Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, 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("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.36 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.335014 | 0.236891 | 0.118445 | − | 0.992961i | \(-0.462209\pi\) | ||||
0.118445 | + | 0.992961i | \(0.462209\pi\) | |||||||
\(3\) | −2.24041 | −1.29350 | −0.646751 | − | 0.762702i | \(-0.723873\pi\) | ||||
−0.646751 | + | 0.762702i | \(0.723873\pi\) | |||||||
\(4\) | −1.88777 | −0.943883 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −0.750569 | −0.306419 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.30246 | −0.460488 | ||||||||
\(9\) | 2.01944 | 0.673145 | ||||||||
\(10\) | −0.335014 | −0.105941 | ||||||||
\(11\) | 3.08966 | 0.931569 | 0.465784 | − | 0.884898i | \(-0.345772\pi\) | ||||
0.465784 | + | 0.884898i | \(0.345772\pi\) | |||||||
\(12\) | 4.22937 | 1.22091 | ||||||||
\(13\) | −2.34431 | −0.650195 | −0.325098 | − | 0.945680i | \(-0.605397\pi\) | ||||
−0.325098 | + | 0.945680i | \(0.605397\pi\) | |||||||
\(14\) | −0.335014 | −0.0895364 | ||||||||
\(15\) | 2.24041 | 0.578471 | ||||||||
\(16\) | 3.33919 | 0.834797 | ||||||||
\(17\) | 0.387513 | 0.0939857 | 0.0469928 | − | 0.998895i | \(-0.485036\pi\) | ||||
0.0469928 | + | 0.998895i | \(0.485036\pi\) | |||||||
\(18\) | 0.676540 | 0.159462 | ||||||||
\(19\) | 2.68213 | 0.615323 | 0.307661 | − | 0.951496i | \(-0.400454\pi\) | ||||
0.307661 | + | 0.951496i | \(0.400454\pi\) | |||||||
\(20\) | 1.88777 | 0.422117 | ||||||||
\(21\) | 2.24041 | 0.488897 | ||||||||
\(22\) | 1.03508 | 0.220680 | ||||||||
\(23\) | 7.98383 | 1.66474 | 0.832372 | − | 0.554217i | \(-0.186982\pi\) | ||||
0.832372 | + | 0.554217i | \(0.186982\pi\) | |||||||
\(24\) | 2.91804 | 0.595642 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.785378 | −0.154025 | ||||||||
\(27\) | 2.19687 | 0.422787 | ||||||||
\(28\) | 1.88777 | 0.356754 | ||||||||
\(29\) | −9.13609 | −1.69653 | −0.848265 | − | 0.529572i | \(-0.822353\pi\) | ||||
−0.848265 | + | 0.529572i | \(0.822353\pi\) | |||||||
\(30\) | 0.750569 | 0.137035 | ||||||||
\(31\) | −5.31346 | −0.954326 | −0.477163 | − | 0.878815i | \(-0.658335\pi\) | ||||
−0.477163 | + | 0.878815i | \(0.658335\pi\) | |||||||
\(32\) | 3.72359 | 0.658244 | ||||||||
\(33\) | −6.92211 | −1.20499 | ||||||||
\(34\) | 0.129822 | 0.0222644 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −3.81222 | −0.635370 | ||||||||
\(37\) | −0.994796 | −0.163543 | −0.0817717 | − | 0.996651i | \(-0.526058\pi\) | ||||
−0.0817717 | + | 0.996651i | \(0.526058\pi\) | |||||||
\(38\) | 0.898552 | 0.145764 | ||||||||
\(39\) | 5.25222 | 0.841028 | ||||||||
\(40\) | 1.30246 | 0.205937 | ||||||||
\(41\) | 4.24736 | 0.663326 | 0.331663 | − | 0.943398i | \(-0.392390\pi\) | ||||
0.331663 | + | 0.943398i | \(0.392390\pi\) | |||||||
\(42\) | 0.750569 | 0.115815 | ||||||||
\(43\) | 4.40582 | 0.671881 | 0.335941 | − | 0.941883i | \(-0.390946\pi\) | ||||
0.335941 | + | 0.941883i | \(0.390946\pi\) | |||||||
\(44\) | −5.83256 | −0.879292 | ||||||||
\(45\) | −2.01944 | −0.301040 | ||||||||
\(46\) | 2.67470 | 0.394363 | ||||||||
\(47\) | 4.86496 | 0.709627 | 0.354814 | − | 0.934937i | \(-0.384544\pi\) | ||||
0.354814 | + | 0.934937i | \(0.384544\pi\) | |||||||
\(48\) | −7.48115 | −1.07981 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.335014 | 0.0473782 | ||||||||
\(51\) | −0.868188 | −0.121571 | ||||||||
\(52\) | 4.42551 | 0.613708 | ||||||||
\(53\) | −13.1706 | −1.80913 | −0.904564 | − | 0.426338i | \(-0.859803\pi\) | ||||
−0.904564 | + | 0.426338i | \(0.859803\pi\) | |||||||
\(54\) | 0.735982 | 0.100154 | ||||||||
\(55\) | −3.08966 | −0.416610 | ||||||||
\(56\) | 1.30246 | 0.174048 | ||||||||
\(57\) | −6.00907 | −0.795921 | ||||||||
\(58\) | −3.06072 | −0.401893 | ||||||||
\(59\) | 10.2348 | 1.33245 | 0.666226 | − | 0.745750i | \(-0.267909\pi\) | ||||
0.666226 | + | 0.745750i | \(0.267909\pi\) | |||||||
\(60\) | −4.22937 | −0.546009 | ||||||||
\(61\) | −4.84523 | −0.620368 | −0.310184 | − | 0.950676i | \(-0.600391\pi\) | ||||
−0.310184 | + | 0.950676i | \(0.600391\pi\) | |||||||
\(62\) | −1.78009 | −0.226071 | ||||||||
\(63\) | −2.01944 | −0.254425 | ||||||||
\(64\) | −5.43092 | −0.678865 | ||||||||
\(65\) | 2.34431 | 0.290776 | ||||||||
\(66\) | −2.31901 | −0.285450 | ||||||||
\(67\) | −15.4928 | −1.89275 | −0.946376 | − | 0.323067i | \(-0.895286\pi\) | ||||
−0.946376 | + | 0.323067i | \(0.895286\pi\) | |||||||
\(68\) | −0.731533 | −0.0887115 | ||||||||
\(69\) | −17.8871 | −2.15335 | ||||||||
\(70\) | 0.335014 | 0.0400419 | ||||||||
\(71\) | −6.13446 | −0.728027 | −0.364013 | − | 0.931394i | \(-0.618594\pi\) | ||||
−0.364013 | + | 0.931394i | \(0.618594\pi\) | |||||||
\(72\) | −2.63023 | −0.309975 | ||||||||
\(73\) | −6.33820 | −0.741830 | −0.370915 | − | 0.928667i | \(-0.620956\pi\) | ||||
−0.370915 | + | 0.928667i | \(0.620956\pi\) | |||||||
\(74\) | −0.333271 | −0.0387420 | ||||||||
\(75\) | −2.24041 | −0.258700 | ||||||||
\(76\) | −5.06323 | −0.580793 | ||||||||
\(77\) | −3.08966 | −0.352100 | ||||||||
\(78\) | 1.75957 | 0.199232 | ||||||||
\(79\) | −7.92124 | −0.891209 | −0.445604 | − | 0.895230i | \(-0.647011\pi\) | ||||
−0.445604 | + | 0.895230i | \(0.647011\pi\) | |||||||
\(80\) | −3.33919 | −0.373333 | ||||||||
\(81\) | −10.9802 | −1.22002 | ||||||||
\(82\) | 1.42293 | 0.157136 | ||||||||
\(83\) | −9.73242 | −1.06827 | −0.534136 | − | 0.845399i | \(-0.679363\pi\) | ||||
−0.534136 | + | 0.845399i | \(0.679363\pi\) | |||||||
\(84\) | −4.22937 | −0.461462 | ||||||||
\(85\) | −0.387513 | −0.0420317 | ||||||||
\(86\) | 1.47601 | 0.159163 | ||||||||
\(87\) | 20.4686 | 2.19446 | ||||||||
\(88\) | −4.02416 | −0.428976 | ||||||||
\(89\) | 11.9796 | 1.26984 | 0.634919 | − | 0.772579i | \(-0.281033\pi\) | ||||
0.634919 | + | 0.772579i | \(0.281033\pi\) | |||||||
\(90\) | −0.676540 | −0.0713136 | ||||||||
\(91\) | 2.34431 | 0.245751 | ||||||||
\(92\) | −15.0716 | −1.57132 | ||||||||
\(93\) | 11.9043 | 1.23442 | ||||||||
\(94\) | 1.62983 | 0.168104 | ||||||||
\(95\) | −2.68213 | −0.275181 | ||||||||
\(96\) | −8.34237 | −0.851439 | ||||||||
\(97\) | 8.91853 | 0.905539 | 0.452770 | − | 0.891628i | \(-0.350436\pi\) | ||||
0.452770 | + | 0.891628i | \(0.350436\pi\) | |||||||
\(98\) | 0.335014 | 0.0338416 | ||||||||
\(99\) | 6.23938 | 0.627081 | ||||||||
\(100\) | −1.88777 | −0.188777 | ||||||||
\(101\) | −1.24600 | −0.123982 | −0.0619908 | − | 0.998077i | \(-0.519745\pi\) | ||||
−0.0619908 | + | 0.998077i | \(0.519745\pi\) | |||||||
\(102\) | −0.290855 | −0.0287990 | ||||||||
\(103\) | 8.02045 | 0.790278 | 0.395139 | − | 0.918621i | \(-0.370696\pi\) | ||||
0.395139 | + | 0.918621i | \(0.370696\pi\) | |||||||
\(104\) | 3.05337 | 0.299407 | ||||||||
\(105\) | −2.24041 | −0.218642 | ||||||||
\(106\) | −4.41236 | −0.428566 | ||||||||
\(107\) | 13.4191 | 1.29727 | 0.648636 | − | 0.761099i | \(-0.275340\pi\) | ||||
0.648636 | + | 0.761099i | \(0.275340\pi\) | |||||||
\(108\) | −4.14717 | −0.399061 | ||||||||
\(109\) | −5.11814 | −0.490229 | −0.245114 | − | 0.969494i | \(-0.578825\pi\) | ||||
−0.245114 | + | 0.969494i | \(0.578825\pi\) | |||||||
