Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4009,2,Mod(1,4009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4009, 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("4009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4009 = 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4009.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0120261703\) |
Analytic rank: | \(1\) |
Dimension: | \(71\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 4009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.67657 | −1.89262 | −0.946309 | − | 0.323263i | \(-0.895220\pi\) | ||||
−0.946309 | + | 0.323263i | \(0.895220\pi\) | |||||||
\(3\) | 0.00971531 | 0.00560914 | 0.00280457 | − | 0.999996i | \(-0.499107\pi\) | ||||
0.00280457 | + | 0.999996i | \(0.499107\pi\) | |||||||
\(4\) | 5.16401 | 2.58200 | ||||||||
\(5\) | 0.0508514 | 0.0227414 | 0.0113707 | − | 0.999935i | \(-0.496381\pi\) | ||||
0.0113707 | + | 0.999935i | \(0.496381\pi\) | |||||||
\(6\) | −0.0260037 | −0.0106160 | ||||||||
\(7\) | 0.312050 | 0.117944 | 0.0589718 | − | 0.998260i | \(-0.481218\pi\) | ||||
0.0589718 | + | 0.998260i | \(0.481218\pi\) | |||||||
\(8\) | −8.46867 | −2.99413 | ||||||||
\(9\) | −2.99991 | −0.999969 | ||||||||
\(10\) | −0.136107 | −0.0430408 | ||||||||
\(11\) | 3.31590 | 0.999780 | 0.499890 | − | 0.866089i | \(-0.333374\pi\) | ||||
0.499890 | + | 0.866089i | \(0.333374\pi\) | |||||||
\(12\) | 0.0501699 | 0.0144828 | ||||||||
\(13\) | 5.10887 | 1.41695 | 0.708473 | − | 0.705738i | \(-0.249384\pi\) | ||||
0.708473 | + | 0.705738i | \(0.249384\pi\) | |||||||
\(14\) | −0.835221 | −0.223222 | ||||||||
\(15\) | 0.000494037 0 | 0.000127560 0 | ||||||||
\(16\) | 12.3389 | 3.08474 | ||||||||
\(17\) | 2.09802 | 0.508845 | 0.254423 | − | 0.967093i | \(-0.418115\pi\) | ||||
0.254423 | + | 0.967093i | \(0.418115\pi\) | |||||||
\(18\) | 8.02945 | 1.89256 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0.262597 | 0.0587184 | ||||||||
\(21\) | 0.00303166 | 0.000661562 0 | ||||||||
\(22\) | −8.87522 | −1.89220 | ||||||||
\(23\) | −7.00610 | −1.46087 | −0.730436 | − | 0.682981i | \(-0.760683\pi\) | ||||
−0.730436 | + | 0.682981i | \(0.760683\pi\) | |||||||
\(24\) | −0.0822757 | −0.0167945 | ||||||||
\(25\) | −4.99741 | −0.999483 | ||||||||
\(26\) | −13.6742 | −2.68174 | ||||||||
\(27\) | −0.0582909 | −0.0112181 | ||||||||
\(28\) | 1.61143 | 0.304531 | ||||||||
\(29\) | −8.90887 | −1.65434 | −0.827168 | − | 0.561955i | \(-0.810050\pi\) | ||||
−0.827168 | + | 0.561955i | \(0.810050\pi\) | |||||||
\(30\) | −0.00132232 | −0.000241422 0 | ||||||||
\(31\) | 10.8021 | 1.94012 | 0.970058 | − | 0.242875i | \(-0.0780905\pi\) | ||||
0.970058 | + | 0.242875i | \(0.0780905\pi\) | |||||||
\(32\) | −16.0887 | −2.84410 | ||||||||
\(33\) | 0.0322150 | 0.00560790 | ||||||||
\(34\) | −5.61550 | −0.963049 | ||||||||
\(35\) | 0.0158681 | 0.00268221 | ||||||||
\(36\) | −15.4915 | −2.58192 | ||||||||
\(37\) | −7.70478 | −1.26666 | −0.633329 | − | 0.773883i | \(-0.718312\pi\) | ||||
−0.633329 | + | 0.773883i | \(0.718312\pi\) | |||||||
\(38\) | −2.67657 | −0.434196 | ||||||||
\(39\) | 0.0496343 | 0.00794784 | ||||||||
\(40\) | −0.430643 | −0.0680907 | ||||||||
\(41\) | −7.39004 | −1.15413 | −0.577065 | − | 0.816698i | \(-0.695802\pi\) | ||||
−0.577065 | + | 0.816698i | \(0.695802\pi\) | |||||||
\(42\) | −0.00811443 | −0.00125208 | ||||||||
\(43\) | 3.43168 | 0.523326 | 0.261663 | − | 0.965159i | \(-0.415729\pi\) | ||||
0.261663 | + | 0.965159i | \(0.415729\pi\) | |||||||
\(44\) | 17.1233 | 2.58144 | ||||||||
\(45\) | −0.152549 | −0.0227407 | ||||||||
\(46\) | 18.7523 | 2.76487 | ||||||||
\(47\) | 8.02245 | 1.17019 | 0.585097 | − | 0.810963i | \(-0.301056\pi\) | ||||
0.585097 | + | 0.810963i | \(0.301056\pi\) | |||||||
\(48\) | 0.119877 | 0.0173027 | ||||||||
\(49\) | −6.90263 | −0.986089 | ||||||||
\(50\) | 13.3759 | 1.89164 | ||||||||
\(51\) | 0.0203829 | 0.00285418 | ||||||||
\(52\) | 26.3822 | 3.65856 | ||||||||
\(53\) | −11.8021 | −1.62114 | −0.810572 | − | 0.585639i | \(-0.800843\pi\) | ||||
−0.810572 | + | 0.585639i | \(0.800843\pi\) | |||||||
\(54\) | 0.156020 | 0.0212316 | ||||||||
\(55\) | 0.168618 | 0.0227364 | ||||||||
\(56\) | −2.64264 | −0.353138 | ||||||||
\(57\) | 0.00971531 | 0.00128682 | ||||||||
\(58\) | 23.8452 | 3.13103 | ||||||||
\(59\) | 1.08863 | 0.141727 | 0.0708636 | − | 0.997486i | \(-0.477424\pi\) | ||||
0.0708636 | + | 0.997486i | \(0.477424\pi\) | |||||||
\(60\) | 0.00255121 | 0.000329359 0 | ||||||||
\(61\) | −7.03229 | −0.900392 | −0.450196 | − | 0.892930i | \(-0.648646\pi\) | ||||
−0.450196 | + | 0.892930i | \(0.648646\pi\) | |||||||
\(62\) | −28.9125 | −3.67190 | ||||||||
\(63\) | −0.936119 | −0.117940 | ||||||||
\(64\) | 18.3845 | 2.29806 | ||||||||
\(65\) | 0.259793 | 0.0322234 | ||||||||
\(66\) | −0.0862255 | −0.0106136 | ||||||||
\(67\) | 12.1337 | 1.48236 | 0.741182 | − | 0.671304i | \(-0.234266\pi\) | ||||
0.741182 | + | 0.671304i | \(0.234266\pi\) | |||||||
\(68\) | 10.8342 | 1.31384 | ||||||||
\(69\) | −0.0680664 | −0.00819423 | ||||||||
\(70\) | −0.0424721 | −0.00507639 | ||||||||
\(71\) | −0.696458 | −0.0826543 | −0.0413272 | − | 0.999146i | \(-0.513159\pi\) | ||||
−0.0413272 | + | 0.999146i | \(0.513159\pi\) | |||||||
\(72\) | 25.4052 | 2.99403 | ||||||||
\(73\) | 7.75935 | 0.908163 | 0.454082 | − | 0.890960i | \(-0.349967\pi\) | ||||
0.454082 | + | 0.890960i | \(0.349967\pi\) | |||||||
\(74\) | 20.6224 | 2.39730 | ||||||||
\(75\) | −0.0485514 | −0.00560623 | ||||||||
\(76\) | 5.16401 | 0.592352 | ||||||||
\(77\) | 1.03472 | 0.117918 | ||||||||
\(78\) | −0.132849 | −0.0150422 | ||||||||
\(79\) | −16.1473 | −1.81671 | −0.908354 | − | 0.418202i | \(-0.862661\pi\) | ||||
−0.908354 | + | 0.418202i | \(0.862661\pi\) | |||||||
\(80\) | 0.627452 | 0.0701513 | ||||||||
\(81\) | 8.99915 | 0.999906 | ||||||||
\(82\) | 19.7799 | 2.18433 | ||||||||
\(83\) | 4.89708 | 0.537524 | 0.268762 | − | 0.963207i | \(-0.413385\pi\) | ||||
0.268762 | + | 0.963207i | \(0.413385\pi\) | |||||||
\(84\) | 0.0156555 | 0.00170815 | ||||||||
\(85\) | 0.106687 | 0.0115719 | ||||||||
\(86\) | −9.18511 | −0.990456 | ||||||||
\(87\) | −0.0865524 | −0.00927940 | ||||||||
\(88\) | −28.0812 | −2.99347 | ||||||||
\(89\) | −5.11530 | −0.542221 | −0.271110 | − | 0.962548i | \(-0.587391\pi\) | ||||
−0.271110 | + | 0.962548i | \(0.587391\pi\) | |||||||
\(90\) | 0.408308 | 0.0430395 | ||||||||
\(91\) | 1.59422 | 0.167120 | ||||||||
\(92\) | −36.1795 | −3.77198 | ||||||||
\(93\) | 0.104946 | 0.0108824 | ||||||||
\(94\) | −21.4726 | −2.21473 | ||||||||
\(95\) | 0.0508514 | 0.00521724 | ||||||||
\(96\) | −0.156306 | −0.0159529 | ||||||||
\(97\) | −10.3139 | −1.04722 | −0.523611 | − | 0.851958i | \(-0.675415\pi\) | ||||
−0.523611 | + | 0.851958i | \(0.675415\pi\) | |||||||
\(98\) | 18.4753 | 1.86629 | ||||||||
\(99\) | −9.94738 | −0.999749 | ||||||||
\(100\) | −25.8067 | −2.58067 | ||||||||
\(101\) | −8.40702 | −0.836530 | −0.418265 | − | 0.908325i | \(-0.637362\pi\) | ||||
−0.418265 | + | 0.908325i | \(0.637362\pi\) | |||||||
\(102\) | −0.0545563 | −0.00540187 | ||||||||
\(103\) | −12.7961 | −1.26083 | −0.630416 | − | 0.776257i | \(-0.717116\pi\) | ||||
−0.630416 | + | 0.776257i | \(0.717116\pi\) | |||||||
\(104\) | −43.2653 | −4.24252 | ||||||||
\(105\) | 0.000154164 0 | 1.50449e−5 0 | ||||||||
\(106\) | 31.5891 | 3.06821 | ||||||||
