Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [241,2,Mod(1,241)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(241, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("241.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 241.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: | \(1.92439468871\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | 7.7.31056073.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 3x^{5} + 11x^{4} + x^{3} - 9x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.60363\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 241.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.60363 | −1.84104 | −0.920521 | − | 0.390694i | \(-0.872235\pi\) | ||||
−0.920521 | + | 0.390694i | \(0.872235\pi\) | |||||||
\(3\) | 0.980039 | 0.565826 | 0.282913 | − | 0.959146i | \(-0.408699\pi\) | ||||
0.282913 | + | 0.959146i | \(0.408699\pi\) | |||||||
\(4\) | 4.77887 | 2.38943 | ||||||||
\(5\) | −1.69135 | −0.756395 | −0.378197 | − | 0.925725i | \(-0.623456\pi\) | ||||
−0.378197 | + | 0.925725i | \(0.623456\pi\) | |||||||
\(6\) | −2.55166 | −1.04171 | ||||||||
\(7\) | −1.30586 | −0.493569 | −0.246785 | − | 0.969070i | \(-0.579374\pi\) | ||||
−0.246785 | + | 0.969070i | \(0.579374\pi\) | |||||||
\(8\) | −7.23513 | −2.55801 | ||||||||
\(9\) | −2.03952 | −0.679841 | ||||||||
\(10\) | 4.40364 | 1.39255 | ||||||||
\(11\) | −3.27094 | −0.986226 | −0.493113 | − | 0.869965i | \(-0.664141\pi\) | ||||
−0.493113 | + | 0.869965i | \(0.664141\pi\) | |||||||
\(12\) | 4.68348 | 1.35200 | ||||||||
\(13\) | 4.30649 | 1.19441 | 0.597203 | − | 0.802090i | \(-0.296279\pi\) | ||||
0.597203 | + | 0.802090i | \(0.296279\pi\) | |||||||
\(14\) | 3.39998 | 0.908682 | ||||||||
\(15\) | −1.65759 | −0.427988 | ||||||||
\(16\) | 9.27984 | 2.31996 | ||||||||
\(17\) | −1.02456 | −0.248493 | −0.124247 | − | 0.992251i | \(-0.539651\pi\) | ||||
−0.124247 | + | 0.992251i | \(0.539651\pi\) | |||||||
\(18\) | 5.31016 | 1.25162 | ||||||||
\(19\) | −7.01250 | −1.60878 | −0.804388 | − | 0.594104i | \(-0.797507\pi\) | ||||
−0.804388 | + | 0.594104i | \(0.797507\pi\) | |||||||
\(20\) | −8.08274 | −1.80736 | ||||||||
\(21\) | −1.27980 | −0.279274 | ||||||||
\(22\) | 8.51631 | 1.81568 | ||||||||
\(23\) | 0.835873 | 0.174292 | 0.0871458 | − | 0.996196i | \(-0.472225\pi\) | ||||
0.0871458 | + | 0.996196i | \(0.472225\pi\) | |||||||
\(24\) | −7.09071 | −1.44739 | ||||||||
\(25\) | −2.13934 | −0.427867 | ||||||||
\(26\) | −11.2125 | −2.19895 | ||||||||
\(27\) | −4.93893 | −0.950498 | ||||||||
\(28\) | −6.24054 | −1.17935 | ||||||||
\(29\) | −1.11761 | −0.207535 | −0.103767 | − | 0.994602i | \(-0.533090\pi\) | ||||
−0.103767 | + | 0.994602i | \(0.533090\pi\) | |||||||
\(30\) | 4.31574 | 0.787943 | ||||||||
\(31\) | −3.97344 | −0.713652 | −0.356826 | − | 0.934171i | \(-0.616141\pi\) | ||||
−0.356826 | + | 0.934171i | \(0.616141\pi\) | |||||||
\(32\) | −9.69098 | −1.71314 | ||||||||
\(33\) | −3.20565 | −0.558032 | ||||||||
\(34\) | 2.66758 | 0.457486 | ||||||||
\(35\) | 2.20867 | 0.373333 | ||||||||
\(36\) | −9.74661 | −1.62444 | ||||||||
\(37\) | −11.3098 | −1.85932 | −0.929658 | − | 0.368423i | \(-0.879898\pi\) | ||||
−0.929658 | + | 0.368423i | \(0.879898\pi\) | |||||||
\(38\) | 18.2579 | 2.96182 | ||||||||
\(39\) | 4.22053 | 0.675825 | ||||||||
\(40\) | 12.2371 | 1.93486 | ||||||||
\(41\) | 1.22869 | 0.191890 | 0.0959448 | − | 0.995387i | \(-0.469413\pi\) | ||||
0.0959448 | + | 0.995387i | \(0.469413\pi\) | |||||||
\(42\) | 3.33211 | 0.514156 | ||||||||
\(43\) | 10.8406 | 1.65318 | 0.826591 | − | 0.562804i | \(-0.190277\pi\) | ||||
0.826591 | + | 0.562804i | \(0.190277\pi\) | |||||||
\(44\) | −15.6314 | −2.35652 | ||||||||
\(45\) | 3.44955 | 0.514228 | ||||||||
\(46\) | −2.17630 | −0.320878 | ||||||||
\(47\) | −0.151820 | −0.0221453 | −0.0110726 | − | 0.999939i | \(-0.503525\pi\) | ||||
−0.0110726 | + | 0.999939i | \(0.503525\pi\) | |||||||
\(48\) | 9.09461 | 1.31269 | ||||||||
\(49\) | −5.29473 | −0.756389 | ||||||||
\(50\) | 5.57003 | 0.787721 | ||||||||
\(51\) | −1.00411 | −0.140604 | ||||||||
\(52\) | 20.5801 | 2.85395 | ||||||||
\(53\) | 3.02053 | 0.414902 | 0.207451 | − | 0.978245i | \(-0.433483\pi\) | ||||
0.207451 | + | 0.978245i | \(0.433483\pi\) | |||||||
\(54\) | 12.8591 | 1.74991 | ||||||||
\(55\) | 5.53231 | 0.745976 | ||||||||
\(56\) | 9.44808 | 1.26255 | ||||||||
\(57\) | −6.87252 | −0.910287 | ||||||||
\(58\) | 2.90984 | 0.382080 | ||||||||
\(59\) | −4.15373 | −0.540769 | −0.270385 | − | 0.962752i | \(-0.587151\pi\) | ||||
−0.270385 | + | 0.962752i | \(0.587151\pi\) | |||||||
\(60\) | −7.92140 | −1.02265 | ||||||||
\(61\) | 5.62714 | 0.720482 | 0.360241 | − | 0.932859i | \(-0.382694\pi\) | ||||
0.360241 | + | 0.932859i | \(0.382694\pi\) | |||||||
\(62\) | 10.3454 | 1.31386 | ||||||||
\(63\) | 2.66334 | 0.335549 | ||||||||
\(64\) | 6.67199 | 0.833999 | ||||||||
\(65\) | −7.28378 | −0.903442 | ||||||||
\(66\) | 8.34632 | 1.02736 | ||||||||
\(67\) | 12.9934 | 1.58740 | 0.793700 | − | 0.608309i | \(-0.208152\pi\) | ||||
0.793700 | + | 0.608309i | \(0.208152\pi\) | |||||||
\(68\) | −4.89626 | −0.593758 | ||||||||
\(69\) | 0.819188 | 0.0986187 | ||||||||
\(70\) | −5.75055 | −0.687322 | ||||||||
\(71\) | −11.2862 | −1.33942 | −0.669711 | − | 0.742622i | \(-0.733582\pi\) | ||||
−0.669711 | + | 0.742622i | \(0.733582\pi\) | |||||||
\(72\) | 14.7562 | 1.73904 | ||||||||
\(73\) | 11.7148 | 1.37112 | 0.685560 | − | 0.728017i | \(-0.259558\pi\) | ||||
0.685560 | + | 0.728017i | \(0.259558\pi\) | |||||||
\(74\) | 29.4464 | 3.42308 | ||||||||
\(75\) | −2.09663 | −0.242098 | ||||||||
\(76\) | −33.5118 | −3.84407 | ||||||||
\(77\) | 4.27140 | 0.486771 | ||||||||
\(78\) | −10.9887 | −1.24422 | ||||||||
\(79\) | −1.66517 | −0.187346 | −0.0936732 | − | 0.995603i | \(-0.529861\pi\) | ||||
−0.0936732 | + | 0.995603i | \(0.529861\pi\) | |||||||
\(80\) | −15.6955 | −1.75481 | ||||||||
\(81\) | 1.27823 | 0.142025 | ||||||||
\(82\) | −3.19906 | −0.353277 | ||||||||
\(83\) | −2.34322 | −0.257201 | −0.128601 | − | 0.991696i | \(-0.541049\pi\) | ||||
−0.128601 | + | 0.991696i | \(0.541049\pi\) | |||||||
\(84\) | −6.11597 | −0.667308 | ||||||||
\(85\) | 1.73290 | 0.187959 | ||||||||
\(86\) | −28.2250 | −3.04358 | ||||||||
\(87\) | −1.09530 | −0.117429 | ||||||||
\(88\) | 23.6657 | 2.52277 | ||||||||
\(89\) | 18.1099 | 1.91965 | 0.959825 | − | 0.280598i | \(-0.0905329\pi\) | ||||
0.959825 | + | 0.280598i | \(0.0905329\pi\) | |||||||
\(90\) | −8.98133 | −0.946715 | ||||||||
\(91\) | −5.62368 | −0.589522 | ||||||||
\(92\) | 3.99453 | 0.416458 | ||||||||
\(93\) | −3.89413 | −0.403802 | ||||||||
\(94\) | 0.395283 | 0.0407703 | ||||||||
\(95\) | 11.8606 | 1.21687 | ||||||||
\(96\) | −9.49754 | −0.969338 | ||||||||
\(97\) | −7.17873 | −0.728890 | −0.364445 | − | 0.931225i | \(-0.618741\pi\) | ||||
−0.364445 | + | 0.931225i | \(0.618741\pi\) | |||||||
\(98\) | 13.7855 | 1.39254 | ||||||||
\(99\) | 6.67116 | 0.670477 | ||||||||
\(100\) | −10.2236 | −1.02236 | ||||||||
\(101\) | −5.48113 | −0.545393 | −0.272696 | − | 0.962100i | \(-0.587915\pi\) | ||||
−0.272696 | + | 0.962100i | \(0.587915\pi\) | |||||||
\(102\) | 2.61433 | 0.258858 | ||||||||
\(103\) | −15.7371 | −1.55062 | −0.775311 | − | 0.631580i | \(-0.782407\pi\) | ||||
