Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4010,2,Mod(1,4010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4010, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4010 = 2 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4010.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: | \(32.0200112105\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - 16 x^{10} + 30 x^{9} + 93 x^{8} - 162 x^{7} - 238 x^{6} + 391 x^{5} + 240 x^{4} - 408 x^{3} - 42 x^{2} + 120 x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.16326\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4010.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.16326 | −0.671611 | −0.335806 | − | 0.941931i | \(-0.609009\pi\) | ||||
−0.335806 | + | 0.941931i | \(0.609009\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.16326 | −0.474901 | ||||||||
\(7\) | −3.35475 | −1.26798 | −0.633989 | − | 0.773342i | \(-0.718584\pi\) | ||||
−0.633989 | + | 0.773342i | \(0.718584\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.64681 | −0.548938 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 2.96520 | 0.894042 | 0.447021 | − | 0.894523i | \(-0.352485\pi\) | ||||
0.447021 | + | 0.894523i | \(0.352485\pi\) | |||||||
\(12\) | −1.16326 | −0.335806 | ||||||||
\(13\) | 2.83453 | 0.786156 | 0.393078 | − | 0.919505i | \(-0.371410\pi\) | ||||
0.393078 | + | 0.919505i | \(0.371410\pi\) | |||||||
\(14\) | −3.35475 | −0.896596 | ||||||||
\(15\) | 1.16326 | 0.300354 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.60775 | 1.36008 | 0.680039 | − | 0.733176i | \(-0.261963\pi\) | ||||
0.680039 | + | 0.733176i | \(0.261963\pi\) | |||||||
\(18\) | −1.64681 | −0.388158 | ||||||||
\(19\) | −6.23686 | −1.43083 | −0.715417 | − | 0.698698i | \(-0.753763\pi\) | ||||
−0.715417 | + | 0.698698i | \(0.753763\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 3.90247 | 0.851588 | ||||||||
\(22\) | 2.96520 | 0.632183 | ||||||||
\(23\) | −2.99565 | −0.624636 | −0.312318 | − | 0.949978i | \(-0.601105\pi\) | ||||
−0.312318 | + | 0.949978i | \(0.601105\pi\) | |||||||
\(24\) | −1.16326 | −0.237450 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.83453 | 0.555896 | ||||||||
\(27\) | 5.40548 | 1.04028 | ||||||||
\(28\) | −3.35475 | −0.633989 | ||||||||
\(29\) | 6.71384 | 1.24673 | 0.623364 | − | 0.781931i | \(-0.285765\pi\) | ||||
0.623364 | + | 0.781931i | \(0.285765\pi\) | |||||||
\(30\) | 1.16326 | 0.212382 | ||||||||
\(31\) | 7.99833 | 1.43654 | 0.718271 | − | 0.695764i | \(-0.244934\pi\) | ||||
0.718271 | + | 0.695764i | \(0.244934\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −3.44932 | −0.600449 | ||||||||
\(34\) | 5.60775 | 0.961721 | ||||||||
\(35\) | 3.35475 | 0.567057 | ||||||||
\(36\) | −1.64681 | −0.274469 | ||||||||
\(37\) | −8.79576 | −1.44601 | −0.723007 | − | 0.690841i | \(-0.757241\pi\) | ||||
−0.723007 | + | 0.690841i | \(0.757241\pi\) | |||||||
\(38\) | −6.23686 | −1.01175 | ||||||||
\(39\) | −3.29731 | −0.527991 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −12.2963 | −1.92035 | −0.960177 | − | 0.279393i | \(-0.909867\pi\) | ||||
−0.960177 | + | 0.279393i | \(0.909867\pi\) | |||||||
\(42\) | 3.90247 | 0.602164 | ||||||||
\(43\) | −0.840974 | −0.128247 | −0.0641237 | − | 0.997942i | \(-0.520425\pi\) | ||||
−0.0641237 | + | 0.997942i | \(0.520425\pi\) | |||||||
\(44\) | 2.96520 | 0.447021 | ||||||||
\(45\) | 1.64681 | 0.245493 | ||||||||
\(46\) | −2.99565 | −0.441684 | ||||||||
\(47\) | −1.73855 | −0.253594 | −0.126797 | − | 0.991929i | \(-0.540470\pi\) | ||||
−0.126797 | + | 0.991929i | \(0.540470\pi\) | |||||||
\(48\) | −1.16326 | −0.167903 | ||||||||
\(49\) | 4.25438 | 0.607768 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −6.52330 | −0.913444 | ||||||||
\(52\) | 2.83453 | 0.393078 | ||||||||
\(53\) | −10.2164 | −1.40333 | −0.701664 | − | 0.712508i | \(-0.747559\pi\) | ||||
−0.701664 | + | 0.712508i | \(0.747559\pi\) | |||||||
\(54\) | 5.40548 | 0.735592 | ||||||||
\(55\) | −2.96520 | −0.399828 | ||||||||
\(56\) | −3.35475 | −0.448298 | ||||||||
\(57\) | 7.25512 | 0.960964 | ||||||||
\(58\) | 6.71384 | 0.881570 | ||||||||
\(59\) | 13.1910 | 1.71733 | 0.858663 | − | 0.512541i | \(-0.171296\pi\) | ||||
0.858663 | + | 0.512541i | \(0.171296\pi\) | |||||||
\(60\) | 1.16326 | 0.150177 | ||||||||
\(61\) | −8.53190 | −1.09240 | −0.546199 | − | 0.837655i | \(-0.683926\pi\) | ||||
−0.546199 | + | 0.837655i | \(0.683926\pi\) | |||||||
\(62\) | 7.99833 | 1.01579 | ||||||||
\(63\) | 5.52466 | 0.696042 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.83453 | −0.351580 | ||||||||
\(66\) | −3.44932 | −0.424582 | ||||||||
\(67\) | 9.32681 | 1.13945 | 0.569726 | − | 0.821835i | \(-0.307050\pi\) | ||||
0.569726 | + | 0.821835i | \(0.307050\pi\) | |||||||
\(68\) | 5.60775 | 0.680039 | ||||||||
\(69\) | 3.48473 | 0.419512 | ||||||||
\(70\) | 3.35475 | 0.400970 | ||||||||
\(71\) | −9.13221 | −1.08379 | −0.541897 | − | 0.840445i | \(-0.682294\pi\) | ||||
−0.541897 | + | 0.840445i | \(0.682294\pi\) | |||||||
\(72\) | −1.64681 | −0.194079 | ||||||||
\(73\) | −3.85112 | −0.450740 | −0.225370 | − | 0.974273i | \(-0.572359\pi\) | ||||
−0.225370 | + | 0.974273i | \(0.572359\pi\) | |||||||
\(74\) | −8.79576 | −1.02249 | ||||||||
\(75\) | −1.16326 | −0.134322 | ||||||||
\(76\) | −6.23686 | −0.715417 | ||||||||
\(77\) | −9.94753 | −1.13363 | ||||||||
\(78\) | −3.29731 | −0.373346 | ||||||||
\(79\) | 9.04751 | 1.01792 | 0.508962 | − | 0.860789i | \(-0.330029\pi\) | ||||
0.508962 | + | 0.860789i | \(0.330029\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −1.34756 | −0.149728 | ||||||||
\(82\) | −12.2963 | −1.35790 | ||||||||
\(83\) | −15.8755 | −1.74256 | −0.871281 | − | 0.490785i | \(-0.836710\pi\) | ||||
−0.871281 | + | 0.490785i | \(0.836710\pi\) | |||||||
\(84\) | 3.90247 | 0.425794 | ||||||||
\(85\) | −5.60775 | −0.608246 | ||||||||
\(86\) | −0.840974 | −0.0906846 | ||||||||
\(87\) | −7.80997 | −0.837317 | ||||||||
\(88\) | 2.96520 | 0.316092 | ||||||||
\(89\) | −4.65541 | −0.493472 | −0.246736 | − | 0.969083i | \(-0.579358\pi\) | ||||
−0.246736 | + | 0.969083i | \(0.579358\pi\) | |||||||
\(90\) | 1.64681 | 0.173590 | ||||||||
\(91\) | −9.50914 | −0.996829 | ||||||||
\(92\) | −2.99565 | −0.312318 | ||||||||
\(93\) | −9.30417 | −0.964798 | ||||||||
\(94\) | −1.73855 | −0.179318 | ||||||||
\(95\) | 6.23686 | 0.639888 | ||||||||
\(96\) | −1.16326 | −0.118725 | ||||||||
\(97\) | −2.71538 | −0.275705 | −0.137852 | − | 0.990453i | \(-0.544020\pi\) | ||||
−0.137852 | + | 0.990453i | \(0.544020\pi\) | |||||||
\(98\) | 4.25438 | 0.429757 | ||||||||
\(99\) | −4.88314 | −0.490774 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −13.7228 | −1.36547 | −0.682736 | − | 0.730665i | \(-0.739210\pi\) | ||||
−0.682736 | + | 0.730665i | \(0.739210\pi\) | |||||||
\(102\) | −6.52330 | −0.645903 | ||||||||
\(103\) | −15.4538 | −1.52271 | −0.761354 | − | 0.648336i | \(-0.775465\pi\) | ||||
−0.761354 | + | 0.648336i | \(0.775465\pi\) | |||||||
\(104\) | 2.83453 | 0.277948 | ||||||||
\(105\) | −3.90247 | −0.380842 | ||||||||
\(106\) | −10.2164 | −0.992303 | ||||||||
\(107\) | −2.41946 | −0.233898 | −0.116949 | − | 0.993138i | \(-0.537311\pi\) | ||||
