Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2077082653\) |
Analytic rank: | \(1\) |
Dimension: | \(69\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.42698 | −1.71614 | −0.858069 | − | 0.513535i | \(-0.828336\pi\) | ||||
−0.858069 | + | 0.513535i | \(0.828336\pi\) | |||||||
\(3\) | 0.265461 | 0.153264 | 0.0766320 | − | 0.997059i | \(-0.475583\pi\) | ||||
0.0766320 | + | 0.997059i | \(0.475583\pi\) | |||||||
\(4\) | 3.89025 | 1.94513 | ||||||||
\(5\) | 3.56663 | 1.59505 | 0.797523 | − | 0.603288i | \(-0.206143\pi\) | ||||
0.797523 | + | 0.603288i | \(0.206143\pi\) | |||||||
\(6\) | −0.644270 | −0.263022 | ||||||||
\(7\) | −2.27175 | −0.858640 | −0.429320 | − | 0.903152i | \(-0.641247\pi\) | ||||
−0.429320 | + | 0.903152i | \(0.641247\pi\) | |||||||
\(8\) | −4.58762 | −1.62197 | ||||||||
\(9\) | −2.92953 | −0.976510 | ||||||||
\(10\) | −8.65616 | −2.73732 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.03271 | 0.298118 | ||||||||
\(13\) | 0.560903 | 0.155567 | 0.0777833 | − | 0.996970i | \(-0.475216\pi\) | ||||
0.0777833 | + | 0.996970i | \(0.475216\pi\) | |||||||
\(14\) | 5.51350 | 1.47354 | ||||||||
\(15\) | 0.946802 | 0.244463 | ||||||||
\(16\) | 3.35357 | 0.838392 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 7.10992 | 1.67583 | ||||||||
\(19\) | −5.53686 | −1.27024 | −0.635121 | − | 0.772413i | \(-0.719050\pi\) | ||||
−0.635121 | + | 0.772413i | \(0.719050\pi\) | |||||||
\(20\) | 13.8751 | 3.10257 | ||||||||
\(21\) | −0.603061 | −0.131599 | ||||||||
\(22\) | 2.42698 | 0.517435 | ||||||||
\(23\) | 0.0941365 | 0.0196288 | 0.00981441 | − | 0.999952i | \(-0.496876\pi\) | ||||
0.00981441 | + | 0.999952i | \(0.496876\pi\) | |||||||
\(24\) | −1.21783 | −0.248589 | ||||||||
\(25\) | 7.72087 | 1.54417 | ||||||||
\(26\) | −1.36130 | −0.266974 | ||||||||
\(27\) | −1.57406 | −0.302928 | ||||||||
\(28\) | −8.83768 | −1.67016 | ||||||||
\(29\) | 3.09247 | 0.574258 | 0.287129 | − | 0.957892i | \(-0.407299\pi\) | ||||
0.287129 | + | 0.957892i | \(0.407299\pi\) | |||||||
\(30\) | −2.29787 | −0.419532 | ||||||||
\(31\) | 0.672520 | 0.120788 | 0.0603941 | − | 0.998175i | \(-0.480764\pi\) | ||||
0.0603941 | + | 0.998175i | \(0.480764\pi\) | |||||||
\(32\) | 1.03618 | 0.183172 | ||||||||
\(33\) | −0.265461 | −0.0462108 | ||||||||
\(34\) | −2.42698 | −0.416224 | ||||||||
\(35\) | −8.10249 | −1.36957 | ||||||||
\(36\) | −11.3966 | −1.89944 | ||||||||
\(37\) | 1.72926 | 0.284289 | 0.142145 | − | 0.989846i | \(-0.454600\pi\) | ||||
0.142145 | + | 0.989846i | \(0.454600\pi\) | |||||||
\(38\) | 13.4379 | 2.17991 | ||||||||
\(39\) | 0.148898 | 0.0238428 | ||||||||
\(40\) | −16.3623 | −2.58711 | ||||||||
\(41\) | −0.709853 | −0.110860 | −0.0554302 | − | 0.998463i | \(-0.517653\pi\) | ||||
−0.0554302 | + | 0.998463i | \(0.517653\pi\) | |||||||
\(42\) | 1.46362 | 0.225841 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | −3.89025 | −0.586478 | ||||||||
\(45\) | −10.4486 | −1.55758 | ||||||||
\(46\) | −0.228468 | −0.0336857 | ||||||||
\(47\) | −5.78116 | −0.843269 | −0.421634 | − | 0.906766i | \(-0.638543\pi\) | ||||
−0.421634 | + | 0.906766i | \(0.638543\pi\) | |||||||
\(48\) | 0.890241 | 0.128495 | ||||||||
\(49\) | −1.83916 | −0.262737 | ||||||||
\(50\) | −18.7384 | −2.65001 | ||||||||
\(51\) | 0.265461 | 0.0371720 | ||||||||
\(52\) | 2.18206 | 0.302597 | ||||||||
\(53\) | 4.54147 | 0.623818 | 0.311909 | − | 0.950112i | \(-0.399032\pi\) | ||||
0.311909 | + | 0.950112i | \(0.399032\pi\) | |||||||
\(54\) | 3.82022 | 0.519866 | ||||||||
\(55\) | −3.56663 | −0.480925 | ||||||||
\(56\) | 10.4219 | 1.39269 | ||||||||
\(57\) | −1.46982 | −0.194682 | ||||||||
\(58\) | −7.50538 | −0.985505 | ||||||||
\(59\) | 14.9209 | 1.94253 | 0.971266 | − | 0.237998i | \(-0.0764912\pi\) | ||||
0.971266 | + | 0.237998i | \(0.0764912\pi\) | |||||||
\(60\) | 3.68330 | 0.475512 | ||||||||
\(61\) | −3.26994 | −0.418673 | −0.209337 | − | 0.977844i | \(-0.567130\pi\) | ||||
−0.209337 | + | 0.977844i | \(0.567130\pi\) | |||||||
\(62\) | −1.63220 | −0.207289 | ||||||||
\(63\) | 6.65516 | 0.838471 | ||||||||
\(64\) | −9.22192 | −1.15274 | ||||||||
\(65\) | 2.00054 | 0.248136 | ||||||||
\(66\) | 0.644270 | 0.0793041 | ||||||||
\(67\) | −1.08719 | −0.132822 | −0.0664108 | − | 0.997792i | \(-0.521155\pi\) | ||||
−0.0664108 | + | 0.997792i | \(0.521155\pi\) | |||||||
\(68\) | 3.89025 | 0.471763 | ||||||||
\(69\) | 0.0249896 | 0.00300839 | ||||||||
\(70\) | 19.6646 | 2.35037 | ||||||||
\(71\) | 12.9951 | 1.54223 | 0.771116 | − | 0.636695i | \(-0.219699\pi\) | ||||
0.771116 | + | 0.636695i | \(0.219699\pi\) | |||||||
\(72\) | 13.4396 | 1.58387 | ||||||||
\(73\) | −2.05221 | −0.240192 | −0.120096 | − | 0.992762i | \(-0.538320\pi\) | ||||
−0.120096 | + | 0.992762i | \(0.538320\pi\) | |||||||
\(74\) | −4.19690 | −0.487880 | ||||||||
\(75\) | 2.04959 | 0.236666 | ||||||||
\(76\) | −21.5398 | −2.47078 | ||||||||
\(77\) | 2.27175 | 0.258890 | ||||||||
\(78\) | −0.361373 | −0.0409175 | ||||||||
\(79\) | −5.52944 | −0.622110 | −0.311055 | − | 0.950392i | \(-0.600682\pi\) | ||||
−0.311055 | + | 0.950392i | \(0.600682\pi\) | |||||||
\(80\) | 11.9609 | 1.33727 | ||||||||
\(81\) | 8.37074 | 0.930082 | ||||||||
\(82\) | 1.72280 | 0.190252 | ||||||||
\(83\) | −5.42574 | −0.595553 | −0.297776 | − | 0.954636i | \(-0.596245\pi\) | ||||
−0.297776 | + | 0.954636i | \(0.596245\pi\) | |||||||
\(84\) | −2.34606 | −0.255976 | ||||||||
\(85\) | 3.56663 | 0.386856 | ||||||||
\(86\) | −2.42698 | −0.261708 | ||||||||
\(87\) | 0.820931 | 0.0880131 | ||||||||
\(88\) | 4.58762 | 0.489042 | ||||||||
\(89\) | 13.3425 | 1.41431 | 0.707154 | − | 0.707060i | \(-0.249979\pi\) | ||||
0.707154 | + | 0.707060i | \(0.249979\pi\) | |||||||
\(90\) | 25.3585 | 2.67302 | ||||||||
\(91\) | −1.27423 | −0.133576 | ||||||||
\(92\) | 0.366215 | 0.0381805 | ||||||||
\(93\) | 0.178528 | 0.0185125 | ||||||||
\(94\) | 14.0308 | 1.44716 | ||||||||
\(95\) | −19.7479 | −2.02610 | ||||||||
\(96\) | 0.275065 | 0.0280737 | ||||||||
\(97\) | 6.01597 | 0.610830 | 0.305415 | − | 0.952219i | \(-0.401205\pi\) | ||||
0.305415 | + | 0.952219i | \(0.401205\pi\) | |||||||
\(98\) | 4.46361 | 0.450893 | ||||||||
\(99\) | 2.92953 | 0.294429 | ||||||||
\(100\) | 30.0361 | 3.00361 | ||||||||
\(101\) | −4.48745 | −0.446518 | −0.223259 | − | 0.974759i | \(-0.571670\pi\) | ||||
−0.223259 | + | 0.974759i | \(0.571670\pi\) | |||||||
\(102\) | −0.644270 | −0.0637922 | ||||||||
\(103\) | 9.56546 | 0.942512 | 0.471256 | − | 0.881996i | \(-0.343801\pi\) | ||||
0.471256 | + | 0.881996i | \(0.343801\pi\) | |||||||
\(104\) | −2.57321 | −0.252324 | ||||||||
\(105\) | −2.15090 | −0.209906 | ||||||||
\(106\) | −11.0221 | −1.07056 | ||||||||
\(107\) | 1.95259 | 0.188764 | 0.0943821 | − | 0.995536i | \(-0.469912\pi\) | ||||
0.0943821 | + | 0.995536i | \(0.469912\pi\) | |||||||
\(108\) | −6.12349 | −0.589233 | ||||||||
\(109\) | 16.9918 | 1.62752 | 0.813759 | − | 0.581203i | \(-0.197418\pi\) | ||||
0.813759 | + | 0.581203i | \(0.197418\pi\) | |||||||
\(110\) | 8.65616 | 0.825333 | ||||||||
\(111\) | 0.459052 | 0.0435713 | ||||||||
\(112\) | −7.61846 | −0.719877 | ||||||||
\(113\) | −4.77576 | −0.449266 | −0.224633 | − | 0.974443i | \(-0.572118\pi\) | ||||