−0.775311 | + | 0.631580i | \(0.782407\pi\) | |||||||
\(104\) | −31.1580 | −3.05530 | ||||||||
\(105\) | 2.16458 | 0.211242 | ||||||||
\(106\) | −7.86433 | −0.763851 | ||||||||
\(107\) | −11.1816 | −1.08097 | −0.540483 | − | 0.841355i | \(-0.681758\pi\) | ||||
−0.540483 | + | 0.841355i | \(0.681758\pi\) | |||||||
\(108\) | −23.6025 | −2.27115 | ||||||||
\(109\) | −0.296424 | −0.0283922 | −0.0141961 | − | 0.999899i | \(-0.504519\pi\) | ||||
−0.0141961 | + | 0.999899i | \(0.504519\pi\) | |||||||
\(110\) | −14.4041 | −1.37337 | ||||||||
\(111\) | −11.0840 | −1.05205 | ||||||||
\(112\) | −12.1182 | −1.14506 | ||||||||
\(113\) | 10.5881 | 0.996045 | 0.498023 | − | 0.867164i | \(-0.334060\pi\) | ||||
0.498023 | + | 0.867164i | \(0.334060\pi\) | |||||||
\(114\) | 17.8935 | 1.67588 | ||||||||
\(115\) | −1.41375 | −0.131833 | ||||||||
\(116\) | −5.34091 | −0.495891 | ||||||||
\(117\) | −8.78319 | −0.812006 | ||||||||
\(118\) | 10.8147 | 0.995578 | ||||||||
\(119\) | 1.33794 | 0.122649 | ||||||||
\(120\) | 11.9929 | 1.09479 | ||||||||
\(121\) | −0.300940 | −0.0273582 | ||||||||
\(122\) | −14.6510 | −1.32644 | ||||||||
\(123\) | 1.20417 | 0.108576 | ||||||||
\(124\) | −18.9886 | −1.70522 | ||||||||
\(125\) | 12.0751 | 1.08003 | ||||||||
\(126\) | −6.93433 | −0.617759 | ||||||||
\(127\) | 14.6989 | 1.30432 | 0.652160 | − | 0.758081i | \(-0.273863\pi\) | ||||
0.652160 | + | 0.758081i | \(0.273863\pi\) | |||||||
\(128\) | 2.01059 | 0.177713 | ||||||||
\(129\) | 10.6242 | 0.935413 | ||||||||
\(130\) | 18.9642 | 1.66327 | ||||||||
\(131\) | 9.63853 | 0.842122 | 0.421061 | − | 0.907032i | \(-0.361658\pi\) | ||||
0.421061 | + | 0.907032i | \(0.361658\pi\) | |||||||
\(132\) | −15.3194 | −1.33338 | ||||||||
\(133\) | 9.15735 | 0.794043 | ||||||||
\(134\) | −33.8300 | −2.92247 | ||||||||
\(135\) | 8.35346 | 0.718951 | ||||||||
\(136\) | 7.41286 | 0.635647 | ||||||||
\(137\) | 23.2376 | 1.98532 | 0.992661 | − | 0.120933i | \(-0.0385886\pi\) | ||||
0.992661 | + | 0.120933i | \(0.0385886\pi\) | |||||||
\(138\) | −2.13286 | −0.181561 | ||||||||
\(139\) | −1.29376 | −0.109736 | −0.0548678 | − | 0.998494i | \(-0.517474\pi\) | ||||
−0.0548678 | + | 0.998494i | \(0.517474\pi\) | |||||||
\(140\) | 10.5549 | 0.892055 | ||||||||
\(141\) | −0.148790 | −0.0125304 | ||||||||
\(142\) | 29.3850 | 2.46593 | ||||||||
\(143\) | −14.0863 | −1.17795 | ||||||||
\(144\) | −18.9265 | −1.57720 | ||||||||
\(145\) | 1.89027 | 0.156978 | ||||||||
\(146\) | −30.5011 | −2.52429 | ||||||||
\(147\) | −5.18904 | −0.427985 | ||||||||
\(148\) | −54.0480 | −4.44271 | ||||||||
\(149\) | 17.5316 | 1.43625 | 0.718123 | − | 0.695916i | \(-0.245002\pi\) | ||||
0.718123 | + | 0.695916i | \(0.245002\pi\) | |||||||
\(150\) | 5.45885 | 0.445713 | ||||||||
\(151\) | 5.26990 | 0.428858 | 0.214429 | − | 0.976740i | \(-0.431211\pi\) | ||||
0.214429 | + | 0.976740i | \(0.431211\pi\) | |||||||
\(152\) | 50.7363 | 4.11526 | ||||||||
\(153\) | 2.08962 | 0.168936 | ||||||||
\(154\) | −11.1211 | −0.896166 | ||||||||
\(155\) | 6.72048 | 0.539802 | ||||||||
\(156\) | 20.1693 | 1.61484 | ||||||||
\(157\) | −14.2165 | −1.13460 | −0.567299 | − | 0.823512i | \(-0.692012\pi\) | ||||
−0.567299 | + | 0.823512i | \(0.692012\pi\) | |||||||
\(158\) | 4.33548 | 0.344912 | ||||||||
\(159\) | 2.96024 | 0.234762 | ||||||||
\(160\) | 16.3908 | 1.29581 | ||||||||
\(161\) | −1.09153 | −0.0860250 | ||||||||
\(162\) | −3.32802 | −0.261474 | ||||||||
\(163\) | −15.9688 | −1.25077 | −0.625386 | − | 0.780315i | \(-0.715059\pi\) | ||||
−0.625386 | + | 0.780315i | \(0.715059\pi\) | |||||||
\(164\) | 5.87176 | 0.458508 | ||||||||
\(165\) | 5.42188 | 0.422093 | ||||||||
\(166\) | 6.10086 | 0.473518 | ||||||||
\(167\) | −21.5275 | −1.66585 | −0.832925 | − | 0.553386i | \(-0.813335\pi\) | ||||
−0.832925 | + | 0.553386i | \(0.813335\pi\) | |||||||
\(168\) | 9.25949 | 0.714385 | ||||||||
\(169\) | 5.54585 | 0.426604 | ||||||||
\(170\) | −4.51181 | −0.346040 | ||||||||
\(171\) | 14.3021 | 1.09371 | ||||||||
\(172\) | 51.8060 | 3.95017 | ||||||||
\(173\) | −5.82531 | −0.442890 | −0.221445 | − | 0.975173i | \(-0.571077\pi\) | ||||
−0.221445 | + | 0.975173i | \(0.571077\pi\) | |||||||
\(174\) | 2.85175 | 0.216191 | ||||||||
\(175\) | 2.79368 | 0.211182 | ||||||||
\(176\) | −30.3538 | −2.28801 | ||||||||
\(177\) | −4.07081 | −0.305981 | ||||||||
\(178\) | −47.1515 | −3.53416 | ||||||||
\(179\) | −6.03932 | −0.451400 | −0.225700 | − | 0.974197i | \(-0.572467\pi\) | ||||
−0.225700 | + | 0.974197i | \(0.572467\pi\) | |||||||
\(180\) | 16.4849 | 1.22871 | ||||||||
\(181\) | −4.03706 | −0.300073 | −0.150036 | − | 0.988680i | \(-0.547939\pi\) | ||||
−0.150036 | + | 0.988680i | \(0.547939\pi\) | |||||||
\(182\) | 14.6420 | 1.08533 | ||||||||
\(183\) | 5.51482 | 0.407667 | ||||||||
\(184\) | −6.04765 | −0.445839 | ||||||||
\(185\) | 19.1288 | 1.40638 | ||||||||
\(186\) | 10.1389 | 0.743417 | ||||||||
\(187\) | 3.35129 | 0.245071 | ||||||||
\(188\) | −0.725529 | −0.0529146 | ||||||||
\(189\) | 6.44956 | 0.469136 | ||||||||
\(190\) | −30.8805 | −2.24031 | ||||||||
\(191\) | −16.4803 | −1.19247 | −0.596235 | − | 0.802810i | \(-0.703337\pi\) | ||||
−0.596235 | + | 0.802810i | \(0.703337\pi\) | |||||||
\(192\) | 6.53881 | 0.471898 | ||||||||
\(193\) | −23.0631 | −1.66012 | −0.830060 | − | 0.557674i | \(-0.811694\pi\) | ||||
−0.830060 | + | 0.557674i | \(0.811694\pi\) | |||||||
\(194\) | 18.6907 | 1.34192 | ||||||||
\(195\) | −7.13839 | −0.511191 | ||||||||
\(196\) | −25.3028 | −1.80734 | ||||||||
\(197\) | −13.5540 | −0.965680 | −0.482840 | − | 0.875709i | \(-0.660395\pi\) | ||||
−0.482840 | + | 0.875709i | \(0.660395\pi\) | |||||||
\(198\) | −17.3692 | −1.23438 | ||||||||
\(199\) | −25.6725 | −1.81988 | −0.909938 | − | 0.414745i | \(-0.863871\pi\) | ||||
−0.909938 | + | 0.414745i | \(0.863871\pi\) | |||||||
\(200\) | 15.4784 | 1.09449 | ||||||||
\(201\) | 12.7341 | 0.898192 | ||||||||
\(202\) | 14.2708 | 1.00409 | ||||||||
\(203\) | 1.45944 | 0.102433 | ||||||||
\(204\) | −4.79852 | −0.335964 | ||||||||
\(205\) | −2.07815 | −0.145144 | ||||||||
\(206\) | 40.9735 | 2.85476 | ||||||||
\(207\) | −1.70478 | −0.118491 | ||||||||
\(208\) | 39.9635 | 2.77097 | ||||||||
\(209\) | 22.9375 | 1.58662 | ||||||||
\(210\) | −5.63576 | −0.388905 | ||||||||
\(211\) | 5.18301 | 0.356813 | 0.178407 | − | 0.983957i | \(-0.442906\pi\) | ||||
0.178407 | + | 0.983957i | \(0.442906\pi\) | |||||||
\(212\) | 14.4347 | 0.991380 | ||||||||
\(213\) | −11.0609 | −0.757879 | ||||||||
\(214\) | 29.1127 | 1.99010 | ||||||||
\(215\) | −18.3353 | −1.25046 | ||||||||
\(216\) | 35.7338 | 2.43138 | ||||||||
\(217\) | 5.18877 | 0.352237 | ||||||||
\(218\) | 0.771777 | 0.0522713 | ||||||||
\(219\) | 11.4810 | 0.775815 | ||||||||
\(220\) | 26.4382 | 1.78246 | ||||||||
\(221\) | −4.41227 | −0.296802 | ||||||||
\(222\) | 28.8587 | 1.93687 | ||||||||
\(223\) | −6.50914 | −0.435884 | −0.217942 | − | 0.975962i | \(-0.569934\pi\) | ||||
−0.217942 | + | 0.975962i | \(0.569934\pi\) | |||||||
\(224\) | 12.6551 | 0.845553 | ||||||||
\(225\) | 4.36323 | 0.290882 | ||||||||
\(226\) | −27.5675 | −1.83376 | ||||||||
\(227\) | 11.0460 | 0.733150 | 0.366575 | − | 0.930389i | \(-0.380530\pi\) | ||||
0.366575 | + | 0.930389i | \(0.380530\pi\) | |||||||
