Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1518129839\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 4x^{8} - 9x^{7} + 45x^{6} + 7x^{5} - 123x^{4} + 37x^{3} + 87x^{2} - 54x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-1.25914\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.25914 | 0.563106 | 0.281553 | − | 0.959546i | \(-0.409150\pi\) | ||||
0.281553 | + | 0.959546i | \(0.409150\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −0.797445 | −0.301406 | −0.150703 | − | 0.988579i | \(-0.548154\pi\) | ||||
−0.150703 | + | 0.988579i | \(0.548154\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.25914 | 0.398176 | ||||||||
\(11\) | −2.98171 | −0.899020 | −0.449510 | − | 0.893275i | \(-0.648401\pi\) | ||||
−0.449510 | + | 0.893275i | \(0.648401\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −0.797445 | −0.213126 | ||||||||
\(15\) | −1.25914 | −0.325109 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.87471 | 1.18229 | 0.591146 | − | 0.806565i | \(-0.298676\pi\) | ||||
0.591146 | + | 0.806565i | \(0.298676\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −4.45274 | −1.02153 | −0.510764 | − | 0.859721i | \(-0.670637\pi\) | ||||
−0.510764 | + | 0.859721i | \(0.670637\pi\) | |||||||
\(20\) | 1.25914 | 0.281553 | ||||||||
\(21\) | 0.797445 | 0.174017 | ||||||||
\(22\) | −2.98171 | −0.635703 | ||||||||
\(23\) | 4.08918 | 0.852652 | 0.426326 | − | 0.904570i | \(-0.359808\pi\) | ||||
0.426326 | + | 0.904570i | \(0.359808\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −3.41456 | −0.682912 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.797445 | −0.150703 | ||||||||
\(29\) | −9.96702 | −1.85083 | −0.925415 | − | 0.378955i | \(-0.876283\pi\) | ||||
−0.925415 | + | 0.378955i | \(0.876283\pi\) | |||||||
\(30\) | −1.25914 | −0.229887 | ||||||||
\(31\) | 4.04763 | 0.726976 | 0.363488 | − | 0.931599i | \(-0.381586\pi\) | ||||
0.363488 | + | 0.931599i | \(0.381586\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.98171 | 0.519049 | ||||||||
\(34\) | 4.87471 | 0.836006 | ||||||||
\(35\) | −1.00410 | −0.169723 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −3.80662 | −0.625804 | −0.312902 | − | 0.949785i | \(-0.601301\pi\) | ||||
−0.312902 | + | 0.949785i | \(0.601301\pi\) | |||||||
\(38\) | −4.45274 | −0.722330 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 1.25914 | 0.199088 | ||||||||
\(41\) | −2.52399 | −0.394181 | −0.197091 | − | 0.980385i | \(-0.563149\pi\) | ||||
−0.197091 | + | 0.980385i | \(0.563149\pi\) | |||||||
\(42\) | 0.797445 | 0.123048 | ||||||||
\(43\) | −3.00371 | −0.458061 | −0.229031 | − | 0.973419i | \(-0.573556\pi\) | ||||
−0.229031 | + | 0.973419i | \(0.573556\pi\) | |||||||
\(44\) | −2.98171 | −0.449510 | ||||||||
\(45\) | 1.25914 | 0.187702 | ||||||||
\(46\) | 4.08918 | 0.602916 | ||||||||
\(47\) | −3.00222 | −0.437919 | −0.218959 | − | 0.975734i | \(-0.570266\pi\) | ||||
−0.218959 | + | 0.975734i | \(0.570266\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.36408 | −0.909155 | ||||||||
\(50\) | −3.41456 | −0.482891 | ||||||||
\(51\) | −4.87471 | −0.682596 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | −8.63309 | −1.18585 | −0.592923 | − | 0.805259i | \(-0.702026\pi\) | ||||
−0.592923 | + | 0.805259i | \(0.702026\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −3.75440 | −0.506243 | ||||||||
\(56\) | −0.797445 | −0.106563 | ||||||||
\(57\) | 4.45274 | 0.589780 | ||||||||
\(58\) | −9.96702 | −1.30873 | ||||||||
\(59\) | −6.72403 | −0.875394 | −0.437697 | − | 0.899123i | \(-0.644206\pi\) | ||||
−0.437697 | + | 0.899123i | \(0.644206\pi\) | |||||||
\(60\) | −1.25914 | −0.162555 | ||||||||
\(61\) | 4.06686 | 0.520708 | 0.260354 | − | 0.965513i | \(-0.416161\pi\) | ||||
0.260354 | + | 0.965513i | \(0.416161\pi\) | |||||||
\(62\) | 4.04763 | 0.514049 | ||||||||
\(63\) | −0.797445 | −0.100469 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.25914 | 0.156177 | ||||||||
\(66\) | 2.98171 | 0.367023 | ||||||||
\(67\) | 4.94082 | 0.603617 | 0.301808 | − | 0.953369i | \(-0.402410\pi\) | ||||
0.301808 | + | 0.953369i | \(0.402410\pi\) | |||||||
\(68\) | 4.87471 | 0.591146 | ||||||||
\(69\) | −4.08918 | −0.492279 | ||||||||
\(70\) | −1.00410 | −0.120013 | ||||||||
\(71\) | −1.94373 | −0.230679 | −0.115339 | − | 0.993326i | \(-0.536796\pi\) | ||||
−0.115339 | + | 0.993326i | \(0.536796\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −7.45502 | −0.872544 | −0.436272 | − | 0.899815i | \(-0.643702\pi\) | ||||
−0.436272 | + | 0.899815i | \(0.643702\pi\) | |||||||
\(74\) | −3.80662 | −0.442510 | ||||||||
\(75\) | 3.41456 | 0.394279 | ||||||||
\(76\) | −4.45274 | −0.510764 | ||||||||
\(77\) | 2.37775 | 0.270970 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | 14.1834 | 1.59576 | 0.797878 | − | 0.602819i | \(-0.205956\pi\) | ||||
0.797878 | + | 0.602819i | \(0.205956\pi\) | |||||||
\(80\) | 1.25914 | 0.140776 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.52399 | −0.278728 | ||||||||
\(83\) | 15.3797 | 1.68814 | 0.844068 | − | 0.536236i | \(-0.180154\pi\) | ||||
0.844068 | + | 0.536236i | \(0.180154\pi\) | |||||||
\(84\) | 0.797445 | 0.0870083 | ||||||||
\(85\) | 6.13796 | 0.665755 | ||||||||
\(86\) | −3.00371 | −0.323898 | ||||||||
\(87\) | 9.96702 | 1.06858 | ||||||||
\(88\) | −2.98171 | −0.317851 | ||||||||
\(89\) | 14.6866 | 1.55678 | 0.778389 | − | 0.627783i | \(-0.216037\pi\) | ||||
0.778389 | + | 0.627783i | \(0.216037\pi\) | |||||||
\(90\) | 1.25914 | 0.132725 | ||||||||
\(91\) | −0.797445 | −0.0835949 | ||||||||
\(92\) | 4.08918 | 0.426326 | ||||||||
\(93\) | −4.04763 | −0.419720 | ||||||||
\(94\) | −3.00222 | −0.309655 | ||||||||
\(95\) | −5.60664 | −0.575229 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −11.3927 | −1.15675 | −0.578376 | − | 0.815770i | \(-0.696313\pi\) | ||||
−0.578376 | + | 0.815770i | \(0.696313\pi\) | |||||||
\(98\) | −6.36408 | −0.642869 | ||||||||
\(99\) | −2.98171 | −0.299673 | ||||||||
\(100\) | −3.41456 | −0.341456 | ||||||||
\(101\) | −5.48924 | −0.546200 | −0.273100 | − | 0.961986i | \(-0.588049\pi\) | ||||
−0.273100 | + | 0.961986i | \(0.588049\pi\) | |||||||
\(102\) | −4.87471 | −0.482668 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 1.00410 | 0.0979898 | ||||||||
\(106\) | −8.63309 | −0.838520 | ||||||||
\(107\) | 3.92781 | 0.379716 | 0.189858 | − | 0.981812i | \(-0.439197\pi\) | ||||
0.189858 | + | 0.981812i | \(0.439197\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 11.9866 | 1.14810 | 0.574052 | − | 0.818819i | \(-0.305371\pi\) | ||||
0.574052 | + | 0.818819i | \(0.305371\pi\) | |||||||
\(110\) | −3.75440 | −0.357968 | ||||||||
\(111\) | 3.80662 | 0.361308 | ||||||||
\(112\) | −0.797445 | −0.0753514 | ||||||||
\(113\) | −6.53982 | −0.615215 | −0.307607 | − | 0.951513i | \(-0.599528\pi\) | ||||
−0.307607 | + | 0.951513i | \(0.599528\pi\) | |||||||
\(114\) | 4.45274 | 0.417037 | ||||||||
\(115\) | 5.14886 | 0.480134 | ||||||||
\(116\) | −9.96702 | −0.925415 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −6.72403 | −0.618997 | ||||||||