−0.116949 | + | 0.993138i | \(0.537311\pi\) | |||||||
\(108\) | 5.40548 | 0.520142 | ||||||||
\(109\) | −5.07441 | −0.486040 | −0.243020 | − | 0.970021i | \(-0.578138\pi\) | ||||
−0.243020 | + | 0.970021i | \(0.578138\pi\) | |||||||
\(110\) | −2.96520 | −0.282721 | ||||||||
\(111\) | 10.2318 | 0.971159 | ||||||||
\(112\) | −3.35475 | −0.316994 | ||||||||
\(113\) | −16.5001 | −1.55220 | −0.776101 | − | 0.630609i | \(-0.782805\pi\) | ||||
−0.776101 | + | 0.630609i | \(0.782805\pi\) | |||||||
\(114\) | 7.25512 | 0.679504 | ||||||||
\(115\) | 2.99565 | 0.279346 | ||||||||
\(116\) | 6.71384 | 0.623364 | ||||||||
\(117\) | −4.66794 | −0.431551 | ||||||||
\(118\) | 13.1910 | 1.21433 | ||||||||
\(119\) | −18.8126 | −1.72455 | ||||||||
\(120\) | 1.16326 | 0.106191 | ||||||||
\(121\) | −2.20757 | −0.200688 | ||||||||
\(122\) | −8.53190 | −0.772442 | ||||||||
\(123\) | 14.3038 | 1.28973 | ||||||||
\(124\) | 7.99833 | 0.718271 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 5.52466 | 0.492176 | ||||||||
\(127\) | 12.7407 | 1.13055 | 0.565277 | − | 0.824901i | \(-0.308769\pi\) | ||||
0.565277 | + | 0.824901i | \(0.308769\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0.978276 | 0.0861324 | ||||||||
\(130\) | −2.83453 | −0.248604 | ||||||||
\(131\) | 4.48683 | 0.392016 | 0.196008 | − | 0.980602i | \(-0.437202\pi\) | ||||
0.196008 | + | 0.980602i | \(0.437202\pi\) | |||||||
\(132\) | −3.44932 | −0.300224 | ||||||||
\(133\) | 20.9231 | 1.81427 | ||||||||
\(134\) | 9.32681 | 0.805714 | ||||||||
\(135\) | −5.40548 | −0.465229 | ||||||||
\(136\) | 5.60775 | 0.480860 | ||||||||
\(137\) | 13.7647 | 1.17599 | 0.587997 | − | 0.808863i | \(-0.299917\pi\) | ||||
0.587997 | + | 0.808863i | \(0.299917\pi\) | |||||||
\(138\) | 3.48473 | 0.296640 | ||||||||
\(139\) | 15.8688 | 1.34598 | 0.672989 | − | 0.739653i | \(-0.265010\pi\) | ||||
0.672989 | + | 0.739653i | \(0.265010\pi\) | |||||||
\(140\) | 3.35475 | 0.283528 | ||||||||
\(141\) | 2.02240 | 0.170316 | ||||||||
\(142\) | −9.13221 | −0.766358 | ||||||||
\(143\) | 8.40495 | 0.702857 | ||||||||
\(144\) | −1.64681 | −0.137235 | ||||||||
\(145\) | −6.71384 | −0.557554 | ||||||||
\(146\) | −3.85112 | −0.318721 | ||||||||
\(147\) | −4.94897 | −0.408184 | ||||||||
\(148\) | −8.79576 | −0.723007 | ||||||||
\(149\) | −22.9427 | −1.87954 | −0.939769 | − | 0.341811i | \(-0.888960\pi\) | ||||
−0.939769 | + | 0.341811i | \(0.888960\pi\) | |||||||
\(150\) | −1.16326 | −0.0949802 | ||||||||
\(151\) | −12.5535 | −1.02159 | −0.510793 | − | 0.859704i | \(-0.670648\pi\) | ||||
−0.510793 | + | 0.859704i | \(0.670648\pi\) | |||||||
\(152\) | −6.23686 | −0.505876 | ||||||||
\(153\) | −9.23492 | −0.746599 | ||||||||
\(154\) | −9.94753 | −0.801595 | ||||||||
\(155\) | −7.99833 | −0.642441 | ||||||||
\(156\) | −3.29731 | −0.263996 | ||||||||
\(157\) | −7.44522 | −0.594194 | −0.297097 | − | 0.954847i | \(-0.596018\pi\) | ||||
−0.297097 | + | 0.954847i | \(0.596018\pi\) | |||||||
\(158\) | 9.04751 | 0.719781 | ||||||||
\(159\) | 11.8844 | 0.942491 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 10.0497 | 0.792025 | ||||||||
\(162\) | −1.34756 | −0.105874 | ||||||||
\(163\) | −12.7158 | −0.995980 | −0.497990 | − | 0.867183i | \(-0.665928\pi\) | ||||
−0.497990 | + | 0.867183i | \(0.665928\pi\) | |||||||
\(164\) | −12.2963 | −0.960177 | ||||||||
\(165\) | 3.44932 | 0.268529 | ||||||||
\(166\) | −15.8755 | −1.23218 | ||||||||
\(167\) | 16.6894 | 1.29147 | 0.645734 | − | 0.763563i | \(-0.276552\pi\) | ||||
0.645734 | + | 0.763563i | \(0.276552\pi\) | |||||||
\(168\) | 3.90247 | 0.301082 | ||||||||
\(169\) | −4.96546 | −0.381958 | ||||||||
\(170\) | −5.60775 | −0.430095 | ||||||||
\(171\) | 10.2710 | 0.785440 | ||||||||
\(172\) | −0.840974 | −0.0641237 | ||||||||
\(173\) | −13.7598 | −1.04614 | −0.523070 | − | 0.852290i | \(-0.675213\pi\) | ||||
−0.523070 | + | 0.852290i | \(0.675213\pi\) | |||||||
\(174\) | −7.80997 | −0.592073 | ||||||||
\(175\) | −3.35475 | −0.253596 | ||||||||
\(176\) | 2.96520 | 0.223511 | ||||||||
\(177\) | −15.3447 | −1.15338 | ||||||||
\(178\) | −4.65541 | −0.348938 | ||||||||
\(179\) | −2.09821 | −0.156827 | −0.0784137 | − | 0.996921i | \(-0.524986\pi\) | ||||
−0.0784137 | + | 0.996921i | \(0.524986\pi\) | |||||||
\(180\) | 1.64681 | 0.122746 | ||||||||
\(181\) | 16.1159 | 1.19788 | 0.598942 | − | 0.800792i | \(-0.295588\pi\) | ||||
0.598942 | + | 0.800792i | \(0.295588\pi\) | |||||||
\(182\) | −9.50914 | −0.704864 | ||||||||
\(183\) | 9.92486 | 0.733667 | ||||||||
\(184\) | −2.99565 | −0.220842 | ||||||||
\(185\) | 8.79576 | 0.646677 | ||||||||
\(186\) | −9.30417 | −0.682215 | ||||||||
\(187\) | 16.6281 | 1.21597 | ||||||||
\(188\) | −1.73855 | −0.126797 | ||||||||
\(189\) | −18.1340 | −1.31906 | ||||||||
\(190\) | 6.23686 | 0.452469 | ||||||||
\(191\) | 6.77893 | 0.490506 | 0.245253 | − | 0.969459i | \(-0.421129\pi\) | ||||
0.245253 | + | 0.969459i | \(0.421129\pi\) | |||||||
\(192\) | −1.16326 | −0.0839514 | ||||||||
\(193\) | 20.3721 | 1.46641 | 0.733207 | − | 0.680006i | \(-0.238023\pi\) | ||||
0.733207 | + | 0.680006i | \(0.238023\pi\) | |||||||
\(194\) | −2.71538 | −0.194953 | ||||||||
\(195\) | 3.29731 | 0.236125 | ||||||||
\(196\) | 4.25438 | 0.303884 | ||||||||
\(197\) | −18.4708 | −1.31599 | −0.657994 | − | 0.753023i | \(-0.728595\pi\) | ||||
−0.657994 | + | 0.753023i | \(0.728595\pi\) | |||||||
\(198\) | −4.88314 | −0.347030 | ||||||||
\(199\) | −24.5092 | −1.73741 | −0.868704 | − | 0.495331i | \(-0.835047\pi\) | ||||
−0.868704 | + | 0.495331i | \(0.835047\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −10.8495 | −0.765268 | ||||||||
\(202\) | −13.7228 | −0.965534 | ||||||||
\(203\) | −22.5233 | −1.58082 | ||||||||
\(204\) | −6.52330 | −0.456722 | ||||||||
\(205\) | 12.2963 | 0.858808 | ||||||||
\(206\) | −15.4538 | −1.07672 | ||||||||
\(207\) | 4.93328 | 0.342887 | ||||||||
\(208\) | 2.83453 | 0.196539 | ||||||||
\(209\) | −18.4936 | −1.27923 | ||||||||
\(210\) | −3.90247 | −0.269296 | ||||||||
\(211\) | 0.410059 | 0.0282296 | 0.0141148 | − | 0.999900i | \(-0.495507\pi\) | ||||
0.0141148 | + | 0.999900i | \(0.495507\pi\) | |||||||
\(212\) | −10.2164 | −0.701664 | ||||||||
\(213\) | 10.6232 | 0.727888 | ||||||||
\(214\) | −2.41946 | −0.165391 | ||||||||
\(215\) | 0.840974 | 0.0573540 | ||||||||
\(216\) | 5.40548 | 0.367796 | ||||||||
\(217\) | −26.8324 | −1.82150 | ||||||||
\(218\) | −5.07441 | −0.343682 | ||||||||
\(219\) | 4.47987 | 0.302722 | ||||||||
\(220\) | −2.96520 | −0.199914 | ||||||||
\(221\) | 15.8953 | 1.06923 | ||||||||
\(222\) | 10.2318 | 0.686713 | ||||||||
\(223\) | −1.72577 | −0.115566 | −0.0577830 | − | 0.998329i | \(-0.518403\pi\) | ||||
−0.0577830 | + | 0.998329i | \(0.518403\pi\) | |||||||
\(224\) | −3.35475 | −0.224149 | ||||||||
\(225\) | −1.64681 | −0.109788 | ||||||||
\(226\) | −16.5001 | −1.09757 | ||||||||
\(227\) | −8.01949 | −0.532273 | −0.266136 | − | 0.963935i | \(-0.585747\pi\) | ||||
−0.266136 | + | 0.963935i | \(0.585747\pi\) | |||||||
\(228\) | 7.25512 | 0.480482 | ||||||||
\(229\) | 12.8189 | 0.847098 | 0.423549 | − | 0.905873i | \(-0.360784\pi\) | ||||
0.423549 | + | 0.905873i | \(0.360784\pi\) | |||||||
