Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [503,2,Mod(1,503)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(503, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("503.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 503.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: | \(4.01647522167\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 9x^{8} + 14x^{7} + 27x^{6} - 27x^{5} - 34x^{4} + 14x^{3} + 17x^{2} + x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-0.510671\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 503.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.15783 | 1.52582 | 0.762908 | − | 0.646507i | \(-0.223771\pi\) | ||||
0.762908 | + | 0.646507i | \(0.223771\pi\) | |||||||
\(3\) | −1.51067 | −0.872186 | −0.436093 | − | 0.899902i | \(-0.643638\pi\) | ||||
−0.436093 | + | 0.899902i | \(0.643638\pi\) | |||||||
\(4\) | 2.65622 | 1.32811 | ||||||||
\(5\) | −2.23445 | −0.999275 | −0.499638 | − | 0.866235i | \(-0.666534\pi\) | ||||
−0.499638 | + | 0.866235i | \(0.666534\pi\) | |||||||
\(6\) | −3.25977 | −1.33080 | ||||||||
\(7\) | −3.60329 | −1.36192 | −0.680959 | − | 0.732322i | \(-0.738437\pi\) | ||||
−0.680959 | + | 0.732322i | \(0.738437\pi\) | |||||||
\(8\) | 1.41602 | 0.500639 | ||||||||
\(9\) | −0.717874 | −0.239291 | ||||||||
\(10\) | −4.82156 | −1.52471 | ||||||||
\(11\) | −1.50306 | −0.453189 | −0.226595 | − | 0.973989i | \(-0.572759\pi\) | ||||
−0.226595 | + | 0.973989i | \(0.572759\pi\) | |||||||
\(12\) | −4.01268 | −1.15836 | ||||||||
\(13\) | 0.00459548 | 0.00127456 | 0.000637279 | − | 1.00000i | \(-0.499797\pi\) | ||||
0.000637279 | 1.00000i | \(0.499797\pi\) | ||||||||
\(14\) | −7.77529 | −2.07803 | ||||||||
\(15\) | 3.37551 | 0.871554 | ||||||||
\(16\) | −2.25692 | −0.564230 | ||||||||
\(17\) | 1.11927 | 0.271464 | 0.135732 | − | 0.990746i | \(-0.456661\pi\) | ||||
0.135732 | + | 0.990746i | \(0.456661\pi\) | |||||||
\(18\) | −1.54905 | −0.365114 | ||||||||
\(19\) | 2.49963 | 0.573454 | 0.286727 | − | 0.958012i | \(-0.407433\pi\) | ||||
0.286727 | + | 0.958012i | \(0.407433\pi\) | |||||||
\(20\) | −5.93520 | −1.32715 | ||||||||
\(21\) | 5.44339 | 1.18785 | ||||||||
\(22\) | −3.24334 | −0.691483 | ||||||||
\(23\) | 1.72480 | 0.359646 | 0.179823 | − | 0.983699i | \(-0.442447\pi\) | ||||
0.179823 | + | 0.983699i | \(0.442447\pi\) | |||||||
\(24\) | −2.13914 | −0.436650 | ||||||||
\(25\) | −0.00724425 | −0.00144885 | ||||||||
\(26\) | 0.00991627 | 0.00194474 | ||||||||
\(27\) | 5.61648 | 1.08089 | ||||||||
\(28\) | −9.57116 | −1.80878 | ||||||||
\(29\) | −0.572061 | −0.106229 | −0.0531145 | − | 0.998588i | \(-0.516915\pi\) | ||||
−0.0531145 | + | 0.998588i | \(0.516915\pi\) | |||||||
\(30\) | 7.28378 | 1.32983 | ||||||||
\(31\) | 3.25375 | 0.584390 | 0.292195 | − | 0.956359i | \(-0.405614\pi\) | ||||
0.292195 | + | 0.956359i | \(0.405614\pi\) | |||||||
\(32\) | −7.70209 | −1.36155 | ||||||||
\(33\) | 2.27063 | 0.395266 | ||||||||
\(34\) | 2.41520 | 0.414203 | ||||||||
\(35\) | 8.05137 | 1.36093 | ||||||||
\(36\) | −1.90683 | −0.317806 | ||||||||
\(37\) | −6.13809 | −1.00910 | −0.504548 | − | 0.863384i | \(-0.668341\pi\) | ||||
−0.504548 | + | 0.863384i | \(0.668341\pi\) | |||||||
\(38\) | 5.39377 | 0.874986 | ||||||||
\(39\) | −0.00694226 | −0.00111165 | ||||||||
\(40\) | −3.16402 | −0.500276 | ||||||||
\(41\) | −5.89549 | −0.920721 | −0.460360 | − | 0.887732i | \(-0.652280\pi\) | ||||
−0.460360 | + | 0.887732i | \(0.652280\pi\) | |||||||
\(42\) | 11.7459 | 1.81243 | ||||||||
\(43\) | −7.66800 | −1.16936 | −0.584680 | − | 0.811264i | \(-0.698780\pi\) | ||||
−0.584680 | + | 0.811264i | \(0.698780\pi\) | |||||||
\(44\) | −3.99246 | −0.601886 | ||||||||
\(45\) | 1.60405 | 0.239118 | ||||||||
\(46\) | 3.72183 | 0.548754 | ||||||||
\(47\) | 6.44840 | 0.940596 | 0.470298 | − | 0.882508i | \(-0.344146\pi\) | ||||
0.470298 | + | 0.882508i | \(0.344146\pi\) | |||||||
\(48\) | 3.40946 | 0.492113 | ||||||||
\(49\) | 5.98373 | 0.854819 | ||||||||
\(50\) | −0.0156318 | −0.00221068 | ||||||||
\(51\) | −1.69085 | −0.236767 | ||||||||
\(52\) | 0.0122066 | 0.00169276 | ||||||||
\(53\) | −7.82500 | −1.07485 | −0.537423 | − | 0.843313i | \(-0.680602\pi\) | ||||
−0.537423 | + | 0.843313i | \(0.680602\pi\) | |||||||
\(54\) | 12.1194 | 1.64924 | ||||||||
\(55\) | 3.35851 | 0.452861 | ||||||||
\(56\) | −5.10234 | −0.681829 | ||||||||
\(57\) | −3.77612 | −0.500159 | ||||||||
\(58\) | −1.23441 | −0.162086 | ||||||||
\(59\) | 0.253382 | 0.0329875 | 0.0164938 | − | 0.999864i | \(-0.494750\pi\) | ||||
0.0164938 | + | 0.999864i | \(0.494750\pi\) | |||||||
\(60\) | 8.96613 | 1.15752 | ||||||||
\(61\) | 7.08244 | 0.906814 | 0.453407 | − | 0.891304i | \(-0.350208\pi\) | ||||
0.453407 | + | 0.891304i | \(0.350208\pi\) | |||||||
\(62\) | 7.02103 | 0.891672 | ||||||||
\(63\) | 2.58671 | 0.325895 | ||||||||
\(64\) | −12.1059 | −1.51324 | ||||||||
\(65\) | −0.0102684 | −0.00127363 | ||||||||
\(66\) | 4.89963 | 0.603102 | ||||||||
\(67\) | 6.16046 | 0.752621 | 0.376310 | − | 0.926494i | \(-0.377193\pi\) | ||||
0.376310 | + | 0.926494i | \(0.377193\pi\) | |||||||
\(68\) | 2.97304 | 0.360534 | ||||||||
\(69\) | −2.60561 | −0.313678 | ||||||||
\(70\) | 17.3735 | 2.07653 | ||||||||
\(71\) | −9.32311 | −1.10645 | −0.553225 | − | 0.833032i | \(-0.686603\pi\) | ||||
−0.553225 | + | 0.833032i | \(0.686603\pi\) | |||||||
\(72\) | −1.01652 | −0.119799 | ||||||||
\(73\) | −15.2654 | −1.78668 | −0.893338 | − | 0.449385i | \(-0.851643\pi\) | ||||
−0.893338 | + | 0.449385i | \(0.851643\pi\) | |||||||
\(74\) | −13.2450 | −1.53969 | ||||||||
\(75\) | 0.0109437 | 0.00126367 | ||||||||
\(76\) | 6.63958 | 0.761612 | ||||||||
\(77\) | 5.41596 | 0.617206 | ||||||||
\(78\) | −0.0149802 | −0.00169618 | ||||||||
\(79\) | −1.99661 | −0.224636 | −0.112318 | − | 0.993672i | \(-0.535828\pi\) | ||||
−0.112318 | + | 0.993672i | \(0.535828\pi\) | |||||||
\(80\) | 5.04297 | 0.563821 | ||||||||
\(81\) | −6.33104 | −0.703448 | ||||||||
\(82\) | −12.7215 | −1.40485 | ||||||||
\(83\) | 6.91660 | 0.759196 | 0.379598 | − | 0.925152i | \(-0.376062\pi\) | ||||
0.379598 | + | 0.925152i | \(0.376062\pi\) | |||||||
\(84\) | 14.4589 | 1.57759 | ||||||||
\(85\) | −2.50096 | −0.271267 | ||||||||
\(86\) | −16.5462 | −1.78423 | ||||||||
\(87\) | 0.864195 | 0.0926514 | ||||||||
\(88\) | −2.12836 | −0.226884 | ||||||||
\(89\) | 3.37422 | 0.357666 | 0.178833 | − | 0.983879i | \(-0.442768\pi\) | ||||
0.178833 | + | 0.983879i | \(0.442768\pi\) | |||||||
\(90\) | 3.46127 | 0.364850 | ||||||||
\(91\) | −0.0165589 | −0.00173584 | ||||||||
\(92\) | 4.58146 | 0.477651 | ||||||||
\(93\) | −4.91534 | −0.509697 | ||||||||
\(94\) | 13.9146 | 1.43518 | ||||||||
\(95\) | −5.58529 | −0.573039 | ||||||||
\(96\) | 11.6353 | 1.18752 | ||||||||
\(97\) | −14.8842 | −1.51126 | −0.755631 | − | 0.654997i | \(-0.772670\pi\) | ||||
−0.755631 | + | 0.654997i | \(0.772670\pi\) | |||||||
\(98\) | 12.9119 | 1.30430 | ||||||||
\(99\) | 1.07901 | 0.108444 | ||||||||
\(100\) | −0.0192424 | −0.00192424 | ||||||||
\(101\) | 11.2591 | 1.12032 | 0.560159 | − | 0.828385i | \(-0.310740\pi\) | ||||
0.560159 | + | 0.828385i | \(0.310740\pi\) | |||||||
\(102\) | −3.64857 | −0.361262 | ||||||||
\(103\) | 4.65004 | 0.458182 | 0.229091 | − | 0.973405i | \(-0.426425\pi\) | ||||
0.229091 | + | 0.973405i | \(0.426425\pi\) | |||||||
