Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1003,2,Mod(1,1003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1003, 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("1003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1003 = 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1003.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: | \(8.00899532273\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} - 5 x^{14} + 90 x^{13} - 82 x^{12} - 456 x^{11} + 723 x^{10} + 951 x^{9} - 2105 x^{8} + \cdots - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.79724\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1003.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.79724 | −1.27084 | −0.635419 | − | 0.772168i | \(-0.719172\pi\) | ||||
−0.635419 | + | 0.772168i | \(0.719172\pi\) | |||||||
\(3\) | −2.09283 | −1.20829 | −0.604147 | − | 0.796873i | \(-0.706486\pi\) | ||||
−0.604147 | + | 0.796873i | \(0.706486\pi\) | |||||||
\(4\) | 1.23006 | 0.615028 | ||||||||
\(5\) | −2.26932 | −1.01487 | −0.507435 | − | 0.861690i | \(-0.669406\pi\) | ||||
−0.507435 | + | 0.861690i | \(0.669406\pi\) | |||||||
\(6\) | 3.76130 | 1.53555 | ||||||||
\(7\) | −0.408229 | −0.154296 | −0.0771480 | − | 0.997020i | \(-0.524581\pi\) | ||||
−0.0771480 | + | 0.997020i | \(0.524581\pi\) | |||||||
\(8\) | 1.38377 | 0.489237 | ||||||||
\(9\) | 1.37993 | 0.459975 | ||||||||
\(10\) | 4.07850 | 1.28974 | ||||||||
\(11\) | −5.30925 | −1.60080 | −0.800399 | − | 0.599467i | \(-0.795379\pi\) | ||||
−0.800399 | + | 0.599467i | \(0.795379\pi\) | |||||||
\(12\) | −2.57429 | −0.743135 | ||||||||
\(13\) | 4.40136 | 1.22072 | 0.610359 | − | 0.792125i | \(-0.291025\pi\) | ||||
0.610359 | + | 0.792125i | \(0.291025\pi\) | |||||||
\(14\) | 0.733683 | 0.196085 | ||||||||
\(15\) | 4.74929 | 1.22626 | ||||||||
\(16\) | −4.94707 | −1.23677 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −2.48005 | −0.584554 | ||||||||
\(19\) | 6.57252 | 1.50784 | 0.753920 | − | 0.656967i | \(-0.228161\pi\) | ||||
0.753920 | + | 0.656967i | \(0.228161\pi\) | |||||||
\(20\) | −2.79139 | −0.624174 | ||||||||
\(21\) | 0.854352 | 0.186435 | ||||||||
\(22\) | 9.54197 | 2.03436 | ||||||||
\(23\) | −3.22305 | −0.672052 | −0.336026 | − | 0.941853i | \(-0.609083\pi\) | ||||
−0.336026 | + | 0.941853i | \(0.609083\pi\) | |||||||
\(24\) | −2.89599 | −0.591142 | ||||||||
\(25\) | 0.149808 | 0.0299617 | ||||||||
\(26\) | −7.91029 | −1.55133 | ||||||||
\(27\) | 3.39054 | 0.652509 | ||||||||
\(28\) | −0.502144 | −0.0948963 | ||||||||
\(29\) | 5.31587 | 0.987133 | 0.493566 | − | 0.869708i | \(-0.335693\pi\) | ||||
0.493566 | + | 0.869708i | \(0.335693\pi\) | |||||||
\(30\) | −8.53560 | −1.55838 | ||||||||
\(31\) | 8.06505 | 1.44853 | 0.724263 | − | 0.689524i | \(-0.242180\pi\) | ||||
0.724263 | + | 0.689524i | \(0.242180\pi\) | |||||||
\(32\) | 6.12352 | 1.08250 | ||||||||
\(33\) | 11.1113 | 1.93424 | ||||||||
\(34\) | −1.79724 | −0.308223 | ||||||||
\(35\) | 0.926401 | 0.156590 | ||||||||
\(36\) | 1.69739 | 0.282898 | ||||||||
\(37\) | −7.46060 | −1.22651 | −0.613257 | − | 0.789883i | \(-0.710141\pi\) | ||||
−0.613257 | + | 0.789883i | \(0.710141\pi\) | |||||||
\(38\) | −11.8124 | −1.91622 | ||||||||
\(39\) | −9.21129 | −1.47499 | ||||||||
\(40\) | −3.14022 | −0.496512 | ||||||||
\(41\) | 0.557550 | 0.0870748 | 0.0435374 | − | 0.999052i | \(-0.486137\pi\) | ||||
0.0435374 | + | 0.999052i | \(0.486137\pi\) | |||||||
\(42\) | −1.53547 | −0.236929 | ||||||||
\(43\) | 7.66459 | 1.16884 | 0.584420 | − | 0.811452i | \(-0.301322\pi\) | ||||
0.584420 | + | 0.811452i | \(0.301322\pi\) | |||||||
\(44\) | −6.53067 | −0.984536 | ||||||||
\(45\) | −3.13149 | −0.466815 | ||||||||
\(46\) | 5.79258 | 0.854069 | ||||||||
\(47\) | 10.2475 | 1.49476 | 0.747379 | − | 0.664398i | \(-0.231312\pi\) | ||||
0.747379 | + | 0.664398i | \(0.231312\pi\) | |||||||
\(48\) | 10.3534 | 1.49438 | ||||||||
\(49\) | −6.83335 | −0.976193 | ||||||||
\(50\) | −0.269241 | −0.0380764 | ||||||||
\(51\) | −2.09283 | −0.293054 | ||||||||
\(52\) | 5.41392 | 0.750776 | ||||||||
\(53\) | −13.4282 | −1.84450 | −0.922249 | − | 0.386595i | \(-0.873651\pi\) | ||||
−0.922249 | + | 0.386595i | \(0.873651\pi\) | |||||||
\(54\) | −6.09359 | −0.829233 | ||||||||
\(55\) | 12.0484 | 1.62460 | ||||||||
\(56\) | −0.564895 | −0.0754873 | ||||||||
\(57\) | −13.7551 | −1.82191 | ||||||||
\(58\) | −9.55387 | −1.25449 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 5.84190 | 0.754185 | ||||||||
\(61\) | 2.66493 | 0.341209 | 0.170604 | − | 0.985340i | \(-0.445428\pi\) | ||||
0.170604 | + | 0.985340i | \(0.445428\pi\) | |||||||
\(62\) | −14.4948 | −1.84084 | ||||||||
\(63\) | −0.563325 | −0.0709723 | ||||||||
\(64\) | −1.11125 | −0.138907 | ||||||||
\(65\) | −9.98810 | −1.23887 | ||||||||
\(66\) | −19.9697 | −2.45810 | ||||||||
\(67\) | −7.99404 | −0.976627 | −0.488313 | − | 0.872668i | \(-0.662388\pi\) | ||||
−0.488313 | + | 0.872668i | \(0.662388\pi\) | |||||||
\(68\) | 1.23006 | 0.149166 | ||||||||
\(69\) | 6.74528 | 0.812036 | ||||||||
\(70\) | −1.66496 | −0.199001 | ||||||||
\(71\) | −6.23963 | −0.740508 | −0.370254 | − | 0.928931i | \(-0.620729\pi\) | ||||
−0.370254 | + | 0.928931i | \(0.620729\pi\) | |||||||
\(72\) | 1.90950 | 0.225037 | ||||||||
\(73\) | −11.2914 | −1.32156 | −0.660782 | − | 0.750578i | \(-0.729775\pi\) | ||||
−0.660782 | + | 0.750578i | \(0.729775\pi\) | |||||||
\(74\) | 13.4084 | 1.55870 | ||||||||
\(75\) | −0.313523 | −0.0362025 | ||||||||
\(76\) | 8.08457 | 0.927363 | ||||||||
\(77\) | 2.16739 | 0.246997 | ||||||||
\(78\) | 16.5549 | 1.87447 | ||||||||
\(79\) | 10.6386 | 1.19693 | 0.598466 | − | 0.801148i | \(-0.295777\pi\) | ||||
0.598466 | + | 0.801148i | \(0.295777\pi\) | |||||||
\(80\) | 11.2265 | 1.25516 | ||||||||
\(81\) | −11.2356 | −1.24840 | ||||||||
\(82\) | −1.00205 | −0.110658 | ||||||||
\(83\) | −7.40405 | −0.812700 | −0.406350 | − | 0.913718i | \(-0.633199\pi\) | ||||
−0.406350 | + | 0.913718i | \(0.633199\pi\) | |||||||
\(84\) | 1.05090 | 0.114663 | ||||||||
\(85\) | −2.26932 | −0.246142 | ||||||||
\(86\) | −13.7751 | −1.48541 | ||||||||
\(87\) | −11.1252 | −1.19275 | ||||||||
\(88\) | −7.34678 | −0.783170 | ||||||||
\(89\) | 7.94689 | 0.842369 | 0.421184 | − | 0.906975i | \(-0.361615\pi\) | ||||
0.421184 | + | 0.906975i | \(0.361615\pi\) | |||||||
\(90\) | 5.62803 | 0.593246 | ||||||||
\(91\) | −1.79676 | −0.188352 | ||||||||
\(92\) | −3.96453 | −0.413331 | ||||||||
\(93\) | −16.8788 | −1.75025 | ||||||||
\(94\) | −18.4173 | −1.89959 | ||||||||
\(95\) | −14.9151 | −1.53026 | ||||||||
\(96\) | −12.8155 | −1.30797 | ||||||||
\(97\) | −10.0130 | −1.01666 | −0.508331 | − | 0.861161i | \(-0.669738\pi\) | ||||
−0.508331 | + | 0.861161i | \(0.669738\pi\) | |||||||
\(98\) | 12.2811 | 1.24058 | ||||||||
\(99\) | −7.32637 | −0.736328 | ||||||||
\(100\) | 0.184273 | 0.0184273 | ||||||||
\(101\) | −13.4990 | −1.34320 | −0.671600 | − | 0.740914i | \(-0.734393\pi\) | ||||
−0.671600 | + | 0.740914i | \(0.734393\pi\) | |||||||
\(102\) | 3.76130 | 0.372425 | ||||||||
\(103\) | 11.9951 | 1.18191 | 0.590955 | − | 0.806705i | \(-0.298751\pi\) | ||||
0.590955 | + | 0.806705i | \(0.298751\pi\) | |||||||
\(104\) | 6.09048 | 0.597221 | ||||||||