\(119\) | −3.88731 | −0.356349 | ||||||||
\(120\) | −1.25914 | −0.114944 | ||||||||
\(121\) | −2.10940 | −0.191764 | ||||||||
\(122\) | 4.06686 | 0.368196 | ||||||||
\(123\) | 2.52399 | 0.227581 | ||||||||
\(124\) | 4.04763 | 0.363488 | ||||||||
\(125\) | −10.5951 | −0.947658 | ||||||||
\(126\) | −0.797445 | −0.0710420 | ||||||||
\(127\) | 11.0198 | 0.977845 | 0.488923 | − | 0.872327i | \(-0.337390\pi\) | ||||
0.488923 | + | 0.872327i | \(0.337390\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.00371 | 0.264462 | ||||||||
\(130\) | 1.25914 | 0.110434 | ||||||||
\(131\) | −11.0610 | −0.966402 | −0.483201 | − | 0.875509i | \(-0.660526\pi\) | ||||
−0.483201 | + | 0.875509i | \(0.660526\pi\) | |||||||
\(132\) | 2.98171 | 0.259525 | ||||||||
\(133\) | 3.55081 | 0.307895 | ||||||||
\(134\) | 4.94082 | 0.426822 | ||||||||
\(135\) | −1.25914 | −0.108370 | ||||||||
\(136\) | 4.87471 | 0.418003 | ||||||||
\(137\) | −21.6808 | −1.85232 | −0.926159 | − | 0.377133i | \(-0.876910\pi\) | ||||
−0.926159 | + | 0.377133i | \(0.876910\pi\) | |||||||
\(138\) | −4.08918 | −0.348094 | ||||||||
\(139\) | −4.01573 | −0.340609 | −0.170305 | − | 0.985391i | \(-0.554475\pi\) | ||||
−0.170305 | + | 0.985391i | \(0.554475\pi\) | |||||||
\(140\) | −1.00410 | −0.0848617 | ||||||||
\(141\) | 3.00222 | 0.252833 | ||||||||
\(142\) | −1.94373 | −0.163114 | ||||||||
\(143\) | −2.98171 | −0.249343 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −12.5499 | −1.04221 | ||||||||
\(146\) | −7.45502 | −0.616982 | ||||||||
\(147\) | 6.36408 | 0.524901 | ||||||||
\(148\) | −3.80662 | −0.312902 | ||||||||
\(149\) | −18.0807 | −1.48123 | −0.740615 | − | 0.671930i | \(-0.765466\pi\) | ||||
−0.740615 | + | 0.671930i | \(0.765466\pi\) | |||||||
\(150\) | 3.41456 | 0.278798 | ||||||||
\(151\) | −9.37983 | −0.763320 | −0.381660 | − | 0.924303i | \(-0.624647\pi\) | ||||
−0.381660 | + | 0.924303i | \(0.624647\pi\) | |||||||
\(152\) | −4.45274 | −0.361165 | ||||||||
\(153\) | 4.87471 | 0.394097 | ||||||||
\(154\) | 2.37775 | 0.191605 | ||||||||
\(155\) | 5.09654 | 0.409364 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | −18.1379 | −1.44756 | −0.723780 | − | 0.690030i | \(-0.757597\pi\) | ||||
−0.723780 | + | 0.690030i | \(0.757597\pi\) | |||||||
\(158\) | 14.1834 | 1.12837 | ||||||||
\(159\) | 8.63309 | 0.684649 | ||||||||
\(160\) | 1.25914 | 0.0995440 | ||||||||
\(161\) | −3.26089 | −0.256994 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −15.9568 | −1.24983 | −0.624915 | − | 0.780693i | \(-0.714866\pi\) | ||||
−0.624915 | + | 0.780693i | \(0.714866\pi\) | |||||||
\(164\) | −2.52399 | −0.197091 | ||||||||
\(165\) | 3.75440 | 0.292280 | ||||||||
\(166\) | 15.3797 | 1.19369 | ||||||||
\(167\) | −21.4308 | −1.65836 | −0.829182 | − | 0.558979i | \(-0.811193\pi\) | ||||
−0.829182 | + | 0.558979i | \(0.811193\pi\) | |||||||
\(168\) | 0.797445 | 0.0615242 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 6.13796 | 0.470760 | ||||||||
\(171\) | −4.45274 | −0.340509 | ||||||||
\(172\) | −3.00371 | −0.229031 | ||||||||
\(173\) | −22.1020 | −1.68038 | −0.840192 | − | 0.542288i | \(-0.817558\pi\) | ||||
−0.840192 | + | 0.542288i | \(0.817558\pi\) | |||||||
\(174\) | 9.96702 | 0.755598 | ||||||||
\(175\) | 2.72292 | 0.205833 | ||||||||
\(176\) | −2.98171 | −0.224755 | ||||||||
\(177\) | 6.72403 | 0.505409 | ||||||||
\(178\) | 14.6866 | 1.10081 | ||||||||
\(179\) | 8.00632 | 0.598421 | 0.299210 | − | 0.954187i | \(-0.403277\pi\) | ||||
0.299210 | + | 0.954187i | \(0.403277\pi\) | |||||||
\(180\) | 1.25914 | 0.0938510 | ||||||||
\(181\) | −21.8618 | −1.62497 | −0.812487 | − | 0.582979i | \(-0.801887\pi\) | ||||
−0.812487 | + | 0.582979i | \(0.801887\pi\) | |||||||
\(182\) | −0.797445 | −0.0591105 | ||||||||
\(183\) | −4.06686 | −0.300631 | ||||||||
\(184\) | 4.08918 | 0.301458 | ||||||||
\(185\) | −4.79308 | −0.352394 | ||||||||
\(186\) | −4.04763 | −0.296787 | ||||||||
\(187\) | −14.5350 | −1.06290 | ||||||||
\(188\) | −3.00222 | −0.218959 | ||||||||
\(189\) | 0.797445 | 0.0580056 | ||||||||
\(190\) | −5.60664 | −0.406748 | ||||||||
\(191\) | 22.9946 | 1.66383 | 0.831915 | − | 0.554904i | \(-0.187245\pi\) | ||||
0.831915 | + | 0.554904i | \(0.187245\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 12.0887 | 0.870165 | 0.435083 | − | 0.900391i | \(-0.356719\pi\) | ||||
0.435083 | + | 0.900391i | \(0.356719\pi\) | |||||||
\(194\) | −11.3927 | −0.817948 | ||||||||
\(195\) | −1.25914 | −0.0901691 | ||||||||
\(196\) | −6.36408 | −0.454577 | ||||||||
\(197\) | −0.828221 | −0.0590083 | −0.0295042 | − | 0.999565i | \(-0.509393\pi\) | ||||
−0.0295042 | + | 0.999565i | \(0.509393\pi\) | |||||||
\(198\) | −2.98171 | −0.211901 | ||||||||
\(199\) | −16.9393 | −1.20080 | −0.600399 | − | 0.799701i | \(-0.704991\pi\) | ||||
−0.600399 | + | 0.799701i | \(0.704991\pi\) | |||||||
\(200\) | −3.41456 | −0.241446 | ||||||||
\(201\) | −4.94082 | −0.348498 | ||||||||
\(202\) | −5.48924 | −0.386222 | ||||||||
\(203\) | 7.94815 | 0.557851 | ||||||||
\(204\) | −4.87471 | −0.341298 | ||||||||
\(205\) | −3.17807 | −0.221966 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | 4.08918 | 0.284217 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 13.2768 | 0.918374 | ||||||||
\(210\) | 1.00410 | 0.0692893 | ||||||||
\(211\) | 26.7360 | 1.84058 | 0.920291 | − | 0.391235i | \(-0.127952\pi\) | ||||
0.920291 | + | 0.391235i | \(0.127952\pi\) | |||||||
\(212\) | −8.63309 | −0.592923 | ||||||||
\(213\) | 1.94373 | 0.133182 | ||||||||
\(214\) | 3.92781 | 0.268500 | ||||||||
\(215\) | −3.78210 | −0.257937 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −3.22776 | −0.219115 | ||||||||
\(218\) | 11.9866 | 0.811832 | ||||||||
\(219\) | 7.45502 | 0.503764 | ||||||||
\(220\) | −3.75440 | −0.253122 | ||||||||
\(221\) | 4.87471 | 0.327909 | ||||||||
\(222\) | 3.80662 | 0.255483 | ||||||||
\(223\) | 16.4842 | 1.10387 | 0.551933 | − | 0.833889i | \(-0.313891\pi\) | ||||
0.551933 | + | 0.833889i | \(0.313891\pi\) | |||||||
\(224\) | −0.797445 | −0.0532815 | ||||||||
\(225\) | −3.41456 | −0.227637 | ||||||||
\(226\) | −6.53982 | −0.435023 | ||||||||
\(227\) | 4.26467 | 0.283056 | 0.141528 | − | 0.989934i | \(-0.454798\pi\) | ||||
0.141528 | + | 0.989934i | \(0.454798\pi\) | |||||||
\(228\) | 4.45274 | 0.294890 | ||||||||
\(229\) | 21.0701 | 1.39235 | 0.696177 | − | 0.717870i | \(-0.254883\pi\) | ||||
0.696177 | + | 0.717870i | \(0.254883\pi\) | |||||||
\(230\) | 5.14886 | 0.339506 | ||||||||
\(231\) | −2.37775 | −0.156444 | ||||||||
\(232\) | −9.96702 | −0.654367 | ||||||||
\(233\) | 13.3803 | 0.876572 | 0.438286 | − | 0.898836i | \(-0.355586\pi\) | ||||
0.438286 | + | 0.898836i | \(0.355586\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | −3.78023 | −0.246595 | ||||||||
\(236\) | −6.72403 | −0.437697 | ||||||||
\(237\) | −14.1834 | −0.921310 | ||||||||
\(238\) | −3.88731 | −0.251977 | ||||||||
\(239\) | 29.5612 | 1.91215 | 0.956076 | − | 0.293118i | \(-0.0946930\pi\) | ||||
0.956076 | + | 0.293118i | \(0.0946930\pi\) | |||||||
\(240\) | −1.25914 | −0.0812773 | ||||||||
