Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2166,2,Mod(1,2166)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2166, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2166.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2166 = 2 \cdot 3 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2166.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: | \(17.2955970778\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{18})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 114) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.53209\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2166.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.18479 | 0.529855 | 0.264928 | − | 0.964268i | \(-0.414652\pi\) | ||||
0.264928 | + | 0.964268i | \(0.414652\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0.532089 | 0.201111 | 0.100555 | − | 0.994931i | \(-0.467938\pi\) | ||||
0.100555 | + | 0.994931i | \(0.467938\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.18479 | 0.374664 | ||||||||
\(11\) | 1.87939 | 0.566656 | 0.283328 | − | 0.959023i | \(-0.408561\pi\) | ||||
0.283328 | + | 0.959023i | \(0.408561\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 3.87939 | 1.07595 | 0.537974 | − | 0.842961i | \(-0.319190\pi\) | ||||
0.537974 | + | 0.842961i | \(0.319190\pi\) | |||||||
\(14\) | 0.532089 | 0.142207 | ||||||||
\(15\) | 1.18479 | 0.305912 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.16250 | 0.281949 | 0.140974 | − | 0.990013i | \(-0.454977\pi\) | ||||
0.140974 | + | 0.990013i | \(0.454977\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 1.18479 | 0.264928 | ||||||||
\(21\) | 0.532089 | 0.116111 | ||||||||
\(22\) | 1.87939 | 0.400686 | ||||||||
\(23\) | −6.70233 | −1.39753 | −0.698767 | − | 0.715350i | \(-0.746267\pi\) | ||||
−0.698767 | + | 0.715350i | \(0.746267\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −3.59627 | −0.719253 | ||||||||
\(26\) | 3.87939 | 0.760810 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.532089 | 0.100555 | ||||||||
\(29\) | 4.02229 | 0.746920 | 0.373460 | − | 0.927646i | \(-0.378171\pi\) | ||||
0.373460 | + | 0.927646i | \(0.378171\pi\) | |||||||
\(30\) | 1.18479 | 0.216313 | ||||||||
\(31\) | 1.95811 | 0.351687 | 0.175844 | − | 0.984418i | \(-0.443735\pi\) | ||||
0.175844 | + | 0.984418i | \(0.443735\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.87939 | 0.327159 | ||||||||
\(34\) | 1.16250 | 0.199368 | ||||||||
\(35\) | 0.630415 | 0.106560 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −6.88713 | −1.13224 | −0.566118 | − | 0.824324i | \(-0.691555\pi\) | ||||
−0.566118 | + | 0.824324i | \(0.691555\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.87939 | 0.621199 | ||||||||
\(40\) | 1.18479 | 0.187332 | ||||||||
\(41\) | 8.98545 | 1.40329 | 0.701646 | − | 0.712526i | \(-0.252449\pi\) | ||||
0.701646 | + | 0.712526i | \(0.252449\pi\) | |||||||
\(42\) | 0.532089 | 0.0821031 | ||||||||
\(43\) | 2.42602 | 0.369965 | 0.184982 | − | 0.982742i | \(-0.440777\pi\) | ||||
0.184982 | + | 0.982742i | \(0.440777\pi\) | |||||||
\(44\) | 1.87939 | 0.283328 | ||||||||
\(45\) | 1.18479 | 0.176618 | ||||||||
\(46\) | −6.70233 | −0.988205 | ||||||||
\(47\) | 2.04189 | 0.297840 | 0.148920 | − | 0.988849i | \(-0.452420\pi\) | ||||
0.148920 | + | 0.988849i | \(0.452420\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −6.71688 | −0.959554 | ||||||||
\(50\) | −3.59627 | −0.508589 | ||||||||
\(51\) | 1.16250 | 0.162783 | ||||||||
\(52\) | 3.87939 | 0.537974 | ||||||||
\(53\) | −12.9709 | −1.78169 | −0.890845 | − | 0.454307i | \(-0.849887\pi\) | ||||
−0.890845 | + | 0.454307i | \(0.849887\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 2.22668 | 0.300246 | ||||||||
\(56\) | 0.532089 | 0.0711034 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.02229 | 0.528152 | ||||||||
\(59\) | 2.68004 | 0.348912 | 0.174456 | − | 0.984665i | \(-0.444183\pi\) | ||||
0.174456 | + | 0.984665i | \(0.444183\pi\) | |||||||
\(60\) | 1.18479 | 0.152956 | ||||||||
\(61\) | −11.3473 | −1.45287 | −0.726436 | − | 0.687234i | \(-0.758825\pi\) | ||||
−0.726436 | + | 0.687234i | \(0.758825\pi\) | |||||||
\(62\) | 1.95811 | 0.248680 | ||||||||
\(63\) | 0.532089 | 0.0670369 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.59627 | 0.570097 | ||||||||
\(66\) | 1.87939 | 0.231336 | ||||||||
\(67\) | 11.1702 | 1.36466 | 0.682331 | − | 0.731043i | \(-0.260966\pi\) | ||||
0.682331 | + | 0.731043i | \(0.260966\pi\) | |||||||
\(68\) | 1.16250 | 0.140974 | ||||||||
\(69\) | −6.70233 | −0.806866 | ||||||||
\(70\) | 0.630415 | 0.0753490 | ||||||||
\(71\) | −6.07192 | −0.720604 | −0.360302 | − | 0.932836i | \(-0.617326\pi\) | ||||
−0.360302 | + | 0.932836i | \(0.617326\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −0.327696 | −0.0383539 | −0.0191770 | − | 0.999816i | \(-0.506105\pi\) | ||||
−0.0191770 | + | 0.999816i | \(0.506105\pi\) | |||||||
\(74\) | −6.88713 | −0.800612 | ||||||||
\(75\) | −3.59627 | −0.415261 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 3.87939 | 0.439254 | ||||||||
\(79\) | 16.1334 | 1.81515 | 0.907575 | − | 0.419890i | \(-0.137931\pi\) | ||||
0.907575 | + | 0.419890i | \(0.137931\pi\) | |||||||
\(80\) | 1.18479 | 0.132464 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 8.98545 | 0.992277 | ||||||||
\(83\) | 11.5740 | 1.27041 | 0.635205 | − | 0.772344i | \(-0.280916\pi\) | ||||
0.635205 | + | 0.772344i | \(0.280916\pi\) | |||||||
\(84\) | 0.532089 | 0.0580557 | ||||||||
\(85\) | 1.37733 | 0.149392 | ||||||||
\(86\) | 2.42602 | 0.261605 | ||||||||
\(87\) | 4.02229 | 0.431235 | ||||||||
\(88\) | 1.87939 | 0.200343 | ||||||||
\(89\) | 3.55943 | 0.377299 | 0.188649 | − | 0.982044i | \(-0.439589\pi\) | ||||
0.188649 | + | 0.982044i | \(0.439589\pi\) | |||||||
\(90\) | 1.18479 | 0.124888 | ||||||||
\(91\) | 2.06418 | 0.216385 | ||||||||
\(92\) | −6.70233 | −0.698767 | ||||||||
\(93\) | 1.95811 | 0.203047 | ||||||||
\(94\) | 2.04189 | 0.210605 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −5.87939 | −0.596961 | −0.298481 | − | 0.954416i | \(-0.596480\pi\) | ||||
−0.298481 | + | 0.954416i | \(0.596480\pi\) | |||||||
\(98\) | −6.71688 | −0.678507 | ||||||||
\(99\) | 1.87939 | 0.188885 | ||||||||
\(100\) | −3.59627 | −0.359627 | ||||||||
\(101\) | 12.6459 | 1.25831 | 0.629157 | − | 0.777278i | \(-0.283400\pi\) | ||||
0.629157 | + | 0.777278i | \(0.283400\pi\) | |||||||
\(102\) | 1.16250 | 0.115105 | ||||||||
\(103\) | −2.96316 | −0.291969 | −0.145985 | − | 0.989287i | \(-0.546635\pi\) | ||||
−0.145985 | + | 0.989287i | \(0.546635\pi\) | |||||||
\(104\) | 3.87939 | 0.380405 | ||||||||
\(105\) | 0.630415 | 0.0615222 | ||||||||
\(106\) | −12.9709 | −1.25985 | ||||||||
\(107\) | −19.1138 | −1.84780 | −0.923901 | − | 0.382632i | \(-0.875018\pi\) | ||||
−0.923901 | + | 0.382632i | \(0.875018\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 16.4115 | 1.57193 | 0.785967 | − | 0.618268i | \(-0.212166\pi\) | ||||
0.785967 | + | 0.618268i | \(0.212166\pi\) | |||||||
\(110\) | 2.22668 | 0.212306 | ||||||||
\(111\) | −6.88713 | −0.653697 | ||||||||
\(112\) | 0.532089 | 0.0502777 | ||||||||
