Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6037,2,Mod(1,6037)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6037, 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("6037.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6037 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6037.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: | \(48.2056877002\) |
Analytic rank: | \(1\) |
Dimension: | \(243\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 6037.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.75691 | −1.94943 | −0.974714 | − | 0.223456i | \(-0.928266\pi\) | ||||
−0.974714 | + | 0.223456i | \(0.928266\pi\) | |||||||
\(3\) | −3.25303 | −1.87814 | −0.939068 | − | 0.343731i | \(-0.888309\pi\) | ||||
−0.939068 | + | 0.343731i | \(0.888309\pi\) | |||||||
\(4\) | 5.60054 | 2.80027 | ||||||||
\(5\) | 1.79806 | 0.804116 | 0.402058 | − | 0.915614i | \(-0.368295\pi\) | ||||
0.402058 | + | 0.915614i | \(0.368295\pi\) | |||||||
\(6\) | 8.96830 | 3.66129 | ||||||||
\(7\) | −3.80594 | −1.43851 | −0.719255 | − | 0.694747i | \(-0.755517\pi\) | ||||
−0.719255 | + | 0.694747i | \(0.755517\pi\) | |||||||
\(8\) | −9.92635 | −3.50950 | ||||||||
\(9\) | 7.58219 | 2.52740 | ||||||||
\(10\) | −4.95708 | −1.56757 | ||||||||
\(11\) | −2.49038 | −0.750878 | −0.375439 | − | 0.926847i | \(-0.622508\pi\) | ||||
−0.375439 | + | 0.926847i | \(0.622508\pi\) | |||||||
\(12\) | −18.2187 | −5.25929 | ||||||||
\(13\) | −3.74920 | −1.03984 | −0.519921 | − | 0.854214i | \(-0.674039\pi\) | ||||
−0.519921 | + | 0.854214i | \(0.674039\pi\) | |||||||
\(14\) | 10.4926 | 2.80427 | ||||||||
\(15\) | −5.84913 | −1.51024 | ||||||||
\(16\) | 16.1650 | 4.04124 | ||||||||
\(17\) | 7.01748 | 1.70199 | 0.850994 | − | 0.525176i | \(-0.176000\pi\) | ||||
0.850994 | + | 0.525176i | \(0.176000\pi\) | |||||||
\(18\) | −20.9034 | −4.92698 | ||||||||
\(19\) | −7.37522 | −1.69199 | −0.845996 | − | 0.533190i | \(-0.820993\pi\) | ||||
−0.845996 | + | 0.533190i | \(0.820993\pi\) | |||||||
\(20\) | 10.0701 | 2.25174 | ||||||||
\(21\) | 12.3808 | 2.70172 | ||||||||
\(22\) | 6.86575 | 1.46378 | ||||||||
\(23\) | −7.99585 | −1.66725 | −0.833625 | − | 0.552331i | \(-0.813739\pi\) | ||||
−0.833625 | + | 0.552331i | \(0.813739\pi\) | |||||||
\(24\) | 32.2907 | 6.59131 | ||||||||
\(25\) | −1.76699 | −0.353398 | ||||||||
\(26\) | 10.3362 | 2.02710 | ||||||||
\(27\) | −14.9060 | −2.86866 | ||||||||
\(28\) | −21.3153 | −4.02821 | ||||||||
\(29\) | −3.30028 | −0.612847 | −0.306424 | − | 0.951895i | \(-0.599132\pi\) | ||||
−0.306424 | + | 0.951895i | \(0.599132\pi\) | |||||||
\(30\) | 16.1255 | 2.94410 | ||||||||
\(31\) | 8.57601 | 1.54030 | 0.770148 | − | 0.637865i | \(-0.220182\pi\) | ||||
0.770148 | + | 0.637865i | \(0.220182\pi\) | |||||||
\(32\) | −24.7126 | −4.36861 | ||||||||
\(33\) | 8.10128 | 1.41025 | ||||||||
\(34\) | −19.3465 | −3.31790 | ||||||||
\(35\) | −6.84329 | −1.15673 | ||||||||
\(36\) | 42.4643 | 7.07739 | ||||||||
\(37\) | −1.64652 | −0.270686 | −0.135343 | − | 0.990799i | \(-0.543214\pi\) | ||||
−0.135343 | + | 0.990799i | \(0.543214\pi\) | |||||||
\(38\) | 20.3328 | 3.29842 | ||||||||
\(39\) | 12.1963 | 1.95296 | ||||||||
\(40\) | −17.8482 | −2.82204 | ||||||||
\(41\) | 7.49158 | 1.16999 | 0.584994 | − | 0.811037i | \(-0.301097\pi\) | ||||
0.584994 | + | 0.811037i | \(0.301097\pi\) | |||||||
\(42\) | −34.1328 | −5.26680 | ||||||||
\(43\) | −0.706248 | −0.107702 | −0.0538509 | − | 0.998549i | \(-0.517150\pi\) | ||||
−0.0538509 | + | 0.998549i | \(0.517150\pi\) | |||||||
\(44\) | −13.9475 | −2.10266 | ||||||||
\(45\) | 13.6332 | 2.03232 | ||||||||
\(46\) | 22.0438 | 3.25018 | ||||||||
\(47\) | 6.01634 | 0.877574 | 0.438787 | − | 0.898591i | \(-0.355408\pi\) | ||||
0.438787 | + | 0.898591i | \(0.355408\pi\) | |||||||
\(48\) | −52.5851 | −7.59000 | ||||||||
\(49\) | 7.48516 | 1.06931 | ||||||||
\(50\) | 4.87143 | 0.688924 | ||||||||
\(51\) | −22.8280 | −3.19656 | ||||||||
\(52\) | −20.9976 | −2.91184 | ||||||||
\(53\) | 7.77088 | 1.06741 | 0.533707 | − | 0.845670i | \(-0.320799\pi\) | ||||
0.533707 | + | 0.845670i | \(0.320799\pi\) | |||||||
\(54\) | 41.0944 | 5.59224 | ||||||||
\(55\) | −4.47785 | −0.603793 | ||||||||
\(56\) | 37.7791 | 5.04844 | ||||||||
\(57\) | 23.9918 | 3.17779 | ||||||||
\(58\) | 9.09857 | 1.19470 | ||||||||
\(59\) | 7.55279 | 0.983290 | 0.491645 | − | 0.870796i | \(-0.336396\pi\) | ||||
0.491645 | + | 0.870796i | \(0.336396\pi\) | |||||||
\(60\) | −32.7583 | −4.22908 | ||||||||
\(61\) | −3.23030 | −0.413597 | −0.206799 | − | 0.978384i | \(-0.566305\pi\) | ||||
−0.206799 | + | 0.978384i | \(0.566305\pi\) | |||||||
\(62\) | −23.6433 | −3.00270 | ||||||||
\(63\) | −28.8573 | −3.63568 | ||||||||
\(64\) | 35.8004 | 4.47505 | ||||||||
\(65\) | −6.74128 | −0.836153 | ||||||||
\(66\) | −22.3345 | −2.74918 | ||||||||
\(67\) | 12.7529 | 1.55802 | 0.779010 | − | 0.627012i | \(-0.215722\pi\) | ||||
0.779010 | + | 0.627012i | \(0.215722\pi\) | |||||||
\(68\) | 39.3016 | 4.76602 | ||||||||
\(69\) | 26.0107 | 3.13132 | ||||||||
\(70\) | 18.8663 | 2.25496 | ||||||||
\(71\) | 0.510338 | 0.0605659 | 0.0302830 | − | 0.999541i | \(-0.490359\pi\) | ||||
0.0302830 | + | 0.999541i | \(0.490359\pi\) | |||||||
\(72\) | −75.2635 | −8.86989 | ||||||||
\(73\) | −3.61194 | −0.422746 | −0.211373 | − | 0.977405i | \(-0.567793\pi\) | ||||
−0.211373 | + | 0.977405i | \(0.567793\pi\) | |||||||
\(74\) | 4.53930 | 0.527682 | ||||||||
\(75\) | 5.74807 | 0.663730 | ||||||||
\(76\) | −41.3052 | −4.73803 | ||||||||
\(77\) | 9.47824 | 1.08015 | ||||||||
\(78\) | −33.6240 | −3.80716 | ||||||||
\(79\) | −5.15244 | −0.579695 | −0.289848 | − | 0.957073i | \(-0.593605\pi\) | ||||
−0.289848 | + | 0.957073i | \(0.593605\pi\) | |||||||
\(80\) | 29.0655 | 3.24963 | ||||||||
\(81\) | 25.7430 | 2.86033 | ||||||||
\(82\) | −20.6536 | −2.28081 | ||||||||
\(83\) | −14.0763 | −1.54508 | −0.772539 | − | 0.634967i | \(-0.781014\pi\) | ||||
−0.772539 | + | 0.634967i | \(0.781014\pi\) | |||||||
\(84\) | 69.3393 | 7.56553 | ||||||||
\(85\) | 12.6178 | 1.36859 | ||||||||
\(86\) | 1.94706 | 0.209957 | ||||||||
\(87\) | 10.7359 | 1.15101 | ||||||||
\(88\) | 24.7204 | 2.63521 | ||||||||
\(89\) | −7.39389 | −0.783750 | −0.391875 | − | 0.920018i | \(-0.628174\pi\) | ||||
−0.391875 | + | 0.920018i | \(0.628174\pi\) | |||||||
\(90\) | −37.5855 | −3.96186 | ||||||||
\(91\) | 14.2692 | 1.49582 | ||||||||
\(92\) | −44.7811 | −4.66875 | ||||||||
\(93\) | −27.8980 | −2.89289 | ||||||||
\(94\) | −16.5865 | −1.71077 | ||||||||
\(95\) | −13.2611 | −1.36056 | ||||||||
\(96\) | 80.3908 | 8.20485 | ||||||||
\(97\) | 8.70729 | 0.884091 | 0.442045 | − | 0.896993i | \(-0.354253\pi\) | ||||
0.442045 | + | 0.896993i | \(0.354253\pi\) | |||||||
\(98\) | −20.6359 | −2.08454 | ||||||||
\(99\) | −18.8825 | −1.89777 | ||||||||
\(100\) | −9.89610 | −0.989610 | ||||||||
\(101\) | −12.6284 | −1.25657 | −0.628287 | − | 0.777982i | \(-0.716244\pi\) | ||||
−0.628287 | + | 0.777982i | \(0.716244\pi\) | |||||||
\(102\) | 62.9348 | 6.23147 | ||||||||
\(103\) | −3.62814 | −0.357491 | −0.178746 | − | 0.983895i | \(-0.557204\pi\) | ||||
−0.178746 | + | 0.983895i | \(0.557204\pi\) | |||||||