\(105\) | −1.93880 | −0.189207 | ||||||||
\(106\) | 24.1336 | 2.34406 | ||||||||
\(107\) | −8.04700 | −0.777933 | −0.388966 | − | 0.921252i | \(-0.627168\pi\) | ||||
−0.388966 | + | 0.921252i | \(0.627168\pi\) | |||||||
\(108\) | 4.17055 | 0.401311 | ||||||||
\(109\) | −9.33510 | −0.894141 | −0.447070 | − | 0.894499i | \(-0.647533\pi\) | ||||
−0.447070 | + | 0.894499i | \(0.647533\pi\) | |||||||
\(110\) | −21.6538 | −2.06461 | ||||||||
\(111\) | 15.6137 | 1.48199 | ||||||||
\(112\) | 2.01954 | 0.190828 | ||||||||
\(113\) | −0.517224 | −0.0486564 | −0.0243282 | − | 0.999704i | \(-0.507745\pi\) | ||||
−0.0243282 | + | 0.999704i | \(0.507745\pi\) | |||||||
\(114\) | 24.7212 | 2.31536 | ||||||||
\(115\) | 7.31412 | 0.682045 | ||||||||
\(116\) | 6.53882 | 0.607114 | ||||||||
\(117\) | 6.07355 | 0.561500 | ||||||||
\(118\) | −1.79724 | −0.165449 | ||||||||
\(119\) | −0.408229 | −0.0374223 | ||||||||
\(120\) | 6.57193 | 0.599933 | ||||||||
\(121\) | 17.1881 | 1.56256 | ||||||||
\(122\) | −4.78950 | −0.433621 | ||||||||
\(123\) | −1.16686 | −0.105212 | ||||||||
\(124\) | 9.92047 | 0.890884 | ||||||||
\(125\) | 11.0066 | 0.984463 | ||||||||
\(126\) | 1.01243 | 0.0901943 | ||||||||
\(127\) | −16.3025 | −1.44661 | −0.723305 | − | 0.690529i | \(-0.757378\pi\) | ||||
−0.723305 | + | 0.690529i | \(0.757378\pi\) | |||||||
\(128\) | −10.2498 | −0.905967 | ||||||||
\(129\) | −16.0407 | −1.41230 | ||||||||
\(130\) | 17.9510 | 1.57440 | ||||||||
\(131\) | −0.386273 | −0.0337488 | −0.0168744 | − | 0.999858i | \(-0.505372\pi\) | ||||
−0.0168744 | + | 0.999858i | \(0.505372\pi\) | |||||||
\(132\) | 13.6676 | 1.18961 | ||||||||
\(133\) | −2.68309 | −0.232653 | ||||||||
\(134\) | 14.3672 | 1.24113 | ||||||||
\(135\) | −7.69421 | −0.662212 | ||||||||
\(136\) | 1.38377 | 0.118657 | ||||||||
\(137\) | 15.9224 | 1.36034 | 0.680170 | − | 0.733054i | \(-0.261906\pi\) | ||||
0.680170 | + | 0.733054i | \(0.261906\pi\) | |||||||
\(138\) | −12.1229 | −1.03197 | ||||||||
\(139\) | 2.19073 | 0.185816 | 0.0929078 | − | 0.995675i | \(-0.470384\pi\) | ||||
0.0929078 | + | 0.995675i | \(0.470384\pi\) | |||||||
\(140\) | 1.13953 | 0.0963075 | ||||||||
\(141\) | −21.4463 | −1.80611 | ||||||||
\(142\) | 11.2141 | 0.941065 | ||||||||
\(143\) | −23.3679 | −1.95412 | ||||||||
\(144\) | −6.82659 | −0.568883 | ||||||||
\(145\) | −12.0634 | −1.00181 | ||||||||
\(146\) | 20.2934 | 1.67949 | ||||||||
\(147\) | 14.3010 | 1.17953 | ||||||||
\(148\) | −9.17695 | −0.754341 | ||||||||
\(149\) | 15.1567 | 1.24169 | 0.620843 | − | 0.783935i | \(-0.286791\pi\) | ||||
0.620843 | + | 0.783935i | \(0.286791\pi\) | |||||||
\(150\) | 0.563474 | 0.0460075 | ||||||||
\(151\) | 1.44767 | 0.117810 | 0.0589050 | − | 0.998264i | \(-0.481239\pi\) | ||||
0.0589050 | + | 0.998264i | \(0.481239\pi\) | |||||||
\(152\) | 9.09486 | 0.737690 | ||||||||
\(153\) | 1.37993 | 0.111560 | ||||||||
\(154\) | −3.89531 | −0.313893 | ||||||||
\(155\) | −18.3022 | −1.47007 | ||||||||
\(156\) | −11.3304 | −0.907158 | ||||||||
\(157\) | 14.7791 | 1.17950 | 0.589750 | − | 0.807586i | \(-0.299226\pi\) | ||||
0.589750 | + | 0.807586i | \(0.299226\pi\) | |||||||
\(158\) | −19.1200 | −1.52111 | ||||||||
\(159\) | 28.1028 | 2.22870 | ||||||||
\(160\) | −13.8962 | −1.09859 | ||||||||
\(161\) | 1.31574 | 0.103695 | ||||||||
\(162\) | 20.1930 | 1.58651 | ||||||||
\(163\) | −18.8295 | −1.47484 | −0.737420 | − | 0.675434i | \(-0.763956\pi\) | ||||
−0.737420 | + | 0.675434i | \(0.763956\pi\) | |||||||
\(164\) | 0.685818 | 0.0535534 | ||||||||
\(165\) | −25.2152 | −1.96300 | ||||||||
\(166\) | 13.3068 | 1.03281 | ||||||||
\(167\) | −2.98946 | −0.231331 | −0.115666 | − | 0.993288i | \(-0.536900\pi\) | ||||
−0.115666 | + | 0.993288i | \(0.536900\pi\) | |||||||
\(168\) | 1.18223 | 0.0912108 | ||||||||
\(169\) | 6.37200 | 0.490154 | ||||||||
\(170\) | 4.07850 | 0.312807 | ||||||||
\(171\) | 9.06958 | 0.693568 | ||||||||
\(172\) | 9.42788 | 0.718869 | ||||||||
\(173\) | −19.2358 | −1.46247 | −0.731237 | − | 0.682123i | \(-0.761057\pi\) | ||||
−0.731237 | + | 0.682123i | \(0.761057\pi\) | |||||||
\(174\) | 19.9946 | 1.51579 | ||||||||
\(175\) | −0.0611561 | −0.00462296 | ||||||||
\(176\) | 26.2653 | 1.97982 | ||||||||
\(177\) | −2.09283 | −0.157307 | ||||||||
\(178\) | −14.2824 | −1.07051 | ||||||||
\(179\) | −14.0525 | −1.05033 | −0.525166 | − | 0.851000i | \(-0.675997\pi\) | ||||
−0.525166 | + | 0.851000i | \(0.675997\pi\) | |||||||
\(180\) | −3.85191 | −0.287104 | ||||||||
\(181\) | −15.0117 | −1.11581 | −0.557905 | − | 0.829905i | \(-0.688395\pi\) | ||||
−0.557905 | + | 0.829905i | \(0.688395\pi\) | |||||||
\(182\) | 3.22921 | 0.239365 | ||||||||
\(183\) | −5.57723 | −0.412281 | ||||||||
\(184\) | −4.45996 | −0.328793 | ||||||||
\(185\) | 16.9305 | 1.24475 | ||||||||
\(186\) | 30.3351 | 2.22428 | ||||||||
\(187\) | −5.30925 | −0.388251 | ||||||||
\(188\) | 12.6051 | 0.919318 | ||||||||
\(189\) | −1.38411 | −0.100680 | ||||||||
\(190\) | 26.8060 | 1.94471 | ||||||||
\(191\) | 8.34634 | 0.603920 | 0.301960 | − | 0.953321i | \(-0.402359\pi\) | ||||
0.301960 | + | 0.953321i | \(0.402359\pi\) | |||||||
\(192\) | 2.32566 | 0.167840 | ||||||||
\(193\) | 24.6445 | 1.77395 | 0.886975 | − | 0.461818i | \(-0.152803\pi\) | ||||
0.886975 | + | 0.461818i | \(0.152803\pi\) | |||||||
\(194\) | 17.9957 | 1.29201 | ||||||||
\(195\) | 20.9034 | 1.49692 | ||||||||
\(196\) | −8.40540 | −0.600386 | ||||||||
\(197\) | −14.1500 | −1.00815 | −0.504073 | − | 0.863661i | \(-0.668166\pi\) | ||||
−0.504073 | + | 0.863661i | \(0.668166\pi\) | |||||||
\(198\) | 13.1672 | 0.935753 | ||||||||
\(199\) | 2.23545 | 0.158467 | 0.0792335 | − | 0.996856i | \(-0.474753\pi\) | ||||
0.0792335 | + | 0.996856i | \(0.474753\pi\) | |||||||
\(200\) | 0.207300 | 0.0146583 | ||||||||
\(201\) | 16.7301 | 1.18005 | ||||||||
\(202\) | 24.2609 | 1.70699 | ||||||||
\(203\) | −2.17009 | −0.152311 | ||||||||
\(204\) | −2.57429 | −0.180237 | ||||||||
\(205\) | −1.26526 | −0.0883696 | ||||||||
\(206\) | −21.5580 | −1.50201 | ||||||||
\(207\) | −4.44756 | −0.309127 | ||||||||
\(208\) | −21.7739 | −1.50975 | ||||||||
\(209\) | −34.8951 | −2.41375 | ||||||||
\(210\) | 3.48448 | 0.240452 | ||||||||
\(211\) | 22.8014 | 1.56971 | 0.784857 | − | 0.619678i | \(-0.212737\pi\) | ||||
0.784857 | + | 0.619678i | \(0.212737\pi\) | |||||||
\(212\) | −16.5174 | −1.13442 | ||||||||
\(213\) | 13.0585 | 0.894751 | ||||||||
\(214\) | 14.4624 | 0.988626 | ||||||||
\(215\) | −17.3934 | −1.18622 | ||||||||
\(216\) | 4.69173 | 0.319231 | ||||||||
\(217\) | −3.29239 | −0.223502 | ||||||||
\(218\) | 16.7774 | 1.13631 | ||||||||
\(219\) | 23.6310 | 1.59684 | ||||||||
\(220\) | 14.8202 | 0.999176 | ||||||||
\(221\) | 4.40136 | 0.296068 | ||||||||
\(222\) | −28.0616 | −1.88337 | ||||||||
\(223\) | 5.42718 | 0.363431 | 0.181715 | − | 0.983351i | \(-0.441835\pi\) | ||||
0.181715 | + | 0.983351i | \(0.441835\pi\) | |||||||
\(224\) | −2.49980 | −0.167025 | ||||||||
\(225\) | 0.206724 | 0.0137816 | ||||||||
\(226\) | 0.929574 | 0.0618344 | ||||||||
\(227\) | −20.0954 | −1.33378 | −0.666890 | − | 0.745156i | \(-0.732375\pi\) | ||||
−0.666890 | + | 0.745156i | \(0.732375\pi\) | |||||||
\(228\) | −16.9196 | −1.12053 | ||||||||