\(228\) | −32.8429 | −2.17507 | ||||||||
\(229\) | 8.95679 | 0.591881 | 0.295941 | − | 0.955206i | \(-0.404367\pi\) | ||||
0.295941 | + | 0.955206i | \(0.404367\pi\) | |||||||
\(230\) | 3.68089 | 0.242710 | ||||||||
\(231\) | 4.18614 | 0.275428 | ||||||||
\(232\) | 8.08605 | 0.530875 | ||||||||
\(233\) | −6.46647 | −0.423632 | −0.211816 | − | 0.977310i | \(-0.567938\pi\) | ||||
−0.211816 | + | 0.977310i | \(0.567938\pi\) | |||||||
\(234\) | 22.8681 | 1.49494 | ||||||||
\(235\) | 0.256781 | 0.0167506 | ||||||||
\(236\) | −19.8501 | −1.29213 | ||||||||
\(237\) | −1.63193 | −0.106005 | ||||||||
\(238\) | −3.48349 | −0.225801 | ||||||||
\(239\) | −25.0588 | −1.62092 | −0.810460 | − | 0.585794i | \(-0.800783\pi\) | ||||
−0.810460 | + | 0.585794i | \(0.800783\pi\) | |||||||
\(240\) | −15.3822 | −0.992915 | ||||||||
\(241\) | −1.00000 | −0.0644157 | ||||||||
\(242\) | 0.783536 | 0.0503676 | ||||||||
\(243\) | 16.0695 | 1.03086 | ||||||||
\(244\) | 26.8914 | 1.72154 | ||||||||
\(245\) | 8.95523 | 0.572129 | ||||||||
\(246\) | −3.13520 | −0.199893 | ||||||||
\(247\) | −30.1992 | −1.92153 | ||||||||
\(248\) | 28.7484 | 1.82552 | ||||||||
\(249\) | −2.29644 | −0.145531 | ||||||||
\(250\) | −31.4391 | −1.98838 | ||||||||
\(251\) | −12.5611 | −0.792847 | −0.396424 | − | 0.918068i | \(-0.629749\pi\) | ||||
−0.396424 | + | 0.918068i | \(0.629749\pi\) | |||||||
\(252\) | 12.7277 | 0.801772 | ||||||||
\(253\) | −2.73409 | −0.171891 | ||||||||
\(254\) | −38.2706 | −2.40131 | ||||||||
\(255\) | 1.69831 | 0.106352 | ||||||||
\(256\) | −18.5788 | −1.16117 | ||||||||
\(257\) | 16.0367 | 1.00034 | 0.500171 | − | 0.865927i | \(-0.333270\pi\) | ||||
0.500171 | + | 0.865927i | \(0.333270\pi\) | |||||||
\(258\) | −27.6616 | −1.72213 | ||||||||
\(259\) | 14.7690 | 0.917702 | ||||||||
\(260\) | −34.8082 | −2.15871 | ||||||||
\(261\) | 2.27939 | 0.141091 | ||||||||
\(262\) | −25.0951 | −1.55038 | ||||||||
\(263\) | 3.33210 | 0.205466 | 0.102733 | − | 0.994709i | \(-0.467241\pi\) | ||||
0.102733 | + | 0.994709i | \(0.467241\pi\) | |||||||
\(264\) | 23.1933 | 1.42745 | ||||||||
\(265\) | −5.10877 | −0.313829 | ||||||||
\(266\) | −23.8423 | −1.46187 | ||||||||
\(267\) | 17.7485 | 1.08619 | ||||||||
\(268\) | 62.0939 | 3.79299 | ||||||||
\(269\) | −7.44101 | −0.453686 | −0.226843 | − | 0.973931i | \(-0.572840\pi\) | ||||
−0.226843 | + | 0.973931i | \(0.572840\pi\) | |||||||
\(270\) | −21.7493 | −1.32362 | ||||||||
\(271\) | −20.6031 | −1.25155 | −0.625774 | − | 0.780005i | \(-0.715217\pi\) | ||||
−0.625774 | + | 0.780005i | \(0.715217\pi\) | |||||||
\(272\) | −9.50779 | −0.576495 | ||||||||
\(273\) | −5.51143 | −0.333567 | ||||||||
\(274\) | −60.5020 | −3.65506 | ||||||||
\(275\) | 6.99764 | 0.421974 | ||||||||
\(276\) | 3.91479 | 0.235643 | ||||||||
\(277\) | 5.17667 | 0.311036 | 0.155518 | − | 0.987833i | \(-0.450295\pi\) | ||||
0.155518 | + | 0.987833i | \(0.450295\pi\) | |||||||
\(278\) | 3.36848 | 0.202028 | ||||||||
\(279\) | 8.10393 | 0.485170 | ||||||||
\(280\) | −15.9800 | −0.954988 | ||||||||
\(281\) | −14.1821 | −0.846031 | −0.423015 | − | 0.906123i | \(-0.639028\pi\) | ||||
−0.423015 | + | 0.906123i | \(0.639028\pi\) | |||||||
\(282\) | 0.387393 | 0.0230689 | ||||||||
\(283\) | −7.05196 | −0.419196 | −0.209598 | − | 0.977788i | \(-0.567215\pi\) | ||||
−0.209598 | + | 0.977788i | \(0.567215\pi\) | |||||||
\(284\) | −53.9351 | −3.20046 | ||||||||
\(285\) | 11.6238 | 0.688537 | ||||||||
\(286\) | 36.6754 | 2.16866 | ||||||||
\(287\) | −1.60450 | −0.0947109 | ||||||||
\(288\) | 19.7650 | 1.16466 | ||||||||
\(289\) | −15.9503 | −0.938251 | ||||||||
\(290\) | −4.92155 | −0.289004 | ||||||||
\(291\) | −7.03544 | −0.412425 | ||||||||
\(292\) | 55.9837 | 3.27620 | ||||||||
\(293\) | −2.78966 | −0.162974 | −0.0814869 | − | 0.996674i | \(-0.525967\pi\) | ||||
−0.0814869 | + | 0.996674i | \(0.525967\pi\) | |||||||
\(294\) | 13.5103 | 0.787937 | ||||||||
\(295\) | 7.02540 | 0.409035 | ||||||||
\(296\) | 81.8278 | 4.75614 | ||||||||
\(297\) | 16.1550 | 0.937405 | ||||||||
\(298\) | −45.6458 | −2.64419 | ||||||||
\(299\) | 3.59968 | 0.208175 | ||||||||
\(300\) | −10.0195 | −0.578478 | ||||||||
\(301\) | −14.1564 | −0.815960 | ||||||||
\(302\) | −13.7208 | −0.789546 | ||||||||
\(303\) | −5.37172 | −0.308597 | ||||||||
\(304\) | −65.0749 | −3.73230 | ||||||||
\(305\) | −9.51747 | −0.544969 | ||||||||
\(306\) | −5.44060 | −0.311018 | ||||||||
\(307\) | 19.8285 | 1.13167 | 0.565837 | − | 0.824517i | \(-0.308553\pi\) | ||||
0.565837 | + | 0.824517i | \(0.308553\pi\) | |||||||
\(308\) | 20.4124 | 1.16311 | ||||||||
\(309\) | −15.4230 | −0.877382 | ||||||||
\(310\) | −17.4976 | −0.993798 | ||||||||
\(311\) | 33.5109 | 1.90023 | 0.950114 | − | 0.311902i | \(-0.100966\pi\) | ||||
0.950114 | + | 0.311902i | \(0.100966\pi\) | |||||||
\(312\) | −30.5361 | −1.72877 | ||||||||
\(313\) | 19.4152 | 1.09741 | 0.548705 | − | 0.836016i | \(-0.315121\pi\) | ||||
0.548705 | + | 0.836016i | \(0.315121\pi\) | |||||||
\(314\) | 37.0144 | 2.08884 | ||||||||
\(315\) | −4.50463 | −0.253807 | ||||||||
\(316\) | −7.95763 | −0.447652 | ||||||||
\(317\) | −11.7255 | −0.658569 | −0.329284 | − | 0.944231i | \(-0.606807\pi\) | ||||
−0.329284 | + | 0.944231i | \(0.606807\pi\) | |||||||
\(318\) | −7.70735 | −0.432207 | ||||||||
\(319\) | 3.65564 | 0.204676 | ||||||||
\(320\) | −11.2847 | −0.630832 | ||||||||
\(321\) | −10.9584 | −0.611638 | ||||||||
\(322\) | 2.84195 | 0.158376 | ||||||||
\(323\) | 7.18475 | 0.399770 | ||||||||
\(324\) | 6.10847 | 0.339359 | ||||||||
\(325\) | −9.21303 | −0.511047 | ||||||||
\(326\) | 41.5768 | 2.30272 | ||||||||
\(327\) | −0.290507 | −0.0160651 | ||||||||
\(328\) | −8.88976 | −0.490855 | ||||||||
\(329\) | 0.198256 | 0.0109302 | ||||||||
\(330\) | −14.1165 | −0.777090 | ||||||||
\(331\) | 4.93072 | 0.271017 | 0.135509 | − | 0.990776i | \(-0.456733\pi\) | ||||
0.135509 | + | 0.990776i | \(0.456733\pi\) | |||||||
\(332\) | −11.1979 | −0.614566 | ||||||||
\(333\) | 23.0666 | 1.26404 | ||||||||
\(334\) | 56.0496 | 3.06690 | ||||||||
\(335\) | −21.9764 | −1.20070 | ||||||||
\(336\) | −11.8763 | −0.647905 | ||||||||
\(337\) | 34.4425 | 1.87620 | 0.938100 | − | 0.346364i | \(-0.112584\pi\) | ||||
0.938100 | + | 0.346364i | \(0.112584\pi\) | |||||||
\(338\) | −14.4393 | −0.785395 | ||||||||
\(339\) | 10.3768 | 0.563588 | ||||||||
\(340\) | 8.28128 | 0.449116 | ||||||||
\(341\) | 12.9969 | 0.703822 | ||||||||
\(342\) | −37.2374 | −2.01357 | ||||||||
\(343\) | 16.0552 | 0.866900 | ||||||||
\(344\) | −78.4334 | −4.22885 | ||||||||
\(345\) | −1.38553 | −0.0745946 | ||||||||
\(346\) | 15.1669 | 0.815378 | ||||||||
\(347\) | −23.4553 | −1.25915 | −0.629574 | − | 0.776940i | \(-0.716771\pi\) | ||||
−0.629574 | + | 0.776940i | \(0.716771\pi\) | |||||||
\(348\) | −5.23430 | −0.280588 | ||||||||
\(349\) | 15.8727 | 0.849648 | 0.424824 | − | 0.905276i | \(-0.360336\pi\) | ||||
0.424824 | + | 0.905276i | \(0.360336\pi\) | |||||||
\(350\) | −7.27369 | −0.388795 | ||||||||
\(351\) | −21.2694 | −1.13528 | ||||||||
\(352\) | 31.6986 | 1.68954 | ||||||||
\(353\) | −28.4598 | −1.51476 | −0.757382 | − | 0.652972i | \(-0.773522\pi\) | ||||
−0.757382 | + | 0.652972i | \(0.773522\pi\) | |||||||
\(354\) | 10.5989 | 0.563324 | ||||||||
