Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6046,2,Mod(1,6046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6046, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6046 = 2 \cdot 3023 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6046.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: | \(48.2775530621\) |
Analytic rank: | \(0\) |
Dimension: | \(69\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 6046.1 |
$q$-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 | ||||||||
\(3\) | −2.29528 | −1.32518 | −0.662589 | − | 0.748983i | \(-0.730542\pi\) | ||||
−0.662589 | + | 0.748983i | \(0.730542\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.67586 | 1.19668 | 0.598340 | − | 0.801242i | \(-0.295827\pi\) | ||||
0.598340 | + | 0.801242i | \(0.295827\pi\) | |||||||
\(6\) | 2.29528 | 0.937042 | ||||||||
\(7\) | −0.797143 | −0.301292 | −0.150646 | − | 0.988588i | \(-0.548135\pi\) | ||||
−0.150646 | + | 0.988588i | \(0.548135\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.26829 | 0.756097 | ||||||||
\(10\) | −2.67586 | −0.846181 | ||||||||
\(11\) | −4.72849 | −1.42569 | −0.712847 | − | 0.701320i | \(-0.752595\pi\) | ||||
−0.712847 | + | 0.701320i | \(0.752595\pi\) | |||||||
\(12\) | −2.29528 | −0.662589 | ||||||||
\(13\) | 2.21536 | 0.614432 | 0.307216 | − | 0.951640i | \(-0.400603\pi\) | ||||
0.307216 | + | 0.951640i | \(0.400603\pi\) | |||||||
\(14\) | 0.797143 | 0.213045 | ||||||||
\(15\) | −6.14183 | −1.58581 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.95149 | 1.44345 | 0.721724 | − | 0.692181i | \(-0.243350\pi\) | ||||
0.721724 | + | 0.692181i | \(0.243350\pi\) | |||||||
\(18\) | −2.26829 | −0.534641 | ||||||||
\(19\) | −8.03117 | −1.84248 | −0.921238 | − | 0.389000i | \(-0.872821\pi\) | ||||
−0.921238 | + | 0.389000i | \(0.872821\pi\) | |||||||
\(20\) | 2.67586 | 0.598340 | ||||||||
\(21\) | 1.82966 | 0.399265 | ||||||||
\(22\) | 4.72849 | 1.00812 | ||||||||
\(23\) | −2.81923 | −0.587850 | −0.293925 | − | 0.955829i | \(-0.594962\pi\) | ||||
−0.293925 | + | 0.955829i | \(0.594962\pi\) | |||||||
\(24\) | 2.29528 | 0.468521 | ||||||||
\(25\) | 2.16022 | 0.432044 | ||||||||
\(26\) | −2.21536 | −0.434469 | ||||||||
\(27\) | 1.67947 | 0.323215 | ||||||||
\(28\) | −0.797143 | −0.150646 | ||||||||
\(29\) | −0.0257294 | −0.00477784 | −0.00238892 | − | 0.999997i | \(-0.500760\pi\) | ||||
−0.00238892 | + | 0.999997i | \(0.500760\pi\) | |||||||
\(30\) | 6.14183 | 1.12134 | ||||||||
\(31\) | 2.78469 | 0.500145 | 0.250073 | − | 0.968227i | \(-0.419546\pi\) | ||||
0.250073 | + | 0.968227i | \(0.419546\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 10.8532 | 1.88930 | ||||||||
\(34\) | −5.95149 | −1.02067 | ||||||||
\(35\) | −2.13304 | −0.360550 | ||||||||
\(36\) | 2.26829 | 0.378048 | ||||||||
\(37\) | −10.1286 | −1.66513 | −0.832566 | − | 0.553926i | \(-0.813129\pi\) | ||||
−0.832566 | + | 0.553926i | \(0.813129\pi\) | |||||||
\(38\) | 8.03117 | 1.30283 | ||||||||
\(39\) | −5.08487 | −0.814231 | ||||||||
\(40\) | −2.67586 | −0.423090 | ||||||||
\(41\) | −6.45270 | −1.00774 | −0.503871 | − | 0.863779i | \(-0.668091\pi\) | ||||
−0.503871 | + | 0.863779i | \(0.668091\pi\) | |||||||
\(42\) | −1.82966 | −0.282323 | ||||||||
\(43\) | 5.94048 | 0.905915 | 0.452957 | − | 0.891532i | \(-0.350369\pi\) | ||||
0.452957 | + | 0.891532i | \(0.350369\pi\) | |||||||
\(44\) | −4.72849 | −0.712847 | ||||||||
\(45\) | 6.06963 | 0.904806 | ||||||||
\(46\) | 2.81923 | 0.415673 | ||||||||
\(47\) | 6.16027 | 0.898568 | 0.449284 | − | 0.893389i | \(-0.351679\pi\) | ||||
0.449284 | + | 0.893389i | \(0.351679\pi\) | |||||||
\(48\) | −2.29528 | −0.331295 | ||||||||
\(49\) | −6.36456 | −0.909223 | ||||||||
\(50\) | −2.16022 | −0.305501 | ||||||||
\(51\) | −13.6603 | −1.91283 | ||||||||
\(52\) | 2.21536 | 0.307216 | ||||||||
\(53\) | −3.53867 | −0.486074 | −0.243037 | − | 0.970017i | \(-0.578144\pi\) | ||||
−0.243037 | + | 0.970017i | \(0.578144\pi\) | |||||||
\(54\) | −1.67947 | −0.228548 | ||||||||
\(55\) | −12.6528 | −1.70610 | ||||||||
\(56\) | 0.797143 | 0.106523 | ||||||||
\(57\) | 18.4337 | 2.44161 | ||||||||
\(58\) | 0.0257294 | 0.00337844 | ||||||||
\(59\) | −4.31537 | −0.561814 | −0.280907 | − | 0.959735i | \(-0.590635\pi\) | ||||
−0.280907 | + | 0.959735i | \(0.590635\pi\) | |||||||
\(60\) | −6.14183 | −0.792907 | ||||||||
\(61\) | 10.1809 | 1.30352 | 0.651762 | − | 0.758423i | \(-0.274030\pi\) | ||||
0.651762 | + | 0.758423i | \(0.274030\pi\) | |||||||
\(62\) | −2.78469 | −0.353656 | ||||||||
\(63\) | −1.80815 | −0.227806 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.92800 | 0.735278 | ||||||||
\(66\) | −10.8532 | −1.33594 | ||||||||
\(67\) | 3.52973 | 0.431226 | 0.215613 | − | 0.976479i | \(-0.430825\pi\) | ||||
0.215613 | + | 0.976479i | \(0.430825\pi\) | |||||||
\(68\) | 5.95149 | 0.721724 | ||||||||
\(69\) | 6.47091 | 0.779006 | ||||||||
\(70\) | 2.13304 | 0.254947 | ||||||||
\(71\) | −0.491838 | −0.0583704 | −0.0291852 | − | 0.999574i | \(-0.509291\pi\) | ||||
−0.0291852 | + | 0.999574i | \(0.509291\pi\) | |||||||
\(72\) | −2.26829 | −0.267321 | ||||||||
\(73\) | 11.9382 | 1.39727 | 0.698633 | − | 0.715481i | \(-0.253792\pi\) | ||||
0.698633 | + | 0.715481i | \(0.253792\pi\) | |||||||
\(74\) | 10.1286 | 1.17743 | ||||||||
\(75\) | −4.95830 | −0.572535 | ||||||||
\(76\) | −8.03117 | −0.921238 | ||||||||
\(77\) | 3.76928 | 0.429550 | ||||||||
\(78\) | 5.08487 | 0.575749 | ||||||||
\(79\) | 4.37177 | 0.491862 | 0.245931 | − | 0.969287i | \(-0.420906\pi\) | ||||
0.245931 | + | 0.969287i | \(0.420906\pi\) | |||||||
\(80\) | 2.67586 | 0.299170 | ||||||||
\(81\) | −10.6597 | −1.18441 | ||||||||
\(82\) | 6.45270 | 0.712582 | ||||||||
\(83\) | −15.8166 | −1.73610 | −0.868048 | − | 0.496480i | \(-0.834626\pi\) | ||||
−0.868048 | + | 0.496480i | \(0.834626\pi\) | |||||||
\(84\) | 1.82966 | 0.199633 | ||||||||
\(85\) | 15.9253 | 1.72735 | ||||||||
\(86\) | −5.94048 | −0.640578 | ||||||||
\(87\) | 0.0590561 | 0.00633148 | ||||||||
\(88\) | 4.72849 | 0.504059 | ||||||||
\(89\) | 13.0607 | 1.38443 | 0.692215 | − | 0.721692i | \(-0.256635\pi\) | ||||
0.692215 | + | 0.721692i | \(0.256635\pi\) | |||||||
\(90\) | −6.06963 | −0.639795 | ||||||||
\(91\) | −1.76596 | −0.185123 | ||||||||
\(92\) | −2.81923 | −0.293925 | ||||||||
\(93\) | −6.39163 | −0.662781 | ||||||||
\(94\) | −6.16027 | −0.635383 | ||||||||
\(95\) | −21.4903 | −2.20485 | ||||||||
\(96\) | 2.29528 | 0.234261 | ||||||||
\(97\) | −17.5486 | −1.78179 | −0.890893 | − | 0.454213i | \(-0.849921\pi\) | ||||
−0.890893 | + | 0.454213i | \(0.849921\pi\) | |||||||
\(98\) | 6.36456 | 0.642918 | ||||||||
\(99\) | −10.7256 | −1.07796 | ||||||||
\(100\) | 2.16022 | 0.216022 | ||||||||
\(101\) | 0.211788 | 0.0210737 | 0.0105368 | − | 0.999944i | \(-0.496646\pi\) | ||||
0.0105368 | + | 0.999944i | \(0.496646\pi\) | |||||||
\(102\) | 13.6603 | 1.35257 | ||||||||
\(103\) | 15.0701 | 1.48490 | 0.742450 | − | 0.669901i | \(-0.233664\pi\) | ||||
0.742450 | + | 0.669901i | \(0.233664\pi\) | |||||||
\(104\) | −2.21536 | −0.217234 | ||||||||
\(105\) | 4.89592 | 0.477793 | ||||||||
\(106\) | 3.53867 | 0.343706 | ||||||||
\(107\) | 9.01855 | 0.871856 | 0.435928 | − | 0.899982i | \(-0.356420\pi\) | ||||