\(104\) | 0.00650730 | 0.000638093 0 | ||||||||
\(105\) | −12.1630 | −1.18698 | ||||||||
\(106\) | −16.8850 | −1.64002 | ||||||||
\(107\) | −8.08323 | −0.781435 | −0.390718 | − | 0.920511i | \(-0.627773\pi\) | ||||
−0.390718 | + | 0.920511i | \(0.627773\pi\) | |||||||
\(108\) | 14.9186 | 1.43555 | ||||||||
\(109\) | −1.20991 | −0.115889 | −0.0579444 | − | 0.998320i | \(-0.518455\pi\) | ||||
−0.0579444 | + | 0.998320i | \(0.518455\pi\) | |||||||
\(110\) | 7.24708 | 0.690982 | ||||||||
\(111\) | 9.27264 | 0.880120 | ||||||||
\(112\) | 8.13234 | 0.768434 | ||||||||
\(113\) | 7.68412 | 0.722861 | 0.361431 | − | 0.932399i | \(-0.382288\pi\) | ||||
0.361431 | + | 0.932399i | \(0.382288\pi\) | |||||||
\(114\) | −8.14822 | −0.763150 | ||||||||
\(115\) | −3.85398 | −0.359386 | ||||||||
\(116\) | −1.51952 | −0.141084 | ||||||||
\(117\) | −0.00329898 | −0.000304991 0 | ||||||||
\(118\) | 0.546755 | 0.0503329 | ||||||||
\(119\) | −4.03307 | −0.369711 | ||||||||
\(120\) | 4.77980 | 0.436334 | ||||||||
\(121\) | −8.74081 | −0.794619 | ||||||||
\(122\) | 15.2827 | 1.38363 | ||||||||
\(123\) | 8.90614 | 0.803040 | ||||||||
\(124\) | 8.64268 | 0.776136 | ||||||||
\(125\) | 11.1884 | 1.00072 | ||||||||
\(126\) | 5.58168 | 0.497255 | ||||||||
\(127\) | 8.83928 | 0.784360 | 0.392180 | − | 0.919889i | \(-0.371721\pi\) | ||||
0.392180 | + | 0.919889i | \(0.371721\pi\) | |||||||
\(128\) | −10.7184 | −0.947380 | ||||||||
\(129\) | 11.5838 | 1.01990 | ||||||||
\(130\) | −0.0221574 | −0.00194333 | ||||||||
\(131\) | −12.9102 | −1.12797 | −0.563984 | − | 0.825786i | \(-0.690732\pi\) | ||||
−0.563984 | + | 0.825786i | \(0.690732\pi\) | |||||||
\(132\) | 6.03130 | 0.524957 | ||||||||
\(133\) | −9.00690 | −0.780998 | ||||||||
\(134\) | 13.2932 | 1.14836 | ||||||||
\(135\) | −12.5497 | −1.08011 | ||||||||
\(136\) | 1.58491 | 0.135905 | ||||||||
\(137\) | 3.83616 | 0.327745 | 0.163873 | − | 0.986482i | \(-0.447601\pi\) | ||||
0.163873 | + | 0.986482i | \(0.447601\pi\) | |||||||
\(138\) | −5.62246 | −0.478615 | ||||||||
\(139\) | 9.22921 | 0.782811 | 0.391406 | − | 0.920218i | \(-0.371989\pi\) | ||||
0.391406 | + | 0.920218i | \(0.371989\pi\) | |||||||
\(140\) | 21.3863 | 1.80747 | ||||||||
\(141\) | −9.74142 | −0.820375 | ||||||||
\(142\) | −20.1177 | −1.68824 | ||||||||
\(143\) | −0.00690728 | −0.000577616 0 | ||||||||
\(144\) | 1.62018 | 0.135015 | ||||||||
\(145\) | 1.27824 | 0.106152 | ||||||||
\(146\) | −32.9401 | −2.72614 | ||||||||
\(147\) | −9.03945 | −0.745561 | ||||||||
\(148\) | −16.3042 | −1.34019 | ||||||||
\(149\) | 22.6884 | 1.85871 | 0.929353 | − | 0.369191i | \(-0.120365\pi\) | ||||
0.929353 | + | 0.369191i | \(0.120365\pi\) | |||||||
\(150\) | 0.0236146 | 0.00192812 | ||||||||
\(151\) | −2.22521 | −0.181085 | −0.0905427 | − | 0.995893i | \(-0.528860\pi\) | ||||
−0.0905427 | + | 0.995893i | \(0.528860\pi\) | |||||||
\(152\) | 3.53953 | 0.287094 | ||||||||
\(153\) | −0.803497 | −0.0649589 | ||||||||
\(154\) | 11.6867 | 0.941743 | ||||||||
\(155\) | −7.27033 | −0.583967 | ||||||||
\(156\) | −0.0184402 | −0.00147640 | ||||||||
\(157\) | −22.3177 | −1.78114 | −0.890571 | − | 0.454844i | \(-0.849695\pi\) | ||||
−0.890571 | + | 0.454844i | \(0.849695\pi\) | |||||||
\(158\) | −4.30834 | −0.342753 | ||||||||
\(159\) | 11.8210 | 0.937466 | ||||||||
\(160\) | 17.2099 | 1.36056 | ||||||||
\(161\) | −6.21497 | −0.489808 | ||||||||
\(162\) | −13.6613 | −1.07333 | ||||||||
\(163\) | 7.22321 | 0.565765 | 0.282883 | − | 0.959155i | \(-0.408709\pi\) | ||||
0.282883 | + | 0.959155i | \(0.408709\pi\) | |||||||
\(164\) | −15.6597 | −1.22282 | ||||||||
\(165\) | −5.07360 | −0.394979 | ||||||||
\(166\) | 14.9248 | 1.15839 | ||||||||
\(167\) | −11.4485 | −0.885915 | −0.442958 | − | 0.896543i | \(-0.646071\pi\) | ||||
−0.442958 | + | 0.896543i | \(0.646071\pi\) | |||||||
\(168\) | 7.70796 | 0.594682 | ||||||||
\(169\) | −13.0000 | −0.999998 | ||||||||
\(170\) | −5.39664 | −0.413903 | ||||||||
\(171\) | −1.79442 | −0.137223 | ||||||||
\(172\) | −20.3679 | −1.55304 | ||||||||
\(173\) | −12.5821 | −0.956599 | −0.478300 | − | 0.878197i | \(-0.658747\pi\) | ||||
−0.478300 | + | 0.878197i | \(0.658747\pi\) | |||||||
\(174\) | 1.86479 | 0.141369 | ||||||||
\(175\) | 0.0261032 | 0.00197321 | ||||||||
\(176\) | 3.39228 | 0.255703 | ||||||||
\(177\) | −0.382777 | −0.0287713 | ||||||||
\(178\) | 7.28098 | 0.545732 | ||||||||
\(179\) | 1.23407 | 0.0922389 | 0.0461194 | − | 0.998936i | \(-0.485315\pi\) | ||||
0.0461194 | + | 0.998936i | \(0.485315\pi\) | |||||||
\(180\) | 4.26072 | 0.317575 | ||||||||
\(181\) | −17.0030 | −1.26382 | −0.631911 | − | 0.775041i | \(-0.717729\pi\) | ||||
−0.631911 | + | 0.775041i | \(0.717729\pi\) | |||||||
\(182\) | −0.0357312 | −0.00264858 | ||||||||
\(183\) | −10.6992 | −0.790910 | ||||||||
\(184\) | 2.44236 | 0.180053 | ||||||||
\(185\) | 13.7152 | 1.00836 | ||||||||
\(186\) | −10.6065 | −0.777704 | ||||||||
\(187\) | −1.68233 | −0.123024 | ||||||||
\(188\) | 17.1284 | 1.24922 | ||||||||
\(189\) | −20.2378 | −1.47209 | ||||||||
\(190\) | −12.0521 | −0.874352 | ||||||||
\(191\) | 0.213652 | 0.0154593 | 0.00772966 | − | 0.999970i | \(-0.497540\pi\) | ||||
0.00772966 | + | 0.999970i | \(0.497540\pi\) | |||||||
\(192\) | 18.2881 | 1.31983 | ||||||||
\(193\) | −3.51336 | −0.252897 | −0.126449 | − | 0.991973i | \(-0.540358\pi\) | ||||
−0.126449 | + | 0.991973i | \(0.540358\pi\) | |||||||
\(194\) | −32.1176 | −2.30591 | ||||||||
\(195\) | 0.0155121 | 0.00111085 | ||||||||
\(196\) | 15.8941 | 1.13530 | ||||||||
\(197\) | −11.5456 | −0.822587 | −0.411294 | − | 0.911503i | \(-0.634923\pi\) | ||||
−0.411294 | + | 0.911503i | \(0.634923\pi\) | |||||||
\(198\) | 2.32831 | 0.165466 | ||||||||
\(199\) | −4.63698 | −0.328707 | −0.164353 | − | 0.986402i | \(-0.552554\pi\) | ||||
−0.164353 | + | 0.986402i | \(0.552554\pi\) | |||||||
\(200\) | −0.0102580 | −0.000725351 0 | ||||||||
\(201\) | −9.30643 | −0.656425 | ||||||||
\(202\) | 24.2951 | 1.70940 | ||||||||
\(203\) | 2.06130 | 0.144675 | ||||||||
\(204\) | −4.49129 | −0.314453 | ||||||||
\(205\) | 13.1732 | 0.920054 | ||||||||
\(206\) | 10.0340 | 0.699101 | ||||||||
\(207\) | −1.23819 | −0.0860602 | ||||||||
\(208\) | −0.0103716 | −0.000719144 0 | ||||||||
\(209\) | −3.75709 | −0.259883 | ||||||||
\(210\) | −26.2456 | −1.81112 | ||||||||
\(211\) | −0.622411 | −0.0428485 | −0.0214243 | − | 0.999770i | \(-0.506820\pi\) | ||||
−0.0214243 | + | 0.999770i | \(0.506820\pi\) | |||||||
\(212\) | −20.7850 | −1.42752 | ||||||||
\(213\) | 14.0841 | 0.965030 | ||||||||
\(214\) | −17.4422 | −1.19233 | ||||||||
\(215\) | 17.1338 | 1.16851 | ||||||||
\(216\) | 7.95306 | 0.541137 | ||||||||
\(217\) | −11.7242 | −0.795891 | ||||||||
\(218\) | −2.61079 | −0.176825 | ||||||||
\(219\) | 23.0609 | 1.55831 | ||||||||
\(220\) | 8.92095 | 0.601450 | ||||||||
\(221\) | 0.00514360 | 0.000345996 0 | ||||||||
\(222\) | 20.0088 | 1.34290 | ||||||||
\(223\) | 0.0281489 | 0.00188499 | 0.000942495 | − | 1.00000i | \(-0.499700\pi\) | ||||
0.000942495 | 1.00000i | \(0.499700\pi\) | ||||||||
\(224\) | 27.7529 | 1.85432 | ||||||||
\(225\) | 0.00520046 | 0.000346697 0 | ||||||||
\(226\) | 16.5810 | 1.10295 | ||||||||
\(227\) | −8.12837 | −0.539499 | −0.269749 | − | 0.962931i | \(-0.586941\pi\) | ||||
−0.269749 | + | 0.962931i | \(0.586941\pi\) | |||||||