\(230\) | 2.99565 | 0.197527 | ||||||||
\(231\) | 11.5716 | 0.761356 | ||||||||
\(232\) | 6.71384 | 0.440785 | ||||||||
\(233\) | −1.42208 | −0.0931633 | −0.0465817 | − | 0.998914i | \(-0.514833\pi\) | ||||
−0.0465817 | + | 0.998914i | \(0.514833\pi\) | |||||||
\(234\) | −4.66794 | −0.305153 | ||||||||
\(235\) | 1.73855 | 0.113411 | ||||||||
\(236\) | 13.1910 | 0.858663 | ||||||||
\(237\) | −10.5246 | −0.683649 | ||||||||
\(238\) | −18.8126 | −1.21944 | ||||||||
\(239\) | −9.78933 | −0.633219 | −0.316609 | − | 0.948556i | \(-0.602544\pi\) | ||||
−0.316609 | + | 0.948556i | \(0.602544\pi\) | |||||||
\(240\) | 1.16326 | 0.0750884 | ||||||||
\(241\) | 0.658045 | 0.0423884 | 0.0211942 | − | 0.999775i | \(-0.493253\pi\) | ||||
0.0211942 | + | 0.999775i | \(0.493253\pi\) | |||||||
\(242\) | −2.20757 | −0.141908 | ||||||||
\(243\) | −14.6489 | −0.939725 | ||||||||
\(244\) | −8.53190 | −0.546199 | ||||||||
\(245\) | −4.25438 | −0.271802 | ||||||||
\(246\) | 14.3038 | 0.911978 | ||||||||
\(247\) | −17.6785 | −1.12486 | ||||||||
\(248\) | 7.99833 | 0.507894 | ||||||||
\(249\) | 18.4674 | 1.17032 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 14.2838 | 0.901587 | 0.450793 | − | 0.892628i | \(-0.351141\pi\) | ||||
0.450793 | + | 0.892628i | \(0.351141\pi\) | |||||||
\(252\) | 5.52466 | 0.348021 | ||||||||
\(253\) | −8.88271 | −0.558451 | ||||||||
\(254\) | 12.7407 | 0.799423 | ||||||||
\(255\) | 6.52330 | 0.408505 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −0.865966 | −0.0540175 | −0.0270087 | − | 0.999635i | \(-0.508598\pi\) | ||||
−0.0270087 | + | 0.999635i | \(0.508598\pi\) | |||||||
\(258\) | 0.978276 | 0.0609048 | ||||||||
\(259\) | 29.5076 | 1.83351 | ||||||||
\(260\) | −2.83453 | −0.175790 | ||||||||
\(261\) | −11.0565 | −0.684377 | ||||||||
\(262\) | 4.48683 | 0.277197 | ||||||||
\(263\) | −13.8708 | −0.855312 | −0.427656 | − | 0.903942i | \(-0.640661\pi\) | ||||
−0.427656 | + | 0.903942i | \(0.640661\pi\) | |||||||
\(264\) | −3.44932 | −0.212291 | ||||||||
\(265\) | 10.2164 | 0.627587 | ||||||||
\(266\) | 20.9231 | 1.28288 | ||||||||
\(267\) | 5.41547 | 0.331422 | ||||||||
\(268\) | 9.32681 | 0.569726 | ||||||||
\(269\) | 27.4725 | 1.67503 | 0.837513 | − | 0.546418i | \(-0.184009\pi\) | ||||
0.837513 | + | 0.546418i | \(0.184009\pi\) | |||||||
\(270\) | −5.40548 | −0.328967 | ||||||||
\(271\) | 31.6496 | 1.92258 | 0.961289 | − | 0.275542i | \(-0.0888574\pi\) | ||||
0.961289 | + | 0.275542i | \(0.0888574\pi\) | |||||||
\(272\) | 5.60775 | 0.340020 | ||||||||
\(273\) | 11.0616 | 0.669481 | ||||||||
\(274\) | 13.7647 | 0.831553 | ||||||||
\(275\) | 2.96520 | 0.178808 | ||||||||
\(276\) | 3.48473 | 0.209756 | ||||||||
\(277\) | −2.48866 | −0.149529 | −0.0747644 | − | 0.997201i | \(-0.523820\pi\) | ||||
−0.0747644 | + | 0.997201i | \(0.523820\pi\) | |||||||
\(278\) | 15.8688 | 0.951750 | ||||||||
\(279\) | −13.1718 | −0.788573 | ||||||||
\(280\) | 3.35475 | 0.200485 | ||||||||
\(281\) | 7.69352 | 0.458957 | 0.229478 | − | 0.973314i | \(-0.426298\pi\) | ||||
0.229478 | + | 0.973314i | \(0.426298\pi\) | |||||||
\(282\) | 2.02240 | 0.120432 | ||||||||
\(283\) | −10.9512 | −0.650981 | −0.325490 | − | 0.945545i | \(-0.605529\pi\) | ||||
−0.325490 | + | 0.945545i | \(0.605529\pi\) | |||||||
\(284\) | −9.13221 | −0.541897 | ||||||||
\(285\) | −7.25512 | −0.429756 | ||||||||
\(286\) | 8.40495 | 0.496995 | ||||||||
\(287\) | 41.2509 | 2.43497 | ||||||||
\(288\) | −1.64681 | −0.0970395 | ||||||||
\(289\) | 14.4468 | 0.849814 | ||||||||
\(290\) | −6.71384 | −0.394250 | ||||||||
\(291\) | 3.15870 | 0.185167 | ||||||||
\(292\) | −3.85112 | −0.225370 | ||||||||
\(293\) | 16.5844 | 0.968869 | 0.484435 | − | 0.874828i | \(-0.339025\pi\) | ||||
0.484435 | + | 0.874828i | \(0.339025\pi\) | |||||||
\(294\) | −4.94897 | −0.288630 | ||||||||
\(295\) | −13.1910 | −0.768011 | ||||||||
\(296\) | −8.79576 | −0.511243 | ||||||||
\(297\) | 16.0283 | 0.930058 | ||||||||
\(298\) | −22.9427 | −1.32903 | ||||||||
\(299\) | −8.49125 | −0.491061 | ||||||||
\(300\) | −1.16326 | −0.0671611 | ||||||||
\(301\) | 2.82126 | 0.162615 | ||||||||
\(302\) | −12.5535 | −0.722370 | ||||||||
\(303\) | 15.9633 | 0.917066 | ||||||||
\(304\) | −6.23686 | −0.357709 | ||||||||
\(305\) | 8.53190 | 0.488535 | ||||||||
\(306\) | −9.23492 | −0.527925 | ||||||||
\(307\) | −17.5543 | −1.00188 | −0.500938 | − | 0.865483i | \(-0.667011\pi\) | ||||
−0.500938 | + | 0.865483i | \(0.667011\pi\) | |||||||
\(308\) | −9.94753 | −0.566813 | ||||||||
\(309\) | 17.9769 | 1.02267 | ||||||||
\(310\) | −7.99833 | −0.454274 | ||||||||
\(311\) | 14.0724 | 0.797973 | 0.398986 | − | 0.916957i | \(-0.369362\pi\) | ||||
0.398986 | + | 0.916957i | \(0.369362\pi\) | |||||||
\(312\) | −3.29731 | −0.186673 | ||||||||
\(313\) | −19.1958 | −1.08501 | −0.542507 | − | 0.840052i | \(-0.682525\pi\) | ||||
−0.542507 | + | 0.840052i | \(0.682525\pi\) | |||||||
\(314\) | −7.44522 | −0.420158 | ||||||||
\(315\) | −5.52466 | −0.311279 | ||||||||
\(316\) | 9.04751 | 0.508962 | ||||||||
\(317\) | −25.6040 | −1.43807 | −0.719033 | − | 0.694976i | \(-0.755415\pi\) | ||||
−0.719033 | + | 0.694976i | \(0.755415\pi\) | |||||||
\(318\) | 11.8844 | 0.666442 | ||||||||
\(319\) | 19.9079 | 1.11463 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 2.81447 | 0.157088 | ||||||||
\(322\) | 10.0497 | 0.560046 | ||||||||
\(323\) | −34.9747 | −1.94605 | ||||||||
\(324\) | −1.34756 | −0.0748642 | ||||||||
\(325\) | 2.83453 | 0.157231 | ||||||||
\(326\) | −12.7158 | −0.704264 | ||||||||
\(327\) | 5.90288 | 0.326430 | ||||||||
\(328\) | −12.2963 | −0.678948 | ||||||||
\(329\) | 5.83241 | 0.321551 | ||||||||
\(330\) | 3.44932 | 0.189879 | ||||||||
\(331\) | −13.4718 | −0.740480 | −0.370240 | − | 0.928936i | \(-0.620725\pi\) | ||||
−0.370240 | + | 0.928936i | \(0.620725\pi\) | |||||||
\(332\) | −15.8755 | −0.871281 | ||||||||
\(333\) | 14.4850 | 0.793772 | ||||||||
\(334\) | 16.6894 | 0.913206 | ||||||||
\(335\) | −9.32681 | −0.509578 | ||||||||
\(336\) | 3.90247 | 0.212897 | ||||||||
\(337\) | 12.1885 | 0.663952 | 0.331976 | − | 0.943288i | \(-0.392285\pi\) | ||||
0.331976 | + | 0.943288i | \(0.392285\pi\) | |||||||
\(338\) | −4.96546 | −0.270085 | ||||||||
\(339\) | 19.1940 | 1.04248 | ||||||||
\(340\) | −5.60775 | −0.304123 | ||||||||
\(341\) | 23.7167 | 1.28433 | ||||||||
\(342\) | 10.2710 | 0.555390 | ||||||||
\(343\) | 9.21089 | 0.497341 | ||||||||
\(344\) | −0.840974 | −0.0453423 | ||||||||
\(345\) | −3.48473 | −0.187612 | ||||||||
\(346\) | −13.7598 | −0.739733 | ||||||||
\(347\) | 1.94541 | 0.104435 | 0.0522176 | − | 0.998636i | \(-0.483371\pi\) | ||||
0.0522176 | + | 0.998636i | \(0.483371\pi\) | |||||||
\(348\) | −7.80997 | −0.418659 | ||||||||
\(349\) | −10.2515 | −0.548752 | −0.274376 | − | 0.961623i | \(-0.588471\pi\) | ||||
−0.274376 | + | 0.961623i | \(0.588471\pi\) | |||||||
\(350\) | −3.35475 | −0.179319 | ||||||||
\(351\) | 15.3220 | 0.817826 | ||||||||
\(352\) | 2.96520 | 0.158046 | ||||||||
\(353\) | −32.3292 | −1.72071 | −0.860355 | − | 0.509696i | \(-0.829758\pi\) | ||||
−0.860355 | + | 0.509696i | \(0.829758\pi\) | |||||||
\(354\) | −15.3447 | −0.815559 | ||||||||
