Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9025,2,Mod(1,9025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9025, 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("9025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9025 = 5^{2} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9025.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: | \(72.0649878242\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 6x^{7} + 16x^{6} + 12x^{5} - 27x^{4} - 8x^{3} + 15x^{2} - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.789016\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9025.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.210984 | 0.149188 | 0.0745940 | − | 0.997214i | \(-0.476234\pi\) | ||||
0.0745940 | + | 0.997214i | \(0.476234\pi\) | |||||||
\(3\) | 0.0798955 | 0.0461277 | 0.0230639 | − | 0.999734i | \(-0.492658\pi\) | ||||
0.0230639 | + | 0.999734i | \(0.492658\pi\) | |||||||
\(4\) | −1.95549 | −0.977743 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.0168566 | 0.00688170 | ||||||||
\(7\) | 1.68723 | 0.637712 | 0.318856 | − | 0.947803i | \(-0.396701\pi\) | ||||
0.318856 | + | 0.947803i | \(0.396701\pi\) | |||||||
\(8\) | −0.834543 | −0.295055 | ||||||||
\(9\) | −2.99362 | −0.997872 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.88678 | −0.870398 | −0.435199 | − | 0.900334i | \(-0.643322\pi\) | ||||
−0.435199 | + | 0.900334i | \(0.643322\pi\) | |||||||
\(12\) | −0.156235 | −0.0451010 | ||||||||
\(13\) | −6.46601 | −1.79335 | −0.896674 | − | 0.442691i | \(-0.854024\pi\) | ||||
−0.896674 | + | 0.442691i | \(0.854024\pi\) | |||||||
\(14\) | 0.355977 | 0.0951390 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.73490 | 0.933724 | ||||||||
\(17\) | −2.98649 | −0.724329 | −0.362165 | − | 0.932114i | \(-0.617962\pi\) | ||||
−0.362165 | + | 0.932114i | \(0.617962\pi\) | |||||||
\(18\) | −0.631604 | −0.148871 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.134802 | 0.0294162 | ||||||||
\(22\) | −0.609064 | −0.129853 | ||||||||
\(23\) | −8.25754 | −1.72182 | −0.860908 | − | 0.508761i | \(-0.830104\pi\) | ||||
−0.860908 | + | 0.508761i | \(0.830104\pi\) | |||||||
\(24\) | −0.0666762 | −0.0136102 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.36422 | −0.267546 | ||||||||
\(27\) | −0.478863 | −0.0921573 | ||||||||
\(28\) | −3.29935 | −0.623519 | ||||||||
\(29\) | −7.25727 | −1.34764 | −0.673820 | − | 0.738895i | \(-0.735348\pi\) | ||||
−0.673820 | + | 0.738895i | \(0.735348\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.05600 | −0.728480 | −0.364240 | − | 0.931305i | \(-0.618671\pi\) | ||||
−0.364240 | + | 0.931305i | \(0.618671\pi\) | |||||||
\(32\) | 2.45709 | 0.434356 | ||||||||
\(33\) | −0.230641 | −0.0401495 | ||||||||
\(34\) | −0.630100 | −0.108061 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.85398 | 0.975663 | ||||||||
\(37\) | 7.96989 | 1.31024 | 0.655121 | − | 0.755524i | \(-0.272618\pi\) | ||||
0.655121 | + | 0.755524i | \(0.272618\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.516605 | −0.0827230 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.45595 | −0.852076 | −0.426038 | − | 0.904705i | \(-0.640091\pi\) | ||||
−0.426038 | + | 0.904705i | \(0.640091\pi\) | |||||||
\(42\) | 0.0284410 | 0.00438854 | ||||||||
\(43\) | 5.33164 | 0.813068 | 0.406534 | − | 0.913636i | \(-0.366737\pi\) | ||||
0.406534 | + | 0.913636i | \(0.366737\pi\) | |||||||
\(44\) | 5.64506 | 0.851025 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.74221 | −0.256874 | ||||||||
\(47\) | −1.64961 | −0.240620 | −0.120310 | − | 0.992736i | \(-0.538389\pi\) | ||||
−0.120310 | + | 0.992736i | \(0.538389\pi\) | |||||||
\(48\) | 0.298402 | 0.0430706 | ||||||||
\(49\) | −4.15326 | −0.593323 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.238607 | −0.0334117 | ||||||||
\(52\) | 12.6442 | 1.75343 | ||||||||
\(53\) | 1.91194 | 0.262625 | 0.131312 | − | 0.991341i | \(-0.458081\pi\) | ||||
0.131312 | + | 0.991341i | \(0.458081\pi\) | |||||||
\(54\) | −0.101032 | −0.0137488 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.40806 | −0.188160 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.53116 | −0.201052 | ||||||||
\(59\) | −3.55276 | −0.462530 | −0.231265 | − | 0.972891i | \(-0.574286\pi\) | ||||
−0.231265 | + | 0.972891i | \(0.574286\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.90014 | −1.01151 | −0.505755 | − | 0.862677i | \(-0.668786\pi\) | ||||
−0.505755 | + | 0.862677i | \(0.668786\pi\) | |||||||
\(62\) | −0.855750 | −0.108680 | ||||||||
\(63\) | −5.05091 | −0.636355 | ||||||||
\(64\) | −6.95139 | −0.868924 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.0486615 | −0.00598982 | ||||||||
\(67\) | 2.26533 | 0.276754 | 0.138377 | − | 0.990380i | \(-0.455811\pi\) | ||||
0.138377 | + | 0.990380i | \(0.455811\pi\) | |||||||
\(68\) | 5.84003 | 0.708208 | ||||||||
\(69\) | −0.659740 | −0.0794234 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.4224 | −1.23692 | −0.618458 | − | 0.785818i | \(-0.712242\pi\) | ||||
−0.618458 | + | 0.785818i | \(0.712242\pi\) | |||||||
\(72\) | 2.49830 | 0.294428 | ||||||||
\(73\) | −1.41186 | −0.165246 | −0.0826231 | − | 0.996581i | \(-0.526330\pi\) | ||||
−0.0826231 | + | 0.996581i | \(0.526330\pi\) | |||||||
\(74\) | 1.68152 | 0.195472 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.87066 | −0.555063 | ||||||||
\(78\) | −0.108995 | −0.0123413 | ||||||||
\(79\) | 2.41076 | 0.271232 | 0.135616 | − | 0.990761i | \(-0.456699\pi\) | ||||
0.135616 | + | 0.990761i | \(0.456699\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.94259 | 0.993621 | ||||||||
\(82\) | −1.15112 | −0.127120 | ||||||||
\(83\) | 11.4006 | 1.25138 | 0.625688 | − | 0.780073i | \(-0.284818\pi\) | ||||
0.625688 | + | 0.780073i | \(0.284818\pi\) | |||||||
\(84\) | −0.263603 | −0.0287615 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.12489 | 0.121300 | ||||||||
\(87\) | −0.579823 | −0.0621636 | ||||||||
\(88\) | 2.40914 | 0.256816 | ||||||||
\(89\) | 10.1161 | 1.07230 | 0.536152 | − | 0.844121i | \(-0.319877\pi\) | ||||
0.536152 | + | 0.844121i | \(0.319877\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.9096 | −1.14364 | ||||||||
\(92\) | 16.1475 | 1.68349 | ||||||||
\(93\) | −0.324057 | −0.0336031 | ||||||||
\(94\) | −0.348041 | −0.0358977 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.196310 | 0.0200358 | ||||||||
\(97\) | −9.86820 | −1.00196 | −0.500982 | − | 0.865458i | \(-0.667028\pi\) | ||||
−0.500982 | + | 0.865458i | \(0.667028\pi\) | |||||||
\(98\) | −0.876270 | −0.0885167 | ||||||||
\(99\) | 8.64192 | 0.868546 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.16975 | 0.414906 | 0.207453 | − | 0.978245i | \(-0.433483\pi\) | ||||
0.207453 | + | 0.978245i | \(0.433483\pi\) | |||||||
\(102\) | −0.0503422 | −0.00498462 | ||||||||
\(103\) | −12.5636 | −1.23793 | −0.618964 | − | 0.785419i | \(-0.712448\pi\) | ||||
−0.618964 | + | 0.785419i | \(0.712448\pi\) | |||||||
\(104\) | 5.39616 | 0.529137 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.403387 | 0.0391805 | ||||||||