\(241\) | −2.85139 | −0.183674 | −0.0918371 | − | 0.995774i | \(-0.529274\pi\) | ||||
−0.0918371 | + | 0.995774i | \(0.529274\pi\) | |||||||
\(242\) | −2.10940 | −0.135597 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 4.06686 | 0.260354 | ||||||||
\(245\) | −8.01329 | −0.511950 | ||||||||
\(246\) | 2.52399 | 0.160924 | ||||||||
\(247\) | −4.45274 | −0.283321 | ||||||||
\(248\) | 4.04763 | 0.257025 | ||||||||
\(249\) | −15.3797 | −0.974646 | ||||||||
\(250\) | −10.5951 | −0.670095 | ||||||||
\(251\) | −17.9435 | −1.13258 | −0.566292 | − | 0.824205i | \(-0.691622\pi\) | ||||
−0.566292 | + | 0.824205i | \(0.691622\pi\) | |||||||
\(252\) | −0.797445 | −0.0502343 | ||||||||
\(253\) | −12.1927 | −0.766551 | ||||||||
\(254\) | 11.0198 | 0.691441 | ||||||||
\(255\) | −6.13796 | −0.384374 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.24943 | −0.265072 | −0.132536 | − | 0.991178i | \(-0.542312\pi\) | ||||
−0.132536 | + | 0.991178i | \(0.542312\pi\) | |||||||
\(258\) | 3.00371 | 0.187003 | ||||||||
\(259\) | 3.03557 | 0.188621 | ||||||||
\(260\) | 1.25914 | 0.0780887 | ||||||||
\(261\) | −9.96702 | −0.616943 | ||||||||
\(262\) | −11.0610 | −0.683350 | ||||||||
\(263\) | 13.4098 | 0.826881 | 0.413440 | − | 0.910531i | \(-0.364327\pi\) | ||||
0.413440 | + | 0.910531i | \(0.364327\pi\) | |||||||
\(264\) | 2.98171 | 0.183512 | ||||||||
\(265\) | −10.8703 | −0.667757 | ||||||||
\(266\) | 3.55081 | 0.217714 | ||||||||
\(267\) | −14.6866 | −0.898806 | ||||||||
\(268\) | 4.94082 | 0.301808 | ||||||||
\(269\) | 26.4982 | 1.61562 | 0.807811 | − | 0.589442i | \(-0.200652\pi\) | ||||
0.807811 | + | 0.589442i | \(0.200652\pi\) | |||||||
\(270\) | −1.25914 | −0.0766290 | ||||||||
\(271\) | −13.3519 | −0.811073 | −0.405537 | − | 0.914079i | \(-0.632915\pi\) | ||||
−0.405537 | + | 0.914079i | \(0.632915\pi\) | |||||||
\(272\) | 4.87471 | 0.295573 | ||||||||
\(273\) | 0.797445 | 0.0482635 | ||||||||
\(274\) | −21.6808 | −1.30979 | ||||||||
\(275\) | 10.1812 | 0.613951 | ||||||||
\(276\) | −4.08918 | −0.246140 | ||||||||
\(277\) | −5.91529 | −0.355415 | −0.177708 | − | 0.984083i | \(-0.556868\pi\) | ||||
−0.177708 | + | 0.984083i | \(0.556868\pi\) | |||||||
\(278\) | −4.01573 | −0.240847 | ||||||||
\(279\) | 4.04763 | 0.242325 | ||||||||
\(280\) | −1.00410 | −0.0600063 | ||||||||
\(281\) | 8.20337 | 0.489372 | 0.244686 | − | 0.969602i | \(-0.421315\pi\) | ||||
0.244686 | + | 0.969602i | \(0.421315\pi\) | |||||||
\(282\) | 3.00222 | 0.178780 | ||||||||
\(283\) | −18.8189 | −1.11867 | −0.559333 | − | 0.828943i | \(-0.688943\pi\) | ||||
−0.559333 | + | 0.828943i | \(0.688943\pi\) | |||||||
\(284\) | −1.94373 | −0.115339 | ||||||||
\(285\) | 5.60664 | 0.332108 | ||||||||
\(286\) | −2.98171 | −0.176312 | ||||||||
\(287\) | 2.01274 | 0.118808 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 6.76281 | 0.397813 | ||||||||
\(290\) | −12.5499 | −0.736956 | ||||||||
\(291\) | 11.3927 | 0.667851 | ||||||||
\(292\) | −7.45502 | −0.436272 | ||||||||
\(293\) | −33.5092 | −1.95763 | −0.978815 | − | 0.204746i | \(-0.934363\pi\) | ||||
−0.978815 | + | 0.204746i | \(0.934363\pi\) | |||||||
\(294\) | 6.36408 | 0.371161 | ||||||||
\(295\) | −8.46651 | −0.492940 | ||||||||
\(296\) | −3.80662 | −0.221255 | ||||||||
\(297\) | 2.98171 | 0.173016 | ||||||||
\(298\) | −18.0807 | −1.04739 | ||||||||
\(299\) | 4.08918 | 0.236483 | ||||||||
\(300\) | 3.41456 | 0.197140 | ||||||||
\(301\) | 2.39529 | 0.138062 | ||||||||
\(302\) | −9.37983 | −0.539748 | ||||||||
\(303\) | 5.48924 | 0.315349 | ||||||||
\(304\) | −4.45274 | −0.255382 | ||||||||
\(305\) | 5.12075 | 0.293214 | ||||||||
\(306\) | 4.87471 | 0.278669 | ||||||||
\(307\) | 4.39459 | 0.250812 | 0.125406 | − | 0.992105i | \(-0.459977\pi\) | ||||
0.125406 | + | 0.992105i | \(0.459977\pi\) | |||||||
\(308\) | 2.37775 | 0.135485 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 5.09654 | 0.289464 | ||||||||
\(311\) | −10.2447 | −0.580925 | −0.290462 | − | 0.956886i | \(-0.593809\pi\) | ||||
−0.290462 | + | 0.956886i | \(0.593809\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | −25.1202 | −1.41988 | −0.709939 | − | 0.704264i | \(-0.751277\pi\) | ||||
−0.709939 | + | 0.704264i | \(0.751277\pi\) | |||||||
\(314\) | −18.1379 | −1.02358 | ||||||||
\(315\) | −1.00410 | −0.0565745 | ||||||||
\(316\) | 14.1834 | 0.797878 | ||||||||
\(317\) | −5.81992 | −0.326879 | −0.163440 | − | 0.986553i | \(-0.552259\pi\) | ||||
−0.163440 | + | 0.986553i | \(0.552259\pi\) | |||||||
\(318\) | 8.63309 | 0.484120 | ||||||||
\(319\) | 29.7188 | 1.66393 | ||||||||
\(320\) | 1.25914 | 0.0703882 | ||||||||
\(321\) | −3.92781 | −0.219229 | ||||||||
\(322\) | −3.26089 | −0.181722 | ||||||||
\(323\) | −21.7058 | −1.20774 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −3.41456 | −0.189406 | ||||||||
\(326\) | −15.9568 | −0.883763 | ||||||||
\(327\) | −11.9866 | −0.662858 | ||||||||
\(328\) | −2.52399 | −0.139364 | ||||||||
\(329\) | 2.39411 | 0.131991 | ||||||||
\(330\) | 3.75440 | 0.206673 | ||||||||
\(331\) | −20.4154 | −1.12213 | −0.561067 | − | 0.827771i | \(-0.689609\pi\) | ||||
−0.561067 | + | 0.827771i | \(0.689609\pi\) | |||||||
\(332\) | 15.3797 | 0.844068 | ||||||||
\(333\) | −3.80662 | −0.208601 | ||||||||
\(334\) | −21.4308 | −1.17264 | ||||||||
\(335\) | 6.22120 | 0.339900 | ||||||||
\(336\) | 0.797445 | 0.0435042 | ||||||||
\(337\) | −13.7105 | −0.746859 | −0.373430 | − | 0.927658i | \(-0.621818\pi\) | ||||
−0.373430 | + | 0.927658i | \(0.621818\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | 6.53982 | 0.355194 | ||||||||
\(340\) | 6.13796 | 0.332878 | ||||||||
\(341\) | −12.0689 | −0.653565 | ||||||||
\(342\) | −4.45274 | −0.240777 | ||||||||
\(343\) | 10.6571 | 0.575430 | ||||||||
\(344\) | −3.00371 | −0.161949 | ||||||||
\(345\) | −5.14886 | −0.277205 | ||||||||
\(346\) | −22.1020 | −1.18821 | ||||||||
\(347\) | 28.3176 | 1.52017 | 0.760084 | − | 0.649825i | \(-0.225158\pi\) | ||||
0.760084 | + | 0.649825i | \(0.225158\pi\) | |||||||
\(348\) | 9.96702 | 0.534289 | ||||||||
\(349\) | −2.68702 | −0.143833 | −0.0719164 | − | 0.997411i | \(-0.522911\pi\) | ||||
−0.0719164 | + | 0.997411i | \(0.522911\pi\) | |||||||
\(350\) | 2.72292 | 0.145546 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −2.98171 | −0.158926 | ||||||||
\(353\) | 31.9501 | 1.70053 | 0.850266 | − | 0.526354i | \(-0.176441\pi\) | ||||
0.850266 | + | 0.526354i | \(0.176441\pi\) | |||||||
\(354\) | 6.72403 | 0.357378 | ||||||||
\(355\) | −2.44744 | −0.129896 | ||||||||
\(356\) | 14.6866 | 0.778389 | ||||||||
\(357\) | 3.88731 | 0.205738 | ||||||||
\(358\) | 8.00632 | 0.423147 | ||||||||
\(359\) | −23.3446 | −1.23208 | −0.616040 | − | 0.787715i | \(-0.711264\pi\) | ||||
−0.616040 | + | 0.787715i | \(0.711264\pi\) | |||||||
\(360\) | 1.25914 | 0.0663627 | ||||||||
\(361\) | 0.826888 | 0.0435204 | ||||||||
\(362\) | −21.8618 | −1.14903 | ||||||||
\(363\) | 2.10940 | 0.110715 | ||||||||
\(364\) | −0.797445 | −0.0417975 | ||||||||
\(365\) | −9.38694 | −0.491335 | ||||||||
\(366\) | −4.06686 | −0.212578 | ||||||||
