Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8619,2,Mod(1,8619)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8619, 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("8619.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8619 = 3 \cdot 13^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8619.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: | \(68.8230615021\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8619.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.575048 | 0.406620 | 0.203310 | − | 0.979114i | \(-0.434830\pi\) | ||||
0.203310 | + | 0.979114i | \(0.434830\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.66932 | −0.834660 | ||||||||
\(5\) | 1.38919 | 0.621264 | 0.310632 | − | 0.950530i | \(-0.399459\pi\) | ||||
0.310632 | + | 0.950530i | \(0.399459\pi\) | |||||||
\(6\) | 0.575048 | 0.234762 | ||||||||
\(7\) | −4.30260 | −1.62623 | −0.813116 | − | 0.582102i | \(-0.802230\pi\) | ||||
−0.813116 | + | 0.582102i | \(0.802230\pi\) | |||||||
\(8\) | −2.11004 | −0.746010 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.798850 | 0.252619 | ||||||||
\(11\) | 0.556120 | 0.167677 | 0.0838383 | − | 0.996479i | \(-0.473282\pi\) | ||||
0.0838383 | + | 0.996479i | \(0.473282\pi\) | |||||||
\(12\) | −1.66932 | −0.481891 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −2.47420 | −0.661259 | ||||||||
\(15\) | 1.38919 | 0.358687 | ||||||||
\(16\) | 2.12527 | 0.531317 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0.575048 | 0.135540 | ||||||||
\(19\) | −7.33062 | −1.68176 | −0.840880 | − | 0.541222i | \(-0.817962\pi\) | ||||
−0.840880 | + | 0.541222i | \(0.817962\pi\) | |||||||
\(20\) | −2.31900 | −0.518544 | ||||||||
\(21\) | −4.30260 | −0.938905 | ||||||||
\(22\) | 0.319796 | 0.0681807 | ||||||||
\(23\) | −9.41329 | −1.96281 | −0.981403 | − | 0.191958i | \(-0.938516\pi\) | ||||
−0.981403 | + | 0.191958i | \(0.938516\pi\) | |||||||
\(24\) | −2.11004 | −0.430709 | ||||||||
\(25\) | −3.07016 | −0.614031 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 7.18242 | 1.35735 | ||||||||
\(29\) | 6.13375 | 1.13901 | 0.569504 | − | 0.821988i | \(-0.307135\pi\) | ||||
0.569504 | + | 0.821988i | \(0.307135\pi\) | |||||||
\(30\) | 0.798850 | 0.145849 | ||||||||
\(31\) | 5.57311 | 1.00096 | 0.500480 | − | 0.865748i | \(-0.333157\pi\) | ||||
0.500480 | + | 0.865748i | \(0.333157\pi\) | |||||||
\(32\) | 5.44220 | 0.962054 | ||||||||
\(33\) | 0.556120 | 0.0968082 | ||||||||
\(34\) | −0.575048 | −0.0986199 | ||||||||
\(35\) | −5.97713 | −1.01032 | ||||||||
\(36\) | −1.66932 | −0.278220 | ||||||||
\(37\) | −2.07677 | −0.341419 | −0.170709 | − | 0.985321i | \(-0.554606\pi\) | ||||
−0.170709 | + | 0.985321i | \(0.554606\pi\) | |||||||
\(38\) | −4.21546 | −0.683838 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.93124 | −0.463469 | ||||||||
\(41\) | 5.45346 | 0.851688 | 0.425844 | − | 0.904797i | \(-0.359977\pi\) | ||||
0.425844 | + | 0.904797i | \(0.359977\pi\) | |||||||
\(42\) | −2.47420 | −0.381778 | ||||||||
\(43\) | −8.29324 | −1.26471 | −0.632354 | − | 0.774680i | \(-0.717911\pi\) | ||||
−0.632354 | + | 0.774680i | \(0.717911\pi\) | |||||||
\(44\) | −0.928343 | −0.139953 | ||||||||
\(45\) | 1.38919 | 0.207088 | ||||||||
\(46\) | −5.41309 | −0.798117 | ||||||||
\(47\) | 7.47038 | 1.08967 | 0.544833 | − | 0.838544i | \(-0.316593\pi\) | ||||
0.544833 | + | 0.838544i | \(0.316593\pi\) | |||||||
\(48\) | 2.12527 | 0.306756 | ||||||||
\(49\) | 11.5124 | 1.64463 | ||||||||
\(50\) | −1.76549 | −0.249678 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.69124 | −0.781752 | −0.390876 | − | 0.920443i | \(-0.627828\pi\) | ||||
−0.390876 | + | 0.920443i | \(0.627828\pi\) | |||||||
\(54\) | 0.575048 | 0.0782541 | ||||||||
\(55\) | 0.772556 | 0.104171 | ||||||||
\(56\) | 9.07865 | 1.21319 | ||||||||
\(57\) | −7.33062 | −0.970964 | ||||||||
\(58\) | 3.52720 | 0.463144 | ||||||||
\(59\) | 0.523791 | 0.0681918 | 0.0340959 | − | 0.999419i | \(-0.489145\pi\) | ||||
0.0340959 | + | 0.999419i | \(0.489145\pi\) | |||||||
\(60\) | −2.31900 | −0.299382 | ||||||||
\(61\) | −0.333468 | −0.0426962 | −0.0213481 | − | 0.999772i | \(-0.506796\pi\) | ||||
−0.0213481 | + | 0.999772i | \(0.506796\pi\) | |||||||
\(62\) | 3.20481 | 0.407011 | ||||||||
\(63\) | −4.30260 | −0.542077 | ||||||||
\(64\) | −1.12101 | −0.140126 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.319796 | 0.0393642 | ||||||||
\(67\) | 5.02874 | 0.614358 | 0.307179 | − | 0.951652i | \(-0.400615\pi\) | ||||
0.307179 | + | 0.951652i | \(0.400615\pi\) | |||||||
\(68\) | 1.66932 | 0.202435 | ||||||||
\(69\) | −9.41329 | −1.13323 | ||||||||
\(70\) | −3.43714 | −0.410816 | ||||||||
\(71\) | 7.85716 | 0.932474 | 0.466237 | − | 0.884660i | \(-0.345609\pi\) | ||||
0.466237 | + | 0.884660i | \(0.345609\pi\) | |||||||
\(72\) | −2.11004 | −0.248670 | ||||||||
\(73\) | 12.9237 | 1.51261 | 0.756303 | − | 0.654221i | \(-0.227003\pi\) | ||||
0.756303 | + | 0.654221i | \(0.227003\pi\) | |||||||
\(74\) | −1.19424 | −0.138828 | ||||||||
\(75\) | −3.07016 | −0.354511 | ||||||||
\(76\) | 12.2371 | 1.40370 | ||||||||
\(77\) | −2.39277 | −0.272681 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.3004 | 1.27139 | 0.635695 | − | 0.771940i | \(-0.280714\pi\) | ||||
0.635695 | + | 0.771940i | \(0.280714\pi\) | |||||||
\(80\) | 2.95240 | 0.330088 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.13600 | 0.346314 | ||||||||
\(83\) | −3.66884 | −0.402708 | −0.201354 | − | 0.979519i | \(-0.564534\pi\) | ||||
−0.201354 | + | 0.979519i | \(0.564534\pi\) | |||||||
\(84\) | 7.18242 | 0.783667 | ||||||||
\(85\) | −1.38919 | −0.150679 | ||||||||
\(86\) | −4.76901 | −0.514256 | ||||||||
\(87\) | 6.13375 | 0.657607 | ||||||||
\(88\) | −1.17343 | −0.125088 | ||||||||
\(89\) | 9.80657 | 1.03949 | 0.519747 | − | 0.854320i | \(-0.326026\pi\) | ||||
0.519747 | + | 0.854320i | \(0.326026\pi\) | |||||||
\(90\) | 0.798850 | 0.0842062 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 15.7138 | 1.63828 | ||||||||
\(93\) | 5.57311 | 0.577905 | ||||||||
\(94\) | 4.29583 | 0.443081 | ||||||||
\(95\) | −10.1836 | −1.04482 | ||||||||
\(96\) | 5.44220 | 0.555442 | ||||||||
\(97\) | 0.527132 | 0.0535222 | 0.0267611 | − | 0.999642i | \(-0.491481\pi\) | ||||
0.0267611 | + | 0.999642i | \(0.491481\pi\) | |||||||
\(98\) | 6.62019 | 0.668740 | ||||||||
\(99\) | 0.556120 | 0.0558922 | ||||||||
\(100\) | 5.12507 | 0.512507 | ||||||||
\(101\) | 7.17027 | 0.713469 | 0.356734 | − | 0.934206i | \(-0.383890\pi\) | ||||
0.356734 | + | 0.934206i | \(0.383890\pi\) | |||||||
\(102\) | −0.575048 | −0.0569382 | ||||||||
\(103\) | 5.76258 | 0.567804 | 0.283902 | − | 0.958853i | \(-0.408371\pi\) | ||||
0.283902 | + | 0.958853i | \(0.408371\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.97713 | −0.583308 | ||||||||
\(106\) | −3.27274 | −0.317876 | ||||||||
\(107\) | −9.66909 | −0.934747 | −0.467373 | − | 0.884060i | \(-0.654800\pi\) | ||||
−0.467373 | + | 0.884060i | \(0.654800\pi\) | |||||||
\(108\) | −1.66932 | −0.160630 | ||||||||
\(109\) | −12.3646 | −1.18431 | −0.592156 | − | 0.805823i | \(-0.701723\pi\) | ||||