\(107\) | 14.9423 | 1.44453 | 0.722264 | − | 0.691617i | \(-0.243102\pi\) | ||||
0.722264 | + | 0.691617i | \(0.243102\pi\) | |||||||
\(108\) | 0.936410 | 0.0901061 | ||||||||
\(109\) | −5.20496 | −0.498545 | −0.249272 | − | 0.968433i | \(-0.580191\pi\) | ||||
−0.249272 | + | 0.968433i | \(0.580191\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.636759 | 0.0604385 | ||||||||
\(112\) | 6.30162 | 0.595447 | ||||||||
\(113\) | 8.57064 | 0.806258 | 0.403129 | − | 0.915143i | \(-0.367923\pi\) | ||||
0.403129 | + | 0.915143i | \(0.367923\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 14.1915 | 1.31765 | ||||||||
\(117\) | 19.3568 | 1.78953 | ||||||||
\(118\) | −0.749575 | −0.0690039 | ||||||||
\(119\) | −5.03888 | −0.461914 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.66648 | −0.242407 | ||||||||
\(122\) | −1.66680 | −0.150905 | ||||||||
\(123\) | −0.435906 | −0.0393043 | ||||||||
\(124\) | 7.93146 | 0.712266 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.06566 | −0.0949365 | ||||||||
\(127\) | 13.0369 | 1.15684 | 0.578421 | − | 0.815738i | \(-0.303669\pi\) | ||||
0.578421 | + | 0.815738i | \(0.303669\pi\) | |||||||
\(128\) | −6.38080 | −0.563989 | ||||||||
\(129\) | 0.425974 | 0.0375050 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.187083 | 0.0163456 | 0.00817278 | − | 0.999967i | \(-0.497398\pi\) | ||||
0.00817278 | + | 0.999967i | \(0.497398\pi\) | |||||||
\(132\) | 0.451015 | 0.0392558 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.477948 | 0.0412884 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.49235 | 0.213717 | ||||||||
\(137\) | −2.15559 | −0.184164 | −0.0920821 | − | 0.995751i | \(-0.529352\pi\) | ||||
−0.0920821 | + | 0.995751i | \(0.529352\pi\) | |||||||
\(138\) | −0.139194 | −0.0118490 | ||||||||
\(139\) | −7.89712 | −0.669825 | −0.334913 | − | 0.942249i | \(-0.608707\pi\) | ||||
−0.334913 | + | 0.942249i | \(0.608707\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.131796 | −0.0110993 | ||||||||
\(142\) | −2.19897 | −0.184533 | ||||||||
\(143\) | 18.6660 | 1.56093 | ||||||||
\(144\) | −11.1808 | −0.931737 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.297880 | −0.0246527 | ||||||||
\(147\) | −0.331827 | −0.0273686 | ||||||||
\(148\) | −15.5850 | −1.28108 | ||||||||
\(149\) | 17.8966 | 1.46615 | 0.733074 | − | 0.680149i | \(-0.238085\pi\) | ||||
0.733074 | + | 0.680149i | \(0.238085\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.93984 | −0.239241 | −0.119620 | − | 0.992820i | \(-0.538168\pi\) | ||||
−0.119620 | + | 0.992820i | \(0.538168\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.94040 | 0.722788 | ||||||||
\(154\) | −1.02763 | −0.0828088 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.01021 | 0.0808819 | ||||||||
\(157\) | −6.76687 | −0.540055 | −0.270028 | − | 0.962853i | \(-0.587033\pi\) | ||||
−0.270028 | + | 0.962853i | \(0.587033\pi\) | |||||||
\(158\) | 0.508631 | 0.0404645 | ||||||||
\(159\) | 0.152755 | 0.0121143 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.9323 | −1.09802 | ||||||||
\(162\) | 1.88674 | 0.148236 | ||||||||
\(163\) | 0.907834 | 0.0711070 | 0.0355535 | − | 0.999368i | \(-0.488681\pi\) | ||||
0.0355535 | + | 0.999368i | \(0.488681\pi\) | |||||||
\(164\) | 10.6690 | 0.833111 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.40534 | 0.186690 | ||||||||
\(167\) | 14.2716 | 1.10437 | 0.552184 | − | 0.833722i | \(-0.313795\pi\) | ||||
0.552184 | + | 0.833722i | \(0.313795\pi\) | |||||||
\(168\) | −0.112498 | −0.00867941 | ||||||||
\(169\) | 28.8093 | 2.21610 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.4260 | −0.794971 | ||||||||
\(173\) | 14.0774 | 1.07029 | 0.535144 | − | 0.844761i | \(-0.320257\pi\) | ||||
0.535144 | + | 0.844761i | \(0.320257\pi\) | |||||||
\(174\) | −0.122333 | −0.00927406 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −10.7818 | −0.812712 | ||||||||
\(177\) | −0.283850 | −0.0213355 | ||||||||
\(178\) | 2.13433 | 0.159975 | ||||||||
\(179\) | −15.7498 | −1.17719 | −0.588596 | − | 0.808427i | \(-0.700319\pi\) | ||||
−0.588596 | + | 0.808427i | \(0.700319\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.55831 | −0.338816 | −0.169408 | − | 0.985546i | \(-0.554186\pi\) | ||||
−0.169408 | + | 0.985546i | \(0.554186\pi\) | |||||||
\(182\) | −2.30175 | −0.170617 | ||||||||
\(183\) | −0.631186 | −0.0466586 | ||||||||
\(184\) | 6.89127 | 0.508031 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.0683706 | −0.00501318 | ||||||||
\(187\) | 8.62134 | 0.630455 | ||||||||
\(188\) | 3.22579 | 0.235265 | ||||||||
\(189\) | −0.807951 | −0.0587698 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.95887 | −0.720599 | −0.360299 | − | 0.932837i | \(-0.617325\pi\) | ||||
−0.360299 | + | 0.932837i | \(0.617325\pi\) | |||||||
\(192\) | −0.555385 | −0.0400814 | ||||||||
\(193\) | −21.4012 | −1.54049 | −0.770247 | − | 0.637746i | \(-0.779867\pi\) | ||||
−0.770247 | + | 0.637746i | \(0.779867\pi\) | |||||||
\(194\) | −2.08203 | −0.149481 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.12165 | 0.580118 | ||||||||
\(197\) | −1.36674 | −0.0973765 | −0.0486883 | − | 0.998814i | \(-0.515504\pi\) | ||||
−0.0486883 | + | 0.998814i | \(0.515504\pi\) | |||||||
\(198\) | 1.82330 | 0.129577 | ||||||||
\(199\) | −17.9359 | −1.27144 | −0.635722 | − | 0.771918i | \(-0.719298\pi\) | ||||
−0.635722 | + | 0.771918i | \(0.719298\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.180990 | 0.0127660 | ||||||||
\(202\) | 0.879749 | 0.0618989 | ||||||||
\(203\) | −12.2447 | −0.859407 | ||||||||
\(204\) | 0.466592 | 0.0326680 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.65072 | −0.184684 | ||||||||
\(207\) | 24.7199 | 1.71815 | ||||||||
\(208\) | −24.1499 | −1.67449 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.7678 | −1.42971 | −0.714857 | − | 0.699270i | \(-0.753508\pi\) | ||||
−0.714857 | + | 0.699270i | \(0.753508\pi\) | |||||||
\(212\) | −3.73877 | −0.256779 | ||||||||
\(213\) | −0.832707 | −0.0570561 | ||||||||
\(214\) | 3.15258 | 0.215506 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.399632 | 0.0271915 | ||||||||
\(217\) | −6.84340 | −0.464560 | ||||||||
\(218\) | −1.09816 | −0.0743769 | ||||||||
\(219\) | −0.112802 | −0.00762243 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.3107 | 1.29898 | ||||||||
\(222\) | 0.134346 | 0.00901669 | ||||||||
\(223\) | 1.94996 | 0.130579 | 0.0652894 | − | 0.997866i | \(-0.479203\pi\) | ||||
0.0652894 | + | 0.997866i | \(0.479203\pi\) | |||||||
\(224\) | 4.14567 | 0.276994 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.80827 | 0.120284 | ||||||||
\(227\) | 12.6099 | 0.836950 | 0.418475 | − | 0.908228i | \(-0.362565\pi\) | ||||
0.418475 | + | 0.908228i | \(0.362565\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.12765 | −0.404926 | −0.202463 | − | 0.979290i | \(-0.564895\pi\) | ||||
−0.202463 | + | 0.979290i | \(0.564895\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.389144 | −0.0256038 | ||||||||