\(228\) | −10.0302 | −0.664267 | ||||||||
\(229\) | 23.9995 | 1.58593 | 0.792966 | − | 0.609266i | \(-0.208536\pi\) | ||||
0.792966 | + | 0.609266i | \(0.208536\pi\) | |||||||
\(230\) | −8.31623 | −0.548356 | ||||||||
\(231\) | −8.18174 | −0.538319 | ||||||||
\(232\) | −0.810050 | −0.0531824 | ||||||||
\(233\) | −12.5903 | −0.824819 | −0.412410 | − | 0.910999i | \(-0.635313\pi\) | ||||
−0.412410 | + | 0.910999i | \(0.635313\pi\) | |||||||
\(234\) | −0.00711863 | −0.000465359 0 | ||||||||
\(235\) | −14.4086 | −0.939915 | ||||||||
\(236\) | 0.673040 | 0.0438112 | ||||||||
\(237\) | 3.01622 | 0.195925 | ||||||||
\(238\) | −8.70268 | −0.564111 | ||||||||
\(239\) | 24.1351 | 1.56117 | 0.780586 | − | 0.625049i | \(-0.214921\pi\) | ||||
0.780586 | + | 0.625049i | \(0.214921\pi\) | |||||||
\(240\) | −7.61826 | −0.491757 | ||||||||
\(241\) | 25.4713 | 1.64075 | 0.820374 | − | 0.571827i | \(-0.193765\pi\) | ||||
0.820374 | + | 0.571827i | \(0.193765\pi\) | |||||||
\(242\) | −18.8612 | −1.21244 | ||||||||
\(243\) | −7.28534 | −0.467355 | ||||||||
\(244\) | 18.8126 | 1.20435 | ||||||||
\(245\) | −13.3703 | −0.854199 | ||||||||
\(246\) | 19.2179 | 1.22529 | ||||||||
\(247\) | 0.0114870 | 0.000730901 0 | ||||||||
\(248\) | 4.60737 | 0.292569 | ||||||||
\(249\) | −10.4487 | −0.662160 | ||||||||
\(250\) | 24.1427 | 1.52692 | ||||||||
\(251\) | 4.12389 | 0.260298 | 0.130149 | − | 0.991494i | \(-0.458454\pi\) | ||||
0.130149 | + | 0.991494i | \(0.458454\pi\) | |||||||
\(252\) | 6.87088 | 0.432825 | ||||||||
\(253\) | −2.59248 | −0.162988 | ||||||||
\(254\) | 19.0737 | 1.19679 | ||||||||
\(255\) | 3.77812 | 0.236595 | ||||||||
\(256\) | 1.08345 | 0.0677158 | ||||||||
\(257\) | −16.7266 | −1.04337 | −0.521687 | − | 0.853137i | \(-0.674697\pi\) | ||||
−0.521687 | + | 0.853137i | \(0.674697\pi\) | |||||||
\(258\) | 24.9959 | 1.55618 | ||||||||
\(259\) | 22.1174 | 1.37431 | ||||||||
\(260\) | −0.0272751 | −0.00169153 | ||||||||
\(261\) | 0.410667 | 0.0254197 | ||||||||
\(262\) | −27.8579 | −1.72107 | ||||||||
\(263\) | 28.7329 | 1.77174 | 0.885872 | − | 0.463930i | \(-0.153561\pi\) | ||||
0.885872 | + | 0.463930i | \(0.153561\pi\) | |||||||
\(264\) | 3.21526 | 0.197885 | ||||||||
\(265\) | 17.4845 | 1.07407 | ||||||||
\(266\) | −19.4354 | −1.19166 | ||||||||
\(267\) | −5.09733 | −0.311951 | ||||||||
\(268\) | 16.3636 | 0.999565 | ||||||||
\(269\) | 28.6099 | 1.74438 | 0.872189 | − | 0.489169i | \(-0.162700\pi\) | ||||
0.872189 | + | 0.489169i | \(0.162700\pi\) | |||||||
\(270\) | −27.0802 | −1.64805 | ||||||||
\(271\) | −13.8852 | −0.843467 | −0.421733 | − | 0.906720i | \(-0.638578\pi\) | ||||
−0.421733 | + | 0.906720i | \(0.638578\pi\) | |||||||
\(272\) | −2.52611 | −0.153168 | ||||||||
\(273\) | 0.0250150 | 0.00151398 | ||||||||
\(274\) | 8.27778 | 0.500079 | ||||||||
\(275\) | 0.0108885 | 0.000656603 0 | ||||||||
\(276\) | −6.92108 | −0.416600 | ||||||||
\(277\) | −14.4664 | −0.869200 | −0.434600 | − | 0.900624i | \(-0.643110\pi\) | ||||
−0.434600 | + | 0.900624i | \(0.643110\pi\) | |||||||
\(278\) | 19.9150 | 1.19443 | ||||||||
\(279\) | −2.33578 | −0.139839 | ||||||||
\(280\) | 11.4009 | 0.681335 | ||||||||
\(281\) | −15.4967 | −0.924456 | −0.462228 | − | 0.886761i | \(-0.652950\pi\) | ||||
−0.462228 | + | 0.886761i | \(0.652950\pi\) | |||||||
\(282\) | −21.0203 | −1.25174 | ||||||||
\(283\) | 10.4295 | 0.619970 | 0.309985 | − | 0.950741i | \(-0.399676\pi\) | ||||
0.309985 | + | 0.950741i | \(0.399676\pi\) | |||||||
\(284\) | −24.7643 | −1.46949 | ||||||||
\(285\) | 8.43754 | 0.499797 | ||||||||
\(286\) | −0.0149047 | −0.000881336 0 | ||||||||
\(287\) | 21.2432 | 1.25395 | ||||||||
\(288\) | 5.52913 | 0.325807 | ||||||||
\(289\) | −15.7472 | −0.926307 | ||||||||
\(290\) | 2.75822 | 0.161968 | ||||||||
\(291\) | 22.4851 | 1.31810 | ||||||||
\(292\) | −40.5483 | −2.37291 | ||||||||
\(293\) | −1.90244 | −0.111142 | −0.0555708 | − | 0.998455i | \(-0.517698\pi\) | ||||
−0.0555708 | + | 0.998455i | \(0.517698\pi\) | |||||||
\(294\) | −19.5056 | −1.13759 | ||||||||
\(295\) | −0.566169 | −0.0329636 | ||||||||
\(296\) | −8.69167 | −0.505193 | ||||||||
\(297\) | −8.44191 | −0.489849 | ||||||||
\(298\) | 48.9577 | 2.83604 | ||||||||
\(299\) | 0.00792630 | 0.000458390 0 | ||||||||
\(300\) | 0.0290689 | 0.00167829 | ||||||||
\(301\) | 27.6301 | 1.59257 | ||||||||
\(302\) | −4.80163 | −0.276303 | ||||||||
\(303\) | −17.0087 | −0.977127 | ||||||||
\(304\) | −5.64146 | −0.323560 | ||||||||
\(305\) | −15.8253 | −0.906157 | ||||||||
\(306\) | −1.73381 | −0.0991152 | ||||||||
\(307\) | −17.6876 | −1.00949 | −0.504744 | − | 0.863269i | \(-0.668413\pi\) | ||||
−0.504744 | + | 0.863269i | \(0.668413\pi\) | |||||||
\(308\) | 14.3860 | 0.819720 | ||||||||
\(309\) | −7.02468 | −0.399620 | ||||||||
\(310\) | −15.6881 | −0.891025 | ||||||||
\(311\) | −28.0074 | −1.58815 | −0.794076 | − | 0.607818i | \(-0.792045\pi\) | ||||
−0.794076 | + | 0.607818i | \(0.792045\pi\) | |||||||
\(312\) | −0.00983039 | −0.000556536 0 | ||||||||
\(313\) | 5.02123 | 0.283817 | 0.141908 | − | 0.989880i | \(-0.454676\pi\) | ||||
0.141908 | + | 0.989880i | \(0.454676\pi\) | |||||||
\(314\) | −48.1577 | −2.71769 | ||||||||
\(315\) | −5.77987 | −0.325659 | ||||||||
\(316\) | −5.30344 | −0.298342 | ||||||||
\(317\) | 0.356974 | 0.0200496 | 0.0100248 | − | 0.999950i | \(-0.496809\pi\) | ||||
0.0100248 | + | 0.999950i | \(0.496809\pi\) | |||||||
\(318\) | 25.5077 | 1.43040 | ||||||||
\(319\) | 0.859841 | 0.0481418 | ||||||||
\(320\) | 27.0501 | 1.51215 | ||||||||
\(321\) | 12.2111 | 0.681557 | ||||||||
\(322\) | −13.4108 | −0.747357 | ||||||||
\(323\) | 2.79777 | 0.155672 | ||||||||
\(324\) | −16.8167 | −0.934259 | ||||||||
\(325\) | −3.32908e−5 0 | −1.84664e−6 0 | ||||||||
\(326\) | 15.5864 | 0.863253 | ||||||||
\(327\) | 1.82778 | 0.101077 | ||||||||
\(328\) | −8.34814 | −0.460949 | ||||||||
\(329\) | −23.2355 | −1.28101 | ||||||||
\(330\) | −10.9480 | −0.602665 | ||||||||
\(331\) | 16.2490 | 0.893123 | 0.446562 | − | 0.894753i | \(-0.352648\pi\) | ||||
0.446562 | + | 0.894753i | \(0.352648\pi\) | |||||||
\(332\) | 18.3720 | 1.00830 | ||||||||
\(333\) | 4.40637 | 0.241468 | ||||||||
\(334\) | −24.7040 | −1.35174 | ||||||||
\(335\) | −13.7652 | −0.752075 | ||||||||
\(336\) | −12.2853 | −0.670218 | ||||||||
\(337\) | −24.0444 | −1.30978 | −0.654892 | − | 0.755722i | \(-0.727286\pi\) | ||||
−0.654892 | + | 0.755722i | \(0.727286\pi\) | |||||||
\(338\) | −28.0517 | −1.52581 | ||||||||
\(339\) | −11.6082 | −0.630469 | ||||||||
\(340\) | −6.64310 | −0.360273 | ||||||||
\(341\) | −4.89057 | −0.264839 | ||||||||
\(342\) | −3.87205 | −0.209376 | ||||||||
\(343\) | 3.66192 | 0.197725 | ||||||||
\(344\) | −10.8581 | −0.585427 | ||||||||
\(345\) | 5.82210 | 0.313451 | ||||||||
\(346\) | −27.1500 | −1.45959 | ||||||||
\(347\) | −10.7861 | −0.579028 | −0.289514 | − | 0.957174i | \(-0.593494\pi\) | ||||
−0.289514 | + | 0.957174i | \(0.593494\pi\) | |||||||
\(348\) | 2.29550 | 0.123052 | ||||||||
\(349\) | 17.2044 | 0.920933 | 0.460466 | − | 0.887677i | \(-0.347682\pi\) | ||||
0.460466 | + | 0.887677i | \(0.347682\pi\) | |||||||
\(350\) | 0.0563262 | 0.00301076 | ||||||||
\(351\) | 0.0258105 | 0.00137766 | ||||||||
\(352\) | 11.5767 | 0.617040 | ||||||||
\(353\) | −2.83276 | −0.150773 | −0.0753863 | − | 0.997154i | \(-0.524019\pi\) | ||||