−0.592156 | + | 0.805823i | \(0.701723\pi\) | |||||||
\(110\) | 0.444257 | 0.0423582 | ||||||||
\(111\) | −2.07677 | −0.197118 | ||||||||
\(112\) | −9.14419 | −0.864045 | ||||||||
\(113\) | −7.09878 | −0.667797 | −0.333898 | − | 0.942609i | \(-0.608364\pi\) | ||||
−0.333898 | + | 0.942609i | \(0.608364\pi\) | |||||||
\(114\) | −4.21546 | −0.394814 | ||||||||
\(115\) | −13.0768 | −1.21942 | ||||||||
\(116\) | −10.2392 | −0.950685 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.301205 | 0.0277282 | ||||||||
\(119\) | 4.30260 | 0.394419 | ||||||||
\(120\) | −2.93124 | −0.267584 | ||||||||
\(121\) | −10.6907 | −0.971885 | ||||||||
\(122\) | −0.191760 | −0.0173611 | ||||||||
\(123\) | 5.45346 | 0.491722 | ||||||||
\(124\) | −9.30331 | −0.835462 | ||||||||
\(125\) | −11.2110 | −1.00274 | ||||||||
\(126\) | −2.47420 | −0.220420 | ||||||||
\(127\) | 18.4645 | 1.63846 | 0.819231 | − | 0.573463i | \(-0.194401\pi\) | ||||
0.819231 | + | 0.573463i | \(0.194401\pi\) | |||||||
\(128\) | −11.5290 | −1.01903 | ||||||||
\(129\) | −8.29324 | −0.730179 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.23991 | −0.283072 | −0.141536 | − | 0.989933i | \(-0.545204\pi\) | ||||
−0.141536 | + | 0.989933i | \(0.545204\pi\) | |||||||
\(132\) | −0.928343 | −0.0808019 | ||||||||
\(133\) | 31.5408 | 2.73493 | ||||||||
\(134\) | 2.89177 | 0.249811 | ||||||||
\(135\) | 1.38919 | 0.119562 | ||||||||
\(136\) | 2.11004 | 0.180934 | ||||||||
\(137\) | 13.4040 | 1.14518 | 0.572592 | − | 0.819840i | \(-0.305938\pi\) | ||||
0.572592 | + | 0.819840i | \(0.305938\pi\) | |||||||
\(138\) | −5.41309 | −0.460793 | ||||||||
\(139\) | 11.6895 | 0.991494 | 0.495747 | − | 0.868467i | \(-0.334894\pi\) | ||||
0.495747 | + | 0.868467i | \(0.334894\pi\) | |||||||
\(140\) | 9.97774 | 0.843273 | ||||||||
\(141\) | 7.47038 | 0.629119 | ||||||||
\(142\) | 4.51825 | 0.379163 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.12527 | 0.177106 | ||||||||
\(145\) | 8.52093 | 0.707625 | ||||||||
\(146\) | 7.43176 | 0.615057 | ||||||||
\(147\) | 11.5124 | 0.949527 | ||||||||
\(148\) | 3.46679 | 0.284968 | ||||||||
\(149\) | 15.8060 | 1.29488 | 0.647438 | − | 0.762118i | \(-0.275841\pi\) | ||||
0.647438 | + | 0.762118i | \(0.275841\pi\) | |||||||
\(150\) | −1.76549 | −0.144151 | ||||||||
\(151\) | −5.26099 | −0.428133 | −0.214067 | − | 0.976819i | \(-0.568671\pi\) | ||||
−0.214067 | + | 0.976819i | \(0.568671\pi\) | |||||||
\(152\) | 15.4679 | 1.25461 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −1.37596 | −0.110878 | ||||||||
\(155\) | 7.74211 | 0.621861 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.9972 | −0.957483 | −0.478741 | − | 0.877956i | \(-0.658907\pi\) | ||||
−0.478741 | + | 0.877956i | \(0.658907\pi\) | |||||||
\(158\) | 6.49825 | 0.516973 | ||||||||
\(159\) | −5.69124 | −0.451345 | ||||||||
\(160\) | 7.56024 | 0.597690 | ||||||||
\(161\) | 40.5017 | 3.19198 | ||||||||
\(162\) | 0.575048 | 0.0451800 | ||||||||
\(163\) | 18.3521 | 1.43745 | 0.718725 | − | 0.695294i | \(-0.244726\pi\) | ||||
0.718725 | + | 0.695294i | \(0.244726\pi\) | |||||||
\(164\) | −9.10358 | −0.710870 | ||||||||
\(165\) | 0.772556 | 0.0601434 | ||||||||
\(166\) | −2.10976 | −0.163749 | ||||||||
\(167\) | −18.3480 | −1.41981 | −0.709905 | − | 0.704297i | \(-0.751262\pi\) | ||||
−0.709905 | + | 0.704297i | \(0.751262\pi\) | |||||||
\(168\) | 9.07865 | 0.700433 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −0.798850 | −0.0612690 | ||||||||
\(171\) | −7.33062 | −0.560586 | ||||||||
\(172\) | 13.8441 | 1.05560 | ||||||||
\(173\) | 0.155919 | 0.0118543 | 0.00592715 | − | 0.999982i | \(-0.498113\pi\) | ||||
0.00592715 | + | 0.999982i | \(0.498113\pi\) | |||||||
\(174\) | 3.52720 | 0.267396 | ||||||||
\(175\) | 13.2097 | 0.998557 | ||||||||
\(176\) | 1.18191 | 0.0890894 | ||||||||
\(177\) | 0.523791 | 0.0393705 | ||||||||
\(178\) | 5.63925 | 0.422680 | ||||||||
\(179\) | 17.5244 | 1.30983 | 0.654916 | − | 0.755702i | \(-0.272704\pi\) | ||||
0.654916 | + | 0.755702i | \(0.272704\pi\) | |||||||
\(180\) | −2.31900 | −0.172848 | ||||||||
\(181\) | 6.66347 | 0.495291 | 0.247646 | − | 0.968851i | \(-0.420343\pi\) | ||||
0.247646 | + | 0.968851i | \(0.420343\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.333468 | −0.0246506 | ||||||||
\(184\) | 19.8624 | 1.46427 | ||||||||
\(185\) | −2.88502 | −0.212111 | ||||||||
\(186\) | 3.20481 | 0.234988 | ||||||||
\(187\) | −0.556120 | −0.0406676 | ||||||||
\(188\) | −12.4705 | −0.909501 | ||||||||
\(189\) | −4.30260 | −0.312968 | ||||||||
\(190\) | −5.85607 | −0.424844 | ||||||||
\(191\) | −8.21408 | −0.594350 | −0.297175 | − | 0.954823i | \(-0.596045\pi\) | ||||
−0.297175 | + | 0.954823i | \(0.596045\pi\) | |||||||
\(192\) | −1.12101 | −0.0809018 | ||||||||
\(193\) | 4.39726 | 0.316522 | 0.158261 | − | 0.987397i | \(-0.449411\pi\) | ||||
0.158261 | + | 0.987397i | \(0.449411\pi\) | |||||||
\(194\) | 0.303126 | 0.0217632 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −19.2179 | −1.37271 | ||||||||
\(197\) | −17.5911 | −1.25331 | −0.626656 | − | 0.779296i | \(-0.715577\pi\) | ||||
−0.626656 | + | 0.779296i | \(0.715577\pi\) | |||||||
\(198\) | 0.319796 | 0.0227269 | ||||||||
\(199\) | −26.7645 | −1.89729 | −0.948643 | − | 0.316349i | \(-0.897543\pi\) | ||||
−0.948643 | + | 0.316349i | \(0.897543\pi\) | |||||||
\(200\) | 6.47814 | 0.458073 | ||||||||
\(201\) | 5.02874 | 0.354700 | ||||||||
\(202\) | 4.12325 | 0.290111 | ||||||||
\(203\) | −26.3911 | −1.85229 | ||||||||
\(204\) | 1.66932 | 0.116876 | ||||||||
\(205\) | 7.57589 | 0.529123 | ||||||||
\(206\) | 3.31376 | 0.230881 | ||||||||
\(207\) | −9.41329 | −0.654269 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.07671 | −0.281992 | ||||||||
\(210\) | −3.43714 | −0.237185 | ||||||||
\(211\) | −15.2569 | −1.05033 | −0.525164 | − | 0.851001i | \(-0.675996\pi\) | ||||
−0.525164 | + | 0.851001i | \(0.675996\pi\) | |||||||
\(212\) | 9.50050 | 0.652497 | ||||||||
\(213\) | 7.85716 | 0.538364 | ||||||||
\(214\) | −5.56019 | −0.380087 | ||||||||
\(215\) | −11.5209 | −0.785717 | ||||||||
\(216\) | −2.11004 | −0.143570 | ||||||||
\(217\) | −23.9789 | −1.62779 | ||||||||
\(218\) | −7.11023 | −0.481565 | ||||||||
\(219\) | 12.9237 | 0.873304 | ||||||||
\(220\) | −1.28964 | −0.0869477 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1.19424 | −0.0801522 | ||||||||
\(223\) | −2.75963 | −0.184798 | −0.0923992 | − | 0.995722i | \(-0.529454\pi\) | ||||
−0.0923992 | + | 0.995722i | \(0.529454\pi\) | |||||||
\(224\) | −23.4156 | −1.56452 | ||||||||
\(225\) | −3.07016 | −0.204677 | ||||||||
\(226\) | −4.08214 | −0.271540 | ||||||||
\(227\) | −12.1227 | −0.804609 | −0.402305 | − | 0.915506i | \(-0.631791\pi\) | ||||
−0.402305 | + | 0.915506i | \(0.631791\pi\) | |||||||
\(228\) | 12.2371 | 0.810425 | ||||||||
\(229\) | 22.1475 | 1.46355 | 0.731774 | − | 0.681548i | \(-0.238693\pi\) | ||||
0.731774 | + | 0.681548i | \(0.238693\pi\) | |||||||
\(230\) | −7.51981 | −0.495841 | ||||||||
\(231\) | −2.39277 | −0.157432 | ||||||||
\(232\) | −12.9424 | −0.849712 | ||||||||