\(104\) | 37.2159 | 3.64932 | ||||||||
\(105\) | 22.2614 | 2.17249 | ||||||||
\(106\) | −21.4236 | −2.08084 | ||||||||
\(107\) | −0.0585757 | −0.00566273 | −0.00283137 | − | 0.999996i | \(-0.500901\pi\) | ||||
−0.00283137 | + | 0.999996i | \(0.500901\pi\) | |||||||
\(108\) | −83.4815 | −8.03301 | ||||||||
\(109\) | 17.3209 | 1.65904 | 0.829518 | − | 0.558479i | \(-0.188615\pi\) | ||||
0.829518 | + | 0.558479i | \(0.188615\pi\) | |||||||
\(110\) | 12.3450 | 1.17705 | ||||||||
\(111\) | 5.35617 | 0.508385 | ||||||||
\(112\) | −61.5228 | −5.81336 | ||||||||
\(113\) | 12.2456 | 1.15197 | 0.575983 | − | 0.817462i | \(-0.304619\pi\) | ||||
0.575983 | + | 0.817462i | \(0.304619\pi\) | |||||||
\(114\) | −66.1431 | −6.19487 | ||||||||
\(115\) | −14.3770 | −1.34066 | ||||||||
\(116\) | −18.4834 | −1.71614 | ||||||||
\(117\) | −28.4272 | −2.62809 | ||||||||
\(118\) | −20.8223 | −1.91685 | ||||||||
\(119\) | −26.7081 | −2.44833 | ||||||||
\(120\) | 58.0605 | 5.30018 | ||||||||
\(121\) | −4.79800 | −0.436182 | ||||||||
\(122\) | 8.90563 | 0.806278 | ||||||||
\(123\) | −24.3703 | −2.19740 | ||||||||
\(124\) | 48.0303 | 4.31325 | ||||||||
\(125\) | −12.1674 | −1.08829 | ||||||||
\(126\) | 79.5570 | 7.08750 | ||||||||
\(127\) | 13.8729 | 1.23102 | 0.615512 | − | 0.788127i | \(-0.288949\pi\) | ||||
0.615512 | + | 0.788127i | \(0.288949\pi\) | |||||||
\(128\) | −49.2733 | −4.35518 | ||||||||
\(129\) | 2.29744 | 0.202279 | ||||||||
\(130\) | 18.5851 | 1.63002 | ||||||||
\(131\) | −16.0684 | −1.40390 | −0.701950 | − | 0.712226i | \(-0.747687\pi\) | ||||
−0.701950 | + | 0.712226i | \(0.747687\pi\) | |||||||
\(132\) | 45.3715 | 3.94909 | ||||||||
\(133\) | 28.0696 | 2.43395 | ||||||||
\(134\) | −35.1587 | −3.03725 | ||||||||
\(135\) | −26.8018 | −2.30673 | ||||||||
\(136\) | −69.6579 | −5.97312 | ||||||||
\(137\) | −10.1798 | −0.869722 | −0.434861 | − | 0.900498i | \(-0.643203\pi\) | ||||
−0.434861 | + | 0.900498i | \(0.643203\pi\) | |||||||
\(138\) | −71.7092 | −6.10429 | ||||||||
\(139\) | 12.9963 | 1.10233 | 0.551165 | − | 0.834396i | \(-0.314183\pi\) | ||||
0.551165 | + | 0.834396i | \(0.314183\pi\) | |||||||
\(140\) | −38.3261 | −3.23915 | ||||||||
\(141\) | −19.5713 | −1.64820 | ||||||||
\(142\) | −1.40695 | −0.118069 | ||||||||
\(143\) | 9.33695 | 0.780795 | ||||||||
\(144\) | 122.566 | 10.2138 | ||||||||
\(145\) | −5.93410 | −0.492800 | ||||||||
\(146\) | 9.95779 | 0.824113 | ||||||||
\(147\) | −24.3494 | −2.00831 | ||||||||
\(148\) | −9.22138 | −0.757993 | ||||||||
\(149\) | 4.42574 | 0.362571 | 0.181285 | − | 0.983431i | \(-0.441974\pi\) | ||||
0.181285 | + | 0.983431i | \(0.441974\pi\) | |||||||
\(150\) | −15.8469 | −1.29389 | ||||||||
\(151\) | 7.32228 | 0.595878 | 0.297939 | − | 0.954585i | \(-0.403701\pi\) | ||||
0.297939 | + | 0.954585i | \(0.403701\pi\) | |||||||
\(152\) | 73.2090 | 5.93804 | ||||||||
\(153\) | 53.2078 | 4.30160 | ||||||||
\(154\) | −26.1306 | −2.10567 | ||||||||
\(155\) | 15.4202 | 1.23858 | ||||||||
\(156\) | 68.3056 | 5.46883 | ||||||||
\(157\) | 11.5458 | 0.921457 | 0.460728 | − | 0.887541i | \(-0.347588\pi\) | ||||
0.460728 | + | 0.887541i | \(0.347588\pi\) | |||||||
\(158\) | 14.2048 | 1.13007 | ||||||||
\(159\) | −25.2789 | −2.00475 | ||||||||
\(160\) | −44.4347 | −3.51287 | ||||||||
\(161\) | 30.4317 | 2.39835 | ||||||||
\(162\) | −70.9711 | −5.57601 | ||||||||
\(163\) | 9.41451 | 0.737402 | 0.368701 | − | 0.929548i | \(-0.379803\pi\) | ||||
0.368701 | + | 0.929548i | \(0.379803\pi\) | |||||||
\(164\) | 41.9569 | 3.27628 | ||||||||
\(165\) | 14.5666 | 1.13401 | ||||||||
\(166\) | 38.8072 | 3.01202 | ||||||||
\(167\) | 6.57335 | 0.508661 | 0.254331 | − | 0.967117i | \(-0.418145\pi\) | ||||
0.254331 | + | 0.967117i | \(0.418145\pi\) | |||||||
\(168\) | −122.896 | −9.48166 | ||||||||
\(169\) | 1.05653 | 0.0812713 | ||||||||
\(170\) | −34.7862 | −2.66798 | ||||||||
\(171\) | −55.9203 | −4.27633 | ||||||||
\(172\) | −3.95537 | −0.301594 | ||||||||
\(173\) | −12.3020 | −0.935306 | −0.467653 | − | 0.883912i | \(-0.654900\pi\) | ||||
−0.467653 | + | 0.883912i | \(0.654900\pi\) | |||||||
\(174\) | −29.5979 | −2.24381 | ||||||||
\(175\) | 6.72505 | 0.508366 | ||||||||
\(176\) | −40.2569 | −3.03448 | ||||||||
\(177\) | −24.5694 | −1.84675 | ||||||||
\(178\) | 20.3843 | 1.52787 | ||||||||
\(179\) | −0.101825 | −0.00761077 | −0.00380538 | − | 0.999993i | \(-0.501211\pi\) | ||||
−0.00380538 | + | 0.999993i | \(0.501211\pi\) | |||||||
\(180\) | 76.3533 | 5.69104 | ||||||||
\(181\) | −7.46934 | −0.555192 | −0.277596 | − | 0.960698i | \(-0.589538\pi\) | ||||
−0.277596 | + | 0.960698i | \(0.589538\pi\) | |||||||
\(182\) | −39.3390 | −2.91600 | ||||||||
\(183\) | 10.5082 | 0.776792 | ||||||||
\(184\) | 79.3696 | 5.85121 | ||||||||
\(185\) | −2.96053 | −0.217663 | ||||||||
\(186\) | 76.9122 | 5.63947 | ||||||||
\(187\) | −17.4762 | −1.27799 | ||||||||
\(188\) | 33.6948 | 2.45744 | ||||||||
\(189\) | 56.7312 | 4.12659 | ||||||||
\(190\) | 36.5595 | 2.65231 | ||||||||
\(191\) | 9.56732 | 0.692267 | 0.346133 | − | 0.938185i | \(-0.387494\pi\) | ||||
0.346133 | + | 0.938185i | \(0.387494\pi\) | |||||||
\(192\) | −116.460 | −8.40476 | ||||||||
\(193\) | −6.68570 | −0.481247 | −0.240624 | − | 0.970618i | \(-0.577352\pi\) | ||||
−0.240624 | + | 0.970618i | \(0.577352\pi\) | |||||||
\(194\) | −24.0052 | −1.72347 | ||||||||
\(195\) | 21.9296 | 1.57041 | ||||||||
\(196\) | 41.9209 | 2.99435 | ||||||||
\(197\) | −15.5028 | −1.10453 | −0.552265 | − | 0.833668i | \(-0.686236\pi\) | ||||
−0.552265 | + | 0.833668i | \(0.686236\pi\) | |||||||
\(198\) | 52.0574 | 3.69956 | ||||||||
\(199\) | 13.2417 | 0.938679 | 0.469339 | − | 0.883018i | \(-0.344492\pi\) | ||||
0.469339 | + | 0.883018i | \(0.344492\pi\) | |||||||
\(200\) | 17.5398 | 1.24025 | ||||||||
\(201\) | −41.4857 | −2.92617 | ||||||||
\(202\) | 34.8153 | 2.44960 | ||||||||
\(203\) | 12.5607 | 0.881586 | ||||||||
\(204\) | −127.849 | −8.95124 | ||||||||
\(205\) | 13.4703 | 0.940806 | ||||||||
\(206\) | 10.0025 | 0.696904 | ||||||||
\(207\) | −60.6260 | −4.21380 | ||||||||
\(208\) | −60.6057 | −4.20225 | ||||||||
\(209\) | 18.3671 | 1.27048 | ||||||||
\(210\) | −61.3727 | −4.23512 | ||||||||
\(211\) | 1.78065 | 0.122585 | 0.0612926 | − | 0.998120i | \(-0.480478\pi\) | ||||
0.0612926 | + | 0.998120i | \(0.480478\pi\) | |||||||
\(212\) | 43.5211 | 2.98904 | ||||||||
\(213\) | −1.66014 | −0.113751 | ||||||||
\(214\) | 0.161488 | 0.0110391 | ||||||||
\(215\) | −1.26987 | −0.0866047 | ||||||||
\(216\) | 147.962 | 10.0675 | ||||||||
\(217\) | −32.6397 | −2.21573 | ||||||||
\(218\) | −47.7520 | −3.23417 | ||||||||
\(219\) | 11.7498 | 0.793975 | ||||||||
\(220\) | −25.0784 | −1.69078 | ||||||||
\(221\) | −26.3099 | −1.76980 | ||||||||
\(222\) | −14.7665 | −0.991059 | ||||||||
\(223\) | 3.07804 | 0.206121 | 0.103060 | − | 0.994675i | \(-0.467137\pi\) | ||||
0.103060 | + | 0.994675i | \(0.467137\pi\) | |||||||
\(224\) | 94.0546 | 6.28429 | ||||||||
\(225\) | −13.3976 | −0.893177 | ||||||||
\(226\) | −33.7599 | −2.24567 | ||||||||
\(227\) | 2.80487 | 0.186166 | 0.0930829 | − | 0.995658i | \(-0.470328\pi\) | ||||
0.0930829 | + | 0.995658i | \(0.470328\pi\) | |||||||