\(355\) | 9.13221 | 0.484687 | ||||||||
\(356\) | −4.65541 | −0.246736 | ||||||||
\(357\) | 21.8841 | 1.15823 | ||||||||
\(358\) | −2.09821 | −0.110894 | ||||||||
\(359\) | 4.50747 | 0.237895 | 0.118948 | − | 0.992901i | \(-0.462048\pi\) | ||||
0.118948 | + | 0.992901i | \(0.462048\pi\) | |||||||
\(360\) | 1.64681 | 0.0867948 | ||||||||
\(361\) | 19.8984 | 1.04729 | ||||||||
\(362\) | 16.1159 | 0.847032 | ||||||||
\(363\) | 2.56799 | 0.134784 | ||||||||
\(364\) | −9.50914 | −0.498414 | ||||||||
\(365\) | 3.85112 | 0.201577 | ||||||||
\(366\) | 9.92486 | 0.518781 | ||||||||
\(367\) | −4.62156 | −0.241244 | −0.120622 | − | 0.992699i | \(-0.538489\pi\) | ||||
−0.120622 | + | 0.992699i | \(0.538489\pi\) | |||||||
\(368\) | −2.99565 | −0.156159 | ||||||||
\(369\) | 20.2497 | 1.05416 | ||||||||
\(370\) | 8.79576 | 0.457270 | ||||||||
\(371\) | 34.2735 | 1.77939 | ||||||||
\(372\) | −9.30417 | −0.482399 | ||||||||
\(373\) | −23.2544 | −1.20407 | −0.602035 | − | 0.798470i | \(-0.705643\pi\) | ||||
−0.602035 | + | 0.798470i | \(0.705643\pi\) | |||||||
\(374\) | 16.6281 | 0.859819 | ||||||||
\(375\) | 1.16326 | 0.0600707 | ||||||||
\(376\) | −1.73855 | −0.0896589 | ||||||||
\(377\) | 19.0306 | 0.980124 | ||||||||
\(378\) | −18.1340 | −0.932715 | ||||||||
\(379\) | −18.0541 | −0.927374 | −0.463687 | − | 0.885999i | \(-0.653474\pi\) | ||||
−0.463687 | + | 0.885999i | \(0.653474\pi\) | |||||||
\(380\) | 6.23686 | 0.319944 | ||||||||
\(381\) | −14.8208 | −0.759293 | ||||||||
\(382\) | 6.77893 | 0.346840 | ||||||||
\(383\) | 5.71349 | 0.291946 | 0.145973 | − | 0.989289i | \(-0.453369\pi\) | ||||
0.145973 | + | 0.989289i | \(0.453369\pi\) | |||||||
\(384\) | −1.16326 | −0.0593626 | ||||||||
\(385\) | 9.94753 | 0.506973 | ||||||||
\(386\) | 20.3721 | 1.03691 | ||||||||
\(387\) | 1.38493 | 0.0703999 | ||||||||
\(388\) | −2.71538 | −0.137852 | ||||||||
\(389\) | 26.0785 | 1.32223 | 0.661117 | − | 0.750283i | \(-0.270083\pi\) | ||||
0.661117 | + | 0.750283i | \(0.270083\pi\) | |||||||
\(390\) | 3.29731 | 0.166966 | ||||||||
\(391\) | −16.7988 | −0.849554 | ||||||||
\(392\) | 4.25438 | 0.214878 | ||||||||
\(393\) | −5.21937 | −0.263282 | ||||||||
\(394\) | −18.4708 | −0.930545 | ||||||||
\(395\) | −9.04751 | −0.455230 | ||||||||
\(396\) | −4.88314 | −0.245387 | ||||||||
\(397\) | 4.13836 | 0.207698 | 0.103849 | − | 0.994593i | \(-0.466884\pi\) | ||||
0.103849 | + | 0.994593i | \(0.466884\pi\) | |||||||
\(398\) | −24.5092 | −1.22853 | ||||||||
\(399\) | −24.3391 | −1.21848 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | −10.8495 | −0.541126 | ||||||||
\(403\) | 22.6715 | 1.12935 | ||||||||
\(404\) | −13.7228 | −0.682736 | ||||||||
\(405\) | 1.34756 | 0.0669606 | ||||||||
\(406\) | −22.5233 | −1.11781 | ||||||||
\(407\) | −26.0812 | −1.29280 | ||||||||
\(408\) | −6.52330 | −0.322951 | ||||||||
\(409\) | 10.4102 | 0.514752 | 0.257376 | − | 0.966311i | \(-0.417142\pi\) | ||||
0.257376 | + | 0.966311i | \(0.417142\pi\) | |||||||
\(410\) | 12.2963 | 0.607269 | ||||||||
\(411\) | −16.0119 | −0.789811 | ||||||||
\(412\) | −15.4538 | −0.761354 | ||||||||
\(413\) | −44.2527 | −2.17753 | ||||||||
\(414\) | 4.93328 | 0.242457 | ||||||||
\(415\) | 15.8755 | 0.779297 | ||||||||
\(416\) | 2.83453 | 0.138974 | ||||||||
\(417\) | −18.4597 | −0.903974 | ||||||||
\(418\) | −18.4936 | −0.904550 | ||||||||
\(419\) | 2.10590 | 0.102880 | 0.0514400 | − | 0.998676i | \(-0.483619\pi\) | ||||
0.0514400 | + | 0.998676i | \(0.483619\pi\) | |||||||
\(420\) | −3.90247 | −0.190421 | ||||||||
\(421\) | 4.89803 | 0.238716 | 0.119358 | − | 0.992851i | \(-0.461916\pi\) | ||||
0.119358 | + | 0.992851i | \(0.461916\pi\) | |||||||
\(422\) | 0.410059 | 0.0199613 | ||||||||
\(423\) | 2.86307 | 0.139207 | ||||||||
\(424\) | −10.2164 | −0.496151 | ||||||||
\(425\) | 5.60775 | 0.272016 | ||||||||
\(426\) | 10.6232 | 0.514695 | ||||||||
\(427\) | 28.6224 | 1.38514 | ||||||||
\(428\) | −2.41946 | −0.116949 | ||||||||
\(429\) | −9.77718 | −0.472047 | ||||||||
\(430\) | 0.840974 | 0.0405554 | ||||||||
\(431\) | 5.86490 | 0.282502 | 0.141251 | − | 0.989974i | \(-0.454887\pi\) | ||||
0.141251 | + | 0.989974i | \(0.454887\pi\) | |||||||
\(432\) | 5.40548 | 0.260071 | ||||||||
\(433\) | 7.60619 | 0.365530 | 0.182765 | − | 0.983157i | \(-0.441495\pi\) | ||||
0.182765 | + | 0.983157i | \(0.441495\pi\) | |||||||
\(434\) | −26.8324 | −1.28800 | ||||||||
\(435\) | 7.80997 | 0.374460 | ||||||||
\(436\) | −5.07441 | −0.243020 | ||||||||
\(437\) | 18.6834 | 0.893750 | ||||||||
\(438\) | 4.47987 | 0.214057 | ||||||||
\(439\) | −2.73186 | −0.130384 | −0.0651922 | − | 0.997873i | \(-0.520766\pi\) | ||||
−0.0651922 | + | 0.997873i | \(0.520766\pi\) | |||||||
\(440\) | −2.96520 | −0.141361 | ||||||||
\(441\) | −7.00617 | −0.333627 | ||||||||
\(442\) | 15.8953 | 0.756063 | ||||||||
\(443\) | −21.0264 | −0.998996 | −0.499498 | − | 0.866315i | \(-0.666482\pi\) | ||||
−0.499498 | + | 0.866315i | \(0.666482\pi\) | |||||||
\(444\) | 10.2318 | 0.485580 | ||||||||
\(445\) | 4.65541 | 0.220688 | ||||||||
\(446\) | −1.72577 | −0.0817176 | ||||||||
\(447\) | 26.6884 | 1.26232 | ||||||||
\(448\) | −3.35475 | −0.158497 | ||||||||
\(449\) | 26.2757 | 1.24003 | 0.620013 | − | 0.784592i | \(-0.287127\pi\) | ||||
0.620013 | + | 0.784592i | \(0.287127\pi\) | |||||||
\(450\) | −1.64681 | −0.0776316 | ||||||||
\(451\) | −36.4609 | −1.71688 | ||||||||
\(452\) | −16.5001 | −0.776101 | ||||||||
\(453\) | 14.6030 | 0.686108 | ||||||||
\(454\) | −8.01949 | −0.376374 | ||||||||
\(455\) | 9.50914 | 0.445795 | ||||||||
\(456\) | 7.25512 | 0.339752 | ||||||||
\(457\) | −20.4868 | −0.958332 | −0.479166 | − | 0.877724i | \(-0.659061\pi\) | ||||
−0.479166 | + | 0.877724i | \(0.659061\pi\) | |||||||
\(458\) | 12.8189 | 0.598989 | ||||||||
\(459\) | 30.3126 | 1.41487 | ||||||||
\(460\) | 2.99565 | 0.139673 | ||||||||
\(461\) | −6.83475 | −0.318326 | −0.159163 | − | 0.987252i | \(-0.550880\pi\) | ||||
−0.159163 | + | 0.987252i | \(0.550880\pi\) | |||||||
\(462\) | 11.5716 | 0.538360 | ||||||||
\(463\) | −13.1377 | −0.610560 | −0.305280 | − | 0.952263i | \(-0.598750\pi\) | ||||
−0.305280 | + | 0.952263i | \(0.598750\pi\) | |||||||
\(464\) | 6.71384 | 0.311682 | ||||||||
\(465\) | 9.30417 | 0.431471 | ||||||||
\(466\) | −1.42208 | −0.0658764 | ||||||||
\(467\) | −9.73693 | −0.450571 | −0.225286 | − | 0.974293i | \(-0.572332\pi\) | ||||
−0.225286 | + | 0.974293i | \(0.572332\pi\) | |||||||
\(468\) | −4.66794 | −0.215776 | ||||||||
\(469\) | −31.2892 | −1.44480 | ||||||||
\(470\) | 1.73855 | 0.0801934 | ||||||||
\(471\) | 8.66077 | 0.399067 | ||||||||
\(472\) | 13.1910 | 0.607166 | ||||||||
\(473\) | −2.49366 | −0.114659 | ||||||||
\(474\) | −10.5246 | −0.483413 | ||||||||
\(475\) | −6.23686 | −0.286167 | ||||||||
\(476\) | −18.8126 | −0.862275 | ||||||||
\(477\) | 16.8245 | 0.770341 | ||||||||
\(478\) | −9.78933 | −0.447753 | ||||||||
\(479\) | −32.0677 | −1.46521 | −0.732604 | − | 0.680655i | \(-0.761695\pi\) | ||||
−0.732604 | + | 0.680655i | \(0.761695\pi\) | |||||||
\(480\) | 1.16326 | 0.0530955 | ||||||||
\(481\) | −24.9318 | −1.13679 | ||||||||
\(482\) | 0.658045 | 0.0299731 | ||||||||
\(483\) | −11.6904 | −0.531933 | ||||||||