\(232\) | 6.05650 | 0.397629 | ||||||||
\(233\) | −6.60713 | −0.432848 | −0.216424 | − | 0.976299i | \(-0.569439\pi\) | ||||
−0.216424 | + | 0.976299i | \(0.569439\pi\) | |||||||
\(234\) | 4.08396 | 0.266977 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.94738 | 0.452236 | ||||||||
\(237\) | 0.192609 | 0.0125113 | ||||||||
\(238\) | −1.06312 | −0.0689120 | ||||||||
\(239\) | −2.20382 | −0.142553 | −0.0712766 | − | 0.997457i | \(-0.522707\pi\) | ||||
−0.0712766 | + | 0.997457i | \(0.522707\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.124850 | 0.00804232 | 0.00402116 | − | 0.999992i | \(-0.498720\pi\) | ||||
0.00402116 | + | 0.999992i | \(0.498720\pi\) | |||||||
\(242\) | −0.562584 | −0.0361643 | ||||||||
\(243\) | 2.15106 | 0.137991 | ||||||||
\(244\) | 15.4486 | 0.988996 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.0919690 | −0.00586373 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.38491 | 0.214942 | ||||||||
\(249\) | 0.910855 | 0.0577231 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.71679 | 0.234602 | 0.117301 | − | 0.993096i | \(-0.462576\pi\) | ||||
0.117301 | + | 0.993096i | \(0.462576\pi\) | |||||||
\(252\) | 9.87699 | 0.622192 | ||||||||
\(253\) | 23.8377 | 1.49866 | ||||||||
\(254\) | 2.75058 | 0.172587 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.5565 | 0.784783 | ||||||||
\(257\) | −26.9757 | −1.68270 | −0.841349 | − | 0.540492i | \(-0.818238\pi\) | ||||
−0.841349 | + | 0.540492i | \(0.818238\pi\) | |||||||
\(258\) | 0.0898736 | 0.00559529 | ||||||||
\(259\) | 13.4470 | 0.835557 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 21.7255 | 1.34477 | ||||||||
\(262\) | 0.0394715 | 0.00243856 | ||||||||
\(263\) | −20.6759 | −1.27493 | −0.637464 | − | 0.770480i | \(-0.720017\pi\) | ||||
−0.637464 | + | 0.770480i | \(0.720017\pi\) | |||||||
\(264\) | 0.192480 | 0.0118463 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.808231 | 0.0494629 | ||||||||
\(268\) | −4.42982 | −0.270594 | ||||||||
\(269\) | 13.7249 | 0.836820 | 0.418410 | − | 0.908258i | \(-0.362587\pi\) | ||||
0.418410 | + | 0.908258i | \(0.362587\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.38346 | −0.327022 | −0.163511 | − | 0.986542i | \(-0.552282\pi\) | ||||
−0.163511 | + | 0.986542i | \(0.552282\pi\) | |||||||
\(272\) | −11.1542 | −0.676324 | ||||||||
\(273\) | −0.871631 | −0.0527535 | ||||||||
\(274\) | −0.454794 | −0.0274751 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.29011 | 0.0776557 | ||||||||
\(277\) | −22.7985 | −1.36983 | −0.684916 | − | 0.728622i | \(-0.740161\pi\) | ||||
−0.684916 | + | 0.728622i | \(0.740161\pi\) | |||||||
\(278\) | −1.66616 | −0.0999299 | ||||||||
\(279\) | 12.1421 | 0.726930 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.2290 | 1.02780 | 0.513899 | − | 0.857851i | \(-0.328201\pi\) | ||||
0.513899 | + | 0.857851i | \(0.328201\pi\) | |||||||
\(282\) | −0.0278069 | −0.00165588 | ||||||||
\(283\) | −16.2988 | −0.968866 | −0.484433 | − | 0.874828i | \(-0.660974\pi\) | ||||
−0.484433 | + | 0.874828i | \(0.660974\pi\) | |||||||
\(284\) | 20.3809 | 1.20939 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.93821 | 0.232871 | ||||||||
\(287\) | −9.20543 | −0.543379 | ||||||||
\(288\) | −7.35558 | −0.433432 | ||||||||
\(289\) | −8.08090 | −0.475347 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.788425 | −0.0462183 | ||||||||
\(292\) | 2.76088 | 0.161568 | ||||||||
\(293\) | 25.2882 | 1.47735 | 0.738675 | − | 0.674061i | \(-0.235452\pi\) | ||||
0.738675 | + | 0.674061i | \(0.235452\pi\) | |||||||
\(294\) | −0.0700101 | −0.00408307 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.65122 | −0.386594 | ||||||||
\(297\) | 1.38237 | 0.0802135 | ||||||||
\(298\) | 3.77589 | 0.218731 | ||||||||
\(299\) | 53.3933 | 3.08781 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.99570 | 0.518503 | ||||||||
\(302\) | −0.620258 | −0.0356918 | ||||||||
\(303\) | 0.333144 | 0.0191386 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.88628 | 0.107831 | ||||||||
\(307\) | 17.2290 | 0.983309 | 0.491655 | − | 0.870790i | \(-0.336392\pi\) | ||||
0.491655 | + | 0.870790i | \(0.336392\pi\) | |||||||
\(308\) | 9.52451 | 0.542709 | ||||||||
\(309\) | −1.00378 | −0.0571028 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.9724 | 1.41606 | 0.708028 | − | 0.706184i | \(-0.249585\pi\) | ||||
0.708028 | + | 0.706184i | \(0.249585\pi\) | |||||||
\(312\) | 0.431129 | 0.0244079 | ||||||||
\(313\) | 16.8633 | 0.953167 | 0.476584 | − | 0.879129i | \(-0.341875\pi\) | ||||
0.476584 | + | 0.879129i | \(0.341875\pi\) | |||||||
\(314\) | −1.42770 | −0.0805697 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.71421 | −0.265195 | ||||||||
\(317\) | 24.1211 | 1.35478 | 0.677389 | − | 0.735625i | \(-0.263111\pi\) | ||||
0.677389 | + | 0.735625i | \(0.263111\pi\) | |||||||
\(318\) | 0.0322288 | 0.00180730 | ||||||||
\(319\) | 20.9502 | 1.17298 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.19382 | 0.0666328 | ||||||||
\(322\) | −2.93950 | −0.163812 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −17.4871 | −0.971506 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.191538 | 0.0106083 | ||||||||
\(327\) | −0.415853 | −0.0229967 | ||||||||
\(328\) | 4.55322 | 0.251410 | ||||||||
\(329\) | −2.78327 | −0.153447 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.5403 | −0.854174 | −0.427087 | − | 0.904211i | \(-0.640460\pi\) | ||||
−0.427087 | + | 0.904211i | \(0.640460\pi\) | |||||||
\(332\) | −22.2937 | −1.22352 | ||||||||
\(333\) | −23.8588 | −1.30745 | ||||||||
\(334\) | 3.01107 | 0.164758 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.503471 | 0.0274666 | ||||||||
\(337\) | 11.0057 | 0.599516 | 0.299758 | − | 0.954015i | \(-0.403094\pi\) | ||||
0.299758 | + | 0.954015i | \(0.403094\pi\) | |||||||
\(338\) | 6.07829 | 0.330615 | ||||||||
\(339\) | 0.684756 | 0.0371908 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.7088 | 0.634067 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.8181 | −1.01608 | ||||||||
\(344\) | −4.44948 | −0.239900 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.97011 | 0.159674 | ||||||||
\(347\) | −30.4697 | −1.63570 | −0.817849 | − | 0.575433i | \(-0.804833\pi\) | ||||
−0.817849 | + | 0.575433i | \(0.804833\pi\) | |||||||
\(348\) | 1.13384 | 0.0607800 | ||||||||
\(349\) | 5.61744 | 0.300695 | 0.150347 | − | 0.988633i | \(-0.451961\pi\) | ||||
0.150347 | + | 0.988633i | \(0.451961\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.09633 | 0.165270 | ||||||||
\(352\) | −7.09308 | −0.378062 | ||||||||
\(353\) | 7.48617 | 0.398449 | 0.199224 | − | 0.979954i | \(-0.436158\pi\) | ||||
0.199224 | + | 0.979954i | \(0.436158\pi\) | |||||||
\(354\) | −0.0598877 | −0.00318299 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −19.7819 | −1.04844 | ||||||||
\(357\) | −0.402584 | −0.0213070 | ||||||||
\(358\) | −3.32294 | −0.175623 | ||||||||
\(359\) | −25.4854 | −1.34507 | −0.672534 | − | 0.740066i | \(-0.734794\pi\) | ||||