−0.224633 | + | 0.974443i | \(0.572118\pi\) | |||||||
\(114\) | 3.56723 | 0.334102 | ||||||||
\(115\) | 0.335750 | 0.0313089 | ||||||||
\(116\) | 12.0305 | 1.11700 | ||||||||
\(117\) | −1.64318 | −0.151912 | ||||||||
\(118\) | −36.2127 | −3.33365 | ||||||||
\(119\) | −2.27175 | −0.208251 | ||||||||
\(120\) | −4.34356 | −0.396511 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 7.93610 | 0.718501 | ||||||||
\(123\) | −0.188438 | −0.0169909 | ||||||||
\(124\) | 2.61627 | 0.234948 | ||||||||
\(125\) | 9.70434 | 0.867982 | ||||||||
\(126\) | −16.1520 | −1.43893 | ||||||||
\(127\) | −14.6468 | −1.29970 | −0.649849 | − | 0.760063i | \(-0.725168\pi\) | ||||
−0.649849 | + | 0.760063i | \(0.725168\pi\) | |||||||
\(128\) | 20.3091 | 1.79509 | ||||||||
\(129\) | 0.265461 | 0.0233725 | ||||||||
\(130\) | −4.85527 | −0.425835 | ||||||||
\(131\) | −10.2817 | −0.898313 | −0.449156 | − | 0.893453i | \(-0.648275\pi\) | ||||
−0.449156 | + | 0.893453i | \(0.648275\pi\) | |||||||
\(132\) | −1.03271 | −0.0898859 | ||||||||
\(133\) | 12.5783 | 1.09068 | ||||||||
\(134\) | 2.63860 | 0.227940 | ||||||||
\(135\) | −5.61409 | −0.483184 | ||||||||
\(136\) | −4.58762 | −0.393385 | ||||||||
\(137\) | −11.5639 | −0.987973 | −0.493987 | − | 0.869470i | \(-0.664461\pi\) | ||||
−0.493987 | + | 0.869470i | \(0.664461\pi\) | |||||||
\(138\) | −0.0606493 | −0.00516281 | ||||||||
\(139\) | −8.22923 | −0.697994 | −0.348997 | − | 0.937124i | \(-0.613478\pi\) | ||||
−0.348997 | + | 0.937124i | \(0.613478\pi\) | |||||||
\(140\) | −31.5207 | −2.66399 | ||||||||
\(141\) | −1.53467 | −0.129243 | ||||||||
\(142\) | −31.5388 | −2.64668 | ||||||||
\(143\) | −0.560903 | −0.0469051 | ||||||||
\(144\) | −9.82437 | −0.818698 | ||||||||
\(145\) | 11.0297 | 0.915968 | ||||||||
\(146\) | 4.98067 | 0.412203 | ||||||||
\(147\) | −0.488225 | −0.0402682 | ||||||||
\(148\) | 6.72728 | 0.552979 | ||||||||
\(149\) | −12.3816 | −1.01434 | −0.507169 | − | 0.861847i | \(-0.669308\pi\) | ||||
−0.507169 | + | 0.861847i | \(0.669308\pi\) | |||||||
\(150\) | −4.97432 | −0.406152 | ||||||||
\(151\) | 7.09973 | 0.577768 | 0.288884 | − | 0.957364i | \(-0.406716\pi\) | ||||
0.288884 | + | 0.957364i | \(0.406716\pi\) | |||||||
\(152\) | 25.4010 | 2.06029 | ||||||||
\(153\) | −2.92953 | −0.236838 | ||||||||
\(154\) | −5.51350 | −0.444290 | ||||||||
\(155\) | 2.39863 | 0.192663 | ||||||||
\(156\) | 0.579251 | 0.0463772 | ||||||||
\(157\) | −21.0258 | −1.67804 | −0.839021 | − | 0.544100i | \(-0.816871\pi\) | ||||
−0.839021 | + | 0.544100i | \(0.816871\pi\) | |||||||
\(158\) | 13.4199 | 1.06763 | ||||||||
\(159\) | 1.20558 | 0.0956089 | ||||||||
\(160\) | 3.69567 | 0.292169 | ||||||||
\(161\) | −0.213854 | −0.0168541 | ||||||||
\(162\) | −20.3157 | −1.59615 | ||||||||
\(163\) | −4.43888 | −0.347680 | −0.173840 | − | 0.984774i | \(-0.555618\pi\) | ||||
−0.173840 | + | 0.984774i | \(0.555618\pi\) | |||||||
\(164\) | −2.76151 | −0.215638 | ||||||||
\(165\) | −0.946802 | −0.0737084 | ||||||||
\(166\) | 13.1682 | 1.02205 | ||||||||
\(167\) | −22.7629 | −1.76144 | −0.880722 | − | 0.473633i | \(-0.842942\pi\) | ||||
−0.880722 | + | 0.473633i | \(0.842942\pi\) | |||||||
\(168\) | 2.76661 | 0.213449 | ||||||||
\(169\) | −12.6854 | −0.975799 | ||||||||
\(170\) | −8.65616 | −0.663897 | ||||||||
\(171\) | 16.2204 | 1.24040 | ||||||||
\(172\) | 3.89025 | 0.296629 | ||||||||
\(173\) | 11.0979 | 0.843759 | 0.421880 | − | 0.906652i | \(-0.361370\pi\) | ||||
0.421880 | + | 0.906652i | \(0.361370\pi\) | |||||||
\(174\) | −1.99239 | −0.151042 | ||||||||
\(175\) | −17.5399 | −1.32589 | ||||||||
\(176\) | −3.35357 | −0.252785 | ||||||||
\(177\) | 3.96091 | 0.297720 | ||||||||
\(178\) | −32.3822 | −2.42715 | ||||||||
\(179\) | −9.24728 | −0.691174 | −0.345587 | − | 0.938387i | \(-0.612320\pi\) | ||||
−0.345587 | + | 0.938387i | \(0.612320\pi\) | |||||||
\(180\) | −40.6475 | −3.02969 | ||||||||
\(181\) | −21.0477 | −1.56446 | −0.782232 | − | 0.622987i | \(-0.785919\pi\) | ||||
−0.782232 | + | 0.622987i | \(0.785919\pi\) | |||||||
\(182\) | 3.09254 | 0.229234 | ||||||||
\(183\) | −0.868042 | −0.0641675 | ||||||||
\(184\) | −0.431862 | −0.0318373 | ||||||||
\(185\) | 6.16765 | 0.453455 | ||||||||
\(186\) | −0.433284 | −0.0317699 | ||||||||
\(187\) | −1.00000 | −0.0731272 | ||||||||
\(188\) | −22.4902 | −1.64026 | ||||||||
\(189\) | 3.57587 | 0.260106 | ||||||||
\(190\) | 47.9279 | 3.47706 | ||||||||
\(191\) | 12.4313 | 0.899500 | 0.449750 | − | 0.893154i | \(-0.351513\pi\) | ||||
0.449750 | + | 0.893154i | \(0.351513\pi\) | |||||||
\(192\) | −2.44806 | −0.176674 | ||||||||
\(193\) | −0.198958 | −0.0143213 | −0.00716064 | − | 0.999974i | \(-0.502279\pi\) | ||||
−0.00716064 | + | 0.999974i | \(0.502279\pi\) | |||||||
\(194\) | −14.6007 | −1.04827 | ||||||||
\(195\) | 0.531065 | 0.0380303 | ||||||||
\(196\) | −7.15480 | −0.511057 | ||||||||
\(197\) | 0.475159 | 0.0338537 | 0.0169268 | − | 0.999857i | \(-0.494612\pi\) | ||||
0.0169268 | + | 0.999857i | \(0.494612\pi\) | |||||||
\(198\) | −7.10992 | −0.505280 | ||||||||
\(199\) | −4.61260 | −0.326979 | −0.163489 | − | 0.986545i | \(-0.552275\pi\) | ||||
−0.163489 | + | 0.986545i | \(0.552275\pi\) | |||||||
\(200\) | −35.4204 | −2.50460 | ||||||||
\(201\) | −0.288607 | −0.0203568 | ||||||||
\(202\) | 10.8910 | 0.766287 | ||||||||
\(203\) | −7.02532 | −0.493081 | ||||||||
\(204\) | 1.03271 | 0.0723042 | ||||||||
\(205\) | −2.53179 | −0.176828 | ||||||||
\(206\) | −23.2152 | −1.61748 | ||||||||
\(207\) | −0.275776 | −0.0191677 | ||||||||
\(208\) | 1.88103 | 0.130426 | ||||||||
\(209\) | 5.53686 | 0.382992 | ||||||||
\(210\) | 5.22019 | 0.360227 | ||||||||
\(211\) | −4.98729 | −0.343339 | −0.171669 | − | 0.985155i | \(-0.554916\pi\) | ||||
−0.171669 | + | 0.985155i | \(0.554916\pi\) | |||||||
\(212\) | 17.6675 | 1.21341 | ||||||||
\(213\) | 3.44969 | 0.236369 | ||||||||
\(214\) | −4.73891 | −0.323945 | ||||||||
\(215\) | 3.56663 | 0.243242 | ||||||||
\(216\) | 7.22118 | 0.491339 | ||||||||
\(217\) | −1.52780 | −0.103714 | ||||||||
\(218\) | −41.2388 | −2.79304 | ||||||||
\(219\) | −0.544781 | −0.0368129 | ||||||||
\(220\) | −13.8751 | −0.935459 | ||||||||
\(221\) | 0.560903 | 0.0377304 | ||||||||
\(222\) | −1.11411 | −0.0747744 | ||||||||
\(223\) | −4.70781 | −0.315259 | −0.157629 | − | 0.987498i | \(-0.550385\pi\) | ||||
−0.157629 | + | 0.987498i | \(0.550385\pi\) | |||||||
\(224\) | −2.35394 | −0.157279 | ||||||||
\(225\) | −22.6185 | −1.50790 | ||||||||
\(226\) | 11.5907 | 0.771001 | ||||||||
\(227\) | −1.63824 | −0.108734 | −0.0543669 | − | 0.998521i | \(-0.517314\pi\) | ||||
−0.0543669 | + | 0.998521i | \(0.517314\pi\) | |||||||
\(228\) | −5.71797 | −0.378682 | ||||||||
\(229\) | −11.0325 | −0.729045 | −0.364523 | − | 0.931195i | \(-0.618768\pi\) | ||||
−0.364523 | + | 0.931195i | \(0.618768\pi\) | |||||||
\(230\) | −0.814861 | −0.0537303 | ||||||||
\(231\) | 0.603061 | 0.0396785 | ||||||||
\(232\) | −14.1871 | −0.931427 | ||||||||
\(233\) | −15.0223 | −0.984144 | −0.492072 | − | 0.870554i | \(-0.663760\pi\) | ||||
−0.492072 | + | 0.870554i | \(0.663760\pi\) | |||||||
\(234\) | 3.98798 | 0.260702 | ||||||||
\(235\) | −20.6193 | −1.34505 | ||||||||