\(113\) | 5.73648 | 0.539643 | 0.269821 | − | 0.962910i | \(-0.413035\pi\) | ||||
0.269821 | + | 0.962910i | \(0.413035\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.94087 | −0.740490 | ||||||||
\(116\) | 4.02229 | 0.373460 | ||||||||
\(117\) | 3.87939 | 0.358649 | ||||||||
\(118\) | 2.68004 | 0.246718 | ||||||||
\(119\) | 0.618555 | 0.0567029 | ||||||||
\(120\) | 1.18479 | 0.108156 | ||||||||
\(121\) | −7.46791 | −0.678901 | ||||||||
\(122\) | −11.3473 | −1.02734 | ||||||||
\(123\) | 8.98545 | 0.810191 | ||||||||
\(124\) | 1.95811 | 0.175844 | ||||||||
\(125\) | −10.1848 | −0.910956 | ||||||||
\(126\) | 0.532089 | 0.0474022 | ||||||||
\(127\) | 1.88713 | 0.167455 | 0.0837277 | − | 0.996489i | \(-0.473317\pi\) | ||||
0.0837277 | + | 0.996489i | \(0.473317\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.42602 | 0.213599 | ||||||||
\(130\) | 4.59627 | 0.403119 | ||||||||
\(131\) | 10.7023 | 0.935067 | 0.467534 | − | 0.883975i | \(-0.345143\pi\) | ||||
0.467534 | + | 0.883975i | \(0.345143\pi\) | |||||||
\(132\) | 1.87939 | 0.163579 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 11.1702 | 0.964962 | ||||||||
\(135\) | 1.18479 | 0.101971 | ||||||||
\(136\) | 1.16250 | 0.0996839 | ||||||||
\(137\) | −11.2567 | −0.961726 | −0.480863 | − | 0.876796i | \(-0.659677\pi\) | ||||
−0.480863 | + | 0.876796i | \(0.659677\pi\) | |||||||
\(138\) | −6.70233 | −0.570541 | ||||||||
\(139\) | −12.1702 | −1.03227 | −0.516133 | − | 0.856508i | \(-0.672629\pi\) | ||||
−0.516133 | + | 0.856508i | \(0.672629\pi\) | |||||||
\(140\) | 0.630415 | 0.0532798 | ||||||||
\(141\) | 2.04189 | 0.171958 | ||||||||
\(142\) | −6.07192 | −0.509544 | ||||||||
\(143\) | 7.29086 | 0.609692 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 4.76558 | 0.395760 | ||||||||
\(146\) | −0.327696 | −0.0271203 | ||||||||
\(147\) | −6.71688 | −0.553999 | ||||||||
\(148\) | −6.88713 | −0.566118 | ||||||||
\(149\) | −16.3550 | −1.33986 | −0.669928 | − | 0.742426i | \(-0.733675\pi\) | ||||
−0.669928 | + | 0.742426i | \(0.733675\pi\) | |||||||
\(150\) | −3.59627 | −0.293634 | ||||||||
\(151\) | −20.5226 | −1.67010 | −0.835052 | − | 0.550170i | \(-0.814563\pi\) | ||||
−0.835052 | + | 0.550170i | \(0.814563\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.16250 | 0.0939829 | ||||||||
\(154\) | 1.00000 | 0.0805823 | ||||||||
\(155\) | 2.31996 | 0.186343 | ||||||||
\(156\) | 3.87939 | 0.310599 | ||||||||
\(157\) | −3.19934 | −0.255335 | −0.127668 | − | 0.991817i | \(-0.540749\pi\) | ||||
−0.127668 | + | 0.991817i | \(0.540749\pi\) | |||||||
\(158\) | 16.1334 | 1.28351 | ||||||||
\(159\) | −12.9709 | −1.02866 | ||||||||
\(160\) | 1.18479 | 0.0936661 | ||||||||
\(161\) | −3.56624 | −0.281059 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −24.0077 | −1.88043 | −0.940216 | − | 0.340580i | \(-0.889377\pi\) | ||||
−0.940216 | + | 0.340580i | \(0.889377\pi\) | |||||||
\(164\) | 8.98545 | 0.701646 | ||||||||
\(165\) | 2.22668 | 0.173347 | ||||||||
\(166\) | 11.5740 | 0.898315 | ||||||||
\(167\) | −3.66044 | −0.283254 | −0.141627 | − | 0.989920i | \(-0.545233\pi\) | ||||
−0.141627 | + | 0.989920i | \(0.545233\pi\) | |||||||
\(168\) | 0.532089 | 0.0410515 | ||||||||
\(169\) | 2.04963 | 0.157664 | ||||||||
\(170\) | 1.37733 | 0.105636 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.42602 | 0.184982 | ||||||||
\(173\) | 5.33275 | 0.405441 | 0.202721 | − | 0.979237i | \(-0.435022\pi\) | ||||
0.202721 | + | 0.979237i | \(0.435022\pi\) | |||||||
\(174\) | 4.02229 | 0.304929 | ||||||||
\(175\) | −1.91353 | −0.144650 | ||||||||
\(176\) | 1.87939 | 0.141664 | ||||||||
\(177\) | 2.68004 | 0.201445 | ||||||||
\(178\) | 3.55943 | 0.266791 | ||||||||
\(179\) | 25.2567 | 1.88778 | 0.943888 | − | 0.330267i | \(-0.107139\pi\) | ||||
0.943888 | + | 0.330267i | \(0.107139\pi\) | |||||||
\(180\) | 1.18479 | 0.0883092 | ||||||||
\(181\) | 17.3063 | 1.28637 | 0.643185 | − | 0.765711i | \(-0.277613\pi\) | ||||
0.643185 | + | 0.765711i | \(0.277613\pi\) | |||||||
\(182\) | 2.06418 | 0.153007 | ||||||||
\(183\) | −11.3473 | −0.838816 | ||||||||
\(184\) | −6.70233 | −0.494103 | ||||||||
\(185\) | −8.15982 | −0.599922 | ||||||||
\(186\) | 1.95811 | 0.143576 | ||||||||
\(187\) | 2.18479 | 0.159768 | ||||||||
\(188\) | 2.04189 | 0.148920 | ||||||||
\(189\) | 0.532089 | 0.0387038 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.1780 | −1.09824 | −0.549120 | − | 0.835743i | \(-0.685037\pi\) | ||||
−0.549120 | + | 0.835743i | \(0.685037\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −13.0077 | −0.936318 | −0.468159 | − | 0.883644i | \(-0.655082\pi\) | ||||
−0.468159 | + | 0.883644i | \(0.655082\pi\) | |||||||
\(194\) | −5.87939 | −0.422115 | ||||||||
\(195\) | 4.59627 | 0.329145 | ||||||||
\(196\) | −6.71688 | −0.479777 | ||||||||
\(197\) | −8.94862 | −0.637562 | −0.318781 | − | 0.947828i | \(-0.603274\pi\) | ||||
−0.318781 | + | 0.947828i | \(0.603274\pi\) | |||||||
\(198\) | 1.87939 | 0.133562 | ||||||||
\(199\) | −4.50475 | −0.319333 | −0.159667 | − | 0.987171i | \(-0.551042\pi\) | ||||
−0.159667 | + | 0.987171i | \(0.551042\pi\) | |||||||
\(200\) | −3.59627 | −0.254294 | ||||||||
\(201\) | 11.1702 | 0.787888 | ||||||||
\(202\) | 12.6459 | 0.889762 | ||||||||
\(203\) | 2.14022 | 0.150214 | ||||||||
\(204\) | 1.16250 | 0.0813915 | ||||||||
\(205\) | 10.6459 | 0.743542 | ||||||||
\(206\) | −2.96316 | −0.206453 | ||||||||
\(207\) | −6.70233 | −0.465844 | ||||||||
\(208\) | 3.87939 | 0.268987 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.630415 | 0.0435028 | ||||||||
\(211\) | 6.40373 | 0.440851 | 0.220426 | − | 0.975404i | \(-0.429255\pi\) | ||||
0.220426 | + | 0.975404i | \(0.429255\pi\) | |||||||
\(212\) | −12.9709 | −0.890845 | ||||||||
\(213\) | −6.07192 | −0.416041 | ||||||||
\(214\) | −19.1138 | −1.30659 | ||||||||
\(215\) | 2.87433 | 0.196028 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 1.04189 | 0.0707280 | ||||||||
\(218\) | 16.4115 | 1.11153 | ||||||||
\(219\) | −0.327696 | −0.0221436 | ||||||||
\(220\) | 2.22668 | 0.150123 | ||||||||
\(221\) | 4.50980 | 0.303362 | ||||||||
\(222\) | −6.88713 | −0.462234 | ||||||||
\(223\) | −3.24897 | −0.217567 | −0.108784 | − | 0.994065i | \(-0.534696\pi\) | ||||
−0.108784 | + | 0.994065i | \(0.534696\pi\) | |||||||
\(224\) | 0.532089 | 0.0355517 | ||||||||
\(225\) | −3.59627 | −0.239751 | ||||||||
\(226\) | 5.73648 | 0.381585 | ||||||||
\(227\) | 11.7023 | 0.776711 | 0.388356 | − | 0.921510i | \(-0.373043\pi\) | ||||
0.388356 | + | 0.921510i | \(0.373043\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.9067 | −1.51372 | −0.756860 | − | 0.653578i | \(-0.773267\pi\) | ||||
−0.756860 | + | 0.653578i | \(0.773267\pi\) | |||||||
\(230\) | −7.94087 | −0.523606 | ||||||||
\(231\) | 1.00000 | 0.0657952 | ||||||||
\(232\) | 4.02229 | 0.264076 | ||||||||
\(233\) | −3.19934 | −0.209596 | −0.104798 | − | 0.994494i | \(-0.533420\pi\) | ||||
−0.104798 | + | 0.994494i | \(0.533420\pi\) | |||||||
\(234\) | 3.87939 | 0.253603 | ||||||||
\(235\) | 2.41921 | 0.157812 | ||||||||
\(236\) | 2.68004 | 0.174456 | ||||||||
\(237\) | 16.1334 | 1.04798 | ||||||||
\(238\) | 0.618555 | 0.0400950 | ||||||||
