570335\pi\) | ||||
−0.219169 | + | 0.975687i | \(0.570335\pi\) | |||||||
\(788\) | 29.2376 | 1.04154 | ||||||||
\(789\) | −20.8443 | −0.742076 | ||||||||
\(790\) | 11.3272 | 0.403002 | ||||||||
\(791\) | 11.9777 | 0.425877 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.2874 | 0.471851 | ||||||||
\(794\) | −58.1286 | −2.06291 | ||||||||
\(795\) | −4.46730 | −0.158439 | ||||||||
\(796\) | −22.4343 | −0.795163 | ||||||||
\(797\) | −24.9795 | −0.884818 | −0.442409 | − | 0.896813i | \(-0.645876\pi\) | ||||
−0.442409 | + | 0.896813i | \(0.645876\pi\) | |||||||
\(798\) | −3.34622 | −0.118455 | ||||||||
\(799\) | 60.3775 | 2.13600 | ||||||||
\(800\) | 8.07504 | 0.285496 | ||||||||
\(801\) | 5.10950 | 0.180535 | ||||||||
\(802\) | 48.0619 | 1.69712 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −34.1223 | −1.20340 | ||||||||
\(805\) | 4.12817 | 0.145499 | ||||||||
\(806\) | 3.46006 | 0.121876 | ||||||||
\(807\) | −17.4119 | −0.612926 | ||||||||
\(808\) | −5.10501 | −0.179594 | ||||||||
\(809\) | −29.7899 | −1.04736 | −0.523679 | − | 0.851916i | \(-0.675441\pi\) | ||||
−0.523679 | + | 0.851916i | \(0.675441\pi\) | |||||||
\(810\) | 3.07830 | 0.108161 | ||||||||
\(811\) | 17.8361 | 0.626311 | 0.313156 | − | 0.949702i | \(-0.398614\pi\) | ||||
0.313156 | + | 0.949702i | \(0.398614\pi\) | |||||||
\(812\) | 16.4143 | 0.576030 | ||||||||
\(813\) | 15.4379 | 0.541430 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.53849 | 0.264062 | ||||||||
\(816\) | −18.3443 | −0.642177 | ||||||||
\(817\) | 10.4938 | 0.367131 | ||||||||
\(818\) | 75.1455 | 2.62740 | ||||||||
\(819\) | 1.73997 | 0.0607995 | ||||||||
\(820\) | −8.79369 | −0.307089 | ||||||||
\(821\) | −37.5866 | −1.31178 | −0.655890 | − | 0.754857i | \(-0.727706\pi\) | ||||
−0.655890 | + | 0.754857i | \(0.727706\pi\) | |||||||
\(822\) | −13.2936 | −0.463667 | ||||||||
\(823\) | −4.98553 | −0.173785 | −0.0868923 | − | 0.996218i | \(-0.527694\pi\) | ||||
−0.0868923 | + | 0.996218i | \(0.527694\pi\) | |||||||
\(824\) | −1.10201 | −0.0383902 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 18.2483 | 0.634938 | ||||||||
\(827\) | 8.03345 | 0.279351 | 0.139675 | − | 0.990197i | \(-0.455394\pi\) | ||||
0.139675 | + | 0.990197i | \(0.455394\pi\) | |||||||
\(828\) | −15.9238 | −0.553391 | ||||||||
\(829\) | −31.0863 | −1.07967 | −0.539836 | − | 0.841770i | \(-0.681514\pi\) | ||||
−0.539836 | + | 0.841770i | \(0.681514\pi\) | |||||||
\(830\) | −0.0975241 | −0.00338511 | ||||||||
\(831\) | −5.77511 | −0.200336 | ||||||||
\(832\) | 11.3809 | 0.394561 | ||||||||
\(833\) | −5.01686 | −0.173824 | ||||||||
\(834\) | 7.37469 | 0.255365 | ||||||||
\(835\) | 11.5314 | 0.399060 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.38995 | 0.289999 | ||||||||
\(838\) | 40.0248 | 1.38263 | ||||||||
\(839\) | −16.6694 | −0.575492 | −0.287746 | − | 0.957707i | \(-0.592906\pi\) | ||||
−0.287746 | + | 0.957707i | \(0.592906\pi\) | |||||||