0.435928 | + | 0.899982i | \(0.356420\pi\) | |||||||
\(108\) | 1.67947 | 0.161608 | ||||||||
\(109\) | 12.2861 | 1.17680 | 0.588398 | − | 0.808572i | \(-0.299759\pi\) | ||||
0.588398 | + | 0.808572i | \(0.299759\pi\) | |||||||
\(110\) | 12.6528 | 1.20639 | ||||||||
\(111\) | 23.2479 | 2.20660 | ||||||||
\(112\) | −0.797143 | −0.0753229 | ||||||||
\(113\) | 19.4534 | 1.83002 | 0.915011 | − | 0.403429i | \(-0.132182\pi\) | ||||
0.915011 | + | 0.403429i | \(0.132182\pi\) | |||||||
\(114\) | −18.4337 | −1.72648 | ||||||||
\(115\) | −7.54386 | −0.703468 | ||||||||
\(116\) | −0.0257294 | −0.00238892 | ||||||||
\(117\) | 5.02509 | 0.464570 | ||||||||
\(118\) | 4.31537 | 0.397262 | ||||||||
\(119\) | −4.74419 | −0.434899 | ||||||||
\(120\) | 6.14183 | 0.560670 | ||||||||
\(121\) | 11.3586 | 1.03260 | ||||||||
\(122\) | −10.1809 | −0.921731 | ||||||||
\(123\) | 14.8107 | 1.33544 | ||||||||
\(124\) | 2.78469 | 0.250073 | ||||||||
\(125\) | −7.59885 | −0.679662 | ||||||||
\(126\) | 1.80815 | 0.161083 | ||||||||
\(127\) | −5.89558 | −0.523149 | −0.261574 | − | 0.965183i | \(-0.584242\pi\) | ||||
−0.261574 | + | 0.965183i | \(0.584242\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −13.6350 | −1.20050 | ||||||||
\(130\) | −5.92800 | −0.519920 | ||||||||
\(131\) | −3.79936 | −0.331952 | −0.165976 | − | 0.986130i | \(-0.553077\pi\) | ||||
−0.165976 | + | 0.986130i | \(0.553077\pi\) | |||||||
\(132\) | 10.8532 | 0.944649 | ||||||||
\(133\) | 6.40199 | 0.555123 | ||||||||
\(134\) | −3.52973 | −0.304923 | ||||||||
\(135\) | 4.49404 | 0.386785 | ||||||||
\(136\) | −5.95149 | −0.510336 | ||||||||
\(137\) | 8.27956 | 0.707371 | 0.353685 | − | 0.935364i | \(-0.384928\pi\) | ||||
0.353685 | + | 0.935364i | \(0.384928\pi\) | |||||||
\(138\) | −6.47091 | −0.550840 | ||||||||
\(139\) | 7.07166 | 0.599810 | 0.299905 | − | 0.953969i | \(-0.403045\pi\) | ||||
0.299905 | + | 0.953969i | \(0.403045\pi\) | |||||||
\(140\) | −2.13304 | −0.180275 | ||||||||
\(141\) | −14.1395 | −1.19076 | ||||||||
\(142\) | 0.491838 | 0.0412741 | ||||||||
\(143\) | −10.4753 | −0.875991 | ||||||||
\(144\) | 2.26829 | 0.189024 | ||||||||
\(145\) | −0.0688483 | −0.00571754 | ||||||||
\(146\) | −11.9382 | −0.988016 | ||||||||
\(147\) | 14.6084 | 1.20488 | ||||||||
\(148\) | −10.1286 | −0.832566 | ||||||||
\(149\) | −5.35489 | −0.438690 | −0.219345 | − | 0.975647i | \(-0.570392\pi\) | ||||
−0.219345 | + | 0.975647i | \(0.570392\pi\) | |||||||
\(150\) | 4.95830 | 0.404844 | ||||||||
\(151\) | −2.19805 | −0.178875 | −0.0894375 | − | 0.995992i | \(-0.528507\pi\) | ||||
−0.0894375 | + | 0.995992i | \(0.528507\pi\) | |||||||
\(152\) | 8.03117 | 0.651414 | ||||||||
\(153\) | 13.4997 | 1.09139 | ||||||||
\(154\) | −3.76928 | −0.303737 | ||||||||
\(155\) | 7.45144 | 0.598514 | ||||||||
\(156\) | −5.08487 | −0.407116 | ||||||||
\(157\) | 16.0486 | 1.28081 | 0.640407 | − | 0.768035i | \(-0.278766\pi\) | ||||
0.640407 | + | 0.768035i | \(0.278766\pi\) | |||||||
\(158\) | −4.37177 | −0.347799 | ||||||||
\(159\) | 8.12223 | 0.644135 | ||||||||
\(160\) | −2.67586 | −0.211545 | ||||||||
\(161\) | 2.24733 | 0.177114 | ||||||||
\(162\) | 10.6597 | 0.837507 | ||||||||
\(163\) | −21.3215 | −1.67003 | −0.835014 | − | 0.550229i | \(-0.814541\pi\) | ||||
−0.835014 | + | 0.550229i | \(0.814541\pi\) | |||||||
\(164\) | −6.45270 | −0.503871 | ||||||||
\(165\) | 29.0416 | 2.26089 | ||||||||
\(166\) | 15.8166 | 1.22761 | ||||||||
\(167\) | −5.39808 | −0.417716 | −0.208858 | − | 0.977946i | \(-0.566975\pi\) | ||||
−0.208858 | + | 0.977946i | \(0.566975\pi\) | |||||||
\(168\) | −1.82966 | −0.141162 | ||||||||
\(169\) | −8.09216 | −0.622474 | ||||||||
\(170\) | −15.9253 | −1.22142 | ||||||||
\(171\) | −18.2170 | −1.39309 | ||||||||
\(172\) | 5.94048 | 0.452957 | ||||||||
\(173\) | 6.45502 | 0.490766 | 0.245383 | − | 0.969426i | \(-0.421086\pi\) | ||||
0.245383 | + | 0.969426i | \(0.421086\pi\) | |||||||
\(174\) | −0.0590561 | −0.00447703 | ||||||||
\(175\) | −1.72200 | −0.130171 | ||||||||
\(176\) | −4.72849 | −0.356423 | ||||||||
\(177\) | 9.90497 | 0.744503 | ||||||||
\(178\) | −13.0607 | −0.978939 | ||||||||
\(179\) | −13.0398 | −0.974637 | −0.487318 | − | 0.873224i | \(-0.662025\pi\) | ||||
−0.487318 | + | 0.873224i | \(0.662025\pi\) | |||||||
\(180\) | 6.06963 | 0.452403 | ||||||||
\(181\) | 17.9465 | 1.33395 | 0.666977 | − | 0.745078i | \(-0.267588\pi\) | ||||
0.666977 | + | 0.745078i | \(0.267588\pi\) | |||||||
\(182\) | 1.76596 | 0.130902 | ||||||||
\(183\) | −23.3679 | −1.72740 | ||||||||
\(184\) | 2.81923 | 0.207836 | ||||||||
\(185\) | −27.1027 | −1.99263 | ||||||||
\(186\) | 6.39163 | 0.468657 | ||||||||
\(187\) | −28.1416 | −2.05792 | ||||||||
\(188\) | 6.16027 | 0.449284 | ||||||||
\(189\) | −1.33878 | −0.0973820 | ||||||||
\(190\) | 21.4903 | 1.55907 | ||||||||
\(191\) | −4.33850 | −0.313923 | −0.156961 | − | 0.987605i | \(-0.550170\pi\) | ||||
−0.156961 | + | 0.987605i | \(0.550170\pi\) | |||||||
\(192\) | −2.29528 | −0.165647 | ||||||||
\(193\) | −22.0936 | −1.59033 | −0.795167 | − | 0.606391i | \(-0.792617\pi\) | ||||
−0.795167 | + | 0.606391i | \(0.792617\pi\) | |||||||
\(194\) | 17.5486 | 1.25991 | ||||||||
\(195\) | −13.6064 | −0.974375 | ||||||||
\(196\) | −6.36456 | −0.454612 | ||||||||
\(197\) | −21.1403 | −1.50618 | −0.753092 | − | 0.657916i | \(-0.771438\pi\) | ||||
−0.753092 | + | 0.657916i | \(0.771438\pi\) | |||||||
\(198\) | 10.7256 | 0.762235 | ||||||||
\(199\) | 6.95972 | 0.493362 | 0.246681 | − | 0.969097i | \(-0.420660\pi\) | ||||
0.246681 | + | 0.969097i | \(0.420660\pi\) | |||||||
\(200\) | −2.16022 | −0.152751 | ||||||||
\(201\) | −8.10171 | −0.571451 | ||||||||
\(202\) | −0.211788 | −0.0149013 | ||||||||
\(203\) | 0.0205100 | 0.00143952 | ||||||||
\(204\) | −13.6603 | −0.956413 | ||||||||
\(205\) | −17.2665 | −1.20595 | ||||||||
\(206\) | −15.0701 | −1.04998 | ||||||||
\(207\) | −6.39483 | −0.444471 | ||||||||
\(208\) | 2.21536 | 0.153608 | ||||||||
\(209\) | 37.9753 | 2.62681 | ||||||||
\(210\) | −4.89592 | −0.337850 | ||||||||
\(211\) | −11.6737 | −0.803652 | −0.401826 | − | 0.915716i | \(-0.631624\pi\) | ||||
−0.401826 | + | 0.915716i | \(0.631624\pi\) | |||||||
\(212\) | −3.53867 | −0.243037 | ||||||||
\(213\) | 1.12890 | 0.0773511 | ||||||||
\(214\) | −9.01855 | −0.616495 | ||||||||
\(215\) | 15.8959 | 1.08409 | ||||||||
\(216\) | −1.67947 | −0.114274 | ||||||||
\(217\) | −2.21980 | −0.150690 | ||||||||
\(218\) | −12.2861 | −0.832120 | ||||||||
\(219\) | −27.4016 | −1.85163 | ||||||||
\(220\) | −12.6528 | −0.853050 | ||||||||
\(221\) | 13.1847 | 0.886901 | ||||||||
\(222\) | −23.2479 | −1.56030 | ||||||||
\(223\) | −1.81507 | −0.121546 | −0.0607731 | − | 0.998152i | \(-0.519357\pi\) | ||||
−0.0607731 | + | 0.998152i | \(0.519357\pi\) | |||||||
\(224\) | 0.797143 | 0.0532613 | ||||||||
\(225\) | 4.90001 | 0.326667 | ||||||||
\(226\) | −19.4534 | −1.29402 | ||||||||
\(227\) | 16.1950 | 1.07490 | 0.537450 | − | 0.843295i | \(-0.319387\pi\) | ||||
0.537450 | + | 0.843295i | \(0.319387\pi\) | |||||||
\(228\) | 18.4337 | 1.22080 | ||||||||
\(229\) | −8.80688 | −0.581975 | −0.290988 | − | 0.956727i | \(-0.593984\pi\) | ||||
−0.290988 | + | 0.956727i | \(0.593984\pi\) | |||||||