\(484\) | −2.20757 | −0.100344 | ||||||||
\(485\) | 2.71538 | 0.123299 | ||||||||
\(486\) | −14.6489 | −0.664486 | ||||||||
\(487\) | 1.95740 | 0.0886984 | 0.0443492 | − | 0.999016i | \(-0.485879\pi\) | ||||
0.0443492 | + | 0.999016i | \(0.485879\pi\) | |||||||
\(488\) | −8.53190 | −0.386221 | ||||||||
\(489\) | 14.7919 | 0.668911 | ||||||||
\(490\) | −4.25438 | −0.192193 | ||||||||
\(491\) | 30.0347 | 1.35545 | 0.677725 | − | 0.735316i | \(-0.262966\pi\) | ||||
0.677725 | + | 0.735316i | \(0.262966\pi\) | |||||||
\(492\) | 14.3038 | 0.644866 | ||||||||
\(493\) | 37.6495 | 1.69565 | ||||||||
\(494\) | −17.6785 | −0.795396 | ||||||||
\(495\) | 4.88314 | 0.219481 | ||||||||
\(496\) | 7.99833 | 0.359135 | ||||||||
\(497\) | 30.6363 | 1.37423 | ||||||||
\(498\) | 18.4674 | 0.827544 | ||||||||
\(499\) | −12.0810 | −0.540821 | −0.270410 | − | 0.962745i | \(-0.587159\pi\) | ||||
−0.270410 | + | 0.962745i | \(0.587159\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −19.4142 | −0.867364 | ||||||||
\(502\) | 14.2838 | 0.637518 | ||||||||
\(503\) | −4.48425 | −0.199943 | −0.0999714 | − | 0.994990i | \(-0.531875\pi\) | ||||
−0.0999714 | + | 0.994990i | \(0.531875\pi\) | |||||||
\(504\) | 5.52466 | 0.246088 | ||||||||
\(505\) | 13.7228 | 0.610658 | ||||||||
\(506\) | −8.88271 | −0.394884 | ||||||||
\(507\) | 5.77614 | 0.256528 | ||||||||
\(508\) | 12.7407 | 0.565277 | ||||||||
\(509\) | 0.883360 | 0.0391543 | 0.0195771 | − | 0.999808i | \(-0.493768\pi\) | ||||
0.0195771 | + | 0.999808i | \(0.493768\pi\) | |||||||
\(510\) | 6.52330 | 0.288856 | ||||||||
\(511\) | 12.9196 | 0.571528 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −33.7132 | −1.48847 | ||||||||
\(514\) | −0.865966 | −0.0381961 | ||||||||
\(515\) | 15.4538 | 0.680976 | ||||||||
\(516\) | 0.978276 | 0.0430662 | ||||||||
\(517\) | −5.15516 | −0.226724 | ||||||||
\(518\) | 29.5076 | 1.29649 | ||||||||
\(519\) | 16.0063 | 0.702600 | ||||||||
\(520\) | −2.83453 | −0.124302 | ||||||||
\(521\) | 22.3938 | 0.981090 | 0.490545 | − | 0.871416i | \(-0.336798\pi\) | ||||
0.490545 | + | 0.871416i | \(0.336798\pi\) | |||||||
\(522\) | −11.0565 | −0.483928 | ||||||||
\(523\) | −7.86014 | −0.343700 | −0.171850 | − | 0.985123i | \(-0.554974\pi\) | ||||
−0.171850 | + | 0.985123i | \(0.554974\pi\) | |||||||
\(524\) | 4.48683 | 0.196008 | ||||||||
\(525\) | 3.90247 | 0.170318 | ||||||||
\(526\) | −13.8708 | −0.604797 | ||||||||
\(527\) | 44.8526 | 1.95381 | ||||||||
\(528\) | −3.44932 | −0.150112 | ||||||||
\(529\) | −14.0261 | −0.609830 | ||||||||
\(530\) | 10.2164 | 0.443771 | ||||||||
\(531\) | −21.7232 | −0.942706 | ||||||||
\(532\) | 20.9231 | 0.907133 | ||||||||
\(533\) | −34.8541 | −1.50970 | ||||||||
\(534\) | 5.41547 | 0.234351 | ||||||||
\(535\) | 2.41946 | 0.104602 | ||||||||
\(536\) | 9.32681 | 0.402857 | ||||||||
\(537\) | 2.44077 | 0.105327 | ||||||||
\(538\) | 27.4725 | 1.18442 | ||||||||
\(539\) | 12.6151 | 0.543370 | ||||||||
\(540\) | −5.40548 | −0.232615 | ||||||||
\(541\) | −23.4352 | −1.00756 | −0.503779 | − | 0.863833i | \(-0.668057\pi\) | ||||
−0.503779 | + | 0.863833i | \(0.668057\pi\) | |||||||
\(542\) | 31.6496 | 1.35947 | ||||||||
\(543\) | −18.7470 | −0.804512 | ||||||||
\(544\) | 5.60775 | 0.240430 | ||||||||
\(545\) | 5.07441 | 0.217364 | ||||||||
\(546\) | 11.0616 | 0.473395 | ||||||||
\(547\) | 12.4018 | 0.530262 | 0.265131 | − | 0.964212i | \(-0.414585\pi\) | ||||
0.265131 | + | 0.964212i | \(0.414585\pi\) | |||||||
\(548\) | 13.7647 | 0.587997 | ||||||||
\(549\) | 14.0505 | 0.599659 | ||||||||
\(550\) | 2.96520 | 0.126437 | ||||||||
\(551\) | −41.8733 | −1.78386 | ||||||||
\(552\) | 3.48473 | 0.148320 | ||||||||
\(553\) | −30.3522 | −1.29071 | ||||||||
\(554\) | −2.48866 | −0.105733 | ||||||||
\(555\) | −10.2318 | −0.434316 | ||||||||
\(556\) | 15.8688 | 0.672989 | ||||||||
\(557\) | 31.8490 | 1.34949 | 0.674743 | − | 0.738053i | \(-0.264255\pi\) | ||||
0.674743 | + | 0.738053i | \(0.264255\pi\) | |||||||
\(558\) | −13.1718 | −0.557605 | ||||||||
\(559\) | −2.38376 | −0.100822 | ||||||||
\(560\) | 3.35475 | 0.141764 | ||||||||
\(561\) | −19.3429 | −0.816658 | ||||||||
\(562\) | 7.69352 | 0.324532 | ||||||||
\(563\) | 30.9414 | 1.30402 | 0.652012 | − | 0.758208i | \(-0.273925\pi\) | ||||
0.652012 | + | 0.758208i | \(0.273925\pi\) | |||||||
\(564\) | 2.02240 | 0.0851582 | ||||||||
\(565\) | 16.5001 | 0.694166 | ||||||||
\(566\) | −10.9512 | −0.460313 | ||||||||
\(567\) | 4.52072 | 0.189852 | ||||||||
\(568\) | −9.13221 | −0.383179 | ||||||||
\(569\) | −11.6170 | −0.487011 | −0.243506 | − | 0.969899i | \(-0.578297\pi\) | ||||
−0.243506 | + | 0.969899i | \(0.578297\pi\) | |||||||
\(570\) | −7.25512 | −0.303884 | ||||||||
\(571\) | −12.6405 | −0.528987 | −0.264494 | − | 0.964387i | \(-0.585205\pi\) | ||||
−0.264494 | + | 0.964387i | \(0.585205\pi\) | |||||||
\(572\) | 8.40495 | 0.351429 | ||||||||
\(573\) | −7.88569 | −0.329429 | ||||||||
\(574\) | 41.2509 | 1.72178 | ||||||||
\(575\) | −2.99565 | −0.124927 | ||||||||
\(576\) | −1.64681 | −0.0686173 | ||||||||
\(577\) | −21.8733 | −0.910598 | −0.455299 | − | 0.890339i | \(-0.650468\pi\) | ||||
−0.455299 | + | 0.890339i | \(0.650468\pi\) | |||||||
\(578\) | 14.4468 | 0.600909 | ||||||||
\(579\) | −23.6981 | −0.984860 | ||||||||
\(580\) | −6.71384 | −0.278777 | ||||||||
\(581\) | 53.2584 | 2.20953 | ||||||||
\(582\) | 3.15870 | 0.130933 | ||||||||
\(583\) | −30.2937 | −1.25463 | ||||||||
\(584\) | −3.85112 | −0.159361 | ||||||||
\(585\) | 4.66794 | 0.192996 | ||||||||
\(586\) | 16.5844 | 0.685094 | ||||||||
\(587\) | 15.2251 | 0.628406 | 0.314203 | − | 0.949356i | \(-0.398263\pi\) | ||||
0.314203 | + | 0.949356i | \(0.398263\pi\) | |||||||
\(588\) | −4.94897 | −0.204092 | ||||||||
\(589\) | −49.8844 | −2.05545 | ||||||||
\(590\) | −13.1910 | −0.543066 | ||||||||
\(591\) | 21.4864 | 0.883833 | ||||||||
\(592\) | −8.79576 | −0.361503 | ||||||||
\(593\) | −29.4662 | −1.21003 | −0.605015 | − | 0.796214i | \(-0.706833\pi\) | ||||
−0.605015 | + | 0.796214i | \(0.706833\pi\) | |||||||
\(594\) | 16.0283 | 0.657651 | ||||||||
\(595\) | 18.8126 | 0.771242 | ||||||||
\(596\) | −22.9427 | −0.939769 | ||||||||
\(597\) | 28.5107 | 1.16686 | ||||||||
\(598\) | −8.49125 | −0.347233 | ||||||||
\(599\) | 28.8464 | 1.17863 | 0.589315 | − | 0.807903i | \(-0.299398\pi\) | ||||
0.589315 | + | 0.807903i | \(0.299398\pi\) | |||||||
\(600\) | −1.16326 | −0.0474901 | ||||||||
\(601\) | 48.2291 | 1.96731 | 0.983653 | − | 0.180073i | \(-0.0576335\pi\) | ||||
0.983653 | + | 0.180073i | \(0.0576335\pi\) | |||||||
\(602\) | 2.82126 | 0.114986 | ||||||||
\(603\) | −15.3595 | −0.625488 | ||||||||
\(604\) | −12.5535 | −0.510793 | ||||||||
\(605\) | 2.20757 | 0.0897505 | ||||||||
\(606\) | 15.9633 | 0.648464 | ||||||||
\(607\) | −13.9833 | −0.567566 | −0.283783 | − | 0.958889i | \(-0.591589\pi\) | ||||
−0.283783 | + | 0.958889i | \(0.591589\pi\) | |||||||
\(608\) | −6.23686 | −0.252938 | ||||||||
\(609\) | 26.2005 | 1.06170 | ||||||||
\(610\) | 8.53190 | 0.345447 | ||||||||
\(611\) | −4.92797 | −0.199364 | ||||||||
\(612\) | −9.23492 | −0.373300 | ||||||||
\(613\) | −8.71593 | −0.352033 | −0.176017 | − | 0.984387i | \(-0.556321\pi\) | ||||