\(367\) | −1.63073 | −0.0851236 | −0.0425618 | − | 0.999094i | \(-0.513552\pi\) | ||||
−0.0425618 | + | 0.999094i | \(0.513552\pi\) | |||||||
\(368\) | 4.08918 | 0.213163 | ||||||||
\(369\) | −2.52399 | −0.131394 | ||||||||
\(370\) | −4.79308 | −0.249180 | ||||||||
\(371\) | 6.88441 | 0.357421 | ||||||||
\(372\) | −4.04763 | −0.209860 | ||||||||
\(373\) | −9.90305 | −0.512761 | −0.256380 | − | 0.966576i | \(-0.582530\pi\) | ||||
−0.256380 | + | 0.966576i | \(0.582530\pi\) | |||||||
\(374\) | −14.5350 | −0.751586 | ||||||||
\(375\) | 10.5951 | 0.547130 | ||||||||
\(376\) | −3.00222 | −0.154828 | ||||||||
\(377\) | −9.96702 | −0.513328 | ||||||||
\(378\) | 0.797445 | 0.0410161 | ||||||||
\(379\) | 7.74486 | 0.397827 | 0.198913 | − | 0.980017i | \(-0.436259\pi\) | ||||
0.198913 | + | 0.980017i | \(0.436259\pi\) | |||||||
\(380\) | −5.60664 | −0.287614 | ||||||||
\(381\) | −11.0198 | −0.564559 | ||||||||
\(382\) | 22.9946 | 1.17650 | ||||||||
\(383\) | 37.7230 | 1.92756 | 0.963779 | − | 0.266703i | \(-0.0859342\pi\) | ||||
0.963779 | + | 0.266703i | \(0.0859342\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 2.99393 | 0.152585 | ||||||||
\(386\) | 12.0887 | 0.615300 | ||||||||
\(387\) | −3.00371 | −0.152687 | ||||||||
\(388\) | −11.3927 | −0.578376 | ||||||||
\(389\) | −18.3085 | −0.928276 | −0.464138 | − | 0.885763i | \(-0.653636\pi\) | ||||
−0.464138 | + | 0.885763i | \(0.653636\pi\) | |||||||
\(390\) | −1.25914 | −0.0637592 | ||||||||
\(391\) | 19.9336 | 1.00808 | ||||||||
\(392\) | −6.36408 | −0.321435 | ||||||||
\(393\) | 11.0610 | 0.557953 | ||||||||
\(394\) | −0.828221 | −0.0417252 | ||||||||
\(395\) | 17.8589 | 0.898580 | ||||||||
\(396\) | −2.98171 | −0.149837 | ||||||||
\(397\) | −22.2253 | −1.11546 | −0.557728 | − | 0.830023i | \(-0.688327\pi\) | ||||
−0.557728 | + | 0.830023i | \(0.688327\pi\) | |||||||
\(398\) | −16.9393 | −0.849092 | ||||||||
\(399\) | −3.55081 | −0.177763 | ||||||||
\(400\) | −3.41456 | −0.170728 | ||||||||
\(401\) | 10.6908 | 0.533875 | 0.266937 | − | 0.963714i | \(-0.413988\pi\) | ||||
0.266937 | + | 0.963714i | \(0.413988\pi\) | |||||||
\(402\) | −4.94082 | −0.246426 | ||||||||
\(403\) | 4.04763 | 0.201627 | ||||||||
\(404\) | −5.48924 | −0.273100 | ||||||||
\(405\) | 1.25914 | 0.0625673 | ||||||||
\(406\) | 7.94815 | 0.394460 | ||||||||
\(407\) | 11.3502 | 0.562610 | ||||||||
\(408\) | −4.87471 | −0.241334 | ||||||||
\(409\) | 5.36398 | 0.265232 | 0.132616 | − | 0.991168i | \(-0.457662\pi\) | ||||
0.132616 | + | 0.991168i | \(0.457662\pi\) | |||||||
\(410\) | −3.17807 | −0.156954 | ||||||||
\(411\) | 21.6808 | 1.06944 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | 5.36204 | 0.263849 | ||||||||
\(414\) | 4.08918 | 0.200972 | ||||||||
\(415\) | 19.3652 | 0.950599 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | 4.01573 | 0.196651 | ||||||||
\(418\) | 13.2768 | 0.649389 | ||||||||
\(419\) | −24.4431 | −1.19412 | −0.597061 | − | 0.802196i | \(-0.703665\pi\) | ||||
−0.597061 | + | 0.802196i | \(0.703665\pi\) | |||||||
\(420\) | 1.00410 | 0.0489949 | ||||||||
\(421\) | 15.5098 | 0.755900 | 0.377950 | − | 0.925826i | \(-0.376629\pi\) | ||||
0.377950 | + | 0.925826i | \(0.376629\pi\) | |||||||
\(422\) | 26.7360 | 1.30149 | ||||||||
\(423\) | −3.00222 | −0.145973 | ||||||||
\(424\) | −8.63309 | −0.419260 | ||||||||
\(425\) | −16.6450 | −0.807400 | ||||||||
\(426\) | 1.94373 | 0.0941741 | ||||||||
\(427\) | −3.24309 | −0.156944 | ||||||||
\(428\) | 3.92781 | 0.189858 | ||||||||
\(429\) | 2.98171 | 0.143958 | ||||||||
\(430\) | −3.78210 | −0.182389 | ||||||||
\(431\) | −21.4370 | −1.03258 | −0.516292 | − | 0.856413i | \(-0.672688\pi\) | ||||
−0.516292 | + | 0.856413i | \(0.672688\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −6.20622 | −0.298252 | −0.149126 | − | 0.988818i | \(-0.547646\pi\) | ||||
−0.149126 | + | 0.988818i | \(0.547646\pi\) | |||||||
\(434\) | −3.22776 | −0.154937 | ||||||||
\(435\) | 12.5499 | 0.601722 | ||||||||
\(436\) | 11.9866 | 0.574052 | ||||||||
\(437\) | −18.2080 | −0.871009 | ||||||||
\(438\) | 7.45502 | 0.356215 | ||||||||
\(439\) | 11.1121 | 0.530350 | 0.265175 | − | 0.964200i | \(-0.414570\pi\) | ||||
0.265175 | + | 0.964200i | \(0.414570\pi\) | |||||||
\(440\) | −3.75440 | −0.178984 | ||||||||
\(441\) | −6.36408 | −0.303052 | ||||||||
\(442\) | 4.87471 | 0.231866 | ||||||||
\(443\) | −8.79189 | −0.417715 | −0.208858 | − | 0.977946i | \(-0.566975\pi\) | ||||
−0.208858 | + | 0.977946i | \(0.566975\pi\) | |||||||
\(444\) | 3.80662 | 0.180654 | ||||||||
\(445\) | 18.4925 | 0.876630 | ||||||||
\(446\) | 16.4842 | 0.780550 | ||||||||
\(447\) | 18.0807 | 0.855188 | ||||||||
\(448\) | −0.797445 | −0.0376757 | ||||||||
\(449\) | −14.1718 | −0.668811 | −0.334405 | − | 0.942429i | \(-0.608535\pi\) | ||||
−0.334405 | + | 0.942429i | \(0.608535\pi\) | |||||||
\(450\) | −3.41456 | −0.160964 | ||||||||
\(451\) | 7.52581 | 0.354377 | ||||||||
\(452\) | −6.53982 | −0.307607 | ||||||||
\(453\) | 9.37983 | 0.440703 | ||||||||
\(454\) | 4.26467 | 0.200151 | ||||||||
\(455\) | −1.00410 | −0.0470728 | ||||||||
\(456\) | 4.45274 | 0.208519 | ||||||||
\(457\) | 0.0240313 | 0.00112414 | 0.000562069 | − | 1.00000i | \(-0.499821\pi\) | ||||
0.000562069 | 1.00000i | \(0.499821\pi\) | ||||||||
\(458\) | 21.0701 | 0.984543 | ||||||||
\(459\) | −4.87471 | −0.227532 | ||||||||
\(460\) | 5.14886 | 0.240067 | ||||||||
\(461\) | −9.22105 | −0.429467 | −0.214734 | − | 0.976673i | \(-0.568888\pi\) | ||||
−0.214734 | + | 0.976673i | \(0.568888\pi\) | |||||||
\(462\) | −2.37775 | −0.110623 | ||||||||
\(463\) | −4.11875 | −0.191415 | −0.0957073 | − | 0.995410i | \(-0.530511\pi\) | ||||
−0.0957073 | + | 0.995410i | \(0.530511\pi\) | |||||||
\(464\) | −9.96702 | −0.462708 | ||||||||
\(465\) | −5.09654 | −0.236347 | ||||||||
\(466\) | 13.3803 | 0.619830 | ||||||||
\(467\) | 11.3460 | 0.525032 | 0.262516 | − | 0.964928i | \(-0.415448\pi\) | ||||
0.262516 | + | 0.964928i | \(0.415448\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | −3.94003 | −0.181934 | ||||||||
\(470\) | −3.78023 | −0.174369 | ||||||||
\(471\) | 18.1379 | 0.835750 | ||||||||
\(472\) | −6.72403 | −0.309498 | ||||||||
\(473\) | 8.95619 | 0.411806 | ||||||||
\(474\) | −14.1834 | −0.651465 | ||||||||
\(475\) | 15.2041 | 0.697614 | ||||||||
\(476\) | −3.88731 | −0.178175 | ||||||||
\(477\) | −8.63309 | −0.395282 | ||||||||
\(478\) | 29.5612 | 1.35210 | ||||||||
\(479\) | −18.0330 | −0.823949 | −0.411975 | − | 0.911195i | \(-0.635161\pi\) | ||||
−0.411975 | + | 0.911195i | \(0.635161\pi\) | |||||||
\(480\) | −1.25914 | −0.0574718 | ||||||||
\(481\) | −3.80662 | −0.173567 | ||||||||
\(482\) | −2.85139 | −0.129877 | ||||||||
\(483\) | 3.26089 | 0.148376 | ||||||||
\(484\) | −2.10940 | −0.0958818 | ||||||||
\(485\) | −14.3450 | −0.651374 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −41.4619 | −1.87882 | −0.939409 | − | 0.342799i | \(-0.888625\pi\) | ||||
−0.939409 | + | 0.342799i | \(0.888625\pi\) | |||||||
\(488\) | 4.06686 | 0.184098 | ||||||||
\(489\) | 15.9568 | 0.721590 | ||||||||
\(490\) | −8.01329 | −0.362004 | ||||||||