−0.672534 | + | 0.740066i | \(0.734794\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −0.961728 | −0.0505473 | ||||||||
\(363\) | −0.213040 | −0.0111817 | ||||||||
\(364\) | 21.3336 | 1.11819 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.133170 | −0.00696090 | ||||||||
\(367\) | 33.4662 | 1.74692 | 0.873461 | − | 0.486894i | \(-0.161870\pi\) | ||||
0.873461 | + | 0.486894i | \(0.161870\pi\) | |||||||
\(368\) | −30.8410 | −1.60770 | ||||||||
\(369\) | 16.3330 | 0.850263 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.22587 | 0.167479 | ||||||||
\(372\) | 0.633688 | 0.0328552 | ||||||||
\(373\) | −10.4787 | −0.542566 | −0.271283 | − | 0.962500i | \(-0.587448\pi\) | ||||
−0.271283 | + | 0.962500i | \(0.587448\pi\) | |||||||
\(374\) | 1.81896 | 0.0940563 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.37667 | 0.0709964 | ||||||||
\(377\) | 46.9256 | 2.41679 | ||||||||
\(378\) | −0.170464 | −0.00876775 | ||||||||
\(379\) | 14.2962 | 0.734344 | 0.367172 | − | 0.930153i | \(-0.380326\pi\) | ||||
0.367172 | + | 0.930153i | \(0.380326\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.04159 | 0.0533625 | ||||||||
\(382\) | −2.10116 | −0.107505 | ||||||||
\(383\) | 36.9815 | 1.88967 | 0.944833 | − | 0.327552i | \(-0.106224\pi\) | ||||
0.944833 | + | 0.327552i | \(0.106224\pi\) | |||||||
\(384\) | −0.509798 | −0.0260155 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.51531 | −0.229823 | ||||||||
\(387\) | −15.9609 | −0.811338 | ||||||||
\(388\) | 19.2971 | 0.979663 | ||||||||
\(389\) | −16.6074 | −0.842029 | −0.421015 | − | 0.907054i | \(-0.638326\pi\) | ||||
−0.421015 | + | 0.907054i | \(0.638326\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.6610 | 1.24716 | ||||||||
\(392\) | 3.46608 | 0.175063 | ||||||||
\(393\) | 0.0149471 | 0.000753983 0 | ||||||||
\(394\) | −0.288361 | −0.0145274 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −16.8992 | −0.849215 | ||||||||
\(397\) | 26.6383 | 1.33694 | 0.668470 | − | 0.743739i | \(-0.266949\pi\) | ||||
0.668470 | + | 0.743739i | \(0.266949\pi\) | |||||||
\(398\) | −3.78419 | −0.189684 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.29475 | −0.0646570 | −0.0323285 | − | 0.999477i | \(-0.510292\pi\) | ||||
−0.0323285 | + | 0.999477i | \(0.510292\pi\) | |||||||
\(402\) | 0.0381859 | 0.00190454 | ||||||||
\(403\) | 26.2262 | 1.30642 | ||||||||
\(404\) | −8.15389 | −0.405671 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.58342 | −0.128213 | ||||||||
\(407\) | −23.0074 | −1.14043 | ||||||||
\(408\) | 0.199128 | 0.00985829 | ||||||||
\(409\) | −27.0318 | −1.33664 | −0.668318 | − | 0.743876i | \(-0.732985\pi\) | ||||
−0.668318 | + | 0.743876i | \(0.732985\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.172222 | −0.00849507 | ||||||||
\(412\) | 24.5680 | 1.21038 | ||||||||
\(413\) | −5.99432 | −0.294961 | ||||||||
\(414\) | 5.21549 | 0.256328 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −15.8876 | −0.778951 | ||||||||
\(417\) | −0.630945 | −0.0308975 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.15498 | −0.202984 | −0.101492 | − | 0.994836i | \(-0.532362\pi\) | ||||
−0.101492 | + | 0.994836i | \(0.532362\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.4050 | 1.28690 | 0.643449 | − | 0.765489i | \(-0.277503\pi\) | ||||
0.643449 | + | 0.765489i | \(0.277503\pi\) | |||||||
\(422\) | −4.38167 | −0.213296 | ||||||||
\(423\) | 4.93830 | 0.240108 | ||||||||
\(424\) | −1.59559 | −0.0774889 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.175687 | −0.00851209 | ||||||||
\(427\) | −13.3293 | −0.645052 | ||||||||
\(428\) | −29.2195 | −1.41238 | ||||||||
\(429\) | 1.49133 | 0.0720020 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.72137 | 0.468262 | 0.234131 | − | 0.972205i | \(-0.424776\pi\) | ||||
0.234131 | + | 0.972205i | \(0.424776\pi\) | |||||||
\(432\) | −1.78850 | −0.0860495 | ||||||||
\(433\) | −0.659842 | −0.0317100 | −0.0158550 | − | 0.999874i | \(-0.505047\pi\) | ||||
−0.0158550 | + | 0.999874i | \(0.505047\pi\) | |||||||
\(434\) | −1.44385 | −0.0693068 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.1782 | 0.487449 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −0.0237993 | −0.00113717 | ||||||||
\(439\) | −27.1898 | −1.29770 | −0.648849 | − | 0.760917i | \(-0.724749\pi\) | ||||
−0.648849 | + | 0.760917i | \(0.724749\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.4333 | 0.592061 | ||||||||
\(442\) | 4.07423 | 0.193791 | ||||||||
\(443\) | −37.7880 | −1.79536 | −0.897682 | − | 0.440644i | \(-0.854750\pi\) | ||||
−0.897682 | + | 0.440644i | \(0.854750\pi\) | |||||||
\(444\) | −1.24517 | −0.0590933 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.411409 | 0.0194808 | ||||||||
\(447\) | 1.42986 | 0.0676300 | ||||||||
\(448\) | −11.7286 | −0.554123 | ||||||||
\(449\) | 16.5499 | 0.781039 | 0.390520 | − | 0.920595i | \(-0.372295\pi\) | ||||
0.390520 | + | 0.920595i | \(0.372295\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.7501 | 0.741645 | ||||||||
\(452\) | −16.7598 | −0.788313 | ||||||||
\(453\) | −0.234880 | −0.0110356 | ||||||||
\(454\) | 2.66049 | 0.124863 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.4492 | −0.535571 | −0.267785 | − | 0.963479i | \(-0.586292\pi\) | ||||
−0.267785 | + | 0.963479i | \(0.586292\pi\) | |||||||
\(458\) | −1.29283 | −0.0604101 | ||||||||
\(459\) | 1.43012 | 0.0667522 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.7597 | −0.501127 | −0.250563 | − | 0.968100i | \(-0.580616\pi\) | ||||
−0.250563 | + | 0.968100i | \(0.580616\pi\) | |||||||
\(462\) | −0.0821030 | −0.00381978 | ||||||||
\(463\) | −17.0882 | −0.794155 | −0.397078 | − | 0.917785i | \(-0.629976\pi\) | ||||
−0.397078 | + | 0.917785i | \(0.629976\pi\) | |||||||
\(464\) | −27.1051 | −1.25832 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.39400 | −0.0645757 | ||||||||
\(467\) | −31.8559 | −1.47412 | −0.737058 | − | 0.675829i | \(-0.763786\pi\) | ||||
−0.737058 | + | 0.675829i | \(0.763786\pi\) | |||||||
\(468\) | −37.8519 | −1.74970 | ||||||||
\(469\) | 3.82213 | 0.176489 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.540643 | −0.0249115 | ||||||||
\(472\) | 2.96493 | 0.136472 | ||||||||
\(473\) | −15.3913 | −0.707693 | ||||||||
\(474\) | 0.0406374 | 0.00186654 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9.85346 | 0.451633 | ||||||||
\(477\) | −5.72361 | −0.262066 | ||||||||
\(478\) | −0.464970 | −0.0212672 | ||||||||
\(479\) | −3.85027 | −0.175923 | −0.0879616 | − | 0.996124i | \(-0.528035\pi\) | ||||
−0.0879616 | + | 0.996124i | \(0.528035\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −51.5334 | −2.34972 | ||||||||
\(482\) | 0.0263414 | 0.00119982 | ||||||||
\(483\) | −1.11313 | −0.0506493 | ||||||||
\(484\) | 5.21427 | 0.237012 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.453839 | 0.0205866 | ||||||||
\(487\) | 35.4075 | 1.60447 | 0.802233 | − | 0.597011i | \(-0.203645\pi\) | ||||
0.802233 | + | 0.597011i | \(0.203645\pi\) | |||||||
\(488\) | 6.59300 | 0.298451 | ||||||||
