Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, 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("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.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: | \(28.3389076774\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 11x^{7} + 8x^{6} + 37x^{5} - 18x^{4} - 41x^{3} + 12x^{2} + 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-2.31147\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.31147 | 1.63445 | 0.817227 | − | 0.576316i | \(-0.195510\pi\) | ||||
0.817227 | + | 0.576316i | \(0.195510\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.34288 | 1.67144 | ||||||||
\(5\) | 1.46052 | 0.653166 | 0.326583 | − | 0.945168i | \(-0.394103\pi\) | ||||
0.326583 | + | 0.945168i | \(0.394103\pi\) | |||||||
\(6\) | −2.31147 | −0.943652 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 3.10401 | 1.09743 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.37595 | 1.06757 | ||||||||
\(11\) | 0.0565977 | 0.0170648 | 0.00853242 | − | 0.999964i | \(-0.497284\pi\) | ||||
0.00853242 | + | 0.999964i | \(0.497284\pi\) | |||||||
\(12\) | −3.34288 | −0.965005 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.31147 | 0.617765 | ||||||||
\(15\) | −1.46052 | −0.377106 | ||||||||
\(16\) | 0.489065 | 0.122266 | ||||||||
\(17\) | 5.75421 | 1.39560 | 0.697801 | − | 0.716292i | \(-0.254162\pi\) | ||||
0.697801 | + | 0.716292i | \(0.254162\pi\) | |||||||
\(18\) | 2.31147 | 0.544818 | ||||||||
\(19\) | −0.807619 | −0.185281 | −0.0926403 | − | 0.995700i | \(-0.529531\pi\) | ||||
−0.0926403 | + | 0.995700i | \(0.529531\pi\) | |||||||
\(20\) | 4.88235 | 1.09173 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0.130824 | 0.0278917 | ||||||||
\(23\) | 6.01403 | 1.25401 | 0.627006 | − | 0.779014i | \(-0.284280\pi\) | ||||
0.627006 | + | 0.779014i | \(0.284280\pi\) | |||||||
\(24\) | −3.10401 | −0.633604 | ||||||||
\(25\) | −2.86687 | −0.573374 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.34288 | 0.631744 | ||||||||
\(29\) | 3.22124 | 0.598168 | 0.299084 | − | 0.954227i | \(-0.403319\pi\) | ||||
0.299084 | + | 0.954227i | \(0.403319\pi\) | |||||||
\(30\) | −3.37595 | −0.616362 | ||||||||
\(31\) | 5.59058 | 1.00410 | 0.502049 | − | 0.864839i | \(-0.332580\pi\) | ||||
0.502049 | + | 0.864839i | \(0.332580\pi\) | |||||||
\(32\) | −5.07756 | −0.897595 | ||||||||
\(33\) | −0.0565977 | −0.00985239 | ||||||||
\(34\) | 13.3007 | 2.28105 | ||||||||
\(35\) | 1.46052 | 0.246874 | ||||||||
\(36\) | 3.34288 | 0.557146 | ||||||||
\(37\) | 0.780896 | 0.128378 | 0.0641892 | − | 0.997938i | \(-0.479554\pi\) | ||||
0.0641892 | + | 0.997938i | \(0.479554\pi\) | |||||||
\(38\) | −1.86679 | −0.302833 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.53348 | 0.716807 | ||||||||
\(41\) | −5.30154 | −0.827961 | −0.413980 | − | 0.910286i | \(-0.635862\pi\) | ||||
−0.413980 | + | 0.910286i | \(0.635862\pi\) | |||||||
\(42\) | −2.31147 | −0.356667 | ||||||||
\(43\) | 2.38217 | 0.363278 | 0.181639 | − | 0.983365i | \(-0.441860\pi\) | ||||
0.181639 | + | 0.983365i | \(0.441860\pi\) | |||||||
\(44\) | 0.189199 | 0.0285228 | ||||||||
\(45\) | 1.46052 | 0.217722 | ||||||||
\(46\) | 13.9012 | 2.04963 | ||||||||
\(47\) | −3.32663 | −0.485239 | −0.242620 | − | 0.970122i | \(-0.578007\pi\) | ||||
−0.242620 | + | 0.970122i | \(0.578007\pi\) | |||||||
\(48\) | −0.489065 | −0.0705905 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −6.62667 | −0.937153 | ||||||||
\(51\) | −5.75421 | −0.805751 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.52747 | −1.30870 | −0.654350 | − | 0.756192i | \(-0.727058\pi\) | ||||
−0.654350 | + | 0.756192i | \(0.727058\pi\) | |||||||
\(54\) | −2.31147 | −0.314551 | ||||||||
\(55\) | 0.0826623 | 0.0111462 | ||||||||
\(56\) | 3.10401 | 0.414791 | ||||||||
\(57\) | 0.807619 | 0.106972 | ||||||||
\(58\) | 7.44578 | 0.977678 | ||||||||
\(59\) | 10.3267 | 1.34443 | 0.672214 | − | 0.740357i | \(-0.265344\pi\) | ||||
0.672214 | + | 0.740357i | \(0.265344\pi\) | |||||||
\(60\) | −4.88235 | −0.630309 | ||||||||
\(61\) | 8.88239 | 1.13727 | 0.568637 | − | 0.822589i | \(-0.307471\pi\) | ||||
0.568637 | + | 0.822589i | \(0.307471\pi\) | |||||||
\(62\) | 12.9224 | 1.64115 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −12.7147 | −1.58934 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.130824 | −0.0161033 | ||||||||
\(67\) | 7.80744 | 0.953830 | 0.476915 | − | 0.878949i | \(-0.341755\pi\) | ||||
0.476915 | + | 0.878949i | \(0.341755\pi\) | |||||||
\(68\) | 19.2356 | 2.33266 | ||||||||
\(69\) | −6.01403 | −0.724005 | ||||||||
\(70\) | 3.37595 | 0.403504 | ||||||||
\(71\) | −11.4706 | −1.36131 | −0.680657 | − | 0.732602i | \(-0.738306\pi\) | ||||
−0.680657 | + | 0.732602i | \(0.738306\pi\) | |||||||
\(72\) | 3.10401 | 0.365811 | ||||||||
\(73\) | 13.1445 | 1.53845 | 0.769223 | − | 0.638980i | \(-0.220643\pi\) | ||||
0.769223 | + | 0.638980i | \(0.220643\pi\) | |||||||
\(74\) | 1.80501 | 0.209829 | ||||||||
\(75\) | 2.86687 | 0.331037 | ||||||||
\(76\) | −2.69977 | −0.309685 | ||||||||
\(77\) | 0.0565977 | 0.00644991 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.8565 | 1.22145 | 0.610726 | − | 0.791842i | \(-0.290878\pi\) | ||||
0.610726 | + | 0.791842i | \(0.290878\pi\) | |||||||
\(80\) | 0.714292 | 0.0798602 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −12.2543 | −1.35326 | ||||||||
\(83\) | −7.70243 | −0.845452 | −0.422726 | − | 0.906258i | \(-0.638927\pi\) | ||||
−0.422726 | + | 0.906258i | \(0.638927\pi\) | |||||||
\(84\) | −3.34288 | −0.364738 | ||||||||
\(85\) | 8.40417 | 0.911560 | ||||||||
\(86\) | 5.50631 | 0.593760 | ||||||||
\(87\) | −3.22124 | −0.345353 | ||||||||
\(88\) | 0.175680 | 0.0187275 | ||||||||
\(89\) | 8.12369 | 0.861109 | 0.430555 | − | 0.902564i | \(-0.358318\pi\) | ||||
0.430555 | + | 0.902564i | \(0.358318\pi\) | |||||||
\(90\) | 3.37595 | 0.355857 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 20.1042 | 2.09600 | ||||||||
\(93\) | −5.59058 | −0.579716 | ||||||||
\(94\) | −7.68939 | −0.793101 | ||||||||
\(95\) | −1.17955 | −0.121019 | ||||||||
\(96\) | 5.07756 | 0.518227 | ||||||||
\(97\) | 3.93035 | 0.399066 | 0.199533 | − | 0.979891i | \(-0.436057\pi\) | ||||
0.199533 | + | 0.979891i | \(0.436057\pi\) | |||||||
\(98\) | 2.31147 | 0.233493 | ||||||||
\(99\) | 0.0565977 | 0.00568828 | ||||||||
\(100\) | −9.58358 | −0.958358 | ||||||||
\(101\) | 6.75818 | 0.672464 | 0.336232 | − | 0.941779i | \(-0.390847\pi\) | ||||
0.336232 | + | 0.941779i | \(0.390847\pi\) | |||||||
\(102\) | −13.3007 | −1.31696 | ||||||||
\(103\) | −12.4083 | −1.22262 | −0.611312 | − | 0.791390i | \(-0.709358\pi\) | ||||
−0.611312 | + | 0.791390i | \(0.709358\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.46052 | −0.142533 | ||||||||
\(106\) | −22.0224 | −2.13901 | ||||||||
\(107\) | 18.1781 | 1.75734 | 0.878672 | − | 0.477425i | \(-0.158430\pi\) | ||||
0.878672 | + | 0.477425i | \(0.158430\pi\) | |||||||
\(108\) | −3.34288 | −0.321668 | ||||||||
\(109\) | −9.12019 | −0.873556 | −0.436778 | − | 0.899569i | \(-0.643880\pi\) | ||||