\(233\) | −22.3005 | −1.46096 | −0.730478 | − | 0.682936i | \(-0.760703\pi\) | ||||
−0.730478 | + | 0.682936i | \(0.760703\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.3778 | 0.676971 | ||||||||
\(236\) | −0.874374 | −0.0569169 | ||||||||
\(237\) | 11.3004 | 0.734037 | ||||||||
\(238\) | 2.47420 | 0.160379 | ||||||||
\(239\) | 13.6415 | 0.882396 | 0.441198 | − | 0.897410i | \(-0.354554\pi\) | ||||
0.441198 | + | 0.897410i | \(0.354554\pi\) | |||||||
\(240\) | 2.95240 | 0.190576 | ||||||||
\(241\) | 15.9632 | 1.02828 | 0.514140 | − | 0.857706i | \(-0.328111\pi\) | ||||
0.514140 | + | 0.857706i | \(0.328111\pi\) | |||||||
\(242\) | −6.14768 | −0.395188 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0.556664 | 0.0356368 | ||||||||
\(245\) | 15.9929 | 1.02175 | ||||||||
\(246\) | 3.13600 | 0.199944 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −11.7595 | −0.746727 | ||||||||
\(249\) | −3.66884 | −0.232504 | ||||||||
\(250\) | −6.44684 | −0.407734 | ||||||||
\(251\) | 13.3503 | 0.842664 | 0.421332 | − | 0.906906i | \(-0.361563\pi\) | ||||
0.421332 | + | 0.906906i | \(0.361563\pi\) | |||||||
\(252\) | 7.18242 | 0.452450 | ||||||||
\(253\) | −5.23492 | −0.329117 | ||||||||
\(254\) | 10.6180 | 0.666232 | ||||||||
\(255\) | −1.38919 | −0.0869944 | ||||||||
\(256\) | −4.38773 | −0.274233 | ||||||||
\(257\) | 16.4554 | 1.02646 | 0.513231 | − | 0.858251i | \(-0.328448\pi\) | ||||
0.513231 | + | 0.858251i | \(0.328448\pi\) | |||||||
\(258\) | −4.76901 | −0.296906 | ||||||||
\(259\) | 8.93551 | 0.555226 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.13375 | 0.379670 | ||||||||
\(262\) | −1.86310 | −0.115103 | ||||||||
\(263\) | −22.8587 | −1.40953 | −0.704764 | − | 0.709442i | \(-0.748947\pi\) | ||||
−0.704764 | + | 0.709442i | \(0.748947\pi\) | |||||||
\(264\) | −1.17343 | −0.0722199 | ||||||||
\(265\) | −7.90621 | −0.485675 | ||||||||
\(266\) | 18.1374 | 1.11208 | ||||||||
\(267\) | 9.80657 | 0.600153 | ||||||||
\(268\) | −8.39457 | −0.512780 | ||||||||
\(269\) | 0.521231 | 0.0317800 | 0.0158900 | − | 0.999874i | \(-0.494942\pi\) | ||||
0.0158900 | + | 0.999874i | \(0.494942\pi\) | |||||||
\(270\) | 0.798850 | 0.0486165 | ||||||||
\(271\) | 12.7522 | 0.774640 | 0.387320 | − | 0.921945i | \(-0.373401\pi\) | ||||
0.387320 | + | 0.921945i | \(0.373401\pi\) | |||||||
\(272\) | −2.12527 | −0.128863 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.70797 | 0.465655 | ||||||||
\(275\) | −1.70738 | −0.102959 | ||||||||
\(276\) | 15.7138 | 0.945859 | ||||||||
\(277\) | 28.7261 | 1.72598 | 0.862992 | − | 0.505217i | \(-0.168588\pi\) | ||||
0.862992 | + | 0.505217i | \(0.168588\pi\) | |||||||
\(278\) | 6.72205 | 0.403162 | ||||||||
\(279\) | 5.57311 | 0.333654 | ||||||||
\(280\) | 12.6120 | 0.753708 | ||||||||
\(281\) | 10.1207 | 0.603752 | 0.301876 | − | 0.953347i | \(-0.402387\pi\) | ||||
0.301876 | + | 0.953347i | \(0.402387\pi\) | |||||||
\(282\) | 4.29583 | 0.255813 | ||||||||
\(283\) | 32.2916 | 1.91953 | 0.959767 | − | 0.280797i | \(-0.0905989\pi\) | ||||
0.959767 | + | 0.280797i | \(0.0905989\pi\) | |||||||
\(284\) | −13.1161 | −0.778298 | ||||||||
\(285\) | −10.1836 | −0.603225 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −23.4641 | −1.38504 | ||||||||
\(288\) | 5.44220 | 0.320685 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 4.89995 | 0.287735 | ||||||||
\(291\) | 0.527132 | 0.0309010 | ||||||||
\(292\) | −21.5738 | −1.26251 | ||||||||
\(293\) | −21.0648 | −1.23062 | −0.615310 | − | 0.788285i | \(-0.710969\pi\) | ||||
−0.615310 | + | 0.788285i | \(0.710969\pi\) | |||||||
\(294\) | 6.62019 | 0.386097 | ||||||||
\(295\) | 0.727644 | 0.0423651 | ||||||||
\(296\) | 4.38205 | 0.254702 | ||||||||
\(297\) | 0.556120 | 0.0322694 | ||||||||
\(298\) | 9.08919 | 0.526523 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 5.12507 | 0.295896 | ||||||||
\(301\) | 35.6825 | 2.05671 | ||||||||
\(302\) | −3.02532 | −0.174088 | ||||||||
\(303\) | 7.17027 | 0.411921 | ||||||||
\(304\) | −15.5795 | −0.893547 | ||||||||
\(305\) | −0.463250 | −0.0265256 | ||||||||
\(306\) | −0.575048 | −0.0328733 | ||||||||
\(307\) | 9.77755 | 0.558034 | 0.279017 | − | 0.960286i | \(-0.409991\pi\) | ||||
0.279017 | + | 0.960286i | \(0.409991\pi\) | |||||||
\(308\) | 3.99429 | 0.227596 | ||||||||
\(309\) | 5.76258 | 0.327822 | ||||||||
\(310\) | 4.45208 | 0.252861 | ||||||||
\(311\) | 7.09378 | 0.402251 | 0.201126 | − | 0.979565i | \(-0.435540\pi\) | ||||
0.201126 | + | 0.979565i | \(0.435540\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.46344 | 0.421858 | 0.210929 | − | 0.977501i | \(-0.432351\pi\) | ||||
0.210929 | + | 0.977501i | \(0.432351\pi\) | |||||||
\(314\) | −6.89898 | −0.389332 | ||||||||
\(315\) | −5.97713 | −0.336773 | ||||||||
\(316\) | −18.8639 | −1.06118 | ||||||||
\(317\) | 33.6602 | 1.89055 | 0.945273 | − | 0.326280i | \(-0.105795\pi\) | ||||
0.945273 | + | 0.326280i | \(0.105795\pi\) | |||||||
\(318\) | −3.27274 | −0.183526 | ||||||||
\(319\) | 3.41110 | 0.190985 | ||||||||
\(320\) | −1.55729 | −0.0870553 | ||||||||
\(321\) | −9.66909 | −0.539676 | ||||||||
\(322\) | 23.2904 | 1.29792 | ||||||||
\(323\) | 7.33062 | 0.407887 | ||||||||
\(324\) | −1.66932 | −0.0927400 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.5534 | 0.584497 | ||||||||
\(327\) | −12.3646 | −0.683763 | ||||||||
\(328\) | −11.5070 | −0.635368 | ||||||||
\(329\) | −32.1421 | −1.77205 | ||||||||
\(330\) | 0.444257 | 0.0244555 | ||||||||
\(331\) | 13.0770 | 0.718779 | 0.359389 | − | 0.933188i | \(-0.382985\pi\) | ||||
0.359389 | + | 0.933188i | \(0.382985\pi\) | |||||||
\(332\) | 6.12447 | 0.336124 | ||||||||
\(333\) | −2.07677 | −0.113806 | ||||||||
\(334\) | −10.5510 | −0.577324 | ||||||||
\(335\) | 6.98586 | 0.381679 | ||||||||
\(336\) | −9.14419 | −0.498856 | ||||||||
\(337\) | 24.5919 | 1.33961 | 0.669803 | − | 0.742538i | \(-0.266378\pi\) | ||||
0.669803 | + | 0.742538i | \(0.266378\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.09878 | −0.385553 | ||||||||
\(340\) | 2.31900 | 0.125765 | ||||||||
\(341\) | 3.09932 | 0.167838 | ||||||||
\(342\) | −4.21546 | −0.227946 | ||||||||
\(343\) | −19.4151 | −1.04832 | ||||||||
\(344\) | 17.4990 | 0.943485 | ||||||||
\(345\) | −13.0768 | −0.704033 | ||||||||
\(346\) | 0.0896609 | 0.00482020 | ||||||||
\(347\) | 8.60823 | 0.462114 | 0.231057 | − | 0.972940i | \(-0.425782\pi\) | ||||
0.231057 | + | 0.972940i | \(0.425782\pi\) | |||||||
\(348\) | −10.2392 | −0.548878 | ||||||||
\(349\) | −2.18913 | −0.117181 | −0.0585907 | − | 0.998282i | \(-0.518661\pi\) | ||||
−0.0585907 | + | 0.998282i | \(0.518661\pi\) | |||||||
\(350\) | 7.59619 | 0.406033 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.02652 | 0.161314 | ||||||||
\(353\) | −3.30506 | −0.175910 | −0.0879552 | − | 0.996124i | \(-0.528033\pi\) | ||||
−0.0879552 | + | 0.996124i | \(0.528033\pi\) | |||||||
\(354\) | 0.301205 | 0.0160089 | ||||||||
\(355\) | 10.9151 | 0.579312 | ||||||||
\(356\) | −16.3703 | −0.867625 | ||||||||
\(357\) | 4.30260 | 0.227718 | ||||||||
\(358\) | 10.0773 | 0.532604 | ||||||||