\(491\) | −34.9707 | −1.57820 | −0.789102 | − | 0.614262i | \(-0.789454\pi\) | ||||
−0.789102 | + | 0.614262i | \(0.789454\pi\) | |||||||
\(492\) | 2.52399 | 0.113790 | ||||||||
\(493\) | −48.5864 | −2.18822 | ||||||||
\(494\) | −4.45274 | −0.200338 | ||||||||
\(495\) | −3.75440 | −0.168748 | ||||||||
\(496\) | 4.04763 | 0.181744 | ||||||||
\(497\) | 1.55002 | 0.0695278 | ||||||||
\(498\) | −15.3797 | −0.689179 | ||||||||
\(499\) | −18.4859 | −0.827542 | −0.413771 | − | 0.910381i | \(-0.635789\pi\) | ||||
−0.413771 | + | 0.910381i | \(0.635789\pi\) | |||||||
\(500\) | −10.5951 | −0.473829 | ||||||||
\(501\) | 21.4308 | 0.957457 | ||||||||
\(502\) | −17.9435 | −0.800857 | ||||||||
\(503\) | −35.5052 | −1.58310 | −0.791550 | − | 0.611104i | \(-0.790726\pi\) | ||||
−0.791550 | + | 0.611104i | \(0.790726\pi\) | |||||||
\(504\) | −0.797445 | −0.0355210 | ||||||||
\(505\) | −6.91174 | −0.307568 | ||||||||
\(506\) | −12.1927 | −0.542034 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 11.0198 | 0.488923 | ||||||||
\(509\) | 1.89530 | 0.0840078 | 0.0420039 | − | 0.999117i | \(-0.486626\pi\) | ||||
0.0420039 | + | 0.999117i | \(0.486626\pi\) | |||||||
\(510\) | −6.13796 | −0.271793 | ||||||||
\(511\) | 5.94497 | 0.262990 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 4.45274 | 0.196593 | ||||||||
\(514\) | −4.24943 | −0.187434 | ||||||||
\(515\) | −1.25914 | −0.0554845 | ||||||||
\(516\) | 3.00371 | 0.132231 | ||||||||
\(517\) | 8.95176 | 0.393698 | ||||||||
\(518\) | 3.03557 | 0.133375 | ||||||||
\(519\) | 22.1020 | 0.970171 | ||||||||
\(520\) | 1.25914 | 0.0552171 | ||||||||
\(521\) | 27.6583 | 1.21173 | 0.605865 | − | 0.795567i | \(-0.292827\pi\) | ||||
0.605865 | + | 0.795567i | \(0.292827\pi\) | |||||||
\(522\) | −9.96702 | −0.436245 | ||||||||
\(523\) | −14.4338 | −0.631147 | −0.315573 | − | 0.948901i | \(-0.602197\pi\) | ||||
−0.315573 | + | 0.948901i | \(0.602197\pi\) | |||||||
\(524\) | −11.0610 | −0.483201 | ||||||||
\(525\) | −2.72292 | −0.118838 | ||||||||
\(526\) | 13.4098 | 0.584693 | ||||||||
\(527\) | 19.7310 | 0.859497 | ||||||||
\(528\) | 2.98171 | 0.129762 | ||||||||
\(529\) | −6.27863 | −0.272984 | ||||||||
\(530\) | −10.8703 | −0.472176 | ||||||||
\(531\) | −6.72403 | −0.291798 | ||||||||
\(532\) | 3.55081 | 0.153947 | ||||||||
\(533\) | −2.52399 | −0.109326 | ||||||||
\(534\) | −14.6866 | −0.635552 | ||||||||
\(535\) | 4.94568 | 0.213820 | ||||||||
\(536\) | 4.94082 | 0.213411 | ||||||||
\(537\) | −8.00632 | −0.345498 | ||||||||
\(538\) | 26.4982 | 1.14242 | ||||||||
\(539\) | 18.9759 | 0.817348 | ||||||||
\(540\) | −1.25914 | −0.0541849 | ||||||||
\(541\) | 12.3984 | 0.533050 | 0.266525 | − | 0.963828i | \(-0.414125\pi\) | ||||
0.266525 | + | 0.963828i | \(0.414125\pi\) | |||||||
\(542\) | −13.3519 | −0.573515 | ||||||||
\(543\) | 21.8618 | 0.938179 | ||||||||
\(544\) | 4.87471 | 0.209002 | ||||||||
\(545\) | 15.0928 | 0.646504 | ||||||||
\(546\) | 0.797445 | 0.0341275 | ||||||||
\(547\) | 7.76399 | 0.331964 | 0.165982 | − | 0.986129i | \(-0.446921\pi\) | ||||
0.165982 | + | 0.986129i | \(0.446921\pi\) | |||||||
\(548\) | −21.6808 | −0.926159 | ||||||||
\(549\) | 4.06686 | 0.173569 | ||||||||
\(550\) | 10.1812 | 0.434129 | ||||||||
\(551\) | 44.3806 | 1.89068 | ||||||||
\(552\) | −4.08918 | −0.174047 | ||||||||
\(553\) | −11.3105 | −0.480970 | ||||||||
\(554\) | −5.91529 | −0.251317 | ||||||||
\(555\) | 4.79308 | 0.203455 | ||||||||
\(556\) | −4.01573 | −0.170305 | ||||||||
\(557\) | 15.2003 | 0.644059 | 0.322029 | − | 0.946730i | \(-0.395635\pi\) | ||||
0.322029 | + | 0.946730i | \(0.395635\pi\) | |||||||
\(558\) | 4.04763 | 0.171350 | ||||||||
\(559\) | −3.00371 | −0.127043 | ||||||||
\(560\) | −1.00410 | −0.0424308 | ||||||||
\(561\) | 14.5350 | 0.613667 | ||||||||
\(562\) | 8.20337 | 0.346038 | ||||||||
\(563\) | 28.7671 | 1.21239 | 0.606195 | − | 0.795316i | \(-0.292695\pi\) | ||||
0.606195 | + | 0.795316i | \(0.292695\pi\) | |||||||
\(564\) | 3.00222 | 0.126416 | ||||||||
\(565\) | −8.23457 | −0.346431 | ||||||||
\(566\) | −18.8189 | −0.791017 | ||||||||
\(567\) | −0.797445 | −0.0334895 | ||||||||
\(568\) | −1.94373 | −0.0815572 | ||||||||
\(569\) | −13.8644 | −0.581226 | −0.290613 | − | 0.956841i | \(-0.593859\pi\) | ||||
−0.290613 | + | 0.956841i | \(0.593859\pi\) | |||||||
\(570\) | 5.60664 | 0.234836 | ||||||||
\(571\) | 4.34900 | 0.182000 | 0.0909999 | − | 0.995851i | \(-0.470994\pi\) | ||||
0.0909999 | + | 0.995851i | \(0.470994\pi\) | |||||||
\(572\) | −2.98171 | −0.124672 | ||||||||
\(573\) | −22.9946 | −0.960612 | ||||||||
\(574\) | 2.01274 | 0.0840103 | ||||||||
\(575\) | −13.9627 | −0.582286 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −26.1842 | −1.09006 | −0.545030 | − | 0.838416i | \(-0.683482\pi\) | ||||
−0.545030 | + | 0.838416i | \(0.683482\pi\) | |||||||
\(578\) | 6.76281 | 0.281296 | ||||||||
\(579\) | −12.0887 | −0.502390 | ||||||||
\(580\) | −12.5499 | −0.521107 | ||||||||
\(581\) | −12.2644 | −0.508814 | ||||||||
\(582\) | 11.3927 | 0.472242 | ||||||||
\(583\) | 25.7414 | 1.06610 | ||||||||
\(584\) | −7.45502 | −0.308491 | ||||||||
\(585\) | 1.25914 | 0.0520592 | ||||||||
\(586\) | −33.5092 | −1.38425 | ||||||||
\(587\) | −13.8575 | −0.571960 | −0.285980 | − | 0.958236i | \(-0.592319\pi\) | ||||
−0.285980 | + | 0.958236i | \(0.592319\pi\) | |||||||
\(588\) | 6.36408 | 0.262450 | ||||||||
\(589\) | −18.0230 | −0.742626 | ||||||||
\(590\) | −8.46651 | −0.348561 | ||||||||
\(591\) | 0.828221 | 0.0340685 | ||||||||
\(592\) | −3.80662 | −0.156451 | ||||||||
\(593\) | 28.9779 | 1.18998 | 0.594989 | − | 0.803734i | \(-0.297156\pi\) | ||||
0.594989 | + | 0.803734i | \(0.297156\pi\) | |||||||
\(594\) | 2.98171 | 0.122341 | ||||||||
\(595\) | −4.89468 | −0.200662 | ||||||||
\(596\) | −18.0807 | −0.740615 | ||||||||
\(597\) | 16.9393 | 0.693281 | ||||||||
\(598\) | 4.08918 | 0.167219 | ||||||||
\(599\) | 36.9924 | 1.51147 | 0.755734 | − | 0.654879i | \(-0.227281\pi\) | ||||
0.755734 | + | 0.654879i | \(0.227281\pi\) | |||||||
\(600\) | 3.41456 | 0.139399 | ||||||||
\(601\) | 1.03333 | 0.0421504 | 0.0210752 | − | 0.999778i | \(-0.493291\pi\) | ||||
0.0210752 | + | 0.999778i | \(0.493291\pi\) | |||||||
\(602\) | 2.39529 | 0.0976247 | ||||||||
\(603\) | 4.94082 | 0.201206 | ||||||||
\(604\) | −9.37983 | −0.381660 | ||||||||
\(605\) | −2.65604 | −0.107983 | ||||||||
\(606\) | 5.48924 | 0.222985 | ||||||||
\(607\) | 22.0381 | 0.894499 | 0.447249 | − | 0.894409i | \(-0.352404\pi\) | ||||
0.447249 | + | 0.894409i | \(0.352404\pi\) | |||||||
\(608\) | −4.45274 | −0.180582 | ||||||||
\(609\) | −7.94815 | −0.322075 | ||||||||
\(610\) | 5.12075 | 0.207333 | ||||||||
\(611\) | −3.00222 | −0.121457 | ||||||||
\(612\) | 4.87471 | 0.197049 | ||||||||
\(613\) | −16.8807 | −0.681804 | −0.340902 | − | 0.940099i | \(-0.610733\pi\) | ||||
−0.340902 | + | 0.940099i | \(0.610733\pi\) | |||||||
\(614\) | 4.39459 | 0.177351 | ||||||||
\(615\) | 3.17807 | 0.128152 | ||||||||
\(616\) | 2.37775 | 0.0958023 | ||||||||
\(617\) | 27.3160 | 1.09970 | 0.549850 | − | 0.835263i | \(-0.314685\pi\) | ||||