−0.436778 | + | 0.899569i | \(0.643880\pi\) | |||||||
\(110\) | 0.191071 | 0.0182179 | ||||||||
\(111\) | −0.780896 | −0.0741193 | ||||||||
\(112\) | 0.489065 | 0.0462123 | ||||||||
\(113\) | −14.7050 | −1.38333 | −0.691664 | − | 0.722220i | \(-0.743122\pi\) | ||||
−0.691664 | + | 0.722220i | \(0.743122\pi\) | |||||||
\(114\) | 1.86679 | 0.174840 | ||||||||
\(115\) | 8.78364 | 0.819079 | ||||||||
\(116\) | 10.7682 | 0.999801 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 23.8699 | 2.19740 | ||||||||
\(119\) | 5.75421 | 0.527488 | ||||||||
\(120\) | −4.53348 | −0.413849 | ||||||||
\(121\) | −10.9968 | −0.999709 | ||||||||
\(122\) | 20.5313 | 1.85882 | ||||||||
\(123\) | 5.30154 | 0.478023 | ||||||||
\(124\) | 18.6886 | 1.67829 | ||||||||
\(125\) | −11.4898 | −1.02767 | ||||||||
\(126\) | 2.31147 | 0.205922 | ||||||||
\(127\) | −10.5900 | −0.939714 | −0.469857 | − | 0.882743i | \(-0.655694\pi\) | ||||
−0.469857 | + | 0.882743i | \(0.655694\pi\) | |||||||
\(128\) | −19.2346 | −1.70011 | ||||||||
\(129\) | −2.38217 | −0.209738 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.31173 | −0.813570 | −0.406785 | − | 0.913524i | \(-0.633350\pi\) | ||||
−0.406785 | + | 0.913524i | \(0.633350\pi\) | |||||||
\(132\) | −0.189199 | −0.0164677 | ||||||||
\(133\) | −0.807619 | −0.0700295 | ||||||||
\(134\) | 18.0466 | 1.55899 | ||||||||
\(135\) | −1.46052 | −0.125702 | ||||||||
\(136\) | 17.8611 | 1.53158 | ||||||||
\(137\) | 4.10255 | 0.350505 | 0.175252 | − | 0.984524i | \(-0.443926\pi\) | ||||
0.175252 | + | 0.984524i | \(0.443926\pi\) | |||||||
\(138\) | −13.9012 | −1.18335 | ||||||||
\(139\) | 16.2754 | 1.38046 | 0.690231 | − | 0.723589i | \(-0.257509\pi\) | ||||
0.690231 | + | 0.723589i | \(0.257509\pi\) | |||||||
\(140\) | 4.88235 | 0.412634 | ||||||||
\(141\) | 3.32663 | 0.280153 | ||||||||
\(142\) | −26.5140 | −2.22500 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.489065 | 0.0407554 | ||||||||
\(145\) | 4.70469 | 0.390704 | ||||||||
\(146\) | 30.3830 | 2.51452 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 2.61044 | 0.214577 | ||||||||
\(149\) | −2.11348 | −0.173143 | −0.0865717 | − | 0.996246i | \(-0.527591\pi\) | ||||
−0.0865717 | + | 0.996246i | \(0.527591\pi\) | |||||||
\(150\) | 6.62667 | 0.541065 | ||||||||
\(151\) | −17.2235 | −1.40163 | −0.700814 | − | 0.713344i | \(-0.747180\pi\) | ||||
−0.700814 | + | 0.713344i | \(0.747180\pi\) | |||||||
\(152\) | −2.50686 | −0.203333 | ||||||||
\(153\) | 5.75421 | 0.465201 | ||||||||
\(154\) | 0.130824 | 0.0105421 | ||||||||
\(155\) | 8.16518 | 0.655843 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.5730 | −1.64190 | −0.820951 | − | 0.570998i | \(-0.806556\pi\) | ||||
−0.820951 | + | 0.570998i | \(0.806556\pi\) | |||||||
\(158\) | 25.0944 | 1.99641 | ||||||||
\(159\) | 9.52747 | 0.755578 | ||||||||
\(160\) | −7.41591 | −0.586279 | ||||||||
\(161\) | 6.01403 | 0.473972 | ||||||||
\(162\) | 2.31147 | 0.181606 | ||||||||
\(163\) | −8.77011 | −0.686928 | −0.343464 | − | 0.939166i | \(-0.611600\pi\) | ||||
−0.343464 | + | 0.939166i | \(0.611600\pi\) | |||||||
\(164\) | −17.7224 | −1.38389 | ||||||||
\(165\) | −0.0826623 | −0.00643525 | ||||||||
\(166\) | −17.8039 | −1.38185 | ||||||||
\(167\) | 16.9542 | 1.31195 | 0.655976 | − | 0.754782i | \(-0.272257\pi\) | ||||
0.655976 | + | 0.754782i | \(0.272257\pi\) | |||||||
\(168\) | −3.10401 | −0.239480 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 19.4260 | 1.48990 | ||||||||
\(171\) | −0.807619 | −0.0617602 | ||||||||
\(172\) | 7.96330 | 0.607196 | ||||||||
\(173\) | 1.91338 | 0.145472 | 0.0727360 | − | 0.997351i | \(-0.476827\pi\) | ||||
0.0727360 | + | 0.997351i | \(0.476827\pi\) | |||||||
\(174\) | −7.44578 | −0.564463 | ||||||||
\(175\) | −2.86687 | −0.216715 | ||||||||
\(176\) | 0.0276800 | 0.00208646 | ||||||||
\(177\) | −10.3267 | −0.776206 | ||||||||
\(178\) | 18.7776 | 1.40744 | ||||||||
\(179\) | −26.1240 | −1.95260 | −0.976300 | − | 0.216421i | \(-0.930562\pi\) | ||||
−0.976300 | + | 0.216421i | \(0.930562\pi\) | |||||||
\(180\) | 4.88235 | 0.363909 | ||||||||
\(181\) | −1.98010 | −0.147180 | −0.0735899 | − | 0.997289i | \(-0.523446\pi\) | ||||
−0.0735899 | + | 0.997289i | \(0.523446\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.88239 | −0.656605 | ||||||||
\(184\) | 18.6676 | 1.37620 | ||||||||
\(185\) | 1.14052 | 0.0838525 | ||||||||
\(186\) | −12.9224 | −0.947520 | ||||||||
\(187\) | 0.325675 | 0.0238157 | ||||||||
\(188\) | −11.1205 | −0.811047 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −2.72649 | −0.197800 | ||||||||
\(191\) | −20.6851 | −1.49672 | −0.748359 | − | 0.663294i | \(-0.769158\pi\) | ||||
−0.748359 | + | 0.663294i | \(0.769158\pi\) | |||||||
\(192\) | 12.7147 | 0.917608 | ||||||||
\(193\) | 2.88929 | 0.207976 | 0.103988 | − | 0.994579i | \(-0.466840\pi\) | ||||
0.103988 | + | 0.994579i | \(0.466840\pi\) | |||||||
\(194\) | 9.08487 | 0.652256 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.34288 | 0.238777 | ||||||||
\(197\) | 3.01713 | 0.214962 | 0.107481 | − | 0.994207i | \(-0.465722\pi\) | ||||
0.107481 | + | 0.994207i | \(0.465722\pi\) | |||||||
\(198\) | 0.130824 | 0.00929723 | ||||||||
\(199\) | 24.5542 | 1.74060 | 0.870301 | − | 0.492520i | \(-0.163924\pi\) | ||||
0.870301 | + | 0.492520i | \(0.163924\pi\) | |||||||
\(200\) | −8.89879 | −0.629240 | ||||||||
\(201\) | −7.80744 | −0.550694 | ||||||||
\(202\) | 15.6213 | 1.09911 | ||||||||
\(203\) | 3.22124 | 0.226086 | ||||||||
\(204\) | −19.2356 | −1.34676 | ||||||||
\(205\) | −7.74302 | −0.540796 | ||||||||
\(206\) | −28.6813 | −1.99832 | ||||||||
\(207\) | 6.01403 | 0.418004 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.0457094 | −0.00316179 | ||||||||
\(210\) | −3.37595 | −0.232963 | ||||||||
\(211\) | 15.2596 | 1.05052 | 0.525259 | − | 0.850943i | \(-0.323969\pi\) | ||||
0.525259 | + | 0.850943i | \(0.323969\pi\) | |||||||
\(212\) | −31.8492 | −2.18741 | ||||||||
\(213\) | 11.4706 | 0.785955 | ||||||||
\(214\) | 42.0181 | 2.87230 | ||||||||
\(215\) | 3.47922 | 0.237281 | ||||||||
\(216\) | −3.10401 | −0.211201 | ||||||||
\(217\) | 5.59058 | 0.379514 | ||||||||
\(218\) | −21.0810 | −1.42779 | ||||||||
\(219\) | −13.1445 | −0.888222 | ||||||||
\(220\) | 0.276330 | 0.0186302 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1.80501 | −0.121145 | ||||||||
\(223\) | −3.41178 | −0.228470 | −0.114235 | − | 0.993454i | \(-0.536442\pi\) | ||||
−0.114235 | + | 0.993454i | \(0.536442\pi\) | |||||||
\(224\) | −5.07756 | −0.339259 | ||||||||
\(225\) | −2.86687 | −0.191125 | ||||||||
\(226\) | −33.9900 | −2.26098 | ||||||||
\(227\) | −1.36962 | −0.0909046 | −0.0454523 | − | 0.998967i | \(-0.514473\pi\) | ||||
−0.0454523 | + | 0.998967i | \(0.514473\pi\) | |||||||
\(228\) | 2.69977 | 0.178797 | ||||||||
\(229\) | −17.3194 | −1.14450 | −0.572249 | − | 0.820080i | \(-0.693929\pi\) | ||||
−0.572249 | + | 0.820080i | \(0.693929\pi\) | |||||||
\(230\) | 20.3031 | 1.33875 | ||||||||
\(231\) | −0.0565977 | −0.00372386 | ||||||||
\(232\) | 9.99875 | 0.656450 | ||||||||
\(233\) | 5.77054 | 0.378041 | 0.189020 | − | 0.981973i | \(-0.439469\pi\) | ||||