\(489\) | 0.0725319 | 0.00328000 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.2571 | 0.914192 | 0.457096 | − | 0.889417i | \(-0.348890\pi\) | ||||
0.457096 | + | 0.889417i | \(0.348890\pi\) | |||||||
\(492\) | 0.852408 | 0.0384295 | ||||||||
\(493\) | 21.6737 | 0.976136 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −15.1488 | −0.680199 | ||||||||
\(497\) | −17.5850 | −0.788797 | ||||||||
\(498\) | 0.192176 | 0.00861159 | ||||||||
\(499\) | 0.589427 | 0.0263864 | 0.0131932 | − | 0.999913i | \(-0.495800\pi\) | ||||
0.0131932 | + | 0.999913i | \(0.495800\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.14024 | 0.0509420 | ||||||||
\(502\) | 0.784181 | 0.0349997 | ||||||||
\(503\) | 11.3500 | 0.506073 | 0.253037 | − | 0.967457i | \(-0.418571\pi\) | ||||
0.253037 | + | 0.967457i | \(0.418571\pi\) | |||||||
\(504\) | 4.21520 | 0.187760 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.02937 | 0.223583 | ||||||||
\(507\) | 2.30173 | 0.102224 | ||||||||
\(508\) | −25.4936 | −1.13109 | ||||||||
\(509\) | −11.8654 | −0.525926 | −0.262963 | − | 0.964806i | \(-0.584700\pi\) | ||||
−0.262963 | + | 0.964806i | \(0.584700\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.38214 | −0.105379 | ||||||||
\(512\) | 15.4108 | 0.681069 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.69143 | −0.251038 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.832987 | −0.0366702 | ||||||||
\(517\) | 4.76207 | 0.209436 | ||||||||
\(518\) | 2.83710 | 0.124655 | ||||||||
\(519\) | 1.12472 | 0.0493699 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.5221 | 1.07433 | 0.537166 | − | 0.843476i | \(-0.319495\pi\) | ||||
0.537166 | + | 0.843476i | \(0.319495\pi\) | |||||||
\(522\) | 4.58372 | 0.200624 | ||||||||
\(523\) | 21.2338 | 0.928488 | 0.464244 | − | 0.885707i | \(-0.346326\pi\) | ||||
0.464244 | + | 0.885707i | \(0.346326\pi\) | |||||||
\(524\) | −0.365839 | −0.0159817 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.36227 | −0.190204 | ||||||||
\(527\) | 12.1132 | 0.527659 | ||||||||
\(528\) | −0.861421 | −0.0374885 | ||||||||
\(529\) | 45.1869 | 1.96465 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.6356 | 0.461546 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 35.2782 | 1.52807 | ||||||||
\(534\) | 0.170524 | 0.00737928 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.89051 | −0.0816578 | ||||||||
\(537\) | −1.25833 | −0.0543012 | ||||||||
\(538\) | 2.89572 | 0.124844 | ||||||||
\(539\) | 11.9896 | 0.516427 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.8259 | 0.637414 | 0.318707 | − | 0.947853i | \(-0.396751\pi\) | ||||
0.318707 | + | 0.947853i | \(0.396751\pi\) | |||||||
\(542\) | −1.13582 | −0.0487877 | ||||||||
\(543\) | −0.364188 | −0.0156288 | ||||||||
\(544\) | −7.33806 | −0.314617 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.183900 | −0.00787019 | ||||||||
\(547\) | 7.96145 | 0.340407 | 0.170203 | − | 0.985409i | \(-0.445558\pi\) | ||||
0.170203 | + | 0.985409i | \(0.445558\pi\) | |||||||
\(548\) | 4.21522 | 0.180065 | ||||||||
\(549\) | 23.6500 | 1.00936 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0.550581 | 0.0234343 | ||||||||
\(553\) | 4.06750 | 0.172968 | ||||||||
\(554\) | −4.81012 | −0.204362 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.4427 | 0.654917 | ||||||||
\(557\) | 8.10522 | 0.343429 | 0.171715 | − | 0.985147i | \(-0.445069\pi\) | ||||
0.171715 | + | 0.985147i | \(0.445069\pi\) | |||||||
\(558\) | 2.56179 | 0.108449 | ||||||||
\(559\) | −34.4745 | −1.45811 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.688806 | 0.0290814 | ||||||||
\(562\) | 3.63504 | 0.153335 | ||||||||
\(563\) | 8.29823 | 0.349729 | 0.174864 | − | 0.984593i | \(-0.444051\pi\) | ||||
0.174864 | + | 0.984593i | \(0.444051\pi\) | |||||||
\(564\) | 0.257726 | 0.0108522 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.43879 | −0.144543 | ||||||||
\(567\) | 15.0882 | 0.633644 | ||||||||
\(568\) | 8.69798 | 0.364959 | ||||||||
\(569\) | 7.28643 | 0.305463 | 0.152732 | − | 0.988268i | \(-0.451193\pi\) | ||||
0.152732 | + | 0.988268i | \(0.451193\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.6974 | −0.866159 | −0.433080 | − | 0.901356i | \(-0.642573\pi\) | ||||
−0.433080 | + | 0.901356i | \(0.642573\pi\) | |||||||
\(572\) | −36.5010 | −1.52619 | ||||||||
\(573\) | −0.795669 | −0.0332396 | ||||||||
\(574\) | −1.94219 | −0.0810657 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 20.8098 | 0.867075 | ||||||||
\(577\) | −14.5909 | −0.607429 | −0.303715 | − | 0.952763i | \(-0.598227\pi\) | ||||
−0.303715 | + | 0.952763i | \(0.598227\pi\) | |||||||
\(578\) | −1.70494 | −0.0709160 | ||||||||
\(579\) | −1.70986 | −0.0710594 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19.2354 | 0.798018 | ||||||||
\(582\) | −0.166345 | −0.00689521 | ||||||||
\(583\) | −5.51935 | −0.228588 | ||||||||
\(584\) | 1.17826 | 0.0487568 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.33539 | 0.220403 | ||||||||
\(587\) | 10.5077 | 0.433699 | 0.216849 | − | 0.976205i | \(-0.430422\pi\) | ||||
0.216849 | + | 0.976205i | \(0.430422\pi\) | |||||||
\(588\) | 0.648883 | 0.0267595 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.109197 | −0.00449175 | ||||||||
\(592\) | 29.7667 | 1.22340 | ||||||||
\(593\) | −24.3159 | −0.998535 | −0.499267 | − | 0.866448i | \(-0.666397\pi\) | ||||
−0.499267 | + | 0.866448i | \(0.666397\pi\) | |||||||
\(594\) | 0.291658 | 0.0119669 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −34.9966 | −1.43351 | ||||||||
\(597\) | −1.43300 | −0.0586488 | ||||||||
\(598\) | 11.2651 | 0.460665 | ||||||||
\(599\) | 37.9095 | 1.54894 | 0.774471 | − | 0.632609i | \(-0.218016\pi\) | ||||
0.774471 | + | 0.632609i | \(0.218016\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.9476 | −1.05843 | −0.529213 | − | 0.848489i | \(-0.677513\pi\) | ||||
−0.529213 | + | 0.848489i | \(0.677513\pi\) | |||||||
\(602\) | 1.89794 | 0.0773544 | ||||||||
\(603\) | −6.78153 | −0.276165 | ||||||||
\(604\) | 5.74881 | 0.233916 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.0702880 | 0.00285525 | ||||||||
\(607\) | −11.5300 | −0.467988 | −0.233994 | − | 0.972238i | \(-0.575180\pi\) | ||||
−0.233994 | + | 0.972238i | \(0.575180\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.978294 | −0.0396425 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.6664 | 0.431516 | ||||||||
\(612\) | −17.4828 | −0.706701 | ||||||||
\(613\) | −22.6581 | −0.915154 | −0.457577 | − | 0.889170i | \(-0.651283\pi\) | ||||
−0.457577 | + | 0.889170i | \(0.651283\pi\) | |||||||
\(614\) | 3.63503 | 0.146698 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.06477 | 0.163774 | ||||||||
\(617\) | −5.97675 | −0.240615 | −0.120307 | − | 0.992737i | \(-0.538388\pi\) | ||||
−0.120307 | + | 0.992737i | \(0.538388\pi\) | |||||||
\(618\) | −0.211780 | −0.00851905 | ||||||||
\(619\) | −34.2062 | −1.37486 | −0.687431 | − | 0.726249i | \(-0.741262\pi\) | ||||
−0.687431 | + | 0.726249i | \(0.741262\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.95423 | 0.158678 | ||||||||