\(110\) | −1.03508 | −0.0986912 | ||||||||
\(111\) | 2.22875 | 0.211544 | ||||||||
\(112\) | −3.33919 | −0.315524 | ||||||||
\(113\) | 9.16426 | 0.862101 | 0.431050 | − | 0.902328i | \(-0.358143\pi\) | ||||
0.431050 | + | 0.902328i | \(0.358143\pi\) | |||||||
\(114\) | −2.01312 | −0.188546 | ||||||||
\(115\) | −7.98383 | −0.744496 | ||||||||
\(116\) | 17.2468 | 1.60133 | ||||||||
\(117\) | −4.73419 | −0.437676 | ||||||||
\(118\) | 3.42879 | 0.315646 | ||||||||
\(119\) | −0.387513 | −0.0355232 | ||||||||
\(120\) | −2.91804 | −0.266379 | ||||||||
\(121\) | −1.45398 | −0.132180 | ||||||||
\(122\) | −1.62322 | −0.146960 | ||||||||
\(123\) | −9.51583 | −0.858014 | ||||||||
\(124\) | 10.0306 | 0.900772 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −0.676540 | −0.0602710 | ||||||||
\(127\) | 16.3534 | 1.45113 | 0.725563 | − | 0.688156i | \(-0.241580\pi\) | ||||
0.725563 | + | 0.688156i | \(0.241580\pi\) | |||||||
\(128\) | −9.26662 | −0.819061 | ||||||||
\(129\) | −9.87084 | −0.869079 | ||||||||
\(130\) | 0.785378 | 0.0688822 | ||||||||
\(131\) | −8.49544 | −0.742250 | −0.371125 | − | 0.928583i | \(-0.621028\pi\) | ||||
−0.371125 | + | 0.928583i | \(0.621028\pi\) | |||||||
\(132\) | 13.0673 | 1.13736 | ||||||||
\(133\) | −2.68213 | −0.232570 | ||||||||
\(134\) | −5.19033 | −0.448376 | ||||||||
\(135\) | −2.19687 | −0.189076 | ||||||||
\(136\) | −0.504719 | −0.0432793 | ||||||||
\(137\) | −6.22459 | −0.531803 | −0.265901 | − | 0.964000i | \(-0.585670\pi\) | ||||
−0.265901 | + | 0.964000i | \(0.585670\pi\) | |||||||
\(138\) | −5.99242 | −0.510109 | ||||||||
\(139\) | −16.1363 | −1.36866 | −0.684330 | − | 0.729172i | \(-0.739905\pi\) | ||||
−0.684330 | + | 0.729172i | \(0.739905\pi\) | |||||||
\(140\) | −1.88777 | −0.159545 | ||||||||
\(141\) | −10.8995 | −0.917903 | ||||||||
\(142\) | −2.05513 | −0.172463 | ||||||||
\(143\) | −7.24314 | −0.605702 | ||||||||
\(144\) | 6.74328 | 0.561940 | ||||||||
\(145\) | 9.13609 | 0.758711 | ||||||||
\(146\) | −2.12339 | −0.175733 | ||||||||
\(147\) | −2.24041 | −0.184786 | ||||||||
\(148\) | 1.87794 | 0.154366 | ||||||||
\(149\) | −4.91856 | −0.402944 | −0.201472 | − | 0.979494i | \(-0.564573\pi\) | ||||
−0.201472 | + | 0.979494i | \(0.564573\pi\) | |||||||
\(150\) | −0.750569 | −0.0612837 | ||||||||
\(151\) | 11.6046 | 0.944371 | 0.472186 | − | 0.881499i | \(-0.343465\pi\) | ||||
0.472186 | + | 0.881499i | \(0.343465\pi\) | |||||||
\(152\) | −3.49336 | −0.283349 | ||||||||
\(153\) | 0.782557 | 0.0632660 | ||||||||
\(154\) | −1.03508 | −0.0834093 | ||||||||
\(155\) | 5.31346 | 0.426788 | ||||||||
\(156\) | −9.91496 | −0.793832 | ||||||||
\(157\) | 13.3293 | 1.06380 | 0.531899 | − | 0.846808i | \(-0.321479\pi\) | ||||
0.531899 | + | 0.846808i | \(0.321479\pi\) | |||||||
\(158\) | −2.65373 | −0.211119 | ||||||||
\(159\) | 29.5076 | 2.34011 | ||||||||
\(160\) | −3.72359 | −0.294376 | ||||||||
\(161\) | −7.98383 | −0.629214 | ||||||||
\(162\) | −3.67852 | −0.289012 | ||||||||
\(163\) | −14.1670 | −1.10965 | −0.554824 | − | 0.831968i | \(-0.687215\pi\) | ||||
−0.554824 | + | 0.831968i | \(0.687215\pi\) | |||||||
\(164\) | −8.01802 | −0.626102 | ||||||||
\(165\) | 6.92211 | 0.538886 | ||||||||
\(166\) | −3.26050 | −0.253064 | ||||||||
\(167\) | 5.01242 | 0.387873 | 0.193936 | − | 0.981014i | \(-0.437874\pi\) | ||||
0.193936 | + | 0.981014i | \(0.437874\pi\) | |||||||
\(168\) | −2.91804 | −0.225131 | ||||||||
\(169\) | −7.50420 | −0.577246 | ||||||||
\(170\) | −0.129822 | −0.00995692 | ||||||||
\(171\) | 5.41639 | 0.414202 | ||||||||
\(172\) | −8.31715 | −0.634177 | ||||||||
\(173\) | 1.96609 | 0.149479 | 0.0747394 | − | 0.997203i | \(-0.476188\pi\) | ||||
0.0747394 | + | 0.997203i | \(0.476188\pi\) | |||||||
\(174\) | 6.85727 | 0.519848 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 10.3170 | 0.777671 | ||||||||
\(177\) | −22.9300 | −1.72353 | ||||||||
\(178\) | 4.01335 | 0.300813 | ||||||||
\(179\) | −6.13097 | −0.458250 | −0.229125 | − | 0.973397i | \(-0.573586\pi\) | ||||
−0.229125 | + | 0.973397i | \(0.573586\pi\) | |||||||
\(180\) | 3.81222 | 0.284146 | ||||||||
\(181\) | −22.1672 | −1.64768 | −0.823839 | − | 0.566824i | \(-0.808172\pi\) | ||||
−0.823839 | + | 0.566824i | \(0.808172\pi\) | |||||||
\(182\) | 0.785378 | 0.0582161 | ||||||||
\(183\) | 10.8553 | 0.802447 | ||||||||
\(184\) | −10.3986 | −0.766595 | ||||||||
\(185\) | 0.994796 | 0.0731388 | ||||||||
\(186\) | 3.98812 | 0.292423 | ||||||||
\(187\) | 1.19728 | 0.0875541 | ||||||||
\(188\) | −9.18390 | −0.669805 | ||||||||
\(189\) | −2.19687 | −0.159799 | ||||||||
\(190\) | −0.898552 | −0.0651878 | ||||||||
\(191\) | 3.66299 | 0.265045 | 0.132522 | − | 0.991180i | \(-0.457692\pi\) | ||||
0.132522 | + | 0.991180i | \(0.457692\pi\) | |||||||
\(192\) | 12.1675 | 0.878113 | ||||||||
\(193\) | −5.69038 | −0.409602 | −0.204801 | − | 0.978804i | \(-0.565655\pi\) | ||||
−0.204801 | + | 0.978804i | \(0.565655\pi\) | |||||||
\(194\) | 2.98784 | 0.214514 | ||||||||
\(195\) | −5.25222 | −0.376119 | ||||||||
\(196\) | −1.88777 | −0.134840 | ||||||||
\(197\) | −11.3511 | −0.808732 | −0.404366 | − | 0.914597i | \(-0.632508\pi\) | ||||
−0.404366 | + | 0.914597i | \(0.632508\pi\) | |||||||
\(198\) | 2.09028 | 0.148550 | ||||||||
\(199\) | 6.02661 | 0.427215 | 0.213608 | − | 0.976920i | \(-0.431479\pi\) | ||||
0.213608 | + | 0.976920i | \(0.431479\pi\) | |||||||
\(200\) | −1.30246 | −0.0920976 | ||||||||
\(201\) | 34.7103 | 2.44828 | ||||||||
\(202\) | −0.417428 | −0.0293701 | ||||||||
\(203\) | 9.13609 | 0.641228 | ||||||||
\(204\) | 1.63893 | 0.114748 | ||||||||
\(205\) | −4.24736 | −0.296649 | ||||||||
\(206\) | 2.68697 | 0.187210 | ||||||||
\(207\) | 16.1228 | 1.12061 | ||||||||
\(208\) | −7.82810 | −0.542781 | ||||||||
\(209\) | 8.28688 | 0.573216 | ||||||||
\(210\) | −0.750569 | −0.0517942 | ||||||||
\(211\) | −12.1781 | −0.838376 | −0.419188 | − | 0.907900i | \(-0.637685\pi\) | ||||
−0.419188 | + | 0.907900i | \(0.637685\pi\) | |||||||
\(212\) | 24.8631 | 1.70760 | ||||||||
\(213\) | 13.7437 | 0.941704 | ||||||||
\(214\) | 4.49558 | 0.307312 | ||||||||
\(215\) | −4.40582 | −0.300474 | ||||||||
\(216\) | −2.86132 | −0.194688 | ||||||||
\(217\) | 5.31346 | 0.360701 | ||||||||
\(218\) | −1.71465 | −0.116131 | ||||||||
\(219\) | 14.2002 | 0.959558 | ||||||||
\(220\) | 5.83256 | 0.393231 | ||||||||
\(221\) | −0.908451 | −0.0611090 | ||||||||
\(222\) | 0.746663 | 0.0501128 | ||||||||
\(223\) | 12.2152 | 0.817992 | 0.408996 | − | 0.912536i | \(-0.365879\pi\) | ||||
0.408996 | + | 0.912536i | \(0.365879\pi\) | |||||||
\(224\) | −3.72359 | −0.248793 | ||||||||
\(225\) | 2.01944 | 0.134629 | ||||||||
\(226\) | 3.07016 | 0.204224 | ||||||||
\(227\) | 26.7572 | 1.77594 | 0.887969 | − | 0.459904i | \(-0.152116\pi\) | ||||
0.887969 | + | 0.459904i | \(0.152116\pi\) | |||||||
\(228\) | 11.3437 | 0.751256 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | −2.67470 | −0.176364 | ||||||||
\(231\) | 6.92211 | 0.455442 | ||||||||
\(232\) | 11.8994 | 0.781232 | ||||||||
\(233\) | −27.2797 | −1.78715 | −0.893577 | − | 0.448911i | \(-0.851812\pi\) | ||||
−0.893577 | + | 0.448911i | \(0.851812\pi\) | |||||||
\(234\) | −1.58602 | −0.103681 | ||||||||