0.189020 | + | 0.981973i | \(0.439469\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.85863 | −0.316942 | ||||||||
\(236\) | 34.5210 | 2.24713 | ||||||||
\(237\) | −10.8565 | −0.705206 | ||||||||
\(238\) | 13.3007 | 0.862154 | ||||||||
\(239\) | −2.80755 | −0.181605 | −0.0908027 | − | 0.995869i | \(-0.528943\pi\) | ||||
−0.0908027 | + | 0.995869i | \(0.528943\pi\) | |||||||
\(240\) | −0.714292 | −0.0461073 | ||||||||
\(241\) | −7.55528 | −0.486678 | −0.243339 | − | 0.969941i | \(-0.578243\pi\) | ||||
−0.243339 | + | 0.969941i | \(0.578243\pi\) | |||||||
\(242\) | −25.4187 | −1.63398 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 29.6927 | 1.90088 | ||||||||
\(245\) | 1.46052 | 0.0933095 | ||||||||
\(246\) | 12.2543 | 0.781307 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 17.3532 | 1.10193 | ||||||||
\(249\) | 7.70243 | 0.488122 | ||||||||
\(250\) | −26.5582 | −1.67969 | ||||||||
\(251\) | 26.2186 | 1.65491 | 0.827453 | − | 0.561535i | \(-0.189789\pi\) | ||||
0.827453 | + | 0.561535i | \(0.189789\pi\) | |||||||
\(252\) | 3.34288 | 0.210581 | ||||||||
\(253\) | 0.340380 | 0.0213995 | ||||||||
\(254\) | −24.4785 | −1.53592 | ||||||||
\(255\) | −8.40417 | −0.526290 | ||||||||
\(256\) | −19.0306 | −1.18941 | ||||||||
\(257\) | −3.58179 | −0.223426 | −0.111713 | − | 0.993741i | \(-0.535634\pi\) | ||||
−0.111713 | + | 0.993741i | \(0.535634\pi\) | |||||||
\(258\) | −5.50631 | −0.342808 | ||||||||
\(259\) | 0.780896 | 0.0485225 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.22124 | 0.199389 | ||||||||
\(262\) | −21.5237 | −1.32974 | ||||||||
\(263\) | 26.7600 | 1.65009 | 0.825046 | − | 0.565066i | \(-0.191149\pi\) | ||||
0.825046 | + | 0.565066i | \(0.191149\pi\) | |||||||
\(264\) | −0.175680 | −0.0108123 | ||||||||
\(265\) | −13.9151 | −0.854798 | ||||||||
\(266\) | −1.86679 | −0.114460 | ||||||||
\(267\) | −8.12369 | −0.497162 | ||||||||
\(268\) | 26.0993 | 1.59427 | ||||||||
\(269\) | 14.7193 | 0.897454 | 0.448727 | − | 0.893669i | \(-0.351878\pi\) | ||||
0.448727 | + | 0.893669i | \(0.351878\pi\) | |||||||
\(270\) | −3.37595 | −0.205454 | ||||||||
\(271\) | 13.1874 | 0.801075 | 0.400537 | − | 0.916280i | \(-0.368824\pi\) | ||||
0.400537 | + | 0.916280i | \(0.368824\pi\) | |||||||
\(272\) | 2.81419 | 0.170635 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.48291 | 0.572884 | ||||||||
\(275\) | −0.162258 | −0.00978454 | ||||||||
\(276\) | −20.1042 | −1.21013 | ||||||||
\(277\) | 21.5726 | 1.29617 | 0.648087 | − | 0.761566i | \(-0.275569\pi\) | ||||
0.648087 | + | 0.761566i | \(0.275569\pi\) | |||||||
\(278\) | 37.6200 | 2.25630 | ||||||||
\(279\) | 5.59058 | 0.334699 | ||||||||
\(280\) | 4.53348 | 0.270927 | ||||||||
\(281\) | −0.186485 | −0.0111248 | −0.00556238 | − | 0.999985i | \(-0.501771\pi\) | ||||
−0.00556238 | + | 0.999985i | \(0.501771\pi\) | |||||||
\(282\) | 7.68939 | 0.457897 | ||||||||
\(283\) | −14.0208 | −0.833452 | −0.416726 | − | 0.909032i | \(-0.636823\pi\) | ||||
−0.416726 | + | 0.909032i | \(0.636823\pi\) | |||||||
\(284\) | −38.3449 | −2.27535 | ||||||||
\(285\) | 1.17955 | 0.0698704 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.30154 | −0.312940 | ||||||||
\(288\) | −5.07756 | −0.299198 | ||||||||
\(289\) | 16.1110 | 0.947705 | ||||||||
\(290\) | 10.8747 | 0.638587 | ||||||||
\(291\) | −3.93035 | −0.230401 | ||||||||
\(292\) | 43.9404 | 2.57142 | ||||||||
\(293\) | −15.8832 | −0.927907 | −0.463953 | − | 0.885860i | \(-0.653570\pi\) | ||||
−0.463953 | + | 0.885860i | \(0.653570\pi\) | |||||||
\(294\) | −2.31147 | −0.134807 | ||||||||
\(295\) | 15.0825 | 0.878135 | ||||||||
\(296\) | 2.42391 | 0.140887 | ||||||||
\(297\) | −0.0565977 | −0.00328413 | ||||||||
\(298\) | −4.88525 | −0.282995 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 9.58358 | 0.553309 | ||||||||
\(301\) | 2.38217 | 0.137306 | ||||||||
\(302\) | −39.8115 | −2.29090 | ||||||||
\(303\) | −6.75818 | −0.388247 | ||||||||
\(304\) | −0.394979 | −0.0226536 | ||||||||
\(305\) | 12.9729 | 0.742829 | ||||||||
\(306\) | 13.3007 | 0.760349 | ||||||||
\(307\) | 12.3994 | 0.707669 | 0.353834 | − | 0.935308i | \(-0.384878\pi\) | ||||
0.353834 | + | 0.935308i | \(0.384878\pi\) | |||||||
\(308\) | 0.189199 | 0.0107806 | ||||||||
\(309\) | 12.4083 | 0.705882 | ||||||||
\(310\) | 18.8735 | 1.07195 | ||||||||
\(311\) | 7.17624 | 0.406927 | 0.203463 | − | 0.979083i | \(-0.434780\pi\) | ||||
0.203463 | + | 0.979083i | \(0.434780\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.8602 | −1.23561 | −0.617806 | − | 0.786330i | \(-0.711978\pi\) | ||||
−0.617806 | + | 0.786330i | \(0.711978\pi\) | |||||||
\(314\) | −47.5537 | −2.68361 | ||||||||
\(315\) | 1.46052 | 0.0822912 | ||||||||
\(316\) | 36.2919 | 2.04158 | ||||||||
\(317\) | −26.2740 | −1.47570 | −0.737848 | − | 0.674967i | \(-0.764158\pi\) | ||||
−0.737848 | + | 0.674967i | \(0.764158\pi\) | |||||||
\(318\) | 22.0224 | 1.23496 | ||||||||
\(319\) | 0.182315 | 0.0102077 | ||||||||
\(320\) | −18.5702 | −1.03811 | ||||||||
\(321\) | −18.1781 | −1.01460 | ||||||||
\(322\) | 13.9012 | 0.774686 | ||||||||
\(323\) | −4.64722 | −0.258578 | ||||||||
\(324\) | 3.34288 | 0.185715 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −20.2718 | −1.12275 | ||||||||
\(327\) | 9.12019 | 0.504348 | ||||||||
\(328\) | −16.4560 | −0.908632 | ||||||||
\(329\) | −3.32663 | −0.183403 | ||||||||
\(330\) | −0.191071 | −0.0105181 | ||||||||
\(331\) | −27.3837 | −1.50515 | −0.752573 | − | 0.658509i | \(-0.771188\pi\) | ||||
−0.752573 | + | 0.658509i | \(0.771188\pi\) | |||||||
\(332\) | −25.7483 | −1.41312 | ||||||||
\(333\) | 0.780896 | 0.0427928 | ||||||||
\(334\) | 39.1889 | 2.14432 | ||||||||
\(335\) | 11.4030 | 0.623010 | ||||||||
\(336\) | −0.489065 | −0.0266807 | ||||||||
\(337\) | −20.0655 | −1.09304 | −0.546520 | − | 0.837446i | \(-0.684048\pi\) | ||||
−0.546520 | + | 0.837446i | \(0.684048\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.7050 | 0.798664 | ||||||||
\(340\) | 28.0941 | 1.52362 | ||||||||
\(341\) | 0.316414 | 0.0171348 | ||||||||
\(342\) | −1.86679 | −0.100944 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 7.39428 | 0.398673 | ||||||||
\(345\) | −8.78364 | −0.472895 | ||||||||
\(346\) | 4.42272 | 0.237767 | ||||||||
\(347\) | 17.6754 | 0.948865 | 0.474432 | − | 0.880292i | \(-0.342653\pi\) | ||||
0.474432 | + | 0.880292i | \(0.342653\pi\) | |||||||
\(348\) | −10.7682 | −0.577236 | ||||||||
\(349\) | −11.8130 | −0.632336 | −0.316168 | − | 0.948703i | \(-0.602396\pi\) | ||||
−0.316168 | + | 0.948703i | \(0.602396\pi\) | |||||||
\(350\) | −6.62667 | −0.354210 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.287378 | −0.0153173 | ||||||||
\(353\) | −28.9315 | −1.53987 | −0.769935 | − | 0.638122i | \(-0.779712\pi\) | ||||
−0.769935 | + | 0.638122i | \(0.779712\pi\) | |||||||
\(354\) | −23.8699 | −1.26867 | ||||||||
\(355\) | −16.7531 | −0.889164 | ||||||||
\(356\) | 27.1565 | 1.43929 | ||||||||
\(357\) | −5.75421 | −0.304545 | ||||||||
\(358\) | −60.3848 | −3.19143 | ||||||||