\(239\) | 6.17293 | 0.399294 | 0.199647 | − | 0.979868i | \(-0.436020\pi\) | ||||
0.199647 | + | 0.979868i | \(0.436020\pi\) | |||||||
\(240\) | 1.18479 | 0.0764780 | ||||||||
\(241\) | −1.53714 | −0.0990160 | −0.0495080 | − | 0.998774i | \(-0.515765\pi\) | ||||
−0.0495080 | + | 0.998774i | \(0.515765\pi\) | |||||||
\(242\) | −7.46791 | −0.480056 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −11.3473 | −0.726436 | ||||||||
\(245\) | −7.95811 | −0.508425 | ||||||||
\(246\) | 8.98545 | 0.572892 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.95811 | 0.124340 | ||||||||
\(249\) | 11.5740 | 0.733471 | ||||||||
\(250\) | −10.1848 | −0.644143 | ||||||||
\(251\) | 17.9436 | 1.13259 | 0.566294 | − | 0.824203i | \(-0.308377\pi\) | ||||
0.566294 | + | 0.824203i | \(0.308377\pi\) | |||||||
\(252\) | 0.532089 | 0.0335184 | ||||||||
\(253\) | −12.5963 | −0.791920 | ||||||||
\(254\) | 1.88713 | 0.118409 | ||||||||
\(255\) | 1.37733 | 0.0862515 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −29.4124 | −1.83470 | −0.917348 | − | 0.398087i | \(-0.869674\pi\) | ||||
−0.917348 | + | 0.398087i | \(0.869674\pi\) | |||||||
\(258\) | 2.42602 | 0.151038 | ||||||||
\(259\) | −3.66456 | −0.227705 | ||||||||
\(260\) | 4.59627 | 0.285048 | ||||||||
\(261\) | 4.02229 | 0.248973 | ||||||||
\(262\) | 10.7023 | 0.661192 | ||||||||
\(263\) | 10.6827 | 0.658726 | 0.329363 | − | 0.944203i | \(-0.393166\pi\) | ||||
0.329363 | + | 0.944203i | \(0.393166\pi\) | |||||||
\(264\) | 1.87939 | 0.115668 | ||||||||
\(265\) | −15.3678 | −0.944038 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.55943 | 0.217834 | ||||||||
\(268\) | 11.1702 | 0.682331 | ||||||||
\(269\) | 20.5767 | 1.25458 | 0.627291 | − | 0.778785i | \(-0.284164\pi\) | ||||
0.627291 | + | 0.778785i | \(0.284164\pi\) | |||||||
\(270\) | 1.18479 | 0.0721042 | ||||||||
\(271\) | 1.87670 | 0.114001 | 0.0570006 | − | 0.998374i | \(-0.481846\pi\) | ||||
0.0570006 | + | 0.998374i | \(0.481846\pi\) | |||||||
\(272\) | 1.16250 | 0.0704871 | ||||||||
\(273\) | 2.06418 | 0.124930 | ||||||||
\(274\) | −11.2567 | −0.680043 | ||||||||
\(275\) | −6.75877 | −0.407569 | ||||||||
\(276\) | −6.70233 | −0.403433 | ||||||||
\(277\) | 4.87258 | 0.292765 | 0.146382 | − | 0.989228i | \(-0.453237\pi\) | ||||
0.146382 | + | 0.989228i | \(0.453237\pi\) | |||||||
\(278\) | −12.1702 | −0.729923 | ||||||||
\(279\) | 1.95811 | 0.117229 | ||||||||
\(280\) | 0.630415 | 0.0376745 | ||||||||
\(281\) | 0.403733 | 0.0240847 | 0.0120424 | − | 0.999927i | \(-0.496167\pi\) | ||||
0.0120424 | + | 0.999927i | \(0.496167\pi\) | |||||||
\(282\) | 2.04189 | 0.121593 | ||||||||
\(283\) | 17.5895 | 1.04558 | 0.522792 | − | 0.852460i | \(-0.324890\pi\) | ||||
0.522792 | + | 0.852460i | \(0.324890\pi\) | |||||||
\(284\) | −6.07192 | −0.360302 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.29086 | 0.431118 | ||||||||
\(287\) | 4.78106 | 0.282217 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −15.6486 | −0.920505 | ||||||||
\(290\) | 4.76558 | 0.279844 | ||||||||
\(291\) | −5.87939 | −0.344656 | ||||||||
\(292\) | −0.327696 | −0.0191770 | ||||||||
\(293\) | 13.1753 | 0.769709 | 0.384855 | − | 0.922977i | \(-0.374252\pi\) | ||||
0.384855 | + | 0.922977i | \(0.374252\pi\) | |||||||
\(294\) | −6.71688 | −0.391736 | ||||||||
\(295\) | 3.17530 | 0.184873 | ||||||||
\(296\) | −6.88713 | −0.400306 | ||||||||
\(297\) | 1.87939 | 0.109053 | ||||||||
\(298\) | −16.3550 | −0.947422 | ||||||||
\(299\) | −26.0009 | −1.50367 | ||||||||
\(300\) | −3.59627 | −0.207631 | ||||||||
\(301\) | 1.29086 | 0.0744039 | ||||||||
\(302\) | −20.5226 | −1.18094 | ||||||||
\(303\) | 12.6459 | 0.726488 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.4442 | −0.769812 | ||||||||
\(306\) | 1.16250 | 0.0664559 | ||||||||
\(307\) | −16.9017 | −0.964629 | −0.482315 | − | 0.875998i | \(-0.660204\pi\) | ||||
−0.482315 | + | 0.875998i | \(0.660204\pi\) | |||||||
\(308\) | 1.00000 | 0.0569803 | ||||||||
\(309\) | −2.96316 | −0.168568 | ||||||||
\(310\) | 2.31996 | 0.131765 | ||||||||
\(311\) | −2.38144 | −0.135039 | −0.0675197 | − | 0.997718i | \(-0.521509\pi\) | ||||
−0.0675197 | + | 0.997718i | \(0.521509\pi\) | |||||||
\(312\) | 3.87939 | 0.219627 | ||||||||
\(313\) | −29.8631 | −1.68796 | −0.843981 | − | 0.536374i | \(-0.819794\pi\) | ||||
−0.843981 | + | 0.536374i | \(0.819794\pi\) | |||||||
\(314\) | −3.19934 | −0.180549 | ||||||||
\(315\) | 0.630415 | 0.0355199 | ||||||||
\(316\) | 16.1334 | 0.907575 | ||||||||
\(317\) | 7.02229 | 0.394411 | 0.197206 | − | 0.980362i | \(-0.436813\pi\) | ||||
0.197206 | + | 0.980362i | \(0.436813\pi\) | |||||||
\(318\) | −12.9709 | −0.727372 | ||||||||
\(319\) | 7.55943 | 0.423247 | ||||||||
\(320\) | 1.18479 | 0.0662319 | ||||||||
\(321\) | −19.1138 | −1.06683 | ||||||||
\(322\) | −3.56624 | −0.198739 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −13.9513 | −0.773879 | ||||||||
\(326\) | −24.0077 | −1.32967 | ||||||||
\(327\) | 16.4115 | 0.907557 | ||||||||
\(328\) | 8.98545 | 0.496139 | ||||||||
\(329\) | 1.08647 | 0.0598988 | ||||||||
\(330\) | 2.22668 | 0.122575 | ||||||||
\(331\) | −27.1985 | −1.49497 | −0.747483 | − | 0.664281i | \(-0.768738\pi\) | ||||
−0.747483 | + | 0.664281i | \(0.768738\pi\) | |||||||
\(332\) | 11.5740 | 0.635205 | ||||||||
\(333\) | −6.88713 | −0.377412 | ||||||||
\(334\) | −3.66044 | −0.200291 | ||||||||
\(335\) | 13.2344 | 0.723074 | ||||||||
\(336\) | 0.532089 | 0.0290278 | ||||||||
\(337\) | 11.2172 | 0.611039 | 0.305520 | − | 0.952186i | \(-0.401170\pi\) | ||||
0.305520 | + | 0.952186i | \(0.401170\pi\) | |||||||
\(338\) | 2.04963 | 0.111485 | ||||||||
\(339\) | 5.73648 | 0.311563 | ||||||||
\(340\) | 1.37733 | 0.0746960 | ||||||||
\(341\) | 3.68004 | 0.199286 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.29860 | −0.394087 | ||||||||
\(344\) | 2.42602 | 0.130802 | ||||||||
\(345\) | −7.94087 | −0.427522 | ||||||||
\(346\) | 5.33275 | 0.286690 | ||||||||
\(347\) | 1.93582 | 0.103920 | 0.0519602 | − | 0.998649i | \(-0.483453\pi\) | ||||
0.0519602 | + | 0.998649i | \(0.483453\pi\) | |||||||
\(348\) | 4.02229 | 0.215617 | ||||||||
\(349\) | 14.3969 | 0.770650 | 0.385325 | − | 0.922781i | \(-0.374089\pi\) | ||||
0.385325 | + | 0.922781i | \(0.374089\pi\) | |||||||
\(350\) | −1.91353 | −0.102283 | ||||||||
\(351\) | 3.87939 | 0.207066 | ||||||||
\(352\) | 1.87939 | 0.100172 | ||||||||
\(353\) | 15.7237 | 0.836887 | 0.418444 | − | 0.908243i | \(-0.362576\pi\) | ||||
0.418444 | + | 0.908243i | \(0.362576\pi\) | |||||||
\(354\) | 2.68004 | 0.142443 | ||||||||
\(355\) | −7.19396 | −0.381816 | ||||||||
\(356\) | 3.55943 | 0.188649 | ||||||||
\(357\) | 0.618555 | 0.0327374 | ||||||||
\(358\) | 25.2567 | 1.33486 | ||||||||
\(359\) | 15.5175 | 0.818984 | 0.409492 | − | 0.912314i | \(-0.365706\pi\) | ||||
0.409492 | + | 0.912314i | \(0.365706\pi\) | |||||||
\(360\) | 1.18479 | 0.0624440 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 17.3063 | 0.909601 | ||||||||
\(363\) | −7.46791 | −0.391964 | ||||||||
\(364\) | 2.06418 | 0.108192 | ||||||||
\(365\) | −0.388252 | −0.0203220 | ||||||||
\(366\) | −11.3473 | −0.593133 | ||||||||