\(355\) | 19.0889 | 1.01313 | ||||||||
\(356\) | 86.5450 | 4.58688 | ||||||||
\(357\) | 1.31123 | 0.0693978 | ||||||||
\(358\) | 15.7241 | 0.831047 | ||||||||
\(359\) | −0.772338 | −0.0407625 | −0.0203812 | − | 0.999792i | \(-0.506488\pi\) | ||||
−0.0203812 | + | 0.999792i | \(0.506488\pi\) | |||||||
\(360\) | −24.9579 | −1.31540 | ||||||||
\(361\) | 30.1751 | 1.58816 | ||||||||
\(362\) | 10.5110 | 0.552446 | ||||||||
\(363\) | −0.294933 | −0.0154800 | ||||||||
\(364\) | −26.8748 | −1.40862 | ||||||||
\(365\) | −19.8139 | −1.03711 | ||||||||
\(366\) | −14.3585 | −0.750532 | ||||||||
\(367\) | −23.3631 | −1.21954 | −0.609772 | − | 0.792577i | \(-0.708739\pi\) | ||||
−0.609772 | + | 0.792577i | \(0.708739\pi\) | |||||||
\(368\) | 7.75677 | 0.404350 | ||||||||
\(369\) | −2.50595 | −0.130454 | ||||||||
\(370\) | −49.8042 | −2.58920 | ||||||||
\(371\) | −3.94439 | −0.204783 | ||||||||
\(372\) | −18.6095 | −0.964859 | ||||||||
\(373\) | 27.7831 | 1.43855 | 0.719277 | − | 0.694724i | \(-0.244473\pi\) | ||||
0.719277 | + | 0.694724i | \(0.244473\pi\) | |||||||
\(374\) | −8.72550 | −0.451185 | ||||||||
\(375\) | 11.8341 | 0.611109 | ||||||||
\(376\) | 1.09844 | 0.0566477 | ||||||||
\(377\) | −4.81297 | −0.247881 | ||||||||
\(378\) | −16.7922 | −0.863700 | ||||||||
\(379\) | 7.33328 | 0.376685 | 0.188343 | − | 0.982103i | \(-0.439688\pi\) | ||||
0.188343 | + | 0.982103i | \(0.439688\pi\) | |||||||
\(380\) | 56.6802 | 2.90763 | ||||||||
\(381\) | 14.4055 | 0.738018 | ||||||||
\(382\) | 42.9084 | 2.19539 | ||||||||
\(383\) | −33.4931 | −1.71142 | −0.855708 | − | 0.517459i | \(-0.826878\pi\) | ||||
−0.855708 | + | 0.517459i | \(0.826878\pi\) | |||||||
\(384\) | 1.97046 | 0.100554 | ||||||||
\(385\) | −7.22443 | −0.368191 | ||||||||
\(386\) | 60.0477 | 3.05635 | ||||||||
\(387\) | −22.1097 | −1.12390 | ||||||||
\(388\) | −34.3062 | −1.74163 | ||||||||
\(389\) | 15.6882 | 0.795425 | 0.397713 | − | 0.917510i | \(-0.369804\pi\) | ||||
0.397713 | + | 0.917510i | \(0.369804\pi\) | |||||||
\(390\) | 18.5857 | 0.941123 | ||||||||
\(391\) | −0.856405 | −0.0433103 | ||||||||
\(392\) | 38.3080 | 1.93485 | ||||||||
\(393\) | 9.44613 | 0.476494 | ||||||||
\(394\) | 35.2894 | 1.77786 | ||||||||
\(395\) | 2.81639 | 0.141708 | ||||||||
\(396\) | 31.8806 | 1.60206 | ||||||||
\(397\) | 8.34483 | 0.418815 | 0.209408 | − | 0.977828i | \(-0.432846\pi\) | ||||
0.209408 | + | 0.977828i | \(0.432846\pi\) | |||||||
\(398\) | 66.8416 | 3.35047 | ||||||||
\(399\) | 8.97456 | 0.449290 | ||||||||
\(400\) | −19.8527 | −0.992635 | ||||||||
\(401\) | −38.5766 | −1.92642 | −0.963211 | − | 0.268747i | \(-0.913391\pi\) | ||||
−0.963211 | + | 0.268747i | \(0.913391\pi\) | |||||||
\(402\) | −33.1548 | −1.65361 | ||||||||
\(403\) | −17.1116 | −0.852389 | ||||||||
\(404\) | −26.1936 | −1.30318 | ||||||||
\(405\) | −2.16193 | −0.107427 | ||||||||
\(406\) | −3.79985 | −0.188583 | ||||||||
\(407\) | 36.9936 | 1.83371 | ||||||||
\(408\) | 7.26489 | 0.359666 | ||||||||
\(409\) | −19.5415 | −0.966266 | −0.483133 | − | 0.875547i | \(-0.660501\pi\) | ||||
−0.483133 | + | 0.875547i | \(0.660501\pi\) | |||||||
\(410\) | 5.41073 | 0.267217 | ||||||||
\(411\) | 22.7737 | 1.12335 | ||||||||
\(412\) | −75.2055 | −3.70511 | ||||||||
\(413\) | 5.42419 | 0.266907 | ||||||||
\(414\) | 4.43862 | 0.218146 | ||||||||
\(415\) | 3.96320 | 0.194546 | ||||||||
\(416\) | −41.7341 | −2.04618 | ||||||||
\(417\) | −1.26794 | −0.0620912 | ||||||||
\(418\) | −59.7206 | −2.92103 | ||||||||
\(419\) | −29.7748 | −1.45459 | −0.727297 | − | 0.686323i | \(-0.759224\pi\) | ||||
−0.727297 | + | 0.686323i | \(0.759224\pi\) | |||||||
\(420\) | 10.3443 | 0.504748 | ||||||||
\(421\) | −4.78920 | −0.233411 | −0.116706 | − | 0.993167i | \(-0.537233\pi\) | ||||
−0.116706 | + | 0.993167i | \(0.537233\pi\) | |||||||
\(422\) | −13.4946 | −0.656908 | ||||||||
\(423\) | 0.309641 | 0.0150553 | ||||||||
\(424\) | −21.8539 | −1.06132 | ||||||||
\(425\) | 2.19189 | 0.106322 | ||||||||
\(426\) | 28.7984 | 1.39529 | ||||||||
\(427\) | −7.34827 | −0.355608 | ||||||||
\(428\) | −53.4354 | −2.58290 | ||||||||
\(429\) | −13.8051 | −0.666517 | ||||||||
\(430\) | 47.7383 | 2.30214 | ||||||||
\(431\) | 5.35939 | 0.258153 | 0.129076 | − | 0.991635i | \(-0.458799\pi\) | ||||
0.129076 | + | 0.991635i | \(0.458799\pi\) | |||||||
\(432\) | −45.8325 | −2.20512 | ||||||||
\(433\) | 21.5028 | 1.03336 | 0.516680 | − | 0.856179i | \(-0.327168\pi\) | ||||
0.516680 | + | 0.856179i | \(0.327168\pi\) | |||||||
\(434\) | −13.5096 | −0.648482 | ||||||||
\(435\) | 1.85254 | 0.0888224 | ||||||||
\(436\) | −1.41657 | −0.0678414 | ||||||||
\(437\) | −5.86156 | −0.280396 | ||||||||
\(438\) | −29.8923 | −1.42831 | ||||||||
\(439\) | 4.22306 | 0.201556 | 0.100778 | − | 0.994909i | \(-0.467867\pi\) | ||||
0.100778 | + | 0.994909i | \(0.467867\pi\) | |||||||
\(440\) | −40.0270 | −1.90821 | ||||||||
\(441\) | 10.7987 | 0.514225 | ||||||||
\(442\) | 11.4879 | 0.546424 | ||||||||
\(443\) | 8.34030 | 0.396260 | 0.198130 | − | 0.980176i | \(-0.436513\pi\) | ||||
0.198130 | + | 0.980176i | \(0.436513\pi\) | |||||||
\(444\) | −52.9691 | −2.51380 | ||||||||
\(445\) | −30.6303 | −1.45201 | ||||||||
\(446\) | 16.9474 | 0.802481 | ||||||||
\(447\) | 17.1817 | 0.812665 | ||||||||
\(448\) | −8.71269 | −0.411636 | ||||||||
\(449\) | 15.7796 | 0.744684 | 0.372342 | − | 0.928096i | \(-0.378555\pi\) | ||||
0.372342 | + | 0.928096i | \(0.378555\pi\) | |||||||
\(450\) | −11.3602 | −0.535525 | ||||||||
\(451\) | −4.01898 | −0.189247 | ||||||||
\(452\) | 50.5992 | 2.37998 | ||||||||
\(453\) | 5.16470 | 0.242659 | ||||||||
\(454\) | −28.7597 | −1.34976 | ||||||||
\(455\) | 9.51161 | 0.445911 | ||||||||
\(456\) | 49.7236 | 2.32852 | ||||||||
\(457\) | −8.71419 | −0.407633 | −0.203816 | − | 0.979009i | \(-0.565335\pi\) | ||||
−0.203816 | + | 0.979009i | \(0.565335\pi\) | |||||||
\(458\) | −23.3201 | −1.08968 | ||||||||
\(459\) | 5.06025 | 0.236192 | ||||||||
\(460\) | −6.75614 | −0.315007 | ||||||||
\(461\) | 24.9140 | 1.16036 | 0.580181 | − | 0.814487i | \(-0.302982\pi\) | ||||
0.580181 | + | 0.814487i | \(0.302982\pi\) | |||||||
\(462\) | −10.8991 | −0.507074 | ||||||||
\(463\) | −2.87272 | −0.133507 | −0.0667534 | − | 0.997770i | \(-0.521264\pi\) | ||||
−0.0667534 | + | 0.997770i | \(0.521264\pi\) | |||||||
\(464\) | −10.3712 | −0.481473 | ||||||||
\(465\) | 6.58634 | 0.305434 | ||||||||
\(466\) | 16.8363 | 0.779925 | ||||||||
\(467\) | 4.87474 | 0.225576 | 0.112788 | − | 0.993619i | \(-0.464022\pi\) | ||||
0.112788 | + | 0.993619i | \(0.464022\pi\) | |||||||
\(468\) | −41.9737 | −1.94023 | ||||||||
\(469\) | −16.9676 | −0.783492 | ||||||||
\(470\) | −0.668562 | −0.0308385 | ||||||||
\(471\) | −13.9327 | −0.641985 | ||||||||
\(472\) | 30.0528 | 1.38329 | ||||||||
\(473\) | −35.4591 | −1.63041 | ||||||||
\(474\) | 4.24894 | 0.195160 | ||||||||
\(475\) | 15.0021 | 0.688343 | ||||||||
\(476\) | 6.39383 | 0.293061 | ||||||||
\(477\) | −6.16044 | −0.282067 | ||||||||
\(478\) | 65.2438 | 2.98418 | ||||||||
\(479\) | 0.194055 | 0.00886661 | 0.00443331 | − | 0.999990i | \(-0.498589\pi\) | ||||
0.00443331 | + | 0.999990i | \(0.498589\pi\) | |||||||
\(480\) | 16.0637 | 0.733202 | ||||||||
\(481\) | −48.7055 | −2.22078 | ||||||||