\(359\) | 1.69739 | 0.0895850 | 0.0447925 | − | 0.998996i | \(-0.485737\pi\) | ||||
0.0447925 | + | 0.998996i | \(0.485737\pi\) | |||||||
\(360\) | 4.53348 | 0.238936 | ||||||||
\(361\) | −18.3478 | −0.965671 | ||||||||
\(362\) | −4.57694 | −0.240559 | ||||||||
\(363\) | 10.9968 | 0.577182 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.1978 | 1.00486 | ||||||||
\(366\) | −20.5313 | −1.07319 | ||||||||
\(367\) | −30.9753 | −1.61690 | −0.808448 | − | 0.588567i | \(-0.799692\pi\) | ||||
−0.808448 | + | 0.588567i | \(0.799692\pi\) | |||||||
\(368\) | 2.94126 | 0.153324 | ||||||||
\(369\) | −5.30154 | −0.275987 | ||||||||
\(370\) | 2.63627 | 0.137053 | ||||||||
\(371\) | −9.52747 | −0.494642 | ||||||||
\(372\) | −18.6886 | −0.968960 | ||||||||
\(373\) | −10.6807 | −0.553026 | −0.276513 | − | 0.961010i | \(-0.589179\pi\) | ||||
−0.276513 | + | 0.961010i | \(0.589179\pi\) | |||||||
\(374\) | 0.752787 | 0.0389257 | ||||||||
\(375\) | 11.4898 | 0.593328 | ||||||||
\(376\) | −10.3259 | −0.532518 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.31147 | −0.118889 | ||||||||
\(379\) | −28.1251 | −1.44469 | −0.722344 | − | 0.691534i | \(-0.756935\pi\) | ||||
−0.722344 | + | 0.691534i | \(0.756935\pi\) | |||||||
\(380\) | −3.94308 | −0.202276 | ||||||||
\(381\) | 10.5900 | 0.542544 | ||||||||
\(382\) | −47.8128 | −2.44632 | ||||||||
\(383\) | 12.2466 | 0.625772 | 0.312886 | − | 0.949791i | \(-0.398704\pi\) | ||||
0.312886 | + | 0.949791i | \(0.398704\pi\) | |||||||
\(384\) | 19.2346 | 0.981561 | ||||||||
\(385\) | 0.0826623 | 0.00421286 | ||||||||
\(386\) | 6.67849 | 0.339926 | ||||||||
\(387\) | 2.38217 | 0.121093 | ||||||||
\(388\) | 13.1387 | 0.667015 | ||||||||
\(389\) | −13.6432 | −0.691738 | −0.345869 | − | 0.938283i | \(-0.612416\pi\) | ||||
−0.345869 | + | 0.938283i | \(0.612416\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 34.6060 | 1.75010 | ||||||||
\(392\) | 3.10401 | 0.156776 | ||||||||
\(393\) | 9.31173 | 0.469715 | ||||||||
\(394\) | 6.97399 | 0.351345 | ||||||||
\(395\) | 15.8562 | 0.797811 | ||||||||
\(396\) | 0.189199 | 0.00950761 | ||||||||
\(397\) | 12.4375 | 0.624219 | 0.312109 | − | 0.950046i | \(-0.398964\pi\) | ||||
0.312109 | + | 0.950046i | \(0.398964\pi\) | |||||||
\(398\) | 56.7562 | 2.84493 | ||||||||
\(399\) | 0.807619 | 0.0404315 | ||||||||
\(400\) | −1.40209 | −0.0701043 | ||||||||
\(401\) | −25.0321 | −1.25004 | −0.625021 | − | 0.780608i | \(-0.714910\pi\) | ||||
−0.625021 | + | 0.780608i | \(0.714910\pi\) | |||||||
\(402\) | −18.0466 | −0.900084 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 22.5918 | 1.12398 | ||||||||
\(405\) | 1.46052 | 0.0725740 | ||||||||
\(406\) | 7.44578 | 0.369528 | ||||||||
\(407\) | 0.0441969 | 0.00219076 | ||||||||
\(408\) | −17.8611 | −0.884258 | ||||||||
\(409\) | −35.3470 | −1.74780 | −0.873899 | − | 0.486108i | \(-0.838416\pi\) | ||||
−0.873899 | + | 0.486108i | \(0.838416\pi\) | |||||||
\(410\) | −17.8977 | −0.883906 | ||||||||
\(411\) | −4.10255 | −0.202364 | ||||||||
\(412\) | −41.4793 | −2.04354 | ||||||||
\(413\) | 10.3267 | 0.508146 | ||||||||
\(414\) | 13.9012 | 0.683208 | ||||||||
\(415\) | −11.2496 | −0.552221 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.2754 | −0.797010 | ||||||||
\(418\) | −0.105656 | −0.00516779 | ||||||||
\(419\) | 26.0985 | 1.27499 | 0.637496 | − | 0.770453i | \(-0.279970\pi\) | ||||
0.637496 | + | 0.770453i | \(0.279970\pi\) | |||||||
\(420\) | −4.88235 | −0.238234 | ||||||||
\(421\) | 0.465309 | 0.0226778 | 0.0113389 | − | 0.999936i | \(-0.496391\pi\) | ||||
0.0113389 | + | 0.999936i | \(0.496391\pi\) | |||||||
\(422\) | 35.2722 | 1.71702 | ||||||||
\(423\) | −3.32663 | −0.161746 | ||||||||
\(424\) | −29.5734 | −1.43621 | ||||||||
\(425\) | −16.4966 | −0.800201 | ||||||||
\(426\) | 26.5140 | 1.28461 | ||||||||
\(427\) | 8.88239 | 0.429849 | ||||||||
\(428\) | 60.7672 | 2.93729 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.04209 | 0.387824 | ||||||||
\(431\) | −26.8469 | −1.29317 | −0.646584 | − | 0.762843i | \(-0.723803\pi\) | ||||
−0.646584 | + | 0.762843i | \(0.723803\pi\) | |||||||
\(432\) | −0.489065 | −0.0235302 | ||||||||
\(433\) | 28.8450 | 1.38620 | 0.693101 | − | 0.720840i | \(-0.256244\pi\) | ||||
0.693101 | + | 0.720840i | \(0.256244\pi\) | |||||||
\(434\) | 12.9224 | 0.620297 | ||||||||
\(435\) | −4.70469 | −0.225573 | ||||||||
\(436\) | −30.4877 | −1.46009 | ||||||||
\(437\) | −4.85705 | −0.232344 | ||||||||
\(438\) | −30.3830 | −1.45176 | ||||||||
\(439\) | −19.1983 | −0.916286 | −0.458143 | − | 0.888879i | \(-0.651485\pi\) | ||||
−0.458143 | + | 0.888879i | \(0.651485\pi\) | |||||||
\(440\) | 0.256585 | 0.0122322 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.9117 | 1.13608 | 0.568040 | − | 0.823001i | \(-0.307702\pi\) | ||||
0.568040 | + | 0.823001i | \(0.307702\pi\) | |||||||
\(444\) | −2.61044 | −0.123886 | ||||||||
\(445\) | 11.8648 | 0.562448 | ||||||||
\(446\) | −7.88621 | −0.373423 | ||||||||
\(447\) | 2.11348 | 0.0999644 | ||||||||
\(448\) | −12.7147 | −0.600715 | ||||||||
\(449\) | −31.8784 | −1.50444 | −0.752218 | − | 0.658914i | \(-0.771016\pi\) | ||||
−0.752218 | + | 0.658914i | \(0.771016\pi\) | |||||||
\(450\) | −6.62667 | −0.312384 | ||||||||
\(451\) | −0.300055 | −0.0141290 | ||||||||
\(452\) | −49.1569 | −2.31215 | ||||||||
\(453\) | 17.2235 | 0.809231 | ||||||||
\(454\) | −3.16582 | −0.148579 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.50686 | 0.117394 | ||||||||
\(457\) | −31.4570 | −1.47149 | −0.735747 | − | 0.677256i | \(-0.763169\pi\) | ||||
−0.735747 | + | 0.677256i | \(0.763169\pi\) | |||||||
\(458\) | −40.0332 | −1.87063 | ||||||||
\(459\) | −5.75421 | −0.268584 | ||||||||
\(460\) | 29.3626 | 1.36904 | ||||||||
\(461\) | −25.1219 | −1.17004 | −0.585021 | − | 0.811018i | \(-0.698914\pi\) | ||||
−0.585021 | + | 0.811018i | \(0.698914\pi\) | |||||||
\(462\) | −0.130824 | −0.00608647 | ||||||||
\(463\) | −20.4492 | −0.950354 | −0.475177 | − | 0.879890i | \(-0.657616\pi\) | ||||
−0.475177 | + | 0.879890i | \(0.657616\pi\) | |||||||
\(464\) | 1.57539 | 0.0731359 | ||||||||
\(465\) | −8.16518 | −0.378651 | ||||||||
\(466\) | 13.3384 | 0.617890 | ||||||||
\(467\) | 22.0746 | 1.02149 | 0.510745 | − | 0.859732i | \(-0.329370\pi\) | ||||
0.510745 | + | 0.859732i | \(0.329370\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.80744 | 0.360514 | ||||||||
\(470\) | −11.2305 | −0.518027 | ||||||||
\(471\) | 20.5730 | 0.947953 | ||||||||
\(472\) | 32.0543 | 1.47542 | ||||||||
\(473\) | 0.134825 | 0.00619928 | ||||||||
\(474\) | −25.0944 | −1.15263 | ||||||||
\(475\) | 2.31534 | 0.106235 | ||||||||
\(476\) | 19.2356 | 0.881663 | ||||||||
\(477\) | −9.52747 | −0.436233 | ||||||||
\(478\) | −6.48956 | −0.296825 | ||||||||
\(479\) | −12.1574 | −0.555486 | −0.277743 | − | 0.960655i | \(-0.589586\pi\) | ||||
−0.277743 | + | 0.960655i | \(0.589586\pi\) | |||||||
\(480\) | 7.41591 | 0.338488 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −17.4638 | −0.795453 | ||||||||
\(483\) | −6.01403 | −0.273648 | ||||||||
\(484\) | −36.7609 | −1.67095 | ||||||||
\(485\) | 5.74037 | 0.260657 | ||||||||