−0.176017 | + | 0.984387i | \(0.556321\pi\) | |||||||
\(614\) | −17.5543 | −0.708433 | ||||||||
\(615\) | −14.3038 | −0.576785 | ||||||||
\(616\) | −9.94753 | −0.400797 | ||||||||
\(617\) | −10.5090 | −0.423075 | −0.211537 | − | 0.977370i | \(-0.567847\pi\) | ||||
−0.211537 | + | 0.977370i | \(0.567847\pi\) | |||||||
\(618\) | 17.9769 | 0.723136 | ||||||||
\(619\) | 13.2480 | 0.532484 | 0.266242 | − | 0.963906i | \(-0.414218\pi\) | ||||
0.266242 | + | 0.963906i | \(0.414218\pi\) | |||||||
\(620\) | −7.99833 | −0.321220 | ||||||||
\(621\) | −16.1929 | −0.649799 | ||||||||
\(622\) | 14.0724 | 0.564252 | ||||||||
\(623\) | 15.6178 | 0.625712 | ||||||||
\(624\) | −3.29731 | −0.131998 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −19.1958 | −0.767220 | ||||||||
\(627\) | 21.5129 | 0.859143 | ||||||||
\(628\) | −7.44522 | −0.297097 | ||||||||
\(629\) | −49.3244 | −1.96669 | ||||||||
\(630\) | −5.52466 | −0.220108 | ||||||||
\(631\) | 7.60870 | 0.302898 | 0.151449 | − | 0.988465i | \(-0.451606\pi\) | ||||
0.151449 | + | 0.988465i | \(0.451606\pi\) | |||||||
\(632\) | 9.04751 | 0.359891 | ||||||||
\(633\) | −0.477007 | −0.0189593 | ||||||||
\(634\) | −25.6040 | −1.01687 | ||||||||
\(635\) | −12.7407 | −0.505600 | ||||||||
\(636\) | 11.8844 | 0.471246 | ||||||||
\(637\) | 12.0591 | 0.477801 | ||||||||
\(638\) | 19.9079 | 0.788161 | ||||||||
\(639\) | 15.0391 | 0.594936 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −39.9166 | −1.57661 | −0.788305 | − | 0.615285i | \(-0.789041\pi\) | ||||
−0.788305 | + | 0.615285i | \(0.789041\pi\) | |||||||
\(642\) | 2.81447 | 0.111078 | ||||||||
\(643\) | −4.98995 | −0.196784 | −0.0983922 | − | 0.995148i | \(-0.531370\pi\) | ||||
−0.0983922 | + | 0.995148i | \(0.531370\pi\) | |||||||
\(644\) | 10.0497 | 0.396012 | ||||||||
\(645\) | −0.978276 | −0.0385196 | ||||||||
\(646\) | −34.9747 | −1.37606 | ||||||||
\(647\) | 5.05124 | 0.198585 | 0.0992924 | − | 0.995058i | \(-0.468342\pi\) | ||||
0.0992924 | + | 0.995058i | \(0.468342\pi\) | |||||||
\(648\) | −1.34756 | −0.0529370 | ||||||||
\(649\) | 39.1141 | 1.53536 | ||||||||
\(650\) | 2.83453 | 0.111179 | ||||||||
\(651\) | 31.2132 | 1.22334 | ||||||||
\(652\) | −12.7158 | −0.497990 | ||||||||
\(653\) | −44.8420 | −1.75480 | −0.877402 | − | 0.479756i | \(-0.840725\pi\) | ||||
−0.877402 | + | 0.479756i | \(0.840725\pi\) | |||||||
\(654\) | 5.90288 | 0.230821 | ||||||||
\(655\) | −4.48683 | −0.175315 | ||||||||
\(656\) | −12.2963 | −0.480088 | ||||||||
\(657\) | 6.34209 | 0.247428 | ||||||||
\(658\) | 5.83241 | 0.227371 | ||||||||
\(659\) | 12.1552 | 0.473500 | 0.236750 | − | 0.971571i | \(-0.423918\pi\) | ||||
0.236750 | + | 0.971571i | \(0.423918\pi\) | |||||||
\(660\) | 3.44932 | 0.134264 | ||||||||
\(661\) | 25.2866 | 0.983534 | 0.491767 | − | 0.870727i | \(-0.336351\pi\) | ||||
0.491767 | + | 0.870727i | \(0.336351\pi\) | |||||||
\(662\) | −13.4718 | −0.523598 | ||||||||
\(663\) | −18.4905 | −0.718110 | ||||||||
\(664\) | −15.8755 | −0.616089 | ||||||||
\(665\) | −20.9231 | −0.811364 | ||||||||
\(666\) | 14.4850 | 0.561282 | ||||||||
\(667\) | −20.1123 | −0.778752 | ||||||||
\(668\) | 16.6894 | 0.645734 | ||||||||
\(669\) | 2.00753 | 0.0776155 | ||||||||
\(670\) | −9.32681 | −0.360326 | ||||||||
\(671\) | −25.2988 | −0.976650 | ||||||||
\(672\) | 3.90247 | 0.150541 | ||||||||
\(673\) | 2.92717 | 0.112834 | 0.0564170 | − | 0.998407i | \(-0.482032\pi\) | ||||
0.0564170 | + | 0.998407i | \(0.482032\pi\) | |||||||
\(674\) | 12.1885 | 0.469485 | ||||||||
\(675\) | 5.40548 | 0.208057 | ||||||||
\(676\) | −4.96546 | −0.190979 | ||||||||
\(677\) | −39.1349 | −1.50408 | −0.752038 | − | 0.659120i | \(-0.770929\pi\) | ||||
−0.752038 | + | 0.659120i | \(0.770929\pi\) | |||||||
\(678\) | 19.1940 | 0.737142 | ||||||||
\(679\) | 9.10943 | 0.349588 | ||||||||
\(680\) | −5.60775 | −0.215047 | ||||||||
\(681\) | 9.32880 | 0.357480 | ||||||||
\(682\) | 23.7167 | 0.908158 | ||||||||
\(683\) | 9.61464 | 0.367894 | 0.183947 | − | 0.982936i | \(-0.441113\pi\) | ||||
0.183947 | + | 0.982936i | \(0.441113\pi\) | |||||||
\(684\) | 10.2710 | 0.392720 | ||||||||
\(685\) | −13.7647 | −0.525921 | ||||||||
\(686\) | 9.21089 | 0.351673 | ||||||||
\(687\) | −14.9118 | −0.568920 | ||||||||
\(688\) | −0.840974 | −0.0320618 | ||||||||
\(689\) | −28.9586 | −1.10324 | ||||||||
\(690\) | −3.48473 | −0.132662 | ||||||||
\(691\) | −10.5130 | −0.399933 | −0.199966 | − | 0.979803i | \(-0.564083\pi\) | ||||
−0.199966 | + | 0.979803i | \(0.564083\pi\) | |||||||
\(692\) | −13.7598 | −0.523070 | ||||||||
\(693\) | 16.3817 | 0.622291 | ||||||||
\(694\) | 1.94541 | 0.0738468 | ||||||||
\(695\) | −15.8688 | −0.601940 | ||||||||
\(696\) | −7.80997 | −0.296036 | ||||||||
\(697\) | −68.9544 | −2.61183 | ||||||||
\(698\) | −10.2515 | −0.388026 | ||||||||
\(699\) | 1.65425 | 0.0625695 | ||||||||
\(700\) | −3.35475 | −0.126798 | ||||||||
\(701\) | 1.33284 | 0.0503408 | 0.0251704 | − | 0.999683i | \(-0.491987\pi\) | ||||
0.0251704 | + | 0.999683i | \(0.491987\pi\) | |||||||
\(702\) | 15.3220 | 0.578290 | ||||||||
\(703\) | 54.8579 | 2.06901 | ||||||||
\(704\) | 2.96520 | 0.111755 | ||||||||
\(705\) | −2.02240 | −0.0761678 | ||||||||
\(706\) | −32.3292 | −1.21673 | ||||||||
\(707\) | 46.0367 | 1.73139 | ||||||||
\(708\) | −15.3447 | −0.576688 | ||||||||
\(709\) | −10.3253 | −0.387774 | −0.193887 | − | 0.981024i | \(-0.562109\pi\) | ||||
−0.193887 | + | 0.981024i | \(0.562109\pi\) | |||||||
\(710\) | 9.13221 | 0.342726 | ||||||||
\(711\) | −14.8996 | −0.558778 | ||||||||
\(712\) | −4.65541 | −0.174469 | ||||||||
\(713\) | −23.9602 | −0.897316 | ||||||||
\(714\) | 21.8841 | 0.818990 | ||||||||
\(715\) | −8.40495 | −0.314327 | ||||||||
\(716\) | −2.09821 | −0.0784137 | ||||||||
\(717\) | 11.3876 | 0.425277 | ||||||||
\(718\) | 4.50747 | 0.168217 | ||||||||
\(719\) | 11.2934 | 0.421172 | 0.210586 | − | 0.977575i | \(-0.432463\pi\) | ||||
0.210586 | + | 0.977575i | \(0.432463\pi\) | |||||||
\(720\) | 1.64681 | 0.0613732 | ||||||||
\(721\) | 51.8437 | 1.93076 | ||||||||
\(722\) | 19.8984 | 0.740543 | ||||||||
\(723\) | −0.765481 | −0.0284685 | ||||||||
\(724\) | 16.1159 | 0.598942 | ||||||||
\(725\) | 6.71384 | 0.249346 | ||||||||
\(726\) | 2.56799 | 0.0953070 | ||||||||
\(727\) | 8.06008 | 0.298932 | 0.149466 | − | 0.988767i | \(-0.452245\pi\) | ||||
0.149466 | + | 0.988767i | \(0.452245\pi\) | |||||||
\(728\) | −9.50914 | −0.352432 | ||||||||
\(729\) | 21.0832 | 0.780858 | ||||||||
\(730\) | 3.85112 | 0.142536 | ||||||||
\(731\) | −4.71597 | −0.174427 | ||||||||
\(732\) | 9.92486 | 0.366833 | ||||||||
\(733\) | 31.9707 | 1.18087 | 0.590433 | − | 0.807087i | \(-0.298957\pi\) | ||||
0.590433 | + | 0.807087i | \(0.298957\pi\) | |||||||
\(734\) | −4.62156 | −0.170585 | ||||||||
\(735\) | 4.94897 | 0.182545 | ||||||||
\(736\) | −2.99565 | −0.110421 | ||||||||
\(737\) | 27.6559 | 1.01872 | ||||||||
\(738\) | 20.2497 | 0.745401 | ||||||||
\(739\) | 20.0705 | 0.738304 | 0.369152 | − | 0.929369i | \(-0.379648\pi\) | ||||
0.369152 | + | 0.929369i | \(0.379648\pi\) | |||||||
\(740\) | 8.79576 | 0.323339 | ||||||||
\(741\) | 20.5648 | 0.755468 | ||||||||