−0.0753863 | + | 0.997154i | \(0.524019\pi\) | |||||||
\(354\) | −0.825967 | −0.0438996 | ||||||||
\(355\) | 20.8320 | 1.10565 | ||||||||
\(356\) | 8.96268 | 0.475021 | ||||||||
\(357\) | 6.09264 | 0.322457 | ||||||||
\(358\) | 2.66292 | 0.140739 | ||||||||
\(359\) | 23.3759 | 1.23373 | 0.616867 | − | 0.787068i | \(-0.288402\pi\) | ||||
0.616867 | + | 0.787068i | \(0.288402\pi\) | |||||||
\(360\) | 2.27137 | 0.119712 | ||||||||
\(361\) | −12.7518 | −0.671150 | ||||||||
\(362\) | −36.6895 | −1.92836 | ||||||||
\(363\) | 13.2045 | 0.693056 | ||||||||
\(364\) | −0.0439841 | −0.00230539 | ||||||||
\(365\) | 34.1097 | 1.78538 | ||||||||
\(366\) | −23.0871 | −1.20678 | ||||||||
\(367\) | −21.8406 | −1.14007 | −0.570034 | − | 0.821621i | \(-0.693070\pi\) | ||||
−0.570034 | + | 0.821621i | \(0.693070\pi\) | |||||||
\(368\) | −3.89274 | −0.202923 | ||||||||
\(369\) | 4.23222 | 0.220320 | ||||||||
\(370\) | 29.5951 | 1.53858 | ||||||||
\(371\) | 28.1958 | 1.46385 | ||||||||
\(372\) | −13.0563 | −0.676935 | ||||||||
\(373\) | 0.594294 | 0.0307714 | 0.0153857 | − | 0.999882i | \(-0.495102\pi\) | ||||
0.0153857 | + | 0.999882i | \(0.495102\pi\) | |||||||
\(374\) | −3.63019 | −0.187713 | ||||||||
\(375\) | −16.9020 | −0.872817 | ||||||||
\(376\) | 9.13108 | 0.470899 | ||||||||
\(377\) | −0.00262890 | −0.000135395 0 | ||||||||
\(378\) | −43.6698 | −2.24613 | ||||||||
\(379\) | −16.0631 | −0.825105 | −0.412553 | − | 0.910934i | \(-0.635363\pi\) | ||||
−0.412553 | + | 0.910934i | \(0.635363\pi\) | |||||||
\(380\) | −14.8358 | −0.761060 | ||||||||
\(381\) | −13.3532 | −0.684108 | ||||||||
\(382\) | 0.461025 | 0.0235881 | ||||||||
\(383\) | 15.0745 | 0.770271 | 0.385135 | − | 0.922860i | \(-0.374155\pi\) | ||||
0.385135 | + | 0.922860i | \(0.374155\pi\) | |||||||
\(384\) | 16.1920 | 0.826292 | ||||||||
\(385\) | −12.1017 | −0.616759 | ||||||||
\(386\) | −7.58123 | −0.385875 | ||||||||
\(387\) | 5.50466 | 0.279818 | ||||||||
\(388\) | −39.5358 | −2.00713 | ||||||||
\(389\) | 8.06793 | 0.409060 | 0.204530 | − | 0.978860i | \(-0.434433\pi\) | ||||
0.204530 | + | 0.978860i | \(0.434433\pi\) | |||||||
\(390\) | 0.0334725 | 0.00169495 | ||||||||
\(391\) | 1.93053 | 0.0976309 | ||||||||
\(392\) | 8.47309 | 0.427956 | ||||||||
\(393\) | 19.5030 | 0.983797 | ||||||||
\(394\) | −24.9133 | −1.25512 | ||||||||
\(395\) | 4.46132 | 0.224473 | ||||||||
\(396\) | 2.86608 | 0.144026 | ||||||||
\(397\) | 7.64285 | 0.383583 | 0.191792 | − | 0.981436i | \(-0.438570\pi\) | ||||
0.191792 | + | 0.981436i | \(0.438570\pi\) | |||||||
\(398\) | −10.0058 | −0.501546 | ||||||||
\(399\) | 13.6065 | 0.681175 | ||||||||
\(400\) | 0.0163497 | 0.000817484 0 | ||||||||
\(401\) | 37.0556 | 1.85047 | 0.925234 | − | 0.379397i | \(-0.123868\pi\) | ||||
0.925234 | + | 0.379397i | \(0.123868\pi\) | |||||||
\(402\) | −20.0817 | −1.00158 | ||||||||
\(403\) | 0.0149525 | 0.000744839 0 | ||||||||
\(404\) | 29.9066 | 1.48791 | ||||||||
\(405\) | 14.1464 | 0.702939 | ||||||||
\(406\) | 4.44794 | 0.220747 | ||||||||
\(407\) | 9.22591 | 0.457312 | ||||||||
\(408\) | −2.39428 | −0.118535 | ||||||||
\(409\) | −29.1516 | −1.44145 | −0.720726 | − | 0.693220i | \(-0.756191\pi\) | ||||
−0.720726 | + | 0.693220i | \(0.756191\pi\) | |||||||
\(410\) | 28.4254 | 1.40383 | ||||||||
\(411\) | −5.79518 | −0.285855 | ||||||||
\(412\) | 12.3515 | 0.608517 | ||||||||
\(413\) | −0.913010 | −0.0449263 | ||||||||
\(414\) | −2.67180 | −0.131312 | ||||||||
\(415\) | −15.4548 | −0.758645 | ||||||||
\(416\) | −0.0353948 | −0.00173537 | ||||||||
\(417\) | −13.9423 | −0.682757 | ||||||||
\(418\) | −8.10716 | −0.396534 | ||||||||
\(419\) | 31.8690 | 1.55690 | 0.778451 | − | 0.627705i | \(-0.216006\pi\) | ||||
0.778451 | + | 0.627705i | \(0.216006\pi\) | |||||||
\(420\) | −32.3076 | −1.57645 | ||||||||
\(421\) | −26.0459 | −1.26940 | −0.634699 | − | 0.772759i | \(-0.718876\pi\) | ||||
−0.634699 | + | 0.772759i | \(0.718876\pi\) | |||||||
\(422\) | −1.34306 | −0.0653790 | ||||||||
\(423\) | −4.62914 | −0.225077 | ||||||||
\(424\) | −11.0804 | −0.538110 | ||||||||
\(425\) | −0.00810829 | −0.000393310 0 | ||||||||
\(426\) | 30.3912 | 1.47246 | ||||||||
\(427\) | −25.5201 | −1.23501 | ||||||||
\(428\) | −21.4709 | −1.03783 | ||||||||
\(429\) | 0.0104346 | 0.000503789 0 | ||||||||
\(430\) | 36.9717 | 1.78293 | ||||||||
\(431\) | −22.6196 | −1.08955 | −0.544774 | − | 0.838583i | \(-0.683384\pi\) | ||||
−0.544774 | + | 0.838583i | \(0.683384\pi\) | |||||||
\(432\) | −12.6759 | −0.609872 | ||||||||
\(433\) | −22.7272 | −1.09220 | −0.546099 | − | 0.837720i | \(-0.683888\pi\) | ||||
−0.546099 | + | 0.837720i | \(0.683888\pi\) | |||||||
\(434\) | −25.2988 | −1.21438 | ||||||||
\(435\) | −1.93100 | −0.0925843 | ||||||||
\(436\) | −3.21380 | −0.153913 | ||||||||
\(437\) | 4.31137 | 0.206241 | ||||||||
\(438\) | 49.7616 | 2.37770 | ||||||||
\(439\) | 24.5936 | 1.17379 | 0.586895 | − | 0.809663i | \(-0.300350\pi\) | ||||
0.586895 | + | 0.809663i | \(0.300350\pi\) | |||||||
\(440\) | 4.75572 | 0.226720 | ||||||||
\(441\) | −4.29556 | −0.204551 | ||||||||
\(442\) | 0.0110990 | 0.000527926 0 | ||||||||
\(443\) | 23.4765 | 1.11540 | 0.557702 | − | 0.830041i | \(-0.311683\pi\) | ||||
0.557702 | + | 0.830041i | \(0.311683\pi\) | |||||||
\(444\) | 24.6302 | 1.16890 | ||||||||
\(445\) | −7.53951 | −0.357407 | ||||||||
\(446\) | 0.0607405 | 0.00287615 | ||||||||
\(447\) | −34.2747 | −1.62114 | ||||||||
\(448\) | 43.6213 | 2.06091 | ||||||||
\(449\) | −13.6452 | −0.643958 | −0.321979 | − | 0.946747i | \(-0.604348\pi\) | ||||
−0.321979 | + | 0.946747i | \(0.604348\pi\) | |||||||
\(450\) | 0.0112217 | 0.000528996 0 | ||||||||
\(451\) | 8.86127 | 0.417261 | ||||||||
\(452\) | 20.4107 | 0.960041 | ||||||||
\(453\) | 3.36157 | 0.157940 | ||||||||
\(454\) | −17.5396 | −0.823176 | ||||||||
\(455\) | 0.0370000 | 0.00173458 | ||||||||
\(456\) | −5.34706 | −0.250399 | ||||||||
\(457\) | −2.17967 | −0.101960 | −0.0509802 | − | 0.998700i | \(-0.516235\pi\) | ||||
−0.0509802 | + | 0.998700i | \(0.516235\pi\) | |||||||
\(458\) | 51.7868 | 2.41984 | ||||||||
\(459\) | 6.28638 | 0.293423 | ||||||||
\(460\) | −10.2370 | −0.477304 | ||||||||
\(461\) | 12.2229 | 0.569276 | 0.284638 | − | 0.958635i | \(-0.408127\pi\) | ||||
0.284638 | + | 0.958635i | \(0.408127\pi\) | |||||||
\(462\) | −17.6548 | −0.821375 | ||||||||
\(463\) | −1.99436 | −0.0926860 | −0.0463430 | − | 0.998926i | \(-0.514757\pi\) | ||||
−0.0463430 | + | 0.998926i | \(0.514757\pi\) | |||||||
\(464\) | 1.29109 | 0.0599375 | ||||||||
\(465\) | 10.9831 | 0.509328 | ||||||||
\(466\) | −27.1677 | −1.25852 | ||||||||
\(467\) | 41.2601 | 1.90929 | 0.954645 | − | 0.297747i | \(-0.0962353\pi\) | ||||
0.954645 | + | 0.297747i | \(0.0962353\pi\) | |||||||
\(468\) | −0.00876283 | −0.000405062 0 | ||||||||
\(469\) | −22.1980 | −1.02501 | ||||||||
\(470\) | −31.0913 | −1.43414 | ||||||||
\(471\) | 33.7146 | 1.55349 | ||||||||
\(472\) | 0.358794 | 0.0165148 | ||||||||
\(473\) | 11.5255 | 0.529941 | ||||||||
\(474\) | 6.50849 | 0.298945 | ||||||||
\(475\) | −0.0181079 | −0.000830849 0 | ||||||||
\(476\) | −10.7127 | −0.491018 | ||||||||
\(477\) | 5.61736 | 0.257201 | ||||||||
\(478\) | 52.0795 | 2.38206 | ||||||||
\(479\) | 23.4921 | 1.07338 | 0.536691 | − | 0.843779i | \(-0.319674\pi\) | ||||
0.536691 | + | 0.843779i | \(0.319674\pi\) | |||||||