\(107\) | 5.37377 | 0.519502 | 0.259751 | − | 0.965676i | \(-0.416360\pi\) | ||||
0.259751 | + | 0.965676i | \(0.416360\pi\) | |||||||
\(108\) | −0.301015 | −0.0289652 | ||||||||
\(109\) | 5.55900 | 0.532455 | 0.266228 | − | 0.963910i | \(-0.414223\pi\) | ||||
0.266228 | + | 0.963910i | \(0.414223\pi\) | |||||||
\(110\) | −0.451317 | −0.0430314 | ||||||||
\(111\) | −0.0748543 | −0.00710486 | ||||||||
\(112\) | 3.85036 | 0.363825 | ||||||||
\(113\) | −6.14935 | −0.578482 | −0.289241 | − | 0.957256i | \(-0.593403\pi\) | ||||
−0.289241 | + | 0.957256i | \(0.593403\pi\) | |||||||
\(114\) | −0.0260037 | −0.00243547 | ||||||||
\(115\) | −0.356270 | −0.0332223 | ||||||||
\(116\) | −46.0055 | −4.27150 | ||||||||
\(117\) | −15.3261 | −1.41690 | ||||||||
\(118\) | −2.91378 | −0.268235 | ||||||||
\(119\) | 0.654687 | 0.0600151 | ||||||||
\(120\) | −0.00418383 | −0.000381930 0 | ||||||||
\(121\) | −0.00482924 | −0.000439022 0 | ||||||||
\(122\) | 18.8224 | 1.70410 | ||||||||
\(123\) | −0.0717965 | −0.00647367 | ||||||||
\(124\) | 55.7821 | 5.00938 | ||||||||
\(125\) | −0.508382 | −0.0454711 | ||||||||
\(126\) | 2.50558 | 0.223215 | ||||||||
\(127\) | 10.8458 | 0.962410 | 0.481205 | − | 0.876608i | \(-0.340199\pi\) | ||||
0.481205 | + | 0.876608i | \(0.340199\pi\) | |||||||
\(128\) | −17.0299 | −1.50525 | ||||||||
\(129\) | 0.0333398 | 0.00293541 | ||||||||
\(130\) | −0.695353 | −0.0609865 | ||||||||
\(131\) | 21.5259 | 1.88072 | 0.940362 | − | 0.340176i | \(-0.110487\pi\) | ||||
0.940362 | + | 0.340176i | \(0.110487\pi\) | |||||||
\(132\) | 0.166358 | 0.0144796 | ||||||||
\(133\) | 0.312050 | 0.0270581 | ||||||||
\(134\) | −32.4766 | −2.80555 | ||||||||
\(135\) | −0.00296417 | −0.000255115 0 | ||||||||
\(136\) | −17.7675 | −1.52355 | ||||||||
\(137\) | 0.702792 | 0.0600435 | 0.0300218 | − | 0.999549i | \(-0.490442\pi\) | ||||
0.0300218 | + | 0.999549i | \(0.490442\pi\) | |||||||
\(138\) | 0.182184 | 0.0155085 | ||||||||
\(139\) | −23.4860 | −1.99205 | −0.996027 | − | 0.0890479i | \(-0.971618\pi\) | ||||
−0.996027 | + | 0.0890479i | \(0.971618\pi\) | |||||||
\(140\) | 0.0819432 | 0.00692546 | ||||||||
\(141\) | 0.0779406 | 0.00656378 | ||||||||
\(142\) | 1.86412 | 0.156433 | ||||||||
\(143\) | 16.9405 | 1.41663 | ||||||||
\(144\) | −37.0157 | −3.08464 | ||||||||
\(145\) | −0.453028 | −0.0376219 | ||||||||
\(146\) | −20.7684 | −1.71881 | ||||||||
\(147\) | −0.0670611 | −0.00553111 | ||||||||
\(148\) | −39.7875 | −3.27052 | ||||||||
\(149\) | 14.2523 | 1.16759 | 0.583797 | − | 0.811899i | \(-0.301566\pi\) | ||||
0.583797 | + | 0.811899i | \(0.301566\pi\) | |||||||
\(150\) | 0.129951 | 0.0106105 | ||||||||
\(151\) | −11.2419 | −0.914851 | −0.457425 | − | 0.889248i | \(-0.651228\pi\) | ||||
−0.457425 | + | 0.889248i | \(0.651228\pi\) | |||||||
\(152\) | −8.46867 | −0.686900 | ||||||||
\(153\) | −6.29387 | −0.508829 | ||||||||
\(154\) | −2.76951 | −0.223173 | ||||||||
\(155\) | 0.549302 | 0.0441210 | ||||||||
\(156\) | 0.256312 | 0.0205213 | ||||||||
\(157\) | −4.16506 | −0.332408 | −0.166204 | − | 0.986091i | \(-0.553151\pi\) | ||||
−0.166204 | + | 0.986091i | \(0.553151\pi\) | |||||||
\(158\) | 43.2192 | 3.43834 | ||||||||
\(159\) | −0.114661 | −0.00909321 | ||||||||
\(160\) | −0.818130 | −0.0646789 | ||||||||
\(161\) | −2.18625 | −0.172301 | ||||||||
\(162\) | −24.0868 | −1.89244 | ||||||||
\(163\) | 3.76722 | 0.295072 | 0.147536 | − | 0.989057i | \(-0.452866\pi\) | ||||
0.147536 | + | 0.989057i | \(0.452866\pi\) | |||||||
\(164\) | −38.1622 | −2.97997 | ||||||||
\(165\) | 0.00163817 | 0.000127532 0 | ||||||||
\(166\) | −13.1074 | −1.01733 | ||||||||
\(167\) | −3.83584 | −0.296826 | −0.148413 | − | 0.988925i | \(-0.547417\pi\) | ||||
−0.148413 | + | 0.988925i | \(0.547417\pi\) | |||||||
\(168\) | −0.0256741 | −0.00198080 | ||||||||
\(169\) | 13.1006 | 1.00774 | ||||||||
\(170\) | −0.285556 | −0.0219011 | ||||||||
\(171\) | −2.99991 | −0.229409 | ||||||||
\(172\) | 17.7212 | 1.35123 | ||||||||
\(173\) | −5.23785 | −0.398226 | −0.199113 | − | 0.979977i | \(-0.563806\pi\) | ||||
−0.199113 | + | 0.979977i | \(0.563806\pi\) | |||||||
\(174\) | 0.231663 | 0.0175624 | ||||||||
\(175\) | −1.55944 | −0.117883 | ||||||||
\(176\) | 40.9147 | 3.08406 | ||||||||
\(177\) | 0.0105763 | 0.000794967 0 | ||||||||
\(178\) | 13.6914 | 1.02622 | ||||||||
\(179\) | −6.00735 | −0.449010 | −0.224505 | − | 0.974473i | \(-0.572077\pi\) | ||||
−0.224505 | + | 0.974473i | \(0.572077\pi\) | |||||||
\(180\) | −0.787765 | −0.0587166 | ||||||||
\(181\) | 2.94504 | 0.218903 | 0.109452 | − | 0.993992i | \(-0.465091\pi\) | ||||
0.109452 | + | 0.993992i | \(0.465091\pi\) | |||||||
\(182\) | −4.26704 | −0.316294 | ||||||||
\(183\) | −0.0683208 | −0.00505042 | ||||||||
\(184\) | 59.3323 | 4.37404 | ||||||||
\(185\) | −0.391798 | −0.0288056 | ||||||||
\(186\) | −0.280894 | −0.0205962 | ||||||||
\(187\) | 6.95682 | 0.508733 | ||||||||
\(188\) | 41.4280 | 3.02145 | ||||||||
\(189\) | −0.0181897 | −0.00132310 | ||||||||
\(190\) | −0.136107 | −0.00987424 | ||||||||
\(191\) | −23.7800 | −1.72066 | −0.860332 | − | 0.509735i | \(-0.829743\pi\) | ||||
−0.860332 | + | 0.509735i | \(0.829743\pi\) | |||||||
\(192\) | 0.178611 | 0.0128901 | ||||||||
\(193\) | 17.8338 | 1.28371 | 0.641853 | − | 0.766828i | \(-0.278166\pi\) | ||||
0.641853 | + | 0.766828i | \(0.278166\pi\) | |||||||
\(194\) | 27.6059 | 1.98199 | ||||||||
\(195\) | 0.00252397 | 0.000180745 0 | ||||||||
\(196\) | −35.6452 | −2.54609 | ||||||||
\(197\) | 10.1250 | 0.721376 | 0.360688 | − | 0.932687i | \(-0.382542\pi\) | ||||
0.360688 | + | 0.932687i | \(0.382542\pi\) | |||||||
\(198\) | 26.6248 | 1.89214 | ||||||||
\(199\) | 19.3464 | 1.37143 | 0.685715 | − | 0.727871i | \(-0.259490\pi\) | ||||
0.685715 | + | 0.727871i | \(0.259490\pi\) | |||||||
\(200\) | 42.3215 | 2.99258 | ||||||||
\(201\) | 0.117882 | 0.00831478 | ||||||||
\(202\) | 22.5019 | 1.58323 | ||||||||
\(203\) | −2.78001 | −0.195118 | ||||||||
\(204\) | 0.105258 | 0.00736950 | ||||||||
\(205\) | −0.375794 | −0.0262466 | ||||||||
\(206\) | 34.2495 | 2.38627 | ||||||||
\(207\) | 21.0176 | 1.46083 | ||||||||
\(208\) | 63.0381 | 4.37090 | ||||||||
\(209\) | 3.31590 | 0.229365 | ||||||||
\(210\) | −0.000412630 0 | −2.84742e−5 0 | ||||||||
\(211\) | 1.00000 | 0.0688428 | ||||||||
\(212\) | −60.9461 | −4.18580 | ||||||||
\(213\) | −0.00676630 | −0.000463619 0 | ||||||||
\(214\) | −14.3832 | −0.983218 | ||||||||
\(215\) | 0.174505 | 0.0119012 | ||||||||
\(216\) | 0.493647 | 0.0335884 | ||||||||
\(217\) | 3.37079 | 0.228824 | ||||||||
\(218\) | −14.8790 | −1.00773 | ||||||||
\(219\) | 0.0753845 | 0.00509401 | ||||||||
\(220\) | 0.870743 | 0.0587055 | ||||||||
\(221\) | 10.7185 | 0.721006 | ||||||||
\(222\) | 0.200353 | 0.0134468 | ||||||||
\(223\) | 16.6180 | 1.11282 | 0.556412 | − | 0.830906i | \(-0.312178\pi\) | ||||
0.556412 | + | 0.830906i | \(0.312178\pi\) | |||||||
\(224\) | −5.02046 | −0.335444 | ||||||||
\(225\) | 14.9918 | 0.999451 | ||||||||
\(226\) | 16.4592 | 1.09485 | ||||||||
\(227\) | −22.6242 | −1.50162 | −0.750812 | − | 0.660516i | \(-0.770337\pi\) | ||||
−0.750812 | + | 0.660516i | \(0.770337\pi\) | |||||||
\(228\) | 0.0501699 | 0.00332258 | ||||||||
\(229\) | −8.40073 | −0.555136 | −0.277568 | − | 0.960706i | \(-0.589528\pi\) | ||||
−0.277568 | + | 0.960706i | \(0.589528\pi\) | |||||||