0.549850 | + | 0.835263i | \(0.314685\pi\) | |||||||
\(618\) | 1.00000 | 0.0402259 | ||||||||
\(619\) | 34.1151 | 1.37120 | 0.685600 | − | 0.727978i | \(-0.259540\pi\) | ||||
0.685600 | + | 0.727978i | \(0.259540\pi\) | |||||||
\(620\) | 5.09654 | 0.204682 | ||||||||
\(621\) | −4.08918 | −0.164093 | ||||||||
\(622\) | −10.2447 | −0.410776 | ||||||||
\(623\) | −11.7118 | −0.469222 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | 3.73200 | 0.149280 | ||||||||
\(626\) | −25.1202 | −1.00400 | ||||||||
\(627\) | −13.2768 | −0.530224 | ||||||||
\(628\) | −18.1379 | −0.723780 | ||||||||
\(629\) | −18.5562 | −0.739883 | ||||||||
\(630\) | −1.00410 | −0.0400042 | ||||||||
\(631\) | 13.4519 | 0.535513 | 0.267756 | − | 0.963487i | \(-0.413718\pi\) | ||||
0.267756 | + | 0.963487i | \(0.413718\pi\) | |||||||
\(632\) | 14.1834 | 0.564185 | ||||||||
\(633\) | −26.7360 | −1.06266 | ||||||||
\(634\) | −5.81992 | −0.231138 | ||||||||
\(635\) | 13.8755 | 0.550630 | ||||||||
\(636\) | 8.63309 | 0.342324 | ||||||||
\(637\) | −6.36408 | −0.252154 | ||||||||
\(638\) | 29.7188 | 1.17658 | ||||||||
\(639\) | −1.94373 | −0.0768928 | ||||||||
\(640\) | 1.25914 | 0.0497720 | ||||||||
\(641\) | −15.5587 | −0.614533 | −0.307266 | − | 0.951624i | \(-0.599414\pi\) | ||||
−0.307266 | + | 0.951624i | \(0.599414\pi\) | |||||||
\(642\) | −3.92781 | −0.155018 | ||||||||
\(643\) | −7.19979 | −0.283932 | −0.141966 | − | 0.989872i | \(-0.545342\pi\) | ||||
−0.141966 | + | 0.989872i | \(0.545342\pi\) | |||||||
\(644\) | −3.26089 | −0.128497 | ||||||||
\(645\) | 3.78210 | 0.148920 | ||||||||
\(646\) | −21.7058 | −0.854004 | ||||||||
\(647\) | −14.9448 | −0.587539 | −0.293769 | − | 0.955876i | \(-0.594910\pi\) | ||||
−0.293769 | + | 0.955876i | \(0.594910\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 20.0491 | 0.786996 | ||||||||
\(650\) | −3.41456 | −0.133930 | ||||||||
\(651\) | 3.22776 | 0.126506 | ||||||||
\(652\) | −15.9568 | −0.624915 | ||||||||
\(653\) | −33.1012 | −1.29535 | −0.647675 | − | 0.761917i | \(-0.724259\pi\) | ||||
−0.647675 | + | 0.761917i | \(0.724259\pi\) | |||||||
\(654\) | −11.9866 | −0.468712 | ||||||||
\(655\) | −13.9274 | −0.544187 | ||||||||
\(656\) | −2.52399 | −0.0985453 | ||||||||
\(657\) | −7.45502 | −0.290848 | ||||||||
\(658\) | 2.39411 | 0.0933319 | ||||||||
\(659\) | −32.9257 | −1.28260 | −0.641302 | − | 0.767289i | \(-0.721605\pi\) | ||||
−0.641302 | + | 0.767289i | \(0.721605\pi\) | |||||||
\(660\) | 3.75440 | 0.146140 | ||||||||
\(661\) | 11.5643 | 0.449798 | 0.224899 | − | 0.974382i | \(-0.427795\pi\) | ||||
0.224899 | + | 0.974382i | \(0.427795\pi\) | |||||||
\(662\) | −20.4154 | −0.793468 | ||||||||
\(663\) | −4.87471 | −0.189318 | ||||||||
\(664\) | 15.3797 | 0.596846 | ||||||||
\(665\) | 4.47098 | 0.173377 | ||||||||
\(666\) | −3.80662 | −0.147503 | ||||||||
\(667\) | −40.7569 | −1.57811 | ||||||||
\(668\) | −21.4308 | −0.829182 | ||||||||
\(669\) | −16.4842 | −0.637317 | ||||||||
\(670\) | 6.22120 | 0.240346 | ||||||||
\(671\) | −12.1262 | −0.468126 | ||||||||
\(672\) | 0.797445 | 0.0307621 | ||||||||
\(673\) | 2.06251 | 0.0795038 | 0.0397519 | − | 0.999210i | \(-0.487343\pi\) | ||||
0.0397519 | + | 0.999210i | \(0.487343\pi\) | |||||||
\(674\) | −13.7105 | −0.528109 | ||||||||
\(675\) | 3.41456 | 0.131426 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −14.5098 | −0.557657 | −0.278829 | − | 0.960341i | \(-0.589946\pi\) | ||||
−0.278829 | + | 0.960341i | \(0.589946\pi\) | |||||||
\(678\) | 6.53982 | 0.251160 | ||||||||
\(679\) | 9.08504 | 0.348652 | ||||||||
\(680\) | 6.13796 | 0.235380 | ||||||||
\(681\) | −4.26467 | −0.163422 | ||||||||
\(682\) | −12.0689 | −0.462140 | ||||||||
\(683\) | −2.22822 | −0.0852604 | −0.0426302 | − | 0.999091i | \(-0.513574\pi\) | ||||
−0.0426302 | + | 0.999091i | \(0.513574\pi\) | |||||||
\(684\) | −4.45274 | −0.170255 | ||||||||
\(685\) | −27.2993 | −1.04305 | ||||||||
\(686\) | 10.6571 | 0.406891 | ||||||||
\(687\) | −21.0701 | −0.803876 | ||||||||
\(688\) | −3.00371 | −0.114515 | ||||||||
\(689\) | −8.63309 | −0.328895 | ||||||||
\(690\) | −5.14886 | −0.196014 | ||||||||
\(691\) | 14.0702 | 0.535256 | 0.267628 | − | 0.963522i | \(-0.413760\pi\) | ||||
0.267628 | + | 0.963522i | \(0.413760\pi\) | |||||||
\(692\) | −22.1020 | −0.840192 | ||||||||
\(693\) | 2.37775 | 0.0903232 | ||||||||
\(694\) | 28.3176 | 1.07492 | ||||||||
\(695\) | −5.05637 | −0.191799 | ||||||||
\(696\) | 9.96702 | 0.377799 | ||||||||
\(697\) | −12.3037 | −0.466037 | ||||||||
\(698\) | −2.68702 | −0.101705 | ||||||||
\(699\) | −13.3803 | −0.506089 | ||||||||
\(700\) | 2.72292 | 0.102917 | ||||||||
\(701\) | −44.1774 | −1.66856 | −0.834280 | − | 0.551342i | \(-0.814116\pi\) | ||||
−0.834280 | + | 0.551342i | \(0.814116\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | 16.9499 | 0.639277 | ||||||||
\(704\) | −2.98171 | −0.112377 | ||||||||
\(705\) | 3.78023 | 0.142372 | ||||||||
\(706\) | 31.9501 | 1.20246 | ||||||||
\(707\) | 4.37737 | 0.164628 | ||||||||
\(708\) | 6.72403 | 0.252704 | ||||||||
\(709\) | 38.7468 | 1.45517 | 0.727583 | − | 0.686019i | \(-0.240643\pi\) | ||||
0.727583 | + | 0.686019i | \(0.240643\pi\) | |||||||
\(710\) | −2.44744 | −0.0918507 | ||||||||
\(711\) | 14.1834 | 0.531919 | ||||||||
\(712\) | 14.6866 | 0.550404 | ||||||||
\(713\) | 16.5515 | 0.619857 | ||||||||
\(714\) | 3.88731 | 0.145479 | ||||||||
\(715\) | −3.75440 | −0.140407 | ||||||||
\(716\) | 8.00632 | 0.299210 | ||||||||
\(717\) | −29.5612 | −1.10398 | ||||||||
\(718\) | −23.3446 | −0.871213 | ||||||||
\(719\) | 4.72624 | 0.176259 | 0.0881295 | − | 0.996109i | \(-0.471911\pi\) | ||||
0.0881295 | + | 0.996109i | \(0.471911\pi\) | |||||||
\(720\) | 1.25914 | 0.0469255 | ||||||||
\(721\) | 0.797445 | 0.0296984 | ||||||||
\(722\) | 0.826888 | 0.0307736 | ||||||||
\(723\) | 2.85139 | 0.106044 | ||||||||
\(724\) | −21.8618 | −0.812487 | ||||||||
\(725\) | 34.0330 | 1.26395 | ||||||||
\(726\) | 2.10940 | 0.0782872 | ||||||||
\(727\) | 49.5432 | 1.83746 | 0.918729 | − | 0.394890i | \(-0.129217\pi\) | ||||
0.918729 | + | 0.394890i | \(0.129217\pi\) | |||||||
\(728\) | −0.797445 | −0.0295553 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −9.38694 | −0.347426 | ||||||||
\(731\) | −14.6422 | −0.541562 | ||||||||
\(732\) | −4.06686 | −0.150315 | ||||||||
\(733\) | 42.5643 | 1.57215 | 0.786075 | − | 0.618131i | \(-0.212110\pi\) | ||||
0.786075 | + | 0.618131i | \(0.212110\pi\) | |||||||
\(734\) | −1.63073 | −0.0601915 | ||||||||
\(735\) | 8.01329 | 0.295575 | ||||||||
\(736\) | 4.08918 | 0.150729 | ||||||||
\(737\) | −14.7321 | −0.542664 | ||||||||
\(738\) | −2.52399 | −0.0929094 | ||||||||
\(739\) | 8.83116 | 0.324859 | 0.162430 | − | 0.986720i | \(-0.448067\pi\) | ||||
0.162430 | + | 0.986720i | \(0.448067\pi\) | |||||||
\(740\) | −4.79308 | −0.176197 | ||||||||
\(741\) | 4.45274 | 0.163575 | ||||||||
\(742\) | 6.88441 | 0.252735 | ||||||||
\(743\) | 18.9037 | 0.693509 | 0.346754 | − | 0.937956i | \(-0.387284\pi\) | ||||
0.346754 | + | 0.937956i | \(0.387284\pi\) | |||||||