\(367\) | −15.7442 | −0.821842 | −0.410921 | − | 0.911671i | \(-0.634793\pi\) | ||||
−0.410921 | + | 0.911671i | \(0.634793\pi\) | |||||||
\(368\) | −6.70233 | −0.349383 | ||||||||
\(369\) | 8.98545 | 0.467764 | ||||||||
\(370\) | −8.15982 | −0.424209 | ||||||||
\(371\) | −6.90167 | −0.358317 | ||||||||
\(372\) | 1.95811 | 0.101523 | ||||||||
\(373\) | 29.6287 | 1.53411 | 0.767057 | − | 0.641579i | \(-0.221720\pi\) | ||||
0.767057 | + | 0.641579i | \(0.221720\pi\) | |||||||
\(374\) | 2.18479 | 0.112973 | ||||||||
\(375\) | −10.1848 | −0.525940 | ||||||||
\(376\) | 2.04189 | 0.105302 | ||||||||
\(377\) | 15.6040 | 0.803647 | ||||||||
\(378\) | 0.532089 | 0.0273677 | ||||||||
\(379\) | −4.72462 | −0.242688 | −0.121344 | − | 0.992611i | \(-0.538720\pi\) | ||||
−0.121344 | + | 0.992611i | \(0.538720\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.88713 | 0.0966804 | ||||||||
\(382\) | −15.1780 | −0.776573 | ||||||||
\(383\) | 5.24123 | 0.267814 | 0.133907 | − | 0.990994i | \(-0.457248\pi\) | ||||
0.133907 | + | 0.990994i | \(0.457248\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 1.18479 | 0.0603826 | ||||||||
\(386\) | −13.0077 | −0.662077 | ||||||||
\(387\) | 2.42602 | 0.123322 | ||||||||
\(388\) | −5.87939 | −0.298481 | ||||||||
\(389\) | −15.0770 | −0.764433 | −0.382216 | − | 0.924073i | \(-0.624839\pi\) | ||||
−0.382216 | + | 0.924073i | \(0.624839\pi\) | |||||||
\(390\) | 4.59627 | 0.232741 | ||||||||
\(391\) | −7.79149 | −0.394033 | ||||||||
\(392\) | −6.71688 | −0.339254 | ||||||||
\(393\) | 10.7023 | 0.539861 | ||||||||
\(394\) | −8.94862 | −0.450825 | ||||||||
\(395\) | 19.1147 | 0.961767 | ||||||||
\(396\) | 1.87939 | 0.0944427 | ||||||||
\(397\) | −14.5449 | −0.729987 | −0.364993 | − | 0.931010i | \(-0.618929\pi\) | ||||
−0.364993 | + | 0.931010i | \(0.618929\pi\) | |||||||
\(398\) | −4.50475 | −0.225803 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.59627 | −0.179813 | ||||||||
\(401\) | −2.85473 | −0.142559 | −0.0712793 | − | 0.997456i | \(-0.522708\pi\) | ||||
−0.0712793 | + | 0.997456i | \(0.522708\pi\) | |||||||
\(402\) | 11.1702 | 0.557121 | ||||||||
\(403\) | 7.59627 | 0.378397 | ||||||||
\(404\) | 12.6459 | 0.629157 | ||||||||
\(405\) | 1.18479 | 0.0588728 | ||||||||
\(406\) | 2.14022 | 0.106217 | ||||||||
\(407\) | −12.9436 | −0.641589 | ||||||||
\(408\) | 1.16250 | 0.0575525 | ||||||||
\(409\) | −34.2276 | −1.69245 | −0.846223 | − | 0.532828i | \(-0.821129\pi\) | ||||
−0.846223 | + | 0.532828i | \(0.821129\pi\) | |||||||
\(410\) | 10.6459 | 0.525763 | ||||||||
\(411\) | −11.2567 | −0.555253 | ||||||||
\(412\) | −2.96316 | −0.145985 | ||||||||
\(413\) | 1.42602 | 0.0701700 | ||||||||
\(414\) | −6.70233 | −0.329402 | ||||||||
\(415\) | 13.7128 | 0.673133 | ||||||||
\(416\) | 3.87939 | 0.190203 | ||||||||
\(417\) | −12.1702 | −0.595979 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.91891 | −0.386864 | −0.193432 | − | 0.981114i | \(-0.561962\pi\) | ||||
−0.193432 | + | 0.981114i | \(0.561962\pi\) | |||||||
\(420\) | 0.630415 | 0.0307611 | ||||||||
\(421\) | −16.2098 | −0.790016 | −0.395008 | − | 0.918678i | \(-0.629258\pi\) | ||||
−0.395008 | + | 0.918678i | \(0.629258\pi\) | |||||||
\(422\) | 6.40373 | 0.311729 | ||||||||
\(423\) | 2.04189 | 0.0992800 | ||||||||
\(424\) | −12.9709 | −0.629923 | ||||||||
\(425\) | −4.18067 | −0.202792 | ||||||||
\(426\) | −6.07192 | −0.294185 | ||||||||
\(427\) | −6.03777 | −0.292188 | ||||||||
\(428\) | −19.1138 | −0.923901 | ||||||||
\(429\) | 7.29086 | 0.352006 | ||||||||
\(430\) | 2.87433 | 0.138613 | ||||||||
\(431\) | −25.4320 | −1.22502 | −0.612508 | − | 0.790464i | \(-0.709839\pi\) | ||||
−0.612508 | + | 0.790464i | \(0.709839\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −11.8479 | −0.569375 | −0.284687 | − | 0.958620i | \(-0.591890\pi\) | ||||
−0.284687 | + | 0.958620i | \(0.591890\pi\) | |||||||
\(434\) | 1.04189 | 0.0500123 | ||||||||
\(435\) | 4.76558 | 0.228492 | ||||||||
\(436\) | 16.4115 | 0.785967 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −0.327696 | −0.0156579 | ||||||||
\(439\) | −25.8598 | −1.23422 | −0.617110 | − | 0.786877i | \(-0.711697\pi\) | ||||
−0.617110 | + | 0.786877i | \(0.711697\pi\) | |||||||
\(440\) | 2.22668 | 0.106153 | ||||||||
\(441\) | −6.71688 | −0.319851 | ||||||||
\(442\) | 4.50980 | 0.214509 | ||||||||
\(443\) | 0.923029 | 0.0438544 | 0.0219272 | − | 0.999760i | \(-0.493020\pi\) | ||||
0.0219272 | + | 0.999760i | \(0.493020\pi\) | |||||||
\(444\) | −6.88713 | −0.326849 | ||||||||
\(445\) | 4.21719 | 0.199914 | ||||||||
\(446\) | −3.24897 | −0.153843 | ||||||||
\(447\) | −16.3550 | −0.773567 | ||||||||
\(448\) | 0.532089 | 0.0251388 | ||||||||
\(449\) | −9.34461 | −0.440999 | −0.220500 | − | 0.975387i | \(-0.570769\pi\) | ||||
−0.220500 | + | 0.975387i | \(0.570769\pi\) | |||||||
\(450\) | −3.59627 | −0.169530 | ||||||||
\(451\) | 16.8871 | 0.795184 | ||||||||
\(452\) | 5.73648 | 0.269821 | ||||||||
\(453\) | −20.5226 | −0.964236 | ||||||||
\(454\) | 11.7023 | 0.549218 | ||||||||
\(455\) | 2.44562 | 0.114653 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.9009 | 1.44548 | 0.722740 | − | 0.691120i | \(-0.242882\pi\) | ||||
0.722740 | + | 0.691120i | \(0.242882\pi\) | |||||||
\(458\) | −22.9067 | −1.07036 | ||||||||
\(459\) | 1.16250 | 0.0542610 | ||||||||
\(460\) | −7.94087 | −0.370245 | ||||||||
\(461\) | −29.6878 | −1.38270 | −0.691349 | − | 0.722521i | \(-0.742983\pi\) | ||||
−0.691349 | + | 0.722521i | \(0.742983\pi\) | |||||||
\(462\) | 1.00000 | 0.0465242 | ||||||||
\(463\) | −11.8307 | −0.549819 | −0.274909 | − | 0.961470i | \(-0.588648\pi\) | ||||
−0.274909 | + | 0.961470i | \(0.588648\pi\) | |||||||
\(464\) | 4.02229 | 0.186730 | ||||||||
\(465\) | 2.31996 | 0.107585 | ||||||||
\(466\) | −3.19934 | −0.148207 | ||||||||
\(467\) | 38.3182 | 1.77315 | 0.886577 | − | 0.462580i | \(-0.153076\pi\) | ||||
0.886577 | + | 0.462580i | \(0.153076\pi\) | |||||||
\(468\) | 3.87939 | 0.179325 | ||||||||
\(469\) | 5.94356 | 0.274448 | ||||||||
\(470\) | 2.41921 | 0.111590 | ||||||||
\(471\) | −3.19934 | −0.147418 | ||||||||
\(472\) | 2.68004 | 0.123359 | ||||||||
\(473\) | 4.55943 | 0.209643 | ||||||||
\(474\) | 16.1334 | 0.741032 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.618555 | 0.0283514 | ||||||||
\(477\) | −12.9709 | −0.593897 | ||||||||
\(478\) | 6.17293 | 0.282343 | ||||||||
\(479\) | 37.2841 | 1.70355 | 0.851776 | − | 0.523906i | \(-0.175526\pi\) | ||||
0.851776 | + | 0.523906i | \(0.175526\pi\) | |||||||
\(480\) | 1.18479 | 0.0540781 | ||||||||
\(481\) | −26.7178 | −1.21823 | ||||||||
\(482\) | −1.53714 | −0.0700149 | ||||||||
\(483\) | −3.56624 | −0.162269 | ||||||||
\(484\) | −7.46791 | −0.339451 | ||||||||
\(485\) | −6.96585 | −0.316303 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −32.9786 | −1.49441 | −0.747203 | − | 0.664596i | \(-0.768603\pi\) | ||||
−0.747203 | + | 0.664596i | \(0.768603\pi\) | |||||||
\(488\) | −11.3473 | −0.513668 | ||||||||
\(489\) | −24.0077 | −1.08567 | ||||||||
\(490\) | −7.95811 | −0.359511 | ||||||||
\(491\) | 17.6810 | 0.797931 | 0.398966 | − | 0.916966i | \(-0.369369\pi\) | ||||
0.398966 | + | 0.916966i | \(0.369369\pi\) | |||||||