\(228\) | 134.367 | 8.89867 | ||||||||
\(229\) | 11.6867 | 0.772276 | 0.386138 | − | 0.922441i | \(-0.373809\pi\) | ||||
0.386138 | + | 0.922441i | \(0.373809\pi\) | |||||||
\(230\) | 39.6361 | 2.61352 | ||||||||
\(231\) | −30.8330 | −2.02866 | ||||||||
\(232\) | 32.7598 | 2.15078 | ||||||||
\(233\) | 14.5461 | 0.952949 | 0.476474 | − | 0.879188i | \(-0.341914\pi\) | ||||
0.476474 | + | 0.879188i | \(0.341914\pi\) | |||||||
\(234\) | 78.3711 | 5.12328 | ||||||||
\(235\) | 10.8177 | 0.705671 | ||||||||
\(236\) | 42.2997 | 2.75348 | ||||||||
\(237\) | 16.7610 | 1.08875 | ||||||||
\(238\) | 73.6317 | 4.77283 | ||||||||
\(239\) | −2.57658 | −0.166665 | −0.0833325 | − | 0.996522i | \(-0.526556\pi\) | ||||
−0.0833325 | + | 0.996522i | \(0.526556\pi\) | |||||||
\(240\) | −94.5510 | −6.10324 | ||||||||
\(241\) | −5.40054 | −0.347879 | −0.173940 | − | 0.984756i | \(-0.555650\pi\) | ||||
−0.173940 | + | 0.984756i | \(0.555650\pi\) | |||||||
\(242\) | 13.2276 | 0.850305 | ||||||||
\(243\) | −39.0248 | −2.50344 | ||||||||
\(244\) | −18.0914 | −1.15818 | ||||||||
\(245\) | 13.4588 | 0.859848 | ||||||||
\(246\) | 67.1867 | 4.28367 | ||||||||
\(247\) | 27.6512 | 1.75940 | ||||||||
\(248\) | −85.1285 | −5.40566 | ||||||||
\(249\) | 45.7907 | 2.90187 | ||||||||
\(250\) | 33.5445 | 2.12154 | ||||||||
\(251\) | 25.2751 | 1.59535 | 0.797676 | − | 0.603086i | \(-0.206062\pi\) | ||||
0.797676 | + | 0.603086i | \(0.206062\pi\) | |||||||
\(252\) | −161.617 | −10.1809 | ||||||||
\(253\) | 19.9127 | 1.25190 | ||||||||
\(254\) | −38.2464 | −2.39979 | ||||||||
\(255\) | −41.0461 | −2.57041 | ||||||||
\(256\) | 64.2410 | 4.01506 | ||||||||
\(257\) | 2.80617 | 0.175044 | 0.0875220 | − | 0.996163i | \(-0.472105\pi\) | ||||
0.0875220 | + | 0.996163i | \(0.472105\pi\) | |||||||
\(258\) | −6.33384 | −0.394328 | ||||||||
\(259\) | 6.26654 | 0.389384 | ||||||||
\(260\) | −37.7548 | −2.34145 | ||||||||
\(261\) | −25.0234 | −1.54891 | ||||||||
\(262\) | 44.2990 | 2.73680 | ||||||||
\(263\) | 14.6623 | 0.904117 | 0.452059 | − | 0.891988i | \(-0.350690\pi\) | ||||
0.452059 | + | 0.891988i | \(0.350690\pi\) | |||||||
\(264\) | −80.4162 | −4.94927 | ||||||||
\(265\) | 13.9725 | 0.858324 | ||||||||
\(266\) | −77.3854 | −4.74480 | ||||||||
\(267\) | 24.0525 | 1.47199 | ||||||||
\(268\) | 71.4233 | 4.36287 | ||||||||
\(269\) | 28.1180 | 1.71439 | 0.857193 | − | 0.514995i | \(-0.172206\pi\) | ||||
0.857193 | + | 0.514995i | \(0.172206\pi\) | |||||||
\(270\) | 73.8901 | 4.49681 | ||||||||
\(271\) | 3.79653 | 0.230623 | 0.115311 | − | 0.993329i | \(-0.463213\pi\) | ||||
0.115311 | + | 0.993329i | \(0.463213\pi\) | |||||||
\(272\) | 113.437 | 6.87814 | ||||||||
\(273\) | −46.4182 | −2.80936 | ||||||||
\(274\) | 28.0649 | 1.69546 | ||||||||
\(275\) | 4.40048 | 0.265359 | ||||||||
\(276\) | 145.674 | 8.76855 | ||||||||
\(277\) | 17.1762 | 1.03202 | 0.516009 | − | 0.856583i | \(-0.327417\pi\) | ||||
0.516009 | + | 0.856583i | \(0.327417\pi\) | |||||||
\(278\) | −35.8296 | −2.14891 | ||||||||
\(279\) | 65.0249 | 3.89294 | ||||||||
\(280\) | 67.9290 | 4.05953 | ||||||||
\(281\) | −18.3358 | −1.09382 | −0.546912 | − | 0.837190i | \(-0.684197\pi\) | ||||
−0.546912 | + | 0.837190i | \(0.684197\pi\) | |||||||
\(282\) | 53.9563 | 3.21305 | ||||||||
\(283\) | −4.39088 | −0.261010 | −0.130505 | − | 0.991448i | \(-0.541660\pi\) | ||||
−0.130505 | + | 0.991448i | \(0.541660\pi\) | |||||||
\(284\) | 2.85817 | 0.169601 | ||||||||
\(285\) | 43.1386 | 2.55531 | ||||||||
\(286\) | −25.7411 | −1.52210 | ||||||||
\(287\) | −28.5125 | −1.68304 | ||||||||
\(288\) | −187.376 | −11.0412 | ||||||||
\(289\) | 32.2450 | 1.89676 | ||||||||
\(290\) | 16.3598 | 0.960678 | ||||||||
\(291\) | −28.3250 | −1.66044 | ||||||||
\(292\) | −20.2288 | −1.18380 | ||||||||
\(293\) | −11.9366 | −0.697343 | −0.348672 | − | 0.937245i | \(-0.613367\pi\) | ||||
−0.348672 | + | 0.937245i | \(0.613367\pi\) | |||||||
\(294\) | 67.1292 | 3.91505 | ||||||||
\(295\) | 13.5804 | 0.790679 | ||||||||
\(296\) | 16.3439 | 0.949971 | ||||||||
\(297\) | 37.1216 | 2.15401 | ||||||||
\(298\) | −12.2014 | −0.706805 | ||||||||
\(299\) | 29.9781 | 1.73368 | ||||||||
\(300\) | 32.1923 | 1.85862 | ||||||||
\(301\) | 2.68793 | 0.154930 | ||||||||
\(302\) | −20.1868 | −1.16162 | ||||||||
\(303\) | 41.0806 | 2.36002 | ||||||||
\(304\) | −119.220 | −6.83774 | ||||||||
\(305\) | −5.80826 | −0.332580 | ||||||||
\(306\) | −146.689 | −8.38565 | ||||||||
\(307\) | 0.0903459 | 0.00515631 | 0.00257816 | − | 0.999997i | \(-0.499179\pi\) | ||||
0.00257816 | + | 0.999997i | \(0.499179\pi\) | |||||||
\(308\) | 53.0833 | 3.02470 | ||||||||
\(309\) | 11.8024 | 0.671418 | ||||||||
\(310\) | −42.5119 | −2.41452 | ||||||||
\(311\) | 9.06814 | 0.514207 | 0.257104 | − | 0.966384i | \(-0.417232\pi\) | ||||
0.257104 | + | 0.966384i | \(0.417232\pi\) | |||||||
\(312\) | −121.064 | −6.85392 | ||||||||
\(313\) | 11.7268 | 0.662839 | 0.331420 | − | 0.943483i | \(-0.392472\pi\) | ||||
0.331420 | + | 0.943483i | \(0.392472\pi\) | |||||||
\(314\) | −31.8308 | −1.79631 | ||||||||
\(315\) | −51.8871 | −2.92351 | ||||||||
\(316\) | −28.8565 | −1.62330 | ||||||||
\(317\) | −17.5604 | −0.986292 | −0.493146 | − | 0.869947i | \(-0.664153\pi\) | ||||
−0.493146 | + | 0.869947i | \(0.664153\pi\) | |||||||
\(318\) | 69.6916 | 3.90811 | ||||||||
\(319\) | 8.21896 | 0.460174 | ||||||||
\(320\) | 64.3712 | 3.59846 | ||||||||
\(321\) | 0.190549 | 0.0106354 | ||||||||
\(322\) | −83.8974 | −4.67542 | ||||||||
\(323\) | −51.7554 | −2.87975 | ||||||||
\(324\) | 144.175 | 8.00971 | ||||||||
\(325\) | 6.62480 | 0.367478 | ||||||||
\(326\) | −25.9549 | −1.43751 | ||||||||
\(327\) | −56.3452 | −3.11590 | ||||||||
\(328\) | −74.3641 | −4.10607 | ||||||||
\(329\) | −22.8978 | −1.26240 | ||||||||
\(330\) | −40.1587 | −2.21066 | ||||||||
\(331\) | −16.8606 | −0.926741 | −0.463370 | − | 0.886165i | \(-0.653360\pi\) | ||||
−0.463370 | + | 0.886165i | \(0.653360\pi\) | |||||||
\(332\) | −78.8351 | −4.32664 | ||||||||
\(333\) | −12.4842 | −0.684130 | ||||||||
\(334\) | −18.1221 | −0.991598 | ||||||||
\(335\) | 22.9305 | 1.25283 | ||||||||
\(336\) | 200.136 | 10.9183 | ||||||||
\(337\) | 18.6598 | 1.01646 | 0.508232 | − | 0.861220i | \(-0.330299\pi\) | ||||
0.508232 | + | 0.861220i | \(0.330299\pi\) | |||||||
\(338\) | −2.91275 | −0.158433 | ||||||||
\(339\) | −39.8352 | −2.16355 | ||||||||
\(340\) | 70.6666 | 3.83244 | ||||||||
\(341\) | −21.3575 | −1.15658 | ||||||||
\(342\) | 154.167 | 8.33640 | ||||||||
\(343\) | −1.84650 | −0.0997015 | ||||||||
\(344\) | 7.01047 | 0.377979 | ||||||||
\(345\) | 46.7688 | 2.51795 | ||||||||
\(346\) | 33.9156 | 1.82331 | ||||||||
\(347\) | 0.398374 | 0.0213859 | 0.0106929 | − | 0.999943i | \(-0.496596\pi\) | ||||
0.0106929 | + | 0.999943i | \(0.496596\pi\) | |||||||
\(348\) | 60.1269 | 3.22314 | ||||||||
\(349\) | −21.4289 | −1.14706 | −0.573530 | − | 0.819184i | \(-0.694426\pi\) | ||||
−0.573530 | + | 0.819184i | \(0.694426\pi\) | |||||||
\(350\) | −18.5404 | −0.991023 | ||||||||
\(351\) | 55.8856 | 2.98295 | ||||||||
\(352\) | 61.5438 | 3.28030 | ||||||||
\(353\) | −24.4171 | −1.29959 | −0.649796 | − | 0.760108i | \(-0.725146\pi\) | ||||