\(230\) | 7.54386 | 0.497427 | ||||||||
\(231\) | −8.65154 | −0.569230 | ||||||||
\(232\) | 0.0257294 | 0.00168922 | ||||||||
\(233\) | 6.09380 | 0.399218 | 0.199609 | − | 0.979876i | \(-0.436033\pi\) | ||||
0.199609 | + | 0.979876i | \(0.436033\pi\) | |||||||
\(234\) | −5.02509 | −0.328500 | ||||||||
\(235\) | 16.4840 | 1.07530 | ||||||||
\(236\) | −4.31537 | −0.280907 | ||||||||
\(237\) | −10.0344 | −0.651805 | ||||||||
\(238\) | 4.74419 | 0.307520 | ||||||||
\(239\) | 17.5768 | 1.13695 | 0.568476 | − | 0.822700i | \(-0.307533\pi\) | ||||
0.568476 | + | 0.822700i | \(0.307533\pi\) | |||||||
\(240\) | −6.14183 | −0.396454 | ||||||||
\(241\) | 1.56163 | 0.100594 | 0.0502969 | − | 0.998734i | \(-0.483983\pi\) | ||||
0.0502969 | + | 0.998734i | \(0.483983\pi\) | |||||||
\(242\) | −11.3586 | −0.730160 | ||||||||
\(243\) | 19.4286 | 1.24634 | ||||||||
\(244\) | 10.1809 | 0.651762 | ||||||||
\(245\) | −17.0307 | −1.08805 | ||||||||
\(246\) | −14.8107 | −0.944298 | ||||||||
\(247\) | −17.7920 | −1.13208 | ||||||||
\(248\) | −2.78469 | −0.176828 | ||||||||
\(249\) | 36.3034 | 2.30064 | ||||||||
\(250\) | 7.59885 | 0.480593 | ||||||||
\(251\) | 22.2420 | 1.40390 | 0.701952 | − | 0.712224i | \(-0.252312\pi\) | ||||
0.701952 | + | 0.712224i | \(0.252312\pi\) | |||||||
\(252\) | −1.80815 | −0.113903 | ||||||||
\(253\) | 13.3307 | 0.838094 | ||||||||
\(254\) | 5.89558 | 0.369922 | ||||||||
\(255\) | −36.5531 | −2.28904 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 21.4026 | 1.33506 | 0.667529 | − | 0.744584i | \(-0.267352\pi\) | ||||
0.667529 | + | 0.744584i | \(0.267352\pi\) | |||||||
\(258\) | 13.6350 | 0.848880 | ||||||||
\(259\) | 8.07394 | 0.501690 | ||||||||
\(260\) | 5.92800 | 0.367639 | ||||||||
\(261\) | −0.0583618 | −0.00361251 | ||||||||
\(262\) | 3.79936 | 0.234725 | ||||||||
\(263\) | 1.93215 | 0.119141 | 0.0595706 | − | 0.998224i | \(-0.481027\pi\) | ||||
0.0595706 | + | 0.998224i | \(0.481027\pi\) | |||||||
\(264\) | −10.8532 | −0.667968 | ||||||||
\(265\) | −9.46899 | −0.581675 | ||||||||
\(266\) | −6.40199 | −0.392531 | ||||||||
\(267\) | −29.9779 | −1.83462 | ||||||||
\(268\) | 3.52973 | 0.215613 | ||||||||
\(269\) | 6.89306 | 0.420277 | 0.210139 | − | 0.977672i | \(-0.432608\pi\) | ||||
0.210139 | + | 0.977672i | \(0.432608\pi\) | |||||||
\(270\) | −4.49404 | −0.273498 | ||||||||
\(271\) | −11.7295 | −0.712516 | −0.356258 | − | 0.934388i | \(-0.615948\pi\) | ||||
−0.356258 | + | 0.934388i | \(0.615948\pi\) | |||||||
\(272\) | 5.95149 | 0.360862 | ||||||||
\(273\) | 4.05337 | 0.245321 | ||||||||
\(274\) | −8.27956 | −0.500187 | ||||||||
\(275\) | −10.2146 | −0.615962 | ||||||||
\(276\) | 6.47091 | 0.389503 | ||||||||
\(277\) | −30.6706 | −1.84282 | −0.921409 | − | 0.388594i | \(-0.872961\pi\) | ||||
−0.921409 | + | 0.388594i | \(0.872961\pi\) | |||||||
\(278\) | −7.07166 | −0.424130 | ||||||||
\(279\) | 6.31649 | 0.378158 | ||||||||
\(280\) | 2.13304 | 0.127474 | ||||||||
\(281\) | 24.4405 | 1.45800 | 0.728998 | − | 0.684516i | \(-0.239986\pi\) | ||||
0.728998 | + | 0.684516i | \(0.239986\pi\) | |||||||
\(282\) | 14.1395 | 0.841996 | ||||||||
\(283\) | 15.8345 | 0.941266 | 0.470633 | − | 0.882329i | \(-0.344026\pi\) | ||||
0.470633 | + | 0.882329i | \(0.344026\pi\) | |||||||
\(284\) | −0.491838 | −0.0291852 | ||||||||
\(285\) | 49.3261 | 2.92182 | ||||||||
\(286\) | 10.4753 | 0.619419 | ||||||||
\(287\) | 5.14372 | 0.303624 | ||||||||
\(288\) | −2.26829 | −0.133660 | ||||||||
\(289\) | 18.4202 | 1.08354 | ||||||||
\(290\) | 0.0688483 | 0.00404291 | ||||||||
\(291\) | 40.2788 | 2.36118 | ||||||||
\(292\) | 11.9382 | 0.698633 | ||||||||
\(293\) | 6.24103 | 0.364605 | 0.182302 | − | 0.983243i | \(-0.441645\pi\) | ||||
0.182302 | + | 0.983243i | \(0.441645\pi\) | |||||||
\(294\) | −14.6084 | −0.851981 | ||||||||
\(295\) | −11.5473 | −0.672311 | ||||||||
\(296\) | 10.1286 | 0.588713 | ||||||||
\(297\) | −7.94138 | −0.460806 | ||||||||
\(298\) | 5.35489 | 0.310201 | ||||||||
\(299\) | −6.24562 | −0.361194 | ||||||||
\(300\) | −4.95830 | −0.286268 | ||||||||
\(301\) | −4.73541 | −0.272945 | ||||||||
\(302\) | 2.19805 | 0.126484 | ||||||||
\(303\) | −0.486111 | −0.0279263 | ||||||||
\(304\) | −8.03117 | −0.460619 | ||||||||
\(305\) | 27.2425 | 1.55990 | ||||||||
\(306\) | −13.4997 | −0.771727 | ||||||||
\(307\) | 2.64951 | 0.151215 | 0.0756077 | − | 0.997138i | \(-0.475910\pi\) | ||||
0.0756077 | + | 0.997138i | \(0.475910\pi\) | |||||||
\(308\) | 3.76928 | 0.214775 | ||||||||
\(309\) | −34.5900 | −1.96776 | ||||||||
\(310\) | −7.45144 | −0.423213 | ||||||||
\(311\) | 0.0266046 | 0.00150861 | 0.000754305 | − | 1.00000i | \(-0.499760\pi\) | ||||
0.000754305 | 1.00000i | \(0.499760\pi\) | ||||||||
\(312\) | 5.08487 | 0.287874 | ||||||||
\(313\) | 13.9540 | 0.788725 | 0.394362 | − | 0.918955i | \(-0.370966\pi\) | ||||
0.394362 | + | 0.918955i | \(0.370966\pi\) | |||||||
\(314\) | −16.0486 | −0.905673 | ||||||||
\(315\) | −4.83836 | −0.272611 | ||||||||
\(316\) | 4.37177 | 0.245931 | ||||||||
\(317\) | −9.84385 | −0.552886 | −0.276443 | − | 0.961030i | \(-0.589156\pi\) | ||||
−0.276443 | + | 0.961030i | \(0.589156\pi\) | |||||||
\(318\) | −8.12223 | −0.455472 | ||||||||
\(319\) | 0.121661 | 0.00681173 | ||||||||
\(320\) | 2.67586 | 0.149585 | ||||||||
\(321\) | −20.7001 | −1.15536 | ||||||||
\(322\) | −2.24733 | −0.125239 | ||||||||
\(323\) | −47.7974 | −2.65952 | ||||||||
\(324\) | −10.6597 | −0.592207 | ||||||||
\(325\) | 4.78568 | 0.265462 | ||||||||
\(326\) | 21.3215 | 1.18089 | ||||||||
\(327\) | −28.2000 | −1.55946 | ||||||||
\(328\) | 6.45270 | 0.356291 | ||||||||
\(329\) | −4.91062 | −0.270731 | ||||||||
\(330\) | −29.0416 | −1.59869 | ||||||||
\(331\) | −4.67627 | −0.257031 | −0.128515 | − | 0.991708i | \(-0.541021\pi\) | ||||
−0.128515 | + | 0.991708i | \(0.541021\pi\) | |||||||
\(332\) | −15.8166 | −0.868048 | ||||||||
\(333\) | −22.9746 | −1.25900 | ||||||||
\(334\) | 5.39808 | 0.295370 | ||||||||
\(335\) | 9.44507 | 0.516039 | ||||||||
\(336\) | 1.82966 | 0.0998163 | ||||||||
\(337\) | −11.8810 | −0.647197 | −0.323599 | − | 0.946194i | \(-0.604893\pi\) | ||||
−0.323599 | + | 0.946194i | \(0.604893\pi\) | |||||||
\(338\) | 8.09216 | 0.440155 | ||||||||
\(339\) | −44.6509 | −2.42510 | ||||||||
\(340\) | 15.9253 | 0.863673 | ||||||||
\(341\) | −13.1674 | −0.713054 | ||||||||
\(342\) | 18.2170 | 0.985063 | ||||||||
\(343\) | 10.6535 | 0.575233 | ||||||||
\(344\) | −5.94048 | −0.320289 | ||||||||
\(345\) | 17.3152 | 0.932221 | ||||||||
\(346\) | −6.45502 | −0.347024 | ||||||||
\(347\) | −35.8859 | −1.92646 | −0.963228 | − | 0.268686i | \(-0.913411\pi\) | ||||
−0.963228 | + | 0.268686i | \(0.913411\pi\) | |||||||
\(348\) | 0.0590561 | 0.00316574 | ||||||||
\(349\) | 24.0051 | 1.28496 | 0.642481 | − | 0.766302i | \(-0.277905\pi\) | ||||
0.642481 | + | 0.766302i | \(0.277905\pi\) | |||||||
\(350\) | 1.72200 | 0.0920450 | ||||||||
\(351\) | 3.72065 | 0.198594 | ||||||||
\(352\) | 4.72849 | 0.252029 | ||||||||
\(353\) | 20.7832 | 1.10618 | 0.553090 | − | 0.833122i | \(-0.313449\pi\) | ||||
0.553090 | + | 0.833122i | \(0.313449\pi\) | |||||||
\(354\) | −9.90497 | −0.526443 | ||||||||
\(355\) | −1.31609 | −0.0698507 | ||||||||