\(492\) | 8.98545 | 0.405095 | ||||||||
\(493\) | 4.67593 | 0.210593 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.22668 | 0.100082 | ||||||||
\(496\) | 1.95811 | 0.0879218 | ||||||||
\(497\) | −3.23080 | −0.144921 | ||||||||
\(498\) | 11.5740 | 0.518642 | ||||||||
\(499\) | 27.1239 | 1.21423 | 0.607117 | − | 0.794613i | \(-0.292326\pi\) | ||||
0.607117 | + | 0.794613i | \(0.292326\pi\) | |||||||
\(500\) | −10.1848 | −0.455478 | ||||||||
\(501\) | −3.66044 | −0.163537 | ||||||||
\(502\) | 17.9436 | 0.800860 | ||||||||
\(503\) | 0.571290 | 0.0254725 | 0.0127363 | − | 0.999919i | \(-0.495946\pi\) | ||||
0.0127363 | + | 0.999919i | \(0.495946\pi\) | |||||||
\(504\) | 0.532089 | 0.0237011 | ||||||||
\(505\) | 14.9828 | 0.666724 | ||||||||
\(506\) | −12.5963 | −0.559972 | ||||||||
\(507\) | 2.04963 | 0.0910273 | ||||||||
\(508\) | 1.88713 | 0.0837277 | ||||||||
\(509\) | −40.5509 | −1.79739 | −0.898693 | − | 0.438579i | \(-0.855482\pi\) | ||||
−0.898693 | + | 0.438579i | \(0.855482\pi\) | |||||||
\(510\) | 1.37733 | 0.0609890 | ||||||||
\(511\) | −0.174363 | −0.00771338 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −29.4124 | −1.29733 | ||||||||
\(515\) | −3.51073 | −0.154701 | ||||||||
\(516\) | 2.42602 | 0.106800 | ||||||||
\(517\) | 3.83750 | 0.168773 | ||||||||
\(518\) | −3.66456 | −0.161012 | ||||||||
\(519\) | 5.33275 | 0.234082 | ||||||||
\(520\) | 4.59627 | 0.201560 | ||||||||
\(521\) | −18.8999 | −0.828020 | −0.414010 | − | 0.910272i | \(-0.635872\pi\) | ||||
−0.414010 | + | 0.910272i | \(0.635872\pi\) | |||||||
\(522\) | 4.02229 | 0.176051 | ||||||||
\(523\) | 4.74186 | 0.207347 | 0.103673 | − | 0.994611i | \(-0.466940\pi\) | ||||
0.103673 | + | 0.994611i | \(0.466940\pi\) | |||||||
\(524\) | 10.7023 | 0.467534 | ||||||||
\(525\) | −1.91353 | −0.0835134 | ||||||||
\(526\) | 10.6827 | 0.465789 | ||||||||
\(527\) | 2.27631 | 0.0991577 | ||||||||
\(528\) | 1.87939 | 0.0817897 | ||||||||
\(529\) | 21.9213 | 0.953099 | ||||||||
\(530\) | −15.3678 | −0.667536 | ||||||||
\(531\) | 2.68004 | 0.116304 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 34.8580 | 1.50987 | ||||||||
\(534\) | 3.55943 | 0.154032 | ||||||||
\(535\) | −22.6459 | −0.979067 | ||||||||
\(536\) | 11.1702 | 0.482481 | ||||||||
\(537\) | 25.2567 | 1.08991 | ||||||||
\(538\) | 20.5767 | 0.887123 | ||||||||
\(539\) | −12.6236 | −0.543737 | ||||||||
\(540\) | 1.18479 | 0.0509854 | ||||||||
\(541\) | −28.3610 | −1.21934 | −0.609668 | − | 0.792657i | \(-0.708697\pi\) | ||||
−0.609668 | + | 0.792657i | \(0.708697\pi\) | |||||||
\(542\) | 1.87670 | 0.0806110 | ||||||||
\(543\) | 17.3063 | 0.742686 | ||||||||
\(544\) | 1.16250 | 0.0498419 | ||||||||
\(545\) | 19.4442 | 0.832898 | ||||||||
\(546\) | 2.06418 | 0.0883387 | ||||||||
\(547\) | 6.88032 | 0.294181 | 0.147091 | − | 0.989123i | \(-0.453009\pi\) | ||||
0.147091 | + | 0.989123i | \(0.453009\pi\) | |||||||
\(548\) | −11.2567 | −0.480863 | ||||||||
\(549\) | −11.3473 | −0.484291 | ||||||||
\(550\) | −6.75877 | −0.288195 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −6.70233 | −0.285270 | ||||||||
\(553\) | 8.58441 | 0.365046 | ||||||||
\(554\) | 4.87258 | 0.207016 | ||||||||
\(555\) | −8.15982 | −0.346365 | ||||||||
\(556\) | −12.1702 | −0.516133 | ||||||||
\(557\) | −14.1625 | −0.600085 | −0.300042 | − | 0.953926i | \(-0.597001\pi\) | ||||
−0.300042 | + | 0.953926i | \(0.597001\pi\) | |||||||
\(558\) | 1.95811 | 0.0828934 | ||||||||
\(559\) | 9.41147 | 0.398063 | ||||||||
\(560\) | 0.630415 | 0.0266399 | ||||||||
\(561\) | 2.18479 | 0.0922420 | ||||||||
\(562\) | 0.403733 | 0.0170305 | ||||||||
\(563\) | 36.2550 | 1.52796 | 0.763982 | − | 0.645237i | \(-0.223242\pi\) | ||||
0.763982 | + | 0.645237i | \(0.223242\pi\) | |||||||
\(564\) | 2.04189 | 0.0859790 | ||||||||
\(565\) | 6.79654 | 0.285933 | ||||||||
\(566\) | 17.5895 | 0.739340 | ||||||||
\(567\) | 0.532089 | 0.0223456 | ||||||||
\(568\) | −6.07192 | −0.254772 | ||||||||
\(569\) | 30.2918 | 1.26990 | 0.634949 | − | 0.772554i | \(-0.281021\pi\) | ||||
0.634949 | + | 0.772554i | \(0.281021\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.39094 | 0.141906 | 0.0709532 | − | 0.997480i | \(-0.477396\pi\) | ||||
0.0709532 | + | 0.997480i | \(0.477396\pi\) | |||||||
\(572\) | 7.29086 | 0.304846 | ||||||||
\(573\) | −15.1780 | −0.634069 | ||||||||
\(574\) | 4.78106 | 0.199558 | ||||||||
\(575\) | 24.1034 | 1.00518 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −22.3027 | −0.928474 | −0.464237 | − | 0.885711i | \(-0.653671\pi\) | ||||
−0.464237 | + | 0.885711i | \(0.653671\pi\) | |||||||
\(578\) | −15.6486 | −0.650895 | ||||||||
\(579\) | −13.0077 | −0.540583 | ||||||||
\(580\) | 4.76558 | 0.197880 | ||||||||
\(581\) | 6.15839 | 0.255493 | ||||||||
\(582\) | −5.87939 | −0.243708 | ||||||||
\(583\) | −24.3773 | −1.00961 | ||||||||
\(584\) | −0.327696 | −0.0135602 | ||||||||
\(585\) | 4.59627 | 0.190032 | ||||||||
\(586\) | 13.1753 | 0.544267 | ||||||||
\(587\) | −28.7502 | −1.18665 | −0.593324 | − | 0.804964i | \(-0.702185\pi\) | ||||
−0.593324 | + | 0.804964i | \(0.702185\pi\) | |||||||
\(588\) | −6.71688 | −0.277000 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 3.17530 | 0.130725 | ||||||||
\(591\) | −8.94862 | −0.368097 | ||||||||
\(592\) | −6.88713 | −0.283059 | ||||||||
\(593\) | 11.7760 | 0.483583 | 0.241791 | − | 0.970328i | \(-0.422265\pi\) | ||||
0.241791 | + | 0.970328i | \(0.422265\pi\) | |||||||
\(594\) | 1.87939 | 0.0771121 | ||||||||
\(595\) | 0.732860 | 0.0300443 | ||||||||
\(596\) | −16.3550 | −0.669928 | ||||||||
\(597\) | −4.50475 | −0.184367 | ||||||||
\(598\) | −26.0009 | −1.06326 | ||||||||
\(599\) | 21.6313 | 0.883833 | 0.441916 | − | 0.897056i | \(-0.354299\pi\) | ||||
0.441916 | + | 0.897056i | \(0.354299\pi\) | |||||||
\(600\) | −3.59627 | −0.146817 | ||||||||
\(601\) | 26.1935 | 1.06845 | 0.534227 | − | 0.845341i | \(-0.320603\pi\) | ||||
0.534227 | + | 0.845341i | \(0.320603\pi\) | |||||||
\(602\) | 1.29086 | 0.0526115 | ||||||||
\(603\) | 11.1702 | 0.454888 | ||||||||
\(604\) | −20.5226 | −0.835052 | ||||||||
\(605\) | −8.84793 | −0.359719 | ||||||||
\(606\) | 12.6459 | 0.513704 | ||||||||
\(607\) | 13.2249 | 0.536783 | 0.268392 | − | 0.963310i | \(-0.413508\pi\) | ||||
0.268392 | + | 0.963310i | \(0.413508\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.14022 | 0.0867259 | ||||||||
\(610\) | −13.4442 | −0.544339 | ||||||||
\(611\) | 7.92127 | 0.320460 | ||||||||
\(612\) | 1.16250 | 0.0469914 | ||||||||
\(613\) | −5.62267 | −0.227098 | −0.113549 | − | 0.993532i | \(-0.536222\pi\) | ||||
−0.113549 | + | 0.993532i | \(0.536222\pi\) | |||||||
\(614\) | −16.9017 | −0.682096 | ||||||||
\(615\) | 10.6459 | 0.429284 | ||||||||
\(616\) | 1.00000 | 0.0402911 | ||||||||
\(617\) | 9.47834 | 0.381584 | 0.190792 | − | 0.981631i | \(-0.438894\pi\) | ||||
0.190792 | + | 0.981631i | \(0.438894\pi\) | |||||||
\(618\) | −2.96316 | −0.119196 | ||||||||
\(619\) | −14.7493 | −0.592823 | −0.296412 | − | 0.955060i | \(-0.595790\pi\) | ||||
−0.296412 | + | 0.955060i | \(0.595790\pi\) | |||||||
\(620\) | 2.31996 | 0.0931716 | ||||||||
\(621\) | −6.70233 | −0.268955 | ||||||||