\(482\) | 2.60363 | 0.118592 | ||||||||
\(483\) | −1.06975 | −0.0486752 | ||||||||
\(484\) | −1.43815 | −0.0653707 | ||||||||
\(485\) | 12.1417 | 0.551328 | ||||||||
\(486\) | −41.8390 | −1.89785 | ||||||||
\(487\) | −30.7592 | −1.39383 | −0.696915 | − | 0.717154i | \(-0.745445\pi\) | ||||
−0.696915 | + | 0.717154i | \(0.745445\pi\) | |||||||
\(488\) | −40.7131 | −1.84300 | ||||||||
\(489\) | −15.6500 | −0.707719 | ||||||||
\(490\) | −23.3161 | −1.05331 | ||||||||
\(491\) | −21.5528 | −0.972663 | −0.486332 | − | 0.873774i | \(-0.661665\pi\) | ||||
−0.486332 | + | 0.873774i | \(0.661665\pi\) | |||||||
\(492\) | 5.75456 | 0.259436 | ||||||||
\(493\) | 1.14506 | 0.0515710 | ||||||||
\(494\) | 78.6275 | 3.53762 | ||||||||
\(495\) | −11.2833 | −0.507145 | ||||||||
\(496\) | −36.8729 | −1.65564 | ||||||||
\(497\) | 14.7382 | 0.661097 | ||||||||
\(498\) | 5.97908 | 0.267929 | ||||||||
\(499\) | 21.8992 | 0.980341 | 0.490170 | − | 0.871627i | \(-0.336935\pi\) | ||||
0.490170 | + | 0.871627i | \(0.336935\pi\) | |||||||
\(500\) | 57.7054 | 2.58066 | ||||||||
\(501\) | −21.0978 | −0.942581 | ||||||||
\(502\) | 32.7043 | 1.45966 | ||||||||
\(503\) | 4.44114 | 0.198021 | 0.0990104 | − | 0.995086i | \(-0.468432\pi\) | ||||
0.0990104 | + | 0.995086i | \(0.468432\pi\) | |||||||
\(504\) | −19.2696 | −0.858336 | ||||||||
\(505\) | 9.27050 | 0.412532 | ||||||||
\(506\) | 7.11855 | 0.316458 | ||||||||
\(507\) | 5.43515 | 0.241383 | ||||||||
\(508\) | 70.2443 | 3.11659 | ||||||||
\(509\) | 29.6966 | 1.31628 | 0.658140 | − | 0.752895i | \(-0.271343\pi\) | ||||
0.658140 | + | 0.752895i | \(0.271343\pi\) | |||||||
\(510\) | −4.42175 | −0.195799 | ||||||||
\(511\) | −15.2980 | −0.676742 | ||||||||
\(512\) | 44.3511 | 1.96006 | ||||||||
\(513\) | 34.6342 | 1.52914 | ||||||||
\(514\) | −41.7536 | −1.84167 | ||||||||
\(515\) | 26.6169 | 1.17288 | ||||||||
\(516\) | 50.7719 | 2.23511 | ||||||||
\(517\) | 0.496595 | 0.0218402 | ||||||||
\(518\) | −38.4530 | −1.68953 | ||||||||
\(519\) | −5.70903 | −0.250598 | ||||||||
\(520\) | 52.6991 | 2.31101 | ||||||||
\(521\) | −32.5336 | −1.42532 | −0.712661 | − | 0.701509i | \(-0.752510\pi\) | ||||
−0.712661 | + | 0.701509i | \(0.752510\pi\) | |||||||
\(522\) | −5.93468 | −0.259754 | ||||||||
\(523\) | −21.6812 | −0.948053 | −0.474027 | − | 0.880510i | \(-0.657200\pi\) | ||||
−0.474027 | + | 0.880510i | \(0.657200\pi\) | |||||||
\(524\) | 46.0612 | 2.01219 | ||||||||
\(525\) | 2.73791 | 0.119492 | ||||||||
\(526\) | −8.67555 | −0.378272 | ||||||||
\(527\) | 4.07105 | 0.177338 | ||||||||
\(528\) | −29.7479 | −1.29461 | ||||||||
\(529\) | −22.3013 | −0.969622 | ||||||||
\(530\) | 13.3013 | 0.577773 | ||||||||
\(531\) | 8.47162 | 0.367637 | ||||||||
\(532\) | 43.7618 | 1.89731 | ||||||||
\(533\) | 5.29135 | 0.229194 | ||||||||
\(534\) | −46.2103 | −1.99972 | ||||||||
\(535\) | 18.9120 | 0.817637 | ||||||||
\(536\) | −94.0092 | −4.06058 | ||||||||
\(537\) | −5.91877 | −0.255414 | ||||||||
\(538\) | 19.3736 | 0.835255 | ||||||||
\(539\) | 17.3187 | 0.745971 | ||||||||
\(540\) | 39.9201 | 1.71789 | ||||||||
\(541\) | 6.08311 | 0.261533 | 0.130767 | − | 0.991413i | \(-0.458256\pi\) | ||||
0.130767 | + | 0.991413i | \(0.458256\pi\) | |||||||
\(542\) | 53.6427 | 2.30415 | ||||||||
\(543\) | −3.95648 | −0.169789 | ||||||||
\(544\) | 9.92903 | 0.425703 | ||||||||
\(545\) | 0.501356 | 0.0214757 | ||||||||
\(546\) | 14.3497 | 0.614110 | ||||||||
\(547\) | −12.1956 | −0.521447 | −0.260723 | − | 0.965414i | \(-0.583961\pi\) | ||||
−0.260723 | + | 0.965414i | \(0.583961\pi\) | |||||||
\(548\) | 111.049 | 4.74379 | ||||||||
\(549\) | −11.4767 | −0.489813 | ||||||||
\(550\) | −18.2192 | −0.776871 | ||||||||
\(551\) | 7.83723 | 0.333877 | ||||||||
\(552\) | −5.92694 | −0.252267 | ||||||||
\(553\) | 2.17448 | 0.0924684 | ||||||||
\(554\) | −13.4781 | −0.572630 | ||||||||
\(555\) | 18.7470 | 0.795765 | ||||||||
\(556\) | −6.18273 | −0.262206 | ||||||||
\(557\) | −37.5982 | −1.59309 | −0.796544 | − | 0.604581i | \(-0.793341\pi\) | ||||
−0.796544 | + | 0.604581i | \(0.793341\pi\) | |||||||
\(558\) | −21.0996 | −0.893217 | ||||||||
\(559\) | 46.6851 | 1.97457 | ||||||||
\(560\) | 20.4961 | 0.866118 | ||||||||
\(561\) | 3.28439 | 0.138667 | ||||||||
\(562\) | 36.9248 | 1.55758 | ||||||||
\(563\) | 20.6037 | 0.868342 | 0.434171 | − | 0.900830i | \(-0.357041\pi\) | ||||
0.434171 | + | 0.900830i | \(0.357041\pi\) | |||||||
\(564\) | −0.711047 | −0.0299405 | ||||||||
\(565\) | −17.9082 | −0.753403 | ||||||||
\(566\) | 18.3607 | 0.771756 | ||||||||
\(567\) | −1.66919 | −0.0700992 | ||||||||
\(568\) | 81.6569 | 3.42625 | ||||||||
\(569\) | 20.5762 | 0.862601 | 0.431301 | − | 0.902208i | \(-0.358055\pi\) | ||||
0.431301 | + | 0.902208i | \(0.358055\pi\) | |||||||
\(570\) | −30.2641 | −1.26762 | ||||||||
\(571\) | 37.1320 | 1.55392 | 0.776962 | − | 0.629547i | \(-0.216760\pi\) | ||||
0.776962 | + | 0.629547i | \(0.216760\pi\) | |||||||
\(572\) | −67.3165 | −2.81464 | ||||||||
\(573\) | −16.1513 | −0.674730 | ||||||||
\(574\) | 4.17753 | 0.174367 | ||||||||
\(575\) | −1.78821 | −0.0745736 | ||||||||
\(576\) | −13.6077 | −0.566986 | ||||||||
\(577\) | −34.7064 | −1.44484 | −0.722422 | − | 0.691452i | \(-0.756971\pi\) | ||||
−0.722422 | + | 0.691452i | \(0.756971\pi\) | |||||||
\(578\) | 41.5285 | 1.72736 | ||||||||
\(579\) | −22.6028 | −0.939339 | ||||||||
\(580\) | 9.03335 | 0.375089 | ||||||||
\(581\) | 3.05992 | 0.126947 | ||||||||
\(582\) | 18.3176 | 0.759291 | ||||||||
\(583\) | −9.87998 | −0.409187 | ||||||||
\(584\) | −84.7585 | −3.50733 | ||||||||
\(585\) | 14.8554 | 0.614197 | ||||||||
\(586\) | 7.26324 | 0.300042 | ||||||||
\(587\) | −1.14455 | −0.0472405 | −0.0236203 | − | 0.999721i | \(-0.507519\pi\) | ||||
−0.0236203 | + | 0.999721i | \(0.507519\pi\) | |||||||
\(588\) | −24.7977 | −1.02264 | ||||||||
\(589\) | 27.8638 | 1.14811 | ||||||||
\(590\) | −18.2915 | −0.753050 | ||||||||
\(591\) | −13.2834 | −0.546407 | ||||||||
\(592\) | −104.953 | −4.31354 | ||||||||
\(593\) | 3.60735 | 0.148136 | 0.0740680 | − | 0.997253i | \(-0.476402\pi\) | ||||
0.0740680 | + | 0.997253i | \(0.476402\pi\) | |||||||
\(594\) | −42.0615 | −1.72580 | ||||||||
\(595\) | −2.26292 | −0.0927708 | ||||||||
\(596\) | 83.7813 | 3.43181 | ||||||||
\(597\) | −25.1601 | −1.02973 | ||||||||
\(598\) | −9.37222 | −0.383258 | ||||||||
\(599\) | −31.6723 | −1.29410 | −0.647048 | − | 0.762449i | \(-0.723997\pi\) | ||||
−0.647048 | + | 0.762449i | \(0.723997\pi\) | |||||||
\(600\) | 15.1694 | 0.619289 | ||||||||
\(601\) | 6.55665 | 0.267451 | 0.133726 | − | 0.991018i | \(-0.457306\pi\) | ||||
0.133726 | + | 0.991018i | \(0.457306\pi\) | |||||||
\(602\) | 36.8579 | 1.50222 | ||||||||
\(603\) | −26.5004 | −1.07918 | ||||||||
\(604\) | 25.1841 | 1.02473 | ||||||||
\(605\) | 0.508996 | 0.0206936 | ||||||||
\(606\) | 13.9859 | 0.568140 | ||||||||
\(607\) | −9.16648 | −0.372056 | −0.186028 | − | 0.982544i | \(-0.559562\pi\) | ||||
−0.186028 | + | 0.982544i | \(0.559562\pi\) | |||||||
\(608\) | 67.9579 | 2.75606 | ||||||||
\(609\) | 1.43031 | 0.0579592 | ||||||||
\(610\) | 24.7799 | 1.00331 | ||||||||
\(611\) | −0.653812 | −0.0264504 | ||||||||
\(612\) | 9.98603 | 0.403661 | ||||||||
\(613\) | 7.92345 | 0.320025 | 0.160012 | − | 0.987115i | \(-0.448847\pi\) | ||||