\(229\) | −10.7871 | −0.712831 | −0.356415 | − | 0.934328i | \(-0.616001\pi\) | ||||
−0.356415 | + | 0.934328i | \(0.616001\pi\) | |||||||
\(230\) | −13.1452 | −0.866769 | ||||||||
\(231\) | −4.53597 | −0.298445 | ||||||||
\(232\) | 7.35595 | 0.482942 | ||||||||
\(233\) | −7.83103 | −0.513028 | −0.256514 | − | 0.966541i | \(-0.582574\pi\) | ||||
−0.256514 | + | 0.966541i | \(0.582574\pi\) | |||||||
\(234\) | −10.9156 | −0.713575 | ||||||||
\(235\) | −23.2549 | −1.51699 | ||||||||
\(236\) | 1.23006 | 0.0800698 | ||||||||
\(237\) | −22.2647 | −1.44625 | ||||||||
\(238\) | 0.733683 | 0.0475576 | ||||||||
\(239\) | 10.0166 | 0.647919 | 0.323960 | − | 0.946071i | \(-0.394986\pi\) | ||||
0.323960 | + | 0.946071i | \(0.394986\pi\) | |||||||
\(240\) | −23.4951 | −1.51660 | ||||||||
\(241\) | 26.5106 | 1.70769 | 0.853847 | − | 0.520523i | \(-0.174263\pi\) | ||||
0.853847 | + | 0.520523i | \(0.174263\pi\) | |||||||
\(242\) | −30.8911 | −1.98576 | ||||||||
\(243\) | 13.3425 | 0.855923 | ||||||||
\(244\) | 3.27801 | 0.209853 | ||||||||
\(245\) | 15.5070 | 0.990709 | ||||||||
\(246\) | 2.09712 | 0.133707 | ||||||||
\(247\) | 28.9280 | 1.84065 | ||||||||
\(248\) | 11.1602 | 0.708673 | ||||||||
\(249\) | 15.4954 | 0.981981 | ||||||||
\(250\) | −19.7815 | −1.25109 | ||||||||
\(251\) | 18.0754 | 1.14091 | 0.570456 | − | 0.821328i | \(-0.306767\pi\) | ||||
0.570456 | + | 0.821328i | \(0.306767\pi\) | |||||||
\(252\) | −0.692922 | −0.0436500 | ||||||||
\(253\) | 17.1120 | 1.07582 | ||||||||
\(254\) | 29.2994 | 1.83841 | ||||||||
\(255\) | 4.74929 | 0.297412 | ||||||||
\(256\) | 20.6439 | 1.29024 | ||||||||
\(257\) | −21.7862 | −1.35899 | −0.679493 | − | 0.733682i | \(-0.737800\pi\) | ||||
−0.679493 | + | 0.733682i | \(0.737800\pi\) | |||||||
\(258\) | 28.8289 | 1.79481 | ||||||||
\(259\) | 3.04563 | 0.189246 | ||||||||
\(260\) | −12.2859 | −0.761940 | ||||||||
\(261\) | 7.33551 | 0.454056 | ||||||||
\(262\) | 0.694224 | 0.0428893 | ||||||||
\(263\) | 15.2245 | 0.938784 | 0.469392 | − | 0.882990i | \(-0.344473\pi\) | ||||
0.469392 | + | 0.882990i | \(0.344473\pi\) | |||||||
\(264\) | 15.3755 | 0.946300 | ||||||||
\(265\) | 30.4728 | 1.87193 | ||||||||
\(266\) | 4.82215 | 0.295665 | ||||||||
\(267\) | −16.6315 | −1.01783 | ||||||||
\(268\) | −9.83311 | −0.600653 | ||||||||
\(269\) | 9.27880 | 0.565738 | 0.282869 | − | 0.959159i | \(-0.408714\pi\) | ||||
0.282869 | + | 0.959159i | \(0.408714\pi\) | |||||||
\(270\) | 13.8283 | 0.841564 | ||||||||
\(271\) | −0.801732 | −0.0487017 | −0.0243509 | − | 0.999703i | \(-0.507752\pi\) | ||||
−0.0243509 | + | 0.999703i | \(0.507752\pi\) | |||||||
\(272\) | −4.94707 | −0.299960 | ||||||||
\(273\) | 3.76031 | 0.227585 | ||||||||
\(274\) | −28.6163 | −1.72877 | ||||||||
\(275\) | −0.795370 | −0.0479626 | ||||||||
\(276\) | 8.29707 | 0.499425 | ||||||||
\(277\) | 0.776227 | 0.0466389 | 0.0233195 | − | 0.999728i | \(-0.492577\pi\) | ||||
0.0233195 | + | 0.999728i | \(0.492577\pi\) | |||||||
\(278\) | −3.93727 | −0.236142 | ||||||||
\(279\) | 11.1292 | 0.666286 | ||||||||
\(280\) | 1.28193 | 0.0766098 | ||||||||
\(281\) | −9.76558 | −0.582566 | −0.291283 | − | 0.956637i | \(-0.594082\pi\) | ||||
−0.291283 | + | 0.956637i | \(0.594082\pi\) | |||||||
\(282\) | 38.5441 | 2.29527 | ||||||||
\(283\) | 15.9857 | 0.950251 | 0.475126 | − | 0.879918i | \(-0.342403\pi\) | ||||
0.475126 | + | 0.879918i | \(0.342403\pi\) | |||||||
\(284\) | −7.67509 | −0.455433 | ||||||||
\(285\) | 31.2148 | 1.84901 | ||||||||
\(286\) | 41.9977 | 2.48338 | ||||||||
\(287\) | −0.227608 | −0.0134353 | ||||||||
\(288\) | 8.45000 | 0.497921 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 21.6808 | 1.27314 | ||||||||
\(291\) | 20.9554 | 1.22843 | ||||||||
\(292\) | −13.8891 | −0.812799 | ||||||||
\(293\) | −26.0983 | −1.52468 | −0.762339 | − | 0.647178i | \(-0.775949\pi\) | ||||
−0.762339 | + | 0.647178i | \(0.775949\pi\) | |||||||
\(294\) | −25.7023 | −1.49899 | ||||||||
\(295\) | −2.26932 | −0.132125 | ||||||||
\(296\) | −10.3238 | −0.600056 | ||||||||
\(297\) | −18.0012 | −1.04454 | ||||||||
\(298\) | −27.2402 | −1.57798 | ||||||||
\(299\) | −14.1858 | −0.820386 | ||||||||
\(300\) | −0.385651 | −0.0222656 | ||||||||
\(301\) | −3.12891 | −0.180347 | ||||||||
\(302\) | −2.60181 | −0.149717 | ||||||||
\(303\) | 28.2511 | 1.62298 | ||||||||
\(304\) | −32.5147 | −1.86485 | ||||||||
\(305\) | −6.04757 | −0.346283 | ||||||||
\(306\) | −2.48005 | −0.141775 | ||||||||
\(307\) | 6.13677 | 0.350244 | 0.175122 | − | 0.984547i | \(-0.443968\pi\) | ||||
0.175122 | + | 0.984547i | \(0.443968\pi\) | |||||||
\(308\) | 2.66601 | 0.151910 | ||||||||
\(309\) | −25.1036 | −1.42809 | ||||||||
\(310\) | 32.8933 | 1.86822 | ||||||||
\(311\) | 29.9029 | 1.69564 | 0.847819 | − | 0.530285i | \(-0.177915\pi\) | ||||
0.847819 | + | 0.530285i | \(0.177915\pi\) | |||||||
\(312\) | −12.7463 | −0.721618 | ||||||||
\(313\) | −35.2016 | −1.98971 | −0.994857 | − | 0.101293i | \(-0.967702\pi\) | ||||
−0.994857 | + | 0.101293i | \(0.967702\pi\) | |||||||
\(314\) | −26.5615 | −1.49895 | ||||||||
\(315\) | 1.27836 | 0.0720277 | ||||||||
\(316\) | 13.0860 | 0.736147 | ||||||||
\(317\) | 6.02594 | 0.338451 | 0.169225 | − | 0.985577i | \(-0.445873\pi\) | ||||
0.169225 | + | 0.985577i | \(0.445873\pi\) | |||||||
\(318\) | −50.5074 | −2.83231 | ||||||||
\(319\) | −28.2233 | −1.58020 | ||||||||
\(320\) | 2.52179 | 0.140972 | ||||||||
\(321\) | 16.8410 | 0.939972 | ||||||||
\(322\) | −2.36470 | −0.131779 | ||||||||
\(323\) | 6.57252 | 0.365705 | ||||||||
\(324\) | −13.8204 | −0.767800 | ||||||||
\(325\) | 0.659361 | 0.0365748 | ||||||||
\(326\) | 33.8411 | 1.87428 | ||||||||
\(327\) | 19.5368 | 1.08039 | ||||||||
\(328\) | 0.771522 | 0.0426002 | ||||||||
\(329\) | −4.18334 | −0.230635 | ||||||||
\(330\) | 45.3176 | 2.49465 | ||||||||
\(331\) | −26.4681 | −1.45482 | −0.727409 | − | 0.686204i | \(-0.759276\pi\) | ||||
−0.727409 | + | 0.686204i | \(0.759276\pi\) | |||||||
\(332\) | −9.10740 | −0.499833 | ||||||||
\(333\) | −10.2951 | −0.564166 | ||||||||
\(334\) | 5.37277 | 0.293985 | ||||||||
\(335\) | 18.1410 | 0.991150 | ||||||||
\(336\) | −4.22654 | −0.230577 | ||||||||
\(337\) | −7.25909 | −0.395428 | −0.197714 | − | 0.980260i | \(-0.563352\pi\) | ||||
−0.197714 | + | 0.980260i | \(0.563352\pi\) | |||||||
\(338\) | −11.4520 | −0.622906 | ||||||||
\(339\) | 1.08246 | 0.0587912 | ||||||||
\(340\) | −2.79139 | −0.151384 | ||||||||
\(341\) | −42.8194 | −2.31880 | ||||||||
\(342\) | −16.3002 | −0.881413 | ||||||||
\(343\) | 5.64717 | 0.304919 | ||||||||
\(344\) | 10.6060 | 0.571839 | ||||||||
\(345\) | −15.3072 | −0.824112 | ||||||||
\(346\) | 34.5714 | 1.85857 | ||||||||
\(347\) | −32.6943 | −1.75512 | −0.877561 | − | 0.479465i | \(-0.840831\pi\) | ||||
−0.877561 | + | 0.479465i | \(0.840831\pi\) | |||||||
\(348\) | −13.6846 | −0.733573 | ||||||||
\(349\) | −25.5156 | −1.36582 | −0.682911 | − | 0.730502i | \(-0.739286\pi\) | ||||
−0.682911 | + | 0.730502i | \(0.739286\pi\) | |||||||
\(350\) | 0.109912 | 0.00587503 | ||||||||
\(351\) | 14.9230 | 0.796530 | ||||||||
\(352\) | −32.5113 | −1.73286 | ||||||||
\(353\) | −15.9141 | −0.847021 | −0.423510 | − | 0.905891i | \(-0.639202\pi\) | ||||
−0.423510 | + | 0.905891i | \(0.639202\pi\) | |||||||