\(235\) | −4.86496 | −0.317355 | ||||||||
\(236\) | −19.3208 | −1.25768 | ||||||||
\(237\) | 17.7468 | 1.15278 | ||||||||
\(238\) | −0.129822 | −0.00841514 | ||||||||
\(239\) | −9.68197 | −0.626274 | −0.313137 | − | 0.949708i | \(-0.601380\pi\) | ||||
−0.313137 | + | 0.949708i | \(0.601380\pi\) | |||||||
\(240\) | 7.48115 | 0.482906 | ||||||||
\(241\) | 14.2686 | 0.919122 | 0.459561 | − | 0.888146i | \(-0.348007\pi\) | ||||
0.459561 | + | 0.888146i | \(0.348007\pi\) | |||||||
\(242\) | −0.487103 | −0.0313121 | ||||||||
\(243\) | 18.0095 | 1.15531 | ||||||||
\(244\) | 9.14666 | 0.585555 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −3.18794 | −0.203256 | ||||||||
\(247\) | −6.28775 | −0.400080 | ||||||||
\(248\) | 6.92056 | 0.439456 | ||||||||
\(249\) | 21.8046 | 1.38181 | ||||||||
\(250\) | −0.335014 | −0.0211882 | ||||||||
\(251\) | 22.6824 | 1.43170 | 0.715849 | − | 0.698255i | \(-0.246040\pi\) | ||||
0.715849 | + | 0.698255i | \(0.246040\pi\) | |||||||
\(252\) | 3.81222 | 0.240147 | ||||||||
\(253\) | 24.6674 | 1.55082 | ||||||||
\(254\) | 5.47861 | 0.343758 | ||||||||
\(255\) | 0.868188 | 0.0543680 | ||||||||
\(256\) | 7.75739 | 0.484837 | ||||||||
\(257\) | 17.2507 | 1.07607 | 0.538036 | − | 0.842922i | \(-0.319167\pi\) | ||||
0.538036 | + | 0.842922i | \(0.319167\pi\) | |||||||
\(258\) | −3.30687 | −0.205877 | ||||||||
\(259\) | 0.994796 | 0.0618136 | ||||||||
\(260\) | −4.42551 | −0.274459 | ||||||||
\(261\) | −18.4497 | −1.14201 | ||||||||
\(262\) | −2.84609 | −0.175832 | ||||||||
\(263\) | 17.8368 | 1.09987 | 0.549933 | − | 0.835209i | \(-0.314653\pi\) | ||||
0.549933 | + | 0.835209i | \(0.314653\pi\) | |||||||
\(264\) | 9.01576 | 0.554881 | ||||||||
\(265\) | 13.1706 | 0.809067 | ||||||||
\(266\) | −0.898552 | −0.0550938 | ||||||||
\(267\) | −26.8393 | −1.64254 | ||||||||
\(268\) | 29.2469 | 1.78654 | ||||||||
\(269\) | 21.8253 | 1.33071 | 0.665356 | − | 0.746526i | \(-0.268280\pi\) | ||||
0.665356 | + | 0.746526i | \(0.268280\pi\) | |||||||
\(270\) | −0.735982 | −0.0447904 | ||||||||
\(271\) | 11.1052 | 0.674593 | 0.337297 | − | 0.941398i | \(-0.390488\pi\) | ||||
0.337297 | + | 0.941398i | \(0.390488\pi\) | |||||||
\(272\) | 1.29398 | 0.0784590 | ||||||||
\(273\) | −5.25222 | −0.317879 | ||||||||
\(274\) | −2.08533 | −0.125979 | ||||||||
\(275\) | 3.08966 | 0.186314 | ||||||||
\(276\) | 33.7666 | 2.03251 | ||||||||
\(277\) | 21.2309 | 1.27564 | 0.637820 | − | 0.770185i | \(-0.279836\pi\) | ||||
0.637820 | + | 0.770185i | \(0.279836\pi\) | |||||||
\(278\) | −5.40588 | −0.324223 | ||||||||
\(279\) | −10.7302 | −0.642400 | ||||||||
\(280\) | −1.30246 | −0.0778367 | ||||||||
\(281\) | −10.6590 | −0.635863 | −0.317932 | − | 0.948114i | \(-0.602988\pi\) | ||||
−0.317932 | + | 0.948114i | \(0.602988\pi\) | |||||||
\(282\) | −3.65149 | −0.217443 | ||||||||
\(283\) | −16.4149 | −0.975767 | −0.487884 | − | 0.872909i | \(-0.662231\pi\) | ||||
−0.487884 | + | 0.872909i | \(0.662231\pi\) | |||||||
\(284\) | 11.5804 | 0.687172 | ||||||||
\(285\) | 6.00907 | 0.355947 | ||||||||
\(286\) | −2.42656 | −0.143485 | ||||||||
\(287\) | −4.24736 | −0.250714 | ||||||||
\(288\) | 7.51955 | 0.443094 | ||||||||
\(289\) | −16.8498 | −0.991167 | ||||||||
\(290\) | 3.06072 | 0.179732 | ||||||||
\(291\) | −19.9812 | −1.17132 | ||||||||
\(292\) | 11.9650 | 0.700200 | ||||||||
\(293\) | −11.0893 | −0.647846 | −0.323923 | − | 0.946084i | \(-0.605002\pi\) | ||||
−0.323923 | + | 0.946084i | \(0.605002\pi\) | |||||||
\(294\) | −0.750569 | −0.0437741 | ||||||||
\(295\) | −10.2348 | −0.595890 | ||||||||
\(296\) | 1.29568 | 0.0753098 | ||||||||
\(297\) | 6.78758 | 0.393855 | ||||||||
\(298\) | −1.64779 | −0.0954539 | ||||||||
\(299\) | −18.7166 | −1.08241 | ||||||||
\(300\) | 4.22937 | 0.244183 | ||||||||
\(301\) | −4.40582 | −0.253947 | ||||||||
\(302\) | 3.88772 | 0.223713 | ||||||||
\(303\) | 2.79155 | 0.160370 | ||||||||
\(304\) | 8.95614 | 0.513670 | ||||||||
\(305\) | 4.84523 | 0.277437 | ||||||||
\(306\) | 0.262168 | 0.0149871 | ||||||||
\(307\) | −2.20307 | −0.125736 | −0.0628680 | − | 0.998022i | \(-0.520025\pi\) | ||||
−0.0628680 | + | 0.998022i | \(0.520025\pi\) | |||||||
\(308\) | 5.83256 | 0.332341 | ||||||||
\(309\) | −17.9691 | −1.02223 | ||||||||
\(310\) | 1.78009 | 0.101102 | ||||||||
\(311\) | −6.04539 | −0.342802 | −0.171401 | − | 0.985201i | \(-0.554829\pi\) | ||||
−0.171401 | + | 0.985201i | \(0.554829\pi\) | |||||||
\(312\) | −6.84079 | −0.387284 | ||||||||
\(313\) | −2.93484 | −0.165887 | −0.0829436 | − | 0.996554i | \(-0.526432\pi\) | ||||
−0.0829436 | + | 0.996554i | \(0.526432\pi\) | |||||||
\(314\) | 4.46552 | 0.252004 | ||||||||
\(315\) | 2.01944 | 0.113782 | ||||||||
\(316\) | 14.9534 | 0.841197 | ||||||||
\(317\) | 10.9997 | 0.617807 | 0.308903 | − | 0.951093i | \(-0.400038\pi\) | ||||
0.308903 | + | 0.951093i | \(0.400038\pi\) | |||||||
\(318\) | 9.88549 | 0.554351 | ||||||||
\(319\) | −28.2275 | −1.58043 | ||||||||
\(320\) | 5.43092 | 0.303598 | ||||||||
\(321\) | −30.0642 | −1.67802 | ||||||||
\(322\) | −2.67470 | −0.149055 | ||||||||
\(323\) | 1.03936 | 0.0578315 | ||||||||
\(324\) | 20.7280 | 1.15156 | ||||||||
\(325\) | −2.34431 | −0.130039 | ||||||||
\(326\) | −4.74616 | −0.262866 | ||||||||
\(327\) | 11.4667 | 0.634111 | ||||||||
\(328\) | −5.53201 | −0.305454 | ||||||||
\(329\) | −4.86496 | −0.268214 | ||||||||
\(330\) | 2.31901 | 0.127657 | ||||||||
\(331\) | 27.7886 | 1.52740 | 0.763700 | − | 0.645571i | \(-0.223381\pi\) | ||||
0.763700 | + | 0.645571i | \(0.223381\pi\) | |||||||
\(332\) | 18.3725 | 1.00832 | ||||||||
\(333\) | −2.00893 | −0.110088 | ||||||||
\(334\) | 1.67923 | 0.0918835 | ||||||||
\(335\) | 15.4928 | 0.846465 | ||||||||
\(336\) | 7.48115 | 0.408130 | ||||||||
\(337\) | 3.48215 | 0.189685 | 0.0948424 | − | 0.995492i | \(-0.469765\pi\) | ||||
0.0948424 | + | 0.995492i | \(0.469765\pi\) | |||||||
\(338\) | −2.51401 | −0.136744 | ||||||||
\(339\) | −20.5317 | −1.11513 | ||||||||
\(340\) | 0.731533 | 0.0396730 | ||||||||
\(341\) | −16.4168 | −0.889020 | ||||||||
\(342\) | 1.81457 | 0.0981206 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −5.73839 | −0.309393 | ||||||||
\(345\) | 17.8871 | 0.963007 | ||||||||
\(346\) | 0.658667 | 0.0354102 | ||||||||
\(347\) | 28.6632 | 1.53872 | 0.769360 | − | 0.638815i | \(-0.220575\pi\) | ||||
0.769360 | + | 0.638815i | \(0.220575\pi\) | |||||||
\(348\) | −38.6399 | −2.07132 | ||||||||
\(349\) | 6.12059 | 0.327628 | 0.163814 | − | 0.986491i | \(-0.447620\pi\) | ||||
0.163814 | + | 0.986491i | \(0.447620\pi\) | |||||||
\(350\) | −0.335014 | −0.0179073 | ||||||||
\(351\) | −5.15014 | −0.274894 | ||||||||
\(352\) | 11.5046 | 0.613200 | ||||||||
\(353\) | −1.64350 | −0.0874748 | −0.0437374 | − | 0.999043i | \(-0.513926\pi\) | ||||
−0.0437374 | + | 0.999043i | \(0.513926\pi\) | |||||||
\(354\) | −7.68189 | −0.408288 | ||||||||
\(355\) | 6.13446 | 0.325584 | ||||||||
\(356\) | −22.6147 | −1.19858 | ||||||||
\(357\) | 0.868188 | 0.0459494 | ||||||||
\(358\) | −2.05396 | −0.108555 | ||||||||
\(359\) | −9.75230 | −0.514707 | −0.257353 | − | 0.966317i | \(-0.582850\pi\) | ||||
−0.257353 | + | 0.966317i | \(0.582850\pi\) | |||||||