\(486\) | −2.31147 | −0.104850 | ||||||||
\(487\) | −18.6677 | −0.845914 | −0.422957 | − | 0.906150i | \(-0.639008\pi\) | ||||
−0.422957 | + | 0.906150i | \(0.639008\pi\) | |||||||
\(488\) | 27.5710 | 1.24808 | ||||||||
\(489\) | 8.77011 | 0.396598 | ||||||||
\(490\) | 3.37595 | 0.152510 | ||||||||
\(491\) | 18.8532 | 0.850833 | 0.425416 | − | 0.904998i | \(-0.360128\pi\) | ||||
0.425416 | + | 0.904998i | \(0.360128\pi\) | |||||||
\(492\) | 17.7224 | 0.798986 | ||||||||
\(493\) | 18.5357 | 0.834805 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.0826623 | 0.00371539 | ||||||||
\(496\) | 2.73416 | 0.122767 | ||||||||
\(497\) | −11.4706 | −0.514528 | ||||||||
\(498\) | 17.8039 | 0.797813 | ||||||||
\(499\) | −23.7688 | −1.06404 | −0.532018 | − | 0.846733i | \(-0.678566\pi\) | ||||
−0.532018 | + | 0.846733i | \(0.678566\pi\) | |||||||
\(500\) | −38.4088 | −1.71769 | ||||||||
\(501\) | −16.9542 | −0.757456 | ||||||||
\(502\) | 60.6035 | 2.70487 | ||||||||
\(503\) | 8.31234 | 0.370629 | 0.185314 | − | 0.982679i | \(-0.440670\pi\) | ||||
0.185314 | + | 0.982679i | \(0.440670\pi\) | |||||||
\(504\) | 3.10401 | 0.138264 | ||||||||
\(505\) | 9.87049 | 0.439231 | ||||||||
\(506\) | 0.786778 | 0.0349765 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −35.4012 | −1.57067 | ||||||||
\(509\) | 8.75231 | 0.387939 | 0.193970 | − | 0.981008i | \(-0.437864\pi\) | ||||
0.193970 | + | 0.981008i | \(0.437864\pi\) | |||||||
\(510\) | −19.4260 | −0.860196 | ||||||||
\(511\) | 13.1445 | 0.581478 | ||||||||
\(512\) | −5.51939 | −0.243925 | ||||||||
\(513\) | 0.807619 | 0.0356573 | ||||||||
\(514\) | −8.27918 | −0.365179 | ||||||||
\(515\) | −18.1226 | −0.798577 | ||||||||
\(516\) | −7.96330 | −0.350565 | ||||||||
\(517\) | −0.188280 | −0.00828053 | ||||||||
\(518\) | 1.80501 | 0.0793078 | ||||||||
\(519\) | −1.91338 | −0.0839882 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −32.1915 | −1.41033 | −0.705167 | − | 0.709041i | \(-0.749128\pi\) | ||||
−0.705167 | + | 0.709041i | \(0.749128\pi\) | |||||||
\(522\) | 7.44578 | 0.325893 | ||||||||
\(523\) | −13.3302 | −0.582891 | −0.291446 | − | 0.956587i | \(-0.594136\pi\) | ||||
−0.291446 | + | 0.956587i | \(0.594136\pi\) | |||||||
\(524\) | −31.1280 | −1.35983 | ||||||||
\(525\) | 2.86687 | 0.125120 | ||||||||
\(526\) | 61.8548 | 2.69700 | ||||||||
\(527\) | 32.1694 | 1.40132 | ||||||||
\(528\) | −0.0276800 | −0.00120462 | ||||||||
\(529\) | 13.1686 | 0.572548 | ||||||||
\(530\) | −32.1643 | −1.39713 | ||||||||
\(531\) | 10.3267 | 0.448143 | ||||||||
\(532\) | −2.69977 | −0.117050 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −18.7776 | −0.812588 | ||||||||
\(535\) | 26.5496 | 1.14784 | ||||||||
\(536\) | 24.2344 | 1.04677 | ||||||||
\(537\) | 26.1240 | 1.12733 | ||||||||
\(538\) | 34.0232 | 1.46685 | ||||||||
\(539\) | 0.0565977 | 0.00243784 | ||||||||
\(540\) | −4.88235 | −0.210103 | ||||||||
\(541\) | −22.2023 | −0.954553 | −0.477277 | − | 0.878753i | \(-0.658376\pi\) | ||||
−0.477277 | + | 0.878753i | \(0.658376\pi\) | |||||||
\(542\) | 30.4821 | 1.30932 | ||||||||
\(543\) | 1.98010 | 0.0849743 | ||||||||
\(544\) | −29.2174 | −1.25269 | ||||||||
\(545\) | −13.3203 | −0.570577 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.3118 | 1.55258 | 0.776289 | − | 0.630377i | \(-0.217100\pi\) | ||||
0.776289 | + | 0.630377i | \(0.217100\pi\) | |||||||
\(548\) | 13.7143 | 0.585847 | ||||||||
\(549\) | 8.88239 | 0.379091 | ||||||||
\(550\) | −0.375054 | −0.0159924 | ||||||||
\(551\) | −2.60153 | −0.110829 | ||||||||
\(552\) | −18.6676 | −0.794547 | ||||||||
\(553\) | 10.8565 | 0.461666 | ||||||||
\(554\) | 49.8644 | 2.11854 | ||||||||
\(555\) | −1.14052 | −0.0484123 | ||||||||
\(556\) | 54.4066 | 2.30736 | ||||||||
\(557\) | 42.7664 | 1.81207 | 0.906036 | − | 0.423200i | \(-0.139093\pi\) | ||||
0.906036 | + | 0.423200i | \(0.139093\pi\) | |||||||
\(558\) | 12.9224 | 0.547051 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0.714292 | 0.0301843 | ||||||||
\(561\) | −0.325675 | −0.0137500 | ||||||||
\(562\) | −0.431054 | −0.0181829 | ||||||||
\(563\) | −13.8742 | −0.584728 | −0.292364 | − | 0.956307i | \(-0.594442\pi\) | ||||
−0.292364 | + | 0.956307i | \(0.594442\pi\) | |||||||
\(564\) | 11.1205 | 0.468258 | ||||||||
\(565\) | −21.4770 | −0.903543 | ||||||||
\(566\) | −32.4087 | −1.36224 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −35.6050 | −1.49395 | ||||||||
\(569\) | 7.44608 | 0.312156 | 0.156078 | − | 0.987745i | \(-0.450115\pi\) | ||||
0.156078 | + | 0.987745i | \(0.450115\pi\) | |||||||
\(570\) | 2.72649 | 0.114200 | ||||||||
\(571\) | 24.7091 | 1.03404 | 0.517021 | − | 0.855973i | \(-0.327041\pi\) | ||||
0.517021 | + | 0.855973i | \(0.327041\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.6851 | 0.864131 | ||||||||
\(574\) | −12.2543 | −0.511486 | ||||||||
\(575\) | −17.2414 | −0.719018 | ||||||||
\(576\) | −12.7147 | −0.529781 | ||||||||
\(577\) | −26.2593 | −1.09319 | −0.546595 | − | 0.837397i | \(-0.684076\pi\) | ||||
−0.546595 | + | 0.837397i | \(0.684076\pi\) | |||||||
\(578\) | 37.2400 | 1.54898 | ||||||||
\(579\) | −2.88929 | −0.120075 | ||||||||
\(580\) | 15.7272 | 0.653037 | ||||||||
\(581\) | −7.70243 | −0.319551 | ||||||||
\(582\) | −9.08487 | −0.376580 | ||||||||
\(583\) | −0.539233 | −0.0223328 | ||||||||
\(584\) | 40.8006 | 1.68834 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −36.7135 | −1.51662 | ||||||||
\(587\) | −36.7338 | −1.51617 | −0.758084 | − | 0.652157i | \(-0.773864\pi\) | ||||
−0.758084 | + | 0.652157i | \(0.773864\pi\) | |||||||
\(588\) | −3.34288 | −0.137858 | ||||||||
\(589\) | −4.51506 | −0.186040 | ||||||||
\(590\) | 34.8626 | 1.43527 | ||||||||
\(591\) | −3.01713 | −0.124108 | ||||||||
\(592\) | 0.381909 | 0.0156964 | ||||||||
\(593\) | 8.94989 | 0.367528 | 0.183764 | − | 0.982970i | \(-0.441172\pi\) | ||||
0.183764 | + | 0.982970i | \(0.441172\pi\) | |||||||
\(594\) | −0.130824 | −0.00536776 | ||||||||
\(595\) | 8.40417 | 0.344537 | ||||||||
\(596\) | −7.06511 | −0.289398 | ||||||||
\(597\) | −24.5542 | −1.00494 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.4529 | −1.32599 | −0.662995 | − | 0.748624i | \(-0.730715\pi\) | ||||
−0.662995 | + | 0.748624i | \(0.730715\pi\) | |||||||
\(600\) | 8.89879 | 0.363292 | ||||||||
\(601\) | −30.4411 | −1.24172 | −0.620859 | − | 0.783922i | \(-0.713216\pi\) | ||||
−0.620859 | + | 0.783922i | \(0.713216\pi\) | |||||||
\(602\) | 5.50631 | 0.224420 | ||||||||
\(603\) | 7.80744 | 0.317943 | ||||||||
\(604\) | −57.5760 | −2.34273 | ||||||||
\(605\) | −16.0611 | −0.652976 | ||||||||
\(606\) | −15.6213 | −0.634572 | ||||||||
\(607\) | −18.0074 | −0.730899 | −0.365449 | − | 0.930831i | \(-0.619085\pi\) | ||||
−0.365449 | + | 0.930831i | \(0.619085\pi\) | |||||||
\(608\) | 4.10074 | 0.166307 | ||||||||
\(609\) | −3.22124 | −0.130531 | ||||||||
\(610\) | 29.9865 | 1.21412 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 19.2356 | 0.777554 | ||||||||
\(613\) | 43.6064 | 1.76125 | 0.880623 | − | 0.473817i | \(-0.157124\pi\) | ||||
0.880623 | + | 0.473817i | \(0.157124\pi\) | |||||||