−0.649796 | + | 0.760108i | \(0.725146\pi\) | |||||||
\(354\) | 67.7357 | 3.60011 | ||||||||
\(355\) | 0.917616 | 0.0487020 | ||||||||
\(356\) | −41.4098 | −2.19471 | ||||||||
\(357\) | 86.8821 | 4.59829 | ||||||||
\(358\) | 0.280722 | 0.0148366 | ||||||||
\(359\) | 19.5541 | 1.03203 | 0.516013 | − | 0.856581i | \(-0.327415\pi\) | ||||
0.516013 | + | 0.856581i | \(0.327415\pi\) | |||||||
\(360\) | −135.328 | −7.13241 | ||||||||
\(361\) | 35.3939 | 1.86283 | ||||||||
\(362\) | 20.5923 | 1.08231 | ||||||||
\(363\) | 15.6080 | 0.819208 | ||||||||
\(364\) | 79.9154 | 4.18871 | ||||||||
\(365\) | −6.49448 | −0.339937 | ||||||||
\(366\) | −28.9703 | −1.51430 | ||||||||
\(367\) | −5.90639 | −0.308311 | −0.154156 | − | 0.988047i | \(-0.549266\pi\) | ||||
−0.154156 | + | 0.988047i | \(0.549266\pi\) | |||||||
\(368\) | −129.253 | −6.73776 | ||||||||
\(369\) | 56.8026 | 2.95703 | ||||||||
\(370\) | 8.16191 | 0.424318 | ||||||||
\(371\) | −29.5755 | −1.53548 | ||||||||
\(372\) | −156.244 | −8.10086 | ||||||||
\(373\) | −10.5668 | −0.547126 | −0.273563 | − | 0.961854i | \(-0.588202\pi\) | ||||
−0.273563 | + | 0.961854i | \(0.588202\pi\) | |||||||
\(374\) | 48.1803 | 2.49134 | ||||||||
\(375\) | 39.5810 | 2.04395 | ||||||||
\(376\) | −59.7204 | −3.07984 | ||||||||
\(377\) | 12.3734 | 0.637264 | ||||||||
\(378\) | −156.403 | −8.04449 | ||||||||
\(379\) | 7.56953 | 0.388821 | 0.194410 | − | 0.980920i | \(-0.437721\pi\) | ||||
0.194410 | + | 0.980920i | \(0.437721\pi\) | |||||||
\(380\) | −74.2691 | −3.80993 | ||||||||
\(381\) | −45.1290 | −2.31203 | ||||||||
\(382\) | −26.3762 | −1.34952 | ||||||||
\(383\) | 17.9445 | 0.916922 | 0.458461 | − | 0.888715i | \(-0.348401\pi\) | ||||
0.458461 | + | 0.888715i | \(0.348401\pi\) | |||||||
\(384\) | 160.287 | 8.17963 | ||||||||
\(385\) | 17.0424 | 0.868562 | ||||||||
\(386\) | 18.4319 | 0.938157 | ||||||||
\(387\) | −5.35490 | −0.272205 | ||||||||
\(388\) | 48.7655 | 2.47569 | ||||||||
\(389\) | 6.65460 | 0.337402 | 0.168701 | − | 0.985667i | \(-0.446043\pi\) | ||||
0.168701 | + | 0.985667i | \(0.446043\pi\) | |||||||
\(390\) | −60.4578 | −3.06140 | ||||||||
\(391\) | −56.1107 | −2.83764 | ||||||||
\(392\) | −74.3004 | −3.75274 | ||||||||
\(393\) | 52.2708 | 2.63671 | ||||||||
\(394\) | 42.7399 | 2.15320 | ||||||||
\(395\) | −9.26439 | −0.466142 | ||||||||
\(396\) | −105.752 | −5.31426 | ||||||||
\(397\) | −7.88802 | −0.395888 | −0.197944 | − | 0.980213i | \(-0.563426\pi\) | ||||
−0.197944 | + | 0.980213i | \(0.563426\pi\) | |||||||
\(398\) | −36.5061 | −1.82989 | ||||||||
\(399\) | −91.3113 | −4.57128 | ||||||||
\(400\) | −28.5633 | −1.42817 | ||||||||
\(401\) | −10.6369 | −0.531183 | −0.265591 | − | 0.964086i | \(-0.585567\pi\) | ||||
−0.265591 | + | 0.964086i | \(0.585567\pi\) | |||||||
\(402\) | 114.372 | 5.70436 | ||||||||
\(403\) | −32.1532 | −1.60166 | ||||||||
\(404\) | −70.7259 | −3.51874 | ||||||||
\(405\) | 46.2874 | 2.30004 | ||||||||
\(406\) | −34.6286 | −1.71859 | ||||||||
\(407\) | 4.10046 | 0.203252 | ||||||||
\(408\) | 226.599 | 11.2183 | ||||||||
\(409\) | 14.3395 | 0.709043 | 0.354521 | − | 0.935048i | \(-0.384644\pi\) | ||||
0.354521 | + | 0.935048i | \(0.384644\pi\) | |||||||
\(410\) | −37.1364 | −1.83403 | ||||||||
\(411\) | 33.1153 | 1.63346 | ||||||||
\(412\) | −20.3196 | −1.00107 | ||||||||
\(413\) | −28.7455 | −1.41447 | ||||||||
\(414\) | 167.140 | 8.21450 | ||||||||
\(415\) | −25.3101 | −1.24242 | ||||||||
\(416\) | 92.6526 | 4.54267 | ||||||||
\(417\) | −42.2773 | −2.07033 | ||||||||
\(418\) | −50.6364 | −2.47671 | ||||||||
\(419\) | −3.02610 | −0.147835 | −0.0739174 | − | 0.997264i | \(-0.523550\pi\) | ||||
−0.0739174 | + | 0.997264i | \(0.523550\pi\) | |||||||
\(420\) | 124.676 | 6.08357 | ||||||||
\(421\) | −29.1758 | −1.42194 | −0.710970 | − | 0.703222i | \(-0.751744\pi\) | ||||
−0.710970 | + | 0.703222i | \(0.751744\pi\) | |||||||
\(422\) | −4.90909 | −0.238971 | ||||||||
\(423\) | 45.6170 | 2.21798 | ||||||||
\(424\) | −77.1366 | −3.74608 | ||||||||
\(425\) | −12.3998 | −0.601479 | ||||||||
\(426\) | 4.57686 | 0.221750 | ||||||||
\(427\) | 12.2943 | 0.594964 | ||||||||
\(428\) | −0.328056 | −0.0158572 | ||||||||
\(429\) | −30.3734 | −1.46644 | ||||||||
\(430\) | 3.50092 | 0.168830 | ||||||||
\(431\) | 8.61350 | 0.414898 | 0.207449 | − | 0.978246i | \(-0.433484\pi\) | ||||
0.207449 | + | 0.978246i | \(0.433484\pi\) | |||||||
\(432\) | −240.955 | −11.5929 | ||||||||
\(433\) | −3.09369 | −0.148673 | −0.0743365 | − | 0.997233i | \(-0.523684\pi\) | ||||
−0.0743365 | + | 0.997233i | \(0.523684\pi\) | |||||||
\(434\) | 89.9848 | 4.31941 | ||||||||
\(435\) | 19.3038 | 0.925545 | ||||||||
\(436\) | 97.0061 | 4.64575 | ||||||||
\(437\) | 58.9711 | 2.82097 | ||||||||
\(438\) | −32.3930 | −1.54780 | ||||||||
\(439\) | 12.3698 | 0.590380 | 0.295190 | − | 0.955439i | \(-0.404617\pi\) | ||||
0.295190 | + | 0.955439i | \(0.404617\pi\) | |||||||
\(440\) | 44.4487 | 2.11901 | ||||||||
\(441\) | 56.7539 | 2.70257 | ||||||||
\(442\) | 72.5341 | 3.45009 | ||||||||
\(443\) | −19.3522 | −0.919450 | −0.459725 | − | 0.888061i | \(-0.652052\pi\) | ||||
−0.459725 | + | 0.888061i | \(0.652052\pi\) | |||||||
\(444\) | 29.9974 | 1.42361 | ||||||||
\(445\) | −13.2946 | −0.630226 | ||||||||
\(446\) | −8.48587 | −0.401817 | ||||||||
\(447\) | −14.3970 | −0.680957 | ||||||||
\(448\) | −136.254 | −6.43741 | ||||||||
\(449\) | 17.6185 | 0.831467 | 0.415733 | − | 0.909487i | \(-0.363525\pi\) | ||||
0.415733 | + | 0.909487i | \(0.363525\pi\) | |||||||
\(450\) | 36.9361 | 1.74118 | ||||||||
\(451\) | −18.6569 | −0.878519 | ||||||||
\(452\) | 68.5818 | 3.22581 | ||||||||
\(453\) | −23.8196 | −1.11914 | ||||||||
\(454\) | −7.73277 | −0.362917 | ||||||||
\(455\) | 25.6569 | 1.20281 | ||||||||
\(456\) | −238.151 | −11.1524 | ||||||||
\(457\) | −30.1173 | −1.40883 | −0.704414 | − | 0.709790i | \(-0.748790\pi\) | ||||
−0.704414 | + | 0.709790i | \(0.748790\pi\) | |||||||
\(458\) | −32.2190 | −1.50550 | ||||||||
\(459\) | −104.602 | −4.88242 | ||||||||
\(460\) | −80.5189 | −3.75422 | ||||||||
\(461\) | −39.0856 | −1.82040 | −0.910198 | − | 0.414173i | \(-0.864071\pi\) | ||||
−0.910198 | + | 0.414173i | \(0.864071\pi\) | |||||||
\(462\) | 85.0037 | 3.95473 | ||||||||
\(463\) | 3.77824 | 0.175590 | 0.0877949 | − | 0.996139i | \(-0.472018\pi\) | ||||
0.0877949 | + | 0.996139i | \(0.472018\pi\) | |||||||
\(464\) | −53.3489 | −2.47666 | ||||||||
\(465\) | −50.1622 | −2.32622 | ||||||||
\(466\) | −40.1023 | −1.85771 | ||||||||
\(467\) | −10.3711 | −0.479919 | −0.239960 | − | 0.970783i | \(-0.577134\pi\) | ||||
−0.239960 | + | 0.970783i | \(0.577134\pi\) | |||||||
\(468\) | −159.207 | −7.35937 | ||||||||
\(469\) | −48.5369 | −2.24123 | ||||||||
\(470\) | −29.8235 | −1.37565 | ||||||||
\(471\) | −37.5589 | −1.73062 | ||||||||
\(472\) | −74.9717 | −3.45085 | ||||||||
\(473\) | 1.75883 | 0.0808709 | ||||||||
\(474\) | −46.2086 | −2.12243 | ||||||||
\(475\) | 13.0319 | 0.597946 | ||||||||
\(476\) | −149.580 | −6.85597 | ||||||||
\(477\) | 58.9203 | 2.69778 | ||||||||
\(478\) | 7.10339 | 0.324902 | ||||||||
\(479\) | −38.2741 | −1.74879 | −0.874393 | − | 0.485218i | \(-0.838740\pi\) | ||||