\(354\) | 3.76130 | 0.199911 | ||||||||
\(355\) | 14.1597 | 0.751519 | ||||||||
\(356\) | 9.77512 | 0.518080 | ||||||||
\(357\) | 0.854352 | 0.0452171 | ||||||||
\(358\) | 25.2556 | 1.33480 | ||||||||
\(359\) | −24.6043 | −1.29856 | −0.649282 | − | 0.760548i | \(-0.724930\pi\) | ||||
−0.649282 | + | 0.760548i | \(0.724930\pi\) | |||||||
\(360\) | −4.33327 | −0.228383 | ||||||||
\(361\) | 24.1980 | 1.27358 | ||||||||
\(362\) | 26.9795 | 1.41801 | ||||||||
\(363\) | −35.9718 | −1.88803 | ||||||||
\(364\) | −2.21012 | −0.115842 | ||||||||
\(365\) | 25.6239 | 1.34122 | ||||||||
\(366\) | 10.0236 | 0.523942 | ||||||||
\(367\) | −28.9531 | −1.51134 | −0.755670 | − | 0.654952i | \(-0.772689\pi\) | ||||
−0.755670 | + | 0.654952i | \(0.772689\pi\) | |||||||
\(368\) | 15.9447 | 0.831173 | ||||||||
\(369\) | 0.769378 | 0.0400522 | ||||||||
\(370\) | −30.4280 | −1.58188 | ||||||||
\(371\) | 5.48176 | 0.284599 | ||||||||
\(372\) | −20.7618 | −1.07645 | ||||||||
\(373\) | −10.8727 | −0.562966 | −0.281483 | − | 0.959566i | \(-0.590826\pi\) | ||||
−0.281483 | + | 0.959566i | \(0.590826\pi\) | |||||||
\(374\) | 9.54197 | 0.493404 | ||||||||
\(375\) | −23.0350 | −1.18952 | ||||||||
\(376\) | 14.1803 | 0.731291 | ||||||||
\(377\) | 23.3971 | 1.20501 | ||||||||
\(378\) | 2.48758 | 0.127947 | ||||||||
\(379\) | −22.9098 | −1.17680 | −0.588399 | − | 0.808570i | \(-0.700242\pi\) | ||||
−0.588399 | + | 0.808570i | \(0.700242\pi\) | |||||||
\(380\) | −18.3465 | −0.941153 | ||||||||
\(381\) | 34.1182 | 1.74793 | ||||||||
\(382\) | −15.0003 | −0.767484 | ||||||||
\(383\) | 23.4323 | 1.19734 | 0.598668 | − | 0.800997i | \(-0.295697\pi\) | ||||
0.598668 | + | 0.800997i | \(0.295697\pi\) | |||||||
\(384\) | 21.4512 | 1.09467 | ||||||||
\(385\) | −4.91850 | −0.250670 | ||||||||
\(386\) | −44.2920 | −2.25440 | ||||||||
\(387\) | 10.5766 | 0.537637 | ||||||||
\(388\) | −12.3165 | −0.625276 | ||||||||
\(389\) | −5.62843 | −0.285373 | −0.142686 | − | 0.989768i | \(-0.545574\pi\) | ||||
−0.142686 | + | 0.989768i | \(0.545574\pi\) | |||||||
\(390\) | −37.5683 | −1.90234 | ||||||||
\(391\) | −3.22305 | −0.162997 | ||||||||
\(392\) | −9.45579 | −0.477589 | ||||||||
\(393\) | 0.808403 | 0.0407785 | ||||||||
\(394\) | 25.4309 | 1.28119 | ||||||||
\(395\) | −24.1423 | −1.21473 | ||||||||
\(396\) | −9.01184 | −0.452862 | ||||||||
\(397\) | 0.711987 | 0.0357336 | 0.0178668 | − | 0.999840i | \(-0.494313\pi\) | ||||
0.0178668 | + | 0.999840i | \(0.494313\pi\) | |||||||
\(398\) | −4.01763 | −0.201386 | ||||||||
\(399\) | 5.61525 | 0.281114 | ||||||||
\(400\) | −0.741113 | −0.0370556 | ||||||||
\(401\) | 24.4706 | 1.22200 | 0.611001 | − | 0.791630i | \(-0.290767\pi\) | ||||
0.611001 | + | 0.791630i | \(0.290767\pi\) | |||||||
\(402\) | −30.0680 | −1.49966 | ||||||||
\(403\) | 35.4972 | 1.76824 | ||||||||
\(404\) | −16.6045 | −0.826105 | ||||||||
\(405\) | 25.4971 | 1.26696 | ||||||||
\(406\) | 3.90017 | 0.193562 | ||||||||
\(407\) | 39.6102 | 1.96340 | ||||||||
\(408\) | −2.89599 | −0.143373 | ||||||||
\(409\) | −30.3699 | −1.50170 | −0.750848 | − | 0.660475i | \(-0.770355\pi\) | ||||
−0.750848 | + | 0.660475i | \(0.770355\pi\) | |||||||
\(410\) | 2.27397 | 0.112303 | ||||||||
\(411\) | −33.3228 | −1.64369 | ||||||||
\(412\) | 14.7546 | 0.726907 | ||||||||
\(413\) | −0.408229 | −0.0200876 | ||||||||
\(414\) | 7.99332 | 0.392850 | ||||||||
\(415\) | 16.8021 | 0.824785 | ||||||||
\(416\) | 26.9518 | 1.32142 | ||||||||
\(417\) | −4.58483 | −0.224520 | ||||||||
\(418\) | 62.7148 | 3.06748 | ||||||||
\(419\) | −23.1375 | −1.13034 | −0.565171 | − | 0.824973i | \(-0.691190\pi\) | ||||
−0.565171 | + | 0.824973i | \(0.691190\pi\) | |||||||
\(420\) | −2.38483 | −0.116368 | ||||||||
\(421\) | 5.21432 | 0.254131 | 0.127065 | − | 0.991894i | \(-0.459444\pi\) | ||||
0.127065 | + | 0.991894i | \(0.459444\pi\) | |||||||
\(422\) | −40.9795 | −1.99485 | ||||||||
\(423\) | 14.1408 | 0.687552 | ||||||||
\(424\) | −18.5815 | −0.902397 | ||||||||
\(425\) | 0.149808 | 0.00726677 | ||||||||
\(426\) | −23.4691 | −1.13708 | ||||||||
\(427\) | −1.08790 | −0.0526472 | ||||||||
\(428\) | −9.89826 | −0.478450 | ||||||||
\(429\) | 48.9050 | 2.36116 | ||||||||
\(430\) | 31.2600 | 1.50749 | ||||||||
\(431\) | −4.52664 | −0.218041 | −0.109020 | − | 0.994040i | \(-0.534771\pi\) | ||||
−0.109020 | + | 0.994040i | \(0.534771\pi\) | |||||||
\(432\) | −16.7732 | −0.807003 | ||||||||
\(433\) | −17.8875 | −0.859618 | −0.429809 | − | 0.902920i | \(-0.641419\pi\) | ||||
−0.429809 | + | 0.902920i | \(0.641419\pi\) | |||||||
\(434\) | 5.91720 | 0.284034 | ||||||||
\(435\) | 25.2466 | 1.21048 | ||||||||
\(436\) | −11.4827 | −0.549922 | ||||||||
\(437\) | −21.1835 | −1.01335 | ||||||||
\(438\) | −42.4706 | −2.02932 | ||||||||
\(439\) | −31.1495 | −1.48668 | −0.743342 | − | 0.668911i | \(-0.766761\pi\) | ||||
−0.743342 | + | 0.668911i | \(0.766761\pi\) | |||||||
\(440\) | 16.6722 | 0.794816 | ||||||||
\(441\) | −9.42951 | −0.449024 | ||||||||
\(442\) | −7.91029 | −0.376254 | ||||||||
\(443\) | −15.7170 | −0.746736 | −0.373368 | − | 0.927683i | \(-0.621797\pi\) | ||||
−0.373368 | + | 0.927683i | \(0.621797\pi\) | |||||||
\(444\) | 19.2058 | 0.911466 | ||||||||
\(445\) | −18.0340 | −0.854895 | ||||||||
\(446\) | −9.75392 | −0.461862 | ||||||||
\(447\) | −31.7204 | −1.50032 | ||||||||
\(448\) | 0.453646 | 0.0214327 | ||||||||
\(449\) | −28.3350 | −1.33721 | −0.668605 | − | 0.743618i | \(-0.733108\pi\) | ||||
−0.668605 | + | 0.743618i | \(0.733108\pi\) | |||||||
\(450\) | −0.371532 | −0.0175142 | ||||||||
\(451\) | −2.96017 | −0.139389 | ||||||||
\(452\) | −0.636215 | −0.0299250 | ||||||||
\(453\) | −3.02973 | −0.142349 | ||||||||
\(454\) | 36.1162 | 1.69502 | ||||||||
\(455\) | 4.07743 | 0.191153 | ||||||||
\(456\) | −19.0340 | −0.891347 | ||||||||
\(457\) | 1.11900 | 0.0523446 | 0.0261723 | − | 0.999657i | \(-0.491668\pi\) | ||||
0.0261723 | + | 0.999657i | \(0.491668\pi\) | |||||||
\(458\) | 19.3869 | 0.905892 | ||||||||
\(459\) | 3.39054 | 0.158257 | ||||||||
\(460\) | 8.99678 | 0.419477 | ||||||||
\(461\) | 30.7432 | 1.43185 | 0.715927 | − | 0.698176i | \(-0.246004\pi\) | ||||
0.715927 | + | 0.698176i | \(0.246004\pi\) | |||||||
\(462\) | 8.15221 | 0.379275 | ||||||||
\(463\) | −1.62186 | −0.0753744 | −0.0376872 | − | 0.999290i | \(-0.511999\pi\) | ||||
−0.0376872 | + | 0.999290i | \(0.511999\pi\) | |||||||
\(464\) | −26.2980 | −1.22085 | ||||||||
\(465\) | 38.3033 | 1.77627 | ||||||||
\(466\) | 14.0742 | 0.651975 | ||||||||
\(467\) | 25.9946 | 1.20288 | 0.601442 | − | 0.798916i | \(-0.294593\pi\) | ||||
0.601442 | + | 0.798916i | \(0.294593\pi\) | |||||||
\(468\) | 7.47081 | 0.345338 | ||||||||
\(469\) | 3.26340 | 0.150690 | ||||||||
\(470\) | 41.7946 | 1.92784 | ||||||||
\(471\) | −30.9301 | −1.42518 | ||||||||
\(472\) | 1.38377 | 0.0636932 | ||||||||
\(473\) | −40.6932 | −1.87108 | ||||||||
\(474\) | 40.0149 | 1.83794 | ||||||||
\(475\) | 0.984618 | 0.0451774 | ||||||||
\(476\) | −0.502144 | −0.0230157 | ||||||||
\(477\) | −18.5299 | −0.848424 | ||||||||
\(478\) | −18.0022 | −0.823400 | ||||||||
\(479\) | 14.4383 | 0.659703 | 0.329851 | − | 0.944033i | \(-0.393001\pi\) | ||||
0.329851 | + | 0.944033i | \(0.393001\pi\) | |||||||
\(480\) | 29.0824 | 1.32742 | ||||||||