\(480\) | −25.9985 | −1.18666 | ||||||||
\(481\) | −0.0282075 | −0.00128615 | ||||||||
\(482\) | 54.9626 | 2.50348 | ||||||||
\(483\) | 9.38878 | 0.427204 | ||||||||
\(484\) | −23.2176 | −1.05534 | ||||||||
\(485\) | 33.2580 | 1.51017 | ||||||||
\(486\) | −15.7205 | −0.713097 | ||||||||
\(487\) | 6.09387 | 0.276139 | 0.138070 | − | 0.990423i | \(-0.455910\pi\) | ||||
0.138070 | + | 0.990423i | \(0.455910\pi\) | |||||||
\(488\) | 10.0289 | 0.453986 | ||||||||
\(489\) | −10.9119 | −0.493453 | ||||||||
\(490\) | −28.8509 | −1.30335 | ||||||||
\(491\) | −7.88983 | −0.356063 | −0.178032 | − | 0.984025i | \(-0.556973\pi\) | ||||
−0.178032 | + | 0.984025i | \(0.556973\pi\) | |||||||
\(492\) | 23.6567 | 1.06653 | ||||||||
\(493\) | −0.640292 | −0.0288373 | ||||||||
\(494\) | 0.0247870 | 0.00111522 | ||||||||
\(495\) | −2.41098 | −0.108366 | ||||||||
\(496\) | −7.34344 | −0.329730 | ||||||||
\(497\) | 33.5939 | 1.50689 | ||||||||
\(498\) | −22.5465 | −1.01033 | ||||||||
\(499\) | −0.289120 | −0.0129428 | −0.00647139 | − | 0.999979i | \(-0.502060\pi\) | ||||
−0.00647139 | + | 0.999979i | \(0.502060\pi\) | |||||||
\(500\) | 29.7190 | 1.32907 | ||||||||
\(501\) | 17.2950 | 0.772683 | ||||||||
\(502\) | 8.89865 | 0.397166 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 3.66284 | 0.163156 | ||||||||
\(505\) | −25.1578 | −1.11951 | ||||||||
\(506\) | −5.59413 | −0.248689 | ||||||||
\(507\) | 19.6387 | 0.872185 | ||||||||
\(508\) | 23.4791 | 1.04172 | ||||||||
\(509\) | 27.0889 | 1.20069 | 0.600346 | − | 0.799740i | \(-0.295030\pi\) | ||||
0.600346 | + | 0.799740i | \(0.295030\pi\) | |||||||
\(510\) | 8.15254 | 0.361001 | ||||||||
\(511\) | 55.0056 | 2.43331 | ||||||||
\(512\) | 23.7747 | 1.05070 | ||||||||
\(513\) | 14.0391 | 0.619843 | ||||||||
\(514\) | −36.0931 | −1.59200 | ||||||||
\(515\) | −10.3903 | −0.457850 | ||||||||
\(516\) | 30.7693 | 1.35454 | ||||||||
\(517\) | −9.69233 | −0.426268 | ||||||||
\(518\) | 47.7255 | 2.09694 | ||||||||
\(519\) | 19.0074 | 0.834333 | ||||||||
\(520\) | −0.0145402 | −0.000637631 0 | ||||||||
\(521\) | 21.1689 | 0.927424 | 0.463712 | − | 0.885986i | \(-0.346517\pi\) | ||||
0.463712 | + | 0.885986i | \(0.346517\pi\) | |||||||
\(522\) | 0.886150 | 0.0387857 | ||||||||
\(523\) | −0.868369 | −0.0379711 | −0.0189856 | − | 0.999820i | \(-0.506044\pi\) | ||||
−0.0189856 | + | 0.999820i | \(0.506044\pi\) | |||||||
\(524\) | −34.2923 | −1.49807 | ||||||||
\(525\) | −0.0394333 | −0.00172101 | ||||||||
\(526\) | 62.0006 | 2.70335 | ||||||||
\(527\) | 3.64183 | 0.158641 | ||||||||
\(528\) | −5.12462 | −0.223021 | ||||||||
\(529\) | −20.0251 | −0.870655 | ||||||||
\(530\) | 37.7287 | 1.63883 | ||||||||
\(531\) | −0.181896 | −0.00789363 | ||||||||
\(532\) | −23.9244 | −1.03725 | ||||||||
\(533\) | −0.0270926 | −0.00117351 | ||||||||
\(534\) | −10.9992 | −0.475980 | ||||||||
\(535\) | 18.0616 | 0.780869 | ||||||||
\(536\) | 8.72335 | 0.376791 | ||||||||
\(537\) | −1.86428 | −0.0804495 | ||||||||
\(538\) | 61.7353 | 2.66160 | ||||||||
\(539\) | −8.99390 | −0.387395 | ||||||||
\(540\) | −33.3349 | −1.43451 | ||||||||
\(541\) | 14.8513 | 0.638508 | 0.319254 | − | 0.947669i | \(-0.396568\pi\) | ||||
0.319254 | + | 0.947669i | \(0.396568\pi\) | |||||||
\(542\) | −29.9619 | −1.28697 | ||||||||
\(543\) | 25.6859 | 1.10229 | ||||||||
\(544\) | −8.62074 | −0.369611 | ||||||||
\(545\) | 2.70349 | 0.115805 | ||||||||
\(546\) | 0.0539781 | 0.00231005 | ||||||||
\(547\) | −18.8256 | −0.804925 | −0.402463 | − | 0.915436i | \(-0.631846\pi\) | ||||
−0.402463 | + | 0.915436i | \(0.631846\pi\) | |||||||
\(548\) | 10.1897 | 0.435283 | ||||||||
\(549\) | −5.08430 | −0.216993 | ||||||||
\(550\) | 0.0234956 | 0.00100186 | ||||||||
\(551\) | −1.42994 | −0.0609175 | ||||||||
\(552\) | −3.68960 | −0.157040 | ||||||||
\(553\) | 7.19437 | 0.305936 | ||||||||
\(554\) | −31.2160 | −1.32624 | ||||||||
\(555\) | −20.7192 | −0.879482 | ||||||||
\(556\) | 24.5149 | 1.03966 | ||||||||
\(557\) | 11.9201 | 0.505071 | 0.252535 | − | 0.967588i | \(-0.418736\pi\) | ||||
0.252535 | + | 0.967588i | \(0.418736\pi\) | |||||||
\(558\) | −5.04021 | −0.213369 | ||||||||
\(559\) | −0.0352382 | −0.00149042 | ||||||||
\(560\) | −18.1713 | −0.767877 | ||||||||
\(561\) | 2.54145 | 0.107300 | ||||||||
\(562\) | −33.4392 | −1.41055 | ||||||||
\(563\) | −22.7172 | −0.957414 | −0.478707 | − | 0.877975i | \(-0.658894\pi\) | ||||
−0.478707 | + | 0.877975i | \(0.658894\pi\) | |||||||
\(564\) | −25.8754 | −1.08955 | ||||||||
\(565\) | −17.1698 | −0.722337 | ||||||||
\(566\) | 22.5051 | 0.945960 | ||||||||
\(567\) | 22.8126 | 0.958039 | ||||||||
\(568\) | −13.2017 | −0.553932 | ||||||||
\(569\) | −16.9403 | −0.710176 | −0.355088 | − | 0.934833i | \(-0.615549\pi\) | ||||
−0.355088 | + | 0.934833i | \(0.615549\pi\) | |||||||
\(570\) | 18.2068 | 0.762597 | ||||||||
\(571\) | 16.2940 | 0.681883 | 0.340941 | − | 0.940085i | \(-0.389254\pi\) | ||||
0.340941 | + | 0.940085i | \(0.389254\pi\) | |||||||
\(572\) | −0.0183473 | −0.000767139 0 | ||||||||
\(573\) | −0.322758 | −0.0134834 | ||||||||
\(574\) | 45.8392 | 1.91329 | ||||||||
\(575\) | −0.0124949 | −0.000521073 0 | ||||||||
\(576\) | 8.69054 | 0.362106 | ||||||||
\(577\) | −44.3876 | −1.84788 | −0.923941 | − | 0.382535i | \(-0.875051\pi\) | ||||
−0.923941 | + | 0.382535i | \(0.875051\pi\) | |||||||
\(578\) | −33.9798 | −1.41337 | ||||||||
\(579\) | 5.30753 | 0.220574 | ||||||||
\(580\) | 3.39529 | 0.140982 | ||||||||
\(581\) | −24.9226 | −1.03396 | ||||||||
\(582\) | 48.5191 | 2.01118 | ||||||||
\(583\) | 11.7614 | 0.487109 | ||||||||
\(584\) | −21.6161 | −0.894480 | ||||||||
\(585\) | 0.00737139 | 0.000304770 0 | ||||||||
\(586\) | −4.10513 | −0.169582 | ||||||||
\(587\) | 33.6221 | 1.38773 | 0.693865 | − | 0.720105i | \(-0.255906\pi\) | ||||
0.693865 | + | 0.720105i | \(0.255906\pi\) | |||||||
\(588\) | −24.0108 | −0.990189 | ||||||||
\(589\) | 8.13316 | 0.335121 | ||||||||
\(590\) | −1.22170 | −0.0502964 | ||||||||
\(591\) | 17.4415 | 0.717449 | ||||||||
\(592\) | 13.8532 | 0.569362 | ||||||||
\(593\) | 14.3513 | 0.589336 | 0.294668 | − | 0.955600i | \(-0.404791\pi\) | ||||
0.294668 | + | 0.955600i | \(0.404791\pi\) | |||||||
\(594\) | −18.2162 | −0.747419 | ||||||||
\(595\) | 9.01169 | 0.369443 | ||||||||
\(596\) | 60.2655 | 2.46857 | ||||||||
\(597\) | 7.00495 | 0.286694 | ||||||||
\(598\) | 0.0171036 | 0.000699418 0 | ||||||||
\(599\) | −4.26954 | −0.174449 | −0.0872243 | − | 0.996189i | \(-0.527800\pi\) | ||||
−0.0872243 | + | 0.996189i | \(0.527800\pi\) | |||||||
\(600\) | 0.0154965 | 0.000632641 0 | ||||||||
\(601\) | 18.2764 | 0.745510 | 0.372755 | − | 0.927930i | \(-0.378413\pi\) | ||||
0.372755 | + | 0.927930i | \(0.378413\pi\) | |||||||
\(602\) | 59.6210 | 2.42997 | ||||||||
\(603\) | −4.42244 | −0.180096 | ||||||||
\(604\) | −5.91067 | −0.240502 | ||||||||
\(605\) | 19.5309 | 0.794044 | ||||||||
\(606\) | −36.7020 | −1.49091 | ||||||||
\(607\) | −29.2048 | −1.18539 | −0.592694 | − | 0.805428i | \(-0.701936\pi\) | ||||
−0.592694 | + | 0.805428i | \(0.701936\pi\) | |||||||
\(608\) | −19.2524 | −0.780787 | ||||||||
\(609\) | −3.11395 | −0.126184 | ||||||||
\(610\) | −34.1484 | −1.38263 | ||||||||
\(611\) | 0.0296335 | 0.00119884 | ||||||||
\(612\) | −2.13427 | −0.0862727 | ||||||||