−0.874393 | + | 0.485218i | \(0.838740\pi\) | |||||||
\(480\) | 144.547 | 6.59765 | ||||||||
\(481\) | 6.17313 | 0.281470 | ||||||||
\(482\) | 14.8888 | 0.678165 | ||||||||
\(483\) | −98.9952 | −4.50444 | ||||||||
\(484\) | −26.8714 | −1.22143 | ||||||||
\(485\) | 15.6562 | 0.710911 | ||||||||
\(486\) | 107.588 | 4.88027 | ||||||||
\(487\) | 26.7520 | 1.21225 | 0.606124 | − | 0.795370i | \(-0.292724\pi\) | ||||
0.606124 | + | 0.795370i | \(0.292724\pi\) | |||||||
\(488\) | 32.0651 | 1.45152 | ||||||||
\(489\) | −30.6257 | −1.38494 | ||||||||
\(490\) | −37.1045 | −1.67621 | ||||||||
\(491\) | 37.4636 | 1.69071 | 0.845355 | − | 0.534205i | \(-0.179389\pi\) | ||||
0.845355 | + | 0.534205i | \(0.179389\pi\) | |||||||
\(492\) | −136.487 | −6.15331 | ||||||||
\(493\) | −23.1596 | −1.04306 | ||||||||
\(494\) | −76.2318 | −3.42983 | ||||||||
\(495\) | −33.9519 | −1.52602 | ||||||||
\(496\) | 138.631 | 6.22471 | ||||||||
\(497\) | −1.94231 | −0.0871247 | ||||||||
\(498\) | −126.241 | −5.65698 | ||||||||
\(499\) | −18.1272 | −0.811483 | −0.405742 | − | 0.913988i | \(-0.632987\pi\) | ||||
−0.405742 | + | 0.913988i | \(0.632987\pi\) | |||||||
\(500\) | −68.1442 | −3.04750 | ||||||||
\(501\) | −21.3833 | −0.955335 | ||||||||
\(502\) | −69.6812 | −3.11002 | ||||||||
\(503\) | −8.45159 | −0.376838 | −0.188419 | − | 0.982089i | \(-0.560336\pi\) | ||||
−0.188419 | + | 0.982089i | \(0.560336\pi\) | |||||||
\(504\) | 286.448 | 12.7594 | ||||||||
\(505\) | −22.7066 | −1.01043 | ||||||||
\(506\) | −54.8975 | −2.44049 | ||||||||
\(507\) | −3.43691 | −0.152639 | ||||||||
\(508\) | 77.6959 | 3.44720 | ||||||||
\(509\) | 1.95539 | 0.0866713 | 0.0433357 | − | 0.999061i | \(-0.486202\pi\) | ||||
0.0433357 | + | 0.999061i | \(0.486202\pi\) | |||||||
\(510\) | 113.160 | 5.01083 | ||||||||
\(511\) | 13.7468 | 0.608124 | ||||||||
\(512\) | −78.5600 | −3.47189 | ||||||||
\(513\) | 109.935 | 4.85374 | ||||||||
\(514\) | −7.73635 | −0.341236 | ||||||||
\(515\) | −6.52361 | −0.287464 | ||||||||
\(516\) | 12.8669 | 0.566435 | ||||||||
\(517\) | −14.9830 | −0.658951 | ||||||||
\(518\) | −17.2763 | −0.759076 | ||||||||
\(519\) | 40.0188 | 1.75663 | ||||||||
\(520\) | 66.9164 | 2.93448 | ||||||||
\(521\) | −39.1457 | −1.71500 | −0.857501 | − | 0.514482i | \(-0.827984\pi\) | ||||
−0.857501 | + | 0.514482i | \(0.827984\pi\) | |||||||
\(522\) | 68.9871 | 3.01948 | ||||||||
\(523\) | 32.8282 | 1.43548 | 0.717739 | − | 0.696313i | \(-0.245177\pi\) | ||||
0.717739 | + | 0.696313i | \(0.245177\pi\) | |||||||
\(524\) | −89.9915 | −3.93130 | ||||||||
\(525\) | −21.8768 | −0.954781 | ||||||||
\(526\) | −40.4226 | −1.76251 | ||||||||
\(527\) | 60.1819 | 2.62157 | ||||||||
\(528\) | 130.957 | 5.69917 | ||||||||
\(529\) | 40.9336 | 1.77972 | ||||||||
\(530\) | −38.5209 | −1.67324 | ||||||||
\(531\) | 57.2667 | 2.48516 | ||||||||
\(532\) | 157.205 | 6.81570 | ||||||||
\(533\) | −28.0875 | −1.21660 | ||||||||
\(534\) | −66.3106 | −2.86954 | ||||||||
\(535\) | −0.105323 | −0.00455349 | ||||||||
\(536\) | −126.590 | −5.46786 | ||||||||
\(537\) | 0.331240 | 0.0142941 | ||||||||
\(538\) | −77.5188 | −3.34207 | ||||||||
\(539\) | −18.6409 | −0.802921 | ||||||||
\(540\) | −150.105 | −6.45947 | ||||||||
\(541\) | 31.4410 | 1.35175 | 0.675877 | − | 0.737015i | \(-0.263765\pi\) | ||||
0.675877 | + | 0.737015i | \(0.263765\pi\) | |||||||
\(542\) | −10.4667 | −0.449582 | ||||||||
\(543\) | 24.2980 | 1.04273 | ||||||||
\(544\) | −173.420 | −7.43532 | ||||||||
\(545\) | 31.1439 | 1.33406 | ||||||||
\(546\) | 127.971 | 5.47664 | ||||||||
\(547\) | −2.18087 | −0.0932471 | −0.0466236 | − | 0.998913i | \(-0.514846\pi\) | ||||
−0.0466236 | + | 0.998913i | \(0.514846\pi\) | |||||||
\(548\) | −57.0126 | −2.43546 | ||||||||
\(549\) | −24.4927 | −1.04532 | ||||||||
\(550\) | −12.1317 | −0.517298 | ||||||||
\(551\) | 24.3403 | 1.03693 | ||||||||
\(552\) | −258.192 | −10.9894 | ||||||||
\(553\) | 19.6099 | 0.833897 | ||||||||
\(554\) | −47.3532 | −2.01184 | ||||||||
\(555\) | 9.63069 | 0.408800 | ||||||||
\(556\) | 72.7862 | 3.08682 | ||||||||
\(557\) | 30.5071 | 1.29263 | 0.646314 | − | 0.763071i | \(-0.276310\pi\) | ||||
0.646314 | + | 0.763071i | \(0.276310\pi\) | |||||||
\(558\) | −179.268 | −7.58900 | ||||||||
\(559\) | 2.64787 | 0.111993 | ||||||||
\(560\) | −110.622 | −4.67462 | ||||||||
\(561\) | 56.8505 | 2.40023 | ||||||||
\(562\) | 50.5502 | 2.13233 | ||||||||
\(563\) | 33.8418 | 1.42626 | 0.713131 | − | 0.701031i | \(-0.247277\pi\) | ||||
0.713131 | + | 0.701031i | \(0.247277\pi\) | |||||||
\(564\) | −109.610 | −4.61541 | ||||||||
\(565\) | 22.0182 | 0.926314 | ||||||||
\(566\) | 12.1052 | 0.508821 | ||||||||
\(567\) | −97.9763 | −4.11462 | ||||||||
\(568\) | −5.06579 | −0.212556 | ||||||||
\(569\) | −11.2740 | −0.472632 | −0.236316 | − | 0.971676i | \(-0.575940\pi\) | ||||
−0.236316 | + | 0.971676i | \(0.575940\pi\) | |||||||
\(570\) | −118.929 | −4.98139 | ||||||||
\(571\) | −17.7055 | −0.740952 | −0.370476 | − | 0.928842i | \(-0.620805\pi\) | ||||
−0.370476 | + | 0.928842i | \(0.620805\pi\) | |||||||
\(572\) | 52.2920 | 2.18644 | ||||||||
\(573\) | −31.1227 | −1.30017 | ||||||||
\(574\) | 78.6063 | 3.28097 | ||||||||
\(575\) | 14.1286 | 0.589203 | ||||||||
\(576\) | 271.446 | 11.3102 | ||||||||
\(577\) | 24.2712 | 1.01042 | 0.505211 | − | 0.862996i | \(-0.331415\pi\) | ||||
0.505211 | + | 0.862996i | \(0.331415\pi\) | |||||||
\(578\) | −88.8964 | −3.69760 | ||||||||
\(579\) | 21.7488 | 0.903848 | ||||||||
\(580\) | −33.2341 | −1.37997 | ||||||||
\(581\) | 53.5736 | 2.22261 | ||||||||
\(582\) | 78.0895 | 3.23691 | ||||||||
\(583\) | −19.3525 | −0.801497 | ||||||||
\(584\) | 35.8534 | 1.48363 | ||||||||
\(585\) | −51.1137 | −2.11329 | ||||||||
\(586\) | 32.9081 | 1.35942 | ||||||||
\(587\) | −7.68768 | −0.317305 | −0.158652 | − | 0.987335i | \(-0.550715\pi\) | ||||
−0.158652 | + | 0.987335i | \(0.550715\pi\) | |||||||
\(588\) | −136.370 | −5.62380 | ||||||||
\(589\) | −63.2499 | −2.60617 | ||||||||
\(590\) | −37.4398 | −1.54137 | ||||||||
\(591\) | 50.4311 | 2.07446 | ||||||||
\(592\) | −26.6159 | −1.09391 | ||||||||
\(593\) | 45.1472 | 1.85397 | 0.926987 | − | 0.375093i | \(-0.122389\pi\) | ||||
0.926987 | + | 0.375093i | \(0.122389\pi\) | |||||||
\(594\) | −102.341 | −4.19909 | ||||||||
\(595\) | −48.0226 | −1.96874 | ||||||||
\(596\) | 24.7865 | 1.01530 | ||||||||
\(597\) | −43.0756 | −1.76297 | ||||||||
\(598\) | −82.6468 | −3.37968 | ||||||||
\(599\) | −34.3422 | −1.40318 | −0.701592 | − | 0.712579i | \(-0.747527\pi\) | ||||
−0.701592 | + | 0.712579i | \(0.747527\pi\) | |||||||
\(600\) | −57.0573 | −2.32936 | ||||||||
\(601\) | 28.3016 | 1.15445 | 0.577223 | − | 0.816586i | \(-0.304136\pi\) | ||||
0.577223 | + | 0.816586i | \(0.304136\pi\) | |||||||
\(602\) | −7.41039 | −0.302025 | ||||||||
\(603\) | 96.6952 | 3.93773 | ||||||||
\(604\) | 41.0087 | 1.66862 | ||||||||
\(605\) | −8.62707 | −0.350740 | ||||||||
\(606\) | −113.255 | −4.60068 | ||||||||
\(607\) | −1.92530 | −0.0781456 | −0.0390728 | − | 0.999236i | \(-0.512440\pi\) | ||||
−0.0390728 | + | 0.999236i | \(0.512440\pi\) | |||||||
\(608\) | 182.261 | 7.39165 | ||||||||
\(609\) | −40.8602 | −1.65574 | ||||||||