\(360\) | 2.63023 | 0.138625 | ||||||||
\(361\) | −11.8062 | −0.621378 | ||||||||
\(362\) | −7.42634 | −0.390320 | ||||||||
\(363\) | 3.25750 | 0.170974 | ||||||||
\(364\) | −4.42551 | −0.231960 | ||||||||
\(365\) | 6.33820 | 0.331756 | ||||||||
\(366\) | 3.63668 | 0.190092 | ||||||||
\(367\) | 16.8750 | 0.880868 | 0.440434 | − | 0.897785i | \(-0.354825\pi\) | ||||
0.440434 | + | 0.897785i | \(0.354825\pi\) | |||||||
\(368\) | 26.6595 | 1.38972 | ||||||||
\(369\) | 8.57727 | 0.446515 | ||||||||
\(370\) | 0.333271 | 0.0173259 | ||||||||
\(371\) | 13.1706 | 0.683786 | ||||||||
\(372\) | −22.4726 | −1.16515 | ||||||||
\(373\) | −15.4879 | −0.801932 | −0.400966 | − | 0.916093i | \(-0.631325\pi\) | ||||
−0.400966 | + | 0.916093i | \(0.631325\pi\) | |||||||
\(374\) | 0.401108 | 0.0207408 | ||||||||
\(375\) | 2.24041 | 0.115694 | ||||||||
\(376\) | −6.33640 | −0.326775 | ||||||||
\(377\) | 21.4179 | 1.10308 | ||||||||
\(378\) | −0.735982 | −0.0378548 | ||||||||
\(379\) | −13.4710 | −0.691958 | −0.345979 | − | 0.938242i | \(-0.612453\pi\) | ||||
−0.345979 | + | 0.938242i | \(0.612453\pi\) | |||||||
\(380\) | 5.06323 | 0.259738 | ||||||||
\(381\) | −36.6382 | −1.87703 | ||||||||
\(382\) | 1.22715 | 0.0627867 | ||||||||
\(383\) | −4.84972 | −0.247809 | −0.123905 | − | 0.992294i | \(-0.539542\pi\) | ||||
−0.123905 | + | 0.992294i | \(0.539542\pi\) | |||||||
\(384\) | 20.7610 | 1.05946 | ||||||||
\(385\) | 3.08966 | 0.157464 | ||||||||
\(386\) | −1.90636 | −0.0970311 | ||||||||
\(387\) | 8.89727 | 0.452274 | ||||||||
\(388\) | −16.8361 | −0.854723 | ||||||||
\(389\) | 1.80404 | 0.0914684 | 0.0457342 | − | 0.998954i | \(-0.485437\pi\) | ||||
0.0457342 | + | 0.998954i | \(0.485437\pi\) | |||||||
\(390\) | −1.75957 | −0.0890992 | ||||||||
\(391\) | 3.09384 | 0.156462 | ||||||||
\(392\) | −1.30246 | −0.0657840 | ||||||||
\(393\) | 19.0333 | 0.960101 | ||||||||
\(394\) | −3.80278 | −0.191581 | ||||||||
\(395\) | 7.92124 | 0.398561 | ||||||||
\(396\) | −11.7785 | −0.591891 | ||||||||
\(397\) | 9.67307 | 0.485477 | 0.242739 | − | 0.970092i | \(-0.421954\pi\) | ||||
0.242739 | + | 0.970092i | \(0.421954\pi\) | |||||||
\(398\) | 2.01900 | 0.101203 | ||||||||
\(399\) | 6.00907 | 0.300830 | ||||||||
\(400\) | 3.33919 | 0.166959 | ||||||||
\(401\) | 4.92980 | 0.246183 | 0.123091 | − | 0.992395i | \(-0.460719\pi\) | ||||
0.123091 | + | 0.992395i | \(0.460719\pi\) | |||||||
\(402\) | 11.6285 | 0.579975 | ||||||||
\(403\) | 12.4564 | 0.620498 | ||||||||
\(404\) | 2.35216 | 0.117024 | ||||||||
\(405\) | 10.9802 | 0.545610 | ||||||||
\(406\) | 3.06072 | 0.151901 | ||||||||
\(407\) | −3.07359 | −0.152352 | ||||||||
\(408\) | 1.13078 | 0.0559818 | ||||||||
\(409\) | −5.43787 | −0.268885 | −0.134443 | − | 0.990921i | \(-0.542924\pi\) | ||||
−0.134443 | + | 0.990921i | \(0.542924\pi\) | |||||||
\(410\) | −1.42293 | −0.0702734 | ||||||||
\(411\) | 13.9456 | 0.687887 | ||||||||
\(412\) | −15.1407 | −0.745930 | ||||||||
\(413\) | −10.2348 | −0.503619 | ||||||||
\(414\) | 5.40138 | 0.265463 | ||||||||
\(415\) | 9.73242 | 0.477745 | ||||||||
\(416\) | −8.72926 | −0.427987 | ||||||||
\(417\) | 36.1519 | 1.77036 | ||||||||
\(418\) | 2.77622 | 0.135790 | ||||||||
\(419\) | 3.19118 | 0.155899 | 0.0779497 | − | 0.996957i | \(-0.475163\pi\) | ||||
0.0779497 | + | 0.996957i | \(0.475163\pi\) | |||||||
\(420\) | 4.22937 | 0.206372 | ||||||||
\(421\) | −4.22398 | −0.205864 | −0.102932 | − | 0.994688i | \(-0.532822\pi\) | ||||
−0.102932 | + | 0.994688i | \(0.532822\pi\) | |||||||
\(422\) | −4.07984 | −0.198604 | ||||||||
\(423\) | 9.82447 | 0.477682 | ||||||||
\(424\) | 17.1542 | 0.833082 | ||||||||
\(425\) | 0.387513 | 0.0187971 | ||||||||
\(426\) | 4.60434 | 0.223081 | ||||||||
\(427\) | 4.84523 | 0.234477 | ||||||||
\(428\) | −25.3321 | −1.22447 | ||||||||
\(429\) | 16.2276 | 0.783476 | ||||||||
\(430\) | −1.47601 | −0.0711797 | ||||||||
\(431\) | 30.8051 | 1.48383 | 0.741916 | − | 0.670493i | \(-0.233917\pi\) | ||||
0.741916 | + | 0.670493i | \(0.233917\pi\) | |||||||
\(432\) | 7.33575 | 0.352942 | ||||||||
\(433\) | 13.3957 | 0.643754 | 0.321877 | − | 0.946781i | \(-0.395686\pi\) | ||||
0.321877 | + | 0.946781i | \(0.395686\pi\) | |||||||
\(434\) | 1.78009 | 0.0854469 | ||||||||
\(435\) | −20.4686 | −0.981394 | ||||||||
\(436\) | 9.66184 | 0.462718 | ||||||||
\(437\) | 21.4137 | 1.02436 | ||||||||
\(438\) | 4.75726 | 0.227311 | ||||||||
\(439\) | −19.5760 | −0.934310 | −0.467155 | − | 0.884175i | \(-0.654721\pi\) | ||||
−0.467155 | + | 0.884175i | \(0.654721\pi\) | |||||||
\(440\) | 4.02416 | 0.191844 | ||||||||
\(441\) | 2.01944 | 0.0961636 | ||||||||
\(442\) | −0.304344 | −0.0144762 | ||||||||
\(443\) | 41.3997 | 1.96696 | 0.983480 | − | 0.181016i | \(-0.0579385\pi\) | ||||
0.983480 | + | 0.181016i | \(0.0579385\pi\) | |||||||
\(444\) | −4.20736 | −0.199672 | ||||||||
\(445\) | −11.9796 | −0.567889 | ||||||||
\(446\) | 4.09228 | 0.193775 | ||||||||
\(447\) | 11.0196 | 0.521209 | ||||||||
\(448\) | 5.43092 | 0.256587 | ||||||||
\(449\) | −12.3489 | −0.582781 | −0.291390 | − | 0.956604i | \(-0.594118\pi\) | ||||
−0.291390 | + | 0.956604i | \(0.594118\pi\) | |||||||
\(450\) | 0.676540 | 0.0318924 | ||||||||
\(451\) | 13.1229 | 0.617934 | ||||||||
\(452\) | −17.3000 | −0.813722 | ||||||||
\(453\) | −25.9991 | −1.22155 | ||||||||
\(454\) | 8.96405 | 0.420703 | ||||||||
\(455\) | −2.34431 | −0.109903 | ||||||||
\(456\) | 7.82656 | 0.366512 | ||||||||
\(457\) | 14.2761 | 0.667807 | 0.333904 | − | 0.942607i | \(-0.391634\pi\) | ||||
0.333904 | + | 0.942607i | \(0.391634\pi\) | |||||||
\(458\) | 0.335014 | 0.0156542 | ||||||||
\(459\) | 0.851314 | 0.0397359 | ||||||||
\(460\) | 15.0716 | 0.702717 | ||||||||
\(461\) | −16.3596 | −0.761944 | −0.380972 | − | 0.924587i | \(-0.624411\pi\) | ||||
−0.380972 | + | 0.924587i | \(0.624411\pi\) | |||||||
\(462\) | 2.31901 | 0.107890 | ||||||||
\(463\) | −31.5238 | −1.46504 | −0.732518 | − | 0.680747i | \(-0.761655\pi\) | ||||
−0.732518 | + | 0.680747i | \(0.761655\pi\) | |||||||
\(464\) | −30.5071 | −1.41626 | ||||||||
\(465\) | −11.9043 | −0.552050 | ||||||||
\(466\) | −9.13909 | −0.423360 | ||||||||
\(467\) | −12.2226 | −0.565593 | −0.282797 | − | 0.959180i | \(-0.591262\pi\) | ||||
−0.282797 | + | 0.959180i | \(0.591262\pi\) | |||||||
\(468\) | 8.93704 | 0.413115 | ||||||||
\(469\) | 15.4928 | 0.715393 | ||||||||
\(470\) | −1.62983 | −0.0751785 | ||||||||
\(471\) | −29.8632 | −1.37602 | ||||||||
\(472\) | −13.3303 | −0.613578 | ||||||||
\(473\) | 13.6125 | 0.625904 | ||||||||
\(474\) | 5.94544 | 0.273083 | ||||||||
\(475\) | 2.68213 | 0.123065 | ||||||||
\(476\) | 0.731533 | 0.0335298 | ||||||||
\(477\) | −26.5973 | −1.21781 | ||||||||
\(478\) | −3.24360 | −0.148359 | ||||||||
\(479\) | −4.92589 | −0.225070 | −0.112535 | − | 0.993648i | \(-0.535897\pi\) | ||||
−0.112535 | + | 0.993648i | \(0.535897\pi\) | |||||||
\(480\) | 8.34237 | 0.380775 | ||||||||
\(481\) | 2.33211 | 0.106335 | ||||||||
\(482\) | 4.78019 | 0.217732 | ||||||||
\(483\) | 17.8871 | 0.813889 | ||||||||
\(484\) | 2.74476 | 0.124762 | ||||||||
\(485\) | −8.91853 | −0.404970 | ||||||||
\(486\) | 6.03345 | 0.273683 | ||||||||