\(359\) | −5.76319 | −0.304169 | −0.152085 | − | 0.988367i | \(-0.548599\pi\) | ||||
−0.152085 | + | 0.988367i | \(0.548599\pi\) | |||||||
\(360\) | −2.93124 | −0.154490 | ||||||||
\(361\) | 34.7380 | 1.82831 | ||||||||
\(362\) | 3.83181 | 0.201396 | ||||||||
\(363\) | −10.6907 | −0.561118 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 17.9535 | 0.939728 | ||||||||
\(366\) | −0.191760 | −0.0100235 | ||||||||
\(367\) | −7.36006 | −0.384192 | −0.192096 | − | 0.981376i | \(-0.561528\pi\) | ||||
−0.192096 | + | 0.981376i | \(0.561528\pi\) | |||||||
\(368\) | −20.0058 | −1.04287 | ||||||||
\(369\) | 5.45346 | 0.283896 | ||||||||
\(370\) | −1.65903 | −0.0862487 | ||||||||
\(371\) | 24.4872 | 1.27131 | ||||||||
\(372\) | −9.30331 | −0.482354 | ||||||||
\(373\) | 34.2792 | 1.77491 | 0.887455 | − | 0.460894i | \(-0.152471\pi\) | ||||
0.887455 | + | 0.460894i | \(0.152471\pi\) | |||||||
\(374\) | −0.319796 | −0.0165363 | ||||||||
\(375\) | −11.2110 | −0.578932 | ||||||||
\(376\) | −15.7628 | −0.812902 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.47420 | −0.127259 | ||||||||
\(379\) | −10.9325 | −0.561566 | −0.280783 | − | 0.959771i | \(-0.590594\pi\) | ||||
−0.280783 | + | 0.959771i | \(0.590594\pi\) | |||||||
\(380\) | 16.9997 | 0.872066 | ||||||||
\(381\) | 18.4645 | 0.945967 | ||||||||
\(382\) | −4.72349 | −0.241675 | ||||||||
\(383\) | −19.9948 | −1.02168 | −0.510842 | − | 0.859674i | \(-0.670666\pi\) | ||||
−0.510842 | + | 0.859674i | \(0.670666\pi\) | |||||||
\(384\) | −11.5290 | −0.588339 | ||||||||
\(385\) | −3.32400 | −0.169407 | ||||||||
\(386\) | 2.52864 | 0.128704 | ||||||||
\(387\) | −8.29324 | −0.421569 | ||||||||
\(388\) | −0.879952 | −0.0446728 | ||||||||
\(389\) | 13.5876 | 0.688917 | 0.344458 | − | 0.938802i | \(-0.388063\pi\) | ||||
0.344458 | + | 0.938802i | \(0.388063\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.41329 | 0.476050 | ||||||||
\(392\) | −24.2916 | −1.22691 | ||||||||
\(393\) | −3.23991 | −0.163432 | ||||||||
\(394\) | −10.1157 | −0.509622 | ||||||||
\(395\) | 15.6983 | 0.789869 | ||||||||
\(396\) | −0.928343 | −0.0466510 | ||||||||
\(397\) | 23.0805 | 1.15838 | 0.579189 | − | 0.815193i | \(-0.303369\pi\) | ||||
0.579189 | + | 0.815193i | \(0.303369\pi\) | |||||||
\(398\) | −15.3909 | −0.771475 | ||||||||
\(399\) | 31.5408 | 1.57901 | ||||||||
\(400\) | −6.52490 | −0.326245 | ||||||||
\(401\) | −3.00330 | −0.149978 | −0.0749888 | − | 0.997184i | \(-0.523892\pi\) | ||||
−0.0749888 | + | 0.997184i | \(0.523892\pi\) | |||||||
\(402\) | 2.89177 | 0.144228 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −11.9695 | −0.595504 | ||||||||
\(405\) | 1.38919 | 0.0690293 | ||||||||
\(406\) | −15.1761 | −0.753180 | ||||||||
\(407\) | −1.15493 | −0.0572479 | ||||||||
\(408\) | 2.11004 | 0.104462 | ||||||||
\(409\) | 19.8611 | 0.982067 | 0.491033 | − | 0.871141i | \(-0.336619\pi\) | ||||
0.491033 | + | 0.871141i | \(0.336619\pi\) | |||||||
\(410\) | 4.35650 | 0.215152 | ||||||||
\(411\) | 13.4040 | 0.661173 | ||||||||
\(412\) | −9.61959 | −0.473923 | ||||||||
\(413\) | −2.25366 | −0.110896 | ||||||||
\(414\) | −5.41309 | −0.266039 | ||||||||
\(415\) | −5.09672 | −0.250188 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.6895 | 0.572440 | ||||||||
\(418\) | −2.34430 | −0.114664 | ||||||||
\(419\) | −14.9899 | −0.732305 | −0.366152 | − | 0.930555i | \(-0.619325\pi\) | ||||
−0.366152 | + | 0.930555i | \(0.619325\pi\) | |||||||
\(420\) | 9.97774 | 0.486864 | ||||||||
\(421\) | 31.8609 | 1.55281 | 0.776403 | − | 0.630236i | \(-0.217042\pi\) | ||||
0.776403 | + | 0.630236i | \(0.217042\pi\) | |||||||
\(422\) | −8.77344 | −0.427084 | ||||||||
\(423\) | 7.47038 | 0.363222 | ||||||||
\(424\) | 12.0087 | 0.583195 | ||||||||
\(425\) | 3.07016 | 0.148924 | ||||||||
\(426\) | 4.51825 | 0.218910 | ||||||||
\(427\) | 1.43478 | 0.0694339 | ||||||||
\(428\) | 16.1408 | 0.780195 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.62506 | −0.319489 | ||||||||
\(431\) | 30.5921 | 1.47357 | 0.736784 | − | 0.676128i | \(-0.236343\pi\) | ||||
0.736784 | + | 0.676128i | \(0.236343\pi\) | |||||||
\(432\) | 2.12527 | 0.102252 | ||||||||
\(433\) | −31.1966 | −1.49921 | −0.749606 | − | 0.661884i | \(-0.769757\pi\) | ||||
−0.749606 | + | 0.661884i | \(0.769757\pi\) | |||||||
\(434\) | −13.7890 | −0.661894 | ||||||||
\(435\) | 8.52093 | 0.408548 | ||||||||
\(436\) | 20.6404 | 0.988498 | ||||||||
\(437\) | 69.0052 | 3.30097 | ||||||||
\(438\) | 7.43176 | 0.355103 | ||||||||
\(439\) | −20.2675 | −0.967315 | −0.483658 | − | 0.875257i | \(-0.660692\pi\) | ||||
−0.483658 | + | 0.875257i | \(0.660692\pi\) | |||||||
\(440\) | −1.63012 | −0.0777130 | ||||||||
\(441\) | 11.5124 | 0.548210 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.17345 | 0.103264 | 0.0516319 | − | 0.998666i | \(-0.483558\pi\) | ||||
0.0516319 | + | 0.998666i | \(0.483558\pi\) | |||||||
\(444\) | 3.46679 | 0.164527 | ||||||||
\(445\) | 13.6232 | 0.645801 | ||||||||
\(446\) | −1.58692 | −0.0751428 | ||||||||
\(447\) | 15.8060 | 0.747597 | ||||||||
\(448\) | 4.82326 | 0.227877 | ||||||||
\(449\) | −4.44916 | −0.209969 | −0.104984 | − | 0.994474i | \(-0.533479\pi\) | ||||
−0.104984 | + | 0.994474i | \(0.533479\pi\) | |||||||
\(450\) | −1.76549 | −0.0832258 | ||||||||
\(451\) | 3.03278 | 0.142808 | ||||||||
\(452\) | 11.8501 | 0.557383 | ||||||||
\(453\) | −5.26099 | −0.247183 | ||||||||
\(454\) | −6.97111 | −0.327171 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 15.4679 | 0.724349 | ||||||||
\(457\) | −27.1141 | −1.26835 | −0.634173 | − | 0.773191i | \(-0.718659\pi\) | ||||
−0.634173 | + | 0.773191i | \(0.718659\pi\) | |||||||
\(458\) | 12.7359 | 0.595108 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 21.8294 | 1.01780 | ||||||||
\(461\) | 13.0690 | 0.608683 | 0.304342 | − | 0.952563i | \(-0.401564\pi\) | ||||
0.304342 | + | 0.952563i | \(0.401564\pi\) | |||||||
\(462\) | −1.37596 | −0.0640153 | ||||||||
\(463\) | −0.164751 | −0.00765665 | −0.00382832 | − | 0.999993i | \(-0.501219\pi\) | ||||
−0.00382832 | + | 0.999993i | \(0.501219\pi\) | |||||||
\(464\) | 13.0359 | 0.605175 | ||||||||
\(465\) | 7.74211 | 0.359032 | ||||||||
\(466\) | −12.8239 | −0.594055 | ||||||||
\(467\) | −10.4486 | −0.483502 | −0.241751 | − | 0.970338i | \(-0.577722\pi\) | ||||
−0.241751 | + | 0.970338i | \(0.577722\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.6367 | −0.999089 | ||||||||
\(470\) | 5.96771 | 0.275270 | ||||||||
\(471\) | −11.9972 | −0.552803 | ||||||||
\(472\) | −1.10522 | −0.0508717 | ||||||||
\(473\) | −4.61204 | −0.212062 | ||||||||
\(474\) | 6.49825 | 0.298475 | ||||||||
\(475\) | 22.5061 | 1.03265 | ||||||||
\(476\) | −7.18242 | −0.329206 | ||||||||
\(477\) | −5.69124 | −0.260584 | ||||||||
\(478\) | 7.84452 | 0.358800 | ||||||||
\(479\) | 5.26860 | 0.240728 | 0.120364 | − | 0.992730i | \(-0.461594\pi\) | ||||
0.120364 | + | 0.992730i | \(0.461594\pi\) | |||||||
\(480\) | 7.56024 | 0.345076 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 9.17961 | 0.418120 | ||||||||
\(483\) | 40.5017 | 1.84289 | ||||||||
\(484\) | 17.8462 | 0.811193 | ||||||||