\(610\) | 16.0128 | 0.648341 | ||||||||
\(611\) | −22.5565 | −0.912538 | ||||||||
\(612\) | 297.992 | 12.0456 | ||||||||
\(613\) | −31.3471 | −1.26610 | −0.633048 | − | 0.774112i | \(-0.718197\pi\) | ||||
−0.633048 | + | 0.774112i | \(0.718197\pi\) | |||||||
\(614\) | −0.249075 | −0.0100519 | ||||||||
\(615\) | −43.8192 | −1.76696 | ||||||||
\(616\) | −94.0844 | −3.79077 | ||||||||
\(617\) | 47.3278 | 1.90535 | 0.952674 | − | 0.303995i | \(-0.0983206\pi\) | ||||
0.952674 | + | 0.303995i | \(0.0983206\pi\) | |||||||
\(618\) | −32.5383 | −1.30888 | ||||||||
\(619\) | −23.2218 | −0.933365 | −0.466682 | − | 0.884425i | \(-0.654551\pi\) | ||||
−0.466682 | + | 0.884425i | \(0.654551\pi\) | |||||||
\(620\) | 86.3612 | 3.46835 | ||||||||
\(621\) | 119.186 | 4.78277 | ||||||||
\(622\) | −25.0000 | −1.00241 | ||||||||
\(623\) | 28.1407 | 1.12743 | ||||||||
\(624\) | 197.152 | 7.89240 | ||||||||
\(625\) | −13.0428 | −0.521712 | ||||||||
\(626\) | −32.3298 | −1.29216 | ||||||||
\(627\) | −59.7487 | −2.38613 | ||||||||
\(628\) | 64.6628 | 2.58033 | ||||||||
\(629\) | −11.5544 | −0.460704 | ||||||||
\(630\) | 143.048 | 5.69917 | ||||||||
\(631\) | −31.6782 | −1.26109 | −0.630544 | − | 0.776154i | \(-0.717168\pi\) | ||||
−0.630544 | + | 0.776154i | \(0.717168\pi\) | |||||||
\(632\) | 51.1450 | 2.03444 | ||||||||
\(633\) | −5.79251 | −0.230232 | ||||||||
\(634\) | 48.4125 | 1.92271 | ||||||||
\(635\) | 24.9443 | 0.989886 | ||||||||
\(636\) | −141.575 | −5.61383 | ||||||||
\(637\) | −28.0634 | −1.11191 | ||||||||
\(638\) | −22.6589 | −0.897075 | ||||||||
\(639\) | 3.86948 | 0.153074 | ||||||||
\(640\) | −88.5962 | −3.50207 | ||||||||
\(641\) | 0.985742 | 0.0389345 | 0.0194672 | − | 0.999810i | \(-0.493803\pi\) | ||||
0.0194672 | + | 0.999810i | \(0.493803\pi\) | |||||||
\(642\) | −0.525325 | −0.0207329 | ||||||||
\(643\) | −20.1589 | −0.794991 | −0.397495 | − | 0.917604i | \(-0.630121\pi\) | ||||
−0.397495 | + | 0.917604i | \(0.630121\pi\) | |||||||
\(644\) | 170.434 | 6.71604 | ||||||||
\(645\) | 4.13093 | 0.162655 | ||||||||
\(646\) | 142.685 | 5.61386 | ||||||||
\(647\) | −16.7382 | −0.658045 | −0.329022 | − | 0.944322i | \(-0.606719\pi\) | ||||
−0.329022 | + | 0.944322i | \(0.606719\pi\) | |||||||
\(648\) | −255.534 | −10.0383 | ||||||||
\(649\) | −18.8093 | −0.738331 | ||||||||
\(650\) | −18.2640 | −0.716372 | ||||||||
\(651\) | 106.178 | 4.16144 | ||||||||
\(652\) | 52.7264 | 2.06492 | ||||||||
\(653\) | −39.3900 | −1.54145 | −0.770726 | − | 0.637167i | \(-0.780106\pi\) | ||||
−0.770726 | + | 0.637167i | \(0.780106\pi\) | |||||||
\(654\) | 155.339 | 6.07422 | ||||||||
\(655\) | −28.8918 | −1.12890 | ||||||||
\(656\) | 121.101 | 4.72821 | ||||||||
\(657\) | −27.3864 | −1.06845 | ||||||||
\(658\) | 63.1272 | 2.46095 | ||||||||
\(659\) | −10.9746 | −0.427508 | −0.213754 | − | 0.976887i | \(-0.568569\pi\) | ||||
−0.213754 | + | 0.976887i | \(0.568569\pi\) | |||||||
\(660\) | 81.5806 | 3.17552 | ||||||||
\(661\) | −2.39831 | −0.0932835 | −0.0466418 | − | 0.998912i | \(-0.514852\pi\) | ||||
−0.0466418 | + | 0.998912i | \(0.514852\pi\) | |||||||
\(662\) | 46.4830 | 1.80661 | ||||||||
\(663\) | 85.5870 | 3.32392 | ||||||||
\(664\) | 139.727 | 5.42245 | ||||||||
\(665\) | 50.4708 | 1.95717 | ||||||||
\(666\) | 34.4178 | 1.33366 | ||||||||
\(667\) | 26.3886 | 1.02177 | ||||||||
\(668\) | 36.8143 | 1.42439 | ||||||||
\(669\) | −10.0129 | −0.387123 | ||||||||
\(670\) | −63.2173 | −2.44230 | ||||||||
\(671\) | 8.04468 | 0.310561 | ||||||||
\(672\) | −305.962 | −11.8028 | ||||||||
\(673\) | 15.3560 | 0.591931 | 0.295966 | − | 0.955199i | \(-0.404359\pi\) | ||||
0.295966 | + | 0.955199i | \(0.404359\pi\) | |||||||
\(674\) | −51.4434 | −1.98152 | ||||||||
\(675\) | 26.3387 | 1.01378 | ||||||||
\(676\) | 5.91712 | 0.227582 | ||||||||
\(677\) | −20.5546 | −0.789978 | −0.394989 | − | 0.918686i | \(-0.629252\pi\) | ||||
−0.394989 | + | 0.918686i | \(0.629252\pi\) | |||||||
\(678\) | 109.822 | 4.21768 | ||||||||
\(679\) | −33.1394 | −1.27177 | ||||||||
\(680\) | −125.249 | −4.80308 | ||||||||
\(681\) | −9.12432 | −0.349645 | ||||||||
\(682\) | 58.8807 | 2.25466 | ||||||||
\(683\) | −32.7145 | −1.25179 | −0.625893 | − | 0.779909i | \(-0.715265\pi\) | ||||
−0.625893 | + | 0.779909i | \(0.715265\pi\) | |||||||
\(684\) | −313.184 | −11.9749 | ||||||||
\(685\) | −18.3039 | −0.699357 | ||||||||
\(686\) | 5.09062 | 0.194361 | ||||||||
\(687\) | −38.0170 | −1.45044 | ||||||||
\(688\) | −11.4165 | −0.435249 | ||||||||
\(689\) | −29.1346 | −1.10994 | ||||||||
\(690\) | −128.937 | −4.90855 | ||||||||
\(691\) | −36.9533 | −1.40577 | −0.702884 | − | 0.711304i | \(-0.748105\pi\) | ||||
−0.702884 | + | 0.711304i | \(0.748105\pi\) | |||||||
\(692\) | −68.8980 | −2.61911 | ||||||||
\(693\) | 71.8658 | 2.72996 | ||||||||
\(694\) | −1.09828 | −0.0416902 | ||||||||
\(695\) | 23.3681 | 0.886401 | ||||||||
\(696\) | −106.568 | −4.03947 | ||||||||
\(697\) | 52.5720 | 1.99131 | ||||||||
\(698\) | 59.0774 | 2.23611 | ||||||||
\(699\) | −47.3190 | −1.78977 | ||||||||
\(700\) | 37.6639 | 1.42356 | ||||||||
\(701\) | −42.5056 | −1.60541 | −0.802707 | − | 0.596373i | \(-0.796608\pi\) | ||||
−0.802707 | + | 0.596373i | \(0.796608\pi\) | |||||||
\(702\) | −154.071 | −5.81505 | ||||||||
\(703\) | 12.1434 | 0.457998 | ||||||||
\(704\) | −89.1568 | −3.36022 | ||||||||
\(705\) | −35.1904 | −1.32535 | ||||||||
\(706\) | 67.3158 | 2.53346 | ||||||||
\(707\) | 48.0629 | 1.80759 | ||||||||
\(708\) | −137.602 | −5.17140 | ||||||||
\(709\) | 11.5810 | 0.434935 | 0.217468 | − | 0.976068i | \(-0.430220\pi\) | ||||
0.217468 | + | 0.976068i | \(0.430220\pi\) | |||||||
\(710\) | −2.52978 | −0.0949411 | ||||||||
\(711\) | −39.0668 | −1.46512 | ||||||||
\(712\) | 73.3943 | 2.75057 | ||||||||
\(713\) | −68.5725 | −2.56806 | ||||||||
\(714\) | −239.526 | −8.96403 | ||||||||
\(715\) | 16.7884 | 0.627849 | ||||||||
\(716\) | −0.570276 | −0.0213122 | ||||||||
\(717\) | 8.38168 | 0.313020 | ||||||||
\(718\) | −53.9089 | −2.01186 | ||||||||
\(719\) | −43.5709 | −1.62492 | −0.812460 | − | 0.583017i | \(-0.801872\pi\) | ||||
−0.812460 | + | 0.583017i | \(0.801872\pi\) | |||||||
\(720\) | 220.380 | 8.21309 | ||||||||
\(721\) | 13.8085 | 0.514255 | ||||||||
\(722\) | −97.5776 | −3.63146 | ||||||||
\(723\) | 17.5681 | 0.653364 | ||||||||
\(724\) | −41.8323 | −1.55469 | ||||||||
\(725\) | 5.83157 | 0.216579 | ||||||||
\(726\) | −43.0299 | −1.59699 | ||||||||
\(727\) | 14.5406 | 0.539281 | 0.269641 | − | 0.962961i | \(-0.413095\pi\) | ||||
0.269641 | + | 0.962961i | \(0.413095\pi\) | |||||||
\(728\) | −141.641 | −5.24958 | ||||||||
\(729\) | 49.7196 | 1.84147 | ||||||||
\(730\) | 17.9047 | 0.662682 | ||||||||
\(731\) | −4.95608 | −0.183307 | ||||||||
\(732\) | 58.8519 | 2.17523 | ||||||||
\(733\) | 16.7695 | 0.619396 | 0.309698 | − | 0.950835i | \(-0.399772\pi\) | ||||
0.309698 | + | 0.950835i | \(0.399772\pi\) | |||||||
\(734\) | 16.2834 | 0.601031 | ||||||||
\(735\) | −43.7817 | −1.61491 | ||||||||
\(736\) | 197.598 | 7.28357 | ||||||||
\(737\) | −31.7597 | −1.16988 | ||||||||
\(738\) | −156.600 | −5.76451 | ||||||||
\(739\) | −41.7571 | −1.53606 | −0.768029 | − | 0.640415i | \(-0.778762\pi\) | ||||