\(622\) | −2.38144 | −0.0954872 | ||||||||
\(623\) | 1.89393 | 0.0758788 | ||||||||
\(624\) | 3.87939 | 0.155300 | ||||||||
\(625\) | 5.91447 | 0.236579 | ||||||||
\(626\) | −29.8631 | −1.19357 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.19934 | −0.127668 | ||||||||
\(629\) | −8.00631 | −0.319232 | ||||||||
\(630\) | 0.630415 | 0.0251163 | ||||||||
\(631\) | 25.0009 | 0.995271 | 0.497636 | − | 0.867386i | \(-0.334202\pi\) | ||||
0.497636 | + | 0.867386i | \(0.334202\pi\) | |||||||
\(632\) | 16.1334 | 0.641753 | ||||||||
\(633\) | 6.40373 | 0.254526 | ||||||||
\(634\) | 7.02229 | 0.278891 | ||||||||
\(635\) | 2.23585 | 0.0887271 | ||||||||
\(636\) | −12.9709 | −0.514330 | ||||||||
\(637\) | −26.0574 | −1.03243 | ||||||||
\(638\) | 7.55943 | 0.299281 | ||||||||
\(639\) | −6.07192 | −0.240201 | ||||||||
\(640\) | 1.18479 | 0.0468330 | ||||||||
\(641\) | 43.7306 | 1.72726 | 0.863628 | − | 0.504130i | \(-0.168187\pi\) | ||||
0.863628 | + | 0.504130i | \(0.168187\pi\) | |||||||
\(642\) | −19.1138 | −0.754362 | ||||||||
\(643\) | −33.4534 | −1.31927 | −0.659636 | − | 0.751585i | \(-0.729290\pi\) | ||||
−0.659636 | + | 0.751585i | \(0.729290\pi\) | |||||||
\(644\) | −3.56624 | −0.140529 | ||||||||
\(645\) | 2.87433 | 0.113177 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.1266 | −1.26303 | −0.631514 | − | 0.775365i | \(-0.717566\pi\) | ||||
−0.631514 | + | 0.775365i | \(0.717566\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 5.03684 | 0.197713 | ||||||||
\(650\) | −13.9513 | −0.547215 | ||||||||
\(651\) | 1.04189 | 0.0408349 | ||||||||
\(652\) | −24.0077 | −0.940216 | ||||||||
\(653\) | 2.89630 | 0.113341 | 0.0566704 | − | 0.998393i | \(-0.481952\pi\) | ||||
0.0566704 | + | 0.998393i | \(0.481952\pi\) | |||||||
\(654\) | 16.4115 | 0.641739 | ||||||||
\(655\) | 12.6800 | 0.495450 | ||||||||
\(656\) | 8.98545 | 0.350823 | ||||||||
\(657\) | −0.327696 | −0.0127846 | ||||||||
\(658\) | 1.08647 | 0.0423549 | ||||||||
\(659\) | −18.1935 | −0.708717 | −0.354358 | − | 0.935110i | \(-0.615301\pi\) | ||||
−0.354358 | + | 0.935110i | \(0.615301\pi\) | |||||||
\(660\) | 2.22668 | 0.0866735 | ||||||||
\(661\) | −21.4192 | −0.833111 | −0.416555 | − | 0.909110i | \(-0.636763\pi\) | ||||
−0.416555 | + | 0.909110i | \(0.636763\pi\) | |||||||
\(662\) | −27.1985 | −1.05710 | ||||||||
\(663\) | 4.50980 | 0.175146 | ||||||||
\(664\) | 11.5740 | 0.449157 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.88713 | −0.266871 | ||||||||
\(667\) | −26.9587 | −1.04385 | ||||||||
\(668\) | −3.66044 | −0.141627 | ||||||||
\(669\) | −3.24897 | −0.125612 | ||||||||
\(670\) | 13.2344 | 0.511290 | ||||||||
\(671\) | −21.3259 | −0.823279 | ||||||||
\(672\) | 0.532089 | 0.0205258 | ||||||||
\(673\) | −40.6914 | −1.56854 | −0.784269 | − | 0.620421i | \(-0.786962\pi\) | ||||
−0.784269 | + | 0.620421i | \(0.786962\pi\) | |||||||
\(674\) | 11.2172 | 0.432070 | ||||||||
\(675\) | −3.59627 | −0.138420 | ||||||||
\(676\) | 2.04963 | 0.0788319 | ||||||||
\(677\) | 0.136096 | 0.00523061 | 0.00261530 | − | 0.999997i | \(-0.499168\pi\) | ||||
0.00261530 | + | 0.999997i | \(0.499168\pi\) | |||||||
\(678\) | 5.73648 | 0.220308 | ||||||||
\(679\) | −3.12836 | −0.120055 | ||||||||
\(680\) | 1.37733 | 0.0528180 | ||||||||
\(681\) | 11.7023 | 0.448434 | ||||||||
\(682\) | 3.68004 | 0.140916 | ||||||||
\(683\) | 43.6459 | 1.67006 | 0.835032 | − | 0.550202i | \(-0.185449\pi\) | ||||
0.835032 | + | 0.550202i | \(0.185449\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.3369 | −0.509576 | ||||||||
\(686\) | −7.29860 | −0.278662 | ||||||||
\(687\) | −22.9067 | −0.873946 | ||||||||
\(688\) | 2.42602 | 0.0924912 | ||||||||
\(689\) | −50.3191 | −1.91701 | ||||||||
\(690\) | −7.94087 | −0.302304 | ||||||||
\(691\) | 15.8675 | 0.603629 | 0.301815 | − | 0.953367i | \(-0.402408\pi\) | ||||
0.301815 | + | 0.953367i | \(0.402408\pi\) | |||||||
\(692\) | 5.33275 | 0.202721 | ||||||||
\(693\) | 1.00000 | 0.0379869 | ||||||||
\(694\) | 1.93582 | 0.0734828 | ||||||||
\(695\) | −14.4192 | −0.546952 | ||||||||
\(696\) | 4.02229 | 0.152464 | ||||||||
\(697\) | 10.4456 | 0.395656 | ||||||||
\(698\) | 14.3969 | 0.544932 | ||||||||
\(699\) | −3.19934 | −0.121010 | ||||||||
\(700\) | −1.91353 | −0.0723248 | ||||||||
\(701\) | 19.2098 | 0.725543 | 0.362771 | − | 0.931878i | \(-0.381831\pi\) | ||||
0.362771 | + | 0.931878i | \(0.381831\pi\) | |||||||
\(702\) | 3.87939 | 0.146418 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.87939 | 0.0708320 | ||||||||
\(705\) | 2.41921 | 0.0911129 | ||||||||
\(706\) | 15.7237 | 0.591769 | ||||||||
\(707\) | 6.72874 | 0.253060 | ||||||||
\(708\) | 2.68004 | 0.100722 | ||||||||
\(709\) | 33.0259 | 1.24031 | 0.620157 | − | 0.784478i | \(-0.287069\pi\) | ||||
0.620157 | + | 0.784478i | \(0.287069\pi\) | |||||||
\(710\) | −7.19396 | −0.269985 | ||||||||
\(711\) | 16.1334 | 0.605050 | ||||||||
\(712\) | 3.55943 | 0.133395 | ||||||||
\(713\) | −13.1239 | −0.491494 | ||||||||
\(714\) | 0.618555 | 0.0231489 | ||||||||
\(715\) | 8.63816 | 0.323049 | ||||||||
\(716\) | 25.2567 | 0.943888 | ||||||||
\(717\) | 6.17293 | 0.230532 | ||||||||
\(718\) | 15.5175 | 0.579109 | ||||||||
\(719\) | 39.4448 | 1.47104 | 0.735521 | − | 0.677501i | \(-0.236937\pi\) | ||||
0.735521 | + | 0.677501i | \(0.236937\pi\) | |||||||
\(720\) | 1.18479 | 0.0441546 | ||||||||
\(721\) | −1.57667 | −0.0587181 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.53714 | −0.0571669 | ||||||||
\(724\) | 17.3063 | 0.643185 | ||||||||
\(725\) | −14.4652 | −0.537225 | ||||||||
\(726\) | −7.46791 | −0.277160 | ||||||||
\(727\) | 18.2517 | 0.676917 | 0.338458 | − | 0.940981i | \(-0.390095\pi\) | ||||
0.338458 | + | 0.940981i | \(0.390095\pi\) | |||||||
\(728\) | 2.06418 | 0.0765035 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.388252 | −0.0143698 | ||||||||
\(731\) | 2.82026 | 0.104311 | ||||||||
\(732\) | −11.3473 | −0.419408 | ||||||||
\(733\) | 15.3928 | 0.568546 | 0.284273 | − | 0.958743i | \(-0.408248\pi\) | ||||
0.284273 | + | 0.958743i | \(0.408248\pi\) | |||||||
\(734\) | −15.7442 | −0.581130 | ||||||||
\(735\) | −7.95811 | −0.293539 | ||||||||
\(736\) | −6.70233 | −0.247051 | ||||||||
\(737\) | 20.9932 | 0.773294 | ||||||||
\(738\) | 8.98545 | 0.330759 | ||||||||
\(739\) | 15.1771 | 0.558297 | 0.279148 | − | 0.960248i | \(-0.409948\pi\) | ||||
0.279148 | + | 0.960248i | \(0.409948\pi\) | |||||||
\(740\) | −8.15982 | −0.299961 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.90167 | −0.253368 | ||||||||
\(743\) | 9.86659 | 0.361970 | 0.180985 | − | 0.983486i | \(-0.442071\pi\) | ||||
0.180985 | + | 0.983486i | \(0.442071\pi\) | |||||||
\(744\) | 1.95811 | 0.0717878 | ||||||||
\(745\) | −19.3773 | −0.709930 | ||||||||
\(746\) | 29.6287 | 1.08478 | ||||||||
\(747\) | 11.5740 | 0.423470 | ||||||||
\(748\) | 2.18479 | 0.0798839 | ||||||||
\(749\) | −10.1702 | −0.371613 | ||||||||
\(750\) | −10.1848 | −0.371896 | ||||||||
\(751\) | 9.75877 | 0.356103 | 0.178051 | − | 0.984021i | \(-0.443021\pi\) | ||||
0.178051 | + | 0.984021i | \(0.443021\pi\) | |||||||
\(752\) | 2.04189 | 0.0744600 | ||||||||
\(753\) | 17.9436 | 0.653900 | ||||||||