\(236\) | 58.0460 | 3.77847 | ||||||||
\(237\) | −1.46785 | −0.0953471 | ||||||||
\(238\) | 5.51350 | 0.357387 | ||||||||
\(239\) | −24.6565 | −1.59489 | −0.797447 | − | 0.603389i | \(-0.793817\pi\) | ||||
−0.797447 | + | 0.603389i | \(0.793817\pi\) | |||||||
\(240\) | 3.17516 | 0.204956 | ||||||||
\(241\) | −9.99166 | −0.643620 | −0.321810 | − | 0.946804i | \(-0.604291\pi\) | ||||
−0.321810 | + | 0.946804i | \(0.604291\pi\) | |||||||
\(242\) | −2.42698 | −0.156012 | ||||||||
\(243\) | 6.94428 | 0.445476 | ||||||||
\(244\) | −12.7209 | −0.814372 | ||||||||
\(245\) | −6.55961 | −0.419078 | ||||||||
\(246\) | 0.457337 | 0.0291587 | ||||||||
\(247\) | −3.10564 | −0.197607 | ||||||||
\(248\) | −3.08526 | −0.195914 | ||||||||
\(249\) | −1.44032 | −0.0912768 | ||||||||
\(250\) | −23.5523 | −1.48958 | ||||||||
\(251\) | −0.301048 | −0.0190020 | −0.00950099 | − | 0.999955i | \(-0.503024\pi\) | ||||
−0.00950099 | + | 0.999955i | \(0.503024\pi\) | |||||||
\(252\) | 25.8902 | 1.63093 | ||||||||
\(253\) | −0.0941365 | −0.00591831 | ||||||||
\(254\) | 35.5477 | 2.23046 | ||||||||
\(255\) | 0.946802 | 0.0592911 | ||||||||
\(256\) | −30.8460 | −1.92788 | ||||||||
\(257\) | −15.0251 | −0.937242 | −0.468621 | − | 0.883399i | \(-0.655249\pi\) | ||||
−0.468621 | + | 0.883399i | \(0.655249\pi\) | |||||||
\(258\) | −0.644270 | −0.0401105 | ||||||||
\(259\) | −3.92845 | −0.244102 | ||||||||
\(260\) | 7.78259 | 0.482656 | ||||||||
\(261\) | −9.05949 | −0.560769 | ||||||||
\(262\) | 24.9534 | 1.54163 | ||||||||
\(263\) | −14.6691 | −0.904536 | −0.452268 | − | 0.891882i | \(-0.649385\pi\) | ||||
−0.452268 | + | 0.891882i | \(0.649385\pi\) | |||||||
\(264\) | 1.21783 | 0.0749525 | ||||||||
\(265\) | 16.1977 | 0.995019 | ||||||||
\(266\) | −30.5274 | −1.87176 | ||||||||
\(267\) | 3.54193 | 0.216762 | ||||||||
\(268\) | −4.22945 | −0.258355 | ||||||||
\(269\) | −1.54034 | −0.0939161 | −0.0469581 | − | 0.998897i | \(-0.514953\pi\) | ||||
−0.0469581 | + | 0.998897i | \(0.514953\pi\) | |||||||
\(270\) | 13.6253 | 0.829210 | ||||||||
\(271\) | −20.7782 | −1.26218 | −0.631091 | − | 0.775708i | \(-0.717393\pi\) | ||||
−0.631091 | + | 0.775708i | \(0.717393\pi\) | |||||||
\(272\) | 3.35357 | 0.203340 | ||||||||
\(273\) | −0.338259 | −0.0204724 | ||||||||
\(274\) | 28.0655 | 1.69550 | ||||||||
\(275\) | −7.72087 | −0.465586 | ||||||||
\(276\) | 0.0972158 | 0.00585170 | ||||||||
\(277\) | 12.1567 | 0.730424 | 0.365212 | − | 0.930924i | \(-0.380996\pi\) | ||||
0.365212 | + | 0.930924i | \(0.380996\pi\) | |||||||
\(278\) | 19.9722 | 1.19785 | ||||||||
\(279\) | −1.97017 | −0.117951 | ||||||||
\(280\) | 37.1711 | 2.22140 | ||||||||
\(281\) | 2.10752 | 0.125724 | 0.0628620 | − | 0.998022i | \(-0.479977\pi\) | ||||
0.0628620 | + | 0.998022i | \(0.479977\pi\) | |||||||
\(282\) | 3.72463 | 0.221798 | ||||||||
\(283\) | −21.6008 | −1.28404 | −0.642018 | − | 0.766689i | \(-0.721903\pi\) | ||||
−0.642018 | + | 0.766689i | \(0.721903\pi\) | |||||||
\(284\) | 50.5541 | 2.99984 | ||||||||
\(285\) | −5.24231 | −0.310528 | ||||||||
\(286\) | 1.36130 | 0.0804956 | ||||||||
\(287\) | 1.61261 | 0.0951892 | ||||||||
\(288\) | −3.03552 | −0.178870 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −26.7689 | −1.57193 | ||||||||
\(291\) | 1.59701 | 0.0936182 | ||||||||
\(292\) | −7.98360 | −0.467205 | ||||||||
\(293\) | 4.77366 | 0.278880 | 0.139440 | − | 0.990230i | \(-0.455470\pi\) | ||||
0.139440 | + | 0.990230i | \(0.455470\pi\) | |||||||
\(294\) | 1.18492 | 0.0691057 | ||||||||
\(295\) | 53.2172 | 3.09843 | ||||||||
\(296\) | −7.93320 | −0.461108 | ||||||||
\(297\) | 1.57406 | 0.0913362 | ||||||||
\(298\) | 30.0499 | 1.74074 | ||||||||
\(299\) | 0.0528015 | 0.00305359 | ||||||||
\(300\) | 7.97343 | 0.460346 | ||||||||
\(301\) | −2.27175 | −0.130941 | ||||||||
\(302\) | −17.2309 | −0.991529 | ||||||||
\(303\) | −1.19124 | −0.0684352 | ||||||||
\(304\) | −18.5682 | −1.06496 | ||||||||
\(305\) | −11.6627 | −0.667803 | ||||||||
\(306\) | 7.10992 | 0.406447 | ||||||||
\(307\) | −21.3459 | −1.21828 | −0.609138 | − | 0.793064i | \(-0.708484\pi\) | ||||
−0.609138 | + | 0.793064i | \(0.708484\pi\) | |||||||
\(308\) | 8.83768 | 0.503573 | ||||||||
\(309\) | 2.53926 | 0.144453 | ||||||||
\(310\) | −5.82144 | −0.330636 | ||||||||
\(311\) | −25.7859 | −1.46219 | −0.731093 | − | 0.682278i | \(-0.760990\pi\) | ||||
−0.731093 | + | 0.682278i | \(0.760990\pi\) | |||||||
\(312\) | −0.683087 | −0.0386722 | ||||||||
\(313\) | 11.1647 | 0.631068 | 0.315534 | − | 0.948914i | \(-0.397816\pi\) | ||||
0.315534 | + | 0.948914i | \(0.397816\pi\) | |||||||
\(314\) | 51.0293 | 2.87975 | ||||||||
\(315\) | 23.7365 | 1.33740 | ||||||||
\(316\) | −21.5109 | −1.21008 | ||||||||
\(317\) | 6.58877 | 0.370062 | 0.185031 | − | 0.982733i | \(-0.440761\pi\) | ||||
0.185031 | + | 0.982733i | \(0.440761\pi\) | |||||||
\(318\) | −2.92593 | −0.164078 | ||||||||
\(319\) | −3.09247 | −0.173145 | ||||||||
\(320\) | −32.8912 | −1.83867 | ||||||||
\(321\) | 0.518337 | 0.0289308 | ||||||||
\(322\) | 0.519021 | 0.0289239 | ||||||||
\(323\) | −5.53686 | −0.308079 | ||||||||
\(324\) | 32.5643 | 1.80913 | ||||||||
\(325\) | 4.33066 | 0.240222 | ||||||||
\(326\) | 10.7731 | 0.596666 | ||||||||
\(327\) | 4.51066 | 0.249440 | ||||||||
\(328\) | 3.25653 | 0.179812 | ||||||||
\(329\) | 13.1333 | 0.724064 | ||||||||
\(330\) | 2.29787 | 0.126494 | ||||||||
\(331\) | −5.40053 | −0.296840 | −0.148420 | − | 0.988924i | \(-0.547419\pi\) | ||||
−0.148420 | + | 0.988924i | \(0.547419\pi\) | |||||||
\(332\) | −21.1075 | −1.15843 | ||||||||
\(333\) | −5.06593 | −0.277611 | ||||||||
\(334\) | 55.2452 | 3.02288 | ||||||||
\(335\) | −3.87762 | −0.211857 | ||||||||
\(336\) | −2.02240 | −0.110331 | ||||||||
\(337\) | 22.5485 | 1.22829 | 0.614147 | − | 0.789191i | \(-0.289500\pi\) | ||||
0.614147 | + | 0.789191i | \(0.289500\pi\) | |||||||
\(338\) | 30.7872 | 1.67460 | ||||||||
\(339\) | −1.26778 | −0.0688563 | ||||||||
\(340\) | 13.8751 | 0.752483 | ||||||||
\(341\) | −0.672520 | −0.0364190 | ||||||||
\(342\) | −39.3666 | −2.12870 | ||||||||
\(343\) | 20.0803 | 1.08424 | ||||||||
\(344\) | −4.58762 | −0.247348 | ||||||||
\(345\) | 0.0891286 | 0.00479852 | ||||||||
\(346\) | −26.9345 | −1.44801 | ||||||||
\(347\) | −27.2409 | −1.46237 | −0.731185 | − | 0.682179i | \(-0.761033\pi\) | ||||
−0.731185 | + | 0.682179i | \(0.761033\pi\) | |||||||
\(348\) | 3.19363 | 0.171197 | ||||||||
\(349\) | −16.4422 | −0.880130 | −0.440065 | − | 0.897966i | \(-0.645045\pi\) | ||||
−0.440065 | + | 0.897966i | \(0.645045\pi\) | |||||||
\(350\) | 42.5690 | 2.27541 | ||||||||
\(351\) | −0.882895 | −0.0471255 | ||||||||
\(352\) | −1.03618 | −0.0552286 | ||||||||
\(353\) | 5.60309 | 0.298222 | 0.149111 | − | 0.988820i | \(-0.452359\pi\) | ||||
0.149111 | + | 0.988820i | \(0.452359\pi\) | |||||||
\(354\) | −9.61306 | −0.510929 | ||||||||
\(355\) | 46.3487 | 2.45993 | ||||||||
\(356\) | 51.9059 | 2.75101 | ||||||||
\(357\) | −0.603061 | −0.0319174 | ||||||||
\(358\) | 22.4430 | 1.18615 | ||||||||
\(359\) | −5.37033 | −0.283435 | −0.141718 | − | 0.989907i | \(-0.545262\pi\) | ||||
−0.141718 | + | 0.989907i | \(0.545262\pi\) | |||||||