−0.768029 | + | 0.640415i | \(0.778762\pi\) | |||||||
\(740\) | −16.5806 | −0.609514 | ||||||||
\(741\) | −89.9501 | −3.30440 | ||||||||
\(742\) | 81.5369 | 2.99331 | ||||||||
\(743\) | −8.79215 | −0.322553 | −0.161276 | − | 0.986909i | \(-0.551561\pi\) | ||||
−0.161276 | + | 0.986909i | \(0.551561\pi\) | |||||||
\(744\) | 276.925 | 10.1526 | ||||||||
\(745\) | 7.95773 | 0.291549 | ||||||||
\(746\) | 29.1316 | 1.06658 | ||||||||
\(747\) | −106.729 | −3.90502 | ||||||||
\(748\) | −97.8761 | −3.57871 | ||||||||
\(749\) | 0.222936 | 0.00814589 | ||||||||
\(750\) | −109.121 | −3.98454 | ||||||||
\(751\) | 29.9024 | 1.09116 | 0.545578 | − | 0.838060i | \(-0.316310\pi\) | ||||
0.545578 | + | 0.838060i | \(0.316310\pi\) | |||||||
\(752\) | 97.2540 | 3.54649 | ||||||||
\(753\) | −82.2207 | −2.99629 | ||||||||
\(754\) | −34.1124 | −1.24230 | ||||||||
\(755\) | 13.1659 | 0.479155 | ||||||||
\(756\) | 317.726 | 11.5556 | ||||||||
\(757\) | 23.6158 | 0.858330 | 0.429165 | − | 0.903226i | \(-0.358808\pi\) | ||||
0.429165 | + | 0.903226i | \(0.358808\pi\) | |||||||
\(758\) | −20.8685 | −0.757978 | ||||||||
\(759\) | −64.7766 | −2.35124 | ||||||||
\(760\) | 131.634 | 4.77487 | ||||||||
\(761\) | −24.9825 | −0.905613 | −0.452807 | − | 0.891609i | \(-0.649577\pi\) | ||||
−0.452807 | + | 0.891609i | \(0.649577\pi\) | |||||||
\(762\) | 124.417 | 4.50714 | ||||||||
\(763\) | −65.9221 | −2.38654 | ||||||||
\(764\) | 53.5821 | 1.93853 | ||||||||
\(765\) | 95.6707 | 3.45898 | ||||||||
\(766\) | −49.4714 | −1.78747 | ||||||||
\(767\) | −28.3170 | −1.02247 | ||||||||
\(768\) | −208.978 | −7.54084 | ||||||||
\(769\) | 25.5392 | 0.920969 | 0.460484 | − | 0.887668i | \(-0.347676\pi\) | ||||
0.460484 | + | 0.887668i | \(0.347676\pi\) | |||||||
\(770\) | −46.9844 | −1.69320 | ||||||||
\(771\) | −9.12854 | −0.328756 | ||||||||
\(772\) | −37.4435 | −1.34762 | ||||||||
\(773\) | 31.3072 | 1.12604 | 0.563021 | − | 0.826443i | \(-0.309639\pi\) | ||||
0.563021 | + | 0.826443i | \(0.309639\pi\) | |||||||
\(774\) | 14.7630 | 0.530644 | ||||||||
\(775\) | −15.1537 | −0.544338 | ||||||||
\(776\) | −86.4316 | −3.10271 | ||||||||
\(777\) | −20.3852 | −0.731316 | ||||||||
\(778\) | −18.3461 | −0.657740 | ||||||||
\(779\) | −55.2521 | −1.97961 | ||||||||
\(780\) | 122.817 | 4.39757 | ||||||||
\(781\) | −1.27094 | −0.0454777 | ||||||||
\(782\) | 154.692 | 5.53177 | ||||||||
\(783\) | 49.1939 | 1.75805 | ||||||||
\(784\) | 120.997 | 4.32133 | ||||||||
\(785\) | 20.7600 | 0.740958 | ||||||||
\(786\) | −144.106 | −5.14009 | ||||||||
\(787\) | 31.0498 | 1.10681 | 0.553403 | − | 0.832913i | \(-0.313329\pi\) | ||||
0.553403 | + | 0.832913i | \(0.313329\pi\) | |||||||
\(788\) | −86.8242 | −3.09298 | ||||||||
\(789\) | −47.6969 | −1.69806 | ||||||||
\(790\) | 25.5411 | 0.908710 | ||||||||
\(791\) | −46.6059 | −1.65711 | ||||||||
\(792\) | 187.435 | 6.66021 | ||||||||
\(793\) | 12.1110 | 0.430076 | ||||||||
\(794\) | 21.7465 | 0.771756 | ||||||||
\(795\) | −45.4529 | −1.61205 | ||||||||
\(796\) | 74.1606 | 2.62855 | ||||||||
\(797\) | 6.16871 | 0.218507 | 0.109253 | − | 0.994014i | \(-0.465154\pi\) | ||||
0.109253 | + | 0.994014i | \(0.465154\pi\) | |||||||
\(798\) | 251.737 | 8.91138 | ||||||||
\(799\) | 42.2195 | 1.49362 | ||||||||
\(800\) | 43.6669 | 1.54386 | ||||||||
\(801\) | −56.0618 | −1.98085 | ||||||||
\(802\) | 29.3250 | 1.03550 | ||||||||
\(803\) | 8.99512 | 0.317431 | ||||||||
\(804\) | −232.342 | −8.19407 | ||||||||
\(805\) | 54.7180 | 1.92855 | ||||||||
\(806\) | 88.6434 | 3.12233 | ||||||||
\(807\) | −91.4687 | −3.21985 | ||||||||
\(808\) | 125.354 | 4.40994 | ||||||||
\(809\) | −9.34320 | −0.328489 | −0.164245 | − | 0.986420i | \(-0.552519\pi\) | ||||
−0.164245 | + | 0.986420i | \(0.552519\pi\) | |||||||
\(810\) | −127.610 | −4.48376 | ||||||||
\(811\) | −30.9477 | −1.08672 | −0.543361 | − | 0.839499i | \(-0.682848\pi\) | ||||
−0.543361 | + | 0.839499i | \(0.682848\pi\) | |||||||
\(812\) | 70.3465 | 2.46868 | ||||||||
\(813\) | −12.3502 | −0.433141 | ||||||||
\(814\) | −11.3046 | −0.396225 | ||||||||
\(815\) | 16.9278 | 0.592956 | ||||||||
\(816\) | −369.014 | −12.9181 | ||||||||
\(817\) | 5.20873 | 0.182230 | ||||||||
\(818\) | −39.5327 | −1.38223 | ||||||||
\(819\) | 108.192 | 3.78053 | ||||||||
\(820\) | 75.4409 | 2.63451 | ||||||||
\(821\) | −47.8944 | −1.67153 | −0.835764 | − | 0.549089i | \(-0.814975\pi\) | ||||
−0.835764 | + | 0.549089i | \(0.814975\pi\) | |||||||
\(822\) | −91.2958 | −3.18431 | ||||||||
\(823\) | 42.2488 | 1.47270 | 0.736349 | − | 0.676601i | \(-0.236548\pi\) | ||||
0.736349 | + | 0.676601i | \(0.236548\pi\) | |||||||
\(824\) | 36.0142 | 1.25462 | ||||||||
\(825\) | −14.3149 | −0.498380 | ||||||||
\(826\) | 79.2486 | 2.75741 | ||||||||
\(827\) | 26.7842 | 0.931378 | 0.465689 | − | 0.884948i | \(-0.345807\pi\) | ||||
0.465689 | + | 0.884948i | \(0.345807\pi\) | |||||||
\(828\) | −339.539 | −11.7998 | ||||||||
\(829\) | −41.3255 | −1.43529 | −0.717646 | − | 0.696408i | \(-0.754780\pi\) | ||||
−0.717646 | + | 0.696408i | \(0.754780\pi\) | |||||||
\(830\) | 69.7775 | 2.42201 | ||||||||
\(831\) | −55.8746 | −1.93827 | ||||||||
\(832\) | −134.223 | −4.65335 | ||||||||
\(833\) | 52.5269 | 1.81995 | ||||||||
\(834\) | 116.555 | 4.03595 | ||||||||
\(835\) | 11.8193 | 0.409022 | ||||||||
\(836\) | 102.866 | 3.55769 | ||||||||
\(837\) | −127.834 | −4.41858 | ||||||||
\(838\) | 8.34269 | 0.288193 | ||||||||
\(839\) | −28.0086 | −0.966963 | −0.483481 | − | 0.875355i | \(-0.660628\pi\) | ||||
−0.483481 | + | 0.875355i | \(0.660628\pi\) | |||||||
\(840\) | −220.975 | −7.62435 | ||||||||
\(841\) | −18.1081 | −0.624418 | ||||||||
\(842\) | 80.4349 | 2.77197 | ||||||||
\(843\) | 59.6470 | 2.05435 | ||||||||
\(844\) | 9.97261 | 0.343272 | ||||||||
\(845\) | 1.89970 | 0.0653515 | ||||||||
\(846\) | −125.762 | −4.32379 | ||||||||
\(847\) | 18.2609 | 0.627451 | ||||||||
\(848\) | 125.616 | 4.31367 | ||||||||
\(849\) | 14.2836 | 0.490213 | ||||||||
\(850\) | 34.1851 | 1.17254 | ||||||||
\(851\) | 13.1653 | 0.451301 | ||||||||
\(852\) | −9.29769 | −0.318534 | ||||||||
\(853\) | 37.3733 | 1.27964 | 0.639818 | − | 0.768526i | \(-0.279010\pi\) | ||||
0.639818 | + | 0.768526i | \(0.279010\pi\) | |||||||
\(854\) | −33.8943 | −1.15984 | ||||||||
\(855\) | −100.548 | −3.43867 | ||||||||
\(856\) | 0.581444 | 0.0198733 | ||||||||
\(857\) | −35.3987 | −1.20920 | −0.604598 | − | 0.796531i | \(-0.706666\pi\) | ||||
−0.604598 | + | 0.796531i | \(0.706666\pi\) | |||||||
\(858\) | 83.7365 | 2.85872 | ||||||||
\(859\) | −3.01122 | −0.102741 | −0.0513707 | − | 0.998680i | \(-0.516359\pi\) | ||||
−0.0513707 | + | 0.998680i | \(0.516359\pi\) | |||||||
\(860\) | −7.11198 | −0.242516 | ||||||||
\(861\) | 92.7520 | 3.16098 | ||||||||
\(862\) | −23.7466 | −0.808813 | ||||||||
\(863\) | −51.9625 | −1.76882 | −0.884411 | − | 0.466708i | \(-0.845440\pi\) | ||||
−0.884411 | + | 0.466708i | \(0.845440\pi\) | |||||||
\(864\) | 368.366 | 12.5321 | ||||||||
\(865\) | −22.1198 | −0.752094 | ||||||||
\(866\) | 8.52900 | 0.289827 | ||||||||
\(867\) | −104.894 | −3.56238 | ||||||||
\(868\) | −182.800 | −6.20464 | ||||||||
\(869\) | 12.8315 | 0.435281 | ||||||||
\(870\) | −53.2187 | −1.80428 | ||||||||