\(481\) | −32.8368 | −1.49723 | ||||||||
\(482\) | −47.6457 | −2.17020 | ||||||||
\(483\) | −2.75362 | −0.125294 | ||||||||
\(484\) | 21.1424 | 0.961016 | ||||||||
\(485\) | 22.7226 | 1.03178 | ||||||||
\(486\) | −23.9797 | −1.08774 | ||||||||
\(487\) | −6.25038 | −0.283232 | −0.141616 | − | 0.989922i | \(-0.545230\pi\) | ||||
−0.141616 | + | 0.989922i | \(0.545230\pi\) | |||||||
\(488\) | 3.68765 | 0.166932 | ||||||||
\(489\) | 39.4069 | 1.78204 | ||||||||
\(490\) | −27.8698 | −1.25903 | ||||||||
\(491\) | −28.9856 | −1.30810 | −0.654050 | − | 0.756451i | \(-0.726931\pi\) | ||||
−0.654050 | + | 0.756451i | \(0.726931\pi\) | |||||||
\(492\) | −1.43530 | −0.0647083 | ||||||||
\(493\) | 5.31587 | 0.239415 | ||||||||
\(494\) | −51.9905 | −2.33916 | ||||||||
\(495\) | 16.6259 | 0.747277 | ||||||||
\(496\) | −39.8984 | −1.79149 | ||||||||
\(497\) | 2.54720 | 0.114257 | ||||||||
\(498\) | −27.8489 | −1.24794 | ||||||||
\(499\) | 10.7084 | 0.479373 | 0.239686 | − | 0.970850i | \(-0.422955\pi\) | ||||
0.239686 | + | 0.970850i | \(0.422955\pi\) | |||||||
\(500\) | 13.5388 | 0.605472 | ||||||||
\(501\) | 6.25643 | 0.279517 | ||||||||
\(502\) | −32.4858 | −1.44991 | ||||||||
\(503\) | −35.2508 | −1.57175 | −0.785877 | − | 0.618383i | \(-0.787788\pi\) | ||||
−0.785877 | + | 0.618383i | \(0.787788\pi\) | |||||||
\(504\) | −0.779513 | −0.0347223 | ||||||||
\(505\) | 30.6335 | 1.36317 | ||||||||
\(506\) | −30.7542 | −1.36719 | ||||||||
\(507\) | −13.3355 | −0.592250 | ||||||||
\(508\) | −20.0529 | −0.889705 | ||||||||
\(509\) | 9.17040 | 0.406471 | 0.203235 | − | 0.979130i | \(-0.434854\pi\) | ||||
0.203235 | + | 0.979130i | \(0.434854\pi\) | |||||||
\(510\) | −8.53560 | −0.377963 | ||||||||
\(511\) | 4.60949 | 0.203912 | ||||||||
\(512\) | −16.6023 | −0.733723 | ||||||||
\(513\) | 22.2844 | 0.983879 | ||||||||
\(514\) | 39.1549 | 1.72705 | ||||||||
\(515\) | −27.2206 | −1.19948 | ||||||||
\(516\) | −19.7309 | −0.868605 | ||||||||
\(517\) | −54.4068 | −2.39281 | ||||||||
\(518\) | −5.47371 | −0.240501 | ||||||||
\(519\) | 40.2573 | 1.76710 | ||||||||
\(520\) | −13.8212 | −0.606101 | ||||||||
\(521\) | 38.8660 | 1.70275 | 0.851375 | − | 0.524558i | \(-0.175769\pi\) | ||||
0.851375 | + | 0.524558i | \(0.175769\pi\) | |||||||
\(522\) | −13.1836 | −0.577032 | ||||||||
\(523\) | −10.1174 | −0.442403 | −0.221202 | − | 0.975228i | \(-0.570998\pi\) | ||||
−0.221202 | + | 0.975228i | \(0.570998\pi\) | |||||||
\(524\) | −0.475138 | −0.0207565 | ||||||||
\(525\) | 0.127989 | 0.00558590 | ||||||||
\(526\) | −27.3621 | −1.19304 | ||||||||
\(527\) | 8.06505 | 0.351319 | ||||||||
\(528\) | −54.9686 | −2.39220 | ||||||||
\(529\) | −12.6120 | −0.548346 | ||||||||
\(530\) | −54.7667 | −2.37892 | ||||||||
\(531\) | 1.37993 | 0.0598837 | ||||||||
\(532\) | −3.30035 | −0.143088 | ||||||||
\(533\) | 2.45398 | 0.106294 | ||||||||
\(534\) | 29.8907 | 1.29350 | ||||||||
\(535\) | 18.2612 | 0.789501 | ||||||||
\(536\) | −11.0619 | −0.477802 | ||||||||
\(537\) | 29.4094 | 1.26911 | ||||||||
\(538\) | −16.6762 | −0.718962 | ||||||||
\(539\) | 36.2800 | 1.56269 | ||||||||
\(540\) | −9.46431 | −0.407279 | ||||||||
\(541\) | −10.3499 | −0.444976 | −0.222488 | − | 0.974935i | \(-0.571418\pi\) | ||||
−0.222488 | + | 0.974935i | \(0.571418\pi\) | |||||||
\(542\) | 1.44090 | 0.0618920 | ||||||||
\(543\) | 31.4169 | 1.34823 | ||||||||
\(544\) | 6.12352 | 0.262544 | ||||||||
\(545\) | 21.1843 | 0.907437 | ||||||||
\(546\) | −6.75817 | −0.289223 | ||||||||
\(547\) | −11.9498 | −0.510938 | −0.255469 | − | 0.966817i | \(-0.582230\pi\) | ||||
−0.255469 | + | 0.966817i | \(0.582230\pi\) | |||||||
\(548\) | 19.5854 | 0.836647 | ||||||||
\(549\) | 3.67740 | 0.156948 | ||||||||
\(550\) | 1.42947 | 0.0609527 | ||||||||
\(551\) | 34.9387 | 1.48844 | ||||||||
\(552\) | 9.33392 | 0.397278 | ||||||||
\(553\) | −4.34297 | −0.184682 | ||||||||
\(554\) | −1.39506 | −0.0592705 | ||||||||
\(555\) | −35.4325 | −1.50403 | ||||||||
\(556\) | 2.69473 | 0.114282 | ||||||||
\(557\) | −24.7373 | −1.04815 | −0.524077 | − | 0.851671i | \(-0.675590\pi\) | ||||
−0.524077 | + | 0.851671i | \(0.675590\pi\) | |||||||
\(558\) | −20.0017 | −0.846741 | ||||||||
\(559\) | 33.7347 | 1.42682 | ||||||||
\(560\) | −4.58298 | −0.193666 | ||||||||
\(561\) | 11.1113 | 0.469121 | ||||||||
\(562\) | 17.5511 | 0.740346 | ||||||||
\(563\) | 17.7673 | 0.748804 | 0.374402 | − | 0.927267i | \(-0.377848\pi\) | ||||
0.374402 | + | 0.927267i | \(0.377848\pi\) | |||||||
\(564\) | −26.3802 | −1.11081 | ||||||||
\(565\) | 1.17375 | 0.0493799 | ||||||||
\(566\) | −28.7301 | −1.20762 | ||||||||
\(567\) | 4.58669 | 0.192623 | ||||||||
\(568\) | −8.63422 | −0.362284 | ||||||||
\(569\) | −28.0317 | −1.17515 | −0.587575 | − | 0.809170i | \(-0.699917\pi\) | ||||
−0.587575 | + | 0.809170i | \(0.699917\pi\) | |||||||
\(570\) | −56.1004 | −2.34979 | ||||||||
\(571\) | −0.218760 | −0.00915482 | −0.00457741 | − | 0.999990i | \(-0.501457\pi\) | ||||
−0.00457741 | + | 0.999990i | \(0.501457\pi\) | |||||||
\(572\) | −28.7439 | −1.20184 | ||||||||
\(573\) | −17.4674 | −0.729713 | ||||||||
\(574\) | 0.409065 | 0.0170741 | ||||||||
\(575\) | −0.482839 | −0.0201358 | ||||||||
\(576\) | −1.53345 | −0.0638936 | ||||||||
\(577\) | 16.9609 | 0.706090 | 0.353045 | − | 0.935606i | \(-0.385146\pi\) | ||||
0.353045 | + | 0.935606i | \(0.385146\pi\) | |||||||
\(578\) | −1.79724 | −0.0747551 | ||||||||
\(579\) | −51.5767 | −2.14345 | ||||||||
\(580\) | −14.8387 | −0.616142 | ||||||||
\(581\) | 3.02255 | 0.125396 | ||||||||
\(582\) | −37.6618 | −1.56113 | ||||||||
\(583\) | 71.2934 | 2.95267 | ||||||||
\(584\) | −15.6248 | −0.646558 | ||||||||
\(585\) | −13.7828 | −0.569850 | ||||||||
\(586\) | 46.9048 | 1.93762 | ||||||||
\(587\) | 7.82542 | 0.322990 | 0.161495 | − | 0.986874i | \(-0.448369\pi\) | ||||
0.161495 | + | 0.986874i | \(0.448369\pi\) | |||||||
\(588\) | 17.5911 | 0.725443 | ||||||||
\(589\) | 53.0077 | 2.18414 | ||||||||
\(590\) | 4.07850 | 0.167909 | ||||||||
\(591\) | 29.6135 | 1.21814 | ||||||||
\(592\) | 36.9081 | 1.51691 | ||||||||
\(593\) | −20.3342 | −0.835025 | −0.417512 | − | 0.908671i | \(-0.637098\pi\) | ||||
−0.417512 | + | 0.908671i | \(0.637098\pi\) | |||||||
\(594\) | 32.3524 | 1.32744 | ||||||||
\(595\) | 0.926401 | 0.0379787 | ||||||||
\(596\) | 18.6436 | 0.763671 | ||||||||
\(597\) | −4.67841 | −0.191475 | ||||||||
\(598\) | 25.4952 | 1.04258 | ||||||||
\(599\) | −0.288963 | −0.0118067 | −0.00590335 | − | 0.999983i | \(-0.501879\pi\) | ||||
−0.00590335 | + | 0.999983i | \(0.501879\pi\) | |||||||
\(600\) | −0.433844 | −0.0177116 | ||||||||
\(601\) | 35.0164 | 1.42835 | 0.714174 | − | 0.699968i | \(-0.246802\pi\) | ||||
0.714174 | + | 0.699968i | \(0.246802\pi\) | |||||||
\(602\) | 5.62338 | 0.229192 | ||||||||
\(603\) | −11.0312 | −0.449224 | ||||||||
\(604\) | 1.78072 | 0.0724564 | ||||||||
\(605\) | −39.0053 | −1.58579 | ||||||||
\(606\) | −50.7738 | −2.06254 | ||||||||
\(607\) | 29.8372 | 1.21106 | 0.605528 | − | 0.795824i | \(-0.292962\pi\) | ||||
0.605528 | + | 0.795824i | \(0.292962\pi\) | |||||||
\(608\) | 40.2469 | 1.63223 | ||||||||
\(609\) | 4.54163 | 0.184036 | ||||||||
\(610\) | 10.8689 | 0.440069 | ||||||||
\(611\) | 45.1032 | 1.82468 | ||||||||