\(487\) | 40.3102 | 1.82663 | 0.913315 | − | 0.407253i | \(-0.133513\pi\) | ||||
0.913315 | + | 0.407253i | \(0.133513\pi\) | |||||||
\(488\) | 6.31071 | 0.285672 | ||||||||
\(489\) | 31.7400 | 1.43533 | ||||||||
\(490\) | −0.335014 | −0.0151344 | ||||||||
\(491\) | 20.1638 | 0.909981 | 0.454990 | − | 0.890496i | \(-0.349643\pi\) | ||||
0.454990 | + | 0.890496i | \(0.349643\pi\) | |||||||
\(492\) | 17.9637 | 0.809864 | ||||||||
\(493\) | −3.54035 | −0.159450 | ||||||||
\(494\) | −2.10649 | −0.0947753 | ||||||||
\(495\) | −6.23938 | −0.280439 | ||||||||
\(496\) | −17.7427 | −0.796669 | ||||||||
\(497\) | 6.13446 | 0.275168 | ||||||||
\(498\) | 7.30485 | 0.327338 | ||||||||
\(499\) | −8.30873 | −0.371950 | −0.185975 | − | 0.982555i | \(-0.559544\pi\) | ||||
−0.185975 | + | 0.982555i | \(0.559544\pi\) | |||||||
\(500\) | 1.88777 | 0.0844234 | ||||||||
\(501\) | −11.2299 | −0.501714 | ||||||||
\(502\) | 7.59892 | 0.339156 | ||||||||
\(503\) | 4.33965 | 0.193496 | 0.0967478 | − | 0.995309i | \(-0.469156\pi\) | ||||
0.0967478 | + | 0.995309i | \(0.469156\pi\) | |||||||
\(504\) | 2.63023 | 0.117160 | ||||||||
\(505\) | 1.24600 | 0.0554463 | ||||||||
\(506\) | 8.26392 | 0.367376 | ||||||||
\(507\) | 16.8125 | 0.746668 | ||||||||
\(508\) | −30.8713 | −1.36969 | ||||||||
\(509\) | −6.28405 | −0.278536 | −0.139268 | − | 0.990255i | \(-0.544475\pi\) | ||||
−0.139268 | + | 0.990255i | \(0.544475\pi\) | |||||||
\(510\) | 0.290855 | 0.0128793 | ||||||||
\(511\) | 6.33820 | 0.280385 | ||||||||
\(512\) | 21.1321 | 0.933915 | ||||||||
\(513\) | 5.89228 | 0.260151 | ||||||||
\(514\) | 5.77925 | 0.254912 | ||||||||
\(515\) | −8.02045 | −0.353423 | ||||||||
\(516\) | 18.6338 | 0.820309 | ||||||||
\(517\) | 15.0311 | 0.661066 | ||||||||
\(518\) | 0.333271 | 0.0146431 | ||||||||
\(519\) | −4.40484 | −0.193351 | ||||||||
\(520\) | −3.05337 | −0.133899 | ||||||||
\(521\) | 25.1102 | 1.10010 | 0.550049 | − | 0.835133i | \(-0.314609\pi\) | ||||
0.550049 | + | 0.835133i | \(0.314609\pi\) | |||||||
\(522\) | −6.18093 | −0.270532 | ||||||||
\(523\) | −13.7141 | −0.599675 | −0.299837 | − | 0.953990i | \(-0.596932\pi\) | ||||
−0.299837 | + | 0.953990i | \(0.596932\pi\) | |||||||
\(524\) | 16.0374 | 0.700597 | ||||||||
\(525\) | 2.24041 | 0.0977795 | ||||||||
\(526\) | 5.97559 | 0.260548 | ||||||||
\(527\) | −2.05903 | −0.0896930 | ||||||||
\(528\) | −23.1142 | −1.00592 | ||||||||
\(529\) | 40.7416 | 1.77137 | ||||||||
\(530\) | 4.41236 | 0.191661 | ||||||||
\(531\) | 20.6684 | 0.896933 | ||||||||
\(532\) | 5.06323 | 0.219519 | ||||||||
\(533\) | −9.95714 | −0.431292 | ||||||||
\(534\) | −8.99154 | −0.389102 | ||||||||
\(535\) | −13.4191 | −0.580157 | ||||||||
\(536\) | 20.1788 | 0.871590 | ||||||||
\(537\) | 13.7359 | 0.592747 | ||||||||
\(538\) | 7.31179 | 0.315234 | ||||||||
\(539\) | 3.08966 | 0.133081 | ||||||||
\(540\) | 4.14717 | 0.178466 | ||||||||
\(541\) | 6.28269 | 0.270114 | 0.135057 | − | 0.990838i | \(-0.456878\pi\) | ||||
0.135057 | + | 0.990838i | \(0.456878\pi\) | |||||||
\(542\) | 3.72040 | 0.159805 | ||||||||
\(543\) | 49.6637 | 2.13127 | ||||||||
\(544\) | 1.44294 | 0.0618655 | ||||||||
\(545\) | 5.11814 | 0.219237 | ||||||||
\(546\) | −1.75957 | −0.0753026 | ||||||||
\(547\) | −24.6002 | −1.05183 | −0.525915 | − | 0.850537i | \(-0.676277\pi\) | ||||
−0.525915 | + | 0.850537i | \(0.676277\pi\) | |||||||
\(548\) | 11.7506 | 0.501959 | ||||||||
\(549\) | −9.78463 | −0.417598 | ||||||||
\(550\) | 1.03508 | 0.0441360 | ||||||||
\(551\) | −24.5042 | −1.04391 | ||||||||
\(552\) | 23.2971 | 0.991592 | ||||||||
\(553\) | 7.92124 | 0.336845 | ||||||||
\(554\) | 7.11265 | 0.302188 | ||||||||
\(555\) | −2.22875 | −0.0946052 | ||||||||
\(556\) | 30.4615 | 1.29186 | ||||||||
\(557\) | 24.3518 | 1.03182 | 0.515910 | − | 0.856643i | \(-0.327454\pi\) | ||||
0.515910 | + | 0.856643i | \(0.327454\pi\) | |||||||
\(558\) | −3.59477 | −0.152179 | ||||||||
\(559\) | −10.3286 | −0.436854 | ||||||||
\(560\) | 3.33919 | 0.141106 | ||||||||
\(561\) | −2.68241 | −0.113251 | ||||||||
\(562\) | −3.57092 | −0.150630 | ||||||||
\(563\) | −40.9017 | −1.72380 | −0.861900 | − | 0.507078i | \(-0.830726\pi\) | ||||
−0.861900 | + | 0.507078i | \(0.830726\pi\) | |||||||
\(564\) | 20.5757 | 0.866393 | ||||||||
\(565\) | −9.16426 | −0.385543 | ||||||||
\(566\) | −5.49924 | −0.231150 | ||||||||
\(567\) | 10.9802 | 0.461125 | ||||||||
\(568\) | 7.98988 | 0.335248 | ||||||||
\(569\) | 30.8329 | 1.29258 | 0.646291 | − | 0.763091i | \(-0.276319\pi\) | ||||
0.646291 | + | 0.763091i | \(0.276319\pi\) | |||||||
\(570\) | 2.01312 | 0.0843205 | ||||||||
\(571\) | −12.1919 | −0.510214 | −0.255107 | − | 0.966913i | \(-0.582111\pi\) | ||||
−0.255107 | + | 0.966913i | \(0.582111\pi\) | |||||||
\(572\) | 13.6733 | 0.571711 | ||||||||
\(573\) | −8.20660 | −0.342836 | ||||||||
\(574\) | −1.42293 | −0.0593918 | ||||||||
\(575\) | 7.98383 | 0.332949 | ||||||||
\(576\) | −10.9674 | −0.456975 | ||||||||
\(577\) | −35.5602 | −1.48039 | −0.740196 | − | 0.672391i | \(-0.765267\pi\) | ||||
−0.740196 | + | 0.672391i | \(0.765267\pi\) | |||||||
\(578\) | −5.64494 | −0.234798 | ||||||||
\(579\) | 12.7488 | 0.529821 | ||||||||
\(580\) | −17.2468 | −0.716134 | ||||||||
\(581\) | 9.73242 | 0.403769 | ||||||||
\(582\) | −6.69397 | −0.277474 | ||||||||
\(583\) | −40.6929 | −1.68533 | ||||||||
\(584\) | 8.25523 | 0.341604 | ||||||||
\(585\) | 4.73419 | 0.195735 | ||||||||
\(586\) | −3.71509 | −0.153469 | ||||||||
\(587\) | 3.31738 | 0.136923 | 0.0684616 | − | 0.997654i | \(-0.478191\pi\) | ||||
0.0684616 | + | 0.997654i | \(0.478191\pi\) | |||||||
\(588\) | 4.22937 | 0.174416 | ||||||||
\(589\) | −14.2514 | −0.587219 | ||||||||
\(590\) | −3.42879 | −0.141161 | ||||||||
\(591\) | 25.4311 | 1.04610 | ||||||||
\(592\) | −3.32181 | −0.136526 | ||||||||
\(593\) | 16.6255 | 0.682727 | 0.341364 | − | 0.939931i | \(-0.389111\pi\) | ||||
0.341364 | + | 0.939931i | \(0.389111\pi\) | |||||||
\(594\) | 2.27394 | 0.0933007 | ||||||||
\(595\) | 0.387513 | 0.0158865 | ||||||||
\(596\) | 9.28509 | 0.380332 | ||||||||
\(597\) | −13.5021 | −0.552604 | ||||||||
\(598\) | −6.27033 | −0.256413 | ||||||||
\(599\) | −1.47184 | −0.0601378 | −0.0300689 | − | 0.999548i | \(-0.509573\pi\) | ||||
−0.0300689 | + | 0.999548i | \(0.509573\pi\) | |||||||
\(600\) | 2.91804 | 0.119128 | ||||||||
\(601\) | 24.4064 | 0.995558 | 0.497779 | − | 0.867304i | \(-0.334149\pi\) | ||||
0.497779 | + | 0.867304i | \(0.334149\pi\) | |||||||
\(602\) | −1.47601 | −0.0601578 | ||||||||
\(603\) | −31.2868 | −1.27410 | ||||||||
\(604\) | −21.9068 | −0.891376 | ||||||||
\(605\) | 1.45398 | 0.0591125 | ||||||||
\(606\) | 0.935209 | 0.0379903 | ||||||||
\(607\) | −30.4277 | −1.23502 | −0.617511 | − | 0.786563i | \(-0.711859\pi\) | ||||
−0.617511 | + | 0.786563i | \(0.711859\pi\) | |||||||
\(608\) | 9.98716 | 0.405033 | ||||||||
\(609\) | −20.4686 | −0.829429 | ||||||||
\(610\) | 1.62322 | 0.0657224 | ||||||||
\(611\) | −11.4050 | −0.461396 | ||||||||
\(612\) | −1.47728 | −0.0597157 | ||||||||
\(613\) | −6.16136 | −0.248855 | −0.124427 | − | 0.992229i | \(-0.539709\pi\) | ||||
−0.124427 | + | 0.992229i | \(0.539709\pi\) | |||||||