\(840\) | 0.908789 | 0.0313562 | ||||||||
\(841\) | 18.9290 | 0.652724 | ||||||||
\(842\) | −60.0601 | −2.06981 | ||||||||
\(843\) | 30.0192 | 1.03392 | ||||||||
\(844\) | −24.7355 | −0.851432 | ||||||||
\(845\) | −11.8562 | −0.407865 | ||||||||
\(846\) | −40.9353 | −1.40738 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −11.8964 | −0.408526 | ||||||||
\(849\) | 29.6203 | 1.01657 | ||||||||
\(850\) | 10.4887 | 0.359758 | ||||||||
\(851\) | 41.8581 | 1.43488 | ||||||||
\(852\) | −20.2629 | −0.694197 | ||||||||
\(853\) | −13.9370 | −0.477195 | −0.238598 | − | 0.971119i | \(-0.576688\pi\) | ||||
−0.238598 | + | 0.971119i | \(0.576688\pi\) | |||||||
\(854\) | 25.9749 | 0.888842 | ||||||||
\(855\) | 2.22220 | 0.0759977 | ||||||||
\(856\) | −8.19289 | −0.280027 | ||||||||
\(857\) | −53.5529 | −1.82933 | −0.914666 | − | 0.404211i | \(-0.867546\pi\) | ||||
−0.914666 | + | 0.404211i | \(0.867546\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.4377 | 0.458488 | 0.229244 | − | 0.973369i | \(-0.426375\pi\) | ||||
0.229244 | + | 0.973369i | \(0.426375\pi\) | |||||||
\(860\) | −18.2154 | −0.621139 | ||||||||
\(861\) | 4.34606 | 0.148113 | ||||||||
\(862\) | −27.1284 | −0.923997 | ||||||||
\(863\) | −23.5880 | −0.802943 | −0.401472 | − | 0.915871i | \(-0.631501\pi\) | ||||
−0.401472 | + | 0.915871i | \(0.631501\pi\) | |||||||
\(864\) | 43.7809 | 1.48946 | ||||||||
\(865\) | −10.0459 | −0.341572 | ||||||||
\(866\) | 78.4805 | 2.66688 | ||||||||
\(867\) | −9.57214 | −0.325087 | ||||||||
\(868\) | 3.66896 | 0.124533 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 16.9604 | 0.575011 | ||||||||
\(871\) | −13.1354 | −0.445075 | ||||||||
\(872\) | 6.45625 | 0.218636 | ||||||||
\(873\) | −20.8588 | −0.705962 | ||||||||
\(874\) | 11.7887 | 0.398757 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 20.3536 | 0.687684 | ||||||||
\(877\) | −41.4253 | −1.39883 | −0.699416 | − | 0.714715i | \(-0.746556\pi\) | ||||
−0.699416 | + | 0.714715i | \(0.746556\pi\) | |||||||
\(878\) | 33.9055 | 1.14425 | ||||||||
\(879\) | −27.9892 | −0.944053 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.9662 | 0.740059 | 0.370029 | − | 0.929020i | \(-0.379348\pi\) | ||||
0.370029 | + | 0.929020i | \(0.379348\pi\) | |||||||
\(882\) | 3.40137 | 0.114530 | ||||||||
\(883\) | −21.2030 | −0.713539 | −0.356770 | − | 0.934192i | \(-0.616122\pi\) | ||||
−0.356770 | + | 0.934192i | \(0.616122\pi\) | |||||||
\(884\) | 12.7213 | 0.427864 | ||||||||
\(885\) | 10.2278 | 0.343803 | ||||||||
\(886\) | 72.3096 | 2.42929 | ||||||||
\(887\) | 7.91729 | 0.265837 | 0.132918 | − | 0.991127i | \(-0.457565\pi\) | ||||
0.132918 | + | 0.991127i | \(0.457565\pi\) | |||||||
\(888\) | 9.21478 | 0.309228 | ||||||||
\(889\) | 1.16924 | 0.0392151 | ||||||||
\(890\) | 6.56601 | 0.220093 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.97257 | −0.266941 | ||||||||
\(893\) | 16.4385 | 0.550093 | ||||||||