\(754\) | 15.6040 | 0.568264 | ||||||||
\(755\) | −24.3150 | −0.884914 | ||||||||
\(756\) | 0.532089 | 0.0193519 | ||||||||
\(757\) | −43.5039 | −1.58118 | −0.790589 | − | 0.612348i | \(-0.790225\pi\) | ||||
−0.790589 | + | 0.612348i | \(0.790225\pi\) | |||||||
\(758\) | −4.72462 | −0.171606 | ||||||||
\(759\) | −12.5963 | −0.457216 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 44.7137 | 1.62087 | 0.810435 | − | 0.585828i | \(-0.199231\pi\) | ||||
0.810435 | + | 0.585828i | \(0.199231\pi\) | |||||||
\(762\) | 1.88713 | 0.0683634 | ||||||||
\(763\) | 8.73236 | 0.316133 | ||||||||
\(764\) | −15.1780 | −0.549120 | ||||||||
\(765\) | 1.37733 | 0.0497973 | ||||||||
\(766\) | 5.24123 | 0.189373 | ||||||||
\(767\) | 10.3969 | 0.375411 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 22.1019 | 0.797017 | 0.398508 | − | 0.917165i | \(-0.369528\pi\) | ||||
0.398508 | + | 0.917165i | \(0.369528\pi\) | |||||||
\(770\) | 1.18479 | 0.0426970 | ||||||||
\(771\) | −29.4124 | −1.05926 | ||||||||
\(772\) | −13.0077 | −0.468159 | ||||||||
\(773\) | −42.1789 | −1.51707 | −0.758535 | − | 0.651632i | \(-0.774085\pi\) | ||||
−0.758535 | + | 0.651632i | \(0.774085\pi\) | |||||||
\(774\) | 2.42602 | 0.0872016 | ||||||||
\(775\) | −7.04189 | −0.252952 | ||||||||
\(776\) | −5.87939 | −0.211058 | ||||||||
\(777\) | −3.66456 | −0.131465 | ||||||||
\(778\) | −15.0770 | −0.540536 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 4.59627 | 0.164573 | ||||||||
\(781\) | −11.4115 | −0.408335 | ||||||||
\(782\) | −7.79149 | −0.278623 | ||||||||
\(783\) | 4.02229 | 0.143745 | ||||||||
\(784\) | −6.71688 | −0.239889 | ||||||||
\(785\) | −3.79055 | −0.135291 | ||||||||
\(786\) | 10.7023 | 0.381740 | ||||||||
\(787\) | 28.4793 | 1.01518 | 0.507588 | − | 0.861600i | \(-0.330537\pi\) | ||||
0.507588 | + | 0.861600i | \(0.330537\pi\) | |||||||
\(788\) | −8.94862 | −0.318781 | ||||||||
\(789\) | 10.6827 | 0.380315 | ||||||||
\(790\) | 19.1147 | 0.680072 | ||||||||
\(791\) | 3.05232 | 0.108528 | ||||||||
\(792\) | 1.87939 | 0.0667810 | ||||||||
\(793\) | −44.0205 | −1.56321 | ||||||||
\(794\) | −14.5449 | −0.516179 | ||||||||
\(795\) | −15.3678 | −0.545041 | ||||||||
\(796\) | −4.50475 | −0.159667 | ||||||||
\(797\) | −16.6081 | −0.588290 | −0.294145 | − | 0.955761i | \(-0.595035\pi\) | ||||
−0.294145 | + | 0.955761i | \(0.595035\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.37370 | 0.0839756 | ||||||||
\(800\) | −3.59627 | −0.127147 | ||||||||
\(801\) | 3.55943 | 0.125766 | ||||||||
\(802\) | −2.85473 | −0.100804 | ||||||||
\(803\) | −0.615867 | −0.0217335 | ||||||||
\(804\) | 11.1702 | 0.393944 | ||||||||
\(805\) | −4.22525 | −0.148921 | ||||||||
\(806\) | 7.59627 | 0.267567 | ||||||||
\(807\) | 20.5767 | 0.724333 | ||||||||
\(808\) | 12.6459 | 0.444881 | ||||||||
\(809\) | −13.6783 | −0.480903 | −0.240452 | − | 0.970661i | \(-0.577296\pi\) | ||||
−0.240452 | + | 0.970661i | \(0.577296\pi\) | |||||||
\(810\) | 1.18479 | 0.0416294 | ||||||||
\(811\) | 0.618231 | 0.0217090 | 0.0108545 | − | 0.999941i | \(-0.496545\pi\) | ||||
0.0108545 | + | 0.999941i | \(0.496545\pi\) | |||||||
\(812\) | 2.14022 | 0.0751068 | ||||||||
\(813\) | 1.87670 | 0.0658186 | ||||||||
\(814\) | −12.9436 | −0.453672 | ||||||||
\(815\) | −28.4442 | −0.996357 | ||||||||
\(816\) | 1.16250 | 0.0406958 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −34.2276 | −1.19674 | ||||||||
\(819\) | 2.06418 | 0.0721282 | ||||||||
\(820\) | 10.6459 | 0.371771 | ||||||||
\(821\) | 6.11205 | 0.213312 | 0.106656 | − | 0.994296i | \(-0.465986\pi\) | ||||
0.106656 | + | 0.994296i | \(0.465986\pi\) | |||||||
\(822\) | −11.2567 | −0.392623 | ||||||||
\(823\) | 30.6546 | 1.06855 | 0.534276 | − | 0.845310i | \(-0.320584\pi\) | ||||
0.534276 | + | 0.845310i | \(0.320584\pi\) | |||||||
\(824\) | −2.96316 | −0.103227 | ||||||||
\(825\) | −6.75877 | −0.235310 | ||||||||
\(826\) | 1.42602 | 0.0496177 | ||||||||
\(827\) | 50.7134 | 1.76348 | 0.881738 | − | 0.471739i | \(-0.156373\pi\) | ||||
0.881738 | + | 0.471739i | \(0.156373\pi\) | |||||||
\(828\) | −6.70233 | −0.232922 | ||||||||
\(829\) | 13.0000 | 0.451509 | 0.225754 | − | 0.974184i | \(-0.427515\pi\) | ||||
0.225754 | + | 0.974184i | \(0.427515\pi\) | |||||||
\(830\) | 13.7128 | 0.475977 | ||||||||
\(831\) | 4.87258 | 0.169028 | ||||||||
\(832\) | 3.87939 | 0.134493 | ||||||||
\(833\) | −7.80840 | −0.270545 | ||||||||
\(834\) | −12.1702 | −0.421421 | ||||||||
\(835\) | −4.33687 | −0.150083 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.95811 | 0.0676822 | ||||||||
\(838\) | −7.91891 | −0.273554 | ||||||||
\(839\) | 21.4979 | 0.742191 | 0.371096 | − | 0.928595i | \(-0.378982\pi\) | ||||
0.371096 | + | 0.928595i | \(0.378982\pi\) | |||||||
\(840\) | 0.630415 | 0.0217514 | ||||||||
\(841\) | −12.8212 | −0.442110 | ||||||||
\(842\) | −16.2098 | −0.558626 | ||||||||
\(843\) | 0.403733 | 0.0139053 | ||||||||
\(844\) | 6.40373 | 0.220426 | ||||||||
\(845\) | 2.42839 | 0.0835390 | ||||||||
\(846\) | 2.04189 | 0.0702016 | ||||||||
\(847\) | −3.97359 | −0.136534 | ||||||||
\(848\) | −12.9709 | −0.445423 | ||||||||
\(849\) | 17.5895 | 0.603669 | ||||||||
\(850\) | −4.18067 | −0.143396 | ||||||||
\(851\) | 46.1598 | 1.58234 | ||||||||
\(852\) | −6.07192 | −0.208021 | ||||||||
\(853\) | −46.2276 | −1.58280 | −0.791402 | − | 0.611296i | \(-0.790648\pi\) | ||||
−0.791402 | + | 0.611296i | \(0.790648\pi\) | |||||||
\(854\) | −6.03777 | −0.206608 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −19.1138 | −0.653296 | ||||||||
\(857\) | 43.6623 | 1.49148 | 0.745738 | − | 0.666239i | \(-0.232097\pi\) | ||||
0.745738 | + | 0.666239i | \(0.232097\pi\) | |||||||
\(858\) | 7.29086 | 0.248906 | ||||||||
\(859\) | 20.1652 | 0.688027 | 0.344014 | − | 0.938965i | \(-0.388213\pi\) | ||||
0.344014 | + | 0.938965i | \(0.388213\pi\) | |||||||
\(860\) | 2.87433 | 0.0980139 | ||||||||
\(861\) | 4.78106 | 0.162938 | ||||||||
\(862\) | −25.4320 | −0.866218 | ||||||||
\(863\) | 32.6932 | 1.11289 | 0.556444 | − | 0.830885i | \(-0.312165\pi\) | ||||
0.556444 | + | 0.830885i | \(0.312165\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 6.31820 | 0.214825 | ||||||||
\(866\) | −11.8479 | −0.402609 | ||||||||
\(867\) | −15.6486 | −0.531454 | ||||||||
\(868\) | 1.04189 | 0.0353640 | ||||||||
\(869\) | 30.3209 | 1.02857 | ||||||||
\(870\) | 4.76558 | 0.161568 | ||||||||
\(871\) | 43.3337 | 1.46831 | ||||||||
\(872\) | 16.4115 | 0.555763 | ||||||||
\(873\) | −5.87939 | −0.198987 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.41921 | −0.183203 | ||||||||
\(876\) | −0.327696 | −0.0110718 | ||||||||
\(877\) | −30.2968 | −1.02305 | −0.511526 | − | 0.859268i | \(-0.670920\pi\) | ||||
−0.511526 | + | 0.859268i | \(0.670920\pi\) | |||||||
\(878\) | −25.8598 | −0.872725 | ||||||||
\(879\) | 13.1753 | 0.444392 | ||||||||
\(880\) | 2.22668 | 0.0750614 | ||||||||
\(881\) | 23.5577 | 0.793678 | 0.396839 | − | 0.917888i | \(-0.370107\pi\) | ||||
0.396839 | + | 0.917888i | \(0.370107\pi\) | |||||||
\(882\) | −6.71688 | −0.226169 | ||||||||
\(883\) | 36.8289 | 1.23939 | 0.619696 | − | 0.784842i | \(-0.287256\pi\) | ||||
0.619696 | + | 0.784842i | \(0.287256\pi\) | |||||||