\(230\) | 0.953579 | 0.0628771 | ||||||||
\(231\) | 0.0100527 | 0.000661417 0 | ||||||||
\(232\) | 75.4463 | 4.95329 | ||||||||
\(233\) | 9.75135 | 0.638832 | 0.319416 | − | 0.947615i | \(-0.396513\pi\) | ||||
0.319416 | + | 0.947615i | \(0.396513\pi\) | |||||||
\(234\) | 41.0214 | 2.68165 | ||||||||
\(235\) | 0.407952 | 0.0266119 | ||||||||
\(236\) | 5.62168 | 0.365940 | ||||||||
\(237\) | −0.156876 | −0.0101902 | ||||||||
\(238\) | −1.75231 | −0.113586 | ||||||||
\(239\) | −19.5717 | −1.26599 | −0.632994 | − | 0.774157i | \(-0.718174\pi\) | ||||
−0.632994 | + | 0.774157i | \(0.718174\pi\) | |||||||
\(240\) | 0.00609589 | 0.000393488 0 | ||||||||
\(241\) | 3.44503 | 0.221914 | 0.110957 | − | 0.993825i | \(-0.464608\pi\) | ||||
0.110957 | + | 0.993825i | \(0.464608\pi\) | |||||||
\(242\) | 0.0129258 | 0.000830901 0 | ||||||||
\(243\) | 0.262302 | 0.0168267 | ||||||||
\(244\) | −36.3148 | −2.32482 | ||||||||
\(245\) | −0.351008 | −0.0224251 | ||||||||
\(246\) | 0.192168 | 0.0122522 | ||||||||
\(247\) | 5.10887 | 0.325070 | ||||||||
\(248\) | −91.4795 | −5.80895 | ||||||||
\(249\) | 0.0475766 | 0.00301505 | ||||||||
\(250\) | 1.36072 | 0.0860594 | ||||||||
\(251\) | 3.60550 | 0.227577 | 0.113789 | − | 0.993505i | \(-0.463701\pi\) | ||||
0.113789 | + | 0.993505i | \(0.463701\pi\) | |||||||
\(252\) | −4.83413 | −0.304521 | ||||||||
\(253\) | −23.2315 | −1.46055 | ||||||||
\(254\) | −29.0295 | −1.82148 | ||||||||
\(255\) | 0.00103650 | 6.49081e−5 0 | ||||||||
\(256\) | 8.81280 | 0.550800 | ||||||||
\(257\) | −18.1123 | −1.12982 | −0.564908 | − | 0.825154i | \(-0.691089\pi\) | ||||
−0.564908 | + | 0.825154i | \(0.691089\pi\) | |||||||
\(258\) | −0.0892362 | −0.00555560 | ||||||||
\(259\) | −2.40427 | −0.149394 | ||||||||
\(260\) | 1.34157 | 0.0832008 | ||||||||
\(261\) | 26.7258 | 1.65428 | ||||||||
\(262\) | −57.6154 | −3.55949 | ||||||||
\(263\) | −7.90176 | −0.487243 | −0.243622 | − | 0.969870i | \(-0.578336\pi\) | ||||
−0.243622 | + | 0.969870i | \(0.578336\pi\) | |||||||
\(264\) | −0.272818 | −0.0167908 | ||||||||
\(265\) | −0.600153 | −0.0368671 | ||||||||
\(266\) | −0.835221 | −0.0512107 | ||||||||
\(267\) | −0.0496967 | −0.00304139 | ||||||||
\(268\) | 62.6583 | 3.82747 | ||||||||
\(269\) | −11.1503 | −0.679846 | −0.339923 | − | 0.940453i | \(-0.610401\pi\) | ||||
−0.339923 | + | 0.940453i | \(0.610401\pi\) | |||||||
\(270\) | 0.00793380 | 0.000482836 0 | ||||||||
\(271\) | 24.3653 | 1.48009 | 0.740044 | − | 0.672559i | \(-0.234805\pi\) | ||||
0.740044 | + | 0.672559i | \(0.234805\pi\) | |||||||
\(272\) | 25.8874 | 1.56965 | ||||||||
\(273\) | 0.0154883 | 0.000937397 0 | ||||||||
\(274\) | −1.88107 | −0.113639 | ||||||||
\(275\) | −16.5709 | −0.999263 | ||||||||
\(276\) | −0.351495 | −0.0211575 | ||||||||
\(277\) | 22.0031 | 1.32204 | 0.661019 | − | 0.750369i | \(-0.270124\pi\) | ||||
0.661019 | + | 0.750369i | \(0.270124\pi\) | |||||||
\(278\) | 62.8618 | 3.77020 | ||||||||
\(279\) | −32.4053 | −1.94005 | ||||||||
\(280\) | −0.134382 | −0.00803086 | ||||||||
\(281\) | 9.30136 | 0.554873 | 0.277436 | − | 0.960744i | \(-0.410515\pi\) | ||||
0.277436 | + | 0.960744i | \(0.410515\pi\) | |||||||
\(282\) | −0.208613 | −0.0124227 | ||||||||
\(283\) | 11.4299 | 0.679435 | 0.339718 | − | 0.940527i | \(-0.389668\pi\) | ||||
0.339718 | + | 0.940527i | \(0.389668\pi\) | |||||||
\(284\) | −3.59651 | −0.213414 | ||||||||
\(285\) | 0.000494037 0 | 2.92642e−5 0 | ||||||||
\(286\) | −45.3423 | −2.68115 | ||||||||
\(287\) | −2.30606 | −0.136122 | ||||||||
\(288\) | 48.2645 | 2.84401 | ||||||||
\(289\) | −12.5983 | −0.741077 | ||||||||
\(290\) | 1.21256 | 0.0712040 | ||||||||
\(291\) | −0.100203 | −0.00587401 | ||||||||
\(292\) | 40.0693 | 2.34488 | ||||||||
\(293\) | −30.7965 | −1.79915 | −0.899575 | − | 0.436767i | \(-0.856123\pi\) | ||||
−0.899575 | + | 0.436767i | \(0.856123\pi\) | |||||||
\(294\) | 0.179494 | 0.0104683 | ||||||||
\(295\) | 0.0553582 | 0.00322308 | ||||||||
\(296\) | 65.2493 | 3.79254 | ||||||||
\(297\) | −0.193287 | −0.0112156 | ||||||||
\(298\) | −38.1472 | −2.20981 | ||||||||
\(299\) | −35.7932 | −2.06998 | ||||||||
\(300\) | −0.250720 | −0.0144753 | ||||||||
\(301\) | 1.07085 | 0.0617230 | ||||||||
\(302\) | 30.0896 | 1.73146 | ||||||||
\(303\) | −0.0816768 | −0.00469221 | ||||||||
\(304\) | 12.3389 | 0.707687 | ||||||||
\(305\) | −0.357601 | −0.0204762 | ||||||||
\(306\) | 16.8460 | 0.963019 | ||||||||
\(307\) | −0.145552 | −0.00830708 | −0.00415354 | − | 0.999991i | \(-0.501322\pi\) | ||||
−0.00415354 | + | 0.999991i | \(0.501322\pi\) | |||||||
\(308\) | 5.34332 | 0.304464 | ||||||||
\(309\) | −0.124318 | −0.00707218 | ||||||||
\(310\) | −1.47024 | −0.0835041 | ||||||||
\(311\) | −12.3563 | −0.700663 | −0.350332 | − | 0.936626i | \(-0.613931\pi\) | ||||
−0.350332 | + | 0.936626i | \(0.613931\pi\) | |||||||
\(312\) | −0.420336 | −0.0237968 | ||||||||
\(313\) | 19.3586 | 1.09421 | 0.547105 | − | 0.837064i | \(-0.315730\pi\) | ||||
0.547105 | + | 0.837064i | \(0.315730\pi\) | |||||||
\(314\) | 11.1480 | 0.629121 | ||||||||
\(315\) | −0.0476029 | −0.00268212 | ||||||||
\(316\) | −83.3845 | −4.69075 | ||||||||
\(317\) | −28.8292 | −1.61921 | −0.809606 | − | 0.586974i | \(-0.800319\pi\) | ||||
−0.809606 | + | 0.586974i | \(0.800319\pi\) | |||||||
\(318\) | 0.306898 | 0.0172100 | ||||||||
\(319\) | −29.5409 | −1.65397 | ||||||||
\(320\) | 0.934875 | 0.0522611 | ||||||||
\(321\) | 0.0522078 | 0.00291396 | ||||||||
\(322\) | 5.85164 | 0.326099 | ||||||||
\(323\) | 2.09802 | 0.116737 | ||||||||
\(324\) | 46.4717 | 2.58176 | ||||||||
\(325\) | −25.5311 | −1.41621 | ||||||||
\(326\) | −10.0832 | −0.558458 | ||||||||
\(327\) | 0.0540074 | 0.00298661 | ||||||||
\(328\) | 62.5838 | 3.45561 | ||||||||
\(329\) | 2.50340 | 0.138017 | ||||||||
\(330\) | −0.00438468 | −0.000241369 0 | ||||||||
\(331\) | −15.3315 | −0.842698 | −0.421349 | − | 0.906899i | \(-0.638443\pi\) | ||||
−0.421349 | + | 0.906899i | \(0.638443\pi\) | |||||||
\(332\) | 25.2886 | 1.38789 | ||||||||
\(333\) | 23.1136 | 1.26662 | ||||||||
\(334\) | 10.2669 | 0.561778 | ||||||||
\(335\) | 0.617014 | 0.0337111 | ||||||||
\(336\) | 0.0374075 | 0.00204074 | ||||||||
\(337\) | −8.22610 | −0.448104 | −0.224052 | − | 0.974577i | \(-0.571929\pi\) | ||||
−0.224052 | + | 0.974577i | \(0.571929\pi\) | |||||||
\(338\) | −35.0645 | −1.90726 | ||||||||
\(339\) | −0.0597429 | −0.00324479 | ||||||||
\(340\) | 0.550934 | 0.0298786 | ||||||||
\(341\) | 35.8187 | 1.93969 | ||||||||
\(342\) | 8.02945 | 0.434183 | ||||||||
\(343\) | −4.33831 | −0.234247 | ||||||||
\(344\) | −29.0618 | −1.56690 | ||||||||
\(345\) | −0.00346127 | −0.000186348 0 | ||||||||
\(346\) | 14.0194 | 0.753690 | ||||||||
\(347\) | −14.9891 | −0.804656 | −0.402328 | − | 0.915496i | \(-0.631799\pi\) | ||||
−0.402328 | + | 0.915496i | \(0.631799\pi\) | |||||||
\(348\) | −0.446957 | −0.0239594 | ||||||||
\(349\) | −8.38995 | −0.449104 | −0.224552 | − | 0.974462i | \(-0.572092\pi\) | ||||
−0.224552 | + | 0.974462i | \(0.572092\pi\) | |||||||
\(350\) | 4.17395 | 0.223107 | ||||||||
\(351\) | −0.297801 | −0.0158954 | ||||||||
\(352\) | −53.3483 | −2.84348 | ||||||||
\(353\) | 22.0563 | 1.17394 | 0.586969 | − | 0.809609i | \(-0.300321\pi\) | ||||
0.586969 | + | 0.809609i | \(0.300321\pi\) | |||||||
\(354\) | −0.0283083 | −0.00150457 | ||||||||
\(355\) | −0.0354158 | −0.00187968 | ||||||||