\(485\) | 0.732286 | 0.0332514 | ||||||||
\(486\) | 0.575048 | 0.0260847 | ||||||||
\(487\) | 4.95998 | 0.224758 | 0.112379 | − | 0.993665i | \(-0.464153\pi\) | ||||
0.112379 | + | 0.993665i | \(0.464153\pi\) | |||||||
\(488\) | 0.703629 | 0.0318518 | ||||||||
\(489\) | 18.3521 | 0.829913 | ||||||||
\(490\) | 9.19669 | 0.415464 | ||||||||
\(491\) | −13.8599 | −0.625488 | −0.312744 | − | 0.949837i | \(-0.601248\pi\) | ||||
−0.312744 | + | 0.949837i | \(0.601248\pi\) | |||||||
\(492\) | −9.10358 | −0.410421 | ||||||||
\(493\) | −6.13375 | −0.276250 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.772556 | 0.0347238 | ||||||||
\(496\) | 11.8444 | 0.531827 | ||||||||
\(497\) | −33.8063 | −1.51642 | ||||||||
\(498\) | −2.10976 | −0.0945407 | ||||||||
\(499\) | 16.4165 | 0.734902 | 0.367451 | − | 0.930043i | \(-0.380230\pi\) | ||||
0.367451 | + | 0.930043i | \(0.380230\pi\) | |||||||
\(500\) | 18.7147 | 0.836946 | ||||||||
\(501\) | −18.3480 | −0.819728 | ||||||||
\(502\) | 7.67707 | 0.342645 | ||||||||
\(503\) | −24.2095 | −1.07945 | −0.539724 | − | 0.841842i | \(-0.681471\pi\) | ||||
−0.539724 | + | 0.841842i | \(0.681471\pi\) | |||||||
\(504\) | 9.07865 | 0.404395 | ||||||||
\(505\) | 9.96086 | 0.443252 | ||||||||
\(506\) | −3.01033 | −0.133826 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −30.8232 | −1.36756 | ||||||||
\(509\) | 18.5740 | 0.823276 | 0.411638 | − | 0.911347i | \(-0.364957\pi\) | ||||
0.411638 | + | 0.911347i | \(0.364957\pi\) | |||||||
\(510\) | −0.798850 | −0.0353737 | ||||||||
\(511\) | −55.6056 | −2.45985 | ||||||||
\(512\) | 20.5349 | 0.907524 | ||||||||
\(513\) | −7.33062 | −0.323655 | ||||||||
\(514\) | 9.46267 | 0.417380 | ||||||||
\(515\) | 8.00531 | 0.352756 | ||||||||
\(516\) | 13.8441 | 0.609451 | ||||||||
\(517\) | 4.15443 | 0.182712 | ||||||||
\(518\) | 5.13835 | 0.225766 | ||||||||
\(519\) | 0.155919 | 0.00684409 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.3147 | −1.28430 | −0.642151 | − | 0.766578i | \(-0.721958\pi\) | ||||
−0.642151 | + | 0.766578i | \(0.721958\pi\) | |||||||
\(522\) | 3.52720 | 0.154381 | ||||||||
\(523\) | −28.5384 | −1.24790 | −0.623949 | − | 0.781465i | \(-0.714473\pi\) | ||||
−0.623949 | + | 0.781465i | \(0.714473\pi\) | |||||||
\(524\) | 5.40845 | 0.236269 | ||||||||
\(525\) | 13.2097 | 0.576517 | ||||||||
\(526\) | −13.1448 | −0.573143 | ||||||||
\(527\) | −5.57311 | −0.242769 | ||||||||
\(528\) | 1.18191 | 0.0514358 | ||||||||
\(529\) | 65.6100 | 2.85261 | ||||||||
\(530\) | −4.54645 | −0.197485 | ||||||||
\(531\) | 0.523791 | 0.0227306 | ||||||||
\(532\) | −52.6516 | −2.28274 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 5.63925 | 0.244034 | ||||||||
\(535\) | −13.4322 | −0.580724 | ||||||||
\(536\) | −10.6108 | −0.458317 | ||||||||
\(537\) | 17.5244 | 0.756232 | ||||||||
\(538\) | 0.299733 | 0.0129224 | ||||||||
\(539\) | 6.40229 | 0.275766 | ||||||||
\(540\) | −2.31900 | −0.0997939 | ||||||||
\(541\) | −24.5062 | −1.05360 | −0.526801 | − | 0.849989i | \(-0.676609\pi\) | ||||
−0.526801 | + | 0.849989i | \(0.676609\pi\) | |||||||
\(542\) | 7.33312 | 0.314984 | ||||||||
\(543\) | 6.66347 | 0.285957 | ||||||||
\(544\) | −5.44220 | −0.233332 | ||||||||
\(545\) | −17.1767 | −0.735770 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.29262 | −0.354567 | −0.177284 | − | 0.984160i | \(-0.556731\pi\) | ||||
−0.177284 | + | 0.984160i | \(0.556731\pi\) | |||||||
\(548\) | −22.3756 | −0.955840 | ||||||||
\(549\) | −0.333468 | −0.0142321 | ||||||||
\(550\) | −0.981823 | −0.0418651 | ||||||||
\(551\) | −44.9642 | −1.91554 | ||||||||
\(552\) | 19.8624 | 0.845398 | ||||||||
\(553\) | −48.6210 | −2.06757 | ||||||||
\(554\) | 16.5189 | 0.701821 | ||||||||
\(555\) | −2.88502 | −0.122462 | ||||||||
\(556\) | −19.5136 | −0.827561 | ||||||||
\(557\) | −41.7827 | −1.77039 | −0.885195 | − | 0.465221i | \(-0.845975\pi\) | ||||
−0.885195 | + | 0.465221i | \(0.845975\pi\) | |||||||
\(558\) | 3.20481 | 0.135670 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −12.7030 | −0.536800 | ||||||||
\(561\) | −0.556120 | −0.0234794 | ||||||||
\(562\) | 5.81990 | 0.245498 | ||||||||
\(563\) | 21.5098 | 0.906530 | 0.453265 | − | 0.891376i | \(-0.350259\pi\) | ||||
0.453265 | + | 0.891376i | \(0.350259\pi\) | |||||||
\(564\) | −12.4705 | −0.525101 | ||||||||
\(565\) | −9.86154 | −0.414878 | ||||||||
\(566\) | 18.5692 | 0.780522 | ||||||||
\(567\) | −4.30260 | −0.180692 | ||||||||
\(568\) | −16.5789 | −0.695635 | ||||||||
\(569\) | 17.6313 | 0.739143 | 0.369572 | − | 0.929202i | \(-0.379504\pi\) | ||||
0.369572 | + | 0.929202i | \(0.379504\pi\) | |||||||
\(570\) | −5.85607 | −0.245284 | ||||||||
\(571\) | −16.2098 | −0.678360 | −0.339180 | − | 0.940722i | \(-0.610149\pi\) | ||||
−0.339180 | + | 0.940722i | \(0.610149\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.21408 | −0.343148 | ||||||||
\(574\) | −13.4930 | −0.563186 | ||||||||
\(575\) | 28.9003 | 1.20522 | ||||||||
\(576\) | −1.12101 | −0.0467087 | ||||||||
\(577\) | −32.4596 | −1.35131 | −0.675656 | − | 0.737217i | \(-0.736140\pi\) | ||||
−0.675656 | + | 0.737217i | \(0.736140\pi\) | |||||||
\(578\) | 0.575048 | 0.0239188 | ||||||||
\(579\) | 4.39726 | 0.182744 | ||||||||
\(580\) | −14.2242 | −0.590626 | ||||||||
\(581\) | 15.7856 | 0.654896 | ||||||||
\(582\) | 0.303126 | 0.0125650 | ||||||||
\(583\) | −3.16502 | −0.131082 | ||||||||
\(584\) | −27.2695 | −1.12842 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.1133 | −0.500395 | ||||||||
\(587\) | −11.5581 | −0.477053 | −0.238527 | − | 0.971136i | \(-0.576664\pi\) | ||||
−0.238527 | + | 0.971136i | \(0.576664\pi\) | |||||||
\(588\) | −19.2179 | −0.792532 | ||||||||
\(589\) | −40.8544 | −1.68338 | ||||||||
\(590\) | 0.418430 | 0.0172265 | ||||||||
\(591\) | −17.5911 | −0.723600 | ||||||||
\(592\) | −4.41369 | −0.181401 | ||||||||
\(593\) | 44.0984 | 1.81091 | 0.905453 | − | 0.424447i | \(-0.139531\pi\) | ||||
0.905453 | + | 0.424447i | \(0.139531\pi\) | |||||||
\(594\) | 0.319796 | 0.0131214 | ||||||||
\(595\) | 5.97713 | 0.245038 | ||||||||
\(596\) | −26.3852 | −1.08078 | ||||||||
\(597\) | −26.7645 | −1.09540 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −42.6781 | −1.74378 | −0.871891 | − | 0.489701i | \(-0.837106\pi\) | ||||
−0.871891 | + | 0.489701i | \(0.837106\pi\) | |||||||
\(600\) | 6.47814 | 0.264469 | ||||||||
\(601\) | 0.0941182 | 0.00383916 | 0.00191958 | − | 0.999998i | \(-0.499389\pi\) | ||||
0.00191958 | + | 0.999998i | \(0.499389\pi\) | |||||||
\(602\) | 20.5192 | 0.836299 | ||||||||
\(603\) | 5.02874 | 0.204786 | ||||||||
\(604\) | 8.78227 | 0.357346 | ||||||||
\(605\) | −14.8514 | −0.603797 | ||||||||
\(606\) | 4.12325 | 0.167496 | ||||||||
\(607\) | −24.7098 | −1.00294 | −0.501471 | − | 0.865175i | \(-0.667207\pi\) | ||||
−0.501471 | + | 0.865175i | \(0.667207\pi\) | |||||||
\(608\) | −39.8947 | −1.61794 | ||||||||
\(609\) | −26.3911 | −1.06942 | ||||||||
\(610\) | −0.266391 | −0.0107858 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1.66932 | 0.0674783 | ||||||||
\(613\) | 25.8186 | 1.04280 | 0.521402 | − | 0.853311i | \(-0.325409\pi\) | ||||