\(612\) | 1.69739 | 0.0686127 | ||||||||
\(613\) | −31.4163 | −1.26889 | −0.634447 | − | 0.772967i | \(-0.718772\pi\) | ||||
−0.634447 | + | 0.772967i | \(0.718772\pi\) | |||||||
\(614\) | −11.0292 | −0.445103 | ||||||||
\(615\) | 2.64797 | 0.106776 | ||||||||
\(616\) | 2.99917 | 0.120840 | ||||||||
\(617\) | −2.88720 | −0.116234 | −0.0581171 | − | 0.998310i | \(-0.518510\pi\) | ||||
−0.0581171 | + | 0.998310i | \(0.518510\pi\) | |||||||
\(618\) | 45.1171 | 1.81488 | ||||||||
\(619\) | 22.9640 | 0.923002 | 0.461501 | − | 0.887140i | \(-0.347311\pi\) | ||||
0.461501 | + | 0.887140i | \(0.347311\pi\) | |||||||
\(620\) | −22.5127 | −0.904132 | ||||||||
\(621\) | −10.9279 | −0.438520 | ||||||||
\(622\) | −53.7426 | −2.15488 | ||||||||
\(623\) | −3.24415 | −0.129974 | ||||||||
\(624\) | 45.5689 | 1.82422 | ||||||||
\(625\) | −25.7266 | −1.02906 | ||||||||
\(626\) | 63.2656 | 2.52860 | ||||||||
\(627\) | 73.0295 | 2.91652 | ||||||||
\(628\) | 18.1791 | 0.725426 | ||||||||
\(629\) | −7.46060 | −0.297473 | ||||||||
\(630\) | −2.29752 | −0.0915355 | ||||||||
\(631\) | 7.02466 | 0.279647 | 0.139824 | − | 0.990176i | \(-0.455346\pi\) | ||||
0.139824 | + | 0.990176i | \(0.455346\pi\) | |||||||
\(632\) | 14.7213 | 0.585583 | ||||||||
\(633\) | −47.7194 | −1.89668 | ||||||||
\(634\) | −10.8300 | −0.430116 | ||||||||
\(635\) | 36.9955 | 1.46812 | ||||||||
\(636\) | 34.5680 | 1.37071 | ||||||||
\(637\) | −30.0761 | −1.19166 | ||||||||
\(638\) | 50.7239 | 2.00818 | ||||||||
\(639\) | −8.61022 | −0.340615 | ||||||||
\(640\) | 23.2602 | 0.919439 | ||||||||
\(641\) | −14.8212 | −0.585401 | −0.292700 | − | 0.956204i | \(-0.594554\pi\) | ||||
−0.292700 | + | 0.956204i | \(0.594554\pi\) | |||||||
\(642\) | −30.2672 | −1.19455 | ||||||||
\(643\) | −13.5317 | −0.533637 | −0.266819 | − | 0.963747i | \(-0.585972\pi\) | ||||
−0.266819 | + | 0.963747i | \(0.585972\pi\) | |||||||
\(644\) | 1.61843 | 0.0637753 | ||||||||
\(645\) | 36.4014 | 1.43330 | ||||||||
\(646\) | −11.8124 | −0.464751 | ||||||||
\(647\) | −1.58681 | −0.0623840 | −0.0311920 | − | 0.999513i | \(-0.509930\pi\) | ||||
−0.0311920 | + | 0.999513i | \(0.509930\pi\) | |||||||
\(648\) | −15.5475 | −0.610762 | ||||||||
\(649\) | −5.30925 | −0.208406 | ||||||||
\(650\) | −1.18503 | −0.0464806 | ||||||||
\(651\) | 6.89040 | 0.270056 | ||||||||
\(652\) | −23.1613 | −0.907068 | ||||||||
\(653\) | −3.79245 | −0.148410 | −0.0742051 | − | 0.997243i | \(-0.523642\pi\) | ||||
−0.0742051 | + | 0.997243i | \(0.523642\pi\) | |||||||
\(654\) | −35.1122 | −1.37299 | ||||||||
\(655\) | 0.876577 | 0.0342507 | ||||||||
\(656\) | −2.75824 | −0.107691 | ||||||||
\(657\) | −15.5814 | −0.607887 | ||||||||
\(658\) | 7.51845 | 0.293100 | ||||||||
\(659\) | −14.3354 | −0.558429 | −0.279215 | − | 0.960229i | \(-0.590074\pi\) | ||||
−0.279215 | + | 0.960229i | \(0.590074\pi\) | |||||||
\(660\) | −31.0161 | −1.20730 | ||||||||
\(661\) | −32.8805 | −1.27890 | −0.639451 | − | 0.768832i | \(-0.720838\pi\) | ||||
−0.639451 | + | 0.768832i | \(0.720838\pi\) | |||||||
\(662\) | 47.5694 | 1.84884 | ||||||||
\(663\) | −9.21129 | −0.357737 | ||||||||
\(664\) | −10.2455 | −0.397603 | ||||||||
\(665\) | 6.08879 | 0.236113 | ||||||||
\(666\) | 18.5027 | 0.716963 | ||||||||
\(667\) | −17.1333 | −0.663404 | ||||||||
\(668\) | −3.67721 | −0.142275 | ||||||||
\(669\) | −11.3582 | −0.439132 | ||||||||
\(670\) | −32.6037 | −1.25959 | ||||||||
\(671\) | −14.1488 | −0.546207 | ||||||||
\(672\) | 5.23164 | 0.201815 | ||||||||
\(673\) | 12.7775 | 0.492536 | 0.246268 | − | 0.969202i | \(-0.420796\pi\) | ||||
0.246268 | + | 0.969202i | \(0.420796\pi\) | |||||||
\(674\) | 13.0463 | 0.502524 | ||||||||
\(675\) | 0.507930 | 0.0195503 | ||||||||
\(676\) | 7.83791 | 0.301458 | ||||||||
\(677\) | 11.3002 | 0.434301 | 0.217151 | − | 0.976138i | \(-0.430324\pi\) | ||||
0.217151 | + | 0.976138i | \(0.430324\pi\) | |||||||
\(678\) | −1.94544 | −0.0747141 | ||||||||
\(679\) | 4.08758 | 0.156867 | ||||||||
\(680\) | −3.14022 | −0.120422 | ||||||||
\(681\) | 42.0563 | 1.61160 | ||||||||
\(682\) | 76.9565 | 2.94682 | ||||||||
\(683\) | 34.4759 | 1.31918 | 0.659591 | − | 0.751625i | \(-0.270730\pi\) | ||||
0.659591 | + | 0.751625i | \(0.270730\pi\) | |||||||
\(684\) | 11.1561 | 0.426564 | ||||||||
\(685\) | −36.1329 | −1.38057 | ||||||||
\(686\) | −10.1493 | −0.387502 | ||||||||
\(687\) | 22.5755 | 0.861310 | ||||||||
\(688\) | −37.9173 | −1.44558 | ||||||||
\(689\) | −59.1022 | −2.25161 | ||||||||
\(690\) | 27.5106 | 1.04731 | ||||||||
\(691\) | −45.8225 | −1.74317 | −0.871586 | − | 0.490243i | \(-0.836908\pi\) | ||||
−0.871586 | + | 0.490243i | \(0.836908\pi\) | |||||||
\(692\) | −23.6612 | −0.899463 | ||||||||
\(693\) | 2.99083 | 0.113612 | ||||||||
\(694\) | 58.7594 | 2.23047 | ||||||||
\(695\) | −4.97148 | −0.188579 | ||||||||
\(696\) | −15.3947 | −0.583536 | ||||||||
\(697\) | 0.557550 | 0.0211187 | ||||||||
\(698\) | 45.8576 | 1.73574 | ||||||||
\(699\) | 16.3890 | 0.619889 | ||||||||
\(700\) | −0.0752254 | −0.00284325 | ||||||||
\(701\) | 36.1668 | 1.36600 | 0.683000 | − | 0.730418i | \(-0.260675\pi\) | ||||
0.683000 | + | 0.730418i | \(0.260675\pi\) | |||||||
\(702\) | −26.8201 | −1.01226 | ||||||||
\(703\) | −49.0349 | −1.84939 | ||||||||
\(704\) | 5.89992 | 0.222362 | ||||||||
\(705\) | 48.6686 | 1.83297 | ||||||||
\(706\) | 28.6013 | 1.07643 | ||||||||
\(707\) | 5.51068 | 0.207250 | ||||||||
\(708\) | −2.57429 | −0.0967479 | ||||||||
\(709\) | −14.9976 | −0.563248 | −0.281624 | − | 0.959525i | \(-0.590873\pi\) | ||||
−0.281624 | + | 0.959525i | \(0.590873\pi\) | |||||||
\(710\) | −25.4483 | −0.955059 | ||||||||
\(711\) | 14.6804 | 0.550559 | ||||||||
\(712\) | 10.9967 | 0.412118 | ||||||||
\(713\) | −25.9941 | −0.973485 | ||||||||
\(714\) | −1.53547 | −0.0574636 | ||||||||
\(715\) | 53.0293 | 1.98318 | ||||||||
\(716\) | −17.2853 | −0.645983 | ||||||||
\(717\) | −20.9630 | −0.782877 | ||||||||
\(718\) | 44.2197 | 1.65026 | ||||||||
\(719\) | 14.8293 | 0.553040 | 0.276520 | − | 0.961008i | \(-0.410819\pi\) | ||||
0.276520 | + | 0.961008i | \(0.410819\pi\) | |||||||
\(720\) | 15.4917 | 0.577342 | ||||||||
\(721\) | −4.89673 | −0.182364 | ||||||||
\(722\) | −43.4895 | −1.61851 | ||||||||
\(723\) | −55.4820 | −2.06340 | ||||||||
\(724\) | −18.4652 | −0.686254 | ||||||||
\(725\) | 0.796362 | 0.0295761 | ||||||||
\(726\) | 64.6498 | 2.39938 | ||||||||
\(727\) | 19.7502 | 0.732495 | 0.366248 | − | 0.930517i | \(-0.380642\pi\) | ||||
0.366248 | + | 0.930517i | \(0.380642\pi\) | |||||||
\(728\) | −2.48631 | −0.0921487 | ||||||||
\(729\) | 5.78315 | 0.214191 | ||||||||
\(730\) | −46.0522 | −1.70447 | ||||||||
\(731\) | 7.66459 | 0.283485 | ||||||||
\(732\) | −6.86031 | −0.253564 | ||||||||
\(733\) | −1.57449 | −0.0581551 | −0.0290775 | − | 0.999577i | \(-0.509257\pi\) | ||||
−0.0290775 | + | 0.999577i | \(0.509257\pi\) | |||||||
\(734\) | 52.0356 | 1.92067 | ||||||||
\(735\) | −32.4536 | −1.19707 | ||||||||
\(736\) | −19.7364 | −0.727493 | ||||||||
\(737\) | 42.4423 | 1.56338 | ||||||||
\(738\) | −1.38275 | −0.0508999 | ||||||||
\(739\) | 28.4966 | 1.04826 | 0.524132 | − | 0.851637i | \(-0.324390\pi\) | ||||
0.524132 | + | 0.851637i | \(0.324390\pi\) | |||||||
\(740\) | 20.8254 | 0.765558 | ||||||||