\(360\) | 47.9340 | 2.52634 | ||||||||
\(361\) | 11.6568 | 0.613515 | ||||||||
\(362\) | 51.0825 | 2.68483 | ||||||||
\(363\) | 0.265461 | 0.0139331 | ||||||||
\(364\) | −4.95708 | −0.259822 | ||||||||
\(365\) | −7.31946 | −0.383118 | ||||||||
\(366\) | 2.10673 | 0.110120 | ||||||||
\(367\) | −28.0390 | −1.46362 | −0.731811 | − | 0.681508i | \(-0.761325\pi\) | ||||
−0.731811 | + | 0.681508i | \(0.761325\pi\) | |||||||
\(368\) | 0.315693 | 0.0164566 | ||||||||
\(369\) | 2.07954 | 0.108256 | ||||||||
\(370\) | −14.9688 | −0.778191 | ||||||||
\(371\) | −10.3171 | −0.535635 | ||||||||
\(372\) | 0.694519 | 0.0360091 | ||||||||
\(373\) | 2.74950 | 0.142364 | 0.0711819 | − | 0.997463i | \(-0.477323\pi\) | ||||
0.0711819 | + | 0.997463i | \(0.477323\pi\) | |||||||
\(374\) | 2.42698 | 0.125496 | ||||||||
\(375\) | 2.57612 | 0.133030 | ||||||||
\(376\) | 26.5217 | 1.36775 | ||||||||
\(377\) | 1.73458 | 0.0893353 | ||||||||
\(378\) | −8.67857 | −0.446378 | ||||||||
\(379\) | −18.1234 | −0.930936 | −0.465468 | − | 0.885065i | \(-0.654114\pi\) | ||||
−0.465468 | + | 0.885065i | \(0.654114\pi\) | |||||||
\(380\) | −76.8245 | −3.94101 | ||||||||
\(381\) | −3.88817 | −0.199197 | ||||||||
\(382\) | −30.1707 | −1.54367 | ||||||||
\(383\) | 4.58617 | 0.234342 | 0.117171 | − | 0.993112i | \(-0.462617\pi\) | ||||
0.117171 | + | 0.993112i | \(0.462617\pi\) | |||||||
\(384\) | 5.39128 | 0.275122 | ||||||||
\(385\) | 8.10249 | 0.412941 | ||||||||
\(386\) | 0.482867 | 0.0245773 | ||||||||
\(387\) | −2.92953 | −0.148916 | ||||||||
\(388\) | 23.4037 | 1.18814 | ||||||||
\(389\) | 17.0800 | 0.865990 | 0.432995 | − | 0.901396i | \(-0.357457\pi\) | ||||
0.432995 | + | 0.901396i | \(0.357457\pi\) | |||||||
\(390\) | −1.28889 | −0.0652653 | ||||||||
\(391\) | 0.0941365 | 0.00476069 | ||||||||
\(392\) | 8.43736 | 0.426151 | ||||||||
\(393\) | −2.72938 | −0.137679 | ||||||||
\(394\) | −1.15320 | −0.0580976 | ||||||||
\(395\) | −19.7215 | −0.992295 | ||||||||
\(396\) | 11.3966 | 0.572702 | ||||||||
\(397\) | 36.6708 | 1.84045 | 0.920226 | − | 0.391387i | \(-0.128005\pi\) | ||||
0.920226 | + | 0.391387i | \(0.128005\pi\) | |||||||
\(398\) | 11.1947 | 0.561140 | ||||||||
\(399\) | 3.33906 | 0.167162 | ||||||||
\(400\) | 25.8924 | 1.29462 | ||||||||
\(401\) | 1.32855 | 0.0663445 | 0.0331722 | − | 0.999450i | \(-0.489439\pi\) | ||||
0.0331722 | + | 0.999450i | \(0.489439\pi\) | |||||||
\(402\) | 0.700445 | 0.0349350 | ||||||||
\(403\) | 0.377219 | 0.0187906 | ||||||||
\(404\) | −17.4573 | −0.868535 | ||||||||
\(405\) | 29.8554 | 1.48352 | ||||||||
\(406\) | 17.0503 | 0.846194 | ||||||||
\(407\) | −1.72926 | −0.0857165 | ||||||||
\(408\) | −1.21783 | −0.0602917 | ||||||||
\(409\) | −22.7390 | −1.12437 | −0.562186 | − | 0.827011i | \(-0.690040\pi\) | ||||
−0.562186 | + | 0.827011i | \(0.690040\pi\) | |||||||
\(410\) | 6.14460 | 0.303460 | ||||||||
\(411\) | −3.06977 | −0.151421 | ||||||||
\(412\) | 37.2121 | 1.83331 | ||||||||
\(413\) | −33.8964 | −1.66794 | ||||||||
\(414\) | 0.669303 | 0.0328945 | ||||||||
\(415\) | −19.3516 | −0.949934 | ||||||||
\(416\) | 0.581197 | 0.0284955 | ||||||||
\(417\) | −2.18454 | −0.106977 | ||||||||
\(418\) | −13.4379 | −0.657268 | ||||||||
\(419\) | −24.0820 | −1.17648 | −0.588242 | − | 0.808685i | \(-0.700180\pi\) | ||||
−0.588242 | + | 0.808685i | \(0.700180\pi\) | |||||||
\(420\) | −8.36753 | −0.408294 | ||||||||
\(421\) | −35.2258 | −1.71680 | −0.858401 | − | 0.512980i | \(-0.828541\pi\) | ||||
−0.858401 | + | 0.512980i | \(0.828541\pi\) | |||||||
\(422\) | 12.1041 | 0.589217 | ||||||||
\(423\) | 16.9361 | 0.823461 | ||||||||
\(424\) | −20.8345 | −1.01181 | ||||||||
\(425\) | 7.72087 | 0.374517 | ||||||||
\(426\) | −8.37234 | −0.405641 | ||||||||
\(427\) | 7.42848 | 0.359490 | ||||||||
\(428\) | 7.59608 | 0.367170 | ||||||||
\(429\) | −0.148898 | −0.00718886 | ||||||||
\(430\) | −8.65616 | −0.417437 | ||||||||
\(431\) | 12.4389 | 0.599158 | 0.299579 | − | 0.954071i | \(-0.403154\pi\) | ||||
0.299579 | + | 0.954071i | \(0.403154\pi\) | |||||||
\(432\) | −5.27871 | −0.253972 | ||||||||
\(433\) | 21.5156 | 1.03398 | 0.516988 | − | 0.855993i | \(-0.327053\pi\) | ||||
0.516988 | + | 0.855993i | \(0.327053\pi\) | |||||||
\(434\) | 3.70794 | 0.177987 | ||||||||
\(435\) | 2.92796 | 0.140385 | ||||||||
\(436\) | 66.1023 | 3.16573 | ||||||||
\(437\) | −0.521220 | −0.0249333 | ||||||||
\(438\) | 1.32217 | 0.0631759 | ||||||||
\(439\) | 14.2630 | 0.680736 | 0.340368 | − | 0.940292i | \(-0.389448\pi\) | ||||
0.340368 | + | 0.940292i | \(0.389448\pi\) | |||||||
\(440\) | 16.3623 | 0.780044 | ||||||||
\(441\) | 5.38788 | 0.256566 | ||||||||
\(442\) | −1.36130 | −0.0647506 | ||||||||
\(443\) | 30.6206 | 1.45483 | 0.727415 | − | 0.686198i | \(-0.240722\pi\) | ||||
0.727415 | + | 0.686198i | \(0.240722\pi\) | |||||||
\(444\) | 1.78583 | 0.0847518 | ||||||||
\(445\) | 47.5880 | 2.25589 | ||||||||
\(446\) | 11.4258 | 0.541027 | ||||||||
\(447\) | −3.28682 | −0.155461 | ||||||||
\(448\) | 20.9499 | 0.989789 | ||||||||
\(449\) | −25.3899 | −1.19822 | −0.599112 | − | 0.800665i | \(-0.704479\pi\) | ||||
−0.599112 | + | 0.800665i | \(0.704479\pi\) | |||||||
\(450\) | 54.8948 | 2.58777 | ||||||||
\(451\) | 0.709853 | 0.0334257 | ||||||||
\(452\) | −18.5789 | −0.873879 | ||||||||
\(453\) | 1.88470 | 0.0885510 | ||||||||
\(454\) | 3.97599 | 0.186602 | ||||||||
\(455\) | −4.54472 | −0.213060 | ||||||||
\(456\) | 6.74297 | 0.315769 | ||||||||
\(457\) | 33.6698 | 1.57501 | 0.787503 | − | 0.616311i | \(-0.211374\pi\) | ||||
0.787503 | + | 0.616311i | \(0.211374\pi\) | |||||||
\(458\) | 26.7756 | 1.25114 | ||||||||
\(459\) | −1.57406 | −0.0734708 | ||||||||
\(460\) | 1.30615 | 0.0608997 | ||||||||
\(461\) | 2.67596 | 0.124632 | 0.0623159 | − | 0.998056i | \(-0.480151\pi\) | ||||
0.0623159 | + | 0.998056i | \(0.480151\pi\) | |||||||
\(462\) | −1.46362 | −0.0680937 | ||||||||
\(463\) | 20.9166 | 0.972076 | 0.486038 | − | 0.873938i | \(-0.338442\pi\) | ||||
0.486038 | + | 0.873938i | \(0.338442\pi\) | |||||||
\(464\) | 10.3708 | 0.481453 | ||||||||
\(465\) | 0.636743 | 0.0295283 | ||||||||
\(466\) | 36.4589 | 1.68893 | ||||||||
\(467\) | 35.6656 | 1.65041 | 0.825204 | − | 0.564835i | \(-0.191060\pi\) | ||||
0.825204 | + | 0.564835i | \(0.191060\pi\) | |||||||
\(468\) | −6.39240 | −0.295489 | ||||||||
\(469\) | 2.46983 | 0.114046 | ||||||||
\(470\) | 50.0427 | 2.30830 | ||||||||
\(471\) | −5.58153 | −0.257183 | ||||||||
\(472\) | −68.4512 | −3.15072 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | 3.56245 | 0.163629 | ||||||||
\(475\) | −42.7493 | −1.96147 | ||||||||
\(476\) | −8.83768 | −0.405074 | ||||||||
\(477\) | −13.3044 | −0.609165 | ||||||||
\(478\) | 59.8409 | 2.73706 | ||||||||
\(479\) | −22.3899 | −1.02302 | −0.511511 | − | 0.859277i | \(-0.670914\pi\) | ||||
−0.511511 | + | 0.859277i | \(0.670914\pi\) | |||||||
\(480\) | 0.981057 | 0.0447789 | ||||||||
\(481\) | 0.969950 | 0.0442259 | ||||||||
\(482\) | 24.2496 | 1.10454 | ||||||||
\(483\) | −0.0567700 | −0.00258312 | ||||||||
\(484\) | 3.89025 | 0.176830 | ||||||||
\(485\) | 21.4568 | 0.974302 | ||||||||
\(486\) | −16.8537 | −0.764498 | ||||||||
\(487\) | 8.46910 | 0.383771 | 0.191886 | − | 0.981417i | \(-0.438540\pi\) | ||||