\(356\) | −26.4154 | −1.40002 | ||||||||
\(357\) | 0.00636048 | 0.000336633 0 | ||||||||
\(358\) | 16.0791 | 0.849805 | ||||||||
\(359\) | −33.7608 | −1.78183 | −0.890913 | − | 0.454174i | \(-0.849934\pi\) | ||||
−0.890913 | + | 0.454174i | \(0.849934\pi\) | |||||||
\(360\) | 1.29189 | 0.0680885 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −7.88259 | −0.414300 | ||||||||
\(363\) | −4.69176e−5 0 | −2.46253e−6 0 | ||||||||
\(364\) | 8.23257 | 0.431504 | ||||||||
\(365\) | 0.394573 | 0.0206529 | ||||||||
\(366\) | 0.182865 | 0.00955852 | ||||||||
\(367\) | 2.53376 | 0.132261 | 0.0661307 | − | 0.997811i | \(-0.478935\pi\) | ||||
0.0661307 | + | 0.997811i | \(0.478935\pi\) | |||||||
\(368\) | −86.4479 | −4.50641 | ||||||||
\(369\) | 22.1694 | 1.15409 | ||||||||
\(370\) | 1.04867 | 0.0545180 | ||||||||
\(371\) | −3.68284 | −0.191204 | ||||||||
\(372\) | 0.541941 | 0.0280983 | ||||||||
\(373\) | −20.1830 | −1.04504 | −0.522518 | − | 0.852628i | \(-0.675007\pi\) | ||||
−0.522518 | + | 0.852628i | \(0.675007\pi\) | |||||||
\(374\) | −18.6204 | −0.962838 | ||||||||
\(375\) | −0.00493909 | −0.000255053 0 | ||||||||
\(376\) | −67.9395 | −3.50371 | ||||||||
\(377\) | −45.5143 | −2.34410 | ||||||||
\(378\) | 0.0486858 | 0.00250413 | ||||||||
\(379\) | −5.23122 | −0.268710 | −0.134355 | − | 0.990933i | \(-0.542896\pi\) | ||||
−0.134355 | + | 0.990933i | \(0.542896\pi\) | |||||||
\(380\) | 0.262597 | 0.0134709 | ||||||||
\(381\) | 0.105370 | 0.00539829 | ||||||||
\(382\) | 63.6488 | 3.25656 | ||||||||
\(383\) | −22.3359 | −1.14131 | −0.570656 | − | 0.821189i | \(-0.693311\pi\) | ||||
−0.570656 | + | 0.821189i | \(0.693311\pi\) | |||||||
\(384\) | −0.165451 | −0.00844314 | ||||||||
\(385\) | 0.0526171 | 0.00268162 | ||||||||
\(386\) | −47.7334 | −2.42956 | ||||||||
\(387\) | −10.2947 | −0.523310 | ||||||||
\(388\) | −53.2612 | −2.70393 | ||||||||
\(389\) | 3.17900 | 0.161182 | 0.0805910 | − | 0.996747i | \(-0.474319\pi\) | ||||
0.0805910 | + | 0.996747i | \(0.474319\pi\) | |||||||
\(390\) | −0.00675557 | −0.000342082 0 | ||||||||
\(391\) | −14.6989 | −0.743358 | ||||||||
\(392\) | 58.4561 | 2.95248 | ||||||||
\(393\) | 0.209130 | 0.0105492 | ||||||||
\(394\) | −27.1002 | −1.36529 | ||||||||
\(395\) | −0.821110 | −0.0413145 | ||||||||
\(396\) | −51.3683 | −2.58135 | ||||||||
\(397\) | 17.0059 | 0.853501 | 0.426751 | − | 0.904369i | \(-0.359658\pi\) | ||||
0.426751 | + | 0.904369i | \(0.359658\pi\) | |||||||
\(398\) | −51.7819 | −2.59559 | ||||||||
\(399\) | 0.00303166 | 0.000151773 0 | ||||||||
\(400\) | −61.6628 | −3.08314 | ||||||||
\(401\) | 15.9396 | 0.795984 | 0.397992 | − | 0.917389i | \(-0.369707\pi\) | ||||
0.397992 | + | 0.917389i | \(0.369707\pi\) | |||||||
\(402\) | −0.315520 | −0.0157367 | ||||||||
\(403\) | 55.1866 | 2.74904 | ||||||||
\(404\) | −43.4139 | −2.15992 | ||||||||
\(405\) | 0.457619 | 0.0227393 | ||||||||
\(406\) | 7.44088 | 0.369285 | ||||||||
\(407\) | −25.5483 | −1.26638 | ||||||||
\(408\) | −0.172616 | −0.00854578 | ||||||||
\(409\) | −26.5975 | −1.31516 | −0.657580 | − | 0.753385i | \(-0.728420\pi\) | ||||
−0.657580 | + | 0.753385i | \(0.728420\pi\) | |||||||
\(410\) | 1.00584 | 0.0496747 | ||||||||
\(411\) | 0.00682784 | 0.000336792 0 | ||||||||
\(412\) | −66.0789 | −3.25547 | ||||||||
\(413\) | 0.339706 | 0.0167158 | ||||||||
\(414\) | −56.2551 | −2.76479 | ||||||||
\(415\) | 0.249023 | 0.0122241 | ||||||||
\(416\) | −82.1949 | −4.02994 | ||||||||
\(417\) | −0.228174 | −0.0111737 | ||||||||
\(418\) | −8.87522 | −0.434101 | ||||||||
\(419\) | 9.21385 | 0.450126 | 0.225063 | − | 0.974344i | \(-0.427741\pi\) | ||||
0.225063 | + | 0.974344i | \(0.427741\pi\) | |||||||
\(420\) | 0.000796103 0 | 3.88459e−5 0 | ||||||||
\(421\) | −27.3477 | −1.33285 | −0.666424 | − | 0.745573i | \(-0.732176\pi\) | ||||
−0.666424 | + | 0.745573i | \(0.732176\pi\) | |||||||
\(422\) | −2.67657 | −0.130293 | ||||||||
\(423\) | −24.0666 | −1.17016 | ||||||||
\(424\) | 99.9481 | 4.85391 | ||||||||
\(425\) | −10.4847 | −0.508582 | ||||||||
\(426\) | 0.0181105 | 0.000877454 0 | ||||||||
\(427\) | −2.19442 | −0.106196 | ||||||||
\(428\) | 27.7502 | 1.34135 | ||||||||
\(429\) | 0.164582 | 0.00794610 | ||||||||
\(430\) | −0.467075 | −0.0225244 | ||||||||
\(431\) | −3.28029 | −0.158006 | −0.0790030 | − | 0.996874i | \(-0.525174\pi\) | ||||
−0.0790030 | + | 0.996874i | \(0.525174\pi\) | |||||||
\(432\) | −0.719249 | −0.0346049 | ||||||||
\(433\) | −9.08006 | −0.436360 | −0.218180 | − | 0.975909i | \(-0.570012\pi\) | ||||
−0.218180 | + | 0.975909i | \(0.570012\pi\) | |||||||
\(434\) | −9.02215 | −0.433077 | ||||||||
\(435\) | −0.00440131 | −0.000211027 0 | ||||||||
\(436\) | 28.7067 | 1.37480 | ||||||||
\(437\) | −7.00610 | −0.335147 | ||||||||
\(438\) | −0.201771 | −0.00964101 | ||||||||
\(439\) | 28.8489 | 1.37688 | 0.688442 | − | 0.725292i | \(-0.258295\pi\) | ||||
0.688442 | + | 0.725292i | \(0.258295\pi\) | |||||||
\(440\) | −1.42797 | −0.0680757 | ||||||||
\(441\) | 20.7072 | 0.986058 | ||||||||
\(442\) | −28.6888 | −1.36459 | ||||||||
\(443\) | −4.54219 | −0.215806 | −0.107903 | − | 0.994161i | \(-0.534414\pi\) | ||||
−0.107903 | + | 0.994161i | \(0.534414\pi\) | |||||||
\(444\) | −0.386548 | −0.0183448 | ||||||||
\(445\) | −0.260120 | −0.0123309 | ||||||||
\(446\) | −44.4792 | −2.10615 | ||||||||
\(447\) | 0.138466 | 0.00654920 | ||||||||
\(448\) | 5.73687 | 0.271041 | ||||||||
\(449\) | 27.7116 | 1.30779 | 0.653895 | − | 0.756586i | \(-0.273134\pi\) | ||||
0.653895 | + | 0.756586i | \(0.273134\pi\) | |||||||
\(450\) | −40.1265 | −1.89158 | ||||||||
\(451\) | −24.5046 | −1.15388 | ||||||||
\(452\) | −31.7553 | −1.49364 | ||||||||
\(453\) | −0.109218 | −0.00513152 | ||||||||
\(454\) | 60.5553 | 2.84200 | ||||||||
\(455\) | 0.0810683 | 0.00380054 | ||||||||
\(456\) | −0.0822757 | −0.00385291 | ||||||||
\(457\) | 22.4814 | 1.05164 | 0.525818 | − | 0.850597i | \(-0.323759\pi\) | ||||
0.525818 | + | 0.850597i | \(0.323759\pi\) | |||||||
\(458\) | 22.4851 | 1.05066 | ||||||||
\(459\) | −0.122296 | −0.00570827 | ||||||||
\(460\) | −1.83978 | −0.0857801 | ||||||||
\(461\) | 11.3605 | 0.529109 | 0.264555 | − | 0.964371i | \(-0.414775\pi\) | ||||
0.264555 | + | 0.964371i | \(0.414775\pi\) | |||||||
\(462\) | −0.0269066 | −0.00125181 | ||||||||
\(463\) | −4.51372 | −0.209770 | −0.104885 | − | 0.994484i | \(-0.533447\pi\) | ||||
−0.104885 | + | 0.994484i | \(0.533447\pi\) | |||||||
\(464\) | −109.926 | −5.10319 | ||||||||
\(465\) | 0.00533663 | 0.000247480 0 | ||||||||
\(466\) | −26.1001 | −1.20907 | ||||||||
\(467\) | −19.3427 | −0.895074 | −0.447537 | − | 0.894265i | \(-0.647699\pi\) | ||||
−0.447537 | + | 0.894265i | \(0.647699\pi\) | |||||||
\(468\) | −79.1442 | −3.65844 | ||||||||
\(469\) | 3.78631 | 0.174835 | ||||||||
\(470\) | −1.09191 | −0.0503661 | ||||||||
\(471\) | −0.0404648 | −0.00186452 | ||||||||
\(472\) | −9.21922 | −0.424349 | ||||||||
\(473\) | 11.3791 | 0.523211 | ||||||||
\(474\) | 0.419888 | 0.0192861 | ||||||||
\(475\) | −4.99741 | −0.229297 | ||||||||
\(476\) | 3.38081 | 0.154959 | ||||||||
\(477\) | 35.4052 | 1.62109 | ||||||||
\(478\) | 52.3850 | 2.39603 | ||||||||
\(479\) | −4.07725 | −0.186294 | −0.0931471 | − | 0.995652i | \(-0.529693\pi\) | ||||
−0.0931471 | + | 0.995652i | \(0.529693\pi\) | |||||||
\(480\) | −0.00794839 | −0.000362792 0 | ||||||||
\(481\) | −39.3627 | −1.79479 | ||||||||