\(622\) | 5.26877 | 0.211259 | ||||||||
\(623\) | 17.0682 | 0.683822 | ||||||||
\(624\) | −1.92947 | −0.0772405 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3.55787 | 0.142201 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.2325 | 0.528035 | ||||||||
\(629\) | −23.8020 | −0.949047 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.2510 | −0.567325 | −0.283662 | − | 0.958924i | \(-0.591549\pi\) | ||||
−0.283662 | + | 0.958924i | \(0.591549\pi\) | |||||||
\(632\) | −2.01188 | −0.0800284 | ||||||||
\(633\) | −1.65925 | −0.0659494 | ||||||||
\(634\) | 5.08916 | 0.202117 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.298711 | −0.0118446 | ||||||||
\(637\) | 26.8550 | 1.06404 | ||||||||
\(638\) | 4.42014 | 0.174995 | ||||||||
\(639\) | 31.2008 | 1.23428 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 39.7444 | 1.56981 | 0.784904 | − | 0.619617i | \(-0.212712\pi\) | ||||
0.784904 | + | 0.619617i | \(0.212712\pi\) | |||||||
\(642\) | 0.251877 | 0.00994081 | ||||||||
\(643\) | −15.9065 | −0.627290 | −0.313645 | − | 0.949540i | \(-0.601550\pi\) | ||||
−0.313645 | + | 0.949540i | \(0.601550\pi\) | |||||||
\(644\) | 27.2445 | 1.07358 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.8549 | −0.741262 | −0.370631 | − | 0.928780i | \(-0.620858\pi\) | ||||
−0.370631 | + | 0.928780i | \(0.620858\pi\) | |||||||
\(648\) | −7.46297 | −0.293173 | ||||||||
\(649\) | 10.2561 | 0.402585 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.546757 | −0.0214291 | ||||||||
\(652\) | −1.77526 | −0.0695244 | ||||||||
\(653\) | 42.5252 | 1.66414 | 0.832070 | − | 0.554670i | \(-0.187156\pi\) | ||||
0.832070 | + | 0.554670i | \(0.187156\pi\) | |||||||
\(654\) | −0.0877382 | −0.00343083 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −20.3774 | −0.795604 | ||||||||
\(657\) | 4.22658 | 0.164895 | ||||||||
\(658\) | −0.587224 | −0.0228924 | ||||||||
\(659\) | 45.8272 | 1.78517 | 0.892587 | − | 0.450874i | \(-0.148888\pi\) | ||||
0.892587 | + | 0.450874i | \(0.148888\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.1676 | 1.79571 | 0.897856 | − | 0.440289i | \(-0.145124\pi\) | ||||
0.897856 | + | 0.440289i | \(0.145124\pi\) | |||||||
\(662\) | −3.27876 | −0.127432 | ||||||||
\(663\) | 1.54283 | 0.0599187 | ||||||||
\(664\) | −9.51427 | −0.369225 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.03382 | −0.195056 | ||||||||
\(667\) | 59.9271 | 2.32039 | ||||||||
\(668\) | −27.9079 | −1.07979 | ||||||||
\(669\) | 0.155793 | 0.00602330 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.8060 | 0.880415 | ||||||||
\(672\) | 0.331220 | 0.0127771 | ||||||||
\(673\) | 5.48820 | 0.211555 | 0.105777 | − | 0.994390i | \(-0.466267\pi\) | ||||
0.105777 | + | 0.994390i | \(0.466267\pi\) | |||||||
\(674\) | 2.32201 | 0.0894406 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −56.3362 | −2.16678 | ||||||||
\(677\) | −29.4307 | −1.13111 | −0.565557 | − | 0.824709i | \(-0.691339\pi\) | ||||
−0.565557 | + | 0.824709i | \(0.691339\pi\) | |||||||
\(678\) | 0.144472 | 0.00554843 | ||||||||
\(679\) | −16.6499 | −0.638965 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.00748 | 0.0386066 | ||||||||
\(682\) | 2.47037 | 0.0945952 | ||||||||
\(683\) | −27.4543 | −1.05051 | −0.525254 | − | 0.850945i | \(-0.676030\pi\) | ||||
−0.525254 | + | 0.850945i | \(0.676030\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3.97031 | −0.151587 | ||||||||
\(687\) | −0.489571 | −0.0186783 | ||||||||
\(688\) | 19.9131 | 0.759181 | ||||||||
\(689\) | −12.3626 | −0.470978 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.42779 | 0.130399 | 0.0651997 | − | 0.997872i | \(-0.479232\pi\) | ||||
0.0651997 | + | 0.997872i | \(0.479232\pi\) | |||||||
\(692\) | −27.5282 | −1.04647 | ||||||||
\(693\) | 14.5809 | 0.553882 | ||||||||
\(694\) | −6.42860 | −0.244026 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.483887 | 0.0183417 | ||||||||
\(697\) | 16.2941 | 0.617184 | ||||||||
\(698\) | 1.18519 | 0.0448600 | ||||||||
\(699\) | −0.527880 | −0.0199663 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.26100 | −0.123166 | −0.0615832 | − | 0.998102i | \(-0.519615\pi\) | ||||
−0.0615832 | + | 0.998102i | \(0.519615\pi\) | |||||||
\(702\) | 0.653276 | 0.0246563 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 20.0672 | 0.756309 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.57946 | 0.0594437 | ||||||||
\(707\) | 7.03532 | 0.264590 | ||||||||
\(708\) | 0.555064 | 0.0208606 | ||||||||
\(709\) | −17.1381 | −0.643633 | −0.321817 | − | 0.946802i | \(-0.604293\pi\) | ||||
−0.321817 | + | 0.946802i | \(0.604293\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.21690 | −0.270655 | ||||||||
\(712\) | −8.44232 | −0.316389 | ||||||||
\(713\) | 33.4926 | 1.25431 | ||||||||
\(714\) | −0.0849387 | −0.00317875 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 30.7984 | 1.15099 | ||||||||
\(717\) | −0.176075 | −0.00657565 | ||||||||
\(718\) | −5.37701 | −0.200668 | ||||||||
\(719\) | 6.22549 | 0.232172 | 0.116086 | − | 0.993239i | \(-0.462965\pi\) | ||||
0.116086 | + | 0.993239i | \(0.462965\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.1977 | −0.789442 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.00997498 | 0.000370974 0 | ||||||||
\(724\) | 8.91371 | 0.331275 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.0449480 | −0.00166817 | ||||||||
\(727\) | 42.3189 | 1.56952 | 0.784760 | − | 0.619800i | \(-0.212786\pi\) | ||||
0.784760 | + | 0.619800i | \(0.212786\pi\) | |||||||
\(728\) | 9.10455 | 0.337437 | ||||||||
\(729\) | −26.6559 | −0.987256 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.9229 | −0.588929 | ||||||||
\(732\) | 1.23427 | 0.0456201 | ||||||||
\(733\) | 22.7630 | 0.840771 | 0.420386 | − | 0.907346i | \(-0.361895\pi\) | ||||
0.420386 | + | 0.907346i | \(0.361895\pi\) | |||||||
\(734\) | 7.06082 | 0.260620 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −20.2895 | −0.747881 | ||||||||
\(737\) | −6.53952 | −0.240886 | ||||||||
\(738\) | 3.44600 | 0.126849 | ||||||||
\(739\) | 17.9424 | 0.660023 | 0.330012 | − | 0.943977i | \(-0.392947\pi\) | ||||
0.330012 | + | 0.943977i | \(0.392947\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.680606 | 0.0249858 | ||||||||
\(743\) | −17.3309 | −0.635810 | −0.317905 | − | 0.948123i | \(-0.602979\pi\) | ||||
−0.317905 | + | 0.948123i | \(0.602979\pi\) | |||||||
\(744\) | 0.270439 | 0.00991478 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.21083 | −0.0809443 | ||||||||
\(747\) | −34.1290 | −1.24871 | ||||||||
\(748\) | −16.8589 | −0.616423 | ||||||||
\(749\) | 25.2111 | 0.921193 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.18627 | 0.0797781 | 0.0398890 | − | 0.999204i | \(-0.487300\pi\) | ||||
0.0398890 | + | 0.999204i | \(0.487300\pi\) | |||||||
\(752\) | −6.16113 | −0.224673 | ||||||||
\(753\) | 0.296955 | 0.0108216 | ||||||||
\(754\) | 9.90053 | 0.360556 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.57994 | 0.0574618 | ||||||||