0.191886 | + | 0.981417i | \(0.438540\pi\) | |||||||
\(488\) | 15.0012 | 0.679074 | ||||||||
\(489\) | −1.17835 | −0.0532868 | ||||||||
\(490\) | 15.9201 | 0.719195 | ||||||||
\(491\) | −5.97261 | −0.269540 | −0.134770 | − | 0.990877i | \(-0.543030\pi\) | ||||
−0.134770 | + | 0.990877i | \(0.543030\pi\) | |||||||
\(492\) | −0.733073 | −0.0330495 | ||||||||
\(493\) | 3.09247 | 0.139278 | ||||||||
\(494\) | 7.53735 | 0.339121 | ||||||||
\(495\) | 10.4486 | 0.469628 | ||||||||
\(496\) | 2.25534 | 0.101268 | ||||||||
\(497\) | −29.5215 | −1.32422 | ||||||||
\(498\) | 3.49564 | 0.156644 | ||||||||
\(499\) | −27.7930 | −1.24419 | −0.622093 | − | 0.782943i | \(-0.713718\pi\) | ||||
−0.622093 | + | 0.782943i | \(0.713718\pi\) | |||||||
\(500\) | 37.7523 | 1.68834 | ||||||||
\(501\) | −6.04266 | −0.269966 | ||||||||
\(502\) | 0.730639 | 0.0326100 | ||||||||
\(503\) | −30.0007 | −1.33767 | −0.668833 | − | 0.743412i | \(-0.733206\pi\) | ||||
−0.668833 | + | 0.743412i | \(0.733206\pi\) | |||||||
\(504\) | −30.5313 | −1.35997 | ||||||||
\(505\) | −16.0051 | −0.712217 | ||||||||
\(506\) | 0.228468 | 0.0101566 | ||||||||
\(507\) | −3.36748 | −0.149555 | ||||||||
\(508\) | −56.9800 | −2.52808 | ||||||||
\(509\) | 7.48214 | 0.331640 | 0.165820 | − | 0.986156i | \(-0.446973\pi\) | ||||
0.165820 | + | 0.986156i | \(0.446973\pi\) | |||||||
\(510\) | −2.29787 | −0.101752 | ||||||||
\(511\) | 4.66209 | 0.206239 | ||||||||
\(512\) | 34.2446 | 1.51341 | ||||||||
\(513\) | 8.71534 | 0.384792 | ||||||||
\(514\) | 36.4658 | 1.60844 | ||||||||
\(515\) | 34.1165 | 1.50335 | ||||||||
\(516\) | 1.03271 | 0.0454626 | ||||||||
\(517\) | 5.78116 | 0.254255 | ||||||||
\(518\) | 9.53430 | 0.418913 | ||||||||
\(519\) | 2.94607 | 0.129318 | ||||||||
\(520\) | −9.17769 | −0.402468 | ||||||||
\(521\) | 7.12546 | 0.312172 | 0.156086 | − | 0.987743i | \(-0.450112\pi\) | ||||
0.156086 | + | 0.987743i | \(0.450112\pi\) | |||||||
\(522\) | 21.9872 | 0.962356 | ||||||||
\(523\) | 30.3756 | 1.32823 | 0.664117 | − | 0.747628i | \(-0.268808\pi\) | ||||
0.664117 | + | 0.747628i | \(0.268808\pi\) | |||||||
\(524\) | −39.9983 | −1.74733 | ||||||||
\(525\) | −4.65615 | −0.203211 | ||||||||
\(526\) | 35.6017 | 1.55231 | ||||||||
\(527\) | 0.672520 | 0.0292954 | ||||||||
\(528\) | −0.890241 | −0.0387428 | ||||||||
\(529\) | −22.9911 | −0.999615 | ||||||||
\(530\) | −39.3117 | −1.70759 | ||||||||
\(531\) | −43.7111 | −1.89690 | ||||||||
\(532\) | 48.9330 | 2.12151 | ||||||||
\(533\) | −0.398159 | −0.0172462 | ||||||||
\(534\) | −8.59620 | −0.371994 | ||||||||
\(535\) | 6.96418 | 0.301088 | ||||||||
\(536\) | 4.98762 | 0.215432 | ||||||||
\(537\) | −2.45479 | −0.105932 | ||||||||
\(538\) | 3.73838 | 0.161173 | ||||||||
\(539\) | 1.83916 | 0.0792182 | ||||||||
\(540\) | −21.8402 | −0.939854 | ||||||||
\(541\) | 40.2347 | 1.72983 | 0.864913 | − | 0.501922i | \(-0.167373\pi\) | ||||
0.864913 | + | 0.501922i | \(0.167373\pi\) | |||||||
\(542\) | 50.4283 | 2.16608 | ||||||||
\(543\) | −5.58735 | −0.239776 | ||||||||
\(544\) | 1.03618 | 0.0444258 | ||||||||
\(545\) | 60.6034 | 2.59597 | ||||||||
\(546\) | 0.820949 | 0.0351334 | ||||||||
\(547\) | 2.24499 | 0.0959890 | 0.0479945 | − | 0.998848i | \(-0.484717\pi\) | ||||
0.0479945 | + | 0.998848i | \(0.484717\pi\) | |||||||
\(548\) | −44.9866 | −1.92173 | ||||||||
\(549\) | 9.57939 | 0.408839 | ||||||||
\(550\) | 18.7384 | 0.799009 | ||||||||
\(551\) | −17.1226 | −0.729446 | ||||||||
\(552\) | −0.114643 | −0.00487951 | ||||||||
\(553\) | 12.5615 | 0.534169 | ||||||||
\(554\) | −29.5041 | −1.25351 | ||||||||
\(555\) | 1.63727 | 0.0694983 | ||||||||
\(556\) | −32.0138 | −1.35769 | ||||||||
\(557\) | −3.78858 | −0.160527 | −0.0802636 | − | 0.996774i | \(-0.525576\pi\) | ||||
−0.0802636 | + | 0.996774i | \(0.525576\pi\) | |||||||
\(558\) | 4.78157 | 0.202420 | ||||||||
\(559\) | 0.560903 | 0.0237237 | ||||||||
\(560\) | −27.1722 | −1.14824 | ||||||||
\(561\) | −0.265461 | −0.0112078 | ||||||||
\(562\) | −5.11491 | −0.215760 | ||||||||
\(563\) | −16.4438 | −0.693022 | −0.346511 | − | 0.938046i | \(-0.612634\pi\) | ||||
−0.346511 | + | 0.938046i | \(0.612634\pi\) | |||||||
\(564\) | −5.97027 | −0.251394 | ||||||||
\(565\) | −17.0334 | −0.716600 | ||||||||
\(566\) | 52.4249 | 2.20358 | ||||||||
\(567\) | −19.0162 | −0.798606 | ||||||||
\(568\) | −59.6164 | −2.50145 | ||||||||
\(569\) | −29.4783 | −1.23579 | −0.617896 | − | 0.786259i | \(-0.712015\pi\) | ||||
−0.617896 | + | 0.786259i | \(0.712015\pi\) | |||||||
\(570\) | 12.7230 | 0.532908 | ||||||||
\(571\) | 4.56327 | 0.190967 | 0.0954834 | − | 0.995431i | \(-0.469560\pi\) | ||||
0.0954834 | + | 0.995431i | \(0.469560\pi\) | |||||||
\(572\) | −2.18206 | −0.0912364 | ||||||||
\(573\) | 3.30004 | 0.137861 | ||||||||
\(574\) | −3.91377 | −0.163358 | ||||||||
\(575\) | 0.726815 | 0.0303103 | ||||||||
\(576\) | 27.0159 | 1.12566 | ||||||||
\(577\) | 17.0384 | 0.709318 | 0.354659 | − | 0.934996i | \(-0.384597\pi\) | ||||
0.354659 | + | 0.934996i | \(0.384597\pi\) | |||||||
\(578\) | −2.42698 | −0.100949 | ||||||||
\(579\) | −0.0528155 | −0.00219494 | ||||||||
\(580\) | 42.9084 | 1.78167 | ||||||||
\(581\) | 12.3259 | 0.511365 | ||||||||
\(582\) | −3.87591 | −0.160662 | ||||||||
\(583\) | −4.54147 | −0.188088 | ||||||||
\(584\) | 9.41473 | 0.389584 | ||||||||
\(585\) | −5.86063 | −0.242307 | ||||||||
\(586\) | −11.5856 | −0.478597 | ||||||||
\(587\) | −10.4283 | −0.430424 | −0.215212 | − | 0.976567i | \(-0.569044\pi\) | ||||
−0.215212 | + | 0.976567i | \(0.569044\pi\) | |||||||
\(588\) | −1.89932 | −0.0783267 | ||||||||
\(589\) | −3.72365 | −0.153430 | ||||||||
\(590\) | −129.157 | −5.31733 | ||||||||
\(591\) | 0.126136 | 0.00518855 | ||||||||
\(592\) | 5.79920 | 0.238346 | ||||||||
\(593\) | 9.00871 | 0.369943 | 0.184972 | − | 0.982744i | \(-0.440781\pi\) | ||||
0.184972 | + | 0.982744i | \(0.440781\pi\) | |||||||
\(594\) | −3.82022 | −0.156745 | ||||||||
\(595\) | −8.10249 | −0.332170 | ||||||||
\(596\) | −48.1674 | −1.97301 | ||||||||
\(597\) | −1.22447 | −0.0501141 | ||||||||
\(598\) | −0.128148 | −0.00524038 | ||||||||
\(599\) | −0.515451 | −0.0210608 | −0.0105304 | − | 0.999945i | \(-0.503352\pi\) | ||||
−0.0105304 | + | 0.999945i | \(0.503352\pi\) | |||||||
\(600\) | −9.40273 | −0.383865 | ||||||||
\(601\) | 5.18341 | 0.211436 | 0.105718 | − | 0.994396i | \(-0.466286\pi\) | ||||
0.105718 | + | 0.994396i | \(0.466286\pi\) | |||||||
\(602\) | 5.51350 | 0.224713 | ||||||||
\(603\) | 3.18496 | 0.129702 | ||||||||
\(604\) | 27.6197 | 1.12383 | ||||||||
\(605\) | 3.56663 | 0.145004 | ||||||||
\(606\) | 2.89113 | 0.117444 | ||||||||
\(607\) | 3.25608 | 0.132160 | 0.0660801 | − | 0.997814i | \(-0.478951\pi\) | ||||
0.0660801 | + | 0.997814i | \(0.478951\pi\) | |||||||
\(608\) | −5.73718 | −0.232673 | ||||||||
\(609\) | −1.86495 | −0.0755715 | ||||||||
\(610\) | 28.3051 | 1.14604 | ||||||||
\(611\) | −3.24267 | −0.131184 | ||||||||
\(612\) | −11.3966 | −0.460681 | ||||||||
\(613\) | 9.21578 | 0.372222 | 0.186111 | − | 0.982529i | \(-0.440412\pi\) | ||||
0.186111 | + | 0.982529i | \(0.440412\pi\) | |||||||
\(614\) | 51.8062 | 2.09073 | ||||||||