\(356\) | 13.0607 | 0.692215 | ||||||||
\(357\) | 10.8892 | 0.576319 | ||||||||
\(358\) | 13.0398 | 0.689172 | ||||||||
\(359\) | 25.8606 | 1.36487 | 0.682436 | − | 0.730945i | \(-0.260921\pi\) | ||||
0.682436 | + | 0.730945i | \(0.260921\pi\) | |||||||
\(360\) | −6.06963 | −0.319897 | ||||||||
\(361\) | 45.4996 | 2.39472 | ||||||||
\(362\) | −17.9465 | −0.943248 | ||||||||
\(363\) | −26.0712 | −1.36838 | ||||||||
\(364\) | −1.76596 | −0.0925616 | ||||||||
\(365\) | 31.9450 | 1.67208 | ||||||||
\(366\) | 23.3679 | 1.22146 | ||||||||
\(367\) | 5.57150 | 0.290830 | 0.145415 | − | 0.989371i | \(-0.453548\pi\) | ||||
0.145415 | + | 0.989371i | \(0.453548\pi\) | |||||||
\(368\) | −2.81923 | −0.146962 | ||||||||
\(369\) | −14.6366 | −0.761951 | ||||||||
\(370\) | 27.1027 | 1.40900 | ||||||||
\(371\) | 2.82083 | 0.146450 | ||||||||
\(372\) | −6.39163 | −0.331391 | ||||||||
\(373\) | −2.72743 | −0.141221 | −0.0706105 | − | 0.997504i | \(-0.522495\pi\) | ||||
−0.0706105 | + | 0.997504i | \(0.522495\pi\) | |||||||
\(374\) | 28.1416 | 1.45517 | ||||||||
\(375\) | 17.4415 | 0.900673 | ||||||||
\(376\) | −6.16027 | −0.317692 | ||||||||
\(377\) | −0.0570001 | −0.00293565 | ||||||||
\(378\) | 1.33878 | 0.0688595 | ||||||||
\(379\) | 31.0762 | 1.59628 | 0.798139 | − | 0.602473i | \(-0.205818\pi\) | ||||
0.798139 | + | 0.602473i | \(0.205818\pi\) | |||||||
\(380\) | −21.4903 | −1.10243 | ||||||||
\(381\) | 13.5320 | 0.693265 | ||||||||
\(382\) | 4.33850 | 0.221977 | ||||||||
\(383\) | −34.7199 | −1.77410 | −0.887052 | − | 0.461669i | \(-0.847251\pi\) | ||||
−0.887052 | + | 0.461669i | \(0.847251\pi\) | |||||||
\(384\) | 2.29528 | 0.117130 | ||||||||
\(385\) | 10.0861 | 0.514034 | ||||||||
\(386\) | 22.0936 | 1.12454 | ||||||||
\(387\) | 13.4747 | 0.684959 | ||||||||
\(388\) | −17.5486 | −0.890893 | ||||||||
\(389\) | 17.2467 | 0.874444 | 0.437222 | − | 0.899354i | \(-0.355962\pi\) | ||||
0.437222 | + | 0.899354i | \(0.355962\pi\) | |||||||
\(390\) | 13.6064 | 0.688987 | ||||||||
\(391\) | −16.7786 | −0.848531 | ||||||||
\(392\) | 6.36456 | 0.321459 | ||||||||
\(393\) | 8.72058 | 0.439895 | ||||||||
\(394\) | 21.1403 | 1.06503 | ||||||||
\(395\) | 11.6982 | 0.588602 | ||||||||
\(396\) | −10.7256 | −0.538981 | ||||||||
\(397\) | 21.1110 | 1.05953 | 0.529764 | − | 0.848145i | \(-0.322280\pi\) | ||||
0.529764 | + | 0.848145i | \(0.322280\pi\) | |||||||
\(398\) | −6.95972 | −0.348859 | ||||||||
\(399\) | −14.6943 | −0.735636 | ||||||||
\(400\) | 2.16022 | 0.108011 | ||||||||
\(401\) | 28.8448 | 1.44044 | 0.720219 | − | 0.693746i | \(-0.244041\pi\) | ||||
0.720219 | + | 0.693746i | \(0.244041\pi\) | |||||||
\(402\) | 8.10171 | 0.404077 | ||||||||
\(403\) | 6.16910 | 0.307305 | ||||||||
\(404\) | 0.211788 | 0.0105368 | ||||||||
\(405\) | −28.5239 | −1.41737 | ||||||||
\(406\) | −0.0205100 | −0.00101790 | ||||||||
\(407\) | 47.8930 | 2.37397 | ||||||||
\(408\) | 13.6603 | 0.676286 | ||||||||
\(409\) | −12.5644 | −0.621272 | −0.310636 | − | 0.950529i | \(-0.600542\pi\) | ||||
−0.310636 | + | 0.950529i | \(0.600542\pi\) | |||||||
\(410\) | 17.2665 | 0.852732 | ||||||||
\(411\) | −19.0039 | −0.937392 | ||||||||
\(412\) | 15.0701 | 0.742450 | ||||||||
\(413\) | 3.43997 | 0.169270 | ||||||||
\(414\) | 6.39483 | 0.314289 | ||||||||
\(415\) | −42.3230 | −2.07755 | ||||||||
\(416\) | −2.21536 | −0.108617 | ||||||||
\(417\) | −16.2314 | −0.794855 | ||||||||
\(418\) | −37.9753 | −1.85743 | ||||||||
\(419\) | −22.1539 | −1.08229 | −0.541145 | − | 0.840929i | \(-0.682009\pi\) | ||||
−0.541145 | + | 0.840929i | \(0.682009\pi\) | |||||||
\(420\) | 4.89592 | 0.238896 | ||||||||
\(421\) | −34.6616 | −1.68930 | −0.844651 | − | 0.535318i | \(-0.820192\pi\) | ||||
−0.844651 | + | 0.535318i | \(0.820192\pi\) | |||||||
\(422\) | 11.6737 | 0.568267 | ||||||||
\(423\) | 13.9733 | 0.679404 | ||||||||
\(424\) | 3.53867 | 0.171853 | ||||||||
\(425\) | 12.8565 | 0.623633 | ||||||||
\(426\) | −1.12890 | −0.0546955 | ||||||||
\(427\) | −8.11559 | −0.392741 | ||||||||
\(428\) | 9.01855 | 0.435928 | ||||||||
\(429\) | 24.0438 | 1.16084 | ||||||||
\(430\) | −15.8959 | −0.766568 | ||||||||
\(431\) | 5.67464 | 0.273338 | 0.136669 | − | 0.990617i | \(-0.456360\pi\) | ||||
0.136669 | + | 0.990617i | \(0.456360\pi\) | |||||||
\(432\) | 1.67947 | 0.0808038 | ||||||||
\(433\) | 22.5861 | 1.08542 | 0.542710 | − | 0.839920i | \(-0.317398\pi\) | ||||
0.542710 | + | 0.839920i | \(0.317398\pi\) | |||||||
\(434\) | 2.21980 | 0.106554 | ||||||||
\(435\) | 0.158026 | 0.00757676 | ||||||||
\(436\) | 12.2861 | 0.588398 | ||||||||
\(437\) | 22.6417 | 1.08310 | ||||||||
\(438\) | 27.4016 | 1.30930 | ||||||||
\(439\) | 31.3216 | 1.49490 | 0.747448 | − | 0.664320i | \(-0.231279\pi\) | ||||
0.747448 | + | 0.664320i | \(0.231279\pi\) | |||||||
\(440\) | 12.6528 | 0.603197 | ||||||||
\(441\) | −14.4367 | −0.687461 | ||||||||
\(442\) | −13.1847 | −0.627133 | ||||||||
\(443\) | −10.5878 | −0.503044 | −0.251522 | − | 0.967852i | \(-0.580931\pi\) | ||||
−0.251522 | + | 0.967852i | \(0.580931\pi\) | |||||||
\(444\) | 23.2479 | 1.10330 | ||||||||
\(445\) | 34.9485 | 1.65672 | ||||||||
\(446\) | 1.81507 | 0.0859461 | ||||||||
\(447\) | 12.2910 | 0.581342 | ||||||||
\(448\) | −0.797143 | −0.0376615 | ||||||||
\(449\) | 19.7320 | 0.931211 | 0.465606 | − | 0.884992i | \(-0.345837\pi\) | ||||
0.465606 | + | 0.884992i | \(0.345837\pi\) | |||||||
\(450\) | −4.90001 | −0.230989 | ||||||||
\(451\) | 30.5115 | 1.43673 | ||||||||
\(452\) | 19.4534 | 0.915011 | ||||||||
\(453\) | 5.04514 | 0.237041 | ||||||||
\(454\) | −16.1950 | −0.760070 | ||||||||
\(455\) | −4.72547 | −0.221533 | ||||||||
\(456\) | −18.4337 | −0.863239 | ||||||||
\(457\) | 8.13562 | 0.380568 | 0.190284 | − | 0.981729i | \(-0.439059\pi\) | ||||
0.190284 | + | 0.981729i | \(0.439059\pi\) | |||||||
\(458\) | 8.80688 | 0.411519 | ||||||||
\(459\) | 9.99538 | 0.466544 | ||||||||
\(460\) | −7.54386 | −0.351734 | ||||||||
\(461\) | 30.0171 | 1.39803 | 0.699017 | − | 0.715105i | \(-0.253621\pi\) | ||||
0.699017 | + | 0.715105i | \(0.253621\pi\) | |||||||
\(462\) | 8.65154 | 0.402506 | ||||||||
\(463\) | −14.1202 | −0.656224 | −0.328112 | − | 0.944639i | \(-0.606412\pi\) | ||||
−0.328112 | + | 0.944639i | \(0.606412\pi\) | |||||||
\(464\) | −0.0257294 | −0.00119446 | ||||||||
\(465\) | −17.1031 | −0.793137 | ||||||||
\(466\) | −6.09380 | −0.282290 | ||||||||
\(467\) | −6.67297 | −0.308788 | −0.154394 | − | 0.988009i | \(-0.549343\pi\) | ||||
−0.154394 | + | 0.988009i | \(0.549343\pi\) | |||||||
\(468\) | 5.02509 | 0.232285 | ||||||||
\(469\) | −2.81370 | −0.129925 | ||||||||
\(470\) | −16.4840 | −0.760351 | ||||||||
\(471\) | −36.8359 | −1.69731 | ||||||||
\(472\) | 4.31537 | 0.198631 | ||||||||
\(473\) | −28.0895 | −1.29156 | ||||||||
\(474\) | 10.0344 | 0.460896 | ||||||||
\(475\) | −17.3491 | −0.796031 | ||||||||
\(476\) | −4.74419 | −0.217450 | ||||||||
\(477\) | −8.02674 | −0.367519 | ||||||||
\(478\) | −17.5768 | −0.803946 | ||||||||
\(479\) | 24.9404 | 1.13955 | 0.569777 | − | 0.821799i | \(-0.307029\pi\) | ||||
0.569777 | + | 0.821799i | \(0.307029\pi\) | |||||||
\(480\) | 6.14183 | 0.280335 | ||||||||
\(481\) | −22.4386 | −1.02311 | ||||||||
\(482\) | −1.56163 | −0.0711305 | ||||||||