\(614\) | −0.738061 | −0.0297857 | ||||||||
\(615\) | 9.51583 | 0.383715 | ||||||||
\(616\) | 4.02416 | 0.162138 | ||||||||
\(617\) | 42.1317 | 1.69616 | 0.848078 | − | 0.529871i | \(-0.177760\pi\) | ||||
0.848078 | + | 0.529871i | \(0.177760\pi\) | |||||||
\(618\) | −6.01990 | −0.242156 | ||||||||
\(619\) | 12.5510 | 0.504468 | 0.252234 | − | 0.967666i | \(-0.418835\pi\) | ||||
0.252234 | + | 0.967666i | \(0.418835\pi\) | |||||||
\(620\) | −10.0306 | −0.402837 | ||||||||
\(621\) | 17.5394 | 0.703833 | ||||||||
\(622\) | −2.02529 | −0.0812068 | ||||||||
\(623\) | −11.9796 | −0.479954 | ||||||||
\(624\) | 17.5382 | 0.702088 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −0.983215 | −0.0392972 | ||||||||
\(627\) | −18.5660 | −0.741455 | ||||||||
\(628\) | −25.1627 | −1.00410 | ||||||||
\(629\) | −0.385496 | −0.0153707 | ||||||||
\(630\) | 0.676540 | 0.0269540 | ||||||||
\(631\) | 20.4775 | 0.815198 | 0.407599 | − | 0.913161i | \(-0.366366\pi\) | ||||
0.407599 | + | 0.913161i | \(0.366366\pi\) | |||||||
\(632\) | 10.3171 | 0.410391 | ||||||||
\(633\) | 27.2840 | 1.08444 | ||||||||
\(634\) | 3.68507 | 0.146353 | ||||||||
\(635\) | −16.3534 | −0.648963 | ||||||||
\(636\) | −55.7035 | −2.20879 | ||||||||
\(637\) | −2.34431 | −0.0928850 | ||||||||
\(638\) | −9.45660 | −0.374391 | ||||||||
\(639\) | −12.3882 | −0.490068 | ||||||||
\(640\) | 9.26662 | 0.366295 | ||||||||
\(641\) | −9.31252 | −0.367822 | −0.183911 | − | 0.982943i | \(-0.558876\pi\) | ||||
−0.183911 | + | 0.982943i | \(0.558876\pi\) | |||||||
\(642\) | −10.0719 | −0.397508 | ||||||||
\(643\) | 29.5314 | 1.16461 | 0.582303 | − | 0.812972i | \(-0.302152\pi\) | ||||
0.582303 | + | 0.812972i | \(0.302152\pi\) | |||||||
\(644\) | 15.0716 | 0.593904 | ||||||||
\(645\) | 9.87084 | 0.388664 | ||||||||
\(646\) | 0.348201 | 0.0136998 | ||||||||
\(647\) | −26.9368 | −1.05899 | −0.529496 | − | 0.848312i | \(-0.677619\pi\) | ||||
−0.529496 | + | 0.848312i | \(0.677619\pi\) | |||||||
\(648\) | 14.3012 | 0.561805 | ||||||||
\(649\) | 31.6220 | 1.24127 | ||||||||
\(650\) | −0.785378 | −0.0308051 | ||||||||
\(651\) | −11.9043 | −0.466568 | ||||||||
\(652\) | 26.7441 | 1.04738 | ||||||||
\(653\) | 5.23289 | 0.204779 | 0.102389 | − | 0.994744i | \(-0.467351\pi\) | ||||
0.102389 | + | 0.994744i | \(0.467351\pi\) | |||||||
\(654\) | 3.84152 | 0.150215 | ||||||||
\(655\) | 8.49544 | 0.331944 | ||||||||
\(656\) | 14.1827 | 0.553743 | ||||||||
\(657\) | −12.7996 | −0.499359 | ||||||||
\(658\) | −1.62983 | −0.0635374 | ||||||||
\(659\) | 8.18222 | 0.318734 | 0.159367 | − | 0.987219i | \(-0.449055\pi\) | ||||
0.159367 | + | 0.987219i | \(0.449055\pi\) | |||||||
\(660\) | −13.0673 | −0.508645 | ||||||||
\(661\) | 36.5815 | 1.42286 | 0.711429 | − | 0.702758i | \(-0.248049\pi\) | ||||
0.711429 | + | 0.702758i | \(0.248049\pi\) | |||||||
\(662\) | 9.30958 | 0.361827 | ||||||||
\(663\) | 2.03530 | 0.0790446 | ||||||||
\(664\) | 12.6761 | 0.491926 | ||||||||
\(665\) | 2.68213 | 0.104009 | ||||||||
\(666\) | −0.673019 | −0.0260790 | ||||||||
\(667\) | −72.9410 | −2.82429 | ||||||||
\(668\) | −9.46227 | −0.366106 | ||||||||
\(669\) | −27.3671 | −1.05807 | ||||||||
\(670\) | 5.19033 | 0.200520 | ||||||||
\(671\) | −14.9701 | −0.577916 | ||||||||
\(672\) | 8.34237 | 0.321814 | ||||||||
\(673\) | 30.5860 | 1.17900 | 0.589502 | − | 0.807767i | \(-0.299324\pi\) | ||||
0.589502 | + | 0.807767i | \(0.299324\pi\) | |||||||
\(674\) | 1.16657 | 0.0449346 | ||||||||
\(675\) | 2.19687 | 0.0845574 | ||||||||
\(676\) | 14.1662 | 0.544853 | ||||||||
\(677\) | 24.9903 | 0.960455 | 0.480228 | − | 0.877144i | \(-0.340554\pi\) | ||||
0.480228 | + | 0.877144i | \(0.340554\pi\) | |||||||
\(678\) | −6.87841 | −0.264164 | ||||||||
\(679\) | −8.91853 | −0.342262 | ||||||||
\(680\) | 0.504719 | 0.0193551 | ||||||||
\(681\) | −59.9471 | −2.29718 | ||||||||
\(682\) | −5.49987 | −0.210601 | ||||||||
\(683\) | 39.1779 | 1.49910 | 0.749550 | − | 0.661948i | \(-0.230270\pi\) | ||||
0.749550 | + | 0.661948i | \(0.230270\pi\) | |||||||
\(684\) | −10.2249 | −0.390958 | ||||||||
\(685\) | 6.22459 | 0.237829 | ||||||||
\(686\) | −0.335014 | −0.0127909 | ||||||||
\(687\) | −2.24041 | −0.0854770 | ||||||||
\(688\) | 14.7119 | 0.560885 | ||||||||
\(689\) | 30.8761 | 1.17629 | ||||||||
\(690\) | 5.99242 | 0.228128 | ||||||||
\(691\) | −18.6598 | −0.709852 | −0.354926 | − | 0.934894i | \(-0.615494\pi\) | ||||
−0.354926 | + | 0.934894i | \(0.615494\pi\) | |||||||
\(692\) | −3.71151 | −0.141090 | ||||||||
\(693\) | −6.23938 | −0.237014 | ||||||||
\(694\) | 9.60258 | 0.364509 | ||||||||
\(695\) | 16.1363 | 0.612084 | ||||||||
\(696\) | −26.6595 | −1.01052 | ||||||||
\(697\) | 1.64591 | 0.0623432 | ||||||||
\(698\) | 2.05048 | 0.0776120 | ||||||||
\(699\) | 61.1177 | 2.31168 | ||||||||
\(700\) | 1.88777 | 0.0713508 | ||||||||
\(701\) | −0.375612 | −0.0141867 | −0.00709334 | − | 0.999975i | \(-0.502258\pi\) | ||||
−0.00709334 | + | 0.999975i | \(0.502258\pi\) | |||||||
\(702\) | −1.72537 | −0.0651199 | ||||||||
\(703\) | −2.66817 | −0.100632 | ||||||||
\(704\) | −16.7797 | −0.632410 | ||||||||
\(705\) | 10.8995 | 0.410499 | ||||||||
\(706\) | −0.550597 | −0.0207220 | ||||||||
\(707\) | 1.24600 | 0.0468607 | ||||||||
\(708\) | 43.2865 | 1.62681 | ||||||||
\(709\) | −7.74436 | −0.290845 | −0.145423 | − | 0.989370i | \(-0.546454\pi\) | ||||
−0.145423 | + | 0.989370i | \(0.546454\pi\) | |||||||
\(710\) | 2.05513 | 0.0771278 | ||||||||
\(711\) | −15.9964 | −0.599913 | ||||||||
\(712\) | −15.6030 | −0.584745 | ||||||||
\(713\) | −42.4218 | −1.58871 | ||||||||
\(714\) | 0.290855 | 0.0108850 | ||||||||
\(715\) | 7.24314 | 0.270878 | ||||||||
\(716\) | 11.5738 | 0.432534 | ||||||||
\(717\) | 21.6916 | 0.810087 | ||||||||
\(718\) | −3.26716 | −0.121929 | ||||||||
\(719\) | −37.2087 | −1.38765 | −0.693824 | − | 0.720144i | \(-0.744076\pi\) | ||||
−0.693824 | + | 0.720144i | \(0.744076\pi\) | |||||||
\(720\) | −6.74328 | −0.251307 | ||||||||
\(721\) | −8.02045 | −0.298697 | ||||||||
\(722\) | −3.95524 | −0.147199 | ||||||||
\(723\) | −31.9675 | −1.18889 | ||||||||
\(724\) | 41.8466 | 1.55521 | ||||||||
\(725\) | −9.13609 | −0.339306 | ||||||||
\(726\) | 1.09131 | 0.0405023 | ||||||||
\(727\) | −9.80771 | −0.363748 | −0.181874 | − | 0.983322i | \(-0.558216\pi\) | ||||
−0.181874 | + | 0.983322i | \(0.558216\pi\) | |||||||
\(728\) | −3.05337 | −0.113165 | ||||||||
\(729\) | −7.40813 | −0.274375 | ||||||||
\(730\) | 2.12339 | 0.0785901 | ||||||||
\(731\) | 1.70731 | 0.0631472 | ||||||||
\(732\) | −20.4923 | −0.757416 | ||||||||
\(733\) | 16.8853 | 0.623673 | 0.311836 | − | 0.950136i | \(-0.399056\pi\) | ||||
0.311836 | + | 0.950136i | \(0.399056\pi\) | |||||||
\(734\) | 5.65337 | 0.208670 | ||||||||
\(735\) | 2.24041 | 0.0826388 | ||||||||
\(736\) | 29.7285 | 1.09581 | ||||||||
\(737\) | −47.8677 | −1.76323 | ||||||||
\(738\) | 2.87351 | 0.105775 | ||||||||
\(739\) | −3.52987 | −0.129849 | −0.0649243 | − | 0.997890i | \(-0.520681\pi\) | ||||
−0.0649243 | + | 0.997890i | \(0.520681\pi\) | |||||||
\(740\) | −1.87794 | −0.0690345 | ||||||||
\(741\) | 14.0871 | 0.517504 | ||||||||
\(742\) | 4.41236 | 0.161983 | ||||||||