\(742\) | 34.2735 | 1.25822 | ||||||||
\(743\) | 26.0838 | 0.956920 | 0.478460 | − | 0.878109i | \(-0.341195\pi\) | ||||
0.478460 | + | 0.878109i | \(0.341195\pi\) | |||||||
\(744\) | −9.30417 | −0.341107 | ||||||||
\(745\) | 22.9427 | 0.840555 | ||||||||
\(746\) | −23.2544 | −0.851405 | ||||||||
\(747\) | 26.1440 | 0.956559 | ||||||||
\(748\) | 16.6281 | 0.607984 | ||||||||
\(749\) | 8.11669 | 0.296577 | ||||||||
\(750\) | 1.16326 | 0.0424764 | ||||||||
\(751\) | −51.9115 | −1.89428 | −0.947139 | − | 0.320824i | \(-0.896040\pi\) | ||||
−0.947139 | + | 0.320824i | \(0.896040\pi\) | |||||||
\(752\) | −1.73855 | −0.0633984 | ||||||||
\(753\) | −16.6159 | −0.605516 | ||||||||
\(754\) | 19.0306 | 0.693052 | ||||||||
\(755\) | 12.5535 | 0.456867 | ||||||||
\(756\) | −18.1340 | −0.659529 | ||||||||
\(757\) | −24.6306 | −0.895215 | −0.447608 | − | 0.894230i | \(-0.647724\pi\) | ||||
−0.447608 | + | 0.894230i | \(0.647724\pi\) | |||||||
\(758\) | −18.0541 | −0.655753 | ||||||||
\(759\) | 10.3329 | 0.375062 | ||||||||
\(760\) | 6.23686 | 0.226235 | ||||||||
\(761\) | −43.7807 | −1.58705 | −0.793525 | − | 0.608538i | \(-0.791756\pi\) | ||||
−0.793525 | + | 0.608538i | \(0.791756\pi\) | |||||||
\(762\) | −14.8208 | −0.536902 | ||||||||
\(763\) | 17.0234 | 0.616288 | ||||||||
\(764\) | 6.77893 | 0.245253 | ||||||||
\(765\) | 9.23492 | 0.333889 | ||||||||
\(766\) | 5.71349 | 0.206437 | ||||||||
\(767\) | 37.3903 | 1.35009 | ||||||||
\(768\) | −1.16326 | −0.0419757 | ||||||||
\(769\) | 5.27100 | 0.190077 | 0.0950385 | − | 0.995474i | \(-0.469703\pi\) | ||||
0.0950385 | + | 0.995474i | \(0.469703\pi\) | |||||||
\(770\) | 9.94753 | 0.358484 | ||||||||
\(771\) | 1.00735 | 0.0362787 | ||||||||
\(772\) | 20.3721 | 0.733207 | ||||||||
\(773\) | 18.0530 | 0.649321 | 0.324660 | − | 0.945831i | \(-0.394750\pi\) | ||||
0.324660 | + | 0.945831i | \(0.394750\pi\) | |||||||
\(774\) | 1.38493 | 0.0497802 | ||||||||
\(775\) | 7.99833 | 0.287308 | ||||||||
\(776\) | −2.71538 | −0.0974764 | ||||||||
\(777\) | −34.3252 | −1.23141 | ||||||||
\(778\) | 26.0785 | 0.934960 | ||||||||
\(779\) | 76.6901 | 2.74771 | ||||||||
\(780\) | 3.29731 | 0.118062 | ||||||||
\(781\) | −27.0789 | −0.968958 | ||||||||
\(782\) | −16.7988 | −0.600725 | ||||||||
\(783\) | 36.2915 | 1.29695 | ||||||||
\(784\) | 4.25438 | 0.151942 | ||||||||
\(785\) | 7.44522 | 0.265731 | ||||||||
\(786\) | −5.21937 | −0.186169 | ||||||||
\(787\) | −1.12359 | −0.0400515 | −0.0200258 | − | 0.999799i | \(-0.506375\pi\) | ||||
−0.0200258 | + | 0.999799i | \(0.506375\pi\) | |||||||
\(788\) | −18.4708 | −0.657994 | ||||||||
\(789\) | 16.1354 | 0.574437 | ||||||||
\(790\) | −9.04751 | −0.321896 | ||||||||
\(791\) | 55.3539 | 1.96816 | ||||||||
\(792\) | −4.88314 | −0.173515 | ||||||||
\(793\) | −24.1839 | −0.858795 | ||||||||
\(794\) | 4.13836 | 0.146865 | ||||||||
\(795\) | −11.8844 | −0.421495 | ||||||||
\(796\) | −24.5092 | −0.868704 | ||||||||
\(797\) | −7.42536 | −0.263020 | −0.131510 | − | 0.991315i | \(-0.541983\pi\) | ||||
−0.131510 | + | 0.991315i | \(0.541983\pi\) | |||||||
\(798\) | −24.3391 | −0.861597 | ||||||||
\(799\) | −9.74936 | −0.344907 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 7.66660 | 0.270886 | ||||||||
\(802\) | 1.00000 | 0.0353112 | ||||||||
\(803\) | −11.4194 | −0.402980 | ||||||||
\(804\) | −10.8495 | −0.382634 | ||||||||
\(805\) | −10.0497 | −0.354204 | ||||||||
\(806\) | 22.6715 | 0.798568 | ||||||||
\(807\) | −31.9577 | −1.12497 | ||||||||
\(808\) | −13.7228 | −0.482767 | ||||||||
\(809\) | 43.4719 | 1.52839 | 0.764195 | − | 0.644985i | \(-0.223137\pi\) | ||||
0.764195 | + | 0.644985i | \(0.223137\pi\) | |||||||
\(810\) | 1.34756 | 0.0473483 | ||||||||
\(811\) | 45.7453 | 1.60633 | 0.803167 | − | 0.595754i | \(-0.203147\pi\) | ||||
0.803167 | + | 0.595754i | \(0.203147\pi\) | |||||||
\(812\) | −22.5233 | −0.790412 | ||||||||
\(813\) | −36.8169 | −1.29122 | ||||||||
\(814\) | −26.0812 | −0.914146 | ||||||||
\(815\) | 12.7158 | 0.445416 | ||||||||
\(816\) | −6.52330 | −0.228361 | ||||||||
\(817\) | 5.24504 | 0.183501 | ||||||||
\(818\) | 10.4102 | 0.363985 | ||||||||
\(819\) | 15.6598 | 0.547198 | ||||||||
\(820\) | 12.2963 | 0.429404 | ||||||||
\(821\) | 24.0502 | 0.839359 | 0.419680 | − | 0.907672i | \(-0.362142\pi\) | ||||
0.419680 | + | 0.907672i | \(0.362142\pi\) | |||||||
\(822\) | −16.0119 | −0.558481 | ||||||||
\(823\) | −2.22191 | −0.0774509 | −0.0387255 | − | 0.999250i | \(-0.512330\pi\) | ||||
−0.0387255 | + | 0.999250i | \(0.512330\pi\) | |||||||
\(824\) | −15.4538 | −0.538359 | ||||||||
\(825\) | −3.44932 | −0.120090 | ||||||||
\(826\) | −44.2527 | −1.53975 | ||||||||
\(827\) | −18.7569 | −0.652240 | −0.326120 | − | 0.945328i | \(-0.605741\pi\) | ||||
−0.326120 | + | 0.945328i | \(0.605741\pi\) | |||||||
\(828\) | 4.93328 | 0.171443 | ||||||||
\(829\) | −30.1510 | −1.04719 | −0.523593 | − | 0.851968i | \(-0.675409\pi\) | ||||
−0.523593 | + | 0.851968i | \(0.675409\pi\) | |||||||
\(830\) | 15.8755 | 0.551046 | ||||||||
\(831\) | 2.89497 | 0.100425 | ||||||||
\(832\) | 2.83453 | 0.0982695 | ||||||||
\(833\) | 23.8575 | 0.826612 | ||||||||
\(834\) | −18.4597 | −0.639206 | ||||||||
\(835\) | −16.6894 | −0.577562 | ||||||||
\(836\) | −18.4936 | −0.639613 | ||||||||
\(837\) | 43.2348 | 1.49441 | ||||||||
\(838\) | 2.10590 | 0.0727471 | ||||||||
\(839\) | 23.4703 | 0.810284 | 0.405142 | − | 0.914254i | \(-0.367222\pi\) | ||||
0.405142 | + | 0.914254i | \(0.367222\pi\) | |||||||
\(840\) | −3.90247 | −0.134648 | ||||||||
\(841\) | 16.0756 | 0.554333 | ||||||||
\(842\) | 4.89803 | 0.168797 | ||||||||
\(843\) | −8.94960 | −0.308241 | ||||||||
\(844\) | 0.410059 | 0.0141148 | ||||||||
\(845\) | 4.96546 | 0.170817 | ||||||||
\(846\) | 2.86307 | 0.0984344 | ||||||||
\(847\) | 7.40586 | 0.254468 | ||||||||
\(848\) | −10.2164 | −0.350832 | ||||||||
\(849\) | 12.7391 | 0.437206 | ||||||||
\(850\) | 5.60775 | 0.192344 | ||||||||
\(851\) | 26.3490 | 0.903232 | ||||||||
\(852\) | 10.6232 | 0.363944 | ||||||||
\(853\) | 27.3501 | 0.936449 | 0.468225 | − | 0.883609i | \(-0.344894\pi\) | ||||
0.468225 | + | 0.883609i | \(0.344894\pi\) | |||||||
\(854\) | 28.6224 | 0.979439 | ||||||||
\(855\) | −10.2710 | −0.351259 | ||||||||
\(856\) | −2.41946 | −0.0826954 | ||||||||
\(857\) | 2.53798 | 0.0866958 | 0.0433479 | − | 0.999060i | \(-0.486198\pi\) | ||||
0.0433479 | + | 0.999060i | \(0.486198\pi\) | |||||||
\(858\) | −9.77718 | −0.333787 | ||||||||
\(859\) | 28.0654 | 0.957581 | 0.478790 | − | 0.877929i | \(-0.341075\pi\) | ||||
0.478790 | + | 0.877929i | \(0.341075\pi\) | |||||||
\(860\) | 0.840974 | 0.0286770 | ||||||||
\(861\) | −47.9858 | −1.63535 | ||||||||
\(862\) | 5.86490 | 0.199759 | ||||||||
\(863\) | 27.7232 | 0.943708 | 0.471854 | − | 0.881677i | \(-0.343585\pi\) | ||||
0.471854 | + | 0.881677i | \(0.343585\pi\) | |||||||
\(864\) | 5.40548 | 0.183898 | ||||||||
\(865\) | 13.7598 | 0.467848 | ||||||||
\(866\) | 7.60619 | 0.258469 | ||||||||
\(867\) | −16.8055 | −0.570745 | ||||||||
\(868\) | −26.8324 | −0.910752 | ||||||||
\(869\) | 26.8277 | 0.910067 | ||||||||
\(870\) | 7.80997 | 0.264783 | ||||||||
\(871\) | 26.4371 | 0.895787 | ||||||||