\(614\) | 28.6607 | 1.15665 | ||||||||
\(615\) | 7.74302 | 0.312229 | ||||||||
\(616\) | 0.175680 | 0.00707834 | ||||||||
\(617\) | 11.4509 | 0.460997 | 0.230499 | − | 0.973073i | \(-0.425964\pi\) | ||||
0.230499 | + | 0.973073i | \(0.425964\pi\) | |||||||
\(618\) | 28.6813 | 1.15373 | ||||||||
\(619\) | 33.0974 | 1.33030 | 0.665148 | − | 0.746712i | \(-0.268369\pi\) | ||||
0.665148 | + | 0.746712i | \(0.268369\pi\) | |||||||
\(620\) | 27.2952 | 1.09620 | ||||||||
\(621\) | −6.01403 | −0.241335 | ||||||||
\(622\) | 16.5876 | 0.665103 | ||||||||
\(623\) | 8.12369 | 0.325469 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.44672 | −0.0978689 | ||||||||
\(626\) | −50.5292 | −2.01955 | ||||||||
\(627\) | 0.0457094 | 0.00182546 | ||||||||
\(628\) | −68.7729 | −2.74434 | ||||||||
\(629\) | 4.49344 | 0.179165 | ||||||||
\(630\) | 3.37595 | 0.134501 | ||||||||
\(631\) | 5.34538 | 0.212796 | 0.106398 | − | 0.994324i | \(-0.466068\pi\) | ||||
0.106398 | + | 0.994324i | \(0.466068\pi\) | |||||||
\(632\) | 33.6987 | 1.34046 | ||||||||
\(633\) | −15.2596 | −0.606517 | ||||||||
\(634\) | −60.7315 | −2.41196 | ||||||||
\(635\) | −15.4670 | −0.613789 | ||||||||
\(636\) | 31.8492 | 1.26290 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.421414 | 0.0166839 | ||||||||
\(639\) | −11.4706 | −0.453771 | ||||||||
\(640\) | −28.0926 | −1.11046 | ||||||||
\(641\) | −18.3832 | −0.726091 | −0.363046 | − | 0.931771i | \(-0.618263\pi\) | ||||
−0.363046 | + | 0.931771i | \(0.618263\pi\) | |||||||
\(642\) | −42.0181 | −1.65832 | ||||||||
\(643\) | 3.77097 | 0.148712 | 0.0743562 | − | 0.997232i | \(-0.476310\pi\) | ||||
0.0743562 | + | 0.997232i | \(0.476310\pi\) | |||||||
\(644\) | 20.1042 | 0.792215 | ||||||||
\(645\) | −3.47922 | −0.136994 | ||||||||
\(646\) | −10.7419 | −0.422634 | ||||||||
\(647\) | −1.95293 | −0.0767775 | −0.0383888 | − | 0.999263i | \(-0.512223\pi\) | ||||
−0.0383888 | + | 0.999263i | \(0.512223\pi\) | |||||||
\(648\) | 3.10401 | 0.121937 | ||||||||
\(649\) | 0.584470 | 0.0229425 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.59058 | −0.219112 | ||||||||
\(652\) | −29.3174 | −1.14816 | ||||||||
\(653\) | 21.9347 | 0.858372 | 0.429186 | − | 0.903216i | \(-0.358801\pi\) | ||||
0.429186 | + | 0.903216i | \(0.358801\pi\) | |||||||
\(654\) | 21.0810 | 0.824333 | ||||||||
\(655\) | −13.6000 | −0.531396 | ||||||||
\(656\) | −2.59280 | −0.101232 | ||||||||
\(657\) | 13.1445 | 0.512815 | ||||||||
\(658\) | −7.68939 | −0.299764 | ||||||||
\(659\) | 34.8515 | 1.35762 | 0.678812 | − | 0.734312i | \(-0.262495\pi\) | ||||
0.678812 | + | 0.734312i | \(0.262495\pi\) | |||||||
\(660\) | −0.276330 | −0.0107561 | ||||||||
\(661\) | 30.3342 | 1.17986 | 0.589931 | − | 0.807454i | \(-0.299155\pi\) | ||||
0.589931 | + | 0.807454i | \(0.299155\pi\) | |||||||
\(662\) | −63.2966 | −2.46009 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −23.9084 | −0.927827 | ||||||||
\(665\) | −1.17955 | −0.0457409 | ||||||||
\(666\) | 1.80501 | 0.0699429 | ||||||||
\(667\) | 19.3726 | 0.750111 | ||||||||
\(668\) | 56.6756 | 2.19285 | ||||||||
\(669\) | 3.41178 | 0.131907 | ||||||||
\(670\) | 26.3575 | 1.01828 | ||||||||
\(671\) | 0.502723 | 0.0194074 | ||||||||
\(672\) | 5.07756 | 0.195871 | ||||||||
\(673\) | 42.8800 | 1.65290 | 0.826451 | − | 0.563009i | \(-0.190356\pi\) | ||||
0.826451 | + | 0.563009i | \(0.190356\pi\) | |||||||
\(674\) | −46.3808 | −1.78652 | ||||||||
\(675\) | 2.86687 | 0.110346 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.2890 | −0.549171 | −0.274586 | − | 0.961563i | \(-0.588541\pi\) | ||||
−0.274586 | + | 0.961563i | \(0.588541\pi\) | |||||||
\(678\) | 33.9900 | 1.30538 | ||||||||
\(679\) | 3.93035 | 0.150833 | ||||||||
\(680\) | 26.0866 | 1.00038 | ||||||||
\(681\) | 1.36962 | 0.0524838 | ||||||||
\(682\) | 0.731381 | 0.0280060 | ||||||||
\(683\) | −24.5455 | −0.939209 | −0.469604 | − | 0.882877i | \(-0.655603\pi\) | ||||
−0.469604 | + | 0.882877i | \(0.655603\pi\) | |||||||
\(684\) | −2.69977 | −0.103228 | ||||||||
\(685\) | 5.99188 | 0.228938 | ||||||||
\(686\) | 2.31147 | 0.0882522 | ||||||||
\(687\) | 17.3194 | 0.660776 | ||||||||
\(688\) | 1.16504 | 0.0444166 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −20.3031 | −0.772926 | ||||||||
\(691\) | −27.7763 | −1.05666 | −0.528331 | − | 0.849039i | \(-0.677182\pi\) | ||||
−0.528331 | + | 0.849039i | \(0.677182\pi\) | |||||||
\(692\) | 6.39620 | 0.243147 | ||||||||
\(693\) | 0.0565977 | 0.00214997 | ||||||||
\(694\) | 40.8561 | 1.55087 | ||||||||
\(695\) | 23.7706 | 0.901671 | ||||||||
\(696\) | −9.99875 | −0.379002 | ||||||||
\(697\) | −30.5062 | −1.15550 | ||||||||
\(698\) | −27.3054 | −1.03352 | ||||||||
\(699\) | −5.77054 | −0.218262 | ||||||||
\(700\) | −9.58358 | −0.362225 | ||||||||
\(701\) | 37.2216 | 1.40584 | 0.702921 | − | 0.711268i | \(-0.251879\pi\) | ||||
0.702921 | + | 0.711268i | \(0.251879\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.630667 | −0.0237860 | ||||||||
\(704\) | −0.719625 | −0.0271219 | ||||||||
\(705\) | 4.85863 | 0.182986 | ||||||||
\(706\) | −66.8743 | −2.51685 | ||||||||
\(707\) | 6.75818 | 0.254168 | ||||||||
\(708\) | −34.5210 | −1.29738 | ||||||||
\(709\) | 40.3434 | 1.51513 | 0.757564 | − | 0.652760i | \(-0.226389\pi\) | ||||
0.757564 | + | 0.652760i | \(0.226389\pi\) | |||||||
\(710\) | −38.7243 | −1.45330 | ||||||||
\(711\) | 10.8565 | 0.407151 | ||||||||
\(712\) | 25.2160 | 0.945010 | ||||||||
\(713\) | 33.6220 | 1.25915 | ||||||||
\(714\) | −13.3007 | −0.497765 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −87.3293 | −3.26365 | ||||||||
\(717\) | 2.80755 | 0.104850 | ||||||||
\(718\) | 3.92347 | 0.146423 | ||||||||
\(719\) | −5.37519 | −0.200461 | −0.100230 | − | 0.994964i | \(-0.531958\pi\) | ||||
−0.100230 | + | 0.994964i | \(0.531958\pi\) | |||||||
\(720\) | 0.714292 | 0.0266201 | ||||||||
\(721\) | −12.4083 | −0.462108 | ||||||||
\(722\) | −42.4102 | −1.57834 | ||||||||
\(723\) | 7.55528 | 0.280984 | ||||||||
\(724\) | −6.61924 | −0.246002 | ||||||||
\(725\) | −9.23486 | −0.342974 | ||||||||
\(726\) | 25.4187 | 0.943377 | ||||||||
\(727\) | −9.42472 | −0.349544 | −0.174772 | − | 0.984609i | \(-0.555919\pi\) | ||||
−0.174772 | + | 0.984609i | \(0.555919\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 44.3752 | 1.64240 | ||||||||
\(731\) | 13.7075 | 0.506991 | ||||||||
\(732\) | −29.6927 | −1.09747 | ||||||||
\(733\) | −33.3006 | −1.22999 | −0.614994 | − | 0.788532i | \(-0.710841\pi\) | ||||
−0.614994 | + | 0.788532i | \(0.710841\pi\) | |||||||
\(734\) | −71.5983 | −2.64274 | ||||||||
\(735\) | −1.46052 | −0.0538723 | ||||||||
\(736\) | −30.5366 | −1.12560 | ||||||||
\(737\) | 0.441883 | 0.0162770 | ||||||||
\(738\) | −12.2543 | −0.451088 | ||||||||
\(739\) | −34.6898 | −1.27608 | −0.638042 | − | 0.770001i | \(-0.720256\pi\) | ||||
−0.638042 | + | 0.770001i | \(0.720256\pi\) | |||||||
\(740\) | 3.81261 | 0.140154 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −22.0224 | −0.808469 | ||||||||
\(743\) | 29.0170 | 1.06453 | 0.532264 | − | 0.846578i | \(-0.321341\pi\) | ||||