\(615\) | −0.672090 | −0.0271013 | ||||||||
\(616\) | −10.4219 | −0.419911 | ||||||||
\(617\) | −15.5452 | −0.625826 | −0.312913 | − | 0.949782i | \(-0.601305\pi\) | ||||
−0.312913 | + | 0.949782i | \(0.601305\pi\) | |||||||
\(618\) | −6.16274 | −0.247902 | ||||||||
\(619\) | 16.6783 | 0.670356 | 0.335178 | − | 0.942155i | \(-0.391204\pi\) | ||||
0.335178 | + | 0.942155i | \(0.391204\pi\) | |||||||
\(620\) | 9.33128 | 0.374753 | ||||||||
\(621\) | −0.148176 | −0.00594611 | ||||||||
\(622\) | 62.5821 | 2.50931 | ||||||||
\(623\) | −30.3109 | −1.21438 | ||||||||
\(624\) | 0.499339 | 0.0199896 | ||||||||
\(625\) | −3.99253 | −0.159701 | ||||||||
\(626\) | −27.0966 | −1.08300 | ||||||||
\(627\) | 1.46982 | 0.0586990 | ||||||||
\(628\) | −81.7957 | −3.26400 | ||||||||
\(629\) | 1.72926 | 0.0689503 | ||||||||
\(630\) | −57.6081 | −2.29516 | ||||||||
\(631\) | −22.5981 | −0.899616 | −0.449808 | − | 0.893125i | \(-0.648508\pi\) | ||||
−0.449808 | + | 0.893125i | \(0.648508\pi\) | |||||||
\(632\) | 25.3669 | 1.00904 | ||||||||
\(633\) | −1.32393 | −0.0526215 | ||||||||
\(634\) | −15.9908 | −0.635078 | ||||||||
\(635\) | −52.2399 | −2.07308 | ||||||||
\(636\) | 4.69002 | 0.185971 | ||||||||
\(637\) | −1.03159 | −0.0408731 | ||||||||
\(638\) | 7.50538 | 0.297141 | ||||||||
\(639\) | −38.0695 | −1.50601 | ||||||||
\(640\) | 72.4351 | 2.86325 | ||||||||
\(641\) | −5.97068 | −0.235828 | −0.117914 | − | 0.993024i | \(-0.537621\pi\) | ||||
−0.117914 | + | 0.993024i | \(0.537621\pi\) | |||||||
\(642\) | −1.25800 | −0.0496492 | ||||||||
\(643\) | 17.8129 | 0.702472 | 0.351236 | − | 0.936287i | \(-0.385761\pi\) | ||||
0.351236 | + | 0.936287i | \(0.385761\pi\) | |||||||
\(644\) | −0.831948 | −0.0327833 | ||||||||
\(645\) | 0.946802 | 0.0372803 | ||||||||
\(646\) | 13.4379 | 0.528706 | ||||||||
\(647\) | −31.2569 | −1.22884 | −0.614419 | − | 0.788980i | \(-0.710609\pi\) | ||||
−0.614419 | + | 0.788980i | \(0.710609\pi\) | |||||||
\(648\) | −38.4017 | −1.50856 | ||||||||
\(649\) | −14.9209 | −0.585695 | ||||||||
\(650\) | −10.5104 | −0.412254 | ||||||||
\(651\) | −0.405570 | −0.0158956 | ||||||||
\(652\) | −17.2684 | −0.676281 | ||||||||
\(653\) | −0.160921 | −0.00629733 | −0.00314867 | − | 0.999995i | \(-0.501002\pi\) | ||||
−0.00314867 | + | 0.999995i | \(0.501002\pi\) | |||||||
\(654\) | −10.9473 | −0.428073 | ||||||||
\(655\) | −36.6709 | −1.43285 | ||||||||
\(656\) | −2.38054 | −0.0929444 | ||||||||
\(657\) | 6.01200 | 0.234550 | ||||||||
\(658\) | −31.8744 | −1.24259 | ||||||||
\(659\) | −14.2421 | −0.554793 | −0.277397 | − | 0.960756i | \(-0.589472\pi\) | ||||
−0.277397 | + | 0.960756i | \(0.589472\pi\) | |||||||
\(660\) | −3.68330 | −0.143372 | ||||||||
\(661\) | 10.6546 | 0.414418 | 0.207209 | − | 0.978297i | \(-0.433562\pi\) | ||||
0.207209 | + | 0.978297i | \(0.433562\pi\) | |||||||
\(662\) | 13.1070 | 0.509418 | ||||||||
\(663\) | 0.148898 | 0.00578272 | ||||||||
\(664\) | 24.8912 | 0.965967 | ||||||||
\(665\) | 44.8623 | 1.73969 | ||||||||
\(666\) | 12.2949 | 0.476419 | ||||||||
\(667\) | 0.291114 | 0.0112720 | ||||||||
\(668\) | −88.5534 | −3.42623 | ||||||||
\(669\) | −1.24974 | −0.0483178 | ||||||||
\(670\) | 9.41091 | 0.363575 | ||||||||
\(671\) | 3.26994 | 0.126235 | ||||||||
\(672\) | −0.624879 | −0.0241052 | ||||||||
\(673\) | 19.6795 | 0.758590 | 0.379295 | − | 0.925276i | \(-0.376167\pi\) | ||||
0.379295 | + | 0.925276i | \(0.376167\pi\) | |||||||
\(674\) | −54.7249 | −2.10792 | ||||||||
\(675\) | −12.1531 | −0.467773 | ||||||||
\(676\) | −49.3494 | −1.89805 | ||||||||
\(677\) | 41.9652 | 1.61285 | 0.806426 | − | 0.591335i | \(-0.201399\pi\) | ||||
0.806426 | + | 0.591335i | \(0.201399\pi\) | |||||||
\(678\) | 3.07688 | 0.118167 | ||||||||
\(679\) | −13.6668 | −0.524483 | ||||||||
\(680\) | −16.3623 | −0.627467 | ||||||||
\(681\) | −0.434889 | −0.0166650 | ||||||||
\(682\) | 1.63220 | 0.0625000 | ||||||||
\(683\) | 1.41580 | 0.0541742 | 0.0270871 | − | 0.999633i | \(-0.491377\pi\) | ||||
0.0270871 | + | 0.999633i | \(0.491377\pi\) | |||||||
\(684\) | 63.1014 | 2.41274 | ||||||||
\(685\) | −41.2443 | −1.57586 | ||||||||
\(686\) | −48.7347 | −1.86070 | ||||||||
\(687\) | −2.92869 | −0.111736 | ||||||||
\(688\) | 3.35357 | 0.127854 | ||||||||
\(689\) | 2.54732 | 0.0970453 | ||||||||
\(690\) | −0.216314 | −0.00823492 | ||||||||
\(691\) | −46.1662 | −1.75624 | −0.878122 | − | 0.478437i | \(-0.841203\pi\) | ||||
−0.878122 | + | 0.478437i | \(0.841203\pi\) | |||||||
\(692\) | 43.1737 | 1.64122 | ||||||||
\(693\) | −6.65516 | −0.252808 | ||||||||
\(694\) | 66.1134 | 2.50963 | ||||||||
\(695\) | −29.3506 | −1.11333 | ||||||||
\(696\) | −3.76612 | −0.142754 | ||||||||
\(697\) | −0.709853 | −0.0268876 | ||||||||
\(698\) | 39.9049 | 1.51042 | ||||||||
\(699\) | −3.98784 | −0.150834 | ||||||||
\(700\) | −68.2345 | −2.57902 | ||||||||
\(701\) | 31.3644 | 1.18462 | 0.592308 | − | 0.805712i | \(-0.298217\pi\) | ||||
0.592308 | + | 0.805712i | \(0.298217\pi\) | |||||||
\(702\) | 2.14277 | 0.0808738 | ||||||||
\(703\) | −9.57469 | −0.361116 | ||||||||
\(704\) | 9.22192 | 0.347564 | ||||||||
\(705\) | −5.47361 | −0.206148 | ||||||||
\(706\) | −13.5986 | −0.511791 | ||||||||
\(707\) | 10.1944 | 0.383398 | ||||||||
\(708\) | 15.4089 | 0.579103 | ||||||||
\(709\) | −16.1781 | −0.607583 | −0.303791 | − | 0.952739i | \(-0.598253\pi\) | ||||
−0.303791 | + | 0.952739i | \(0.598253\pi\) | |||||||
\(710\) | −112.487 | −4.22158 | ||||||||
\(711\) | 16.1987 | 0.607497 | ||||||||
\(712\) | −61.2105 | −2.29396 | ||||||||
\(713\) | 0.0633086 | 0.00237093 | ||||||||
\(714\) | 1.46362 | 0.0547746 | ||||||||
\(715\) | −2.00054 | −0.0748158 | ||||||||
\(716\) | −35.9743 | −1.34442 | ||||||||
\(717\) | −6.54533 | −0.244440 | ||||||||
\(718\) | 13.0337 | 0.486414 | ||||||||
\(719\) | 14.7977 | 0.551861 | 0.275931 | − | 0.961178i | \(-0.411014\pi\) | ||||
0.275931 | + | 0.961178i | \(0.411014\pi\) | |||||||
\(720\) | −35.0399 | −1.30586 | ||||||||
\(721\) | −21.7303 | −0.809279 | ||||||||
\(722\) | −28.2908 | −1.05288 | ||||||||
\(723\) | −2.65240 | −0.0986437 | ||||||||
\(724\) | −81.8809 | −3.04308 | ||||||||
\(725\) | 23.8766 | 0.886754 | ||||||||
\(726\) | −0.644270 | −0.0239111 | ||||||||
\(727\) | 4.00979 | 0.148715 | 0.0743574 | − | 0.997232i | \(-0.476309\pi\) | ||||
0.0743574 | + | 0.997232i | \(0.476309\pi\) | |||||||
\(728\) | 5.84568 | 0.216655 | ||||||||
\(729\) | −23.2688 | −0.861807 | ||||||||
\(730\) | 17.7642 | 0.657483 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | −3.37690 | −0.124814 | ||||||||
\(733\) | −31.8557 | −1.17662 | −0.588308 | − | 0.808637i | \(-0.700206\pi\) | ||||
−0.588308 | + | 0.808637i | \(0.700206\pi\) | |||||||
\(734\) | 68.0501 | 2.51178 | ||||||||
\(735\) | −1.74132 | −0.0642296 | ||||||||
\(736\) | 0.0975423 | 0.00359546 | ||||||||
\(737\) | 1.08719 | 0.0400472 | ||||||||
\(738\) | −5.04700 | −0.185783 | ||||||||
\(739\) | 16.2278 | 0.596951 | 0.298475 | − | 0.954417i | \(-0.403522\pi\) | ||||
0.298475 | + | 0.954417i | \(0.403522\pi\) | |||||||
\(740\) | 23.9937 | 0.882027 | ||||||||
\(741\) | −0.824427 | −0.0302861 | ||||||||
\(742\) | 25.0394 | 0.919224 | ||||||||
\(743\) | −20.1018 | −0.737465 | −0.368733 | − | 0.929536i | \(-0.620208\pi\) | ||||