\(483\) | −5.15824 | −0.234708 | ||||||||
\(484\) | 11.3586 | 0.516301 | ||||||||
\(485\) | −46.9575 | −2.13223 | ||||||||
\(486\) | −19.4286 | −0.881299 | ||||||||
\(487\) | 9.93041 | 0.449990 | 0.224995 | − | 0.974360i | \(-0.427763\pi\) | ||||
0.224995 | + | 0.974360i | \(0.427763\pi\) | |||||||
\(488\) | −10.1809 | −0.460866 | ||||||||
\(489\) | 48.9387 | 2.21308 | ||||||||
\(490\) | 17.0307 | 0.769367 | ||||||||
\(491\) | −3.07555 | −0.138798 | −0.0693988 | − | 0.997589i | \(-0.522108\pi\) | ||||
−0.0693988 | + | 0.997589i | \(0.522108\pi\) | |||||||
\(492\) | 14.8107 | 0.667719 | ||||||||
\(493\) | −0.153128 | −0.00689656 | ||||||||
\(494\) | 17.7920 | 0.800498 | ||||||||
\(495\) | −28.7002 | −1.28998 | ||||||||
\(496\) | 2.78469 | 0.125036 | ||||||||
\(497\) | 0.392065 | 0.0175865 | ||||||||
\(498\) | −36.3034 | −1.62680 | ||||||||
\(499\) | 19.9045 | 0.891048 | 0.445524 | − | 0.895270i | \(-0.353017\pi\) | ||||
0.445524 | + | 0.895270i | \(0.353017\pi\) | |||||||
\(500\) | −7.59885 | −0.339831 | ||||||||
\(501\) | 12.3901 | 0.553548 | ||||||||
\(502\) | −22.2420 | −0.992710 | ||||||||
\(503\) | 40.4470 | 1.80344 | 0.901722 | − | 0.432316i | \(-0.142304\pi\) | ||||
0.901722 | + | 0.432316i | \(0.142304\pi\) | |||||||
\(504\) | 1.80815 | 0.0805415 | ||||||||
\(505\) | 0.566714 | 0.0252184 | ||||||||
\(506\) | −13.3307 | −0.592622 | ||||||||
\(507\) | 18.5737 | 0.824888 | ||||||||
\(508\) | −5.89558 | −0.261574 | ||||||||
\(509\) | −4.01983 | −0.178176 | −0.0890879 | − | 0.996024i | \(-0.528395\pi\) | ||||
−0.0890879 | + | 0.996024i | \(0.528395\pi\) | |||||||
\(510\) | 36.5531 | 1.61860 | ||||||||
\(511\) | −9.51648 | −0.420984 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −13.4881 | −0.595516 | ||||||||
\(514\) | −21.4026 | −0.944028 | ||||||||
\(515\) | 40.3254 | 1.77695 | ||||||||
\(516\) | −13.6350 | −0.600249 | ||||||||
\(517\) | −29.1288 | −1.28108 | ||||||||
\(518\) | −8.07394 | −0.354749 | ||||||||
\(519\) | −14.8160 | −0.650352 | ||||||||
\(520\) | −5.92800 | −0.259960 | ||||||||
\(521\) | 6.65665 | 0.291633 | 0.145817 | − | 0.989312i | \(-0.453419\pi\) | ||||
0.145817 | + | 0.989312i | \(0.453419\pi\) | |||||||
\(522\) | 0.0583618 | 0.00255443 | ||||||||
\(523\) | 35.5975 | 1.55657 | 0.778285 | − | 0.627911i | \(-0.216090\pi\) | ||||
0.778285 | + | 0.627911i | \(0.216090\pi\) | |||||||
\(524\) | −3.79936 | −0.165976 | ||||||||
\(525\) | 3.95247 | 0.172500 | ||||||||
\(526\) | −1.93215 | −0.0842456 | ||||||||
\(527\) | 16.5731 | 0.721934 | ||||||||
\(528\) | 10.8532 | 0.472325 | ||||||||
\(529\) | −15.0519 | −0.654432 | ||||||||
\(530\) | 9.46899 | 0.411307 | ||||||||
\(531\) | −9.78852 | −0.424785 | ||||||||
\(532\) | 6.40199 | 0.277561 | ||||||||
\(533\) | −14.2951 | −0.619189 | ||||||||
\(534\) | 29.9779 | 1.29727 | ||||||||
\(535\) | 24.1324 | 1.04333 | ||||||||
\(536\) | −3.52973 | −0.152461 | ||||||||
\(537\) | 29.9298 | 1.29157 | ||||||||
\(538\) | −6.89306 | −0.297181 | ||||||||
\(539\) | 30.0948 | 1.29627 | ||||||||
\(540\) | 4.49404 | 0.193393 | ||||||||
\(541\) | 17.7852 | 0.764646 | 0.382323 | − | 0.924029i | \(-0.375124\pi\) | ||||
0.382323 | + | 0.924029i | \(0.375124\pi\) | |||||||
\(542\) | 11.7295 | 0.503825 | ||||||||
\(543\) | −41.1922 | −1.76773 | ||||||||
\(544\) | −5.95149 | −0.255168 | ||||||||
\(545\) | 32.8759 | 1.40825 | ||||||||
\(546\) | −4.05337 | −0.173468 | ||||||||
\(547\) | 33.8882 | 1.44895 | 0.724477 | − | 0.689299i | \(-0.242082\pi\) | ||||
0.724477 | + | 0.689299i | \(0.242082\pi\) | |||||||
\(548\) | 8.27956 | 0.353685 | ||||||||
\(549\) | 23.0931 | 0.985591 | ||||||||
\(550\) | 10.2146 | 0.435551 | ||||||||
\(551\) | 0.206637 | 0.00880305 | ||||||||
\(552\) | −6.47091 | −0.275420 | ||||||||
\(553\) | −3.48492 | −0.148194 | ||||||||
\(554\) | 30.6706 | 1.30307 | ||||||||
\(555\) | 62.2082 | 2.64059 | ||||||||
\(556\) | 7.07166 | 0.299905 | ||||||||
\(557\) | −18.3176 | −0.776140 | −0.388070 | − | 0.921630i | \(-0.626858\pi\) | ||||
−0.388070 | + | 0.921630i | \(0.626858\pi\) | |||||||
\(558\) | −6.31649 | −0.267398 | ||||||||
\(559\) | 13.1603 | 0.556623 | ||||||||
\(560\) | −2.13304 | −0.0901375 | ||||||||
\(561\) | 64.5927 | 2.72710 | ||||||||
\(562\) | −24.4405 | −1.03096 | ||||||||
\(563\) | 27.9324 | 1.17721 | 0.588605 | − | 0.808421i | \(-0.299677\pi\) | ||||
0.588605 | + | 0.808421i | \(0.299677\pi\) | |||||||
\(564\) | −14.1395 | −0.595381 | ||||||||
\(565\) | 52.0545 | 2.18995 | ||||||||
\(566\) | −15.8345 | −0.665576 | ||||||||
\(567\) | 8.49733 | 0.356854 | ||||||||
\(568\) | 0.491838 | 0.0206370 | ||||||||
\(569\) | 5.07084 | 0.212581 | 0.106290 | − | 0.994335i | \(-0.466103\pi\) | ||||
0.106290 | + | 0.994335i | \(0.466103\pi\) | |||||||
\(570\) | −49.3261 | −2.06604 | ||||||||
\(571\) | −17.1596 | −0.718107 | −0.359054 | − | 0.933317i | \(-0.616900\pi\) | ||||
−0.359054 | + | 0.933317i | \(0.616900\pi\) | |||||||
\(572\) | −10.4753 | −0.437996 | ||||||||
\(573\) | 9.95805 | 0.416004 | ||||||||
\(574\) | −5.14372 | −0.214695 | ||||||||
\(575\) | −6.09015 | −0.253977 | ||||||||
\(576\) | 2.26829 | 0.0945121 | ||||||||
\(577\) | −6.15940 | −0.256419 | −0.128210 | − | 0.991747i | \(-0.540923\pi\) | ||||
−0.128210 | + | 0.991747i | \(0.540923\pi\) | |||||||
\(578\) | −18.4202 | −0.766181 | ||||||||
\(579\) | 50.7109 | 2.10748 | ||||||||
\(580\) | −0.0688483 | −0.00285877 | ||||||||
\(581\) | 12.6081 | 0.523071 | ||||||||
\(582\) | −40.2788 | −1.66961 | ||||||||
\(583\) | 16.7326 | 0.692993 | ||||||||
\(584\) | −11.9382 | −0.494008 | ||||||||
\(585\) | 13.4464 | 0.555942 | ||||||||
\(586\) | −6.24103 | −0.257815 | ||||||||
\(587\) | 5.63608 | 0.232626 | 0.116313 | − | 0.993213i | \(-0.462892\pi\) | ||||
0.116313 | + | 0.993213i | \(0.462892\pi\) | |||||||
\(588\) | 14.6084 | 0.602441 | ||||||||
\(589\) | −22.3643 | −0.921505 | ||||||||
\(590\) | 11.5473 | 0.475396 | ||||||||
\(591\) | 48.5228 | 1.99596 | ||||||||
\(592\) | −10.1286 | −0.416283 | ||||||||
\(593\) | −44.3124 | −1.81969 | −0.909846 | − | 0.414947i | \(-0.863800\pi\) | ||||
−0.909846 | + | 0.414947i | \(0.863800\pi\) | |||||||
\(594\) | 7.94138 | 0.325839 | ||||||||
\(595\) | −12.6948 | −0.520435 | ||||||||
\(596\) | −5.35489 | −0.219345 | ||||||||
\(597\) | −15.9745 | −0.653792 | ||||||||
\(598\) | 6.24562 | 0.255402 | ||||||||
\(599\) | 24.7389 | 1.01081 | 0.505403 | − | 0.862883i | \(-0.331344\pi\) | ||||
0.505403 | + | 0.862883i | \(0.331344\pi\) | |||||||
\(600\) | 4.95830 | 0.202422 | ||||||||
\(601\) | −22.5642 | −0.920412 | −0.460206 | − | 0.887812i | \(-0.652225\pi\) | ||||
−0.460206 | + | 0.887812i | \(0.652225\pi\) | |||||||
\(602\) | 4.73541 | 0.193001 | ||||||||
\(603\) | 8.00646 | 0.326048 | ||||||||
\(604\) | −2.19805 | −0.0894375 | ||||||||
\(605\) | 30.3941 | 1.23570 | ||||||||
\(606\) | 0.486111 | 0.0197469 | ||||||||
\(607\) | 31.8366 | 1.29221 | 0.646103 | − | 0.763250i | \(-0.276398\pi\) | ||||
0.646103 | + | 0.763250i | \(0.276398\pi\) | |||||||
\(608\) | 8.03117 | 0.325707 | ||||||||
\(609\) | −0.0470762 | −0.00190762 | ||||||||
\(610\) | −27.2425 | −1.10302 | ||||||||
\(611\) | 13.6472 | 0.552109 | ||||||||
\(612\) | 13.4997 | 0.545693 | ||||||||