0.160012 | + | 0.987115i | \(0.448847\pi\) | |||||||
\(614\) | −51.6260 | −2.08346 | ||||||||
\(615\) | −2.03667 | −0.0821264 | ||||||||
\(616\) | −30.9041 | −1.24516 | ||||||||
\(617\) | 16.5959 | 0.668126 | 0.334063 | − | 0.942551i | \(-0.391580\pi\) | ||||
0.334063 | + | 0.942551i | \(0.391580\pi\) | |||||||
\(618\) | 40.1556 | 1.61530 | ||||||||
\(619\) | 4.49086 | 0.180503 | 0.0902514 | − | 0.995919i | \(-0.471233\pi\) | ||||
0.0902514 | + | 0.995919i | \(0.471233\pi\) | |||||||
\(620\) | 32.1163 | 1.28982 | ||||||||
\(621\) | −4.12832 | −0.165664 | ||||||||
\(622\) | −87.2498 | −3.49840 | ||||||||
\(623\) | −23.6491 | −0.947481 | ||||||||
\(624\) | 39.1658 | 1.56789 | ||||||||
\(625\) | −9.72656 | −0.389063 | ||||||||
\(626\) | −50.5499 | −2.02038 | ||||||||
\(627\) | 22.4796 | 0.897749 | ||||||||
\(628\) | −67.9387 | −2.71105 | ||||||||
\(629\) | 11.5876 | 0.462028 | ||||||||
\(630\) | 11.7284 | 0.467270 | ||||||||
\(631\) | −5.96553 | −0.237484 | −0.118742 | − | 0.992925i | \(-0.537886\pi\) | ||||
−0.118742 | + | 0.992925i | \(0.537886\pi\) | |||||||
\(632\) | 12.0477 | 0.479233 | ||||||||
\(633\) | 5.07955 | 0.201894 | ||||||||
\(634\) | 30.5288 | 1.21245 | ||||||||
\(635\) | −24.8611 | −0.986581 | ||||||||
\(636\) | 14.1466 | 0.560949 | ||||||||
\(637\) | −22.8017 | −0.903435 | ||||||||
\(638\) | −9.51791 | −0.376818 | ||||||||
\(639\) | 23.0184 | 0.910594 | ||||||||
\(640\) | −3.40061 | −0.134421 | ||||||||
\(641\) | −1.73375 | −0.0684789 | −0.0342395 | − | 0.999414i | \(-0.510901\pi\) | ||||
−0.0342395 | + | 0.999414i | \(0.510901\pi\) | |||||||
\(642\) | 28.5316 | 1.12605 | ||||||||
\(643\) | 38.3312 | 1.51163 | 0.755817 | − | 0.654783i | \(-0.227240\pi\) | ||||
0.755817 | + | 0.654783i | \(0.227240\pi\) | |||||||
\(644\) | −5.21630 | −0.205551 | ||||||||
\(645\) | −17.9693 | −0.707541 | ||||||||
\(646\) | −18.7064 | −0.735994 | ||||||||
\(647\) | 29.2098 | 1.14836 | 0.574178 | − | 0.818730i | \(-0.305322\pi\) | ||||
0.574178 | + | 0.818730i | \(0.305322\pi\) | |||||||
\(648\) | −9.24813 | −0.363301 | ||||||||
\(649\) | 13.5866 | 0.533321 | ||||||||
\(650\) | 23.9873 | 0.940858 | ||||||||
\(651\) | 5.08520 | 0.199305 | ||||||||
\(652\) | −76.3127 | −2.98864 | ||||||||
\(653\) | −42.7952 | −1.67471 | −0.837353 | − | 0.546662i | \(-0.815898\pi\) | ||||
−0.837353 | + | 0.546662i | \(0.815898\pi\) | |||||||
\(654\) | 0.756371 | 0.0295765 | ||||||||
\(655\) | −16.3021 | −0.636976 | ||||||||
\(656\) | 11.4021 | 0.445177 | ||||||||
\(657\) | −23.8927 | −0.932143 | ||||||||
\(658\) | −0.516185 | −0.0201230 | ||||||||
\(659\) | −23.7004 | −0.923238 | −0.461619 | − | 0.887078i | \(-0.652731\pi\) | ||||
−0.461619 | + | 0.887078i | \(0.652731\pi\) | |||||||
\(660\) | 25.9104 | 1.00856 | ||||||||
\(661\) | 24.1228 | 0.938268 | 0.469134 | − | 0.883127i | \(-0.344566\pi\) | ||||
0.469134 | + | 0.883127i | \(0.344566\pi\) | |||||||
\(662\) | −12.8378 | −0.498954 | ||||||||
\(663\) | −4.32420 | −0.167938 | ||||||||
\(664\) | 16.9535 | 0.657923 | ||||||||
\(665\) | −15.4883 | −0.600610 | ||||||||
\(666\) | −60.0567 | −2.32715 | ||||||||
\(667\) | −0.934180 | −0.0361716 | ||||||||
\(668\) | −102.877 | −3.98044 | ||||||||
\(669\) | −6.37921 | −0.246634 | ||||||||
\(670\) | 57.2184 | 2.21054 | ||||||||
\(671\) | −18.4061 | −0.710558 | ||||||||
\(672\) | 12.4025 | 0.478436 | ||||||||
\(673\) | −3.67522 | −0.141669 | −0.0708346 | − | 0.997488i | \(-0.522566\pi\) | ||||
−0.0708346 | + | 0.997488i | \(0.522566\pi\) | |||||||
\(674\) | −89.6753 | −3.45416 | ||||||||
\(675\) | 10.5660 | 0.406687 | ||||||||
\(676\) | 26.5029 | 1.01934 | ||||||||
\(677\) | 45.7769 | 1.75935 | 0.879675 | − | 0.475575i | \(-0.157760\pi\) | ||||
0.879675 | + | 0.475575i | \(0.157760\pi\) | |||||||
\(678\) | −27.0172 | −1.03759 | ||||||||
\(679\) | 9.37443 | 0.359758 | ||||||||
\(680\) | −12.5377 | −0.480800 | ||||||||
\(681\) | 10.8255 | 0.414835 | ||||||||
\(682\) | −33.8391 | −1.29577 | ||||||||
\(683\) | −1.52419 | −0.0583215 | −0.0291608 | − | 0.999575i | \(-0.509283\pi\) | ||||
−0.0291608 | + | 0.999575i | \(0.509283\pi\) | |||||||
\(684\) | 68.3481 | 2.61335 | ||||||||
\(685\) | −39.3029 | −1.50169 | ||||||||
\(686\) | −41.8018 | −1.59600 | ||||||||
\(687\) | 8.77800 | 0.334902 | ||||||||
\(688\) | 100.599 | 3.83532 | ||||||||
\(689\) | 13.0079 | 0.495561 | ||||||||
\(690\) | 3.60741 | 0.137332 | ||||||||
\(691\) | 20.3036 | 0.772386 | 0.386193 | − | 0.922418i | \(-0.373790\pi\) | ||||
0.386193 | + | 0.922418i | \(0.373790\pi\) | |||||||
\(692\) | −27.8384 | −1.05826 | ||||||||
\(693\) | −8.71162 | −0.330927 | ||||||||
\(694\) | 61.0689 | 2.31814 | ||||||||
\(695\) | 2.18821 | 0.0830034 | ||||||||
\(696\) | 7.92465 | 0.300383 | ||||||||
\(697\) | −1.25888 | −0.0476833 | ||||||||
\(698\) | −41.3267 | −1.56424 | ||||||||
\(699\) | −6.33739 | −0.239702 | ||||||||
\(700\) | 13.3506 | 0.504606 | ||||||||
\(701\) | −10.3863 | −0.392285 | −0.196143 | − | 0.980575i | \(-0.562842\pi\) | ||||
−0.196143 | + | 0.980575i | \(0.562842\pi\) | |||||||
\(702\) | 55.3777 | 2.09010 | ||||||||
\(703\) | 79.3098 | 2.99123 | ||||||||
\(704\) | −21.8237 | −0.822511 | ||||||||
\(705\) | 0.251656 | 0.00947790 | ||||||||
\(706\) | 74.0988 | 2.78874 | ||||||||
\(707\) | 7.15759 | 0.269189 | ||||||||
\(708\) | −19.4539 | −0.731122 | ||||||||
\(709\) | 34.9053 | 1.31090 | 0.655448 | − | 0.755240i | \(-0.272480\pi\) | ||||
0.655448 | + | 0.755240i | \(0.272480\pi\) | |||||||
\(710\) | −49.7002 | −1.86522 | ||||||||
\(711\) | 3.39615 | 0.127366 | ||||||||
\(712\) | −131.028 | −4.91048 | ||||||||
\(713\) | −3.32129 | −0.124383 | ||||||||
\(714\) | −3.41396 | −0.127764 | ||||||||
\(715\) | 23.8248 | 0.890998 | ||||||||
\(716\) | −28.8611 | −1.07859 | ||||||||
\(717\) | −24.5586 | −0.917159 | ||||||||
\(718\) | 2.01088 | 0.0750454 | ||||||||
\(719\) | 5.17696 | 0.193068 | 0.0965341 | − | 0.995330i | \(-0.469224\pi\) | ||||
0.0965341 | + | 0.995330i | \(0.469224\pi\) | |||||||
\(720\) | 32.0113 | 1.19299 | ||||||||
\(721\) | 20.5505 | 0.765339 | ||||||||
\(722\) | −78.5646 | −2.92387 | ||||||||
\(723\) | −0.980039 | −0.0364480 | ||||||||
\(724\) | −19.2926 | −0.717003 | ||||||||
\(725\) | 2.39094 | 0.0887974 | ||||||||
\(726\) | 0.767896 | 0.0284993 | ||||||||
\(727\) | −7.00384 | −0.259758 | −0.129879 | − | 0.991530i | \(-0.541459\pi\) | ||||
−0.129879 | + | 0.991530i | \(0.541459\pi\) | |||||||
\(728\) | 40.6881 | 1.50800 | ||||||||
\(729\) | 11.9141 | 0.441262 | ||||||||
\(730\) | 51.5880 | 1.90936 | ||||||||
\(731\) | −11.1069 | −0.410804 | ||||||||
\(732\) | 26.3546 | 0.974094 | ||||||||
\(733\) | −1.22518 | −0.0452530 | −0.0226265 | − | 0.999744i | \(-0.507203\pi\) | ||||
−0.0226265 | + | 0.999744i | \(0.507203\pi\) | |||||||
\(734\) | 60.8288 | 2.24523 | ||||||||
\(735\) | 8.77648 | 0.323725 | ||||||||
\(736\) | −8.10042 | −0.298586 | ||||||||
\(737\) | −42.5008 | −1.56554 | ||||||||
\(738\) | 6.52455 | 0.240172 | ||||||||
\(739\) | −31.4569 | −1.15716 | −0.578580 | − | 0.815625i | \(-0.696393\pi\) | ||||
−0.578580 | + | 0.815625i | \(0.696393\pi\) | |||||||
\(740\) | 91.4140 | 3.36045 | ||||||||
\(741\) | −29.5964 | −1.08725 | ||||||||
\(742\) | 10.2697 | 0.377014 | ||||||||