\(894\) | −13.8525 | −0.463298 | ||||||||
\(895\) | −16.3072 | −0.545089 | ||||||||
\(896\) | 6.09774 | 0.203711 | ||||||||
\(897\) | 5.17347 | 0.172737 | ||||||||
\(898\) | 24.2766 | 0.810122 | ||||||||
\(899\) | 10.7132 | 0.357305 | ||||||||
\(900\) | −3.85735 | −0.128578 | ||||||||
\(901\) | −19.1262 | −0.637186 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.00249 | 0.299584 | ||||||||
\(904\) | −9.28939 | −0.308960 | ||||||||
\(905\) | −11.7382 | −0.390190 | ||||||||
\(906\) | −44.3440 | −1.47323 | ||||||||
\(907\) | 14.2135 | 0.471951 | 0.235975 | − | 0.971759i | \(-0.424171\pi\) | ||||
0.235975 | + | 0.971759i | \(0.424171\pi\) | |||||||
\(908\) | 11.4319 | 0.379382 | ||||||||
\(909\) | −10.7090 | −0.355194 | ||||||||
\(910\) | 2.23596 | 0.0741215 | ||||||||
\(911\) | 47.1079 | 1.56076 | 0.780378 | − | 0.625308i | \(-0.215027\pi\) | ||||
0.780378 | + | 0.625308i | \(0.215027\pi\) | |||||||
\(912\) | −4.99444 | −0.165382 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 50.4794 | 1.66971 | ||||||||
\(915\) | 14.5584 | 0.481286 | ||||||||
\(916\) | −31.5023 | −1.04086 | ||||||||
\(917\) | −0.200825 | −0.00663184 | ||||||||
\(918\) | 56.8670 | 1.87689 | ||||||||
\(919\) | 27.3086 | 0.900827 | 0.450414 | − | 0.892820i | \(-0.351277\pi\) | ||||
0.450414 | + | 0.892820i | \(0.351277\pi\) | |||||||
\(920\) | −3.20164 | −0.105555 | ||||||||
\(921\) | −32.3200 | −1.06498 | ||||||||
\(922\) | −26.5763 | −0.875243 | ||||||||
\(923\) | −7.80021 | −0.256747 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.1396 | 0.333389 | ||||||||
\(926\) | 41.9839 | 1.37968 | ||||||||
\(927\) | −2.31172 | −0.0759267 | ||||||||
\(928\) | 55.9041 | 1.83514 | ||||||||
\(929\) | −44.6107 | −1.46363 | −0.731815 | − | 0.681503i | \(-0.761326\pi\) | ||||
−0.731815 | + | 0.681503i | \(0.761326\pi\) | |||||||
\(930\) | 3.79102 | 0.124312 | ||||||||
\(931\) | −1.36590 | −0.0447655 | ||||||||
\(932\) | −53.7610 | −1.76100 | ||||||||
\(933\) | −14.9922 | −0.490824 | ||||||||
\(934\) | 41.6320 | 1.36224 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.34945 | −0.0441081 | ||||||||
\(937\) | 44.6166 | 1.45756 | 0.728781 | − | 0.684747i | \(-0.240087\pi\) | ||||
0.728781 | + | 0.684747i | \(0.240087\pi\) | |||||||
\(938\) | −25.6776 | −0.838403 | ||||||||
\(939\) | 4.29737 | 0.140239 | ||||||||
\(940\) | −28.5343 | −0.930687 | ||||||||
\(941\) | 47.7722 | 1.55733 | 0.778665 | − | 0.627440i | \(-0.215897\pi\) | ||||
0.778665 | + | 0.627440i | \(0.215897\pi\) | |||||||
\(942\) | −35.3510 | −1.15180 | ||||||||
\(943\) | −15.3110 | −0.498596 | ||||||||
\(944\) | 27.2366 | 0.886476 | ||||||||
\(945\) | 5.42176 | 0.176370 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −44.1814 | −1.43570 | −0.717851 | − | 0.696197i | \(-0.754874\pi\) | ||||
−0.717851 | + | 0.696197i | \(0.754874\pi\) | |||||||
\(948\) | 15.0524 | 0.488878 | ||||||||
\(949\) | 7.83511 | 0.254338 | ||||||||