0.521402 | + | 0.853311i | \(0.325409\pi\) | |||||||
\(614\) | 5.62256 | 0.226908 | ||||||||
\(615\) | 7.57589 | 0.305489 | ||||||||
\(616\) | 5.04882 | 0.203423 | ||||||||
\(617\) | 29.0951 | 1.17133 | 0.585663 | − | 0.810555i | \(-0.300834\pi\) | ||||
0.585663 | + | 0.810555i | \(0.300834\pi\) | |||||||
\(618\) | 3.31376 | 0.133299 | ||||||||
\(619\) | 4.26680 | 0.171497 | 0.0857486 | − | 0.996317i | \(-0.472672\pi\) | ||||
0.0857486 | + | 0.996317i | \(0.472672\pi\) | |||||||
\(620\) | −12.9241 | −0.519042 | ||||||||
\(621\) | −9.41329 | −0.377742 | ||||||||
\(622\) | 4.07926 | 0.163564 | ||||||||
\(623\) | −42.1938 | −1.69046 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.223373 | −0.00893492 | ||||||||
\(626\) | 4.29183 | 0.171536 | ||||||||
\(627\) | −4.07671 | −0.162808 | ||||||||
\(628\) | 20.0272 | 0.799172 | ||||||||
\(629\) | 2.07677 | 0.0828062 | ||||||||
\(630\) | −3.43714 | −0.136939 | ||||||||
\(631\) | 28.5398 | 1.13615 | 0.568076 | − | 0.822976i | \(-0.307688\pi\) | ||||
0.568076 | + | 0.822976i | \(0.307688\pi\) | |||||||
\(632\) | −23.8442 | −0.948470 | ||||||||
\(633\) | −15.2569 | −0.606407 | ||||||||
\(634\) | 19.3562 | 0.768735 | ||||||||
\(635\) | 25.6507 | 1.01792 | ||||||||
\(636\) | 9.50050 | 0.376719 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.96155 | 0.0776584 | ||||||||
\(639\) | 7.85716 | 0.310825 | ||||||||
\(640\) | −16.0160 | −0.633088 | ||||||||
\(641\) | 24.8751 | 0.982508 | 0.491254 | − | 0.871016i | \(-0.336539\pi\) | ||||
0.491254 | + | 0.871016i | \(0.336539\pi\) | |||||||
\(642\) | −5.56019 | −0.219443 | ||||||||
\(643\) | −29.3109 | −1.15591 | −0.577954 | − | 0.816069i | \(-0.696149\pi\) | ||||
−0.577954 | + | 0.816069i | \(0.696149\pi\) | |||||||
\(644\) | −67.6102 | −2.66422 | ||||||||
\(645\) | −11.5209 | −0.453634 | ||||||||
\(646\) | 4.21546 | 0.165855 | ||||||||
\(647\) | 43.7852 | 1.72137 | 0.860686 | − | 0.509136i | \(-0.170035\pi\) | ||||
0.860686 | + | 0.509136i | \(0.170035\pi\) | |||||||
\(648\) | −2.11004 | −0.0828900 | ||||||||
\(649\) | 0.291291 | 0.0114342 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −23.9789 | −0.939807 | ||||||||
\(652\) | −30.6356 | −1.19978 | ||||||||
\(653\) | 14.0175 | 0.548546 | 0.274273 | − | 0.961652i | \(-0.411563\pi\) | ||||
0.274273 | + | 0.961652i | \(0.411563\pi\) | |||||||
\(654\) | −7.11023 | −0.278032 | ||||||||
\(655\) | −4.50085 | −0.175863 | ||||||||
\(656\) | 11.5901 | 0.452516 | ||||||||
\(657\) | 12.9237 | 0.504202 | ||||||||
\(658\) | −18.4832 | −0.720552 | ||||||||
\(659\) | 10.1133 | 0.393960 | 0.196980 | − | 0.980408i | \(-0.436887\pi\) | ||||
0.196980 | + | 0.980408i | \(0.436887\pi\) | |||||||
\(660\) | −1.28964 | −0.0501993 | ||||||||
\(661\) | 15.6871 | 0.610158 | 0.305079 | − | 0.952327i | \(-0.401317\pi\) | ||||
0.305079 | + | 0.952327i | \(0.401317\pi\) | |||||||
\(662\) | 7.51992 | 0.292270 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.74139 | 0.300424 | ||||||||
\(665\) | 43.8161 | 1.69911 | ||||||||
\(666\) | −1.19424 | −0.0462759 | ||||||||
\(667\) | −57.7387 | −2.23565 | ||||||||
\(668\) | 30.6287 | 1.18506 | ||||||||
\(669\) | −2.75963 | −0.106693 | ||||||||
\(670\) | 4.01721 | 0.155198 | ||||||||
\(671\) | −0.185448 | −0.00715915 | ||||||||
\(672\) | −23.4156 | −0.903278 | ||||||||
\(673\) | −9.80168 | −0.377827 | −0.188913 | − | 0.981994i | \(-0.560497\pi\) | ||||
−0.188913 | + | 0.981994i | \(0.560497\pi\) | |||||||
\(674\) | 14.1415 | 0.544711 | ||||||||
\(675\) | −3.07016 | −0.118170 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.7994 | −0.453488 | −0.226744 | − | 0.973954i | \(-0.572808\pi\) | ||||
−0.226744 | + | 0.973954i | \(0.572808\pi\) | |||||||
\(678\) | −4.08214 | −0.156774 | ||||||||
\(679\) | −2.26804 | −0.0870395 | ||||||||
\(680\) | 2.93124 | 0.112408 | ||||||||
\(681\) | −12.1227 | −0.464541 | ||||||||
\(682\) | 1.78226 | 0.0682462 | ||||||||
\(683\) | 40.8473 | 1.56298 | 0.781489 | − | 0.623920i | \(-0.214461\pi\) | ||||
0.781489 | + | 0.623920i | \(0.214461\pi\) | |||||||
\(684\) | 12.2371 | 0.467899 | ||||||||
\(685\) | 18.6207 | 0.711462 | ||||||||
\(686\) | −11.1646 | −0.426267 | ||||||||
\(687\) | 22.1475 | 0.844980 | ||||||||
\(688\) | −17.6254 | −0.671961 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −7.51981 | −0.286274 | ||||||||
\(691\) | −1.67686 | −0.0637908 | −0.0318954 | − | 0.999491i | \(-0.510154\pi\) | ||||
−0.0318954 | + | 0.999491i | \(0.510154\pi\) | |||||||
\(692\) | −0.260279 | −0.00989431 | ||||||||
\(693\) | −2.39277 | −0.0908937 | ||||||||
\(694\) | 4.95015 | 0.187905 | ||||||||
\(695\) | 16.2390 | 0.615980 | ||||||||
\(696\) | −12.9424 | −0.490581 | ||||||||
\(697\) | −5.45346 | −0.206565 | ||||||||
\(698\) | −1.25886 | −0.0476484 | ||||||||
\(699\) | −22.3005 | −0.843483 | ||||||||
\(700\) | −22.0512 | −0.833455 | ||||||||
\(701\) | −26.4573 | −0.999280 | −0.499640 | − | 0.866233i | \(-0.666534\pi\) | ||||
−0.499640 | + | 0.866233i | \(0.666534\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.2240 | 0.574184 | ||||||||
\(704\) | −0.623416 | −0.0234959 | ||||||||
\(705\) | 10.3778 | 0.390849 | ||||||||
\(706\) | −1.90057 | −0.0715288 | ||||||||
\(707\) | −30.8508 | −1.16027 | ||||||||
\(708\) | −0.874374 | −0.0328610 | ||||||||
\(709\) | 43.5783 | 1.63662 | 0.818309 | − | 0.574779i | \(-0.194912\pi\) | ||||
0.818309 | + | 0.574779i | \(0.194912\pi\) | |||||||
\(710\) | 6.27670 | 0.235560 | ||||||||
\(711\) | 11.3004 | 0.423797 | ||||||||
\(712\) | −20.6922 | −0.775474 | ||||||||
\(713\) | −52.4613 | −1.96469 | ||||||||
\(714\) | 2.47420 | 0.0925948 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −29.2537 | −1.09326 | ||||||||
\(717\) | 13.6415 | 0.509451 | ||||||||
\(718\) | −3.31411 | −0.123681 | ||||||||
\(719\) | −46.3757 | −1.72952 | −0.864760 | − | 0.502185i | \(-0.832530\pi\) | ||||
−0.864760 | + | 0.502185i | \(0.832530\pi\) | |||||||
\(720\) | 2.95240 | 0.110029 | ||||||||
\(721\) | −24.7941 | −0.923381 | ||||||||
\(722\) | 19.9760 | 0.743430 | ||||||||
\(723\) | 15.9632 | 0.593678 | ||||||||
\(724\) | −11.1235 | −0.413400 | ||||||||
\(725\) | −18.8316 | −0.699387 | ||||||||
\(726\) | −6.14768 | −0.228162 | ||||||||
\(727\) | 8.99556 | 0.333627 | 0.166813 | − | 0.985988i | \(-0.446652\pi\) | ||||
0.166813 | + | 0.985988i | \(0.446652\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 10.3241 | 0.382113 | ||||||||
\(731\) | 8.29324 | 0.306737 | ||||||||
\(732\) | 0.556664 | 0.0205749 | ||||||||
\(733\) | −39.8697 | −1.47262 | −0.736311 | − | 0.676643i | \(-0.763434\pi\) | ||||
−0.736311 | + | 0.676643i | \(0.763434\pi\) | |||||||
\(734\) | −4.23239 | −0.156220 | ||||||||
\(735\) | 15.9929 | 0.589907 | ||||||||
\(736\) | −51.2290 | −1.88833 | ||||||||
\(737\) | 2.79658 | 0.103013 | ||||||||
\(738\) | 3.13600 | 0.115438 | ||||||||
\(739\) | −30.1421 | −1.10880 | −0.554398 | − | 0.832252i | \(-0.687052\pi\) | ||||
−0.554398 | + | 0.832252i | \(0.687052\pi\) | |||||||
\(740\) | 4.81602 | 0.177041 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 14.0813 | 0.516941 | ||||||||