\(741\) | −60.5414 | −2.22404 | ||||||||
\(742\) | −9.85201 | −0.361679 | ||||||||
\(743\) | 24.9050 | 0.913676 | 0.456838 | − | 0.889550i | \(-0.348982\pi\) | ||||
0.456838 | + | 0.889550i | \(0.348982\pi\) | |||||||
\(744\) | −23.3563 | −0.856285 | ||||||||
\(745\) | −34.3954 | −1.26015 | ||||||||
\(746\) | 19.5408 | 0.715438 | ||||||||
\(747\) | −10.2170 | −0.373822 | ||||||||
\(748\) | −6.53067 | −0.238785 | ||||||||
\(749\) | 3.28502 | 0.120032 | ||||||||
\(750\) | 41.3993 | 1.51169 | ||||||||
\(751\) | 8.59795 | 0.313744 | 0.156872 | − | 0.987619i | \(-0.449859\pi\) | ||||
0.156872 | + | 0.987619i | \(0.449859\pi\) | |||||||
\(752\) | −50.6954 | −1.84867 | ||||||||
\(753\) | −37.8288 | −1.37856 | ||||||||
\(754\) | −42.0501 | −1.53137 | ||||||||
\(755\) | −3.28523 | −0.119562 | ||||||||
\(756\) | −1.70254 | −0.0619207 | ||||||||
\(757\) | 5.83207 | 0.211970 | 0.105985 | − | 0.994368i | \(-0.466200\pi\) | ||||
0.105985 | + | 0.994368i | \(0.466200\pi\) | |||||||
\(758\) | 41.1744 | 1.49552 | ||||||||
\(759\) | −35.8124 | −1.29991 | ||||||||
\(760\) | −20.6391 | −0.748660 | ||||||||
\(761\) | 6.51484 | 0.236163 | 0.118081 | − | 0.993004i | \(-0.462326\pi\) | ||||
0.118081 | + | 0.993004i | \(0.462326\pi\) | |||||||
\(762\) | −61.3185 | −2.22134 | ||||||||
\(763\) | 3.81086 | 0.137962 | ||||||||
\(764\) | 10.2665 | 0.371428 | ||||||||
\(765\) | −3.13149 | −0.113219 | ||||||||
\(766\) | −42.1134 | −1.52162 | ||||||||
\(767\) | 4.40136 | 0.158924 | ||||||||
\(768\) | −43.2041 | −1.55899 | ||||||||
\(769\) | −28.7287 | −1.03598 | −0.517991 | − | 0.855386i | \(-0.673320\pi\) | ||||
−0.517991 | + | 0.855386i | \(0.673320\pi\) | |||||||
\(770\) | 8.83969 | 0.318560 | ||||||||
\(771\) | 45.5947 | 1.64205 | ||||||||
\(772\) | 30.3141 | 1.09103 | ||||||||
\(773\) | −38.8799 | −1.39841 | −0.699206 | − | 0.714920i | \(-0.746463\pi\) | ||||
−0.699206 | + | 0.714920i | \(0.746463\pi\) | |||||||
\(774\) | −19.0086 | −0.683249 | ||||||||
\(775\) | 1.20821 | 0.0434003 | ||||||||
\(776\) | −13.8557 | −0.497389 | ||||||||
\(777\) | −6.37398 | −0.228665 | ||||||||
\(778\) | 10.1156 | 0.362663 | ||||||||
\(779\) | 3.66451 | 0.131295 | ||||||||
\(780\) | 25.7123 | 0.920648 | ||||||||
\(781\) | 33.1278 | 1.18540 | ||||||||
\(782\) | 5.79258 | 0.207142 | ||||||||
\(783\) | 18.0237 | 0.644113 | ||||||||
\(784\) | 33.8051 | 1.20732 | ||||||||
\(785\) | −33.5385 | −1.19704 | ||||||||
\(786\) | −1.45289 | −0.0518229 | ||||||||
\(787\) | −23.6692 | −0.843714 | −0.421857 | − | 0.906662i | \(-0.638622\pi\) | ||||
−0.421857 | + | 0.906662i | \(0.638622\pi\) | |||||||
\(788\) | −17.4053 | −0.620038 | ||||||||
\(789\) | −31.8623 | −1.13433 | ||||||||
\(790\) | 43.3894 | 1.54373 | ||||||||
\(791\) | 0.211146 | 0.00750748 | ||||||||
\(792\) | −10.1380 | −0.360239 | ||||||||
\(793\) | 11.7293 | 0.416520 | ||||||||
\(794\) | −1.27961 | −0.0454116 | ||||||||
\(795\) | −63.7742 | −2.26184 | ||||||||
\(796\) | 2.74973 | 0.0974616 | ||||||||
\(797\) | 14.9176 | 0.528407 | 0.264204 | − | 0.964467i | \(-0.414891\pi\) | ||||
0.264204 | + | 0.964467i | \(0.414891\pi\) | |||||||
\(798\) | −10.0919 | −0.357250 | ||||||||
\(799\) | 10.2475 | 0.362532 | ||||||||
\(800\) | 0.917354 | 0.0324333 | ||||||||
\(801\) | 10.9661 | 0.387469 | ||||||||
\(802\) | −43.9794 | −1.55297 | ||||||||
\(803\) | 59.9491 | 2.11556 | ||||||||
\(804\) | 20.5790 | 0.725765 | ||||||||
\(805\) | −2.98584 | −0.105237 | ||||||||
\(806\) | −63.7969 | −2.24715 | ||||||||
\(807\) | −19.4189 | −0.683578 | ||||||||
\(808\) | −18.6795 | −0.657143 | ||||||||
\(809\) | 25.5094 | 0.896863 | 0.448431 | − | 0.893817i | \(-0.351983\pi\) | ||||
0.448431 | + | 0.893817i | \(0.351983\pi\) | |||||||
\(810\) | −45.8243 | −1.61010 | ||||||||
\(811\) | −49.7245 | −1.74606 | −0.873032 | − | 0.487663i | \(-0.837849\pi\) | ||||
−0.873032 | + | 0.487663i | \(0.837849\pi\) | |||||||
\(812\) | −2.66933 | −0.0936753 | ||||||||
\(813\) | 1.67789 | 0.0588460 | ||||||||
\(814\) | −71.1888 | −2.49517 | ||||||||
\(815\) | 42.7301 | 1.49677 | ||||||||
\(816\) | 10.3534 | 0.362440 | ||||||||
\(817\) | 50.3757 | 1.76242 | ||||||||
\(818\) | 54.5819 | 1.90841 | ||||||||
\(819\) | −2.47940 | −0.0866372 | ||||||||
\(820\) | −1.55634 | −0.0543498 | ||||||||
\(821\) | −20.1530 | −0.703343 | −0.351672 | − | 0.936123i | \(-0.614387\pi\) | ||||
−0.351672 | + | 0.936123i | \(0.614387\pi\) | |||||||
\(822\) | 59.8889 | 2.08886 | ||||||||
\(823\) | 8.61139 | 0.300174 | 0.150087 | − | 0.988673i | \(-0.452045\pi\) | ||||
0.150087 | + | 0.988673i | \(0.452045\pi\) | |||||||
\(824\) | 16.5984 | 0.578234 | ||||||||
\(825\) | 1.66457 | 0.0579529 | ||||||||
\(826\) | 0.733683 | 0.0255281 | ||||||||
\(827\) | 14.4015 | 0.500790 | 0.250395 | − | 0.968144i | \(-0.419439\pi\) | ||||
0.250395 | + | 0.968144i | \(0.419439\pi\) | |||||||
\(828\) | −5.47075 | −0.190122 | ||||||||
\(829\) | −33.2471 | −1.15472 | −0.577359 | − | 0.816490i | \(-0.695917\pi\) | ||||
−0.577359 | + | 0.816490i | \(0.695917\pi\) | |||||||
\(830\) | −30.1974 | −1.04817 | ||||||||
\(831\) | −1.62451 | −0.0563536 | ||||||||
\(832\) | −4.89103 | −0.169566 | ||||||||
\(833\) | −6.83335 | −0.236762 | ||||||||
\(834\) | 8.24002 | 0.285328 | ||||||||
\(835\) | 6.78404 | 0.234771 | ||||||||
\(836\) | −42.9230 | −1.48452 | ||||||||
\(837\) | 27.3449 | 0.945177 | ||||||||
\(838\) | 41.5836 | 1.43648 | ||||||||
\(839\) | −25.8256 | −0.891597 | −0.445799 | − | 0.895133i | \(-0.647080\pi\) | ||||
−0.445799 | + | 0.895133i | \(0.647080\pi\) | |||||||
\(840\) | −2.68285 | −0.0925672 | ||||||||
\(841\) | −0.741505 | −0.0255692 | ||||||||
\(842\) | −9.37137 | −0.322959 | ||||||||
\(843\) | 20.4377 | 0.703911 | ||||||||
\(844\) | 28.0470 | 0.965417 | ||||||||
\(845\) | −14.4601 | −0.497442 | ||||||||
\(846\) | −25.4144 | −0.873766 | ||||||||
\(847\) | −7.01669 | −0.241096 | ||||||||
\(848\) | 66.4301 | 2.28122 | ||||||||
\(849\) | −33.4553 | −1.14818 | ||||||||
\(850\) | −0.269241 | −0.00923488 | ||||||||
\(851\) | 24.0459 | 0.824281 | ||||||||
\(852\) | 16.0626 | 0.550297 | ||||||||
\(853\) | −25.1851 | −0.862322 | −0.431161 | − | 0.902275i | \(-0.641896\pi\) | ||||
−0.431161 | + | 0.902275i | \(0.641896\pi\) | |||||||
\(854\) | 1.95521 | 0.0669060 | ||||||||
\(855\) | −20.5818 | −0.703882 | ||||||||
\(856\) | −11.1352 | −0.380593 | ||||||||
\(857\) | 51.4921 | 1.75894 | 0.879468 | − | 0.475958i | \(-0.157898\pi\) | ||||
0.879468 | + | 0.475958i | \(0.157898\pi\) | |||||||
\(858\) | −87.8939 | −3.00065 | ||||||||
\(859\) | −20.3915 | −0.695750 | −0.347875 | − | 0.937541i | \(-0.613097\pi\) | ||||
−0.347875 | + | 0.937541i | \(0.613097\pi\) | |||||||
\(860\) | −21.3949 | −0.729559 | ||||||||
\(861\) | 0.476344 | 0.0162338 | ||||||||
\(862\) | 8.13544 | 0.277094 | ||||||||
\(863\) | 8.20953 | 0.279456 | 0.139728 | − | 0.990190i | \(-0.455377\pi\) | ||||
0.139728 | + | 0.990190i | \(0.455377\pi\) | |||||||
\(864\) | 20.7620 | 0.706338 | ||||||||
\(865\) | 43.6523 | 1.48422 | ||||||||
\(866\) | 32.1480 | 1.09244 | ||||||||
\(867\) | −2.09283 | −0.0710761 | ||||||||
\(868\) | −4.04982 | −0.137460 | ||||||||
\(869\) | −56.4828 | −1.91605 | ||||||||
\(870\) | −45.3741 | −1.53833 | ||||||||
\(871\) | −35.1847 | −1.19219 | ||||||||