\(744\) | −4.04763 | −0.148393 | ||||||||
\(745\) | −22.7662 | −0.834089 | ||||||||
\(746\) | −9.90305 | −0.362577 | ||||||||
\(747\) | 15.3797 | 0.562712 | ||||||||
\(748\) | −14.5350 | −0.531452 | ||||||||
\(749\) | −3.13221 | −0.114449 | ||||||||
\(750\) | 10.5951 | 0.386880 | ||||||||
\(751\) | −25.3504 | −0.925049 | −0.462525 | − | 0.886606i | \(-0.653056\pi\) | ||||
−0.462525 | + | 0.886606i | \(0.653056\pi\) | |||||||
\(752\) | −3.00222 | −0.109480 | ||||||||
\(753\) | 17.9435 | 0.653897 | ||||||||
\(754\) | −9.96702 | −0.362978 | ||||||||
\(755\) | −11.8105 | −0.429830 | ||||||||
\(756\) | 0.797445 | 0.0290028 | ||||||||
\(757\) | −47.3667 | −1.72157 | −0.860785 | − | 0.508968i | \(-0.830027\pi\) | ||||
−0.860785 | + | 0.508968i | \(0.830027\pi\) | |||||||
\(758\) | 7.74486 | 0.281306 | ||||||||
\(759\) | 12.1927 | 0.442569 | ||||||||
\(760\) | −5.60664 | −0.203374 | ||||||||
\(761\) | 42.7967 | 1.55138 | 0.775689 | − | 0.631115i | \(-0.217402\pi\) | ||||
0.775689 | + | 0.631115i | \(0.217402\pi\) | |||||||
\(762\) | −11.0198 | −0.399204 | ||||||||
\(763\) | −9.55862 | −0.346045 | ||||||||
\(764\) | 22.9946 | 0.831915 | ||||||||
\(765\) | 6.13796 | 0.221918 | ||||||||
\(766\) | 37.7230 | 1.36299 | ||||||||
\(767\) | −6.72403 | −0.242791 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −24.5633 | −0.885777 | −0.442888 | − | 0.896577i | \(-0.646046\pi\) | ||||
−0.442888 | + | 0.896577i | \(0.646046\pi\) | |||||||
\(770\) | 2.99393 | 0.107894 | ||||||||
\(771\) | 4.24943 | 0.153039 | ||||||||
\(772\) | 12.0887 | 0.435083 | ||||||||
\(773\) | 4.82029 | 0.173374 | 0.0866869 | − | 0.996236i | \(-0.472372\pi\) | ||||
0.0866869 | + | 0.996236i | \(0.472372\pi\) | |||||||
\(774\) | −3.00371 | −0.107966 | ||||||||
\(775\) | −13.8209 | −0.496460 | ||||||||
\(776\) | −11.3927 | −0.408974 | ||||||||
\(777\) | −3.03557 | −0.108900 | ||||||||
\(778\) | −18.3085 | −0.656390 | ||||||||
\(779\) | 11.2387 | 0.402667 | ||||||||
\(780\) | −1.25914 | −0.0450846 | ||||||||
\(781\) | 5.79565 | 0.207385 | ||||||||
\(782\) | 19.9336 | 0.712823 | ||||||||
\(783\) | 9.96702 | 0.356192 | ||||||||
\(784\) | −6.36408 | −0.227289 | ||||||||
\(785\) | −22.8382 | −0.815130 | ||||||||
\(786\) | 11.0610 | 0.394532 | ||||||||
\(787\) | −10.9917 | −0.391812 | −0.195906 | − | 0.980623i | \(-0.562765\pi\) | ||||
−0.195906 | + | 0.980623i | \(0.562765\pi\) | |||||||
\(788\) | −0.828221 | −0.0295042 | ||||||||
\(789\) | −13.4098 | −0.477400 | ||||||||
\(790\) | 17.8589 | 0.635392 | ||||||||
\(791\) | 5.21515 | 0.185429 | ||||||||
\(792\) | −2.98171 | −0.105950 | ||||||||
\(793\) | 4.06686 | 0.144418 | ||||||||
\(794\) | −22.2253 | −0.788747 | ||||||||
\(795\) | 10.8703 | 0.385530 | ||||||||
\(796\) | −16.9393 | −0.600399 | ||||||||
\(797\) | 19.7528 | 0.699680 | 0.349840 | − | 0.936809i | \(-0.386236\pi\) | ||||
0.349840 | + | 0.936809i | \(0.386236\pi\) | |||||||
\(798\) | −3.55081 | −0.125697 | ||||||||
\(799\) | −14.6350 | −0.517748 | ||||||||
\(800\) | −3.41456 | −0.120723 | ||||||||
\(801\) | 14.6866 | 0.518926 | ||||||||
\(802\) | 10.6908 | 0.377506 | ||||||||
\(803\) | 22.2287 | 0.784435 | ||||||||
\(804\) | −4.94082 | −0.174249 | ||||||||
\(805\) | −4.10593 | −0.144715 | ||||||||
\(806\) | 4.04763 | 0.142572 | ||||||||
\(807\) | −26.4982 | −0.932779 | ||||||||
\(808\) | −5.48924 | −0.193111 | ||||||||
\(809\) | 5.92615 | 0.208352 | 0.104176 | − | 0.994559i | \(-0.466779\pi\) | ||||
0.104176 | + | 0.994559i | \(0.466779\pi\) | |||||||
\(810\) | 1.25914 | 0.0442418 | ||||||||
\(811\) | −11.0575 | −0.388281 | −0.194140 | − | 0.980974i | \(-0.562192\pi\) | ||||
−0.194140 | + | 0.980974i | \(0.562192\pi\) | |||||||
\(812\) | 7.94815 | 0.278925 | ||||||||
\(813\) | 13.3519 | 0.468273 | ||||||||
\(814\) | 11.3502 | 0.397825 | ||||||||
\(815\) | −20.0919 | −0.703787 | ||||||||
\(816\) | −4.87471 | −0.170649 | ||||||||
\(817\) | 13.3747 | 0.467922 | ||||||||
\(818\) | 5.36398 | 0.187547 | ||||||||
\(819\) | −0.797445 | −0.0278650 | ||||||||
\(820\) | −3.17807 | −0.110983 | ||||||||
\(821\) | 43.2722 | 1.51021 | 0.755106 | − | 0.655603i | \(-0.227586\pi\) | ||||
0.755106 | + | 0.655603i | \(0.227586\pi\) | |||||||
\(822\) | 21.6808 | 0.756206 | ||||||||
\(823\) | 2.19947 | 0.0766686 | 0.0383343 | − | 0.999265i | \(-0.487795\pi\) | ||||
0.0383343 | + | 0.999265i | \(0.487795\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | −10.1812 | −0.354465 | ||||||||
\(826\) | 5.36204 | 0.186569 | ||||||||
\(827\) | 28.5423 | 0.992512 | 0.496256 | − | 0.868176i | \(-0.334708\pi\) | ||||
0.496256 | + | 0.868176i | \(0.334708\pi\) | |||||||
\(828\) | 4.08918 | 0.142109 | ||||||||
\(829\) | 27.4658 | 0.953926 | 0.476963 | − | 0.878923i | \(-0.341738\pi\) | ||||
0.476963 | + | 0.878923i | \(0.341738\pi\) | |||||||
\(830\) | 19.3652 | 0.672175 | ||||||||
\(831\) | 5.91529 | 0.205199 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | −31.0231 | −1.07489 | ||||||||
\(834\) | 4.01573 | 0.139053 | ||||||||
\(835\) | −26.9844 | −0.933834 | ||||||||
\(836\) | 13.2768 | 0.459187 | ||||||||
\(837\) | −4.04763 | −0.139907 | ||||||||
\(838\) | −24.4431 | −0.844372 | ||||||||
\(839\) | 44.7604 | 1.54530 | 0.772651 | − | 0.634831i | \(-0.218930\pi\) | ||||
0.772651 | + | 0.634831i | \(0.218930\pi\) | |||||||
\(840\) | 1.00410 | 0.0346446 | ||||||||
\(841\) | 70.3416 | 2.42557 | ||||||||
\(842\) | 15.5098 | 0.534502 | ||||||||
\(843\) | −8.20337 | −0.282539 | ||||||||
\(844\) | 26.7360 | 0.920291 | ||||||||
\(845\) | 1.25914 | 0.0433158 | ||||||||
\(846\) | −3.00222 | −0.103218 | ||||||||
\(847\) | 1.68213 | 0.0577986 | ||||||||
\(848\) | −8.63309 | −0.296462 | ||||||||
\(849\) | 18.8189 | 0.645862 | ||||||||
\(850\) | −16.6450 | −0.570918 | ||||||||
\(851\) | −15.5659 | −0.533593 | ||||||||
\(852\) | 1.94373 | 0.0665912 | ||||||||
\(853\) | 5.23001 | 0.179072 | 0.0895361 | − | 0.995984i | \(-0.471462\pi\) | ||||
0.0895361 | + | 0.995984i | \(0.471462\pi\) | |||||||
\(854\) | −3.24309 | −0.110976 | ||||||||
\(855\) | −5.60664 | −0.191743 | ||||||||
\(856\) | 3.92781 | 0.134250 | ||||||||
\(857\) | 50.2733 | 1.71730 | 0.858652 | − | 0.512559i | \(-0.171302\pi\) | ||||
0.858652 | + | 0.512559i | \(0.171302\pi\) | |||||||
\(858\) | 2.98171 | 0.101794 | ||||||||
\(859\) | 8.37204 | 0.285650 | 0.142825 | − | 0.989748i | \(-0.454381\pi\) | ||||
0.142825 | + | 0.989748i | \(0.454381\pi\) | |||||||
\(860\) | −3.78210 | −0.128968 | ||||||||
\(861\) | −2.01274 | −0.0685941 | ||||||||
\(862\) | −21.4370 | −0.730146 | ||||||||
\(863\) | −52.7861 | −1.79686 | −0.898429 | − | 0.439118i | \(-0.855291\pi\) | ||||
−0.898429 | + | 0.439118i | \(0.855291\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −27.8296 | −0.946235 | ||||||||
\(866\) | −6.20622 | −0.210896 | ||||||||
\(867\) | −6.76281 | −0.229677 | ||||||||
\(868\) | −3.22776 | −0.109557 | ||||||||
\(869\) | −42.2908 | −1.43462 | ||||||||
\(870\) | 12.5499 | 0.425482 | ||||||||
\(871\) | 4.94082 | 0.167413 | ||||||||
\(872\) | 11.9866 | 0.405916 | ||||||||
\(873\) | −11.3927 | −0.385584 | ||||||||