\(743\) | 25.8926 | 0.949906 | 0.474953 | − | 0.880011i | \(-0.342465\pi\) | ||||
0.474953 | + | 0.880011i | \(0.342465\pi\) | |||||||
\(744\) | −11.7595 | −0.431123 | ||||||||
\(745\) | 21.9575 | 0.804459 | ||||||||
\(746\) | 19.7122 | 0.721715 | ||||||||
\(747\) | −3.66884 | −0.134236 | ||||||||
\(748\) | 0.928343 | 0.0339436 | ||||||||
\(749\) | 41.6023 | 1.52011 | ||||||||
\(750\) | −6.44684 | −0.235405 | ||||||||
\(751\) | −39.9725 | −1.45862 | −0.729309 | − | 0.684185i | \(-0.760158\pi\) | ||||
−0.729309 | + | 0.684185i | \(0.760158\pi\) | |||||||
\(752\) | 15.8766 | 0.578958 | ||||||||
\(753\) | 13.3503 | 0.486513 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.30851 | −0.265984 | ||||||||
\(756\) | 7.18242 | 0.261222 | ||||||||
\(757\) | 19.3730 | 0.704123 | 0.352062 | − | 0.935977i | \(-0.385481\pi\) | ||||
0.352062 | + | 0.935977i | \(0.385481\pi\) | |||||||
\(758\) | −6.28672 | −0.228344 | ||||||||
\(759\) | −5.23492 | −0.190016 | ||||||||
\(760\) | 21.4878 | 0.779444 | ||||||||
\(761\) | −24.1713 | −0.876208 | −0.438104 | − | 0.898924i | \(-0.644350\pi\) | ||||
−0.438104 | + | 0.898924i | \(0.644350\pi\) | |||||||
\(762\) | 10.6180 | 0.384649 | ||||||||
\(763\) | 53.1999 | 1.92597 | ||||||||
\(764\) | 13.7119 | 0.496080 | ||||||||
\(765\) | −1.38919 | −0.0502262 | ||||||||
\(766\) | −11.4979 | −0.415438 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −4.38773 | −0.158329 | ||||||||
\(769\) | −20.9923 | −0.757000 | −0.378500 | − | 0.925601i | \(-0.623560\pi\) | ||||
−0.378500 | + | 0.925601i | \(0.623560\pi\) | |||||||
\(770\) | −1.91146 | −0.0688843 | ||||||||
\(771\) | 16.4554 | 0.592628 | ||||||||
\(772\) | −7.34044 | −0.264188 | ||||||||
\(773\) | −54.0765 | −1.94500 | −0.972499 | − | 0.232908i | \(-0.925176\pi\) | ||||
−0.972499 | + | 0.232908i | \(0.925176\pi\) | |||||||
\(774\) | −4.76901 | −0.171419 | ||||||||
\(775\) | −17.1103 | −0.614621 | ||||||||
\(776\) | −1.11227 | −0.0399281 | ||||||||
\(777\) | 8.93551 | 0.320560 | ||||||||
\(778\) | 7.81350 | 0.280128 | ||||||||
\(779\) | −39.9773 | −1.43233 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.36953 | 0.156354 | ||||||||
\(782\) | 5.41309 | 0.193572 | ||||||||
\(783\) | 6.13375 | 0.219202 | ||||||||
\(784\) | 24.4669 | 0.873820 | ||||||||
\(785\) | −16.6664 | −0.594850 | ||||||||
\(786\) | −1.86310 | −0.0664547 | ||||||||
\(787\) | 18.4306 | 0.656980 | 0.328490 | − | 0.944508i | \(-0.393460\pi\) | ||||
0.328490 | + | 0.944508i | \(0.393460\pi\) | |||||||
\(788\) | 29.3651 | 1.04609 | ||||||||
\(789\) | −22.8587 | −0.813791 | ||||||||
\(790\) | 9.02730 | 0.321177 | ||||||||
\(791\) | 30.5432 | 1.08599 | ||||||||
\(792\) | −1.17343 | −0.0416962 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 13.2724 | 0.471020 | ||||||||
\(795\) | −7.90621 | −0.280404 | ||||||||
\(796\) | 44.6785 | 1.58359 | ||||||||
\(797\) | −36.3059 | −1.28602 | −0.643010 | − | 0.765858i | \(-0.722315\pi\) | ||||
−0.643010 | + | 0.765858i | \(0.722315\pi\) | |||||||
\(798\) | 18.1374 | 0.642059 | ||||||||
\(799\) | −7.47038 | −0.264283 | ||||||||
\(800\) | −16.7084 | −0.590731 | ||||||||
\(801\) | 9.80657 | 0.346498 | ||||||||
\(802\) | −1.72704 | −0.0609839 | ||||||||
\(803\) | 7.18714 | 0.253629 | ||||||||
\(804\) | −8.39457 | −0.296054 | ||||||||
\(805\) | 56.2644 | 1.98306 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.521231 | 0.0183482 | ||||||||
\(808\) | −15.1295 | −0.532255 | ||||||||
\(809\) | −38.5250 | −1.35447 | −0.677233 | − | 0.735769i | \(-0.736821\pi\) | ||||
−0.677233 | + | 0.735769i | \(0.736821\pi\) | |||||||
\(810\) | 0.798850 | 0.0280687 | ||||||||
\(811\) | −5.87217 | −0.206200 | −0.103100 | − | 0.994671i | \(-0.532876\pi\) | ||||
−0.103100 | + | 0.994671i | \(0.532876\pi\) | |||||||
\(812\) | 44.0552 | 1.54603 | ||||||||
\(813\) | 12.7522 | 0.447238 | ||||||||
\(814\) | −0.664142 | −0.0232782 | ||||||||
\(815\) | 25.4946 | 0.893036 | ||||||||
\(816\) | −2.12527 | −0.0743993 | ||||||||
\(817\) | 60.7946 | 2.12693 | ||||||||
\(818\) | 11.4211 | 0.399328 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.6466 | −0.441638 | ||||||||
\(821\) | −31.4377 | −1.09718 | −0.548591 | − | 0.836091i | \(-0.684836\pi\) | ||||
−0.548591 | + | 0.836091i | \(0.684836\pi\) | |||||||
\(822\) | 7.70797 | 0.268846 | ||||||||
\(823\) | −27.0765 | −0.943826 | −0.471913 | − | 0.881645i | \(-0.656436\pi\) | ||||
−0.471913 | + | 0.881645i | \(0.656436\pi\) | |||||||
\(824\) | −12.1592 | −0.423587 | ||||||||
\(825\) | −1.70738 | −0.0594432 | ||||||||
\(826\) | −1.29597 | −0.0450924 | ||||||||
\(827\) | 30.7203 | 1.06825 | 0.534126 | − | 0.845405i | \(-0.320641\pi\) | ||||
0.534126 | + | 0.845405i | \(0.320641\pi\) | |||||||
\(828\) | 15.7138 | 0.546092 | ||||||||
\(829\) | −14.4126 | −0.500569 | −0.250285 | − | 0.968172i | \(-0.580524\pi\) | ||||
−0.250285 | + | 0.968172i | \(0.580524\pi\) | |||||||
\(830\) | −2.93086 | −0.101732 | ||||||||
\(831\) | 28.7261 | 0.996498 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.5124 | −0.398881 | ||||||||
\(834\) | 6.72205 | 0.232766 | ||||||||
\(835\) | −25.4888 | −0.882077 | ||||||||
\(836\) | 6.80533 | 0.235367 | ||||||||
\(837\) | 5.57311 | 0.192635 | ||||||||
\(838\) | −8.61992 | −0.297770 | ||||||||
\(839\) | −3.30496 | −0.114100 | −0.0570500 | − | 0.998371i | \(-0.518169\pi\) | ||||
−0.0570500 | + | 0.998371i | \(0.518169\pi\) | |||||||
\(840\) | 12.6120 | 0.435154 | ||||||||
\(841\) | 8.62287 | 0.297341 | ||||||||
\(842\) | 18.3216 | 0.631403 | ||||||||
\(843\) | 10.1207 | 0.348576 | ||||||||
\(844\) | 25.4686 | 0.876666 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.29583 | 0.147694 | ||||||||
\(847\) | 45.9980 | 1.58051 | ||||||||
\(848\) | −12.0954 | −0.415358 | ||||||||
\(849\) | 32.2916 | 1.10824 | ||||||||
\(850\) | 1.76549 | 0.0605557 | ||||||||
\(851\) | 19.5492 | 0.670138 | ||||||||
\(852\) | −13.1161 | −0.449351 | ||||||||
\(853\) | −27.6394 | −0.946354 | −0.473177 | − | 0.880967i | \(-0.656893\pi\) | ||||
−0.473177 | + | 0.880967i | \(0.656893\pi\) | |||||||
\(854\) | 0.825067 | 0.0282332 | ||||||||
\(855\) | −10.1836 | −0.348272 | ||||||||
\(856\) | 20.4021 | 0.697330 | ||||||||
\(857\) | 13.5048 | 0.461316 | 0.230658 | − | 0.973035i | \(-0.425912\pi\) | ||||
0.230658 | + | 0.973035i | \(0.425912\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.8913 | 1.46343 | 0.731716 | − | 0.681609i | \(-0.238720\pi\) | ||||
0.731716 | + | 0.681609i | \(0.238720\pi\) | |||||||
\(860\) | 19.2320 | 0.655807 | ||||||||
\(861\) | −23.4641 | −0.799654 | ||||||||
\(862\) | 17.5919 | 0.599183 | ||||||||
\(863\) | −12.0310 | −0.409540 | −0.204770 | − | 0.978810i | \(-0.565645\pi\) | ||||
−0.204770 | + | 0.978810i | \(0.565645\pi\) | |||||||
\(864\) | 5.44220 | 0.185147 | ||||||||
\(865\) | 0.216601 | 0.00736465 | ||||||||
\(866\) | −17.9395 | −0.609610 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 40.0285 | 1.35865 | ||||||||
\(869\) | 6.28436 | 0.213182 | ||||||||
\(870\) | 4.89995 | 0.166124 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 26.0897 | 0.883509 | ||||||||
\(873\) | 0.527132 | 0.0178407 | ||||||||