\(613\) | −24.0622 | −0.971861 | −0.485931 | − | 0.873997i | \(-0.661519\pi\) | ||||
−0.485931 | + | 0.873997i | \(0.661519\pi\) | |||||||
\(614\) | −38.1669 | −1.54029 | ||||||||
\(615\) | −19.9003 | −0.802458 | ||||||||
\(616\) | 7.66912 | 0.308998 | ||||||||
\(617\) | −20.7734 | −0.836307 | −0.418154 | − | 0.908376i | \(-0.637323\pi\) | ||||
−0.418154 | + | 0.908376i | \(0.637323\pi\) | |||||||
\(618\) | −15.1580 | −0.609746 | ||||||||
\(619\) | −6.43218 | −0.258531 | −0.129266 | − | 0.991610i | \(-0.541262\pi\) | ||||
−0.129266 | + | 0.991610i | \(0.541262\pi\) | |||||||
\(620\) | −19.3116 | −0.775574 | ||||||||
\(621\) | 9.68732 | 0.388739 | ||||||||
\(622\) | −60.4351 | −2.42323 | ||||||||
\(623\) | −12.1583 | −0.487112 | ||||||||
\(624\) | 0.0156681 | 0.000627227 0 | ||||||||
\(625\) | −24.9637 | −0.998549 | ||||||||
\(626\) | 10.8350 | 0.433052 | ||||||||
\(627\) | 5.67573 | 0.226667 | ||||||||
\(628\) | −59.2807 | −2.36556 | ||||||||
\(629\) | −6.87020 | −0.273933 | ||||||||
\(630\) | −12.4720 | −0.496895 | ||||||||
\(631\) | −43.2199 | −1.72056 | −0.860279 | − | 0.509824i | \(-0.829710\pi\) | ||||
−0.860279 | + | 0.509824i | \(0.829710\pi\) | |||||||
\(632\) | −2.82724 | −0.112462 | ||||||||
\(633\) | 0.940258 | 0.0373719 | ||||||||
\(634\) | 0.770288 | 0.0305920 | ||||||||
\(635\) | −19.7509 | −0.783791 | ||||||||
\(636\) | 31.3992 | 1.24506 | ||||||||
\(637\) | 0.0274981 | 0.00108952 | ||||||||
\(638\) | 1.85539 | 0.0734556 | ||||||||
\(639\) | 6.69281 | 0.264764 | ||||||||
\(640\) | 23.9497 | 0.946694 | ||||||||
\(641\) | −49.6276 | −1.96017 | −0.980086 | − | 0.198574i | \(-0.936369\pi\) | ||||
−0.980086 | + | 0.198574i | \(0.936369\pi\) | |||||||
\(642\) | 26.3495 | 1.03993 | ||||||||
\(643\) | −45.1377 | −1.78006 | −0.890028 | − | 0.455906i | \(-0.849315\pi\) | ||||
−0.890028 | + | 0.455906i | \(0.849315\pi\) | |||||||
\(644\) | −16.5084 | −0.650521 | ||||||||
\(645\) | −25.8835 | −1.01916 | ||||||||
\(646\) | 6.03711 | 0.237527 | ||||||||
\(647\) | −29.7930 | −1.17128 | −0.585642 | − | 0.810570i | \(-0.699157\pi\) | ||||
−0.585642 | + | 0.810570i | \(0.699157\pi\) | |||||||
\(648\) | −8.96488 | −0.352174 | ||||||||
\(649\) | −0.380848 | −0.0149496 | ||||||||
\(650\) | −7.18359e−5 0 | −2.81764e−6 0 | ||||||||
\(651\) | 17.7114 | 0.694165 | ||||||||
\(652\) | 19.1865 | 0.751400 | ||||||||
\(653\) | 29.1127 | 1.13927 | 0.569635 | − | 0.821898i | \(-0.307085\pi\) | ||||
0.569635 | + | 0.821898i | \(0.307085\pi\) | |||||||
\(654\) | 3.94404 | 0.154224 | ||||||||
\(655\) | 28.8471 | 1.12715 | ||||||||
\(656\) | 13.3056 | 0.519498 | ||||||||
\(657\) | 10.9586 | 0.427536 | ||||||||
\(658\) | −50.1382 | −1.95459 | ||||||||
\(659\) | 17.1327 | 0.667395 | 0.333697 | − | 0.942680i | \(-0.391704\pi\) | ||||
0.333697 | + | 0.942680i | \(0.391704\pi\) | |||||||
\(660\) | −13.4766 | −0.524577 | ||||||||
\(661\) | −0.266846 | −0.0103791 | −0.00518956 | − | 0.999987i | \(-0.501652\pi\) | ||||
−0.00518956 | + | 0.999987i | \(0.501652\pi\) | |||||||
\(662\) | 35.0625 | 1.36274 | ||||||||
\(663\) | −0.00777029 | −0.000301773 0 | ||||||||
\(664\) | 9.79405 | 0.380083 | ||||||||
\(665\) | 20.1255 | 0.780432 | ||||||||
\(666\) | 9.50820 | 0.368435 | ||||||||
\(667\) | −0.986691 | −0.0382048 | ||||||||
\(668\) | −30.4099 | −1.17660 | ||||||||
\(669\) | −0.0425237 | −0.00164406 | ||||||||
\(670\) | −29.7030 | −1.14753 | ||||||||
\(671\) | −10.6453 | −0.410958 | ||||||||
\(672\) | −41.9255 | −1.61731 | ||||||||
\(673\) | 41.4814 | 1.59899 | 0.799495 | − | 0.600673i | \(-0.205101\pi\) | ||||
0.799495 | + | 0.600673i | \(0.205101\pi\) | |||||||
\(674\) | −51.8838 | −1.99849 | ||||||||
\(675\) | −0.0406872 | −0.00156605 | ||||||||
\(676\) | −34.5309 | −1.32811 | ||||||||
\(677\) | 33.0242 | 1.26922 | 0.634611 | − | 0.772832i | \(-0.281160\pi\) | ||||
0.634611 | + | 0.772832i | \(0.281160\pi\) | |||||||
\(678\) | −25.0485 | −0.961980 | ||||||||
\(679\) | 53.6322 | 2.05822 | ||||||||
\(680\) | −3.54141 | −0.135807 | ||||||||
\(681\) | 12.2793 | 0.470543 | ||||||||
\(682\) | −10.5530 | −0.404096 | ||||||||
\(683\) | 0.471704 | 0.0180492 | 0.00902462 | − | 0.999959i | \(-0.497127\pi\) | ||||
0.00902462 | + | 0.999959i | \(0.497127\pi\) | |||||||
\(684\) | −4.76638 | −0.182247 | ||||||||
\(685\) | −8.57170 | −0.327508 | ||||||||
\(686\) | 7.90179 | 0.301692 | ||||||||
\(687\) | −36.2553 | −1.38323 | ||||||||
\(688\) | 17.3061 | 0.659788 | ||||||||
\(689\) | −0.0359597 | −0.00136995 | ||||||||
\(690\) | 12.5631 | 0.478269 | ||||||||
\(691\) | −12.1972 | −0.464003 | −0.232002 | − | 0.972715i | \(-0.574527\pi\) | ||||
−0.232002 | + | 0.972715i | \(0.574527\pi\) | |||||||
\(692\) | −33.4209 | −1.27047 | ||||||||
\(693\) | −3.88798 | −0.147692 | ||||||||
\(694\) | −23.2745 | −0.883489 | ||||||||
\(695\) | −20.6222 | −0.782244 | ||||||||
\(696\) | 1.22372 | 0.0463849 | ||||||||
\(697\) | −6.59866 | −0.249942 | ||||||||
\(698\) | 37.1242 | 1.40517 | ||||||||
\(699\) | 19.0198 | 0.719396 | ||||||||
\(700\) | 0.0693359 | 0.00262065 | ||||||||
\(701\) | −47.0220 | −1.77600 | −0.887999 | − | 0.459846i | \(-0.847905\pi\) | ||||
−0.887999 | + | 0.459846i | \(0.847905\pi\) | |||||||
\(702\) | 0.0556946 | 0.00210206 | ||||||||
\(703\) | −15.3430 | −0.578671 | ||||||||
\(704\) | 18.1960 | 0.685786 | ||||||||
\(705\) | 21.7667 | 0.819781 | ||||||||
\(706\) | −6.11261 | −0.230051 | ||||||||
\(707\) | −40.5697 | −1.52578 | ||||||||
\(708\) | −1.01674 | −0.0382115 | ||||||||
\(709\) | 26.6796 | 1.00197 | 0.500986 | − | 0.865455i | \(-0.332971\pi\) | ||||
0.500986 | + | 0.865455i | \(0.332971\pi\) | |||||||
\(710\) | 44.9519 | 1.68701 | ||||||||
\(711\) | 1.43331 | 0.0537535 | ||||||||
\(712\) | 4.77796 | 0.179062 | ||||||||
\(713\) | 5.61207 | 0.210174 | ||||||||
\(714\) | 13.1469 | 0.492010 | ||||||||
\(715\) | 0.0154340 | 0.000577198 0 | ||||||||
\(716\) | 3.27797 | 0.122504 | ||||||||
\(717\) | −36.4602 | −1.36163 | ||||||||
\(718\) | 50.4412 | 1.88245 | ||||||||
\(719\) | 12.7457 | 0.475336 | 0.237668 | − | 0.971346i | \(-0.423617\pi\) | ||||
0.237668 | + | 0.971346i | \(0.423617\pi\) | |||||||
\(720\) | −3.62021 | −0.134917 | ||||||||
\(721\) | −16.7555 | −0.624006 | ||||||||
\(722\) | −27.5163 | −1.02405 | ||||||||
\(723\) | −38.4787 | −1.43104 | ||||||||
\(724\) | −45.1637 | −1.67850 | ||||||||
\(725\) | 0.00414415 | 0.000153910 0 | ||||||||
\(726\) | 28.4930 | 1.05748 | ||||||||
\(727\) | 1.14219 | 0.0423614 | 0.0211807 | − | 0.999776i | \(-0.493257\pi\) | ||||
0.0211807 | + | 0.999776i | \(0.493257\pi\) | |||||||
\(728\) | −0.0234477 | −0.000869031 0 | ||||||||
\(729\) | 29.9989 | 1.11107 | ||||||||
\(730\) | 73.6028 | 2.72416 | ||||||||
\(731\) | −8.58259 | −0.317439 | ||||||||
\(732\) | −28.4196 | −1.05042 | ||||||||
\(733\) | −20.6111 | −0.761289 | −0.380644 | − | 0.924721i | \(-0.624298\pi\) | ||||
−0.380644 | + | 0.924721i | \(0.624298\pi\) | |||||||
\(734\) | −47.1282 | −1.73953 | ||||||||
\(735\) | 20.1982 | 0.745021 | ||||||||
\(736\) | −13.2846 | −0.489676 | ||||||||
\(737\) | −9.25954 | −0.341080 | ||||||||
\(738\) | 9.13240 | 0.336168 | ||||||||
\(739\) | −40.1054 | −1.47530 | −0.737651 | − | 0.675182i | \(-0.764065\pi\) | ||||
−0.737651 | + | 0.675182i | \(0.764065\pi\) | |||||||
\(740\) | 36.4308 | 1.33922 | ||||||||
\(741\) | −0.0173531 | −0.000637482 0 | ||||||||
\(742\) | 60.8417 | 2.23357 | ||||||||