−0.368733 | + | 0.929536i | \(0.620208\pi\) | |||||||
\(744\) | −0.819017 | −0.0300266 | ||||||||
\(745\) | −44.1605 | −1.61792 | ||||||||
\(746\) | −6.67300 | −0.244316 | ||||||||
\(747\) | 15.8949 | 0.581563 | ||||||||
\(748\) | −3.89025 | −0.142242 | ||||||||
\(749\) | −4.43580 | −0.162081 | ||||||||
\(750\) | −6.25221 | −0.228299 | ||||||||
\(751\) | −30.3326 | −1.10685 | −0.553426 | − | 0.832898i | \(-0.686680\pi\) | ||||
−0.553426 | + | 0.832898i | \(0.686680\pi\) | |||||||
\(752\) | −19.3875 | −0.706989 | ||||||||
\(753\) | −0.0799166 | −0.00291232 | ||||||||
\(754\) | −4.20980 | −0.153312 | ||||||||
\(755\) | 25.3221 | 0.921566 | ||||||||
\(756\) | 13.9110 | 0.505939 | ||||||||
\(757\) | 11.0651 | 0.402167 | 0.201083 | − | 0.979574i | \(-0.435554\pi\) | ||||
0.201083 | + | 0.979574i | \(0.435554\pi\) | |||||||
\(758\) | 43.9852 | 1.59761 | ||||||||
\(759\) | −0.0249896 | −0.000907064 0 | ||||||||
\(760\) | 90.5959 | 3.28626 | ||||||||
\(761\) | −11.8063 | −0.427979 | −0.213989 | − | 0.976836i | \(-0.568646\pi\) | ||||
−0.213989 | + | 0.976836i | \(0.568646\pi\) | |||||||
\(762\) | 9.43652 | 0.341849 | ||||||||
\(763\) | −38.6010 | −1.39745 | ||||||||
\(764\) | 48.3611 | 1.74964 | ||||||||
\(765\) | −10.4486 | −0.377768 | ||||||||
\(766\) | −11.1306 | −0.402163 | ||||||||
\(767\) | 8.36916 | 0.302193 | ||||||||
\(768\) | −8.18842 | −0.295474 | ||||||||
\(769\) | −14.8518 | −0.535570 | −0.267785 | − | 0.963479i | \(-0.586292\pi\) | ||||
−0.267785 | + | 0.963479i | \(0.586292\pi\) | |||||||
\(770\) | −19.6646 | −0.708664 | ||||||||
\(771\) | −3.98859 | −0.143645 | ||||||||
\(772\) | −0.773995 | −0.0278567 | ||||||||
\(773\) | −47.2794 | −1.70052 | −0.850260 | − | 0.526363i | \(-0.823555\pi\) | ||||
−0.850260 | + | 0.526363i | \(0.823555\pi\) | |||||||
\(774\) | 7.10992 | 0.255561 | ||||||||
\(775\) | 5.19244 | 0.186518 | ||||||||
\(776\) | −27.5990 | −0.990746 | ||||||||
\(777\) | −1.04285 | −0.0374121 | ||||||||
\(778\) | −41.4529 | −1.48616 | ||||||||
\(779\) | 3.93036 | 0.140820 | ||||||||
\(780\) | 2.06598 | 0.0739738 | ||||||||
\(781\) | −12.9951 | −0.465000 | ||||||||
\(782\) | −0.228468 | −0.00816999 | ||||||||
\(783\) | −4.86774 | −0.173959 | ||||||||
\(784\) | −6.16775 | −0.220277 | ||||||||
\(785\) | −74.9913 | −2.67655 | ||||||||
\(786\) | 6.62416 | 0.236276 | ||||||||
\(787\) | 7.36580 | 0.262563 | 0.131281 | − | 0.991345i | \(-0.458091\pi\) | ||||
0.131281 | + | 0.991345i | \(0.458091\pi\) | |||||||
\(788\) | 1.84849 | 0.0658497 | ||||||||
\(789\) | −3.89408 | −0.138633 | ||||||||
\(790\) | 47.8637 | 1.70291 | ||||||||
\(791\) | 10.8493 | 0.385757 | ||||||||
\(792\) | −13.4396 | −0.477554 | ||||||||
\(793\) | −1.83412 | −0.0651316 | ||||||||
\(794\) | −88.9993 | −3.15847 | ||||||||
\(795\) | 4.29987 | 0.152501 | ||||||||
\(796\) | −17.9442 | −0.636015 | ||||||||
\(797\) | 20.3167 | 0.719654 | 0.359827 | − | 0.933019i | \(-0.382836\pi\) | ||||
0.359827 | + | 0.933019i | \(0.382836\pi\) | |||||||
\(798\) | −8.10385 | −0.286873 | ||||||||
\(799\) | −5.78116 | −0.204523 | ||||||||
\(800\) | 8.00021 | 0.282850 | ||||||||
\(801\) | −39.0874 | −1.38109 | ||||||||
\(802\) | −3.22436 | −0.113856 | ||||||||
\(803\) | 2.05221 | 0.0724207 | ||||||||
\(804\) | −1.12276 | −0.0395965 | ||||||||
\(805\) | −0.762740 | −0.0268830 | ||||||||
\(806\) | −0.915504 | −0.0322472 | ||||||||
\(807\) | −0.408900 | −0.0143940 | ||||||||
\(808\) | 20.5867 | 0.724238 | ||||||||
\(809\) | −28.3218 | −0.995742 | −0.497871 | − | 0.867251i | \(-0.665885\pi\) | ||||
−0.497871 | + | 0.867251i | \(0.665885\pi\) | |||||||
\(810\) | −72.4585 | −2.54593 | ||||||||
\(811\) | 2.29089 | 0.0804441 | 0.0402221 | − | 0.999191i | \(-0.487193\pi\) | ||||
0.0402221 | + | 0.999191i | \(0.487193\pi\) | |||||||
\(812\) | −27.3303 | −0.959105 | ||||||||
\(813\) | −5.51579 | −0.193447 | ||||||||
\(814\) | 4.19690 | 0.147101 | ||||||||
\(815\) | −15.8319 | −0.554566 | ||||||||
\(816\) | 0.890241 | 0.0311647 | ||||||||
\(817\) | −5.53686 | −0.193710 | ||||||||
\(818\) | 55.1873 | 1.92958 | ||||||||
\(819\) | 3.73290 | 0.130438 | ||||||||
\(820\) | −9.84929 | −0.343952 | ||||||||
\(821\) | −53.0608 | −1.85184 | −0.925918 | − | 0.377725i | \(-0.876706\pi\) | ||||
−0.925918 | + | 0.377725i | \(0.876706\pi\) | |||||||
\(822\) | 7.45029 | 0.259859 | ||||||||
\(823\) | 25.0667 | 0.873772 | 0.436886 | − | 0.899517i | \(-0.356081\pi\) | ||||
0.436886 | + | 0.899517i | \(0.356081\pi\) | |||||||
\(824\) | −43.8826 | −1.52872 | ||||||||
\(825\) | −2.04959 | −0.0713576 | ||||||||
\(826\) | 82.2662 | 2.86241 | ||||||||
\(827\) | −23.7100 | −0.824477 | −0.412238 | − | 0.911076i | \(-0.635253\pi\) | ||||
−0.412238 | + | 0.911076i | \(0.635253\pi\) | |||||||
\(828\) | −1.07284 | −0.0372837 | ||||||||
\(829\) | 23.9376 | 0.831386 | 0.415693 | − | 0.909505i | \(-0.363539\pi\) | ||||
0.415693 | + | 0.909505i | \(0.363539\pi\) | |||||||
\(830\) | 46.9661 | 1.63022 | ||||||||
\(831\) | 3.22713 | 0.111948 | ||||||||
\(832\) | −5.17261 | −0.179328 | ||||||||
\(833\) | −1.83916 | −0.0637231 | ||||||||
\(834\) | 5.30184 | 0.183588 | ||||||||
\(835\) | −81.1868 | −2.80959 | ||||||||
\(836\) | 21.5398 | 0.744969 | ||||||||
\(837\) | −1.05859 | −0.0365901 | ||||||||
\(838\) | 58.4467 | 2.01901 | ||||||||
\(839\) | 44.6869 | 1.54276 | 0.771382 | − | 0.636373i | \(-0.219566\pi\) | ||||
0.771382 | + | 0.636373i | \(0.219566\pi\) | |||||||
\(840\) | 9.86749 | 0.340461 | ||||||||
\(841\) | −19.4366 | −0.670228 | ||||||||
\(842\) | 85.4925 | 2.94627 | ||||||||
\(843\) | 0.559464 | 0.0192690 | ||||||||
\(844\) | −19.4018 | −0.667838 | ||||||||
\(845\) | −45.2441 | −1.55644 | ||||||||
\(846\) | −41.1036 | −1.41317 | ||||||||
\(847\) | −2.27175 | −0.0780582 | ||||||||
\(848\) | 15.2301 | 0.523004 | ||||||||
\(849\) | −5.73418 | −0.196797 | ||||||||
\(850\) | −18.7384 | −0.642723 | ||||||||
\(851\) | 0.162787 | 0.00558026 | ||||||||
\(852\) | 13.4202 | 0.459767 | ||||||||
\(853\) | 33.8753 | 1.15987 | 0.579935 | − | 0.814663i | \(-0.303078\pi\) | ||||
0.579935 | + | 0.814663i | \(0.303078\pi\) | |||||||
\(854\) | −18.0288 | −0.616933 | ||||||||
\(855\) | 57.8522 | 1.97850 | ||||||||
\(856\) | −8.95775 | −0.306169 | ||||||||
\(857\) | −44.2756 | −1.51242 | −0.756212 | − | 0.654327i | \(-0.772952\pi\) | ||||
−0.756212 | + | 0.654327i | \(0.772952\pi\) | |||||||
\(858\) | 0.361373 | 0.0123371 | ||||||||
\(859\) | 1.80274 | 0.0615086 | 0.0307543 | − | 0.999527i | \(-0.490209\pi\) | ||||
0.0307543 | + | 0.999527i | \(0.490209\pi\) | |||||||
\(860\) | 13.8751 | 0.473137 | ||||||||
\(861\) | 0.428085 | 0.0145891 | ||||||||
\(862\) | −30.1889 | −1.02824 | ||||||||
\(863\) | 23.5042 | 0.800092 | 0.400046 | − | 0.916495i | \(-0.368994\pi\) | ||||
0.400046 | + | 0.916495i | \(0.368994\pi\) | |||||||
\(864\) | −1.63101 | −0.0554880 | ||||||||
\(865\) | 39.5822 | 1.34584 | ||||||||
\(866\) | −52.2181 | −1.77444 | ||||||||
\(867\) | 0.265461 | 0.00901553 | ||||||||
\(868\) | −5.94351 | −0.201736 | ||||||||
\(869\) | 5.52944 | 0.187573 | ||||||||
\(870\) | −7.10611 | −0.240920 | ||||||||
\(871\) | −0.609810 | −0.0206626 | ||||||||
\(872\) | −77.9518 | −2.63978 | ||||||||