\(482\) | −9.22084 | −0.419998 | ||||||||
\(483\) | −0.0212401 | −0.000966457 0 | ||||||||
\(484\) | −0.0249382 | −0.00113356 | ||||||||
\(485\) | −0.524478 | −0.0238153 | ||||||||
\(486\) | −0.702069 | −0.0318465 | ||||||||
\(487\) | 9.31487 | 0.422097 | 0.211049 | − | 0.977476i | \(-0.432312\pi\) | ||||
0.211049 | + | 0.977476i | \(0.432312\pi\) | |||||||
\(488\) | 59.5541 | 2.69589 | ||||||||
\(489\) | 0.0365997 | 0.00165510 | ||||||||
\(490\) | 0.939496 | 0.0424421 | ||||||||
\(491\) | −6.82836 | −0.308160 | −0.154080 | − | 0.988058i | \(-0.549241\pi\) | ||||
−0.154080 | + | 0.988058i | \(0.549241\pi\) | |||||||
\(492\) | −0.370758 | −0.0167150 | ||||||||
\(493\) | −18.6910 | −0.841801 | ||||||||
\(494\) | −13.6742 | −0.615233 | ||||||||
\(495\) | −0.505838 | −0.0227357 | ||||||||
\(496\) | 133.287 | 5.98474 | ||||||||
\(497\) | −0.217329 | −0.00974855 | ||||||||
\(498\) | −0.127342 | −0.00570633 | ||||||||
\(499\) | −7.56558 | −0.338682 | −0.169341 | − | 0.985558i | \(-0.554164\pi\) | ||||
−0.169341 | + | 0.985558i | \(0.554164\pi\) | |||||||
\(500\) | −2.62529 | −0.117406 | ||||||||
\(501\) | −0.0372664 | −0.00166494 | ||||||||
\(502\) | −9.65036 | −0.430717 | ||||||||
\(503\) | 10.7541 | 0.479503 | 0.239752 | − | 0.970834i | \(-0.422934\pi\) | ||||
0.239752 | + | 0.970834i | \(0.422934\pi\) | |||||||
\(504\) | 7.92769 | 0.353127 | ||||||||
\(505\) | −0.427508 | −0.0190239 | ||||||||
\(506\) | 62.1806 | 2.76427 | ||||||||
\(507\) | 0.127276 | 0.00565253 | ||||||||
\(508\) | 56.0078 | 2.48495 | ||||||||
\(509\) | −20.6182 | −0.913888 | −0.456944 | − | 0.889496i | \(-0.651056\pi\) | ||||
−0.456944 | + | 0.889496i | \(0.651056\pi\) | |||||||
\(510\) | −0.00277426 | −0.000122846 0 | ||||||||
\(511\) | 2.42130 | 0.107112 | ||||||||
\(512\) | 10.4718 | 0.462794 | ||||||||
\(513\) | −0.0582909 | −0.00257361 | ||||||||
\(514\) | 48.4789 | 2.13831 | ||||||||
\(515\) | −0.650696 | −0.0286731 | ||||||||
\(516\) | 0.172167 | 0.00757923 | ||||||||
\(517\) | 26.6016 | 1.16994 | ||||||||
\(518\) | 6.43520 | 0.282746 | ||||||||
\(519\) | −0.0508873 | −0.00223370 | ||||||||
\(520\) | −2.20010 | −0.0964808 | ||||||||
\(521\) | 0.868898 | 0.0380671 | 0.0190335 | − | 0.999819i | \(-0.493941\pi\) | ||||
0.0190335 | + | 0.999819i | \(0.493941\pi\) | |||||||
\(522\) | −71.5333 | −3.13093 | ||||||||
\(523\) | −6.06984 | −0.265415 | −0.132708 | − | 0.991155i | \(-0.542367\pi\) | ||||
−0.132708 | + | 0.991155i | \(0.542367\pi\) | |||||||
\(524\) | 111.160 | 4.85603 | ||||||||
\(525\) | −0.0151504 | −0.000661220 0 | ||||||||
\(526\) | 21.1496 | 0.922166 | ||||||||
\(527\) | 22.6631 | 0.987218 | ||||||||
\(528\) | 0.397499 | 0.0172989 | ||||||||
\(529\) | 26.0854 | 1.13415 | ||||||||
\(530\) | 1.60635 | 0.0697753 | ||||||||
\(531\) | −3.26578 | −0.141723 | ||||||||
\(532\) | 1.61143 | 0.0698642 | ||||||||
\(533\) | −37.7548 | −1.63534 | ||||||||
\(534\) | 0.133017 | 0.00575619 | ||||||||
\(535\) | 0.273263 | 0.0118142 | ||||||||
\(536\) | −102.756 | −4.43839 | ||||||||
\(537\) | −0.0583632 | −0.00251856 | ||||||||
\(538\) | 29.8445 | 1.28669 | ||||||||
\(539\) | −22.8884 | −0.985873 | ||||||||
\(540\) | −0.0153070 | −0.000658709 0 | ||||||||
\(541\) | −36.9957 | −1.59057 | −0.795284 | − | 0.606237i | \(-0.792678\pi\) | ||||
−0.795284 | + | 0.606237i | \(0.792678\pi\) | |||||||
\(542\) | −65.2154 | −2.80124 | ||||||||
\(543\) | 0.0286120 | 0.00122786 | ||||||||
\(544\) | −33.7544 | −1.44721 | ||||||||
\(545\) | 0.282682 | 0.0121088 | ||||||||
\(546\) | −0.0414556 | −0.00177414 | ||||||||
\(547\) | −15.0555 | −0.643728 | −0.321864 | − | 0.946786i | \(-0.604309\pi\) | ||||
−0.321864 | + | 0.946786i | \(0.604309\pi\) | |||||||
\(548\) | 3.62922 | 0.155033 | ||||||||
\(549\) | 21.0962 | 0.900364 | ||||||||
\(550\) | 44.3531 | 1.89122 | ||||||||
\(551\) | −8.90887 | −0.379531 | ||||||||
\(552\) | 0.576432 | 0.0245346 | ||||||||
\(553\) | −5.03874 | −0.214269 | ||||||||
\(554\) | −58.8927 | −2.50211 | ||||||||
\(555\) | −0.00380644 | −0.000161575 0 | ||||||||
\(556\) | −121.282 | −5.14349 | ||||||||
\(557\) | 37.2893 | 1.58000 | 0.789999 | − | 0.613108i | \(-0.210081\pi\) | ||||
0.789999 | + | 0.613108i | \(0.210081\pi\) | |||||||
\(558\) | 86.7349 | 3.67178 | ||||||||
\(559\) | 17.5320 | 0.741525 | ||||||||
\(560\) | 0.195796 | 0.00827390 | ||||||||
\(561\) | 0.0675877 | 0.00285355 | ||||||||
\(562\) | −24.8957 | −1.05016 | ||||||||
\(563\) | −27.5253 | −1.16005 | −0.580027 | − | 0.814597i | \(-0.696958\pi\) | ||||
−0.580027 | + | 0.814597i | \(0.696958\pi\) | |||||||
\(564\) | 0.402486 | 0.0169477 | ||||||||
\(565\) | −0.312703 | −0.0131555 | ||||||||
\(566\) | −30.5928 | −1.28591 | ||||||||
\(567\) | 2.80818 | 0.117933 | ||||||||
\(568\) | 5.89807 | 0.247478 | ||||||||
\(569\) | −22.2411 | −0.932394 | −0.466197 | − | 0.884681i | \(-0.654376\pi\) | ||||
−0.466197 | + | 0.884681i | \(0.654376\pi\) | |||||||
\(570\) | −0.00132232 | −5.53859e−5 0 | ||||||||
\(571\) | −18.3074 | −0.766139 | −0.383070 | − | 0.923719i | \(-0.625133\pi\) | ||||
−0.383070 | + | 0.923719i | \(0.625133\pi\) | |||||||
\(572\) | 87.4808 | 3.65776 | ||||||||
\(573\) | −0.231030 | −0.00965143 | ||||||||
\(574\) | 6.17232 | 0.257628 | ||||||||
\(575\) | 35.0124 | 1.46012 | ||||||||
\(576\) | −55.1517 | −2.29799 | ||||||||
\(577\) | −27.2921 | −1.13618 | −0.568092 | − | 0.822965i | \(-0.692318\pi\) | ||||
−0.568092 | + | 0.822965i | \(0.692318\pi\) | |||||||
\(578\) | 33.7202 | 1.40257 | ||||||||
\(579\) | 0.173261 | 0.00720048 | ||||||||
\(580\) | −2.33944 | −0.0971400 | ||||||||
\(581\) | 1.52813 | 0.0633976 | ||||||||
\(582\) | 0.268200 | 0.0111173 | ||||||||
\(583\) | −39.1346 | −1.62079 | ||||||||
\(584\) | −65.7114 | −2.71916 | ||||||||
\(585\) | −0.779354 | −0.0322223 | ||||||||
\(586\) | 82.4288 | 3.40510 | ||||||||
\(587\) | 8.24350 | 0.340246 | 0.170123 | − | 0.985423i | \(-0.445584\pi\) | ||||
0.170123 | + | 0.985423i | \(0.445584\pi\) | |||||||
\(588\) | −0.346304 | −0.0142813 | ||||||||
\(589\) | 10.8021 | 0.445093 | ||||||||
\(590\) | −0.148170 | −0.00610005 | ||||||||
\(591\) | 0.0983674 | 0.00404629 | ||||||||
\(592\) | −95.0689 | −3.90731 | ||||||||
\(593\) | 9.89696 | 0.406420 | 0.203210 | − | 0.979135i | \(-0.434863\pi\) | ||||
0.203210 | + | 0.979135i | \(0.434863\pi\) | |||||||
\(594\) | 0.517345 | 0.0212269 | ||||||||
\(595\) | 0.0332917 | 0.00136483 | ||||||||
\(596\) | 73.5990 | 3.01473 | ||||||||
\(597\) | 0.187956 | 0.00769253 | ||||||||
\(598\) | 95.8030 | 3.91768 | ||||||||
\(599\) | 36.1267 | 1.47610 | 0.738048 | − | 0.674749i | \(-0.235748\pi\) | ||||
0.738048 | + | 0.674749i | \(0.235748\pi\) | |||||||
\(600\) | 0.411166 | 0.0167858 | ||||||||
\(601\) | −43.3036 | −1.76639 | −0.883196 | − | 0.469004i | \(-0.844613\pi\) | ||||
−0.883196 | + | 0.469004i | \(0.844613\pi\) | |||||||
\(602\) | −2.86621 | −0.116818 | ||||||||
\(603\) | −36.3999 | −1.48232 | ||||||||
\(604\) | −58.0531 | −2.36215 | ||||||||
\(605\) | −0.000245573 0 | −9.98398e−6 0 | ||||||||
\(606\) | 0.218613 | 0.00888056 | ||||||||
\(607\) | −26.3375 | −1.06901 | −0.534503 | − | 0.845167i | \(-0.679501\pi\) | ||||
−0.534503 | + | 0.845167i | \(0.679501\pi\) | |||||||
\(608\) | −16.0887 | −0.652481 | ||||||||
\(609\) | −0.0270086 | −0.00109445 | ||||||||
\(610\) | 0.957144 | 0.0387536 | ||||||||
\(611\) | 40.9857 | 1.65810 | ||||||||