\(884\) | 4.50980 | 0.151681 | ||||||||
\(885\) | 3.17530 | 0.106736 | ||||||||
\(886\) | 0.923029 | 0.0310098 | ||||||||
\(887\) | −4.30810 | −0.144652 | −0.0723258 | − | 0.997381i | \(-0.523042\pi\) | ||||
−0.0723258 | + | 0.997381i | \(0.523042\pi\) | |||||||
\(888\) | −6.88713 | −0.231117 | ||||||||
\(889\) | 1.00412 | 0.0336771 | ||||||||
\(890\) | 4.21719 | 0.141360 | ||||||||
\(891\) | 1.87939 | 0.0629618 | ||||||||
\(892\) | −3.24897 | −0.108784 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −16.3550 | −0.546994 | ||||||||
\(895\) | 29.9240 | 1.00025 | ||||||||
\(896\) | 0.532089 | 0.0177758 | ||||||||
\(897\) | −26.0009 | −0.868146 | ||||||||
\(898\) | −9.34461 | −0.311834 | ||||||||
\(899\) | 7.87609 | 0.262682 | ||||||||
\(900\) | −3.59627 | −0.119876 | ||||||||
\(901\) | −15.0787 | −0.502345 | ||||||||
\(902\) | 16.8871 | 0.562280 | ||||||||
\(903\) | 1.29086 | 0.0429571 | ||||||||
\(904\) | 5.73648 | 0.190793 | ||||||||
\(905\) | 20.5044 | 0.681590 | ||||||||
\(906\) | −20.5226 | −0.681817 | ||||||||
\(907\) | −23.3405 | −0.775008 | −0.387504 | − | 0.921868i | \(-0.626663\pi\) | ||||
−0.387504 | + | 0.921868i | \(0.626663\pi\) | |||||||
\(908\) | 11.7023 | 0.388356 | ||||||||
\(909\) | 12.6459 | 0.419438 | ||||||||
\(910\) | 2.44562 | 0.0810716 | ||||||||
\(911\) | −22.5631 | −0.747547 | −0.373774 | − | 0.927520i | \(-0.621936\pi\) | ||||
−0.373774 | + | 0.927520i | \(0.621936\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.7520 | 0.719885 | ||||||||
\(914\) | 30.9009 | 1.02211 | ||||||||
\(915\) | −13.4442 | −0.444451 | ||||||||
\(916\) | −22.9067 | −0.756860 | ||||||||
\(917\) | 5.69459 | 0.188052 | ||||||||
\(918\) | 1.16250 | 0.0383683 | ||||||||
\(919\) | 4.25578 | 0.140385 | 0.0701926 | − | 0.997533i | \(-0.477639\pi\) | ||||
0.0701926 | + | 0.997533i | \(0.477639\pi\) | |||||||
\(920\) | −7.94087 | −0.261803 | ||||||||
\(921\) | −16.9017 | −0.556929 | ||||||||
\(922\) | −29.6878 | −0.977715 | ||||||||
\(923\) | −23.5553 | −0.775333 | ||||||||
\(924\) | 1.00000 | 0.0328976 | ||||||||
\(925\) | 24.7679 | 0.814365 | ||||||||
\(926\) | −11.8307 | −0.388781 | ||||||||
\(927\) | −2.96316 | −0.0973231 | ||||||||
\(928\) | 4.02229 | 0.132038 | ||||||||
\(929\) | 59.5245 | 1.95293 | 0.976467 | − | 0.215666i | \(-0.0691924\pi\) | ||||
0.976467 | + | 0.215666i | \(0.0691924\pi\) | |||||||
\(930\) | 2.31996 | 0.0760743 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.19934 | −0.104798 | ||||||||
\(933\) | −2.38144 | −0.0779650 | ||||||||
\(934\) | 38.3182 | 1.25381 | ||||||||
\(935\) | 2.58853 | 0.0846538 | ||||||||
\(936\) | 3.87939 | 0.126802 | ||||||||
\(937\) | 33.5090 | 1.09469 | 0.547345 | − | 0.836907i | \(-0.315638\pi\) | ||||
0.547345 | + | 0.836907i | \(0.315638\pi\) | |||||||
\(938\) | 5.94356 | 0.194064 | ||||||||
\(939\) | −29.8631 | −0.974545 | ||||||||
\(940\) | 2.41921 | 0.0789061 | ||||||||
\(941\) | 5.52435 | 0.180089 | 0.0900443 | − | 0.995938i | \(-0.471299\pi\) | ||||
0.0900443 | + | 0.995938i | \(0.471299\pi\) | |||||||
\(942\) | −3.19934 | −0.104240 | ||||||||
\(943\) | −60.2235 | −1.96115 | ||||||||
\(944\) | 2.68004 | 0.0872280 | ||||||||
\(945\) | 0.630415 | 0.0205074 | ||||||||
\(946\) | 4.55943 | 0.148240 | ||||||||
\(947\) | −14.9050 | −0.484347 | −0.242173 | − | 0.970233i | \(-0.577860\pi\) | ||||
−0.242173 | + | 0.970233i | \(0.577860\pi\) | |||||||
\(948\) | 16.1334 | 0.523989 | ||||||||
\(949\) | −1.27126 | −0.0412668 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.02229 | 0.227713 | ||||||||
\(952\) | 0.618555 | 0.0200475 | ||||||||
\(953\) | 46.3661 | 1.50194 | 0.750972 | − | 0.660334i | \(-0.229585\pi\) | ||||
0.750972 | + | 0.660334i | \(0.229585\pi\) | |||||||
\(954\) | −12.9709 | −0.419949 | ||||||||
\(955\) | −17.9828 | −0.581909 | ||||||||
\(956\) | 6.17293 | 0.199647 | ||||||||
\(957\) | 7.55943 | 0.244362 | ||||||||
\(958\) | 37.2841 | 1.20459 | ||||||||
\(959\) | −5.98957 | −0.193413 | ||||||||
\(960\) | 1.18479 | 0.0382390 | ||||||||
\(961\) | −27.1658 | −0.876316 | ||||||||
\(962\) | −26.7178 | −0.861417 | ||||||||
\(963\) | −19.1138 | −0.615934 | ||||||||
\(964\) | −1.53714 | −0.0495080 | ||||||||
\(965\) | −15.4115 | −0.496113 | ||||||||
\(966\) | −3.56624 | −0.114742 | ||||||||
\(967\) | −23.2431 | −0.747448 | −0.373724 | − | 0.927540i | \(-0.621919\pi\) | ||||
−0.373724 | + | 0.927540i | \(0.621919\pi\) | |||||||
\(968\) | −7.46791 | −0.240028 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −6.96585 | −0.223660 | ||||||||
\(971\) | −4.93045 | −0.158226 | −0.0791128 | − | 0.996866i | \(-0.525209\pi\) | ||||
−0.0791128 | + | 0.996866i | \(0.525209\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −6.47565 | −0.207600 | ||||||||
\(974\) | −32.9786 | −1.05670 | ||||||||
\(975\) | −13.9513 | −0.446799 | ||||||||
\(976\) | −11.3473 | −0.363218 | ||||||||
\(977\) | −32.7442 | −1.04758 | −0.523790 | − | 0.851847i | \(-0.675482\pi\) | ||||
−0.523790 | + | 0.851847i | \(0.675482\pi\) | |||||||
\(978\) | −24.0077 | −0.767683 | ||||||||
\(979\) | 6.68954 | 0.213799 | ||||||||
\(980\) | −7.95811 | −0.254213 | ||||||||
\(981\) | 16.4115 | 0.523978 | ||||||||
\(982\) | 17.6810 | 0.564223 | ||||||||
\(983\) | 25.4406 | 0.811428 | 0.405714 | − | 0.914000i | \(-0.367023\pi\) | ||||
0.405714 | + | 0.914000i | \(0.367023\pi\) | |||||||
\(984\) | 8.98545 | 0.286446 | ||||||||
\(985\) | −10.6023 | −0.337816 | ||||||||
\(986\) | 4.67593 | 0.148912 | ||||||||
\(987\) | 1.08647 | 0.0345826 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.2600 | −0.517038 | ||||||||
\(990\) | 2.22668 | 0.0707686 | ||||||||
\(991\) | −10.1533 | −0.322531 | −0.161266 | − | 0.986911i | \(-0.551558\pi\) | ||||
−0.161266 | + | 0.986911i | \(0.551558\pi\) | |||||||
\(992\) | 1.95811 | 0.0621701 | ||||||||
\(993\) | −27.1985 | −0.863119 | ||||||||
\(994\) | −3.23080 | −0.102475 | ||||||||
\(995\) | −5.33719 | −0.169200 | ||||||||
\(996\) | 11.5740 | 0.366736 | ||||||||
\(997\) | 55.7698 | 1.76625 | 0.883124 | − | 0.469140i | \(-0.155436\pi\) | ||||
0.883124 | + | 0.469140i | \(0.155436\pi\) | |||||||
\(998\) | 27.1239 | 0.858592 | ||||||||
\(999\) | −6.88713 | −0.217899 |
(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 | 2166.2.a.u.1.2 | 3 | ||
3.2 | odd | 2 | 6498.2.a.bn.1.2 | 3 | |||
19.2 | odd | 18 | 114.2.i.d.61.1 | yes | 6 | ||
19.10 | odd | 18 | 114.2.i.d.43.1 | ✓ | 6 | ||
19.18 | odd | 2 | 2166.2.a.o.1.2 | 3 | |||
57.2 | even | 18 | 342.2.u.a.289.1 | 6 | |||
57.29 | even | 18 | 342.2.u.a.271.1 | 6 | |||
57.56 | even | 2 | 6498.2.a.bs.1.2 | 3 | |||
76.59 | even | 18 | 912.2.bo.f.289.1 | 6 | |||
76.67 | even | 18 | 912.2.bo.f.385.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.2.i.d.43.1 | ✓ | 6 | 19.10 | odd | 18 | ||
114.2.i.d.61.1 | yes | 6 | 19.2 | odd | 18 | ||
342.2.u.a.271.1 | 6 | 57.29 | even | 18 | |||
342.2.u.a.289.1 | 6 | 57.2 | even | 18 | |||
912.2.bo.f.289.1 | 6 | 76.59 | even | 18 | |||
912.2.bo.f.385.1 | 6 | 76.67 | even | 18 | |||
2166.2.a.o.1.2 | 3 | 19.18 | odd | 2 | |||
2166.2.a.u.1.2 | 3 | 1.1 | even | 1 | trivial | ||
6498.2.a.bn.1.2 | 3 | 3.2 | odd | 2 | |||
6498.2.a.bs.1.2 | 3 | 57.56 | even | 2 |