\(874\) | 39.6813 | 1.34224 | ||||||||
\(875\) | 48.2364 | 1.63069 | ||||||||
\(876\) | −21.5738 | −0.728912 | ||||||||
\(877\) | 24.0313 | 0.811480 | 0.405740 | − | 0.913989i | \(-0.367014\pi\) | ||||
0.405740 | + | 0.913989i | \(0.367014\pi\) | |||||||
\(878\) | −11.6548 | −0.393330 | ||||||||
\(879\) | −21.0648 | −0.710499 | ||||||||
\(880\) | 1.64189 | 0.0553481 | ||||||||
\(881\) | 29.1093 | 0.980716 | 0.490358 | − | 0.871521i | \(-0.336866\pi\) | ||||
0.490358 | + | 0.871521i | \(0.336866\pi\) | |||||||
\(882\) | 6.62019 | 0.222913 | ||||||||
\(883\) | −39.8535 | −1.34118 | −0.670589 | − | 0.741829i | \(-0.733959\pi\) | ||||
−0.670589 | + | 0.741829i | \(0.733959\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.727644 | 0.0244595 | ||||||||
\(886\) | 1.24984 | 0.0419892 | ||||||||
\(887\) | 38.0628 | 1.27802 | 0.639012 | − | 0.769196i | \(-0.279343\pi\) | ||||
0.639012 | + | 0.769196i | \(0.279343\pi\) | |||||||
\(888\) | 4.38205 | 0.147052 | ||||||||
\(889\) | −79.4456 | −2.66452 | ||||||||
\(890\) | 7.83398 | 0.262596 | ||||||||
\(891\) | 0.556120 | 0.0186307 | ||||||||
\(892\) | 4.60670 | 0.154244 | ||||||||
\(893\) | −54.7625 | −1.83256 | ||||||||
\(894\) | 9.08919 | 0.303988 | ||||||||
\(895\) | 24.3446 | 0.813751 | ||||||||
\(896\) | 49.6049 | 1.65718 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.55848 | −0.0853775 | ||||||||
\(899\) | 34.1841 | 1.14010 | ||||||||
\(900\) | 5.12507 | 0.170836 | ||||||||
\(901\) | 5.69124 | 0.189603 | ||||||||
\(902\) | 1.74400 | 0.0580687 | ||||||||
\(903\) | 35.6825 | 1.18744 | ||||||||
\(904\) | 14.9787 | 0.498183 | ||||||||
\(905\) | 9.25681 | 0.307707 | ||||||||
\(906\) | −3.02532 | −0.100510 | ||||||||
\(907\) | −4.18496 | −0.138959 | −0.0694797 | − | 0.997583i | \(-0.522134\pi\) | ||||
−0.0694797 | + | 0.997583i | \(0.522134\pi\) | |||||||
\(908\) | 20.2366 | 0.671575 | ||||||||
\(909\) | 7.17027 | 0.237823 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.7556 | 1.31716 | 0.658581 | − | 0.752510i | \(-0.271157\pi\) | ||||
0.658581 | + | 0.752510i | \(0.271157\pi\) | |||||||
\(912\) | −15.5795 | −0.515890 | ||||||||
\(913\) | −2.04032 | −0.0675247 | ||||||||
\(914\) | −15.5919 | −0.515735 | ||||||||
\(915\) | −0.463250 | −0.0153146 | ||||||||
\(916\) | −36.9712 | −1.22156 | ||||||||
\(917\) | 13.9401 | 0.460341 | ||||||||
\(918\) | −0.575048 | −0.0189794 | ||||||||
\(919\) | 0.264249 | 0.00871677 | 0.00435839 | − | 0.999991i | \(-0.498613\pi\) | ||||
0.00435839 | + | 0.999991i | \(0.498613\pi\) | |||||||
\(920\) | 27.5926 | 0.909700 | ||||||||
\(921\) | 9.77755 | 0.322181 | ||||||||
\(922\) | 7.51530 | 0.247503 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 3.99429 | 0.131403 | ||||||||
\(925\) | 6.37600 | 0.209642 | ||||||||
\(926\) | −0.0947400 | −0.00311335 | ||||||||
\(927\) | 5.76258 | 0.189268 | ||||||||
\(928\) | 33.3811 | 1.09579 | ||||||||
\(929\) | 31.0637 | 1.01917 | 0.509583 | − | 0.860421i | \(-0.329800\pi\) | ||||
0.509583 | + | 0.860421i | \(0.329800\pi\) | |||||||
\(930\) | 4.45208 | 0.145990 | ||||||||
\(931\) | −84.3931 | −2.76587 | ||||||||
\(932\) | 37.2267 | 1.21940 | ||||||||
\(933\) | 7.09378 | 0.232240 | ||||||||
\(934\) | −6.00843 | −0.196602 | ||||||||
\(935\) | −0.772556 | −0.0252653 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.7978 | 1.69216 | 0.846081 | − | 0.533054i | \(-0.178956\pi\) | ||||
0.846081 | + | 0.533054i | \(0.178956\pi\) | |||||||
\(938\) | −12.4421 | −0.406250 | ||||||||
\(939\) | 7.46344 | 0.243560 | ||||||||
\(940\) | −17.3238 | −0.565040 | ||||||||
\(941\) | 6.56945 | 0.214158 | 0.107079 | − | 0.994251i | \(-0.465850\pi\) | ||||
0.107079 | + | 0.994251i | \(0.465850\pi\) | |||||||
\(942\) | −6.89898 | −0.224781 | ||||||||
\(943\) | −51.3350 | −1.67170 | ||||||||
\(944\) | 1.11320 | 0.0362314 | ||||||||
\(945\) | −5.97713 | −0.194436 | ||||||||
\(946\) | −2.65215 | −0.0862287 | ||||||||
\(947\) | −24.1500 | −0.784768 | −0.392384 | − | 0.919801i | \(-0.628350\pi\) | ||||
−0.392384 | + | 0.919801i | \(0.628350\pi\) | |||||||
\(948\) | −18.8639 | −0.612671 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 12.9421 | 0.419897 | ||||||||
\(951\) | 33.6602 | 1.09151 | ||||||||
\(952\) | −9.07865 | −0.294241 | ||||||||
\(953\) | 30.1570 | 0.976882 | 0.488441 | − | 0.872597i | \(-0.337566\pi\) | ||||
0.488441 | + | 0.872597i | \(0.337566\pi\) | |||||||
\(954\) | −3.27274 | −0.105959 | ||||||||
\(955\) | −11.4109 | −0.369248 | ||||||||
\(956\) | −22.7720 | −0.736500 | ||||||||
\(957\) | 3.41110 | 0.110265 | ||||||||
\(958\) | 3.02970 | 0.0978850 | ||||||||
\(959\) | −57.6723 | −1.86234 | ||||||||
\(960\) | −1.55729 | −0.0502614 | ||||||||
\(961\) | 0.0595994 | 0.00192256 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.66909 | −0.311582 | ||||||||
\(964\) | −26.6477 | −0.858264 | ||||||||
\(965\) | 6.10863 | 0.196644 | ||||||||
\(966\) | 23.2904 | 0.749356 | ||||||||
\(967\) | −19.0267 | −0.611856 | −0.305928 | − | 0.952055i | \(-0.598967\pi\) | ||||
−0.305928 | + | 0.952055i | \(0.598967\pi\) | |||||||
\(968\) | 22.5578 | 0.725036 | ||||||||
\(969\) | 7.33062 | 0.235493 | ||||||||
\(970\) | 0.421100 | 0.0135207 | ||||||||
\(971\) | −7.84570 | −0.251780 | −0.125890 | − | 0.992044i | \(-0.540179\pi\) | ||||
−0.125890 | + | 0.992044i | \(0.540179\pi\) | |||||||
\(972\) | −1.66932 | −0.0535435 | ||||||||
\(973\) | −50.2955 | −1.61240 | ||||||||
\(974\) | 2.85223 | 0.0913912 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.708708 | −0.0226852 | ||||||||
\(977\) | 16.9103 | 0.541008 | 0.270504 | − | 0.962719i | \(-0.412810\pi\) | ||||
0.270504 | + | 0.962719i | \(0.412810\pi\) | |||||||
\(978\) | 10.5534 | 0.337459 | ||||||||
\(979\) | 5.45364 | 0.174299 | ||||||||
\(980\) | −26.6973 | −0.852813 | ||||||||
\(981\) | −12.3646 | −0.394771 | ||||||||
\(982\) | −7.97011 | −0.254336 | ||||||||
\(983\) | −40.0463 | −1.27728 | −0.638639 | − | 0.769506i | \(-0.720502\pi\) | ||||
−0.638639 | + | 0.769506i | \(0.720502\pi\) | |||||||
\(984\) | −11.5070 | −0.366830 | ||||||||
\(985\) | −24.4373 | −0.778638 | ||||||||
\(986\) | −3.52720 | −0.112329 | ||||||||
\(987\) | −32.1421 | −1.02309 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 78.0667 | 2.48238 | ||||||||
\(990\) | 0.444257 | 0.0141194 | ||||||||
\(991\) | 35.4703 | 1.12675 | 0.563375 | − | 0.826201i | \(-0.309503\pi\) | ||||
0.563375 | + | 0.826201i | \(0.309503\pi\) | |||||||
\(992\) | 30.3300 | 0.962979 | ||||||||
\(993\) | 13.0770 | 0.414987 | ||||||||
\(994\) | −19.4402 | −0.616607 | ||||||||
\(995\) | −37.1810 | −1.17872 | ||||||||
\(996\) | 6.12447 | 0.194061 | ||||||||
\(997\) | −41.9651 | −1.32905 | −0.664525 | − | 0.747266i | \(-0.731366\pi\) | ||||
−0.664525 | + | 0.747266i | \(0.731366\pi\) | |||||||
\(998\) | 9.44026 | 0.298826 | ||||||||
\(999\) | −2.07677 | −0.0657060 |
(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 | 8619.2.a.bq.1.11 | yes | 21 | |
13.12 | even | 2 | 8619.2.a.bp.1.11 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8619.2.a.bp.1.11 | ✓ | 21 | 13.12 | even | 2 | ||
8619.2.a.bq.1.11 | yes | 21 | 1.1 | even | 1 | trivial |