\(743\) | −31.7658 | −1.16538 | −0.582688 | − | 0.812696i | \(-0.697999\pi\) | ||||
−0.582688 | + | 0.812696i | \(0.697999\pi\) | |||||||
\(744\) | −6.96023 | −0.255174 | ||||||||
\(745\) | −50.6961 | −1.85736 | ||||||||
\(746\) | 1.28238 | 0.0469514 | ||||||||
\(747\) | −4.96525 | −0.181669 | ||||||||
\(748\) | −4.46866 | −0.163390 | ||||||||
\(749\) | 29.1263 | 1.06425 | ||||||||
\(750\) | −36.4717 | −1.33176 | ||||||||
\(751\) | 3.19661 | 0.116646 | 0.0583230 | − | 0.998298i | \(-0.481425\pi\) | ||||
0.0583230 | + | 0.998298i | \(0.481425\pi\) | |||||||
\(752\) | −14.5535 | −0.530713 | ||||||||
\(753\) | −6.22984 | −0.227028 | ||||||||
\(754\) | −0.00567271 | −0.000206588 0 | ||||||||
\(755\) | 4.97212 | 0.180954 | ||||||||
\(756\) | −53.7563 | −1.95510 | ||||||||
\(757\) | 45.6783 | 1.66021 | 0.830103 | − | 0.557610i | \(-0.188281\pi\) | ||||
0.830103 | + | 0.557610i | \(0.188281\pi\) | |||||||
\(758\) | −34.6614 | −1.25896 | ||||||||
\(759\) | 3.91638 | 0.142156 | ||||||||
\(760\) | −7.90889 | −0.286886 | ||||||||
\(761\) | 37.7902 | 1.36989 | 0.684946 | − | 0.728594i | \(-0.259826\pi\) | ||||
0.684946 | + | 0.728594i | \(0.259826\pi\) | |||||||
\(762\) | −28.8140 | −1.04382 | ||||||||
\(763\) | 4.35968 | 0.157831 | ||||||||
\(764\) | 0.567508 | 0.0205317 | ||||||||
\(765\) | 1.79537 | 0.0649118 | ||||||||
\(766\) | 32.5282 | 1.17529 | ||||||||
\(767\) | 0.00116441 | 4.20445e−5 0 | ||||||||
\(768\) | −1.63674 | −0.0590608 | ||||||||
\(769\) | 11.6770 | 0.421084 | 0.210542 | − | 0.977585i | \(-0.432477\pi\) | ||||
0.210542 | + | 0.977585i | \(0.432477\pi\) | |||||||
\(770\) | −26.1134 | −0.941061 | ||||||||
\(771\) | 25.2683 | 0.910017 | ||||||||
\(772\) | −9.33228 | −0.335876 | ||||||||
\(773\) | −43.2250 | −1.55470 | −0.777348 | − | 0.629070i | \(-0.783436\pi\) | ||||
−0.777348 | + | 0.629070i | \(0.783436\pi\) | |||||||
\(774\) | 11.8781 | 0.426950 | ||||||||
\(775\) | −0.0235710 | −0.000846694 0 | ||||||||
\(776\) | −21.0764 | −0.756597 | ||||||||
\(777\) | −33.4120 | −1.19865 | ||||||||
\(778\) | 17.4092 | 0.624150 | ||||||||
\(779\) | −14.7365 | −0.527992 | ||||||||
\(780\) | 0.0412037 | 0.00147533 | ||||||||
\(781\) | 14.0132 | 0.501431 | ||||||||
\(782\) | 4.16574 | 0.148967 | ||||||||
\(783\) | −3.21297 | −0.114822 | ||||||||
\(784\) | −13.5048 | −0.482314 | ||||||||
\(785\) | 49.8676 | 1.77985 | ||||||||
\(786\) | 42.0842 | 1.50109 | ||||||||
\(787\) | 41.6501 | 1.48467 | 0.742334 | − | 0.670030i | \(-0.233719\pi\) | ||||
0.742334 | + | 0.670030i | \(0.233719\pi\) | |||||||
\(788\) | −30.6676 | −1.09249 | ||||||||
\(789\) | −43.4059 | −1.54529 | ||||||||
\(790\) | 9.62676 | 0.342505 | ||||||||
\(791\) | −27.6881 | −0.984477 | ||||||||
\(792\) | 1.52790 | 0.0542914 | ||||||||
\(793\) | 0.0325473 | 0.00115579 | ||||||||
\(794\) | 16.4920 | 0.585278 | ||||||||
\(795\) | −26.4134 | −0.936787 | ||||||||
\(796\) | −12.3169 | −0.436560 | ||||||||
\(797\) | 20.0955 | 0.711819 | 0.355910 | − | 0.934520i | \(-0.384171\pi\) | ||||
0.355910 | + | 0.934520i | \(0.384171\pi\) | |||||||
\(798\) | 29.3604 | 1.03935 | ||||||||
\(799\) | 7.21753 | 0.255338 | ||||||||
\(800\) | 0.0557958 | 0.00197268 | ||||||||
\(801\) | −2.42226 | −0.0855864 | ||||||||
\(802\) | 79.9596 | 2.82347 | ||||||||
\(803\) | 22.9448 | 0.809703 | ||||||||
\(804\) | −24.7200 | −0.871807 | ||||||||
\(805\) | 13.8870 | 0.489453 | ||||||||
\(806\) | 0.0322650 | 0.00113649 | ||||||||
\(807\) | −43.2202 | −1.52142 | ||||||||
\(808\) | 15.9431 | 0.560875 | ||||||||
\(809\) | −10.5903 | −0.372334 | −0.186167 | − | 0.982518i | \(-0.559607\pi\) | ||||
−0.186167 | + | 0.982518i | \(0.559607\pi\) | |||||||
\(810\) | 30.5254 | 1.07255 | ||||||||
\(811\) | 29.9332 | 1.05110 | 0.525549 | − | 0.850764i | \(-0.323860\pi\) | ||||
0.525549 | + | 0.850764i | \(0.323860\pi\) | |||||||
\(812\) | 5.47528 | 0.192145 | ||||||||
\(813\) | 20.9760 | 0.735660 | ||||||||
\(814\) | 19.9079 | 0.697773 | ||||||||
\(815\) | −16.1399 | −0.565355 | ||||||||
\(816\) | 3.81612 | 0.133591 | ||||||||
\(817\) | −19.1672 | −0.670575 | ||||||||
\(818\) | −62.9041 | −2.19939 | ||||||||
\(819\) | 0.0118872 | 0.000415372 0 | ||||||||
\(820\) | 34.9909 | 1.22193 | ||||||||
\(821\) | 1.47970 | 0.0516419 | 0.0258209 | − | 0.999667i | \(-0.491780\pi\) | ||||
0.0258209 | + | 0.999667i | \(0.491780\pi\) | |||||||
\(822\) | −12.5050 | −0.436162 | ||||||||
\(823\) | −20.9277 | −0.729494 | −0.364747 | − | 0.931107i | \(-0.618845\pi\) | ||||
−0.364747 | + | 0.931107i | \(0.618845\pi\) | |||||||
\(824\) | 6.58455 | 0.229384 | ||||||||
\(825\) | −0.0164490 | −0.000572680 0 | ||||||||
\(826\) | −1.97012 | −0.0685492 | ||||||||
\(827\) | 14.8863 | 0.517646 | 0.258823 | − | 0.965925i | \(-0.416665\pi\) | ||||
0.258823 | + | 0.965925i | \(0.416665\pi\) | |||||||
\(828\) | −3.28891 | −0.114298 | ||||||||
\(829\) | 54.9732 | 1.90930 | 0.954649 | − | 0.297733i | \(-0.0962304\pi\) | ||||
0.954649 | + | 0.297733i | \(0.0962304\pi\) | |||||||
\(830\) | −33.3488 | −1.15755 | ||||||||
\(831\) | 21.8539 | 0.758104 | ||||||||
\(832\) | −0.0556327 | −0.00192872 | ||||||||
\(833\) | 6.69743 | 0.232052 | ||||||||
\(834\) | −30.0851 | −1.04176 | ||||||||
\(835\) | 25.5812 | 0.885273 | ||||||||
\(836\) | −9.97968 | −0.345154 | ||||||||
\(837\) | 18.2746 | 0.631663 | ||||||||
\(838\) | 68.7678 | 2.37554 | ||||||||
\(839\) | −40.8460 | −1.41016 | −0.705080 | − | 0.709128i | \(-0.749089\pi\) | ||||
−0.705080 | + | 0.709128i | \(0.749089\pi\) | |||||||
\(840\) | −17.2230 | −0.594251 | ||||||||
\(841\) | −28.6727 | −0.988715 | ||||||||
\(842\) | −56.2026 | −1.93687 | ||||||||
\(843\) | 23.4104 | 0.806298 | ||||||||
\(844\) | −1.65326 | −0.0569077 | ||||||||
\(845\) | 29.0478 | 0.999274 | ||||||||
\(846\) | −9.98889 | −0.343425 | ||||||||
\(847\) | 31.4957 | 1.08221 | ||||||||
\(848\) | 17.6604 | 0.606460 | ||||||||
\(849\) | −15.7556 | −0.540729 | ||||||||
\(850\) | −0.0174963 | −0.000600118 0 | ||||||||
\(851\) | −10.5870 | −0.362918 | ||||||||
\(852\) | 37.4107 | 1.28167 | ||||||||
\(853\) | −8.90994 | −0.305071 | −0.152535 | − | 0.988298i | \(-0.548744\pi\) | ||||
−0.152535 | + | 0.988298i | \(0.548744\pi\) | |||||||
\(854\) | −55.0681 | −1.88439 | ||||||||
\(855\) | 4.00953 | 0.137123 | ||||||||
\(856\) | −11.4460 | −0.391217 | ||||||||
\(857\) | 32.1479 | 1.09815 | 0.549076 | − | 0.835773i | \(-0.314980\pi\) | ||||
0.549076 | + | 0.835773i | \(0.314980\pi\) | |||||||
\(858\) | 0.0225162 | 0.000768689 0 | ||||||||
\(859\) | −25.4577 | −0.868606 | −0.434303 | − | 0.900767i | \(-0.643005\pi\) | ||||
−0.434303 | + | 0.900767i | \(0.643005\pi\) | |||||||
\(860\) | 45.5111 | 1.55192 | ||||||||
\(861\) | −32.0915 | −1.09367 | ||||||||
\(862\) | −48.8092 | −1.66245 | ||||||||
\(863\) | −42.3500 | −1.44161 | −0.720805 | − | 0.693138i | \(-0.756228\pi\) | ||||
−0.720805 | + | 0.693138i | \(0.756228\pi\) | |||||||
\(864\) | −43.2586 | −1.47169 | ||||||||
\(865\) | 28.1140 | 0.955906 | ||||||||
\(866\) | −49.0414 | −1.66649 | ||||||||
\(867\) | 23.7889 | 0.807913 | ||||||||
\(868\) | −31.1421 | −1.05703 | ||||||||
\(869\) | 3.00102 | 0.101803 | ||||||||
\(870\) | −4.16676 | −0.141267 | ||||||||
\(871\) | 0.0283103 | 0.000959259 0 | ||||||||
\(872\) | −1.71326 | −0.0580184 | ||||||||
\(873\) | 10.6850 | 0.361632 | ||||||||
\(874\) | 9.30319 | 0.314685 | ||||||||