\(872\) | −5.07441 | −0.171841 | ||||||||
\(873\) | 4.47173 | 0.151345 | ||||||||
\(874\) | 18.6834 | 0.631977 | ||||||||
\(875\) | 3.35475 | 0.113411 | ||||||||
\(876\) | 4.47987 | 0.151361 | ||||||||
\(877\) | −7.57190 | −0.255685 | −0.127842 | − | 0.991794i | \(-0.540805\pi\) | ||||
−0.127842 | + | 0.991794i | \(0.540805\pi\) | |||||||
\(878\) | −2.73186 | −0.0921957 | ||||||||
\(879\) | −19.2920 | −0.650703 | ||||||||
\(880\) | −2.96520 | −0.0999570 | ||||||||
\(881\) | 35.2934 | 1.18907 | 0.594533 | − | 0.804072i | \(-0.297337\pi\) | ||||
0.594533 | + | 0.804072i | \(0.297337\pi\) | |||||||
\(882\) | −7.00617 | −0.235910 | ||||||||
\(883\) | 26.6693 | 0.897494 | 0.448747 | − | 0.893659i | \(-0.351870\pi\) | ||||
0.448747 | + | 0.893659i | \(0.351870\pi\) | |||||||
\(884\) | 15.8953 | 0.534617 | ||||||||
\(885\) | 15.3447 | 0.515805 | ||||||||
\(886\) | −21.0264 | −0.706397 | ||||||||
\(887\) | 30.6394 | 1.02877 | 0.514385 | − | 0.857559i | \(-0.328020\pi\) | ||||
0.514385 | + | 0.857559i | \(0.328020\pi\) | |||||||
\(888\) | 10.2318 | 0.343357 | ||||||||
\(889\) | −42.7419 | −1.43352 | ||||||||
\(890\) | 4.65541 | 0.156050 | ||||||||
\(891\) | −3.99578 | −0.133864 | ||||||||
\(892\) | −1.72577 | −0.0577830 | ||||||||
\(893\) | 10.8431 | 0.362851 | ||||||||
\(894\) | 26.6884 | 0.892594 | ||||||||
\(895\) | 2.09821 | 0.0701354 | ||||||||
\(896\) | −3.35475 | −0.112074 | ||||||||
\(897\) | 9.87757 | 0.329802 | ||||||||
\(898\) | 26.2757 | 0.876830 | ||||||||
\(899\) | 53.6995 | 1.79098 | ||||||||
\(900\) | −1.64681 | −0.0548938 | ||||||||
\(901\) | −57.2909 | −1.90864 | ||||||||
\(902\) | −36.4609 | −1.21402 | ||||||||
\(903\) | −3.28188 | −0.109214 | ||||||||
\(904\) | −16.5001 | −0.548786 | ||||||||
\(905\) | −16.1159 | −0.535710 | ||||||||
\(906\) | 14.6030 | 0.485152 | ||||||||
\(907\) | 18.1586 | 0.602946 | 0.301473 | − | 0.953475i | \(-0.402522\pi\) | ||||
0.301473 | + | 0.953475i | \(0.402522\pi\) | |||||||
\(908\) | −8.01949 | −0.266136 | ||||||||
\(909\) | 22.5989 | 0.749560 | ||||||||
\(910\) | 9.50914 | 0.315225 | ||||||||
\(911\) | −41.3697 | −1.37064 | −0.685319 | − | 0.728243i | \(-0.740337\pi\) | ||||
−0.685319 | + | 0.728243i | \(0.740337\pi\) | |||||||
\(912\) | 7.25512 | 0.240241 | ||||||||
\(913\) | −47.0741 | −1.55792 | ||||||||
\(914\) | −20.4868 | −0.677643 | ||||||||
\(915\) | −9.92486 | −0.328106 | ||||||||
\(916\) | 12.8189 | 0.423549 | ||||||||
\(917\) | −15.0522 | −0.497067 | ||||||||
\(918\) | 30.3126 | 1.00046 | ||||||||
\(919\) | −55.5649 | −1.83292 | −0.916459 | − | 0.400128i | \(-0.868966\pi\) | ||||
−0.916459 | + | 0.400128i | \(0.868966\pi\) | |||||||
\(920\) | 2.99565 | 0.0987636 | ||||||||
\(921\) | 20.4203 | 0.672871 | ||||||||
\(922\) | −6.83475 | −0.225090 | ||||||||
\(923\) | −25.8855 | −0.852031 | ||||||||
\(924\) | 11.5716 | 0.380678 | ||||||||
\(925\) | −8.79576 | −0.289203 | ||||||||
\(926\) | −13.1377 | −0.431731 | ||||||||
\(927\) | 25.4496 | 0.835873 | ||||||||
\(928\) | 6.71384 | 0.220393 | ||||||||
\(929\) | 14.4873 | 0.475314 | 0.237657 | − | 0.971349i | \(-0.423621\pi\) | ||||
0.237657 | + | 0.971349i | \(0.423621\pi\) | |||||||
\(930\) | 9.30417 | 0.305096 | ||||||||
\(931\) | −26.5340 | −0.869615 | ||||||||
\(932\) | −1.42208 | −0.0465817 | ||||||||
\(933\) | −16.3699 | −0.535928 | ||||||||
\(934\) | −9.73693 | −0.318602 | ||||||||
\(935\) | −16.6281 | −0.543797 | ||||||||
\(936\) | −4.66794 | −0.152576 | ||||||||
\(937\) | −17.9644 | −0.586870 | −0.293435 | − | 0.955979i | \(-0.594798\pi\) | ||||
−0.293435 | + | 0.955979i | \(0.594798\pi\) | |||||||
\(938\) | −31.2892 | −1.02163 | ||||||||
\(939\) | 22.3298 | 0.728707 | ||||||||
\(940\) | 1.73855 | 0.0567053 | ||||||||
\(941\) | −20.0750 | −0.654427 | −0.327213 | − | 0.944951i | \(-0.606110\pi\) | ||||
−0.327213 | + | 0.944951i | \(0.606110\pi\) | |||||||
\(942\) | 8.66077 | 0.282183 | ||||||||
\(943\) | 36.8353 | 1.19952 | ||||||||
\(944\) | 13.1910 | 0.429331 | ||||||||
\(945\) | 18.1340 | 0.589901 | ||||||||
\(946\) | −2.49366 | −0.0810759 | ||||||||
\(947\) | 42.6727 | 1.38668 | 0.693338 | − | 0.720613i | \(-0.256139\pi\) | ||||
0.693338 | + | 0.720613i | \(0.256139\pi\) | |||||||
\(948\) | −10.5246 | −0.341825 | ||||||||
\(949\) | −10.9161 | −0.354352 | ||||||||
\(950\) | −6.23686 | −0.202350 | ||||||||
\(951\) | 29.7843 | 0.965821 | ||||||||
\(952\) | −18.8126 | −0.609720 | ||||||||
\(953\) | −36.2127 | −1.17304 | −0.586522 | − | 0.809933i | \(-0.699503\pi\) | ||||
−0.586522 | + | 0.809933i | \(0.699503\pi\) | |||||||
\(954\) | 16.8245 | 0.544713 | ||||||||
\(955\) | −6.77893 | −0.219361 | ||||||||
\(956\) | −9.78933 | −0.316609 | ||||||||
\(957\) | −23.1582 | −0.748597 | ||||||||
\(958\) | −32.0677 | −1.03606 | ||||||||
\(959\) | −46.1770 | −1.49113 | ||||||||
\(960\) | 1.16326 | 0.0375442 | ||||||||
\(961\) | 32.9732 | 1.06365 | ||||||||
\(962\) | −24.9318 | −0.803834 | ||||||||
\(963\) | 3.98440 | 0.128396 | ||||||||
\(964\) | 0.658045 | 0.0211942 | ||||||||
\(965\) | −20.3721 | −0.655800 | ||||||||
\(966\) | −11.6904 | −0.376133 | ||||||||
\(967\) | −3.17166 | −0.101994 | −0.0509969 | − | 0.998699i | \(-0.516240\pi\) | ||||
−0.0509969 | + | 0.998699i | \(0.516240\pi\) | |||||||
\(968\) | −2.20757 | −0.0709540 | ||||||||
\(969\) | 40.6849 | 1.30699 | ||||||||
\(970\) | 2.71538 | 0.0871856 | ||||||||
\(971\) | −21.1298 | −0.678088 | −0.339044 | − | 0.940771i | \(-0.610104\pi\) | ||||
−0.339044 | + | 0.940771i | \(0.610104\pi\) | |||||||
\(972\) | −14.6489 | −0.469863 | ||||||||
\(973\) | −53.2361 | −1.70667 | ||||||||
\(974\) | 1.95740 | 0.0627193 | ||||||||
\(975\) | −3.29731 | −0.105598 | ||||||||
\(976\) | −8.53190 | −0.273099 | ||||||||
\(977\) | −47.6806 | −1.52544 | −0.762718 | − | 0.646731i | \(-0.776136\pi\) | ||||
−0.762718 | + | 0.646731i | \(0.776136\pi\) | |||||||
\(978\) | 14.7919 | 0.472992 | ||||||||
\(979\) | −13.8042 | −0.441185 | ||||||||
\(980\) | −4.25438 | −0.135901 | ||||||||
\(981\) | 8.35661 | 0.266806 | ||||||||
\(982\) | 30.0347 | 0.958447 | ||||||||
\(983\) | 22.2103 | 0.708400 | 0.354200 | − | 0.935170i | \(-0.384753\pi\) | ||||
0.354200 | + | 0.935170i | \(0.384753\pi\) | |||||||
\(984\) | 14.3038 | 0.455989 | ||||||||
\(985\) | 18.4708 | 0.588528 | ||||||||
\(986\) | 37.6495 | 1.19901 | ||||||||
\(987\) | −6.78464 | −0.215957 | ||||||||
\(988\) | −17.6785 | −0.562430 | ||||||||
\(989\) | 2.51926 | 0.0801079 | ||||||||
\(990\) | 4.88314 | 0.155196 | ||||||||
\(991\) | −40.0552 | −1.27240 | −0.636198 | − | 0.771526i | \(-0.719494\pi\) | ||||
−0.636198 | + | 0.771526i | \(0.719494\pi\) | |||||||
\(992\) | 7.99833 | 0.253947 | ||||||||
\(993\) | 15.6713 | 0.497315 | ||||||||
\(994\) | 30.6363 | 0.971725 | ||||||||
\(995\) | 24.5092 | 0.776993 | ||||||||
\(996\) | 18.4674 | 0.585162 | ||||||||
\(997\) | −20.6799 | −0.654939 | −0.327470 | − | 0.944862i | \(-0.606196\pi\) | ||||
−0.327470 | + | 0.944862i | \(0.606196\pi\) | |||||||
\(998\) | −12.0810 | −0.382418 | ||||||||
\(999\) | −47.5453 | −1.50427 |
(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 | 4010.2.a.j.1.4 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4010.2.a.j.1.4 | ✓ | 12 | 1.1 | even | 1 | trivial |