\(613\) | 9.83441 | 0.397208 | 0.198604 | − | 0.980080i | \(-0.436359\pi\) | ||||
0.198604 | + | 0.980080i | \(0.436359\pi\) | |||||||
\(614\) | −2.64951 | −0.106925 | ||||||||
\(615\) | 39.6314 | 1.59809 | ||||||||
\(616\) | −3.76928 | −0.151869 | ||||||||
\(617\) | −11.3662 | −0.457587 | −0.228793 | − | 0.973475i | \(-0.573478\pi\) | ||||
−0.228793 | + | 0.973475i | \(0.573478\pi\) | |||||||
\(618\) | 34.5900 | 1.39141 | ||||||||
\(619\) | 27.4330 | 1.10262 | 0.551312 | − | 0.834299i | \(-0.314127\pi\) | ||||
0.551312 | + | 0.834299i | \(0.314127\pi\) | |||||||
\(620\) | 7.45144 | 0.299257 | ||||||||
\(621\) | −4.73482 | −0.190002 | ||||||||
\(622\) | −0.0266046 | −0.00106675 | ||||||||
\(623\) | −10.4112 | −0.417117 | ||||||||
\(624\) | −5.08487 | −0.203558 | ||||||||
\(625\) | −31.1345 | −1.24538 | ||||||||
\(626\) | −13.9540 | −0.557713 | ||||||||
\(627\) | −87.1638 | −3.48099 | ||||||||
\(628\) | 16.0486 | 0.640407 | ||||||||
\(629\) | −60.2803 | −2.40353 | ||||||||
\(630\) | 4.83836 | 0.192765 | ||||||||
\(631\) | 0.801172 | 0.0318941 | 0.0159471 | − | 0.999873i | \(-0.494924\pi\) | ||||
0.0159471 | + | 0.999873i | \(0.494924\pi\) | |||||||
\(632\) | −4.37177 | −0.173900 | ||||||||
\(633\) | 26.7944 | 1.06498 | ||||||||
\(634\) | 9.84385 | 0.390949 | ||||||||
\(635\) | −15.7758 | −0.626042 | ||||||||
\(636\) | 8.12223 | 0.322067 | ||||||||
\(637\) | −14.0998 | −0.558656 | ||||||||
\(638\) | −0.121661 | −0.00481662 | ||||||||
\(639\) | −1.11563 | −0.0441337 | ||||||||
\(640\) | −2.67586 | −0.105773 | ||||||||
\(641\) | −14.3826 | −0.568079 | −0.284040 | − | 0.958813i | \(-0.591675\pi\) | ||||
−0.284040 | + | 0.958813i | \(0.591675\pi\) | |||||||
\(642\) | 20.7001 | 0.816966 | ||||||||
\(643\) | −21.1048 | −0.832294 | −0.416147 | − | 0.909297i | \(-0.636620\pi\) | ||||
−0.416147 | + | 0.909297i | \(0.636620\pi\) | |||||||
\(644\) | 2.24733 | 0.0885571 | ||||||||
\(645\) | −36.4854 | −1.43661 | ||||||||
\(646\) | 47.7974 | 1.88056 | ||||||||
\(647\) | 8.58306 | 0.337435 | 0.168718 | − | 0.985664i | \(-0.446037\pi\) | ||||
0.168718 | + | 0.985664i | \(0.446037\pi\) | |||||||
\(648\) | 10.6597 | 0.418754 | ||||||||
\(649\) | 20.4052 | 0.800974 | ||||||||
\(650\) | −4.78568 | −0.187710 | ||||||||
\(651\) | 5.09504 | 0.199690 | ||||||||
\(652\) | −21.3215 | −0.835014 | ||||||||
\(653\) | 7.99908 | 0.313028 | 0.156514 | − | 0.987676i | \(-0.449974\pi\) | ||||
0.156514 | + | 0.987676i | \(0.449974\pi\) | |||||||
\(654\) | 28.2000 | 1.10271 | ||||||||
\(655\) | −10.1665 | −0.397240 | ||||||||
\(656\) | −6.45270 | −0.251936 | ||||||||
\(657\) | 27.0794 | 1.05647 | ||||||||
\(658\) | 4.91062 | 0.191436 | ||||||||
\(659\) | 2.50165 | 0.0974506 | 0.0487253 | − | 0.998812i | \(-0.484484\pi\) | ||||
0.0487253 | + | 0.998812i | \(0.484484\pi\) | |||||||
\(660\) | 29.0416 | 1.13044 | ||||||||
\(661\) | −14.1074 | −0.548713 | −0.274357 | − | 0.961628i | \(-0.588465\pi\) | ||||
−0.274357 | + | 0.961628i | \(0.588465\pi\) | |||||||
\(662\) | 4.67627 | 0.181748 | ||||||||
\(663\) | −30.2626 | −1.17530 | ||||||||
\(664\) | 15.8166 | 0.613803 | ||||||||
\(665\) | 17.1308 | 0.664304 | ||||||||
\(666\) | 22.9746 | 0.890248 | ||||||||
\(667\) | 0.0725372 | 0.00280865 | ||||||||
\(668\) | −5.39808 | −0.208858 | ||||||||
\(669\) | 4.16609 | 0.161070 | ||||||||
\(670\) | −9.44507 | −0.364895 | ||||||||
\(671\) | −48.1401 | −1.85843 | ||||||||
\(672\) | −1.82966 | −0.0705808 | ||||||||
\(673\) | −1.29326 | −0.0498513 | −0.0249257 | − | 0.999689i | \(-0.507935\pi\) | ||||
−0.0249257 | + | 0.999689i | \(0.507935\pi\) | |||||||
\(674\) | 11.8810 | 0.457637 | ||||||||
\(675\) | 3.62804 | 0.139643 | ||||||||
\(676\) | −8.09216 | −0.311237 | ||||||||
\(677\) | 37.9245 | 1.45756 | 0.728779 | − | 0.684749i | \(-0.240088\pi\) | ||||
0.728779 | + | 0.684749i | \(0.240088\pi\) | |||||||
\(678\) | 44.6509 | 1.71481 | ||||||||
\(679\) | 13.9887 | 0.536837 | ||||||||
\(680\) | −15.9253 | −0.610709 | ||||||||
\(681\) | −37.1720 | −1.42444 | ||||||||
\(682\) | 13.1674 | 0.504205 | ||||||||
\(683\) | 6.84832 | 0.262044 | 0.131022 | − | 0.991379i | \(-0.458174\pi\) | ||||
0.131022 | + | 0.991379i | \(0.458174\pi\) | |||||||
\(684\) | −18.2170 | −0.696545 | ||||||||
\(685\) | 22.1549 | 0.846497 | ||||||||
\(686\) | −10.6535 | −0.406751 | ||||||||
\(687\) | 20.2142 | 0.771221 | ||||||||
\(688\) | 5.94048 | 0.226479 | ||||||||
\(689\) | −7.83945 | −0.298659 | ||||||||
\(690\) | −17.3152 | −0.659180 | ||||||||
\(691\) | 30.0540 | 1.14331 | 0.571654 | − | 0.820495i | \(-0.306302\pi\) | ||||
0.571654 | + | 0.820495i | \(0.306302\pi\) | |||||||
\(692\) | 6.45502 | 0.245383 | ||||||||
\(693\) | 8.54983 | 0.324781 | ||||||||
\(694\) | 35.8859 | 1.36221 | ||||||||
\(695\) | 18.9228 | 0.717781 | ||||||||
\(696\) | −0.0590561 | −0.00223852 | ||||||||
\(697\) | −38.4032 | −1.45462 | ||||||||
\(698\) | −24.0051 | −0.908605 | ||||||||
\(699\) | −13.9870 | −0.529035 | ||||||||
\(700\) | −1.72200 | −0.0650856 | ||||||||
\(701\) | 13.0611 | 0.493311 | 0.246656 | − | 0.969103i | \(-0.420668\pi\) | ||||
0.246656 | + | 0.969103i | \(0.420668\pi\) | |||||||
\(702\) | −3.72065 | −0.140427 | ||||||||
\(703\) | 81.3445 | 3.06797 | ||||||||
\(704\) | −4.72849 | −0.178212 | ||||||||
\(705\) | −37.8354 | −1.42496 | ||||||||
\(706\) | −20.7832 | −0.782187 | ||||||||
\(707\) | −0.168825 | −0.00634932 | ||||||||
\(708\) | 9.90497 | 0.372252 | ||||||||
\(709\) | −13.1844 | −0.495149 | −0.247575 | − | 0.968869i | \(-0.579634\pi\) | ||||
−0.247575 | + | 0.968869i | \(0.579634\pi\) | |||||||
\(710\) | 1.31609 | 0.0493919 | ||||||||
\(711\) | 9.91644 | 0.371896 | ||||||||
\(712\) | −13.0607 | −0.489470 | ||||||||
\(713\) | −7.85068 | −0.294010 | ||||||||
\(714\) | −10.8892 | −0.407519 | ||||||||
\(715\) | −28.0305 | −1.04828 | ||||||||
\(716\) | −13.0398 | −0.487318 | ||||||||
\(717\) | −40.3437 | −1.50666 | ||||||||
\(718\) | −25.8606 | −0.965110 | ||||||||
\(719\) | 35.9265 | 1.33983 | 0.669917 | − | 0.742436i | \(-0.266330\pi\) | ||||
0.669917 | + | 0.742436i | \(0.266330\pi\) | |||||||
\(720\) | 6.06963 | 0.226202 | ||||||||
\(721\) | −12.0130 | −0.447388 | ||||||||
\(722\) | −45.4996 | −1.69332 | ||||||||
\(723\) | −3.58438 | −0.133305 | ||||||||
\(724\) | 17.9465 | 0.666977 | ||||||||
\(725\) | −0.0555812 | −0.00206424 | ||||||||
\(726\) | 26.0712 | 0.967592 | ||||||||
\(727\) | 32.4093 | 1.20200 | 0.600998 | − | 0.799251i | \(-0.294770\pi\) | ||||
0.600998 | + | 0.799251i | \(0.294770\pi\) | |||||||
\(728\) | 1.76596 | 0.0654509 | ||||||||
\(729\) | −12.6148 | −0.467214 | ||||||||
\(730\) | −31.9450 | −1.18234 | ||||||||
\(731\) | 35.3547 | 1.30764 | ||||||||
\(732\) | −23.3679 | −0.863701 | ||||||||
\(733\) | 51.0919 | 1.88712 | 0.943562 | − | 0.331197i | \(-0.107452\pi\) | ||||
0.943562 | + | 0.331197i | \(0.107452\pi\) | |||||||
\(734\) | −5.57150 | −0.205648 | ||||||||
\(735\) | 39.0901 | 1.44186 | ||||||||
\(736\) | 2.81923 | 0.103918 | ||||||||
\(737\) | −16.6903 | −0.614796 | ||||||||
\(738\) | 14.6366 | 0.538781 | ||||||||
\(739\) | −18.9364 | −0.696585 | −0.348293 | − | 0.937386i | \(-0.613238\pi\) | ||||
−0.348293 | + | 0.937386i | \(0.613238\pi\) | |||||||
\(740\) | −27.1027 | −0.996316 | ||||||||
\(741\) | 40.8375 | 1.50020 | ||||||||