\(872\) | −12.9176 | −0.437447 | ||||||||
\(873\) | −13.8171 | −0.467640 | ||||||||
\(874\) | 38.0718 | 1.28780 | ||||||||
\(875\) | −4.49322 | −0.151899 | ||||||||
\(876\) | 29.0675 | 0.982100 | ||||||||
\(877\) | −23.0204 | −0.777344 | −0.388672 | − | 0.921376i | \(-0.627066\pi\) | ||||
−0.388672 | + | 0.921376i | \(0.627066\pi\) | |||||||
\(878\) | 55.9830 | 1.88933 | ||||||||
\(879\) | 54.6192 | 1.84226 | ||||||||
\(880\) | −59.6042 | −2.00926 | ||||||||
\(881\) | 45.7149 | 1.54018 | 0.770088 | − | 0.637938i | \(-0.220212\pi\) | ||||
0.770088 | + | 0.637938i | \(0.220212\pi\) | |||||||
\(882\) | 16.9471 | 0.570637 | ||||||||
\(883\) | 7.54632 | 0.253954 | 0.126977 | − | 0.991906i | \(-0.459473\pi\) | ||||
0.126977 | + | 0.991906i | \(0.459473\pi\) | |||||||
\(884\) | 5.41392 | 0.182090 | ||||||||
\(885\) | 4.74929 | 0.159646 | ||||||||
\(886\) | 28.2471 | 0.948980 | ||||||||
\(887\) | 30.7200 | 1.03148 | 0.515738 | − | 0.856746i | \(-0.327518\pi\) | ||||
0.515738 | + | 0.856746i | \(0.327518\pi\) | |||||||
\(888\) | 21.6058 | 0.725044 | ||||||||
\(889\) | 6.65513 | 0.223206 | ||||||||
\(890\) | 32.4114 | 1.08643 | ||||||||
\(891\) | 59.6525 | 1.99843 | ||||||||
\(892\) | 6.67574 | 0.223520 | ||||||||
\(893\) | 67.3522 | 2.25385 | ||||||||
\(894\) | 57.0090 | 1.90666 | ||||||||
\(895\) | 31.8896 | 1.06595 | ||||||||
\(896\) | 4.18428 | 0.139787 | ||||||||
\(897\) | 29.6884 | 0.991268 | ||||||||
\(898\) | 50.9246 | 1.69938 | ||||||||
\(899\) | 42.8728 | 1.42989 | ||||||||
\(900\) | 0.254282 | 0.00847608 | ||||||||
\(901\) | −13.4282 | −0.447357 | ||||||||
\(902\) | 5.32013 | 0.177141 | ||||||||
\(903\) | 6.54826 | 0.217913 | ||||||||
\(904\) | −0.715720 | −0.0238045 | ||||||||
\(905\) | 34.0663 | 1.13240 | ||||||||
\(906\) | 5.44514 | 0.180903 | ||||||||
\(907\) | 4.99822 | 0.165963 | 0.0829816 | − | 0.996551i | \(-0.473556\pi\) | ||||
0.0829816 | + | 0.996551i | \(0.473556\pi\) | |||||||
\(908\) | −24.7185 | −0.820312 | ||||||||
\(909\) | −18.6276 | −0.617838 | ||||||||
\(910\) | −7.32810 | −0.242924 | ||||||||
\(911\) | 31.8672 | 1.05581 | 0.527904 | − | 0.849304i | \(-0.322978\pi\) | ||||
0.527904 | + | 0.849304i | \(0.322978\pi\) | |||||||
\(912\) | 68.0477 | 2.25329 | ||||||||
\(913\) | 39.3099 | 1.30097 | ||||||||
\(914\) | −2.01111 | −0.0665215 | ||||||||
\(915\) | 12.6565 | 0.418411 | ||||||||
\(916\) | −13.2687 | −0.438411 | ||||||||
\(917\) | 0.157688 | 0.00520731 | ||||||||
\(918\) | −6.09359 | −0.201119 | ||||||||
\(919\) | −9.91638 | −0.327111 | −0.163556 | − | 0.986534i | \(-0.552296\pi\) | ||||
−0.163556 | + | 0.986534i | \(0.552296\pi\) | |||||||
\(920\) | 10.1211 | 0.333682 | ||||||||
\(921\) | −12.8432 | −0.423198 | ||||||||
\(922\) | −55.2528 | −1.81965 | ||||||||
\(923\) | −27.4629 | −0.903952 | ||||||||
\(924\) | −5.57950 | −0.183552 | ||||||||
\(925\) | −1.11766 | −0.0367484 | ||||||||
\(926\) | 2.91487 | 0.0957886 | ||||||||
\(927\) | 16.5523 | 0.543649 | ||||||||
\(928\) | 32.5518 | 1.06857 | ||||||||
\(929\) | 35.4484 | 1.16302 | 0.581512 | − | 0.813538i | \(-0.302461\pi\) | ||||
0.581512 | + | 0.813538i | \(0.302461\pi\) | |||||||
\(930\) | −68.8401 | −2.25735 | ||||||||
\(931\) | −44.9123 | −1.47194 | ||||||||
\(932\) | −9.63261 | −0.315527 | ||||||||
\(933\) | −62.5816 | −2.04883 | ||||||||
\(934\) | −46.7183 | −1.52867 | ||||||||
\(935\) | 12.0484 | 0.394024 | ||||||||
\(936\) | 8.40441 | 0.274707 | ||||||||
\(937\) | 59.5242 | 1.94457 | 0.972286 | − | 0.233794i | \(-0.0751141\pi\) | ||||
0.972286 | + | 0.233794i | \(0.0751141\pi\) | |||||||
\(938\) | −5.86509 | −0.191502 | ||||||||
\(939\) | 73.6709 | 2.40416 | ||||||||
\(940\) | −28.6049 | −0.932989 | ||||||||
\(941\) | −13.8932 | −0.452906 | −0.226453 | − | 0.974022i | \(-0.572713\pi\) | ||||
−0.226453 | + | 0.974022i | \(0.572713\pi\) | |||||||
\(942\) | 55.5887 | 1.81118 | ||||||||
\(943\) | −1.79701 | −0.0585187 | ||||||||
\(944\) | −4.94707 | −0.161014 | ||||||||
\(945\) | 3.14100 | 0.102177 | ||||||||
\(946\) | 73.1353 | 2.37783 | ||||||||
\(947\) | −35.4283 | −1.15126 | −0.575632 | − | 0.817709i | \(-0.695244\pi\) | ||||
−0.575632 | + | 0.817709i | \(0.695244\pi\) | |||||||
\(948\) | −27.3868 | −0.889482 | ||||||||
\(949\) | −49.6978 | −1.61326 | ||||||||
\(950\) | −1.76959 | −0.0574131 | ||||||||
\(951\) | −12.6113 | −0.408948 | ||||||||
\(952\) | −0.564895 | −0.0183084 | ||||||||
\(953\) | −33.6497 | −1.09002 | −0.545010 | − | 0.838430i | \(-0.683474\pi\) | ||||
−0.545010 | + | 0.838430i | \(0.683474\pi\) | |||||||
\(954\) | 33.3025 | 1.07821 | ||||||||
\(955\) | −18.9405 | −0.612900 | ||||||||
\(956\) | 12.3210 | 0.398489 | ||||||||
\(957\) | 59.0665 | 1.90935 | ||||||||
\(958\) | −25.9490 | −0.838375 | ||||||||
\(959\) | −6.49997 | −0.209895 | ||||||||
\(960\) | −5.27767 | −0.170336 | ||||||||
\(961\) | 34.0451 | 1.09823 | ||||||||
\(962\) | 59.0155 | 1.90273 | ||||||||
\(963\) | −11.1043 | −0.357830 | ||||||||
\(964\) | 32.6095 | 1.05028 | ||||||||
\(965\) | −55.9262 | −1.80033 | ||||||||
\(966\) | 4.94890 | 0.159228 | ||||||||
\(967\) | −15.8010 | −0.508125 | −0.254063 | − | 0.967188i | \(-0.581767\pi\) | ||||
−0.254063 | + | 0.967188i | \(0.581767\pi\) | |||||||
\(968\) | 23.7844 | 0.764461 | ||||||||
\(969\) | −13.7551 | −0.441879 | ||||||||
\(970\) | −40.8379 | −1.31123 | ||||||||
\(971\) | 43.9672 | 1.41097 | 0.705487 | − | 0.708723i | \(-0.250728\pi\) | ||||
0.705487 | + | 0.708723i | \(0.250728\pi\) | |||||||
\(972\) | 16.4120 | 0.526417 | ||||||||
\(973\) | −0.894321 | −0.0286706 | ||||||||
\(974\) | 11.2334 | 0.359942 | ||||||||
\(975\) | −1.37993 | −0.0441931 | ||||||||
\(976\) | −13.1836 | −0.421996 | ||||||||
\(977\) | 37.1651 | 1.18902 | 0.594508 | − | 0.804090i | \(-0.297347\pi\) | ||||
0.594508 | + | 0.804090i | \(0.297347\pi\) | |||||||
\(978\) | −70.8235 | −2.26469 | ||||||||
\(979\) | −42.1920 | −1.34846 | ||||||||
\(980\) | 19.0745 | 0.609314 | ||||||||
\(981\) | −12.8817 | −0.411282 | ||||||||
\(982\) | 52.0939 | 1.66238 | ||||||||
\(983\) | −19.5853 | −0.624674 | −0.312337 | − | 0.949971i | \(-0.601112\pi\) | ||||
−0.312337 | + | 0.949971i | \(0.601112\pi\) | |||||||
\(984\) | −1.61466 | −0.0514736 | ||||||||
\(985\) | 32.1109 | 1.02314 | ||||||||
\(986\) | −9.55387 | −0.304257 | ||||||||
\(987\) | 8.75501 | 0.278675 | ||||||||
\(988\) | 35.5831 | 1.13205 | ||||||||
\(989\) | −24.7033 | −0.785521 | ||||||||
\(990\) | −29.8806 | −0.949668 | ||||||||
\(991\) | −13.8116 | −0.438741 | −0.219371 | − | 0.975642i | \(-0.570400\pi\) | ||||
−0.219371 | + | 0.975642i | \(0.570400\pi\) | |||||||
\(992\) | 49.3865 | 1.56802 | ||||||||
\(993\) | 55.3932 | 1.75785 | ||||||||
\(994\) | −4.57791 | −0.145203 | ||||||||
\(995\) | −5.07295 | −0.160823 | ||||||||
\(996\) | 19.0602 | 0.603946 | ||||||||
\(997\) | −38.7439 | −1.22703 | −0.613515 | − | 0.789683i | \(-0.710245\pi\) | ||||
−0.613515 | + | 0.789683i | \(0.710245\pi\) | |||||||
\(998\) | −19.2455 | −0.609205 | ||||||||
\(999\) | −25.2954 | −0.800312 |
(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 | 1003.2.a.h.1.5 | ✓ | 16 | |
3.2 | odd | 2 | 9027.2.a.n.1.12 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1003.2.a.h.1.5 | ✓ | 16 | 1.1 | even | 1 | trivial | |
9027.2.a.n.1.12 | 16 | 3.2 | odd | 2 |