\(757\) | 15.6387 | 0.568397 | 0.284198 | − | 0.958766i | \(-0.408273\pi\) | ||||
0.284198 | + | 0.958766i | \(0.408273\pi\) | |||||||
\(758\) | 3.01625 | 0.109555 | ||||||||
\(759\) | 1.90453 | 0.0691299 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.2993 | 0.953349 | 0.476675 | − | 0.879080i | \(-0.341842\pi\) | ||||
0.476675 | + | 0.879080i | \(0.341842\pi\) | |||||||
\(762\) | 0.219759 | 0.00796104 | ||||||||
\(763\) | −8.78195 | −0.317928 | ||||||||
\(764\) | 19.4744 | 0.704560 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.80249 | 0.281915 | ||||||||
\(767\) | 22.9722 | 0.829478 | ||||||||
\(768\) | 1.00321 | 0.0362002 | ||||||||
\(769\) | 0.0847497 | 0.00305615 | 0.00152808 | − | 0.999999i | \(-0.499514\pi\) | ||||
0.00152808 | + | 0.999999i | \(0.499514\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.15524 | −0.0776190 | ||||||||
\(772\) | 41.8498 | 1.50621 | ||||||||
\(773\) | −0.0114752 | −0.000412734 0 | −0.000206367 | − | 1.00000i | \(-0.500066\pi\) | ||||
−0.000206367 | 1.00000i | \(0.500066\pi\) | ||||||||
\(774\) | −3.36749 | −0.121042 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8.23544 | 0.295635 | ||||||||
\(777\) | 1.07436 | 0.0385423 | ||||||||
\(778\) | −3.50389 | −0.125621 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 30.0873 | 1.07661 | ||||||||
\(782\) | 5.20307 | 0.186061 | ||||||||
\(783\) | 3.47524 | 0.124195 | ||||||||
\(784\) | −15.5120 | −0.554000 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.00315360 | 0.000112485 0 | ||||||||
\(787\) | 30.1068 | 1.07319 | 0.536596 | − | 0.843839i | \(-0.319710\pi\) | ||||
0.536596 | + | 0.843839i | \(0.319710\pi\) | |||||||
\(788\) | 2.67265 | 0.0952092 | ||||||||
\(789\) | −1.65191 | −0.0588095 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.4606 | 0.514161 | ||||||||
\(792\) | −7.21205 | −0.256269 | ||||||||
\(793\) | 51.0824 | 1.81399 | ||||||||
\(794\) | 5.62026 | 0.199455 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 35.0735 | 1.24315 | ||||||||
\(797\) | 38.2339 | 1.35432 | 0.677158 | − | 0.735838i | \(-0.263211\pi\) | ||||
0.677158 | + | 0.735838i | \(0.263211\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.92654 | 0.174288 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −30.2837 | −1.07002 | ||||||||
\(802\) | −0.273172 | −0.00964604 | ||||||||
\(803\) | 4.07574 | 0.143830 | ||||||||
\(804\) | −0.353923 | −0.0124819 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.53329 | 0.194902 | ||||||||
\(807\) | 1.09656 | 0.0386006 | ||||||||
\(808\) | −3.47983 | −0.122420 | ||||||||
\(809\) | 3.70003 | 0.130086 | 0.0650431 | − | 0.997882i | \(-0.479282\pi\) | ||||
0.0650431 | + | 0.997882i | \(0.479282\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.9256 | −1.43709 | −0.718545 | − | 0.695480i | \(-0.755192\pi\) | ||||
−0.718545 | + | 0.695480i | \(0.755192\pi\) | |||||||
\(812\) | 23.9443 | 0.840279 | ||||||||
\(813\) | −0.430114 | −0.0150848 | ||||||||
\(814\) | −4.85417 | −0.170139 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.891172 | −0.0311973 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −5.70327 | −0.199410 | ||||||||
\(819\) | 32.6593 | 1.14121 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.4402 | 0.608666 | 0.304333 | − | 0.952566i | \(-0.401566\pi\) | ||||
0.304333 | + | 0.952566i | \(0.401566\pi\) | |||||||
\(822\) | −0.0363360 | −0.00126736 | ||||||||
\(823\) | 6.50473 | 0.226741 | 0.113370 | − | 0.993553i | \(-0.463835\pi\) | ||||
0.113370 | + | 0.993553i | \(0.463835\pi\) | |||||||
\(824\) | 10.4849 | 0.365258 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.26470 | −0.0440046 | ||||||||
\(827\) | 1.62225 | 0.0564112 | 0.0282056 | − | 0.999602i | \(-0.491021\pi\) | ||||
0.0282056 | + | 0.999602i | \(0.491021\pi\) | |||||||
\(828\) | −48.3394 | −1.67991 | ||||||||
\(829\) | −32.6503 | −1.13399 | −0.566996 | − | 0.823721i | \(-0.691895\pi\) | ||||
−0.566996 | + | 0.823721i | \(0.691895\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.82150 | −0.0631872 | ||||||||
\(832\) | 44.9477 | 1.55828 | ||||||||
\(833\) | 12.4037 | 0.429761 | ||||||||
\(834\) | −0.133119 | −0.00460953 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.94227 | 0.0671347 | ||||||||
\(838\) | −0.876632 | −0.0302827 | ||||||||
\(839\) | 11.5599 | 0.399093 | 0.199547 | − | 0.979888i | \(-0.436053\pi\) | ||||
0.199547 | + | 0.979888i | \(0.436053\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.6679 | 0.816135 | ||||||||
\(842\) | 5.57101 | 0.191990 | ||||||||
\(843\) | 1.37652 | 0.0474099 | ||||||||
\(844\) | 40.6111 | 1.39789 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.04190 | 0.0358213 | ||||||||
\(847\) | −4.49896 | −0.154586 | ||||||||
\(848\) | 7.14089 | 0.245219 | ||||||||
\(849\) | −1.30220 | −0.0446915 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −65.8117 | −2.25600 | ||||||||
\(852\) | 1.62835 | 0.0557862 | ||||||||
\(853\) | −47.7141 | −1.63370 | −0.816850 | − | 0.576850i | \(-0.804282\pi\) | ||||
−0.816850 | + | 0.576850i | \(0.804282\pi\) | |||||||
\(854\) | −2.81227 | −0.0962339 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.4700 | −0.426216 | ||||||||
\(857\) | −38.5358 | −1.31636 | −0.658179 | − | 0.752862i | \(-0.728673\pi\) | ||||
−0.658179 | + | 0.752862i | \(0.728673\pi\) | |||||||
\(858\) | 0.314646 | 0.0107418 | ||||||||
\(859\) | 19.1921 | 0.654826 | 0.327413 | − | 0.944881i | \(-0.393823\pi\) | ||||
0.327413 | + | 0.944881i | \(0.393823\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.735473 | −0.0250648 | ||||||||
\(862\) | 2.05105 | 0.0698591 | ||||||||
\(863\) | −9.16794 | −0.312080 | −0.156040 | − | 0.987751i | \(-0.549873\pi\) | ||||
−0.156040 | + | 0.987751i | \(0.549873\pi\) | |||||||
\(864\) | −1.17661 | −0.0400290 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −0.139216 | −0.00473075 | ||||||||
\(867\) | −0.645628 | −0.0219267 | ||||||||
\(868\) | 13.3822 | 0.454221 | ||||||||
\(869\) | −6.95935 | −0.236080 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.6476 | −0.496317 | ||||||||
\(872\) | 4.34376 | 0.147098 | ||||||||
\(873\) | 29.5416 | 0.999832 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.220582 | 0.00745277 | ||||||||
\(877\) | −3.62989 | −0.122573 | −0.0612864 | − | 0.998120i | \(-0.519520\pi\) | ||||
−0.0612864 | + | 0.998120i | \(0.519520\pi\) | |||||||
\(878\) | −5.73660 | −0.193601 | ||||||||
\(879\) | 2.02041 | 0.0681468 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.34382 | −0.281111 | −0.140555 | − | 0.990073i | \(-0.544889\pi\) | ||||
−0.140555 | + | 0.990073i | \(0.544889\pi\) | |||||||
\(882\) | 2.62322 | 0.0883283 | ||||||||
\(883\) | −28.2122 | −0.949415 | −0.474708 | − | 0.880144i | \(-0.657446\pi\) | ||||
−0.474708 | + | 0.880144i | \(0.657446\pi\) | |||||||
\(884\) | −37.7617 | −1.27006 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.97266 | −0.267847 | ||||||||
\(887\) | −8.84194 | −0.296883 | −0.148442 | − | 0.988921i | \(-0.547426\pi\) | ||||
−0.148442 | + | 0.988921i | \(0.547426\pi\) | |||||||
\(888\) | −0.531402 | −0.0178327 | ||||||||