\(743\) | 17.5176 | 0.642659 | 0.321330 | − | 0.946967i | \(-0.395870\pi\) | ||||
0.321330 | + | 0.946967i | \(0.395870\pi\) | |||||||
\(744\) | 28.1745 | 1.03293 | ||||||||
\(745\) | −29.6521 | −1.08637 | ||||||||
\(746\) | −72.3368 | −2.64844 | ||||||||
\(747\) | 4.77904 | 0.174856 | ||||||||
\(748\) | 16.0154 | 0.585580 | ||||||||
\(749\) | 14.6016 | 0.533532 | ||||||||
\(750\) | −30.8115 | −1.12508 | ||||||||
\(751\) | −35.2893 | −1.28773 | −0.643863 | − | 0.765141i | \(-0.722669\pi\) | ||||
−0.643863 | + | 0.765141i | \(0.722669\pi\) | |||||||
\(752\) | −1.40887 | −0.0513761 | ||||||||
\(753\) | −12.3103 | −0.448614 | ||||||||
\(754\) | 12.5312 | 0.456359 | ||||||||
\(755\) | −8.91324 | −0.324386 | ||||||||
\(756\) | 30.8216 | 1.12097 | ||||||||
\(757\) | −17.2974 | −0.628686 | −0.314343 | − | 0.949309i | \(-0.601784\pi\) | ||||
−0.314343 | + | 0.949309i | \(0.601784\pi\) | |||||||
\(758\) | −19.0931 | −0.693493 | ||||||||
\(759\) | −2.67952 | −0.0972603 | ||||||||
\(760\) | −85.8129 | −3.11276 | ||||||||
\(761\) | 9.53250 | 0.345553 | 0.172776 | − | 0.984961i | \(-0.444726\pi\) | ||||
0.172776 | + | 0.984961i | \(0.444726\pi\) | |||||||
\(762\) | −37.5066 | −1.35872 | ||||||||
\(763\) | 0.387088 | 0.0140135 | ||||||||
\(764\) | −78.7570 | −2.84933 | ||||||||
\(765\) | −3.53428 | −0.127782 | ||||||||
\(766\) | 87.2034 | 3.15079 | ||||||||
\(767\) | −17.8880 | −0.645897 | ||||||||
\(768\) | −18.2079 | −0.657023 | ||||||||
\(769\) | −37.0399 | −1.33569 | −0.667847 | − | 0.744299i | \(-0.732784\pi\) | ||||
−0.667847 | + | 0.744299i | \(0.732784\pi\) | |||||||
\(770\) | 18.8097 | 0.677855 | ||||||||
\(771\) | 15.7166 | 0.566019 | ||||||||
\(772\) | −110.216 | −3.96675 | ||||||||
\(773\) | −6.97450 | −0.250855 | −0.125428 | − | 0.992103i | \(-0.540030\pi\) | ||||
−0.125428 | + | 0.992103i | \(0.540030\pi\) | |||||||
\(774\) | 57.5655 | 2.06915 | ||||||||
\(775\) | 8.50053 | 0.305348 | ||||||||
\(776\) | 51.9391 | 1.86450 | ||||||||
\(777\) | 14.4742 | 0.519259 | ||||||||
\(778\) | −40.8463 | −1.46441 | ||||||||
\(779\) | −8.61621 | −0.308708 | ||||||||
\(780\) | −34.1134 | −1.22146 | ||||||||
\(781\) | 36.9164 | 1.32097 | ||||||||
\(782\) | 2.22976 | 0.0797360 | ||||||||
\(783\) | 5.51980 | 0.197261 | ||||||||
\(784\) | −49.1342 | −1.75479 | ||||||||
\(785\) | 24.0450 | 0.858204 | ||||||||
\(786\) | −24.5942 | −0.877246 | ||||||||
\(787\) | 29.9359 | 1.06710 | 0.533550 | − | 0.845768i | \(-0.320857\pi\) | ||||
0.533550 | + | 0.845768i | \(0.320857\pi\) | |||||||
\(788\) | −64.7726 | −2.30743 | ||||||||
\(789\) | 3.26559 | 0.116258 | ||||||||
\(790\) | −7.33281 | −0.260890 | ||||||||
\(791\) | −13.8266 | −0.491617 | ||||||||
\(792\) | −48.2667 | −1.71508 | ||||||||
\(793\) | 24.2332 | 0.860547 | ||||||||
\(794\) | −21.7268 | −0.771056 | ||||||||
\(795\) | −5.00680 | −0.177573 | ||||||||
\(796\) | −122.685 | −4.34847 | ||||||||
\(797\) | −10.7103 | −0.379380 | −0.189690 | − | 0.981844i | \(-0.560748\pi\) | ||||
−0.189690 | + | 0.981844i | \(0.560748\pi\) | |||||||
\(798\) | −23.3664 | −0.827162 | ||||||||
\(799\) | 0.155550 | 0.00550295 | ||||||||
\(800\) | 20.7323 | 0.732996 | ||||||||
\(801\) | −36.9357 | −1.30506 | ||||||||
\(802\) | 100.439 | 3.54662 | ||||||||
\(803\) | −38.3186 | −1.35223 | ||||||||
\(804\) | 60.8544 | 2.14617 | ||||||||
\(805\) | 1.84617 | 0.0650688 | ||||||||
\(806\) | 44.5522 | 1.56928 | ||||||||
\(807\) | −7.29248 | −0.256707 | ||||||||
\(808\) | 39.6567 | 1.39512 | ||||||||
\(809\) | −30.4625 | −1.07100 | −0.535502 | − | 0.844534i | \(-0.679878\pi\) | ||||
−0.535502 | + | 0.844534i | \(0.679878\pi\) | |||||||
\(810\) | 5.62885 | 0.197778 | ||||||||
\(811\) | −6.38159 | −0.224088 | −0.112044 | − | 0.993703i | \(-0.535740\pi\) | ||||
−0.112044 | + | 0.993703i | \(0.535740\pi\) | |||||||
\(812\) | 6.97449 | 0.244757 | ||||||||
\(813\) | −20.1918 | −0.708158 | ||||||||
\(814\) | −96.3176 | −3.37593 | ||||||||
\(815\) | 27.0088 | 0.946077 | ||||||||
\(816\) | −9.31801 | −0.326196 | ||||||||
\(817\) | −76.0199 | −2.65960 | ||||||||
\(818\) | 50.8788 | 1.77894 | ||||||||
\(819\) | 11.4696 | 0.400781 | ||||||||
\(820\) | −9.93121 | −0.346813 | ||||||||
\(821\) | −31.3814 | −1.09522 | −0.547609 | − | 0.836734i | \(-0.684462\pi\) | ||||
−0.547609 | + | 0.836734i | \(0.684462\pi\) | |||||||
\(822\) | −59.2943 | −2.06813 | ||||||||
\(823\) | −8.61720 | −0.300377 | −0.150188 | − | 0.988657i | \(-0.547988\pi\) | ||||
−0.150188 | + | 0.988657i | \(0.547988\pi\) | |||||||
\(824\) | 113.860 | 3.96650 | ||||||||
\(825\) | 6.85796 | 0.238764 | ||||||||
\(826\) | −14.1226 | −0.491387 | ||||||||
\(827\) | −18.2047 | −0.633039 | −0.316520 | − | 0.948586i | \(-0.602514\pi\) | ||||
−0.316520 | + | 0.948586i | \(0.602514\pi\) | |||||||
\(828\) | −8.14693 | −0.283125 | ||||||||
\(829\) | 38.0162 | 1.32036 | 0.660179 | − | 0.751108i | \(-0.270480\pi\) | ||||
0.660179 | + | 0.751108i | \(0.270480\pi\) | |||||||
\(830\) | −10.3187 | −0.358167 | ||||||||
\(831\) | 5.07334 | 0.175992 | ||||||||
\(832\) | 28.7328 | 0.996132 | ||||||||
\(833\) | 5.42479 | 0.187958 | ||||||||
\(834\) | 3.30124 | 0.114313 | ||||||||
\(835\) | 36.4106 | 1.26004 | ||||||||
\(836\) | 109.615 | 3.79112 | ||||||||
\(837\) | 19.6246 | 0.678324 | ||||||||
\(838\) | 77.5224 | 2.67797 | ||||||||
\(839\) | 45.6228 | 1.57507 | 0.787537 | − | 0.616267i | \(-0.211356\pi\) | ||||
0.787537 | + | 0.616267i | \(0.211356\pi\) | |||||||
\(840\) | −15.6610 | −0.540357 | ||||||||
\(841\) | −27.7509 | −0.956929 | ||||||||
\(842\) | 12.4693 | 0.429720 | ||||||||
\(843\) | −13.8990 | −0.478706 | ||||||||
\(844\) | 24.7689 | 0.852582 | ||||||||
\(845\) | −9.37997 | −0.322681 | ||||||||
\(846\) | −0.806189 | −0.0277174 | ||||||||
\(847\) | 0.392987 | 0.0135032 | ||||||||
\(848\) | 28.0300 | 0.962556 | ||||||||
\(849\) | −6.91120 | −0.237192 | ||||||||
\(850\) | −5.70685 | −0.195743 | ||||||||
\(851\) | −9.45354 | −0.324063 | ||||||||
\(852\) | −52.8585 | −1.81090 | ||||||||
\(853\) | 17.2406 | 0.590307 | 0.295153 | − | 0.955450i | \(-0.404629\pi\) | ||||
0.295153 | + | 0.955450i | \(0.404629\pi\) | |||||||
\(854\) | 19.1321 | 0.654689 | ||||||||
\(855\) | −24.1899 | −0.827278 | ||||||||
\(856\) | 80.9003 | 2.76512 | ||||||||
\(857\) | 9.87638 | 0.337371 | 0.168685 | − | 0.985670i | \(-0.446048\pi\) | ||||
0.168685 | + | 0.985670i | \(0.446048\pi\) | |||||||
\(858\) | 35.9433 | 1.22708 | ||||||||
\(859\) | 25.8904 | 0.883369 | 0.441685 | − | 0.897170i | \(-0.354381\pi\) | ||||
0.441685 | + | 0.897170i | \(0.354381\pi\) | |||||||
\(860\) | −87.6220 | −2.98789 | ||||||||
\(861\) | −1.57248 | −0.0535899 | ||||||||
\(862\) | −13.9538 | −0.475270 | ||||||||
\(863\) | −14.8445 | −0.505311 | −0.252656 | − | 0.967556i | \(-0.581304\pi\) | ||||
−0.252656 | + | 0.967556i | \(0.581304\pi\) | |||||||
\(864\) | 47.8630 | 1.62833 | ||||||||
\(865\) | 9.85263 | 0.334999 | ||||||||
\(866\) | −55.9853 | −1.90246 | ||||||||
\(867\) | −15.6319 | −0.530887 | ||||||||
\(868\) | 24.7964 | 0.841646 | ||||||||
\(869\) | 5.44668 | 0.184766 | ||||||||
\(870\) | −4.82331 | −0.163526 | ||||||||
\(871\) | 55.9561 | 1.89600 | ||||||||
\(872\) | 2.14467 | 0.0726275 | ||||||||
\(873\) | 14.6412 | 0.495529 | ||||||||
\(874\) | 15.2613 | 0.516221 | ||||||||