\(742\) | −2.82083 | −0.103556 | ||||||||
\(743\) | 8.20488 | 0.301008 | 0.150504 | − | 0.988609i | \(-0.451910\pi\) | ||||
0.150504 | + | 0.988609i | \(0.451910\pi\) | |||||||
\(744\) | 6.39163 | 0.234329 | ||||||||
\(745\) | −14.3289 | −0.524971 | ||||||||
\(746\) | 2.72743 | 0.0998583 | ||||||||
\(747\) | −35.8766 | −1.31266 | ||||||||
\(748\) | −28.1416 | −1.02896 | ||||||||
\(749\) | −7.18907 | −0.262683 | ||||||||
\(750\) | −17.4415 | −0.636872 | ||||||||
\(751\) | 22.2586 | 0.812227 | 0.406114 | − | 0.913823i | \(-0.366884\pi\) | ||||
0.406114 | + | 0.913823i | \(0.366884\pi\) | |||||||
\(752\) | 6.16027 | 0.224642 | ||||||||
\(753\) | −51.0516 | −1.86042 | ||||||||
\(754\) | 0.0570001 | 0.00207582 | ||||||||
\(755\) | −5.88168 | −0.214056 | ||||||||
\(756\) | −1.33878 | −0.0486910 | ||||||||
\(757\) | −24.2329 | −0.880760 | −0.440380 | − | 0.897812i | \(-0.645156\pi\) | ||||
−0.440380 | + | 0.897812i | \(0.645156\pi\) | |||||||
\(758\) | −31.0762 | −1.12874 | ||||||||
\(759\) | −30.5976 | −1.11062 | ||||||||
\(760\) | 21.4903 | 0.779534 | ||||||||
\(761\) | 32.9970 | 1.19614 | 0.598070 | − | 0.801444i | \(-0.295935\pi\) | ||||
0.598070 | + | 0.801444i | \(0.295935\pi\) | |||||||
\(762\) | −13.5320 | −0.490212 | ||||||||
\(763\) | −9.79378 | −0.354559 | ||||||||
\(764\) | −4.33850 | −0.156961 | ||||||||
\(765\) | 36.1233 | 1.30604 | ||||||||
\(766\) | 34.7199 | 1.25448 | ||||||||
\(767\) | −9.56012 | −0.345196 | ||||||||
\(768\) | −2.29528 | −0.0828236 | ||||||||
\(769\) | −8.08582 | −0.291582 | −0.145791 | − | 0.989315i | \(-0.546573\pi\) | ||||
−0.145791 | + | 0.989315i | \(0.546573\pi\) | |||||||
\(770\) | −10.0861 | −0.363477 | ||||||||
\(771\) | −49.1249 | −1.76919 | ||||||||
\(772\) | −22.0936 | −0.795167 | ||||||||
\(773\) | 40.9890 | 1.47427 | 0.737136 | − | 0.675744i | \(-0.236178\pi\) | ||||
0.737136 | + | 0.675744i | \(0.236178\pi\) | |||||||
\(774\) | −13.4747 | −0.484339 | ||||||||
\(775\) | 6.01554 | 0.216085 | ||||||||
\(776\) | 17.5486 | 0.629957 | ||||||||
\(777\) | −18.5319 | −0.664829 | ||||||||
\(778\) | −17.2467 | −0.618325 | ||||||||
\(779\) | 51.8227 | 1.85674 | ||||||||
\(780\) | −13.6064 | −0.487187 | ||||||||
\(781\) | 2.32565 | 0.0832183 | ||||||||
\(782\) | 16.7786 | 0.600002 | ||||||||
\(783\) | −0.0432119 | −0.00154427 | ||||||||
\(784\) | −6.36456 | −0.227306 | ||||||||
\(785\) | 42.9437 | 1.53273 | ||||||||
\(786\) | −8.72058 | −0.311053 | ||||||||
\(787\) | 13.3284 | 0.475108 | 0.237554 | − | 0.971374i | \(-0.423654\pi\) | ||||
0.237554 | + | 0.971374i | \(0.423654\pi\) | |||||||
\(788\) | −21.1403 | −0.753092 | ||||||||
\(789\) | −4.43481 | −0.157883 | ||||||||
\(790\) | −11.6982 | −0.416204 | ||||||||
\(791\) | −15.5071 | −0.551370 | ||||||||
\(792\) | 10.7256 | 0.381117 | ||||||||
\(793\) | 22.5543 | 0.800927 | ||||||||
\(794\) | −21.1110 | −0.749200 | ||||||||
\(795\) | 21.7339 | 0.770823 | ||||||||
\(796\) | 6.95972 | 0.246681 | ||||||||
\(797\) | 27.5858 | 0.977140 | 0.488570 | − | 0.872525i | \(-0.337519\pi\) | ||||
0.488570 | + | 0.872525i | \(0.337519\pi\) | |||||||
\(798\) | 14.6943 | 0.520173 | ||||||||
\(799\) | 36.6628 | 1.29704 | ||||||||
\(800\) | −2.16022 | −0.0763753 | ||||||||
\(801\) | 29.6254 | 1.04676 | ||||||||
\(802\) | −28.8448 | −1.01854 | ||||||||
\(803\) | −56.4499 | −1.99207 | ||||||||
\(804\) | −8.10171 | −0.285725 | ||||||||
\(805\) | 6.01353 | 0.211949 | ||||||||
\(806\) | −6.16910 | −0.217297 | ||||||||
\(807\) | −15.8215 | −0.556942 | ||||||||
\(808\) | −0.211788 | −0.00745066 | ||||||||
\(809\) | 36.6445 | 1.28835 | 0.644177 | − | 0.764877i | \(-0.277200\pi\) | ||||
0.644177 | + | 0.764877i | \(0.277200\pi\) | |||||||
\(810\) | 28.5239 | 1.00223 | ||||||||
\(811\) | −20.9697 | −0.736346 | −0.368173 | − | 0.929757i | \(-0.620017\pi\) | ||||
−0.368173 | + | 0.929757i | \(0.620017\pi\) | |||||||
\(812\) | 0.0205100 | 0.000719761 0 | ||||||||
\(813\) | 26.9224 | 0.944210 | ||||||||
\(814\) | −47.8930 | −1.67865 | ||||||||
\(815\) | −57.0533 | −1.99849 | ||||||||
\(816\) | −13.6603 | −0.478207 | ||||||||
\(817\) | −47.7090 | −1.66913 | ||||||||
\(818\) | 12.5644 | 0.439305 | ||||||||
\(819\) | −4.00572 | −0.139971 | ||||||||
\(820\) | −17.2665 | −0.602973 | ||||||||
\(821\) | 9.41005 | 0.328413 | 0.164207 | − | 0.986426i | \(-0.447494\pi\) | ||||
0.164207 | + | 0.986426i | \(0.447494\pi\) | |||||||
\(822\) | 19.0039 | 0.662836 | ||||||||
\(823\) | −49.8448 | −1.73748 | −0.868740 | − | 0.495269i | \(-0.835070\pi\) | ||||
−0.868740 | + | 0.495269i | \(0.835070\pi\) | |||||||
\(824\) | −15.0701 | −0.524992 | ||||||||
\(825\) | 23.4453 | 0.816260 | ||||||||
\(826\) | −3.43997 | −0.119692 | ||||||||
\(827\) | 30.5515 | 1.06238 | 0.531189 | − | 0.847253i | \(-0.321745\pi\) | ||||
0.531189 | + | 0.847253i | \(0.321745\pi\) | |||||||
\(828\) | −6.39483 | −0.222236 | ||||||||
\(829\) | −6.62474 | −0.230087 | −0.115043 | − | 0.993360i | \(-0.536701\pi\) | ||||
−0.115043 | + | 0.993360i | \(0.536701\pi\) | |||||||
\(830\) | 42.3230 | 1.46905 | ||||||||
\(831\) | 70.3975 | 2.44206 | ||||||||
\(832\) | 2.21536 | 0.0768040 | ||||||||
\(833\) | −37.8786 | −1.31242 | ||||||||
\(834\) | 16.2314 | 0.562048 | ||||||||
\(835\) | −14.4445 | −0.499872 | ||||||||
\(836\) | 37.9753 | 1.31340 | ||||||||
\(837\) | 4.67682 | 0.161654 | ||||||||
\(838\) | 22.1539 | 0.765295 | ||||||||
\(839\) | −2.75911 | −0.0952552 | −0.0476276 | − | 0.998865i | \(-0.515166\pi\) | ||||
−0.0476276 | + | 0.998865i | \(0.515166\pi\) | |||||||
\(840\) | −4.89592 | −0.168925 | ||||||||
\(841\) | −28.9993 | −0.999977 | ||||||||
\(842\) | 34.6616 | 1.19452 | ||||||||
\(843\) | −56.0976 | −1.93210 | ||||||||
\(844\) | −11.6737 | −0.401826 | ||||||||
\(845\) | −21.6535 | −0.744902 | ||||||||
\(846\) | −13.9733 | −0.480411 | ||||||||
\(847\) | −9.05445 | −0.311115 | ||||||||
\(848\) | −3.53867 | −0.121519 | ||||||||
\(849\) | −36.3446 | −1.24734 | ||||||||
\(850\) | −12.8565 | −0.440975 | ||||||||
\(851\) | 28.5549 | 0.978848 | ||||||||
\(852\) | 1.12890 | 0.0386756 | ||||||||
\(853\) | −8.26838 | −0.283104 | −0.141552 | − | 0.989931i | \(-0.545209\pi\) | ||||
−0.141552 | + | 0.989931i | \(0.545209\pi\) | |||||||
\(854\) | 8.11559 | 0.277710 | ||||||||
\(855\) | −48.7462 | −1.66708 | ||||||||
\(856\) | −9.01855 | −0.308248 | ||||||||
\(857\) | −4.07156 | −0.139082 | −0.0695409 | − | 0.997579i | \(-0.522153\pi\) | ||||
−0.0695409 | + | 0.997579i | \(0.522153\pi\) | |||||||
\(858\) | −24.0438 | −0.820841 | ||||||||
\(859\) | −21.6744 | −0.739520 | −0.369760 | − | 0.929127i | \(-0.620560\pi\) | ||||
−0.369760 | + | 0.929127i | \(0.620560\pi\) | |||||||
\(860\) | 15.8959 | 0.542045 | ||||||||
\(861\) | −11.8063 | −0.402356 | ||||||||
\(862\) | −5.67464 | −0.193279 | ||||||||
\(863\) | −23.3811 | −0.795901 | −0.397951 | − | 0.917407i | \(-0.630278\pi\) | ||||
−0.397951 | + | 0.917407i | \(0.630278\pi\) | |||||||
\(864\) | −1.67947 | −0.0571369 | ||||||||
\(865\) | 17.2727 | 0.587290 | ||||||||
\(866\) | −22.5861 | −0.767507 | ||||||||
\(867\) | −42.2795 | −1.43589 | ||||||||
\(868\) | −2.21980 | −0.0753448 | ||||||||
\(869\) | −20.6719 | −0.701245 | ||||||||
\(870\) | −0.158026 | −0.00535758 | ||||||||
\(871\) | 7.81965 | 0.264959 | ||||||||