\(743\) | −34.9510 | −1.28223 | −0.641114 | − | 0.767445i | \(-0.721528\pi\) | ||||
−0.641114 | + | 0.767445i | \(0.721528\pi\) | |||||||
\(744\) | −15.5049 | −0.568437 | ||||||||
\(745\) | 4.91856 | 0.180202 | ||||||||
\(746\) | −5.18866 | −0.189970 | ||||||||
\(747\) | −19.6540 | −0.719102 | ||||||||
\(748\) | −2.26019 | −0.0826408 | ||||||||
\(749\) | −13.4191 | −0.490322 | ||||||||
\(750\) | 0.750569 | 0.0274069 | ||||||||
\(751\) | −41.7657 | −1.52405 | −0.762025 | − | 0.647547i | \(-0.775795\pi\) | ||||
−0.762025 | + | 0.647547i | \(0.775795\pi\) | |||||||
\(752\) | 16.2450 | 0.592395 | ||||||||
\(753\) | −50.8178 | −1.85190 | ||||||||
\(754\) | 7.17529 | 0.261309 | ||||||||
\(755\) | −11.6046 | −0.422336 | ||||||||
\(756\) | 4.14717 | 0.150831 | ||||||||
\(757\) | −9.56815 | −0.347760 | −0.173880 | − | 0.984767i | \(-0.555631\pi\) | ||||
−0.173880 | + | 0.984767i | \(0.555631\pi\) | |||||||
\(758\) | −4.51297 | −0.163919 | ||||||||
\(759\) | −55.2650 | −2.00599 | ||||||||
\(760\) | 3.49336 | 0.126717 | ||||||||
\(761\) | 24.5402 | 0.889581 | 0.444790 | − | 0.895635i | \(-0.353278\pi\) | ||||
0.444790 | + | 0.895635i | \(0.353278\pi\) | |||||||
\(762\) | −12.2743 | −0.444652 | ||||||||
\(763\) | 5.11814 | 0.185289 | ||||||||
\(764\) | −6.91487 | −0.250171 | ||||||||
\(765\) | −0.782557 | −0.0282934 | ||||||||
\(766\) | −1.62473 | −0.0587037 | ||||||||
\(767\) | −23.9935 | −0.866354 | ||||||||
\(768\) | −17.3797 | −0.627137 | ||||||||
\(769\) | 1.72991 | 0.0623821 | 0.0311910 | − | 0.999513i | \(-0.490070\pi\) | ||||
0.0311910 | + | 0.999513i | \(0.490070\pi\) | |||||||
\(770\) | 1.03508 | 0.0373018 | ||||||||
\(771\) | −38.6487 | −1.39190 | ||||||||
\(772\) | 10.7421 | 0.386617 | ||||||||
\(773\) | 37.3269 | 1.34256 | 0.671278 | − | 0.741206i | \(-0.265746\pi\) | ||||
0.671278 | + | 0.741206i | \(0.265746\pi\) | |||||||
\(774\) | 2.98071 | 0.107140 | ||||||||
\(775\) | −5.31346 | −0.190865 | ||||||||
\(776\) | −11.6160 | −0.416990 | ||||||||
\(777\) | −2.22875 | −0.0799560 | ||||||||
\(778\) | 0.604379 | 0.0216680 | ||||||||
\(779\) | 11.3920 | 0.408160 | ||||||||
\(780\) | 9.91496 | 0.355013 | ||||||||
\(781\) | −18.9534 | −0.678207 | ||||||||
\(782\) | 1.03648 | 0.0370645 | ||||||||
\(783\) | −20.0708 | −0.717271 | ||||||||
\(784\) | 3.33919 | 0.119257 | ||||||||
\(785\) | −13.3293 | −0.475745 | ||||||||
\(786\) | 6.37641 | 0.227439 | ||||||||
\(787\) | 0.999973 | 0.0356452 | 0.0178226 | − | 0.999841i | \(-0.494327\pi\) | ||||
0.0178226 | + | 0.999841i | \(0.494327\pi\) | |||||||
\(788\) | 21.4282 | 0.763348 | ||||||||
\(789\) | −39.9618 | −1.42268 | ||||||||
\(790\) | 2.65373 | 0.0944154 | ||||||||
\(791\) | −9.16426 | −0.325843 | ||||||||
\(792\) | −8.12652 | −0.288763 | ||||||||
\(793\) | 11.3587 | 0.403361 | ||||||||
\(794\) | 3.24062 | 0.115005 | ||||||||
\(795\) | −29.5076 | −1.04653 | ||||||||
\(796\) | −11.3768 | −0.403241 | ||||||||
\(797\) | −5.95192 | −0.210828 | −0.105414 | − | 0.994428i | \(-0.533617\pi\) | ||||
−0.105414 | + | 0.994428i | \(0.533617\pi\) | |||||||
\(798\) | 2.01312 | 0.0712639 | ||||||||
\(799\) | 1.88523 | 0.0666948 | ||||||||
\(800\) | 3.72359 | 0.131649 | ||||||||
\(801\) | 24.1921 | 0.854785 | ||||||||
\(802\) | 1.65155 | 0.0583184 | ||||||||
\(803\) | −19.5829 | −0.691066 | ||||||||
\(804\) | −65.5249 | −2.31089 | ||||||||
\(805\) | 7.98383 | 0.281393 | ||||||||
\(806\) | 4.17308 | 0.146990 | ||||||||
\(807\) | −48.8976 | −1.72128 | ||||||||
\(808\) | 1.62286 | 0.0570921 | ||||||||
\(809\) | 5.05286 | 0.177649 | 0.0888245 | − | 0.996047i | \(-0.471689\pi\) | ||||
0.0888245 | + | 0.996047i | \(0.471689\pi\) | |||||||
\(810\) | 3.67852 | 0.129250 | ||||||||
\(811\) | 28.0490 | 0.984935 | 0.492467 | − | 0.870331i | \(-0.336095\pi\) | ||||
0.492467 | + | 0.870331i | \(0.336095\pi\) | |||||||
\(812\) | −17.2468 | −0.605244 | ||||||||
\(813\) | −24.8802 | −0.872587 | ||||||||
\(814\) | −1.02970 | −0.0360908 | ||||||||
\(815\) | 14.1670 | 0.496250 | ||||||||
\(816\) | −2.89904 | −0.101487 | ||||||||
\(817\) | 11.8170 | 0.413424 | ||||||||
\(818\) | −1.82176 | −0.0636965 | ||||||||
\(819\) | 4.73419 | 0.165426 | ||||||||
\(820\) | 8.01802 | 0.280001 | ||||||||
\(821\) | −7.31960 | −0.255456 | −0.127728 | − | 0.991809i | \(-0.540768\pi\) | ||||
−0.127728 | + | 0.991809i | \(0.540768\pi\) | |||||||
\(822\) | 4.67199 | 0.162954 | ||||||||
\(823\) | −17.9358 | −0.625202 | −0.312601 | − | 0.949884i | \(-0.601200\pi\) | ||||
−0.312601 | + | 0.949884i | \(0.601200\pi\) | |||||||
\(824\) | −10.4463 | −0.363914 | ||||||||
\(825\) | −6.92211 | −0.240997 | ||||||||
\(826\) | −3.42879 | −0.119303 | ||||||||
\(827\) | −4.40875 | −0.153307 | −0.0766537 | − | 0.997058i | \(-0.524424\pi\) | ||||
−0.0766537 | + | 0.997058i | \(0.524424\pi\) | |||||||
\(828\) | −30.4361 | −1.05773 | ||||||||
\(829\) | 1.28356 | 0.0445800 | 0.0222900 | − | 0.999752i | \(-0.492904\pi\) | ||||
0.0222900 | + | 0.999752i | \(0.492904\pi\) | |||||||
\(830\) | 3.26050 | 0.113174 | ||||||||
\(831\) | −47.5659 | −1.65004 | ||||||||
\(832\) | 12.7318 | 0.441395 | ||||||||
\(833\) | 0.387513 | 0.0134265 | ||||||||
\(834\) | 12.1114 | 0.419383 | ||||||||
\(835\) | −5.01242 | −0.173462 | ||||||||
\(836\) | −15.6437 | −0.541048 | ||||||||
\(837\) | −11.6730 | −0.403477 | ||||||||
\(838\) | 1.06909 | 0.0369311 | ||||||||
\(839\) | −35.5928 | −1.22880 | −0.614401 | − | 0.788994i | \(-0.710602\pi\) | ||||
−0.614401 | + | 0.788994i | \(0.710602\pi\) | |||||||
\(840\) | 2.91804 | 0.100682 | ||||||||
\(841\) | 54.4682 | 1.87821 | ||||||||
\(842\) | −1.41509 | −0.0487674 | ||||||||
\(843\) | 23.8805 | 0.822490 | ||||||||
\(844\) | 22.9894 | 0.791328 | ||||||||
\(845\) | 7.50420 | 0.258152 | ||||||||
\(846\) | 3.29134 | 0.113159 | ||||||||
\(847\) | 1.45398 | 0.0499592 | ||||||||
\(848\) | −43.9793 | −1.51025 | ||||||||
\(849\) | 36.7762 | 1.26216 | ||||||||
\(850\) | 0.129822 | 0.00445287 | ||||||||
\(851\) | −7.94228 | −0.272258 | ||||||||
\(852\) | −25.9449 | −0.888858 | ||||||||
\(853\) | −11.0497 | −0.378334 | −0.189167 | − | 0.981945i | \(-0.560579\pi\) | ||||
−0.189167 | + | 0.981945i | \(0.560579\pi\) | |||||||
\(854\) | 1.62322 | 0.0555455 | ||||||||
\(855\) | −5.41639 | −0.185237 | ||||||||
\(856\) | −17.4778 | −0.597378 | ||||||||
\(857\) | −18.5622 | −0.634072 | −0.317036 | − | 0.948413i | \(-0.602688\pi\) | ||||
−0.317036 | + | 0.948413i | \(0.602688\pi\) | |||||||
\(858\) | 5.43648 | 0.185598 | ||||||||
\(859\) | 48.5446 | 1.65632 | 0.828160 | − | 0.560491i | \(-0.189388\pi\) | ||||
0.828160 | + | 0.560491i | \(0.189388\pi\) | |||||||
\(860\) | 8.31715 | 0.283613 | ||||||||
\(861\) | 9.51583 | 0.324299 | ||||||||
\(862\) | 10.3202 | 0.351506 | ||||||||
\(863\) | 18.5868 | 0.632701 | 0.316350 | − | 0.948642i | \(-0.397542\pi\) | ||||
0.316350 | + | 0.948642i | \(0.397542\pi\) | |||||||
\(864\) | 8.18023 | 0.278297 | ||||||||
\(865\) | −1.96609 | −0.0668489 | ||||||||
\(866\) | 4.48774 | 0.152500 | ||||||||
\(867\) | 37.7505 | 1.28208 | ||||||||
\(868\) | −10.0306 | −0.340460 | ||||||||
\(869\) | −24.4740 | −0.830222 | ||||||||
\(870\) | −6.85727 | −0.232483 | ||||||||
\(871\) | 36.3201 | 1.23066 | ||||||||