\(612\) | −32.5016 | −1.31380 | ||||||||
\(613\) | 32.5703 | 1.31550 | 0.657751 | − | 0.753236i | \(-0.271508\pi\) | ||||
0.657751 | + | 0.753236i | \(0.271508\pi\) | |||||||
\(614\) | 0.389579 | 0.0157221 | ||||||||
\(615\) | −0.00365095 | −0.000147221 0 | ||||||||
\(616\) | −8.76274 | −0.353061 | ||||||||
\(617\) | 14.9660 | 0.602509 | 0.301255 | − | 0.953544i | \(-0.402595\pi\) | ||||
0.301255 | + | 0.953544i | \(0.402595\pi\) | |||||||
\(618\) | 0.332744 | 0.0133849 | ||||||||
\(619\) | −45.5620 | −1.83129 | −0.915646 | − | 0.401986i | \(-0.868320\pi\) | ||||
−0.915646 | + | 0.401986i | \(0.868320\pi\) | |||||||
\(620\) | 2.83660 | 0.113920 | ||||||||
\(621\) | 0.408392 | 0.0163882 | ||||||||
\(622\) | 33.0725 | 1.32609 | ||||||||
\(623\) | −1.59623 | −0.0639515 | ||||||||
\(624\) | 0.612434 | 0.0245170 | ||||||||
\(625\) | 24.9612 | 0.998449 | ||||||||
\(626\) | −51.8145 | −2.07092 | ||||||||
\(627\) | 0.0322150 | 0.00128654 | ||||||||
\(628\) | −21.5084 | −0.858277 | ||||||||
\(629\) | −16.1648 | −0.644533 | ||||||||
\(630\) | 0.127412 | 0.00507623 | ||||||||
\(631\) | −18.4685 | −0.735220 | −0.367610 | − | 0.929980i | \(-0.619824\pi\) | ||||
−0.367610 | + | 0.929980i | \(0.619824\pi\) | |||||||
\(632\) | 136.746 | 5.43946 | ||||||||
\(633\) | 0.00971531 | 0.000386149 0 | ||||||||
\(634\) | 77.1634 | 3.06455 | ||||||||
\(635\) | 0.551524 | 0.0218866 | ||||||||
\(636\) | −0.592110 | −0.0234787 | ||||||||
\(637\) | −35.2646 | −1.39724 | ||||||||
\(638\) | 79.0682 | 3.13034 | ||||||||
\(639\) | 2.08931 | 0.0826517 | ||||||||
\(640\) | −0.865995 | −0.0342315 | ||||||||
\(641\) | −29.2063 | −1.15358 | −0.576789 | − | 0.816893i | \(-0.695695\pi\) | ||||
−0.576789 | + | 0.816893i | \(0.695695\pi\) | |||||||
\(642\) | −0.139738 | −0.00551500 | ||||||||
\(643\) | −12.1699 | −0.479935 | −0.239968 | − | 0.970781i | \(-0.577137\pi\) | ||||
−0.239968 | + | 0.970781i | \(0.577137\pi\) | |||||||
\(644\) | −11.2898 | −0.444881 | ||||||||
\(645\) | 0.00169537 | 6.67553e−5 0 | ||||||||
\(646\) | −5.61550 | −0.220939 | ||||||||
\(647\) | 26.6135 | 1.04629 | 0.523143 | − | 0.852245i | \(-0.324759\pi\) | ||||
0.523143 | + | 0.852245i | \(0.324759\pi\) | |||||||
\(648\) | −76.2108 | −2.99384 | ||||||||
\(649\) | 3.60978 | 0.141696 | ||||||||
\(650\) | 68.3358 | 2.68035 | ||||||||
\(651\) | 0.0327483 | 0.00128351 | ||||||||
\(652\) | 19.4540 | 0.761876 | ||||||||
\(653\) | −28.8949 | −1.13075 | −0.565373 | − | 0.824836i | \(-0.691268\pi\) | ||||
−0.565373 | + | 0.824836i | \(0.691268\pi\) | |||||||
\(654\) | −0.144554 | −0.00565252 | ||||||||
\(655\) | 1.09462 | 0.0427703 | ||||||||
\(656\) | −91.1853 | −3.56019 | ||||||||
\(657\) | −23.2773 | −0.908135 | ||||||||
\(658\) | −6.70052 | −0.261213 | ||||||||
\(659\) | −20.4653 | −0.797215 | −0.398607 | − | 0.917122i | \(-0.630506\pi\) | ||||
−0.398607 | + | 0.917122i | \(0.630506\pi\) | |||||||
\(660\) | 0.00845954 | 0.000329287 0 | ||||||||
\(661\) | −35.3546 | −1.37513 | −0.687567 | − | 0.726121i | \(-0.741321\pi\) | ||||
−0.687567 | + | 0.726121i | \(0.741321\pi\) | |||||||
\(662\) | 41.0359 | 1.59491 | ||||||||
\(663\) | 0.104134 | 0.00404422 | ||||||||
\(664\) | −41.4718 | −1.60942 | ||||||||
\(665\) | 0.0158681 | 0.000615340 0 | ||||||||
\(666\) | −61.8651 | −2.39722 | ||||||||
\(667\) | 62.4164 | 2.41677 | ||||||||
\(668\) | −19.8083 | −0.766406 | ||||||||
\(669\) | 0.161449 | 0.00624198 | ||||||||
\(670\) | −1.65148 | −0.0638021 | ||||||||
\(671\) | −23.3183 | −0.900195 | ||||||||
\(672\) | −0.0487753 | −0.00188155 | ||||||||
\(673\) | −16.1001 | −0.620614 | −0.310307 | − | 0.950636i | \(-0.600432\pi\) | ||||
−0.310307 | + | 0.950636i | \(0.600432\pi\) | |||||||
\(674\) | 22.0177 | 0.848090 | ||||||||
\(675\) | 0.291304 | 0.0112123 | ||||||||
\(676\) | 67.6514 | 2.60198 | ||||||||
\(677\) | 7.97048 | 0.306331 | 0.153165 | − | 0.988201i | \(-0.451053\pi\) | ||||
0.153165 | + | 0.988201i | \(0.451053\pi\) | |||||||
\(678\) | 0.159906 | 0.00614114 | ||||||||
\(679\) | −3.21846 | −0.123513 | ||||||||
\(680\) | −0.903499 | −0.0346476 | ||||||||
\(681\) | −0.219801 | −0.00842281 | ||||||||
\(682\) | −95.8710 | −3.67109 | ||||||||
\(683\) | 5.94746 | 0.227573 | 0.113787 | − | 0.993505i | \(-0.463702\pi\) | ||||
0.113787 | + | 0.993505i | \(0.463702\pi\) | |||||||
\(684\) | −15.4915 | −0.592333 | ||||||||
\(685\) | 0.0357379 | 0.00136548 | ||||||||
\(686\) | 11.6118 | 0.443339 | ||||||||
\(687\) | −0.0816157 | −0.00311383 | ||||||||
\(688\) | 42.3433 | 1.61432 | ||||||||
\(689\) | −60.2954 | −2.29707 | ||||||||
\(690\) | 0.00926431 | 0.000352686 0 | ||||||||
\(691\) | 39.4169 | 1.49949 | 0.749745 | − | 0.661727i | \(-0.230176\pi\) | ||||
0.749745 | + | 0.661727i | \(0.230176\pi\) | |||||||
\(692\) | −27.0483 | −1.02822 | ||||||||
\(693\) | −3.10407 | −0.117914 | ||||||||
\(694\) | 40.1192 | 1.52291 | ||||||||
\(695\) | −1.19429 | −0.0453021 | ||||||||
\(696\) | 0.732984 | 0.0277837 | ||||||||
\(697\) | −15.5045 | −0.587274 | ||||||||
\(698\) | 22.4563 | 0.849982 | ||||||||
\(699\) | 0.0947373 | 0.00358330 | ||||||||
\(700\) | −8.05296 | −0.304373 | ||||||||
\(701\) | −5.14126 | −0.194183 | −0.0970913 | − | 0.995275i | \(-0.530954\pi\) | ||||
−0.0970913 | + | 0.995275i | \(0.530954\pi\) | |||||||
\(702\) | 0.797084 | 0.0300840 | ||||||||
\(703\) | −7.70478 | −0.290591 | ||||||||
\(704\) | 60.9610 | 2.29755 | ||||||||
\(705\) | 0.00396338 | 0.000149270 0 | ||||||||
\(706\) | −59.0352 | −2.22182 | ||||||||
\(707\) | −2.62341 | −0.0986634 | ||||||||
\(708\) | 0.0546163 | 0.00205261 | ||||||||
\(709\) | 28.7691 | 1.08045 | 0.540223 | − | 0.841522i | \(-0.318340\pi\) | ||||
0.540223 | + | 0.841522i | \(0.318340\pi\) | |||||||
\(710\) | 0.0947928 | 0.00355751 | ||||||||
\(711\) | 48.4403 | 1.81665 | ||||||||
\(712\) | 43.3198 | 1.62348 | ||||||||
\(713\) | −75.6806 | −2.83426 | ||||||||
\(714\) | −0.0170243 | −0.000637117 0 | ||||||||
\(715\) | 0.861447 | 0.0322163 | ||||||||
\(716\) | −31.0220 | −1.15935 | ||||||||
\(717\) | −0.190145 | −0.00710110 | ||||||||
\(718\) | 90.3630 | 3.37232 | ||||||||
\(719\) | 2.65464 | 0.0990012 | 0.0495006 | − | 0.998774i | \(-0.484237\pi\) | ||||
0.0495006 | + | 0.998774i | \(0.484237\pi\) | |||||||
\(720\) | −1.88230 | −0.0701491 | ||||||||
\(721\) | −3.99300 | −0.148707 | ||||||||
\(722\) | −2.67657 | −0.0996115 | ||||||||
\(723\) | 0.0334695 | 0.00124474 | ||||||||
\(724\) | 15.2082 | 0.565208 | ||||||||
\(725\) | 44.5213 | 1.65348 | ||||||||
\(726\) | 0.000125578 0 | 4.66063e−6 0 | ||||||||
\(727\) | 5.37778 | 0.199451 | 0.0997254 | − | 0.995015i | \(-0.468204\pi\) | ||||
0.0997254 | + | 0.995015i | \(0.468204\pi\) | |||||||
\(728\) | −13.5009 | −0.500378 | ||||||||
\(729\) | −26.9949 | −0.999811 | ||||||||
\(730\) | −1.05610 | −0.0390881 | ||||||||
\(731\) | 7.19974 | 0.266292 | ||||||||
\(732\) | −0.352809 | −0.0130402 | ||||||||
\(733\) | −23.4025 | −0.864392 | −0.432196 | − | 0.901780i | \(-0.642261\pi\) | ||||
−0.432196 | + | 0.901780i | \(0.642261\pi\) | |||||||
\(734\) | −6.78178 | −0.250320 | ||||||||
\(735\) | −0.00341015 | −0.000125785 0 | ||||||||
\(736\) | 112.719 | 4.15487 | ||||||||
\(737\) | 40.2340 | 1.48204 | ||||||||
\(738\) | −59.3379 | −2.18426 | ||||||||
\(739\) | −24.8539 | −0.914264 | −0.457132 | − | 0.889399i | \(-0.651123\pi\) | ||||
−0.457132 | + | 0.889399i | \(0.651123\pi\) | |||||||