\(871\) | −47.8134 | −1.62009 | ||||||||
\(872\) | −171.933 | −5.82238 | ||||||||
\(873\) | 66.0203 | 2.23445 | ||||||||
\(874\) | −162.578 | −5.49928 | ||||||||
\(875\) | 46.3085 | 1.56551 | ||||||||
\(876\) | 65.8049 | 2.22334 | ||||||||
\(877\) | 31.5440 | 1.06517 | 0.532583 | − | 0.846378i | \(-0.321222\pi\) | ||||
0.532583 | + | 0.846378i | \(0.321222\pi\) | |||||||
\(878\) | −34.1025 | −1.15090 | ||||||||
\(879\) | 38.8301 | 1.30971 | ||||||||
\(880\) | −72.3843 | −2.44007 | ||||||||
\(881\) | −39.1419 | −1.31872 | −0.659362 | − | 0.751826i | \(-0.729174\pi\) | ||||
−0.659362 | + | 0.751826i | \(0.729174\pi\) | |||||||
\(882\) | −156.465 | −5.26846 | ||||||||
\(883\) | 22.5504 | 0.758882 | 0.379441 | − | 0.925216i | \(-0.376116\pi\) | ||||
0.379441 | + | 0.925216i | \(0.376116\pi\) | |||||||
\(884\) | −147.350 | −4.95591 | ||||||||
\(885\) | −44.1773 | −1.48500 | ||||||||
\(886\) | 53.3522 | 1.79240 | ||||||||
\(887\) | −27.8918 | −0.936514 | −0.468257 | − | 0.883592i | \(-0.655118\pi\) | ||||
−0.468257 | + | 0.883592i | \(0.655118\pi\) | |||||||
\(888\) | −53.1672 | −1.78417 | ||||||||
\(889\) | −52.7995 | −1.77084 | ||||||||
\(890\) | 36.6521 | 1.22858 | ||||||||
\(891\) | −64.1099 | −2.14776 | ||||||||
\(892\) | 17.2387 | 0.577194 | ||||||||
\(893\) | −44.3719 | −1.48485 | ||||||||
\(894\) | 39.6913 | 1.32748 | ||||||||
\(895\) | −0.183087 | −0.00611994 | ||||||||
\(896\) | 187.531 | 6.26497 | ||||||||
\(897\) | −97.5195 | −3.25608 | ||||||||
\(898\) | −48.5725 | −1.62088 | ||||||||
\(899\) | −28.3032 | −0.943966 | ||||||||
\(900\) | −75.0341 | −2.50114 | ||||||||
\(901\) | 54.5320 | 1.81672 | ||||||||
\(902\) | 51.4354 | 1.71261 | ||||||||
\(903\) | −8.74393 | −0.290980 | ||||||||
\(904\) | −121.554 | −4.04282 | ||||||||
\(905\) | −13.4303 | −0.446438 | ||||||||
\(906\) | 65.6683 | 2.18168 | ||||||||
\(907\) | −30.0989 | −0.999416 | −0.499708 | − | 0.866194i | \(-0.666559\pi\) | ||||
−0.499708 | + | 0.866194i | \(0.666559\pi\) | |||||||
\(908\) | 15.7088 | 0.521314 | ||||||||
\(909\) | −95.7509 | −3.17586 | ||||||||
\(910\) | −70.7337 | −2.34480 | ||||||||
\(911\) | −21.0655 | −0.697931 | −0.348966 | − | 0.937135i | \(-0.613467\pi\) | ||||
−0.348966 | + | 0.937135i | \(0.613467\pi\) | |||||||
\(912\) | 387.826 | 12.8422 | ||||||||
\(913\) | 35.0554 | 1.16017 | ||||||||
\(914\) | 83.0306 | 2.74641 | ||||||||
\(915\) | 18.8944 | 0.624631 | ||||||||
\(916\) | 65.4516 | 2.16258 | ||||||||
\(917\) | 61.1552 | 2.01952 | ||||||||
\(918\) | 288.379 | 9.51793 | ||||||||
\(919\) | 33.0883 | 1.09148 | 0.545741 | − | 0.837954i | \(-0.316248\pi\) | ||||
0.545741 | + | 0.837954i | \(0.316248\pi\) | |||||||
\(920\) | 142.711 | 4.70505 | ||||||||
\(921\) | −0.293898 | −0.00968426 | ||||||||
\(922\) | 107.755 | 3.54873 | ||||||||
\(923\) | −1.91336 | −0.0629790 | ||||||||
\(924\) | −172.681 | −5.68080 | ||||||||
\(925\) | 2.90938 | 0.0956598 | ||||||||
\(926\) | −10.4163 | −0.342300 | ||||||||
\(927\) | −27.5093 | −0.903522 | ||||||||
\(928\) | 81.5586 | 2.67729 | ||||||||
\(929\) | 3.42559 | 0.112390 | 0.0561949 | − | 0.998420i | \(-0.482103\pi\) | ||||
0.0561949 | + | 0.998420i | \(0.482103\pi\) | |||||||
\(930\) | 138.292 | 4.53479 | ||||||||
\(931\) | −55.2047 | −1.80926 | ||||||||
\(932\) | 81.4662 | 2.66851 | ||||||||
\(933\) | −29.4989 | −0.965751 | ||||||||
\(934\) | 28.5923 | 0.935568 | ||||||||
\(935\) | −31.4232 | −1.02765 | ||||||||
\(936\) | 282.178 | 9.22328 | ||||||||
\(937\) | 13.8708 | 0.453139 | 0.226570 | − | 0.973995i | \(-0.427249\pi\) | ||||
0.226570 | + | 0.973995i | \(0.427249\pi\) | |||||||
\(938\) | 133.812 | 4.36911 | ||||||||
\(939\) | −38.1477 | −1.24490 | ||||||||
\(940\) | 60.5851 | 1.97607 | ||||||||
\(941\) | 15.5257 | 0.506125 | 0.253062 | − | 0.967450i | \(-0.418562\pi\) | ||||
0.253062 | + | 0.967450i | \(0.418562\pi\) | |||||||
\(942\) | 103.546 | 3.37372 | ||||||||
\(943\) | −59.9016 | −1.95066 | ||||||||
\(944\) | 122.091 | 3.97371 | ||||||||
\(945\) | 102.006 | 3.31826 | ||||||||
\(946\) | −4.84892 | −0.157652 | ||||||||
\(947\) | 23.4713 | 0.762714 | 0.381357 | − | 0.924428i | \(-0.375457\pi\) | ||||
0.381357 | + | 0.924428i | \(0.375457\pi\) | |||||||
\(948\) | 93.8708 | 3.04878 | ||||||||
\(949\) | 13.5419 | 0.439589 | ||||||||
\(950\) | −35.9278 | −1.16565 | ||||||||
\(951\) | 57.1246 | 1.85239 | ||||||||
\(952\) | 265.114 | 8.59239 | ||||||||
\(953\) | 25.7524 | 0.834201 | 0.417100 | − | 0.908860i | \(-0.363046\pi\) | ||||
0.417100 | + | 0.908860i | \(0.363046\pi\) | |||||||
\(954\) | −162.438 | −5.25912 | ||||||||
\(955\) | 17.2026 | 0.556663 | ||||||||
\(956\) | −14.4302 | −0.466707 | ||||||||
\(957\) | −26.7365 | −0.864269 | ||||||||
\(958\) | 105.518 | 3.40913 | ||||||||
\(959\) | 38.7438 | 1.25110 | ||||||||
\(960\) | −209.401 | −6.75840 | ||||||||
\(961\) | 42.5479 | 1.37251 | ||||||||
\(962\) | −17.0187 | −0.548706 | ||||||||
\(963\) | −0.444132 | −0.0143120 | ||||||||
\(964\) | −30.2459 | −0.974156 | ||||||||
\(965\) | −12.0213 | −0.386978 | ||||||||
\(966\) | 272.921 | 8.78108 | ||||||||
\(967\) | −40.0011 | −1.28635 | −0.643175 | − | 0.765719i | \(-0.722383\pi\) | ||||
−0.643175 | + | 0.765719i | \(0.722383\pi\) | |||||||
\(968\) | 47.6266 | 1.53078 | ||||||||
\(969\) | 168.362 | 5.40856 | ||||||||
\(970\) | −43.1627 | −1.38587 | ||||||||
\(971\) | 43.6514 | 1.40084 | 0.700421 | − | 0.713730i | \(-0.252996\pi\) | ||||
0.700421 | + | 0.713730i | \(0.252996\pi\) | |||||||
\(972\) | −218.560 | −7.01030 | ||||||||
\(973\) | −49.4631 | −1.58571 | ||||||||
\(974\) | −73.7527 | −2.36319 | ||||||||
\(975\) | −21.5507 | −0.690174 | ||||||||
\(976\) | −52.2177 | −1.67145 | ||||||||
\(977\) | −57.2134 | −1.83042 | −0.915210 | − | 0.402978i | \(-0.867975\pi\) | ||||
−0.915210 | + | 0.402978i | \(0.867975\pi\) | |||||||
\(978\) | 84.4322 | 2.69984 | ||||||||
\(979\) | 18.4136 | 0.588501 | ||||||||
\(980\) | 75.3763 | 2.40781 | ||||||||
\(981\) | 131.330 | 4.19304 | ||||||||
\(982\) | −103.284 | −3.29592 | ||||||||
\(983\) | −1.38910 | −0.0443055 | −0.0221528 | − | 0.999755i | \(-0.507052\pi\) | ||||
−0.0221528 | + | 0.999755i | \(0.507052\pi\) | |||||||
\(984\) | 241.909 | 7.71176 | ||||||||
\(985\) | −27.8750 | −0.888170 | ||||||||
\(986\) | 63.8490 | 2.03337 | ||||||||
\(987\) | 74.4873 | 2.37096 | ||||||||
\(988\) | 154.862 | 4.92680 | ||||||||
\(989\) | 5.64705 | 0.179566 | ||||||||
\(990\) | 93.6022 | 2.97487 | ||||||||
\(991\) | −2.21514 | −0.0703663 | −0.0351831 | − | 0.999381i | \(-0.511201\pi\) | ||||
−0.0351831 | + | 0.999381i | \(0.511201\pi\) | |||||||
\(992\) | −211.935 | −6.72896 | ||||||||
\(993\) | 54.8479 | 1.74055 | ||||||||
\(994\) | 5.35478 | 0.169843 | ||||||||
\(995\) | 23.8093 | 0.754806 | ||||||||
\(996\) | 256.453 | 8.12601 | ||||||||
\(997\) | −6.41302 | −0.203102 | −0.101551 | − | 0.994830i | \(-0.532381\pi\) | ||||
−0.101551 | + | 0.994830i | \(0.532381\pi\) | |||||||
\(998\) | 49.9749 | 1.58193 | ||||||||
\(999\) | 24.5430 | 0.776505 |
(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 | 6037.2.a.a.1.6 | ✓ | 243 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6037.2.a.a.1.6 | ✓ | 243 | 1.1 | even | 1 | trivial |