\(875\) | −40.3152 | −1.36290 | ||||||||
\(876\) | 61.2551 | 2.06962 | ||||||||
\(877\) | −54.7498 | −1.84877 | −0.924385 | − | 0.381461i | \(-0.875421\pi\) | ||||
−0.924385 | + | 0.381461i | \(0.875421\pi\) | |||||||
\(878\) | 53.0688 | 1.79099 | ||||||||
\(879\) | 2.87396 | 0.0969361 | ||||||||
\(880\) | −7.57988 | −0.255518 | ||||||||
\(881\) | −42.7752 | −1.44113 | −0.720566 | − | 0.693386i | \(-0.756118\pi\) | ||||
−0.720566 | + | 0.693386i | \(0.756118\pi\) | |||||||
\(882\) | −9.26909 | −0.312107 | ||||||||
\(883\) | −51.0453 | −1.71781 | −0.858906 | − | 0.512133i | \(-0.828856\pi\) | ||||
−0.858906 | + | 0.512133i | \(0.828856\pi\) | |||||||
\(884\) | 0.0136626 | 0.000459522 0 | ||||||||
\(885\) | 0.855295 | 0.0287504 | ||||||||
\(886\) | 50.6584 | 1.70190 | ||||||||
\(887\) | −15.6713 | −0.526191 | −0.263096 | − | 0.964770i | \(-0.584744\pi\) | ||||
−0.263096 | + | 0.964770i | \(0.584744\pi\) | |||||||
\(888\) | 13.1302 | 0.440622 | ||||||||
\(889\) | −31.8505 | −1.06823 | ||||||||
\(890\) | −16.2690 | −0.545337 | ||||||||
\(891\) | 9.51592 | 0.318795 | ||||||||
\(892\) | 0.0747698 | 0.00250348 | ||||||||
\(893\) | 16.1186 | 0.539389 | ||||||||
\(894\) | −73.9590 | −2.47356 | ||||||||
\(895\) | −2.75747 | −0.0921720 | ||||||||
\(896\) | 38.6215 | 1.29025 | ||||||||
\(897\) | −0.0119740 | −0.000399801 0 | ||||||||
\(898\) | −29.4441 | −0.982561 | ||||||||
\(899\) | −1.86134 | −0.0620792 | ||||||||
\(900\) | 0.0138136 | 0.000460453 0 | ||||||||
\(901\) | −8.75831 | −0.291782 | ||||||||
\(902\) | 19.1211 | 0.636663 | ||||||||
\(903\) | −41.7400 | −1.38902 | ||||||||
\(904\) | 10.8809 | 0.361892 | ||||||||
\(905\) | 37.9923 | 1.26291 | ||||||||
\(906\) | 7.25368 | 0.240988 | ||||||||
\(907\) | 50.8029 | 1.68688 | 0.843442 | − | 0.537221i | \(-0.180526\pi\) | ||||
0.843442 | + | 0.537221i | \(0.180526\pi\) | |||||||
\(908\) | −21.5908 | −0.716515 | ||||||||
\(909\) | −8.08259 | −0.268083 | ||||||||
\(910\) | 0.0798396 | 0.00264666 | ||||||||
\(911\) | −47.4669 | −1.57265 | −0.786324 | − | 0.617815i | \(-0.788018\pi\) | ||||
−0.786324 | + | 0.617815i | \(0.788018\pi\) | |||||||
\(912\) | 8.52239 | 0.282205 | ||||||||
\(913\) | −10.3961 | −0.344059 | ||||||||
\(914\) | −4.70335 | −0.155573 | ||||||||
\(915\) | 23.9069 | 0.790337 | ||||||||
\(916\) | 63.7481 | 2.10630 | ||||||||
\(917\) | 46.5192 | 1.53620 | ||||||||
\(918\) | 13.5649 | 0.447709 | ||||||||
\(919\) | 18.1424 | 0.598462 | 0.299231 | − | 0.954181i | \(-0.403270\pi\) | ||||
0.299231 | + | 0.954181i | \(0.403270\pi\) | |||||||
\(920\) | −5.45732 | −0.179922 | ||||||||
\(921\) | 26.7202 | 0.880461 | ||||||||
\(922\) | 26.3749 | 0.868610 | ||||||||
\(923\) | −0.0428442 | −0.00141023 | ||||||||
\(924\) | −21.7325 | −0.714948 | ||||||||
\(925\) | 0.0444659 | 0.00146203 | ||||||||
\(926\) | −4.30350 | −0.141422 | ||||||||
\(927\) | −3.33814 | −0.109639 | ||||||||
\(928\) | 4.40606 | 0.144636 | ||||||||
\(929\) | −36.7632 | −1.20616 | −0.603081 | − | 0.797680i | \(-0.706060\pi\) | ||||
−0.603081 | + | 0.797680i | \(0.706060\pi\) | |||||||
\(930\) | 23.6996 | 0.777140 | ||||||||
\(931\) | 14.9571 | 0.490200 | ||||||||
\(932\) | −33.4427 | −1.09545 | ||||||||
\(933\) | 42.3099 | 1.38516 | ||||||||
\(934\) | 89.0322 | 2.91322 | ||||||||
\(935\) | 3.75909 | 0.122935 | ||||||||
\(936\) | −0.00467142 | −0.000152690 0 | ||||||||
\(937\) | −29.1597 | −0.952607 | −0.476304 | − | 0.879281i | \(-0.658024\pi\) | ||||
−0.476304 | + | 0.879281i | \(0.658024\pi\) | |||||||
\(938\) | −47.8994 | −1.56397 | ||||||||
\(939\) | −7.58543 | −0.247541 | ||||||||
\(940\) | −38.2725 | −1.24831 | ||||||||
\(941\) | −11.1041 | −0.361983 | −0.180991 | − | 0.983485i | \(-0.557931\pi\) | ||||
−0.180991 | + | 0.983485i | \(0.557931\pi\) | |||||||
\(942\) | 72.7504 | 2.37034 | ||||||||
\(943\) | −10.1686 | −0.331134 | ||||||||
\(944\) | −0.571863 | −0.0186125 | ||||||||
\(945\) | 45.2204 | 1.47102 | ||||||||
\(946\) | 24.8700 | 0.808593 | ||||||||
\(947\) | 7.44473 | 0.241921 | 0.120961 | − | 0.992657i | \(-0.461403\pi\) | ||||
0.120961 | + | 0.992657i | \(0.461403\pi\) | |||||||
\(948\) | 8.01176 | 0.260210 | ||||||||
\(949\) | −0.0701518 | −0.00227722 | ||||||||
\(950\) | −0.0390738 | −0.00126772 | ||||||||
\(951\) | −0.539270 | −0.0174870 | ||||||||
\(952\) | −5.71091 | −0.185092 | ||||||||
\(953\) | −40.8632 | −1.32369 | −0.661844 | − | 0.749641i | \(-0.730226\pi\) | ||||
−0.661844 | + | 0.749641i | \(0.730226\pi\) | |||||||
\(954\) | 12.1213 | 0.392442 | ||||||||
\(955\) | −0.477394 | −0.0154481 | ||||||||
\(956\) | 64.1083 | 2.07341 | ||||||||
\(957\) | −1.29894 | −0.0419886 | ||||||||
\(958\) | 50.6919 | 1.63778 | ||||||||
\(959\) | −13.8228 | −0.446362 | ||||||||
\(960\) | −40.8638 | −1.31887 | ||||||||
\(961\) | −20.4131 | −0.658488 | ||||||||
\(962\) | −0.0608670 | −0.00196243 | ||||||||
\(963\) | 5.80274 | 0.186991 | ||||||||
\(964\) | 67.6574 | 2.17910 | ||||||||
\(965\) | 7.85042 | 0.252714 | ||||||||
\(966\) | 20.2594 | 0.651835 | ||||||||
\(967\) | 2.29088 | 0.0736697 | 0.0368349 | − | 0.999321i | \(-0.488272\pi\) | ||||
0.0368349 | + | 0.999321i | \(0.488272\pi\) | |||||||
\(968\) | −12.3772 | −0.397817 | ||||||||
\(969\) | −4.22651 | −0.135775 | ||||||||
\(970\) | 71.7651 | 2.30424 | ||||||||
\(971\) | −27.8481 | −0.893689 | −0.446845 | − | 0.894612i | \(-0.647452\pi\) | ||||
−0.446845 | + | 0.894612i | \(0.647452\pi\) | |||||||
\(972\) | −19.3515 | −0.620700 | ||||||||
\(973\) | −33.2556 | −1.06612 | ||||||||
\(974\) | 13.1495 | 0.421338 | ||||||||
\(975\) | 5.02915e−5 0 | 1.61062e−6 0 | ||||||||
\(976\) | −15.9845 | −0.511651 | ||||||||
\(977\) | 2.65190 | 0.0848419 | 0.0424209 | − | 0.999100i | \(-0.486493\pi\) | ||||
0.0424209 | + | 0.999100i | \(0.486493\pi\) | |||||||
\(978\) | −23.5460 | −0.752917 | ||||||||
\(979\) | −5.07165 | −0.162090 | ||||||||
\(980\) | −35.5146 | −1.13447 | ||||||||
\(981\) | 0.868565 | 0.0277312 | ||||||||
\(982\) | −17.0249 | −0.543287 | ||||||||
\(983\) | 17.5940 | 0.561162 | 0.280581 | − | 0.959830i | \(-0.409473\pi\) | ||||
0.280581 | + | 0.959830i | \(0.409473\pi\) | |||||||
\(984\) | 12.6113 | 0.402033 | ||||||||
\(985\) | 25.7980 | 0.821991 | ||||||||
\(986\) | −1.38164 | −0.0440004 | ||||||||
\(987\) | 35.1012 | 1.11728 | ||||||||
\(988\) | 0.0305121 | 0.000970719 0 | ||||||||
\(989\) | −13.2258 | −0.420556 | ||||||||
\(990\) | −5.20249 | −0.165346 | ||||||||
\(991\) | −40.1464 | −1.27529 | −0.637646 | − | 0.770329i | \(-0.720092\pi\) | ||||
−0.637646 | + | 0.770329i | \(0.720092\pi\) | |||||||
\(992\) | −25.0606 | −0.795676 | ||||||||
\(993\) | −24.5468 | −0.778970 | ||||||||
\(994\) | 72.4899 | 2.29924 | ||||||||
\(995\) | 10.3611 | 0.328469 | ||||||||
\(996\) | −27.7541 | −0.879423 | ||||||||
\(997\) | −52.3474 | −1.65786 | −0.828930 | − | 0.559353i | \(-0.811050\pi\) | ||||
−0.828930 | + | 0.559353i | \(0.811050\pi\) | |||||||
\(998\) | −0.623871 | −0.0197483 | ||||||||
\(999\) | −34.4745 | −1.09072 |
(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 | 503.2.a.e.1.10 | ✓ | 10 | |
3.2 | odd | 2 | 4527.2.a.k.1.1 | 10 | |||
4.3 | odd | 2 | 8048.2.a.p.1.7 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
503.2.a.e.1.10 | ✓ | 10 | 1.1 | even | 1 | trivial | |
4527.2.a.k.1.1 | 10 | 3.2 | odd | 2 | |||
8048.2.a.p.1.7 | 10 | 4.3 | odd | 2 |