0.532264 | + | 0.846578i | \(0.321341\pi\) | |||||||
\(744\) | −17.3532 | −0.636200 | ||||||||
\(745\) | −3.08679 | −0.113091 | ||||||||
\(746\) | −24.6881 | −0.903895 | ||||||||
\(747\) | −7.70243 | −0.281817 | ||||||||
\(748\) | 1.08869 | 0.0398065 | ||||||||
\(749\) | 18.1781 | 0.664214 | ||||||||
\(750\) | 26.5582 | 0.969767 | ||||||||
\(751\) | −22.3606 | −0.815949 | −0.407974 | − | 0.912993i | \(-0.633765\pi\) | ||||
−0.407974 | + | 0.912993i | \(0.633765\pi\) | |||||||
\(752\) | −1.62694 | −0.0593284 | ||||||||
\(753\) | −26.2186 | −0.955460 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −25.1553 | −0.915497 | ||||||||
\(756\) | −3.34288 | −0.121579 | ||||||||
\(757\) | −41.1339 | −1.49504 | −0.747519 | − | 0.664240i | \(-0.768755\pi\) | ||||
−0.747519 | + | 0.664240i | \(0.768755\pi\) | |||||||
\(758\) | −65.0102 | −2.36128 | ||||||||
\(759\) | −0.340380 | −0.0123550 | ||||||||
\(760\) | −3.66133 | −0.132810 | ||||||||
\(761\) | 34.0410 | 1.23398 | 0.616992 | − | 0.786969i | \(-0.288351\pi\) | ||||
0.616992 | + | 0.786969i | \(0.288351\pi\) | |||||||
\(762\) | 24.4785 | 0.886763 | ||||||||
\(763\) | −9.12019 | −0.330173 | ||||||||
\(764\) | −69.1476 | −2.50167 | ||||||||
\(765\) | 8.40417 | 0.303853 | ||||||||
\(766\) | 28.3076 | 1.02280 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 19.0306 | 0.686707 | ||||||||
\(769\) | 50.1326 | 1.80783 | 0.903914 | − | 0.427714i | \(-0.140681\pi\) | ||||
0.903914 | + | 0.427714i | \(0.140681\pi\) | |||||||
\(770\) | 0.191071 | 0.00688573 | ||||||||
\(771\) | 3.58179 | 0.128995 | ||||||||
\(772\) | 9.65853 | 0.347618 | ||||||||
\(773\) | 10.6809 | 0.384167 | 0.192083 | − | 0.981379i | \(-0.438476\pi\) | ||||
0.192083 | + | 0.981379i | \(0.438476\pi\) | |||||||
\(774\) | 5.50631 | 0.197920 | ||||||||
\(775\) | −16.0275 | −0.575724 | ||||||||
\(776\) | 12.1998 | 0.437949 | ||||||||
\(777\) | −0.780896 | −0.0280145 | ||||||||
\(778\) | −31.5358 | −1.13061 | ||||||||
\(779\) | 4.28162 | 0.153405 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.649211 | −0.0232306 | ||||||||
\(782\) | 79.9907 | 2.86046 | ||||||||
\(783\) | −3.22124 | −0.115118 | ||||||||
\(784\) | 0.489065 | 0.0174666 | ||||||||
\(785\) | −30.0473 | −1.07244 | ||||||||
\(786\) | 21.5237 | 0.767727 | ||||||||
\(787\) | 8.44505 | 0.301033 | 0.150517 | − | 0.988607i | \(-0.451906\pi\) | ||||
0.150517 | + | 0.988607i | \(0.451906\pi\) | |||||||
\(788\) | 10.0859 | 0.359295 | ||||||||
\(789\) | −26.7600 | −0.952681 | ||||||||
\(790\) | 36.6510 | 1.30399 | ||||||||
\(791\) | −14.7050 | −0.522849 | ||||||||
\(792\) | 0.175680 | 0.00624251 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 28.7488 | 1.02026 | ||||||||
\(795\) | 13.9151 | 0.493518 | ||||||||
\(796\) | 82.0817 | 2.90931 | ||||||||
\(797\) | −8.37296 | −0.296586 | −0.148293 | − | 0.988944i | \(-0.547378\pi\) | ||||
−0.148293 | + | 0.988944i | \(0.547378\pi\) | |||||||
\(798\) | 1.86679 | 0.0660835 | ||||||||
\(799\) | −19.1421 | −0.677201 | ||||||||
\(800\) | 14.5567 | 0.514657 | ||||||||
\(801\) | 8.12369 | 0.287036 | ||||||||
\(802\) | −57.8608 | −2.04314 | ||||||||
\(803\) | 0.743948 | 0.0262534 | ||||||||
\(804\) | −26.0993 | −0.920451 | ||||||||
\(805\) | 8.78364 | 0.309583 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.7193 | −0.518145 | ||||||||
\(808\) | 20.9775 | 0.737985 | ||||||||
\(809\) | −4.04870 | −0.142345 | −0.0711723 | − | 0.997464i | \(-0.522674\pi\) | ||||
−0.0711723 | + | 0.997464i | \(0.522674\pi\) | |||||||
\(810\) | 3.37595 | 0.118619 | ||||||||
\(811\) | 40.7122 | 1.42960 | 0.714800 | − | 0.699329i | \(-0.246518\pi\) | ||||
0.714800 | + | 0.699329i | \(0.246518\pi\) | |||||||
\(812\) | 10.7682 | 0.377889 | ||||||||
\(813\) | −13.1874 | −0.462501 | ||||||||
\(814\) | 0.102160 | 0.00358069 | ||||||||
\(815\) | −12.8090 | −0.448678 | ||||||||
\(816\) | −2.81419 | −0.0985162 | ||||||||
\(817\) | −1.92389 | −0.0673083 | ||||||||
\(818\) | −81.7035 | −2.85669 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −25.8840 | −0.903907 | ||||||||
\(821\) | 15.5618 | 0.543110 | 0.271555 | − | 0.962423i | \(-0.412462\pi\) | ||||
0.271555 | + | 0.962423i | \(0.412462\pi\) | |||||||
\(822\) | −9.48291 | −0.330755 | ||||||||
\(823\) | −4.81985 | −0.168009 | −0.0840046 | − | 0.996465i | \(-0.526771\pi\) | ||||
−0.0840046 | + | 0.996465i | \(0.526771\pi\) | |||||||
\(824\) | −38.5154 | −1.34175 | ||||||||
\(825\) | 0.162258 | 0.00564910 | ||||||||
\(826\) | 23.8699 | 0.830541 | ||||||||
\(827\) | 3.38418 | 0.117680 | 0.0588398 | − | 0.998267i | \(-0.481260\pi\) | ||||
0.0588398 | + | 0.998267i | \(0.481260\pi\) | |||||||
\(828\) | 20.1042 | 0.698668 | ||||||||
\(829\) | −14.4519 | −0.501937 | −0.250968 | − | 0.967995i | \(-0.580749\pi\) | ||||
−0.250968 | + | 0.967995i | \(0.580749\pi\) | |||||||
\(830\) | −26.0031 | −0.902579 | ||||||||
\(831\) | −21.5726 | −0.748347 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.75421 | 0.199372 | ||||||||
\(834\) | −37.6200 | −1.30268 | ||||||||
\(835\) | 24.7620 | 0.856923 | ||||||||
\(836\) | −0.152801 | −0.00528473 | ||||||||
\(837\) | −5.59058 | −0.193239 | ||||||||
\(838\) | 60.3257 | 2.08392 | ||||||||
\(839\) | 29.5887 | 1.02152 | 0.510758 | − | 0.859725i | \(-0.329365\pi\) | ||||
0.510758 | + | 0.859725i | \(0.329365\pi\) | |||||||
\(840\) | −4.53348 | −0.156420 | ||||||||
\(841\) | −18.6236 | −0.642194 | ||||||||
\(842\) | 1.07555 | 0.0370657 | ||||||||
\(843\) | 0.186485 | 0.00642289 | ||||||||
\(844\) | 51.0111 | 1.75587 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.68939 | −0.264367 | ||||||||
\(847\) | −10.9968 | −0.377854 | ||||||||
\(848\) | −4.65956 | −0.160010 | ||||||||
\(849\) | 14.0208 | 0.481194 | ||||||||
\(850\) | −38.1313 | −1.30789 | ||||||||
\(851\) | 4.69633 | 0.160988 | ||||||||
\(852\) | 38.3449 | 1.31367 | ||||||||
\(853\) | 30.7580 | 1.05313 | 0.526567 | − | 0.850134i | \(-0.323479\pi\) | ||||
0.526567 | + | 0.850134i | \(0.323479\pi\) | |||||||
\(854\) | 20.5313 | 0.702568 | ||||||||
\(855\) | −1.17955 | −0.0403397 | ||||||||
\(856\) | 56.4251 | 1.92857 | ||||||||
\(857\) | −15.7106 | −0.536663 | −0.268331 | − | 0.963327i | \(-0.586472\pi\) | ||||
−0.268331 | + | 0.963327i | \(0.586472\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.2361 | −0.792807 | −0.396403 | − | 0.918076i | \(-0.629742\pi\) | ||||
−0.396403 | + | 0.918076i | \(0.629742\pi\) | |||||||
\(860\) | 11.6306 | 0.396600 | ||||||||
\(861\) | 5.30154 | 0.180676 | ||||||||
\(862\) | −62.0556 | −2.11362 | ||||||||
\(863\) | 29.7433 | 1.01247 | 0.506236 | − | 0.862395i | \(-0.331036\pi\) | ||||
0.506236 | + | 0.862395i | \(0.331036\pi\) | |||||||
\(864\) | 5.07756 | 0.172742 | ||||||||
\(865\) | 2.79454 | 0.0950174 | ||||||||
\(866\) | 66.6743 | 2.26568 | ||||||||
\(867\) | −16.1110 | −0.547158 | ||||||||
\(868\) | 18.6886 | 0.634333 | ||||||||
\(869\) | 0.614453 | 0.0208439 | ||||||||
\(870\) | −10.8747 | −0.368688 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −28.3092 | −0.958670 | ||||||||
\(873\) | 3.93035 | 0.133022 | ||||||||
\(874\) | −11.2269 | −0.379756 | ||||||||