\(873\) | −17.6240 | −0.596481 | ||||||||
\(874\) | 1.26499 | 0.0427890 | ||||||||
\(875\) | −22.0458 | −0.745284 | ||||||||
\(876\) | −2.11933 | −0.0716057 | ||||||||
\(877\) | −6.32715 | −0.213653 | −0.106826 | − | 0.994278i | \(-0.534069\pi\) | ||||
−0.106826 | + | 0.994278i | \(0.534069\pi\) | |||||||
\(878\) | −34.6161 | −1.16824 | ||||||||
\(879\) | 1.26722 | 0.0427423 | ||||||||
\(880\) | −11.9609 | −0.403203 | ||||||||
\(881\) | −2.60245 | −0.0876786 | −0.0438393 | − | 0.999039i | \(-0.513959\pi\) | ||||
−0.0438393 | + | 0.999039i | \(0.513959\pi\) | |||||||
\(882\) | −13.0763 | −0.440302 | ||||||||
\(883\) | 30.2445 | 1.01781 | 0.508904 | − | 0.860824i | \(-0.330051\pi\) | ||||
0.508904 | + | 0.860824i | \(0.330051\pi\) | |||||||
\(884\) | 2.18206 | 0.0733905 | ||||||||
\(885\) | 14.1271 | 0.474878 | ||||||||
\(886\) | −74.3158 | −2.49669 | ||||||||
\(887\) | −15.3076 | −0.513979 | −0.256989 | − | 0.966414i | \(-0.582731\pi\) | ||||
−0.256989 | + | 0.966414i | \(0.582731\pi\) | |||||||
\(888\) | −2.10596 | −0.0706713 | ||||||||
\(889\) | 33.2740 | 1.11597 | ||||||||
\(890\) | −115.495 | −3.87141 | ||||||||
\(891\) | −8.37074 | −0.280430 | ||||||||
\(892\) | −18.3146 | −0.613218 | ||||||||
\(893\) | 32.0095 | 1.07116 | ||||||||
\(894\) | 7.97707 | 0.266793 | ||||||||
\(895\) | −32.9816 | −1.10245 | ||||||||
\(896\) | −46.1372 | −1.54133 | ||||||||
\(897\) | 0.0140167 | 0.000468005 0 | ||||||||
\(898\) | 61.6209 | 2.05632 | ||||||||
\(899\) | 2.07975 | 0.0693635 | ||||||||
\(900\) | −87.9918 | −2.93306 | ||||||||
\(901\) | 4.54147 | 0.151298 | ||||||||
\(902\) | −1.72280 | −0.0573630 | ||||||||
\(903\) | −0.603061 | −0.0200686 | ||||||||
\(904\) | 21.9093 | 0.728694 | ||||||||
\(905\) | −75.0694 | −2.49539 | ||||||||
\(906\) | −4.57414 | −0.151966 | ||||||||
\(907\) | −9.14766 | −0.303743 | −0.151872 | − | 0.988400i | \(-0.548530\pi\) | ||||
−0.151872 | + | 0.988400i | \(0.548530\pi\) | |||||||
\(908\) | −6.37317 | −0.211501 | ||||||||
\(909\) | 13.1461 | 0.436030 | ||||||||
\(910\) | 11.0300 | 0.365639 | ||||||||
\(911\) | −44.7738 | −1.48342 | −0.741712 | − | 0.670719i | \(-0.765986\pi\) | ||||
−0.741712 | + | 0.670719i | \(0.765986\pi\) | |||||||
\(912\) | −4.92914 | −0.163220 | ||||||||
\(913\) | 5.42574 | 0.179566 | ||||||||
\(914\) | −81.7160 | −2.70293 | ||||||||
\(915\) | −3.09599 | −0.102350 | ||||||||
\(916\) | −42.9191 | −1.41809 | ||||||||
\(917\) | 23.3573 | 0.771327 | ||||||||
\(918\) | 3.82022 | 0.126086 | ||||||||
\(919\) | 6.41709 | 0.211680 | 0.105840 | − | 0.994383i | \(-0.466247\pi\) | ||||
0.105840 | + | 0.994383i | \(0.466247\pi\) | |||||||
\(920\) | −1.54029 | −0.0507820 | ||||||||
\(921\) | −5.66651 | −0.186718 | ||||||||
\(922\) | −6.49451 | −0.213885 | ||||||||
\(923\) | 7.28898 | 0.239920 | ||||||||
\(924\) | 2.34606 | 0.0771797 | ||||||||
\(925\) | 13.3514 | 0.438992 | ||||||||
\(926\) | −50.7642 | −1.66822 | ||||||||
\(927\) | −28.0223 | −0.920373 | ||||||||
\(928\) | 3.20436 | 0.105188 | ||||||||
\(929\) | 3.19854 | 0.104941 | 0.0524704 | − | 0.998622i | \(-0.483290\pi\) | ||||
0.0524704 | + | 0.998622i | \(0.483290\pi\) | |||||||
\(930\) | −1.54537 | −0.0506745 | ||||||||
\(931\) | 10.1832 | 0.333740 | ||||||||
\(932\) | −58.4406 | −1.91429 | ||||||||
\(933\) | −6.84516 | −0.224101 | ||||||||
\(934\) | −86.5599 | −2.83233 | ||||||||
\(935\) | −3.56663 | −0.116641 | ||||||||
\(936\) | 7.53830 | 0.246397 | ||||||||
\(937\) | 49.4621 | 1.61586 | 0.807928 | − | 0.589281i | \(-0.200589\pi\) | ||||
0.807928 | + | 0.589281i | \(0.200589\pi\) | |||||||
\(938\) | −5.99423 | −0.195719 | ||||||||
\(939\) | 2.96380 | 0.0967200 | ||||||||
\(940\) | −80.2142 | −2.61630 | ||||||||
\(941\) | 44.7320 | 1.45822 | 0.729111 | − | 0.684396i | \(-0.239934\pi\) | ||||
0.729111 | + | 0.684396i | \(0.239934\pi\) | |||||||
\(942\) | 13.5463 | 0.441362 | ||||||||
\(943\) | −0.0668231 | −0.00217606 | ||||||||
\(944\) | 50.0381 | 1.62860 | ||||||||
\(945\) | 12.7538 | 0.414881 | ||||||||
\(946\) | 2.42698 | 0.0789081 | ||||||||
\(947\) | −41.5474 | −1.35011 | −0.675054 | − | 0.737768i | \(-0.735880\pi\) | ||||
−0.675054 | + | 0.737768i | \(0.735880\pi\) | |||||||
\(948\) | −5.71031 | −0.185462 | ||||||||
\(949\) | −1.15109 | −0.0373659 | ||||||||
\(950\) | 103.752 | 3.36616 | ||||||||
\(951\) | 1.74906 | 0.0567172 | ||||||||
\(952\) | 10.4219 | 0.337776 | ||||||||
\(953\) | 16.5458 | 0.535970 | 0.267985 | − | 0.963423i | \(-0.413642\pi\) | ||||
0.267985 | + | 0.963423i | \(0.413642\pi\) | |||||||
\(954\) | 32.2895 | 1.04541 | ||||||||
\(955\) | 44.3380 | 1.43474 | ||||||||
\(956\) | −95.9199 | −3.10227 | ||||||||
\(957\) | −0.820931 | −0.0265369 | ||||||||
\(958\) | 54.3400 | 1.75564 | ||||||||
\(959\) | 26.2703 | 0.848313 | ||||||||
\(960\) | −8.73134 | −0.281803 | ||||||||
\(961\) | −30.5477 | −0.985410 | ||||||||
\(962\) | −2.35405 | −0.0758978 | ||||||||
\(963\) | −5.72018 | −0.184330 | ||||||||
\(964\) | −38.8701 | −1.25192 | ||||||||
\(965\) | −0.709609 | −0.0228431 | ||||||||
\(966\) | 0.137780 | 0.00443300 | ||||||||
\(967\) | 53.0556 | 1.70615 | 0.853076 | − | 0.521786i | \(-0.174734\pi\) | ||||
0.853076 | + | 0.521786i | \(0.174734\pi\) | |||||||
\(968\) | −4.58762 | −0.147452 | ||||||||
\(969\) | −1.46982 | −0.0472174 | ||||||||
\(970\) | −52.0752 | −1.67204 | ||||||||
\(971\) | 2.80146 | 0.0899031 | 0.0449516 | − | 0.998989i | \(-0.485687\pi\) | ||||
0.0449516 | + | 0.998989i | \(0.485687\pi\) | |||||||
\(972\) | 27.0150 | 0.866507 | ||||||||
\(973\) | 18.6947 | 0.599326 | ||||||||
\(974\) | −20.5544 | −0.658605 | ||||||||
\(975\) | 1.14962 | 0.0368174 | ||||||||
\(976\) | −10.9660 | −0.351012 | ||||||||
\(977\) | −3.18958 | −0.102044 | −0.0510218 | − | 0.998698i | \(-0.516248\pi\) | ||||
−0.0510218 | + | 0.998698i | \(0.516248\pi\) | |||||||
\(978\) | 2.85984 | 0.0914475 | ||||||||
\(979\) | −13.3425 | −0.426430 | ||||||||
\(980\) | −25.5185 | −0.815160 | ||||||||
\(981\) | −49.7779 | −1.58929 | ||||||||
\(982\) | 14.4954 | 0.462568 | ||||||||
\(983\) | 9.06196 | 0.289032 | 0.144516 | − | 0.989502i | \(-0.453838\pi\) | ||||
0.144516 | + | 0.989502i | \(0.453838\pi\) | |||||||
\(984\) | 0.864483 | 0.0275587 | ||||||||
\(985\) | 1.69472 | 0.0539982 | ||||||||
\(986\) | −7.50538 | −0.239020 | ||||||||
\(987\) | 3.48639 | 0.110973 | ||||||||
\(988\) | −12.0817 | −0.384371 | ||||||||
\(989\) | 0.0941365 | 0.00299337 | ||||||||
\(990\) | −25.3585 | −0.805946 | ||||||||
\(991\) | 21.3956 | 0.679652 | 0.339826 | − | 0.940488i | \(-0.389632\pi\) | ||||
0.339826 | + | 0.940488i | \(0.389632\pi\) | |||||||
\(992\) | 0.696851 | 0.0221251 | ||||||||
\(993\) | −1.43363 | −0.0454949 | ||||||||
\(994\) | 71.6483 | 2.27255 | ||||||||
\(995\) | −16.4515 | −0.521546 | ||||||||
\(996\) | −5.60322 | −0.177545 | ||||||||
\(997\) | −2.71816 | −0.0860850 | −0.0430425 | − | 0.999073i | \(-0.513705\pi\) | ||||
−0.0430425 | + | 0.999073i | \(0.513705\pi\) | |||||||
\(998\) | 67.4532 | 2.13519 | ||||||||
\(999\) | −2.72197 | −0.0861192 |
(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 | 8041.2.a.g.1.9 | ✓ | 69 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.g.1.9 | ✓ | 69 | 1.1 | even | 1 | trivial |