\(872\) | −12.2861 | −0.416060 | ||||||||
\(873\) | −39.8052 | −1.34720 | ||||||||
\(874\) | −22.6417 | −0.765867 | ||||||||
\(875\) | 6.05737 | 0.204776 | ||||||||
\(876\) | −27.4016 | −0.925813 | ||||||||
\(877\) | 10.6455 | 0.359473 | 0.179736 | − | 0.983715i | \(-0.442476\pi\) | ||||
0.179736 | + | 0.983715i | \(0.442476\pi\) | |||||||
\(878\) | −31.3216 | −1.05705 | ||||||||
\(879\) | −14.3249 | −0.483166 | ||||||||
\(880\) | −12.6528 | −0.426525 | ||||||||
\(881\) | −29.5271 | −0.994793 | −0.497396 | − | 0.867523i | \(-0.665711\pi\) | ||||
−0.497396 | + | 0.867523i | \(0.665711\pi\) | |||||||
\(882\) | 14.4367 | 0.486108 | ||||||||
\(883\) | −41.6942 | −1.40312 | −0.701561 | − | 0.712609i | \(-0.747513\pi\) | ||||
−0.701561 | + | 0.712609i | \(0.747513\pi\) | |||||||
\(884\) | 13.1847 | 0.443450 | ||||||||
\(885\) | 26.5043 | 0.890932 | ||||||||
\(886\) | 10.5878 | 0.355706 | ||||||||
\(887\) | 24.2635 | 0.814687 | 0.407344 | − | 0.913275i | \(-0.366455\pi\) | ||||
0.407344 | + | 0.913275i | \(0.366455\pi\) | |||||||
\(888\) | −23.2479 | −0.780150 | ||||||||
\(889\) | 4.69962 | 0.157620 | ||||||||
\(890\) | −34.9485 | −1.17148 | ||||||||
\(891\) | 50.4044 | 1.68861 | ||||||||
\(892\) | −1.81507 | −0.0607731 | ||||||||
\(893\) | −49.4742 | −1.65559 | ||||||||
\(894\) | −12.2910 | −0.411071 | ||||||||
\(895\) | −34.8925 | −1.16633 | ||||||||
\(896\) | 0.797143 | 0.0266307 | ||||||||
\(897\) | 14.3354 | 0.478646 | ||||||||
\(898\) | −19.7320 | −0.658466 | ||||||||
\(899\) | −0.0716485 | −0.00238961 | ||||||||
\(900\) | 4.90001 | 0.163334 | ||||||||
\(901\) | −21.0604 | −0.701623 | ||||||||
\(902\) | −30.5115 | −1.01592 | ||||||||
\(903\) | 10.8691 | 0.361700 | ||||||||
\(904\) | −19.4534 | −0.647010 | ||||||||
\(905\) | 48.0223 | 1.59632 | ||||||||
\(906\) | −5.04514 | −0.167613 | ||||||||
\(907\) | −0.554591 | −0.0184149 | −0.00920745 | − | 0.999958i | \(-0.502931\pi\) | ||||
−0.00920745 | + | 0.999958i | \(0.502931\pi\) | |||||||
\(908\) | 16.1950 | 0.537450 | ||||||||
\(909\) | 0.480396 | 0.0159337 | ||||||||
\(910\) | 4.72547 | 0.156648 | ||||||||
\(911\) | 17.0232 | 0.564003 | 0.282002 | − | 0.959414i | \(-0.409002\pi\) | ||||
0.282002 | + | 0.959414i | \(0.409002\pi\) | |||||||
\(912\) | 18.4337 | 0.610402 | ||||||||
\(913\) | 74.7886 | 2.47514 | ||||||||
\(914\) | −8.13562 | −0.269102 | ||||||||
\(915\) | −62.5291 | −2.06715 | ||||||||
\(916\) | −8.80688 | −0.290988 | ||||||||
\(917\) | 3.02863 | 0.100014 | ||||||||
\(918\) | −9.99538 | −0.329897 | ||||||||
\(919\) | 35.1128 | 1.15826 | 0.579132 | − | 0.815234i | \(-0.303392\pi\) | ||||
0.579132 | + | 0.815234i | \(0.303392\pi\) | |||||||
\(920\) | 7.54386 | 0.248714 | ||||||||
\(921\) | −6.08135 | −0.200387 | ||||||||
\(922\) | −30.0171 | −0.988559 | ||||||||
\(923\) | −1.08960 | −0.0358646 | ||||||||
\(924\) | −8.65154 | −0.284615 | ||||||||
\(925\) | −21.8800 | −0.719410 | ||||||||
\(926\) | 14.1202 | 0.464020 | ||||||||
\(927\) | 34.1834 | 1.12273 | ||||||||
\(928\) | 0.0257294 | 0.000844610 0 | ||||||||
\(929\) | 43.5449 | 1.42866 | 0.714330 | − | 0.699809i | \(-0.246731\pi\) | ||||
0.714330 | + | 0.699809i | \(0.246731\pi\) | |||||||
\(930\) | 17.1031 | 0.560833 | ||||||||
\(931\) | 51.1149 | 1.67522 | ||||||||
\(932\) | 6.09380 | 0.199609 | ||||||||
\(933\) | −0.0610650 | −0.00199918 | ||||||||
\(934\) | 6.67297 | 0.218346 | ||||||||
\(935\) | −75.3029 | −2.46267 | ||||||||
\(936\) | −5.02509 | −0.164250 | ||||||||
\(937\) | −18.9860 | −0.620244 | −0.310122 | − | 0.950697i | \(-0.600370\pi\) | ||||
−0.310122 | + | 0.950697i | \(0.600370\pi\) | |||||||
\(938\) | 2.81370 | 0.0918706 | ||||||||
\(939\) | −32.0282 | −1.04520 | ||||||||
\(940\) | 16.4840 | 0.537649 | ||||||||
\(941\) | −38.2794 | −1.24787 | −0.623937 | − | 0.781475i | \(-0.714468\pi\) | ||||
−0.623937 | + | 0.781475i | \(0.714468\pi\) | |||||||
\(942\) | 36.8359 | 1.20018 | ||||||||
\(943\) | 18.1916 | 0.592401 | ||||||||
\(944\) | −4.31537 | −0.140453 | ||||||||
\(945\) | −3.58239 | −0.116535 | ||||||||
\(946\) | 28.0895 | 0.913269 | ||||||||
\(947\) | −39.6711 | −1.28914 | −0.644569 | − | 0.764546i | \(-0.722963\pi\) | ||||
−0.644569 | + | 0.764546i | \(0.722963\pi\) | |||||||
\(948\) | −10.0344 | −0.325903 | ||||||||
\(949\) | 26.4476 | 0.858524 | ||||||||
\(950\) | 17.3491 | 0.562879 | ||||||||
\(951\) | 22.5944 | 0.732672 | ||||||||
\(952\) | 4.74419 | 0.153760 | ||||||||
\(953\) | 1.41878 | 0.0459588 | 0.0229794 | − | 0.999736i | \(-0.492685\pi\) | ||||
0.0229794 | + | 0.999736i | \(0.492685\pi\) | |||||||
\(954\) | 8.02674 | 0.259875 | ||||||||
\(955\) | −11.6092 | −0.375665 | ||||||||
\(956\) | 17.5768 | 0.568476 | ||||||||
\(957\) | −0.279246 | −0.00902676 | ||||||||
\(958\) | −24.9404 | −0.805787 | ||||||||
\(959\) | −6.59999 | −0.213125 | ||||||||
\(960\) | −6.14183 | −0.198227 | ||||||||
\(961\) | −23.2455 | −0.749855 | ||||||||
\(962\) | 22.4386 | 0.723448 | ||||||||
\(963\) | 20.4567 | 0.659208 | ||||||||
\(964\) | 1.56163 | 0.0502969 | ||||||||
\(965\) | −59.1194 | −1.90312 | ||||||||
\(966\) | 5.15824 | 0.165964 | ||||||||
\(967\) | −21.7303 | −0.698800 | −0.349400 | − | 0.936974i | \(-0.613615\pi\) | ||||
−0.349400 | + | 0.936974i | \(0.613615\pi\) | |||||||
\(968\) | −11.3586 | −0.365080 | ||||||||
\(969\) | 109.708 | 3.52434 | ||||||||
\(970\) | 46.9575 | 1.50771 | ||||||||
\(971\) | 38.7192 | 1.24256 | 0.621279 | − | 0.783590i | \(-0.286614\pi\) | ||||
0.621279 | + | 0.783590i | \(0.286614\pi\) | |||||||
\(972\) | 19.4286 | 0.623172 | ||||||||
\(973\) | −5.63712 | −0.180718 | ||||||||
\(974\) | −9.93041 | −0.318191 | ||||||||
\(975\) | −10.9844 | −0.351784 | ||||||||
\(976\) | 10.1809 | 0.325881 | ||||||||
\(977\) | −42.9478 | −1.37402 | −0.687011 | − | 0.726647i | \(-0.741078\pi\) | ||||
−0.687011 | + | 0.726647i | \(0.741078\pi\) | |||||||
\(978\) | −48.9387 | −1.56489 | ||||||||
\(979\) | −61.7573 | −1.97377 | ||||||||
\(980\) | −17.0307 | −0.544025 | ||||||||
\(981\) | 27.8685 | 0.889772 | ||||||||
\(982\) | 3.07555 | 0.0981447 | ||||||||
\(983\) | −19.2726 | −0.614700 | −0.307350 | − | 0.951597i | \(-0.599442\pi\) | ||||
−0.307350 | + | 0.951597i | \(0.599442\pi\) | |||||||
\(984\) | −14.8107 | −0.472149 | ||||||||
\(985\) | −56.5684 | −1.80242 | ||||||||
\(986\) | 0.153128 | 0.00487660 | ||||||||
\(987\) | 11.2712 | 0.358767 | ||||||||
\(988\) | −17.7920 | −0.566038 | ||||||||
\(989\) | −16.7476 | −0.532542 | ||||||||
\(990\) | 28.7002 | 0.912151 | ||||||||
\(991\) | −54.4445 | −1.72949 | −0.864743 | − | 0.502214i | \(-0.832519\pi\) | ||||
−0.864743 | + | 0.502214i | \(0.832519\pi\) | |||||||
\(992\) | −2.78469 | −0.0884140 | ||||||||
\(993\) | 10.7333 | 0.340612 | ||||||||
\(994\) | −0.392065 | −0.0124355 | ||||||||
\(995\) | 18.6232 | 0.590396 | ||||||||
\(996\) | 36.3034 | 1.15032 | ||||||||
\(997\) | 8.21388 | 0.260136 | 0.130068 | − | 0.991505i | \(-0.458480\pi\) | ||||
0.130068 | + | 0.991505i | \(0.458480\pi\) | |||||||
\(998\) | −19.9045 | −0.630066 | ||||||||
\(999\) | −17.0107 | −0.538196 |
(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 | 6046.2.a.g.1.14 | ✓ | 69 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6046.2.a.g.1.14 | ✓ | 69 | 1.1 | even | 1 | trivial |