\(872\) | 6.66615 | 0.225744 | ||||||||
\(873\) | 18.0104 | 0.609559 | ||||||||
\(874\) | 7.17389 | 0.242660 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −26.8066 | −0.905710 | ||||||||
\(877\) | −3.11892 | −0.105318 | −0.0526592 | − | 0.998613i | \(-0.516770\pi\) | ||||
−0.0526592 | + | 0.998613i | \(0.516770\pi\) | |||||||
\(878\) | −6.55823 | −0.221330 | ||||||||
\(879\) | 24.8446 | 0.837989 | ||||||||
\(880\) | −10.3170 | −0.347785 | ||||||||
\(881\) | −3.25242 | −0.109577 | −0.0547885 | − | 0.998498i | \(-0.517448\pi\) | ||||
−0.0547885 | + | 0.998498i | \(0.517448\pi\) | |||||||
\(882\) | 0.676540 | 0.0227803 | ||||||||
\(883\) | 2.80699 | 0.0944627 | 0.0472314 | − | 0.998884i | \(-0.484960\pi\) | ||||
0.0472314 | + | 0.998884i | \(0.484960\pi\) | |||||||
\(884\) | 1.71494 | 0.0576798 | ||||||||
\(885\) | 22.9300 | 0.770785 | ||||||||
\(886\) | 13.8695 | 0.465955 | ||||||||
\(887\) | −20.4029 | −0.685063 | −0.342532 | − | 0.939506i | \(-0.611284\pi\) | ||||
−0.342532 | + | 0.939506i | \(0.611284\pi\) | |||||||
\(888\) | −2.90285 | −0.0974133 | ||||||||
\(889\) | −16.3534 | −0.548474 | ||||||||
\(890\) | −4.01335 | −0.134528 | ||||||||
\(891\) | −33.9251 | −1.13653 | ||||||||
\(892\) | −23.0595 | −0.772089 | ||||||||
\(893\) | 13.0485 | 0.436650 | ||||||||
\(894\) | 3.69172 | 0.123470 | ||||||||
\(895\) | 6.13097 | 0.204936 | ||||||||
\(896\) | 9.26662 | 0.309576 | ||||||||
\(897\) | 41.9329 | 1.40010 | ||||||||
\(898\) | −4.13706 | −0.138055 | ||||||||
\(899\) | 48.5443 | 1.61904 | ||||||||
\(900\) | −3.81222 | −0.127074 | ||||||||
\(901\) | −5.10380 | −0.170032 | ||||||||
\(902\) | 4.39637 | 0.146383 | ||||||||
\(903\) | 9.87084 | 0.328481 | ||||||||
\(904\) | −11.9360 | −0.396987 | ||||||||
\(905\) | 22.1672 | 0.736864 | ||||||||
\(906\) | −8.71008 | −0.289373 | ||||||||
\(907\) | −45.1193 | −1.49816 | −0.749081 | − | 0.662479i | \(-0.769505\pi\) | ||||
−0.749081 | + | 0.662479i | \(0.769505\pi\) | |||||||
\(908\) | −50.5113 | −1.67628 | ||||||||
\(909\) | −2.51622 | −0.0834576 | ||||||||
\(910\) | −0.785378 | −0.0260350 | ||||||||
\(911\) | −29.4454 | −0.975571 | −0.487785 | − | 0.872964i | \(-0.662195\pi\) | ||||
−0.487785 | + | 0.872964i | \(0.662195\pi\) | |||||||
\(912\) | −20.0654 | −0.664433 | ||||||||
\(913\) | −30.0699 | −0.995168 | ||||||||
\(914\) | 4.78269 | 0.158197 | ||||||||
\(915\) | −10.8553 | −0.358865 | ||||||||
\(916\) | −1.88777 | −0.0623735 | ||||||||
\(917\) | 8.49544 | 0.280544 | ||||||||
\(918\) | 0.285202 | 0.00941308 | ||||||||
\(919\) | 34.4829 | 1.13749 | 0.568743 | − | 0.822515i | \(-0.307430\pi\) | ||||
0.568743 | + | 0.822515i | \(0.307430\pi\) | |||||||
\(920\) | 10.3986 | 0.342832 | ||||||||
\(921\) | 4.93579 | 0.162640 | ||||||||
\(922\) | −5.48071 | −0.180498 | ||||||||
\(923\) | 14.3811 | 0.473360 | ||||||||
\(924\) | −13.0673 | −0.429883 | ||||||||
\(925\) | −0.994796 | −0.0327087 | ||||||||
\(926\) | −10.5609 | −0.347054 | ||||||||
\(927\) | 16.1968 | 0.531972 | ||||||||
\(928\) | −34.0191 | −1.11673 | ||||||||
\(929\) | −25.4432 | −0.834764 | −0.417382 | − | 0.908731i | \(-0.637052\pi\) | ||||
−0.417382 | + | 0.908731i | \(0.637052\pi\) | |||||||
\(930\) | −3.98812 | −0.130776 | ||||||||
\(931\) | 2.68213 | 0.0879033 | ||||||||
\(932\) | 51.4977 | 1.68686 | ||||||||
\(933\) | 13.5441 | 0.443415 | ||||||||
\(934\) | −4.09474 | −0.133984 | ||||||||
\(935\) | −1.19728 | −0.0391554 | ||||||||
\(936\) | 6.16608 | 0.201545 | ||||||||
\(937\) | 47.2850 | 1.54473 | 0.772367 | − | 0.635177i | \(-0.219073\pi\) | ||||
0.772367 | + | 0.635177i | \(0.219073\pi\) | |||||||
\(938\) | 5.19033 | 0.169470 | ||||||||
\(939\) | 6.57525 | 0.214575 | ||||||||
\(940\) | 9.18390 | 0.299546 | ||||||||
\(941\) | −32.3707 | −1.05525 | −0.527627 | − | 0.849476i | \(-0.676918\pi\) | ||||
−0.527627 | + | 0.849476i | \(0.676918\pi\) | |||||||
\(942\) | −10.0046 | −0.325967 | ||||||||
\(943\) | 33.9102 | 1.10427 | ||||||||
\(944\) | 34.1758 | 1.11233 | ||||||||
\(945\) | 2.19687 | 0.0714641 | ||||||||
\(946\) | 4.56038 | 0.148271 | ||||||||
\(947\) | 55.2679 | 1.79597 | 0.897983 | − | 0.440030i | \(-0.145032\pi\) | ||||
0.897983 | + | 0.440030i | \(0.145032\pi\) | |||||||
\(948\) | −33.5018 | −1.08809 | ||||||||
\(949\) | 14.8587 | 0.482334 | ||||||||
\(950\) | 0.898552 | 0.0291529 | ||||||||
\(951\) | −24.6439 | −0.799134 | ||||||||
\(952\) | 0.504719 | 0.0163580 | ||||||||
\(953\) | −40.2474 | −1.30374 | −0.651870 | − | 0.758331i | \(-0.726015\pi\) | ||||
−0.651870 | + | 0.758331i | \(0.726015\pi\) | |||||||
\(954\) | −8.91047 | −0.288487 | ||||||||
\(955\) | −3.66299 | −0.118532 | ||||||||
\(956\) | 18.2773 | 0.591130 | ||||||||
\(957\) | 63.2411 | 2.04429 | ||||||||
\(958\) | −1.65024 | −0.0533170 | ||||||||
\(959\) | 6.22459 | 0.201002 | ||||||||
\(960\) | −12.1675 | −0.392704 | ||||||||
\(961\) | −2.76713 | −0.0892621 | ||||||||
\(962\) | 0.781291 | 0.0251898 | ||||||||
\(963\) | 27.0990 | 0.873252 | ||||||||
\(964\) | −26.9358 | −0.867544 | ||||||||
\(965\) | 5.69038 | 0.183180 | ||||||||
\(966\) | 5.99242 | 0.192803 | ||||||||
\(967\) | 0.139045 | 0.00447140 | 0.00223570 | − | 0.999998i | \(-0.499288\pi\) | ||||
0.00223570 | + | 0.999998i | \(0.499288\pi\) | |||||||
\(968\) | 1.89374 | 0.0608671 | ||||||||
\(969\) | −2.32859 | −0.0748052 | ||||||||
\(970\) | −2.98784 | −0.0959336 | ||||||||
\(971\) | 30.2278 | 0.970057 | 0.485028 | − | 0.874498i | \(-0.338809\pi\) | ||||
0.485028 | + | 0.874498i | \(0.338809\pi\) | |||||||
\(972\) | −33.9977 | −1.09048 | ||||||||
\(973\) | 16.1363 | 0.517305 | ||||||||
\(974\) | 13.5045 | 0.432712 | ||||||||
\(975\) | 5.25222 | 0.168206 | ||||||||
\(976\) | −16.1791 | −0.517882 | ||||||||
\(977\) | 40.6852 | 1.30164 | 0.650818 | − | 0.759234i | \(-0.274426\pi\) | ||||
0.650818 | + | 0.759234i | \(0.274426\pi\) | |||||||
\(978\) | 10.6333 | 0.340017 | ||||||||
\(979\) | 37.0130 | 1.18294 | ||||||||
\(980\) | 1.88777 | 0.0603025 | ||||||||
\(981\) | −10.3357 | −0.329995 | ||||||||
\(982\) | 6.75517 | 0.215566 | ||||||||
\(983\) | 32.1677 | 1.02599 | 0.512996 | − | 0.858391i | \(-0.328536\pi\) | ||||
0.512996 | + | 0.858391i | \(0.328536\pi\) | |||||||
\(984\) | 12.3940 | 0.395105 | ||||||||
\(985\) | 11.3511 | 0.361676 | ||||||||
\(986\) | −1.18607 | −0.0377721 | ||||||||
\(987\) | 10.8995 | 0.346935 | ||||||||
\(988\) | 11.8698 | 0.377629 | ||||||||
\(989\) | 35.1753 | 1.11851 | ||||||||
\(990\) | −2.09028 | −0.0664335 | ||||||||
\(991\) | 14.8819 | 0.472739 | 0.236369 | − | 0.971663i | \(-0.424042\pi\) | ||||
0.236369 | + | 0.971663i | \(0.424042\pi\) | |||||||
\(992\) | −19.7852 | −0.628179 | ||||||||
\(993\) | −62.2579 | −1.97569 | ||||||||
\(994\) | 2.05513 | 0.0651849 | ||||||||
\(995\) | −6.02661 | −0.191057 | ||||||||
\(996\) | −41.1620 | −1.30427 | ||||||||
\(997\) | 54.4571 | 1.72467 | 0.862337 | − | 0.506335i | \(-0.169000\pi\) | ||||
0.862337 | + | 0.506335i | \(0.169000\pi\) | |||||||
\(998\) | −2.78354 | −0.0881115 | ||||||||
\(999\) | −2.18543 | −0.0691441 |
(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 | 8015.2.a.l.1.36 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.36 | ✓ | 62 | 1.1 | even | 1 | trivial |