\(874\) | −18.2080 | −0.615896 | ||||||||
\(875\) | 8.44903 | 0.285629 | ||||||||
\(876\) | 7.45502 | 0.251882 | ||||||||
\(877\) | 55.2655 | 1.86618 | 0.933091 | − | 0.359640i | \(-0.117101\pi\) | ||||
0.933091 | + | 0.359640i | \(0.117101\pi\) | |||||||
\(878\) | 11.1121 | 0.375014 | ||||||||
\(879\) | 33.5092 | 1.13024 | ||||||||
\(880\) | −3.75440 | −0.126561 | ||||||||
\(881\) | −13.6393 | −0.459520 | −0.229760 | − | 0.973247i | \(-0.573794\pi\) | ||||
−0.229760 | + | 0.973247i | \(0.573794\pi\) | |||||||
\(882\) | −6.36408 | −0.214290 | ||||||||
\(883\) | 1.41598 | 0.0476515 | 0.0238257 | − | 0.999716i | \(-0.492415\pi\) | ||||
0.0238257 | + | 0.999716i | \(0.492415\pi\) | |||||||
\(884\) | 4.87471 | 0.163954 | ||||||||
\(885\) | 8.46651 | 0.284599 | ||||||||
\(886\) | −8.79189 | −0.295369 | ||||||||
\(887\) | 48.1239 | 1.61584 | 0.807922 | − | 0.589290i | \(-0.200592\pi\) | ||||
0.807922 | + | 0.589290i | \(0.200592\pi\) | |||||||
\(888\) | 3.80662 | 0.127742 | ||||||||
\(889\) | −8.78764 | −0.294728 | ||||||||
\(890\) | 18.4925 | 0.619871 | ||||||||
\(891\) | −2.98171 | −0.0998911 | ||||||||
\(892\) | 16.4842 | 0.551933 | ||||||||
\(893\) | 13.3681 | 0.447347 | ||||||||
\(894\) | 18.0807 | 0.604709 | ||||||||
\(895\) | 10.0811 | 0.336974 | ||||||||
\(896\) | −0.797445 | −0.0266408 | ||||||||
\(897\) | −4.08918 | −0.136534 | ||||||||
\(898\) | −14.1718 | −0.472921 | ||||||||
\(899\) | −40.3428 | −1.34551 | ||||||||
\(900\) | −3.41456 | −0.113819 | ||||||||
\(901\) | −42.0838 | −1.40202 | ||||||||
\(902\) | 7.52581 | 0.250582 | ||||||||
\(903\) | −2.39529 | −0.0797103 | ||||||||
\(904\) | −6.53982 | −0.217511 | ||||||||
\(905\) | −27.5271 | −0.915033 | ||||||||
\(906\) | 9.37983 | 0.311624 | ||||||||
\(907\) | 11.7722 | 0.390890 | 0.195445 | − | 0.980715i | \(-0.437385\pi\) | ||||
0.195445 | + | 0.980715i | \(0.437385\pi\) | |||||||
\(908\) | 4.26467 | 0.141528 | ||||||||
\(909\) | −5.48924 | −0.182067 | ||||||||
\(910\) | −1.00410 | −0.0332855 | ||||||||
\(911\) | −17.8337 | −0.590858 | −0.295429 | − | 0.955365i | \(-0.595463\pi\) | ||||
−0.295429 | + | 0.955365i | \(0.595463\pi\) | |||||||
\(912\) | 4.45274 | 0.147445 | ||||||||
\(913\) | −45.8577 | −1.51767 | ||||||||
\(914\) | 0.0240313 | 0.000794886 0 | ||||||||
\(915\) | −5.12075 | −0.169287 | ||||||||
\(916\) | 21.0701 | 0.696177 | ||||||||
\(917\) | 8.82052 | 0.291279 | ||||||||
\(918\) | −4.87471 | −0.160889 | ||||||||
\(919\) | −47.9606 | −1.58207 | −0.791037 | − | 0.611769i | \(-0.790458\pi\) | ||||
−0.791037 | + | 0.611769i | \(0.790458\pi\) | |||||||
\(920\) | 5.14886 | 0.169753 | ||||||||
\(921\) | −4.39459 | −0.144807 | ||||||||
\(922\) | −9.22105 | −0.303679 | ||||||||
\(923\) | −1.94373 | −0.0639787 | ||||||||
\(924\) | −2.37775 | −0.0782222 | ||||||||
\(925\) | 12.9979 | 0.427369 | ||||||||
\(926\) | −4.11875 | −0.135351 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | −9.96702 | −0.327184 | ||||||||
\(929\) | 38.1205 | 1.25069 | 0.625346 | − | 0.780347i | \(-0.284958\pi\) | ||||
0.625346 | + | 0.780347i | \(0.284958\pi\) | |||||||
\(930\) | −5.09654 | −0.167122 | ||||||||
\(931\) | 28.3376 | 0.928727 | ||||||||
\(932\) | 13.3803 | 0.438286 | ||||||||
\(933\) | 10.2447 | 0.335397 | ||||||||
\(934\) | 11.3460 | 0.371254 | ||||||||
\(935\) | −18.3016 | −0.598527 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | −5.39528 | −0.176256 | −0.0881280 | − | 0.996109i | \(-0.528088\pi\) | ||||
−0.0881280 | + | 0.996109i | \(0.528088\pi\) | |||||||
\(938\) | −3.94003 | −0.128646 | ||||||||
\(939\) | 25.1202 | 0.819766 | ||||||||
\(940\) | −3.78023 | −0.123297 | ||||||||
\(941\) | 56.5679 | 1.84406 | 0.922030 | − | 0.387118i | \(-0.126530\pi\) | ||||
0.922030 | + | 0.387118i | \(0.126530\pi\) | |||||||
\(942\) | 18.1379 | 0.590964 | ||||||||
\(943\) | −10.3210 | −0.336100 | ||||||||
\(944\) | −6.72403 | −0.218848 | ||||||||
\(945\) | 1.00410 | 0.0326633 | ||||||||
\(946\) | 8.95619 | 0.291191 | ||||||||
\(947\) | 25.7348 | 0.836269 | 0.418134 | − | 0.908385i | \(-0.362684\pi\) | ||||
0.418134 | + | 0.908385i | \(0.362684\pi\) | |||||||
\(948\) | −14.1834 | −0.460655 | ||||||||
\(949\) | −7.45502 | −0.242000 | ||||||||
\(950\) | 15.2041 | 0.493287 | ||||||||
\(951\) | 5.81992 | 0.188724 | ||||||||
\(952\) | −3.88731 | −0.125989 | ||||||||
\(953\) | −14.0912 | −0.456459 | −0.228229 | − | 0.973607i | \(-0.573294\pi\) | ||||
−0.228229 | + | 0.973607i | \(0.573294\pi\) | |||||||
\(954\) | −8.63309 | −0.279507 | ||||||||
\(955\) | 28.9535 | 0.936912 | ||||||||
\(956\) | 29.5612 | 0.956076 | ||||||||
\(957\) | −29.7188 | −0.960672 | ||||||||
\(958\) | −18.0330 | −0.582620 | ||||||||
\(959\) | 17.2893 | 0.558299 | ||||||||
\(960\) | −1.25914 | −0.0406387 | ||||||||
\(961\) | −14.6167 | −0.471507 | ||||||||
\(962\) | −3.80662 | −0.122730 | ||||||||
\(963\) | 3.92781 | 0.126572 | ||||||||
\(964\) | −2.85139 | −0.0918371 | ||||||||
\(965\) | 15.2214 | 0.489995 | ||||||||
\(966\) | 3.26089 | 0.104917 | ||||||||
\(967\) | 17.9570 | 0.577459 | 0.288730 | − | 0.957411i | \(-0.406767\pi\) | ||||
0.288730 | + | 0.957411i | \(0.406767\pi\) | |||||||
\(968\) | −2.10940 | −0.0677987 | ||||||||
\(969\) | 21.7058 | 0.697291 | ||||||||
\(970\) | −14.3450 | −0.460591 | ||||||||
\(971\) | 14.3002 | 0.458915 | 0.229457 | − | 0.973319i | \(-0.426305\pi\) | ||||
0.229457 | + | 0.973319i | \(0.426305\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 3.20232 | 0.102662 | ||||||||
\(974\) | −41.4619 | −1.32852 | ||||||||
\(975\) | 3.41456 | 0.109353 | ||||||||
\(976\) | 4.06686 | 0.130177 | ||||||||
\(977\) | 24.7427 | 0.791588 | 0.395794 | − | 0.918339i | \(-0.370469\pi\) | ||||
0.395794 | + | 0.918339i | \(0.370469\pi\) | |||||||
\(978\) | 15.9568 | 0.510241 | ||||||||
\(979\) | −43.7912 | −1.39957 | ||||||||
\(980\) | −8.01329 | −0.255975 | ||||||||
\(981\) | 11.9866 | 0.382701 | ||||||||
\(982\) | −34.9707 | −1.11596 | ||||||||
\(983\) | 5.61508 | 0.179093 | 0.0895467 | − | 0.995983i | \(-0.471458\pi\) | ||||
0.0895467 | + | 0.995983i | \(0.471458\pi\) | |||||||
\(984\) | 2.52399 | 0.0804619 | ||||||||
\(985\) | −1.04285 | −0.0332279 | ||||||||
\(986\) | −48.5864 | −1.54731 | ||||||||
\(987\) | −2.39411 | −0.0762052 | ||||||||
\(988\) | −4.45274 | −0.141661 | ||||||||
\(989\) | −12.2827 | −0.390567 | ||||||||
\(990\) | −3.75440 | −0.119323 | ||||||||
\(991\) | −36.2473 | −1.15143 | −0.575717 | − | 0.817649i | \(-0.695277\pi\) | ||||
−0.575717 | + | 0.817649i | \(0.695277\pi\) | |||||||
\(992\) | 4.04763 | 0.128512 | ||||||||
\(993\) | 20.4154 | 0.647864 | ||||||||
\(994\) | 1.55002 | 0.0491636 | ||||||||
\(995\) | −21.3290 | −0.676176 | ||||||||
\(996\) | −15.3797 | −0.487323 | ||||||||
\(997\) | −5.00212 | −0.158419 | −0.0792094 | − | 0.996858i | \(-0.525240\pi\) | ||||
−0.0792094 | + | 0.996858i | \(0.525240\pi\) | |||||||
\(998\) | −18.4859 | −0.585161 | ||||||||
\(999\) | 3.80662 | 0.120436 |
(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 | 8034.2.a.r.1.7 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.r.1.7 | ✓ | 9 | 1.1 | even | 1 | trivial |