\(740\) | −2.02325 | −0.0743761 | ||||||||
\(741\) | 0.0496343 | 0.00182336 | ||||||||
\(742\) | 9.85737 | 0.361875 | ||||||||
\(743\) | 8.19222 | 0.300543 | 0.150272 | − | 0.988645i | \(-0.451985\pi\) | ||||
0.150272 | + | 0.988645i | \(0.451985\pi\) | |||||||
\(744\) | −0.888751 | −0.0325832 | ||||||||
\(745\) | 0.724749 | 0.0265528 | ||||||||
\(746\) | 54.0212 | 1.97786 | ||||||||
\(747\) | −14.6908 | −0.537508 | ||||||||
\(748\) | 35.9251 | 1.31355 | ||||||||
\(749\) | 1.67688 | 0.0612719 | ||||||||
\(750\) | 0.0132198 | 0.000482719 0 | ||||||||
\(751\) | 21.7064 | 0.792077 | 0.396039 | − | 0.918234i | \(-0.370385\pi\) | ||||
0.396039 | + | 0.918234i | \(0.370385\pi\) | |||||||
\(752\) | 98.9886 | 3.60974 | ||||||||
\(753\) | 0.0350285 | 0.00127651 | ||||||||
\(754\) | 121.822 | 4.43649 | ||||||||
\(755\) | −0.571665 | −0.0208050 | ||||||||
\(756\) | −0.0939315 | −0.00341626 | ||||||||
\(757\) | 1.64353 | 0.0597351 | 0.0298675 | − | 0.999554i | \(-0.490491\pi\) | ||||
0.0298675 | + | 0.999554i | \(0.490491\pi\) | |||||||
\(758\) | 14.0017 | 0.508565 | ||||||||
\(759\) | −0.225701 | −0.00819243 | ||||||||
\(760\) | −0.430643 | −0.0156211 | ||||||||
\(761\) | −50.0556 | −1.81452 | −0.907258 | − | 0.420576i | \(-0.861828\pi\) | ||||
−0.907258 | + | 0.420576i | \(0.861828\pi\) | |||||||
\(762\) | −0.282031 | −0.0102169 | ||||||||
\(763\) | 1.73468 | 0.0627997 | ||||||||
\(764\) | −122.800 | −4.44276 | ||||||||
\(765\) | −0.320052 | −0.0115715 | ||||||||
\(766\) | 59.7836 | 2.16007 | ||||||||
\(767\) | 5.56166 | 0.200820 | ||||||||
\(768\) | 0.0856190 | 0.00308951 | ||||||||
\(769\) | −10.9413 | −0.394554 | −0.197277 | − | 0.980348i | \(-0.563210\pi\) | ||||
−0.197277 | + | 0.980348i | \(0.563210\pi\) | |||||||
\(770\) | −0.140833 | −0.00507528 | ||||||||
\(771\) | −0.175967 | −0.00633730 | ||||||||
\(772\) | 92.0939 | 3.31453 | ||||||||
\(773\) | −34.4014 | −1.23733 | −0.618665 | − | 0.785655i | \(-0.712326\pi\) | ||||
−0.618665 | + | 0.785655i | \(0.712326\pi\) | |||||||
\(774\) | 27.5545 | 0.990425 | ||||||||
\(775\) | −53.9826 | −1.93911 | ||||||||
\(776\) | 87.3453 | 3.13551 | ||||||||
\(777\) | −0.0233583 | −0.000837973 0 | ||||||||
\(778\) | −8.50882 | −0.305056 | ||||||||
\(779\) | −7.39004 | −0.264776 | ||||||||
\(780\) | 0.0130338 | 0.000466685 0 | ||||||||
\(781\) | −2.30938 | −0.0826362 | ||||||||
\(782\) | 39.3427 | 1.40689 | ||||||||
\(783\) | 0.519306 | 0.0185585 | ||||||||
\(784\) | −85.1711 | −3.04183 | ||||||||
\(785\) | −0.211799 | −0.00755942 | ||||||||
\(786\) | −0.559751 | −0.0199657 | ||||||||
\(787\) | 30.3404 | 1.08152 | 0.540758 | − | 0.841178i | \(-0.318137\pi\) | ||||
0.540758 | + | 0.841178i | \(0.318137\pi\) | |||||||
\(788\) | 52.2855 | 1.86259 | ||||||||
\(789\) | −0.0767680 | −0.00273301 | ||||||||
\(790\) | 2.19775 | 0.0781926 | ||||||||
\(791\) | −1.91890 | −0.0682283 | ||||||||
\(792\) | 84.2411 | 2.99338 | ||||||||
\(793\) | −35.9271 | −1.27581 | ||||||||
\(794\) | −45.5174 | −1.61535 | ||||||||
\(795\) | −0.00583067 | −0.000206793 0 | ||||||||
\(796\) | 99.9049 | 3.54103 | ||||||||
\(797\) | 22.9082 | 0.811450 | 0.405725 | − | 0.913995i | \(-0.367019\pi\) | ||||
0.405725 | + | 0.913995i | \(0.367019\pi\) | |||||||
\(798\) | −0.00811443 | −0.000287248 0 | ||||||||
\(799\) | 16.8313 | 0.595448 | ||||||||
\(800\) | 80.4017 | 2.84263 | ||||||||
\(801\) | 15.3454 | 0.542204 | ||||||||
\(802\) | −42.6633 | −1.50649 | ||||||||
\(803\) | 25.7292 | 0.907964 | ||||||||
\(804\) | 0.608745 | 0.0214688 | ||||||||
\(805\) | −0.111174 | −0.00391836 | ||||||||
\(806\) | −147.710 | −5.20288 | ||||||||
\(807\) | −0.108329 | −0.00381335 | ||||||||
\(808\) | 71.1963 | 2.50468 | ||||||||
\(809\) | −20.7490 | −0.729494 | −0.364747 | − | 0.931107i | \(-0.618845\pi\) | ||||
−0.364747 | + | 0.931107i | \(0.618845\pi\) | |||||||
\(810\) | −1.22485 | −0.0430368 | ||||||||
\(811\) | −25.3708 | −0.890891 | −0.445445 | − | 0.895309i | \(-0.646955\pi\) | ||||
−0.445445 | + | 0.895309i | \(0.646955\pi\) | |||||||
\(812\) | −14.3560 | −0.503796 | ||||||||
\(813\) | 0.236717 | 0.00830201 | ||||||||
\(814\) | 68.3816 | 2.39677 | ||||||||
\(815\) | 0.191568 | 0.00671035 | ||||||||
\(816\) | 0.251504 | 0.00880440 | ||||||||
\(817\) | 3.43168 | 0.120059 | ||||||||
\(818\) | 71.1898 | 2.48909 | ||||||||
\(819\) | −4.78251 | −0.167115 | ||||||||
\(820\) | −1.94060 | −0.0677687 | ||||||||
\(821\) | −13.2015 | −0.460737 | −0.230368 | − | 0.973104i | \(-0.573993\pi\) | ||||
−0.230368 | + | 0.973104i | \(0.573993\pi\) | |||||||
\(822\) | −0.0182752 | −0.000637419 0 | ||||||||
\(823\) | −28.7493 | −1.00214 | −0.501069 | − | 0.865407i | \(-0.667060\pi\) | ||||
−0.501069 | + | 0.865407i | \(0.667060\pi\) | |||||||
\(824\) | 108.366 | 3.77509 | ||||||||
\(825\) | −0.160991 | −0.00560500 | ||||||||
\(826\) | −0.909244 | −0.0316367 | ||||||||
\(827\) | 51.4838 | 1.79027 | 0.895134 | − | 0.445797i | \(-0.147080\pi\) | ||||
0.895134 | + | 0.445797i | \(0.147080\pi\) | |||||||
\(828\) | 108.535 | 3.77186 | ||||||||
\(829\) | 43.9806 | 1.52751 | 0.763754 | − | 0.645507i | \(-0.223354\pi\) | ||||
0.763754 | + | 0.645507i | \(0.223354\pi\) | |||||||
\(830\) | −0.666527 | −0.0231355 | ||||||||
\(831\) | 0.213767 | 0.00741549 | ||||||||
\(832\) | 93.9239 | 3.25623 | ||||||||
\(833\) | −14.4819 | −0.501767 | ||||||||
\(834\) | 0.610721 | 0.0211476 | ||||||||
\(835\) | −0.195058 | −0.00675025 | ||||||||
\(836\) | 17.1233 | 0.592222 | ||||||||
\(837\) | −0.629665 | −0.0217644 | ||||||||
\(838\) | −24.6615 | −0.851916 | ||||||||
\(839\) | 31.8863 | 1.10084 | 0.550419 | − | 0.834888i | \(-0.314468\pi\) | ||||
0.550419 | + | 0.834888i | \(0.314468\pi\) | |||||||
\(840\) | −0.00130556 | −4.50462e−5 0 | ||||||||
\(841\) | 50.3680 | 1.73683 | ||||||||
\(842\) | 73.1980 | 2.52257 | ||||||||
\(843\) | 0.0903656 | 0.00311236 | ||||||||
\(844\) | 5.16401 | 0.177752 | ||||||||
\(845\) | 0.666181 | 0.0229173 | ||||||||
\(846\) | 64.4158 | 2.21466 | ||||||||
\(847\) | −0.00150696 | −5.17798e−5 0 | ||||||||
\(848\) | −145.625 | −5.00080 | ||||||||
\(849\) | 0.111045 | 0.00381104 | ||||||||
\(850\) | 28.0630 | 0.962551 | ||||||||
\(851\) | 53.9804 | 1.85043 | ||||||||
\(852\) | −0.0349412 | −0.00119707 | ||||||||
\(853\) | −26.7839 | −0.917062 | −0.458531 | − | 0.888678i | \(-0.651624\pi\) | ||||
−0.458531 | + | 0.888678i | \(0.651624\pi\) | |||||||
\(854\) | 5.87352 | 0.200988 | ||||||||
\(855\) | −0.152549 | −0.00521707 | ||||||||
\(856\) | −45.5087 | −1.55545 | ||||||||
\(857\) | −51.1904 | −1.74863 | −0.874315 | − | 0.485359i | \(-0.838689\pi\) | ||||
−0.874315 | + | 0.485359i | \(0.838689\pi\) | |||||||
\(858\) | −0.440515 | −0.0150389 | ||||||||
\(859\) | −50.5007 | −1.72306 | −0.861530 | − | 0.507706i | \(-0.830494\pi\) | ||||
−0.861530 | + | 0.507706i | \(0.830494\pi\) | |||||||
\(860\) | 0.901147 | 0.0307289 | ||||||||
\(861\) | −0.0224041 | −0.000763529 0 | ||||||||
\(862\) | 8.77992 | 0.299045 | ||||||||
\(863\) | −32.8867 | −1.11948 | −0.559739 | − | 0.828669i | \(-0.689098\pi\) | ||||
−0.559739 | + | 0.828669i | \(0.689098\pi\) | |||||||
\(864\) | 0.937823 | 0.0319054 | ||||||||
\(865\) | −0.266352 | −0.00905623 | ||||||||
\(866\) | 24.3034 | 0.825862 | ||||||||
\(867\) | −0.122396 | −0.00415680 | ||||||||
\(868\) | 17.4068 | 0.590825 | ||||||||
\(869\) | −53.5426 | −1.81631 | ||||||||
\(870\) | 0.0117804 | 0.000399393 0 | ||||||||