\(875\) | −15.7684 | −0.533070 | ||||||||
\(876\) | 54.8662 | 1.85376 | ||||||||
\(877\) | 42.0781 | 1.42088 | 0.710439 | − | 0.703759i | \(-0.248497\pi\) | ||||
0.710439 | + | 0.703759i | \(0.248497\pi\) | |||||||
\(878\) | −10.9953 | −0.371072 | ||||||||
\(879\) | −2.73398 | −0.0922148 | ||||||||
\(880\) | 51.3389 | 1.73064 | ||||||||
\(881\) | −19.0418 | −0.641534 | −0.320767 | − | 0.947158i | \(-0.603941\pi\) | ||||
−0.320767 | + | 0.947158i | \(0.603941\pi\) | |||||||
\(882\) | −28.1158 | −0.946709 | ||||||||
\(883\) | 6.51087 | 0.219108 | 0.109554 | − | 0.993981i | \(-0.465058\pi\) | ||||
0.109554 | + | 0.993981i | \(0.465058\pi\) | |||||||
\(884\) | −21.0857 | −0.709188 | ||||||||
\(885\) | 6.88517 | 0.231442 | ||||||||
\(886\) | −21.7150 | −0.729531 | ||||||||
\(887\) | 5.59140 | 0.187741 | 0.0938704 | − | 0.995584i | \(-0.470076\pi\) | ||||
0.0938704 | + | 0.995584i | \(0.470076\pi\) | |||||||
\(888\) | 80.1944 | 2.69115 | ||||||||
\(889\) | −19.1948 | −0.643773 | ||||||||
\(890\) | 79.7497 | 2.67322 | ||||||||
\(891\) | −4.18100 | −0.140069 | ||||||||
\(892\) | −31.1063 | −1.04152 | ||||||||
\(893\) | 1.06464 | 0.0356268 | ||||||||
\(894\) | −44.7346 | −1.49615 | ||||||||
\(895\) | 10.2146 | 0.341437 | ||||||||
\(896\) | −2.62555 | −0.0877135 | ||||||||
\(897\) | 3.52783 | 0.117791 | ||||||||
\(898\) | −41.0841 | −1.37099 | ||||||||
\(899\) | 4.44076 | 0.148108 | ||||||||
\(900\) | 20.8513 | 0.695043 | ||||||||
\(901\) | −3.09473 | −0.103100 | ||||||||
\(902\) | 10.4639 | 0.348411 | ||||||||
\(903\) | −13.8738 | −0.461691 | ||||||||
\(904\) | −76.6063 | −2.54789 | ||||||||
\(905\) | 6.82809 | 0.226973 | ||||||||
\(906\) | −13.4470 | −0.446745 | ||||||||
\(907\) | 18.3915 | 0.610681 | 0.305340 | − | 0.952243i | \(-0.401230\pi\) | ||||
0.305340 | + | 0.952243i | \(0.401230\pi\) | |||||||
\(908\) | 52.7874 | 1.75181 | ||||||||
\(909\) | 11.1789 | 0.370780 | ||||||||
\(910\) | −24.7647 | −0.820941 | ||||||||
\(911\) | −38.2665 | −1.26783 | −0.633913 | − | 0.773404i | \(-0.718552\pi\) | ||||
−0.633913 | + | 0.773404i | \(0.718552\pi\) | |||||||
\(912\) | −63.7759 | −2.11183 | ||||||||
\(913\) | 7.66452 | 0.253659 | ||||||||
\(914\) | 22.6885 | 0.750469 | ||||||||
\(915\) | −9.32749 | −0.308357 | ||||||||
\(916\) | 42.8033 | 1.41426 | ||||||||
\(917\) | −12.5866 | −0.415646 | ||||||||
\(918\) | −13.1750 | −0.434840 | ||||||||
\(919\) | −4.89962 | −0.161624 | −0.0808118 | − | 0.996729i | \(-0.525751\pi\) | ||||
−0.0808118 | + | 0.996729i | \(0.525751\pi\) | |||||||
\(920\) | 10.2287 | 0.337230 | ||||||||
\(921\) | 19.4327 | 0.640330 | ||||||||
\(922\) | −64.8669 | −2.13628 | ||||||||
\(923\) | −48.6038 | −1.59981 | ||||||||
\(924\) | 20.0050 | 0.658116 | ||||||||
\(925\) | 24.1954 | 0.795541 | ||||||||
\(926\) | 7.47949 | 0.245791 | ||||||||
\(927\) | 32.0962 | 1.05418 | ||||||||
\(928\) | 10.8307 | 0.355536 | ||||||||
\(929\) | 17.9381 | 0.588528 | 0.294264 | − | 0.955724i | \(-0.404925\pi\) | ||||
0.294264 | + | 0.955724i | \(0.404925\pi\) | |||||||
\(930\) | −17.1484 | −0.562317 | ||||||||
\(931\) | 37.1292 | 1.21686 | ||||||||
\(932\) | −30.9024 | −1.01224 | ||||||||
\(933\) | 32.8420 | 1.07520 | ||||||||
\(934\) | −12.6920 | −0.415295 | ||||||||
\(935\) | −5.66820 | −0.185370 | ||||||||
\(936\) | 63.5475 | 2.07712 | ||||||||
\(937\) | 29.8369 | 0.974730 | 0.487365 | − | 0.873198i | \(-0.337958\pi\) | ||||
0.487365 | + | 0.873198i | \(0.337958\pi\) | |||||||
\(938\) | 44.1773 | 1.44244 | ||||||||
\(939\) | 19.0276 | 0.620943 | ||||||||
\(940\) | 1.22712 | 0.0400243 | ||||||||
\(941\) | 26.8047 | 0.873809 | 0.436904 | − | 0.899508i | \(-0.356075\pi\) | ||||
0.436904 | + | 0.899508i | \(0.356075\pi\) | |||||||
\(942\) | 36.2755 | 1.18192 | ||||||||
\(943\) | 1.02703 | 0.0334448 | ||||||||
\(944\) | −38.5459 | −1.25456 | ||||||||
\(945\) | −10.9085 | −0.354852 | ||||||||
\(946\) | 92.3222 | 3.00165 | ||||||||
\(947\) | 2.94622 | 0.0957393 | 0.0478697 | − | 0.998854i | \(-0.484757\pi\) | ||||
0.0478697 | + | 0.998854i | \(0.484757\pi\) | |||||||
\(948\) | −7.79879 | −0.253293 | ||||||||
\(949\) | 50.4499 | 1.63767 | ||||||||
\(950\) | −39.0598 | −1.26727 | ||||||||
\(951\) | −11.4914 | −0.372635 | ||||||||
\(952\) | −9.68017 | −0.313736 | ||||||||
\(953\) | −4.62861 | −0.149935 | −0.0749676 | − | 0.997186i | \(-0.523885\pi\) | ||||
−0.0749676 | + | 0.997186i | \(0.523885\pi\) | |||||||
\(954\) | 16.0395 | 0.519297 | ||||||||
\(955\) | 27.8739 | 0.901978 | ||||||||
\(956\) | −119.753 | −3.87308 | ||||||||
\(957\) | 3.58267 | 0.115811 | ||||||||
\(958\) | −0.505247 | −0.0163238 | ||||||||
\(959\) | −30.3451 | −0.979894 | ||||||||
\(960\) | −11.0594 | −0.356941 | ||||||||
\(961\) | −15.2117 | −0.490702 | ||||||||
\(962\) | 126.811 | 4.08854 | ||||||||
\(963\) | 22.8051 | 0.734885 | ||||||||
\(964\) | −4.77887 | −0.153917 | ||||||||
\(965\) | 39.0078 | 1.25571 | ||||||||
\(966\) | 2.78522 | 0.0896130 | ||||||||
\(967\) | 20.1721 | 0.648689 | 0.324345 | − | 0.945939i | \(-0.394856\pi\) | ||||
0.324345 | + | 0.945939i | \(0.394856\pi\) | |||||||
\(968\) | 2.17734 | 0.0699825 | ||||||||
\(969\) | 7.04134 | 0.226200 | ||||||||
\(970\) | −31.6126 | −1.01502 | ||||||||
\(971\) | 30.0251 | 0.963550 | 0.481775 | − | 0.876295i | \(-0.339992\pi\) | ||||
0.481775 | + | 0.876295i | \(0.339992\pi\) | |||||||
\(972\) | 76.7940 | 2.46317 | ||||||||
\(973\) | 1.68948 | 0.0541621 | ||||||||
\(974\) | 80.0853 | 2.56610 | ||||||||
\(975\) | −9.02913 | −0.289163 | ||||||||
\(976\) | 52.2190 | 1.67149 | ||||||||
\(977\) | 57.7096 | 1.84629 | 0.923147 | − | 0.384448i | \(-0.125608\pi\) | ||||
0.923147 | + | 0.384448i | \(0.125608\pi\) | |||||||
\(978\) | 40.7469 | 1.30294 | ||||||||
\(979\) | −59.2366 | −1.89321 | ||||||||
\(980\) | 42.7959 | 1.36706 | ||||||||
\(981\) | 0.604563 | 0.0193022 | ||||||||
\(982\) | 56.1154 | 1.79071 | ||||||||
\(983\) | −3.33817 | −0.106471 | −0.0532356 | − | 0.998582i | \(-0.516953\pi\) | ||||
−0.0532356 | + | 0.998582i | \(0.516953\pi\) | |||||||
\(984\) | −8.71231 | −0.277738 | ||||||||
\(985\) | 22.9245 | 0.730435 | ||||||||
\(986\) | −2.98132 | −0.0949444 | ||||||||
\(987\) | 0.194299 | 0.00618460 | ||||||||
\(988\) | −144.318 | −4.59137 | ||||||||
\(989\) | 9.06139 | 0.288136 | ||||||||
\(990\) | 29.3774 | 0.933675 | ||||||||
\(991\) | 4.48757 | 0.142552 | 0.0712762 | − | 0.997457i | \(-0.477293\pi\) | ||||
0.0712762 | + | 0.997457i | \(0.477293\pi\) | |||||||
\(992\) | 38.5065 | 1.22258 | ||||||||
\(993\) | 4.83230 | 0.153349 | ||||||||
\(994\) | −38.3727 | −1.21711 | ||||||||
\(995\) | 43.4212 | 1.37654 | ||||||||
\(996\) | −10.9744 | −0.347737 | ||||||||
\(997\) | −47.4116 | −1.50154 | −0.750770 | − | 0.660564i | \(-0.770317\pi\) | ||||
−0.750770 | + | 0.660564i | \(0.770317\pi\) | |||||||
\(998\) | −57.0172 | −1.80485 | ||||||||
\(999\) | 55.8582 | 1.76728 |
(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 | 241.2.a.a.1.1 | ✓ | 7 | |
3.2 | odd | 2 | 2169.2.a.e.1.7 | 7 | |||
4.3 | odd | 2 | 3856.2.a.j.1.2 | 7 | |||
5.4 | even | 2 | 6025.2.a.f.1.7 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
241.2.a.a.1.1 | ✓ | 7 | 1.1 | even | 1 | trivial | |
2169.2.a.e.1.7 | 7 | 3.2 | odd | 2 | |||
3856.2.a.j.1.2 | 7 | 4.3 | odd | 2 | |||
6025.2.a.f.1.7 | 7 | 5.4 | even | 2 |