\(875\) | −11.4898 | −0.388425 | ||||||||
\(876\) | −43.9404 | −1.48461 | ||||||||
\(877\) | −12.7398 | −0.430193 | −0.215097 | − | 0.976593i | \(-0.569007\pi\) | ||||
−0.215097 | + | 0.976593i | \(0.569007\pi\) | |||||||
\(878\) | −44.3763 | −1.49763 | ||||||||
\(879\) | 15.8832 | 0.535727 | ||||||||
\(880\) | 0.0404273 | 0.00136280 | ||||||||
\(881\) | 10.9904 | 0.370277 | 0.185139 | − | 0.982712i | \(-0.440727\pi\) | ||||
0.185139 | + | 0.982712i | \(0.440727\pi\) | |||||||
\(882\) | 2.31147 | 0.0778311 | ||||||||
\(883\) | 8.60222 | 0.289488 | 0.144744 | − | 0.989469i | \(-0.453764\pi\) | ||||
0.144744 | + | 0.989469i | \(0.453764\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −15.0825 | −0.506991 | ||||||||
\(886\) | 55.2711 | 1.85687 | ||||||||
\(887\) | 21.0197 | 0.705773 | 0.352886 | − | 0.935666i | \(-0.385200\pi\) | ||||
0.352886 | + | 0.935666i | \(0.385200\pi\) | |||||||
\(888\) | −2.42391 | −0.0813410 | ||||||||
\(889\) | −10.5900 | −0.355178 | ||||||||
\(890\) | 27.4252 | 0.919295 | ||||||||
\(891\) | 0.0565977 | 0.00189609 | ||||||||
\(892\) | −11.4052 | −0.381873 | ||||||||
\(893\) | 2.68665 | 0.0899054 | ||||||||
\(894\) | 4.88525 | 0.163387 | ||||||||
\(895\) | −38.1548 | −1.27537 | ||||||||
\(896\) | −19.2346 | −0.642582 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −73.6859 | −2.45893 | ||||||||
\(899\) | 18.0086 | 0.600620 | ||||||||
\(900\) | −9.58358 | −0.319453 | ||||||||
\(901\) | −54.8231 | −1.82642 | ||||||||
\(902\) | −0.693566 | −0.0230932 | ||||||||
\(903\) | −2.38217 | −0.0792737 | ||||||||
\(904\) | −45.6444 | −1.51811 | ||||||||
\(905\) | −2.89199 | −0.0961329 | ||||||||
\(906\) | 39.8115 | 1.32265 | ||||||||
\(907\) | 4.64057 | 0.154087 | 0.0770437 | − | 0.997028i | \(-0.475452\pi\) | ||||
0.0770437 | + | 0.997028i | \(0.475452\pi\) | |||||||
\(908\) | −4.57845 | −0.151941 | ||||||||
\(909\) | 6.75818 | 0.224155 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.2392 | 1.06813 | 0.534067 | − | 0.845442i | \(-0.320663\pi\) | ||||
0.534067 | + | 0.845442i | \(0.320663\pi\) | |||||||
\(912\) | 0.394979 | 0.0130790 | ||||||||
\(913\) | −0.435940 | −0.0144275 | ||||||||
\(914\) | −72.7117 | −2.40509 | ||||||||
\(915\) | −12.9729 | −0.428872 | ||||||||
\(916\) | −57.8965 | −1.91296 | ||||||||
\(917\) | −9.31173 | −0.307500 | ||||||||
\(918\) | −13.3007 | −0.438988 | ||||||||
\(919\) | 21.0489 | 0.694339 | 0.347169 | − | 0.937802i | \(-0.387143\pi\) | ||||
0.347169 | + | 0.937802i | \(0.387143\pi\) | |||||||
\(920\) | 27.2645 | 0.898885 | ||||||||
\(921\) | −12.3994 | −0.408573 | ||||||||
\(922\) | −58.0683 | −1.91238 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −0.189199 | −0.00622419 | ||||||||
\(925\) | −2.23873 | −0.0736088 | ||||||||
\(926\) | −47.2676 | −1.55331 | ||||||||
\(927\) | −12.4083 | −0.407541 | ||||||||
\(928\) | −16.3560 | −0.536913 | ||||||||
\(929\) | −36.3949 | −1.19408 | −0.597038 | − | 0.802213i | \(-0.703656\pi\) | ||||
−0.597038 | + | 0.802213i | \(0.703656\pi\) | |||||||
\(930\) | −18.8735 | −0.618888 | ||||||||
\(931\) | −0.807619 | −0.0264687 | ||||||||
\(932\) | 19.2902 | 0.631871 | ||||||||
\(933\) | −7.17624 | −0.234939 | ||||||||
\(934\) | 51.0246 | 1.66958 | ||||||||
\(935\) | 0.475657 | 0.0155556 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.6753 | 0.773438 | 0.386719 | − | 0.922198i | \(-0.373608\pi\) | ||||
0.386719 | + | 0.922198i | \(0.373608\pi\) | |||||||
\(938\) | 18.0466 | 0.589243 | ||||||||
\(939\) | 21.8602 | 0.713381 | ||||||||
\(940\) | −16.2418 | −0.529748 | ||||||||
\(941\) | −15.2440 | −0.496940 | −0.248470 | − | 0.968640i | \(-0.579928\pi\) | ||||
−0.248470 | + | 0.968640i | \(0.579928\pi\) | |||||||
\(942\) | 47.5537 | 1.54938 | ||||||||
\(943\) | −31.8836 | −1.03827 | ||||||||
\(944\) | 5.05045 | 0.164378 | ||||||||
\(945\) | −1.46052 | −0.0475109 | ||||||||
\(946\) | 0.311644 | 0.0101324 | ||||||||
\(947\) | −5.38308 | −0.174926 | −0.0874632 | − | 0.996168i | \(-0.527876\pi\) | ||||
−0.0874632 | + | 0.996168i | \(0.527876\pi\) | |||||||
\(948\) | −36.2919 | −1.17871 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 5.35183 | 0.173636 | ||||||||
\(951\) | 26.2740 | 0.851994 | ||||||||
\(952\) | 17.8611 | 0.578883 | ||||||||
\(953\) | 20.2342 | 0.655451 | 0.327725 | − | 0.944773i | \(-0.393718\pi\) | ||||
0.327725 | + | 0.944773i | \(0.393718\pi\) | |||||||
\(954\) | −22.0224 | −0.713003 | ||||||||
\(955\) | −30.2110 | −0.977606 | ||||||||
\(956\) | −9.38529 | −0.303542 | ||||||||
\(957\) | −0.182315 | −0.00589339 | ||||||||
\(958\) | −28.1014 | −0.907916 | ||||||||
\(959\) | 4.10255 | 0.132478 | ||||||||
\(960\) | 18.5702 | 0.599351 | ||||||||
\(961\) | 0.254620 | 0.00821356 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.1781 | 0.585782 | ||||||||
\(964\) | −25.2564 | −0.813453 | ||||||||
\(965\) | 4.21988 | 0.135843 | ||||||||
\(966\) | −13.9012 | −0.447265 | ||||||||
\(967\) | −19.0150 | −0.611482 | −0.305741 | − | 0.952115i | \(-0.598904\pi\) | ||||
−0.305741 | + | 0.952115i | \(0.598904\pi\) | |||||||
\(968\) | −34.1342 | −1.09711 | ||||||||
\(969\) | 4.64722 | 0.149290 | ||||||||
\(970\) | 13.2687 | 0.426031 | ||||||||
\(971\) | −25.4007 | −0.815148 | −0.407574 | − | 0.913172i | \(-0.633625\pi\) | ||||
−0.407574 | + | 0.913172i | \(0.633625\pi\) | |||||||
\(972\) | −3.34288 | −0.107223 | ||||||||
\(973\) | 16.2754 | 0.521765 | ||||||||
\(974\) | −43.1497 | −1.38261 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.34407 | 0.139050 | ||||||||
\(977\) | 18.9933 | 0.607650 | 0.303825 | − | 0.952728i | \(-0.401736\pi\) | ||||
0.303825 | + | 0.952728i | \(0.401736\pi\) | |||||||
\(978\) | 20.2718 | 0.648221 | ||||||||
\(979\) | 0.459782 | 0.0146947 | ||||||||
\(980\) | 4.88235 | 0.155961 | ||||||||
\(981\) | −9.12019 | −0.291185 | ||||||||
\(982\) | 43.5785 | 1.39065 | ||||||||
\(983\) | 40.4777 | 1.29104 | 0.645519 | − | 0.763744i | \(-0.276641\pi\) | ||||
0.645519 | + | 0.763744i | \(0.276641\pi\) | |||||||
\(984\) | 16.4560 | 0.524599 | ||||||||
\(985\) | 4.40659 | 0.140406 | ||||||||
\(986\) | 42.8446 | 1.36445 | ||||||||
\(987\) | 3.32663 | 0.105888 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.3265 | 0.455555 | ||||||||
\(990\) | 0.191071 | 0.00607264 | ||||||||
\(991\) | 54.2021 | 1.72179 | 0.860893 | − | 0.508786i | \(-0.169906\pi\) | ||||
0.860893 | + | 0.508786i | \(0.169906\pi\) | |||||||
\(992\) | −28.3865 | −0.901274 | ||||||||
\(993\) | 27.3837 | 0.868997 | ||||||||
\(994\) | −26.5140 | −0.840972 | ||||||||
\(995\) | 35.8620 | 1.13690 | ||||||||
\(996\) | 25.7483 | 0.815865 | ||||||||
\(997\) | −36.0609 | −1.14206 | −0.571029 | − | 0.820930i | \(-0.693456\pi\) | ||||
−0.571029 | + | 0.820930i | \(0.693456\pi\) | |||||||
\(998\) | −54.9407 | −1.73912 | ||||||||
\(999\) | −0.780896 | −0.0247064 |
(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 | 3549.2.a.be.1.9 | ✓ | 9 | |
13.12 | even | 2 | 3549.2.a.bf.1.1 | yes | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3549.2.a.be.1.9 | ✓ | 9 | 1.1 | even | 1 | trivial | |
3549.2.a.bf.1.1 | yes | 9 | 13.12 | even | 2 |