\(871\) | 61.9894 | 2.10043 | ||||||||
\(872\) | −47.0773 | −1.59424 | ||||||||
\(873\) | 30.9408 | 1.04719 | ||||||||
\(874\) | 18.7523 | 0.634305 | ||||||||
\(875\) | −0.158640 | −0.00536302 | ||||||||
\(876\) | 0.389286 | 0.0131527 | ||||||||
\(877\) | −24.8244 | −0.838261 | −0.419131 | − | 0.907926i | \(-0.637665\pi\) | ||||
−0.419131 | + | 0.907926i | \(0.637665\pi\) | |||||||
\(878\) | −77.2160 | −2.60591 | ||||||||
\(879\) | −0.299197 | −0.0100917 | ||||||||
\(880\) | 2.08057 | 0.0701359 | ||||||||
\(881\) | 18.5611 | 0.625338 | 0.312669 | − | 0.949862i | \(-0.398777\pi\) | ||||
0.312669 | + | 0.949862i | \(0.398777\pi\) | |||||||
\(882\) | −55.4243 | −1.86623 | ||||||||
\(883\) | −0.804561 | −0.0270756 | −0.0135378 | − | 0.999908i | \(-0.504309\pi\) | ||||
−0.0135378 | + | 0.999908i | \(0.504309\pi\) | |||||||
\(884\) | 55.3505 | 1.86164 | ||||||||
\(885\) | 0.000537822 0 | 1.80787e−5 0 | ||||||||
\(886\) | 12.1575 | 0.408439 | ||||||||
\(887\) | −1.59841 | −0.0536694 | −0.0268347 | − | 0.999640i | \(-0.508543\pi\) | ||||
−0.0268347 | + | 0.999640i | \(0.508543\pi\) | |||||||
\(888\) | 0.633917 | 0.0212728 | ||||||||
\(889\) | 3.38443 | 0.113510 | ||||||||
\(890\) | 0.696228 | 0.0233376 | ||||||||
\(891\) | 29.8403 | 0.999686 | ||||||||
\(892\) | 85.8155 | 2.87332 | ||||||||
\(893\) | 8.02245 | 0.268461 | ||||||||
\(894\) | −0.370612 | −0.0123951 | ||||||||
\(895\) | −0.305482 | −0.0102111 | ||||||||
\(896\) | −5.31418 | −0.177534 | ||||||||
\(897\) | −0.347742 | −0.0116108 | ||||||||
\(898\) | −74.1718 | −2.47515 | ||||||||
\(899\) | −96.2346 | −3.20960 | ||||||||
\(900\) | 77.4176 | 2.58059 | ||||||||
\(901\) | −24.7611 | −0.824911 | ||||||||
\(902\) | 65.5882 | 2.18385 | ||||||||
\(903\) | 0.0104037 | 0.000346213 0 | ||||||||
\(904\) | 52.0768 | 1.73205 | ||||||||
\(905\) | 0.149759 | 0.00497817 | ||||||||
\(906\) | 0.292330 | 0.00971201 | ||||||||
\(907\) | 26.2220 | 0.870687 | 0.435344 | − | 0.900264i | \(-0.356627\pi\) | ||||
0.435344 | + | 0.900264i | \(0.356627\pi\) | |||||||
\(908\) | −116.832 | −3.87720 | ||||||||
\(909\) | 25.2203 | 0.836504 | ||||||||
\(910\) | −0.216985 | −0.00719297 | ||||||||
\(911\) | 17.9443 | 0.594522 | 0.297261 | − | 0.954796i | \(-0.403927\pi\) | ||||
0.297261 | + | 0.954796i | \(0.403927\pi\) | |||||||
\(912\) | 0.119877 | 0.00396951 | ||||||||
\(913\) | 16.2382 | 0.537406 | ||||||||
\(914\) | −60.1729 | −1.99034 | ||||||||
\(915\) | −0.00347421 | −0.000114854 0 | ||||||||
\(916\) | −43.3814 | −1.43336 | ||||||||
\(917\) | 6.71714 | 0.221819 | ||||||||
\(918\) | 0.327332 | 0.0108036 | ||||||||
\(919\) | −16.6254 | −0.548422 | −0.274211 | − | 0.961669i | \(-0.588417\pi\) | ||||
−0.274211 | + | 0.961669i | \(0.588417\pi\) | |||||||
\(920\) | 3.01713 | 0.0994718 | ||||||||
\(921\) | −0.00141408 | −4.65956e−5 0 | ||||||||
\(922\) | −30.4070 | −1.00140 | ||||||||
\(923\) | −3.55811 | −0.117117 | ||||||||
\(924\) | 0.0519120 | 0.00170778 | ||||||||
\(925\) | 38.5040 | 1.26600 | ||||||||
\(926\) | 12.0813 | 0.397015 | ||||||||
\(927\) | 38.3869 | 1.26079 | ||||||||
\(928\) | 143.332 | 4.70510 | ||||||||
\(929\) | 26.8795 | 0.881886 | 0.440943 | − | 0.897535i | \(-0.354644\pi\) | ||||
0.440943 | + | 0.897535i | \(0.354644\pi\) | |||||||
\(930\) | −0.0142839 | −0.000468386 0 | ||||||||
\(931\) | −6.90263 | −0.226224 | ||||||||
\(932\) | 50.3560 | 1.64947 | ||||||||
\(933\) | −0.120046 | −0.00393012 | ||||||||
\(934\) | 51.7721 | 1.69403 | ||||||||
\(935\) | 0.353764 | 0.0115693 | ||||||||
\(936\) | 129.792 | 4.24238 | ||||||||
\(937\) | −3.83686 | −0.125345 | −0.0626724 | − | 0.998034i | \(-0.519962\pi\) | ||||
−0.0626724 | + | 0.998034i | \(0.519962\pi\) | |||||||
\(938\) | −10.1343 | −0.330897 | ||||||||
\(939\) | 0.188074 | 0.00613758 | ||||||||
\(940\) | 2.10667 | 0.0687120 | ||||||||
\(941\) | −43.9596 | −1.43304 | −0.716521 | − | 0.697566i | \(-0.754267\pi\) | ||||
−0.716521 | + | 0.697566i | \(0.754267\pi\) | |||||||
\(942\) | 0.108307 | 0.00352882 | ||||||||
\(943\) | 51.7753 | 1.68604 | ||||||||
\(944\) | 13.4325 | 0.437191 | ||||||||
\(945\) | −0.000924969 0 | −3.00892e−5 0 | ||||||||
\(946\) | −30.4569 | −0.990239 | ||||||||
\(947\) | 25.2030 | 0.818986 | 0.409493 | − | 0.912313i | \(-0.365706\pi\) | ||||
0.409493 | + | 0.912313i | \(0.365706\pi\) | |||||||
\(948\) | −0.810106 | −0.0263110 | ||||||||
\(949\) | 39.6415 | 1.28682 | ||||||||
\(950\) | 13.3759 | 0.433972 | ||||||||
\(951\) | −0.280085 | −0.00908238 | ||||||||
\(952\) | −5.54433 | −0.179693 | ||||||||
\(953\) | 37.9983 | 1.23089 | 0.615443 | − | 0.788181i | \(-0.288977\pi\) | ||||
0.615443 | + | 0.788181i | \(0.288977\pi\) | |||||||
\(954\) | −94.7643 | −3.06811 | ||||||||
\(955\) | −1.20925 | −0.0391303 | ||||||||
\(956\) | −101.068 | −3.26879 | ||||||||
\(957\) | −0.286999 | −0.00927736 | ||||||||
\(958\) | 10.9130 | 0.352584 | ||||||||
\(959\) | 0.219306 | 0.00708175 | ||||||||
\(960\) | 0.00908260 | 0.000293140 0 | ||||||||
\(961\) | 85.6854 | 2.76405 | ||||||||
\(962\) | 105.357 | 3.39684 | ||||||||
\(963\) | −16.1208 | −0.519485 | ||||||||
\(964\) | 17.7901 | 0.572982 | ||||||||
\(965\) | 0.906873 | 0.0291933 | ||||||||
\(966\) | 0.0568505 | 0.00182913 | ||||||||
\(967\) | 4.15818 | 0.133718 | 0.0668590 | − | 0.997762i | \(-0.478702\pi\) | ||||
0.0668590 | + | 0.997762i | \(0.478702\pi\) | |||||||
\(968\) | 0.0408972 | 0.00131449 | ||||||||
\(969\) | 0.0203829 | 0.000654794 0 | ||||||||
\(970\) | 1.40380 | 0.0450733 | ||||||||
\(971\) | 48.6253 | 1.56046 | 0.780230 | − | 0.625493i | \(-0.215102\pi\) | ||||
0.780230 | + | 0.625493i | \(0.215102\pi\) | |||||||
\(972\) | 1.35453 | 0.0434466 | ||||||||
\(973\) | −7.32879 | −0.234950 | ||||||||
\(974\) | −24.9319 | −0.798869 | ||||||||
\(975\) | −0.248043 | −0.00794373 | ||||||||
\(976\) | −86.7710 | −2.77747 | ||||||||
\(977\) | 19.8285 | 0.634369 | 0.317184 | − | 0.948364i | \(-0.397263\pi\) | ||||
0.317184 | + | 0.948364i | \(0.397263\pi\) | |||||||
\(978\) | −0.0979616 | −0.00313247 | ||||||||
\(979\) | −16.9618 | −0.542102 | ||||||||
\(980\) | −1.81261 | −0.0579016 | ||||||||
\(981\) | −16.6765 | −0.532439 | ||||||||
\(982\) | 18.2766 | 0.583229 | ||||||||
\(983\) | 45.9633 | 1.46600 | 0.733001 | − | 0.680228i | \(-0.238119\pi\) | ||||
0.733001 | + | 0.680228i | \(0.238119\pi\) | |||||||
\(984\) | 0.608021 | 0.0193830 | ||||||||
\(985\) | 0.514869 | 0.0164051 | ||||||||
\(986\) | 50.0277 | 1.59321 | ||||||||
\(987\) | 0.0243213 | 0.000774156 0 | ||||||||
\(988\) | 26.3822 | 0.839331 | ||||||||
\(989\) | −24.0427 | −0.764512 | ||||||||
\(990\) | 1.35391 | 0.0430300 | ||||||||
\(991\) | −6.31435 | −0.200582 | −0.100291 | − | 0.994958i | \(-0.531977\pi\) | ||||
−0.100291 | + | 0.994958i | \(0.531977\pi\) | |||||||
\(992\) | −173.791 | −5.51788 | ||||||||
\(993\) | −0.148951 | −0.00472681 | ||||||||
\(994\) | 0.581696 | 0.0184503 | ||||||||
\(995\) | 0.983790 | 0.0311882 | ||||||||
\(996\) | 0.245686 | 0.00778486 | ||||||||
\(997\) | −12.4894 | −0.395543 | −0.197771 | − | 0.980248i | \(-0.563370\pi\) | ||||
−0.197771 | + | 0.980248i | \(0.563370\pi\) | |||||||
\(998\) | 20.2498 | 0.640996 | ||||||||
\(999\) | 0.449119 | 0.0142095 |
(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 | 4009.2.a.c.1.4 | ✓ | 71 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4009.2.a.c.1.4 | ✓ | 71 | 1.1 | even | 1 | trivial |