\(950\) | 2.85566 | 0.0926499 | ||||||||
\(951\) | −34.4075 | −1.11574 | ||||||||
\(952\) | 3.89086 | 0.126104 | ||||||||
\(953\) | −27.6676 | −0.896241 | −0.448121 | − | 0.893973i | \(-0.647906\pi\) | ||||
−0.448121 | + | 0.893973i | \(0.647906\pi\) | |||||||
\(954\) | 12.9673 | 0.419833 | ||||||||
\(955\) | 11.5859 | 0.374912 | ||||||||
\(956\) | −17.0949 | −0.552890 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 67.1764 | 2.17037 | ||||||||
\(959\) | −5.42631 | −0.175225 | ||||||||
\(960\) | 12.4695 | 0.402450 | ||||||||
\(961\) | −28.6054 | −0.922754 | ||||||||
\(962\) | 22.6718 | 0.730969 | ||||||||
\(963\) | −17.1865 | −0.553828 | ||||||||
\(964\) | 31.4181 | 1.01191 | ||||||||
\(965\) | 11.0124 | 0.354501 | ||||||||
\(966\) | 10.1133 | 0.325391 | ||||||||
\(967\) | 51.9072 | 1.66922 | 0.834611 | − | 0.550840i | \(-0.185693\pi\) | ||||
0.834611 | + | 0.550840i | \(0.185693\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.02968 | −0.257951 | ||||||||
\(970\) | −26.8047 | −0.860648 | ||||||||
\(971\) | −28.4215 | −0.912089 | −0.456045 | − | 0.889957i | \(-0.650734\pi\) | ||||
−0.456045 | + | 0.889957i | \(0.650734\pi\) | |||||||
\(972\) | −34.4736 | −1.10574 | ||||||||
\(973\) | 3.01028 | 0.0965052 | ||||||||
\(974\) | −14.3478 | −0.459735 | ||||||||
\(975\) | 1.25321 | 0.0401349 | ||||||||
\(976\) | 38.7691 | 1.24097 | ||||||||
\(977\) | 7.22406 | 0.231118 | 0.115559 | − | 0.993301i | \(-0.463134\pi\) | ||||
0.115559 | + | 0.993301i | \(0.463134\pi\) | |||||||
\(978\) | 18.4681 | 0.590543 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 2.37096 | 0.0757375 | ||||||||
\(981\) | 13.5435 | 0.432411 | ||||||||
\(982\) | −34.5462 | −1.10241 | ||||||||
\(983\) | −47.4725 | −1.51414 | −0.757068 | − | 0.653336i | \(-0.773369\pi\) | ||||
−0.757068 | + | 0.653336i | \(0.773369\pi\) | |||||||
\(984\) | −3.37062 | −0.107451 | ||||||||
\(985\) | 12.3315 | 0.392915 | ||||||||
\(986\) | 72.6138 | 2.31249 | ||||||||
\(987\) | 14.1024 | 0.448883 | ||||||||
\(988\) | 3.46353 | 0.110190 | ||||||||
\(989\) | −31.7155 | −1.00849 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.7713 | 1.26338 | 0.631688 | − | 0.775223i | \(-0.282362\pi\) | ||||
0.631688 | + | 0.775223i | \(0.282362\pi\) | |||||||
\(992\) | 12.4958 | 0.396742 | ||||||||
\(993\) | 28.0265 | 0.889396 | ||||||||
\(994\) | −15.2482 | −0.483643 | ||||||||
\(995\) | −9.46213 | −0.299970 | ||||||||
\(996\) | −0.129597 | −0.00410645 | ||||||||
\(997\) | 51.0645 | 1.61723 | 0.808614 | − | 0.588339i | \(-0.200218\pi\) | ||||
0.808614 | + | 0.588339i | \(0.200218\pi\) | |||||||
\(998\) | −27.9332 | −0.884210 | ||||||||
\(999\) | 54.9746 | 1.73932 |
(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 | 4235.2.a.bi.1.2 | ✓ | 10 | |
11.10 | odd | 2 | 4235.2.a.bk.1.9 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4235.2.a.bi.1.2 | ✓ | 10 | 1.1 | even | 1 | trivial | |
4235.2.a.bk.1.9 | yes | 10 | 11.10 | odd | 2 |