\(889\) | 21.9963 | 0.737732 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −25.8153 | −0.864846 | ||||||||
\(892\) | −3.81312 | −0.127673 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0.301677 | 0.0100896 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −10.7659 | −0.359662 | ||||||||
\(897\) | 4.26589 | 0.142434 | ||||||||
\(898\) | 3.49176 | 0.116522 | ||||||||
\(899\) | 29.4355 | 0.981729 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.70997 | −0.190227 | ||||||||
\(902\) | 3.32302 | 0.110645 | ||||||||
\(903\) | 0.718716 | 0.0239174 | ||||||||
\(904\) | −7.15257 | −0.237891 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.0495558 | −0.00164638 | ||||||||
\(907\) | 4.22931 | 0.140432 | 0.0702159 | − | 0.997532i | \(-0.477631\pi\) | ||||
0.0702159 | + | 0.997532i | \(0.477631\pi\) | |||||||
\(908\) | −24.6585 | −0.818322 | ||||||||
\(909\) | −12.4826 | −0.414023 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.1182 | −0.335231 | −0.167616 | − | 0.985852i | \(-0.553607\pi\) | ||||
−0.167616 | + | 0.985852i | \(0.553607\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −32.9110 | −1.08920 | ||||||||
\(914\) | −2.41559 | −0.0799007 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 11.9825 | 0.395914 | ||||||||
\(917\) | 0.315652 | 0.0104238 | ||||||||
\(918\) | 0.301732 | 0.00995863 | ||||||||
\(919\) | −47.8757 | −1.57927 | −0.789637 | − | 0.613575i | \(-0.789731\pi\) | ||||
−0.789637 | + | 0.613575i | \(0.789731\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.37652 | 0.0453578 | ||||||||
\(922\) | −2.27011 | −0.0747621 | ||||||||
\(923\) | 67.3916 | 2.21822 | ||||||||
\(924\) | 0.760966 | 0.0250339 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.60533 | −0.118478 | ||||||||
\(927\) | 37.6106 | 1.23529 | ||||||||
\(928\) | −17.8317 | −0.585356 | ||||||||
\(929\) | −21.6302 | −0.709662 | −0.354831 | − | 0.934930i | \(-0.615462\pi\) | ||||
−0.354831 | + | 0.934930i | \(0.615462\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 12.9202 | 0.423214 | ||||||||
\(933\) | 1.99518 | 0.0653194 | ||||||||
\(934\) | −6.72108 | −0.219920 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −16.1540 | −0.528011 | ||||||||
\(937\) | −36.0833 | −1.17879 | −0.589395 | − | 0.807845i | \(-0.700634\pi\) | ||||
−0.589395 | + | 0.807845i | \(0.700634\pi\) | |||||||
\(938\) | 0.806406 | 0.0263301 | ||||||||
\(939\) | 1.34730 | 0.0439674 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 48.4806 | 1.58042 | 0.790212 | − | 0.612834i | \(-0.209970\pi\) | ||||
0.790212 | + | 0.612834i | \(0.209970\pi\) | |||||||
\(942\) | −0.114067 | −0.00371650 | ||||||||
\(943\) | 45.0527 | 1.46712 | ||||||||
\(944\) | −13.2692 | −0.431876 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.24731 | −0.105579 | ||||||||
\(947\) | −35.2103 | −1.14418 | −0.572091 | − | 0.820190i | \(-0.693868\pi\) | ||||
−0.572091 | + | 0.820190i | \(0.693868\pi\) | |||||||
\(948\) | −0.376644 | −0.0122328 | ||||||||
\(949\) | 9.12913 | 0.296344 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.92717 | 0.0624928 | ||||||||
\(952\) | 4.20516 | 0.136290 | ||||||||
\(953\) | 44.5937 | 1.44453 | 0.722265 | − | 0.691616i | \(-0.243101\pi\) | ||||
0.722265 | + | 0.691616i | \(0.243101\pi\) | |||||||
\(954\) | −1.20759 | −0.0390971 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4.30954 | 0.139380 | ||||||||
\(957\) | 1.67382 | 0.0541070 | ||||||||
\(958\) | −0.812343 | −0.0262456 | ||||||||
\(959\) | −3.63697 | −0.117444 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.5488 | −0.469317 | ||||||||
\(962\) | −10.8727 | −0.350550 | ||||||||
\(963\) | −44.7316 | −1.44145 | ||||||||
\(964\) | −0.244143 | −0.00786332 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.234853 | −0.00755626 | ||||||||
\(967\) | −2.70529 | −0.0869963 | −0.0434981 | − | 0.999054i | \(-0.513850\pi\) | ||||
−0.0434981 | + | 0.999054i | \(0.513850\pi\) | |||||||
\(968\) | 2.22529 | 0.0715236 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.14238 | 0.229210 | 0.114605 | − | 0.993411i | \(-0.463440\pi\) | ||||
0.114605 | + | 0.993411i | \(0.463440\pi\) | |||||||
\(972\) | −4.20637 | −0.134919 | ||||||||
\(973\) | −13.3242 | −0.427156 | ||||||||
\(974\) | 7.47040 | 0.239367 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −29.5062 | −0.944471 | ||||||||
\(977\) | −28.8990 | −0.924560 | −0.462280 | − | 0.886734i | \(-0.652968\pi\) | ||||
−0.462280 | + | 0.886734i | \(0.652968\pi\) | |||||||
\(978\) | 0.0153030 | 0.000489337 0 | ||||||||
\(979\) | −29.2030 | −0.933332 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.5817 | 0.497484 | ||||||||
\(982\) | 4.27392 | 0.136386 | ||||||||
\(983\) | 10.3410 | 0.329827 | 0.164914 | − | 0.986308i | \(-0.447265\pi\) | ||||
0.164914 | + | 0.986308i | \(0.447265\pi\) | |||||||
\(984\) | 0.363782 | 0.0115970 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4.57280 | 0.145628 | ||||||||
\(987\) | −0.222371 | −0.00707814 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −44.0262 | −1.39995 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.6203 | −1.00445 | −0.502226 | − | 0.864736i | \(-0.667486\pi\) | ||||
−0.502226 | + | 0.864736i | \(0.667486\pi\) | |||||||
\(992\) | −9.96596 | −0.316419 | ||||||||
\(993\) | −1.24160 | −0.0394011 | ||||||||
\(994\) | −3.71015 | −0.117679 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.78116 | −0.0564384 | ||||||||
\(997\) | −7.87725 | −0.249475 | −0.124737 | − | 0.992190i | \(-0.539809\pi\) | ||||
−0.124737 | + | 0.992190i | \(0.539809\pi\) | |||||||
\(998\) | 0.124359 | 0.00393653 | ||||||||
\(999\) | −3.81649 | −0.120748 |
(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 | 9025.2.a.cf.1.4 | 9 | ||
5.4 | even | 2 | 1805.2.a.s.1.6 | 9 | |||
19.3 | odd | 18 | 475.2.l.c.351.2 | 18 | |||
19.13 | odd | 18 | 475.2.l.c.226.2 | 18 | |||
19.18 | odd | 2 | 9025.2.a.cc.1.6 | 9 | |||
95.3 | even | 36 | 475.2.u.b.199.3 | 36 | |||
95.13 | even | 36 | 475.2.u.b.74.4 | 36 | |||
95.22 | even | 36 | 475.2.u.b.199.4 | 36 | |||
95.32 | even | 36 | 475.2.u.b.74.3 | 36 | |||
95.79 | odd | 18 | 95.2.k.a.66.2 | yes | 18 | ||
95.89 | odd | 18 | 95.2.k.a.36.2 | ✓ | 18 | ||
95.94 | odd | 2 | 1805.2.a.v.1.4 | 9 | |||
285.89 | even | 18 | 855.2.bs.c.226.2 | 18 | |||
285.269 | even | 18 | 855.2.bs.c.541.2 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.k.a.36.2 | ✓ | 18 | 95.89 | odd | 18 | ||
95.2.k.a.66.2 | yes | 18 | 95.79 | odd | 18 | ||
475.2.l.c.226.2 | 18 | 19.13 | odd | 18 | |||
475.2.l.c.351.2 | 18 | 19.3 | odd | 18 | |||
475.2.u.b.74.3 | 36 | 95.32 | even | 36 | |||
475.2.u.b.74.4 | 36 | 95.13 | even | 36 | |||
475.2.u.b.199.3 | 36 | 95.3 | even | 36 | |||
475.2.u.b.199.4 | 36 | 95.22 | even | 36 | |||
855.2.bs.c.226.2 | 18 | 285.89 | even | 18 | |||
855.2.bs.c.541.2 | 18 | 285.269 | even | 18 | |||
1805.2.a.s.1.6 | 9 | 5.4 | even | 2 | |||
1805.2.a.v.1.4 | 9 | 95.94 | odd | 2 | |||
9025.2.a.cc.1.6 | 9 | 19.18 | odd | 2 | |||
9025.2.a.cf.1.4 | 9 | 1.1 | even | 1 | trivial |