Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.14010 | −1.51328 | −0.756639 | − | 0.653833i | \(-0.773160\pi\) | ||||
−0.756639 | + | 0.653833i | \(0.773160\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.58002 | 1.29001 | ||||||||
\(5\) | −0.881570 | −0.394250 | −0.197125 | − | 0.980378i | \(-0.563160\pi\) | ||||
−0.197125 | + | 0.980378i | \(0.563160\pi\) | |||||||
\(6\) | −2.14010 | −0.873691 | ||||||||
\(7\) | −2.47197 | −0.934316 | −0.467158 | − | 0.884174i | \(-0.654722\pi\) | ||||
−0.467158 | + | 0.884174i | \(0.654722\pi\) | |||||||
\(8\) | −1.24130 | −0.438866 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.88665 | 0.596610 | ||||||||
\(11\) | −4.39701 | −1.32575 | −0.662875 | − | 0.748730i | \(-0.730664\pi\) | ||||
−0.662875 | + | 0.748730i | \(0.730664\pi\) | |||||||
\(12\) | 2.58002 | 0.744788 | ||||||||
\(13\) | 0.817662 | 0.226779 | 0.113389 | − | 0.993551i | \(-0.463829\pi\) | ||||
0.113389 | + | 0.993551i | \(0.463829\pi\) | |||||||
\(14\) | 5.29026 | 1.41388 | ||||||||
\(15\) | −0.881570 | −0.227620 | ||||||||
\(16\) | −2.50354 | −0.625884 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −2.14010 | −0.504426 | ||||||||
\(19\) | −5.73800 | −1.31639 | −0.658194 | − | 0.752848i | \(-0.728679\pi\) | ||||
−0.658194 | + | 0.752848i | \(0.728679\pi\) | |||||||
\(20\) | −2.27447 | −0.508586 | ||||||||
\(21\) | −2.47197 | −0.539428 | ||||||||
\(22\) | 9.41004 | 2.00623 | ||||||||
\(23\) | −3.68733 | −0.768862 | −0.384431 | − | 0.923154i | \(-0.625602\pi\) | ||||
−0.384431 | + | 0.923154i | \(0.625602\pi\) | |||||||
\(24\) | −1.24130 | −0.253379 | ||||||||
\(25\) | −4.22283 | −0.844567 | ||||||||
\(26\) | −1.74988 | −0.343179 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −6.37773 | −1.20528 | ||||||||
\(29\) | 6.35222 | 1.17958 | 0.589788 | − | 0.807558i | \(-0.299211\pi\) | ||||
0.589788 | + | 0.807558i | \(0.299211\pi\) | |||||||
\(30\) | 1.88665 | 0.344453 | ||||||||
\(31\) | 3.63413 | 0.652709 | 0.326355 | − | 0.945247i | \(-0.394180\pi\) | ||||
0.326355 | + | 0.945247i | \(0.394180\pi\) | |||||||
\(32\) | 7.84041 | 1.38600 | ||||||||
\(33\) | −4.39701 | −0.765422 | ||||||||
\(34\) | 2.14010 | 0.367024 | ||||||||
\(35\) | 2.17921 | 0.368354 | ||||||||
\(36\) | 2.58002 | 0.430003 | ||||||||
\(37\) | 1.04286 | 0.171446 | 0.0857229 | − | 0.996319i | \(-0.472680\pi\) | ||||
0.0857229 | + | 0.996319i | \(0.472680\pi\) | |||||||
\(38\) | 12.2799 | 1.99206 | ||||||||
\(39\) | 0.817662 | 0.130931 | ||||||||
\(40\) | 1.09429 | 0.173023 | ||||||||
\(41\) | −9.98744 | −1.55978 | −0.779888 | − | 0.625919i | \(-0.784724\pi\) | ||||
−0.779888 | + | 0.625919i | \(0.784724\pi\) | |||||||
\(42\) | 5.29026 | 0.816304 | ||||||||
\(43\) | −7.19149 | −1.09669 | −0.548346 | − | 0.836251i | \(-0.684742\pi\) | ||||
−0.548346 | + | 0.836251i | \(0.684742\pi\) | |||||||
\(44\) | −11.3444 | −1.71023 | ||||||||
\(45\) | −0.881570 | −0.131417 | ||||||||
\(46\) | 7.89125 | 1.16350 | ||||||||
\(47\) | −6.67559 | −0.973735 | −0.486867 | − | 0.873476i | \(-0.661861\pi\) | ||||
−0.486867 | + | 0.873476i | \(0.661861\pi\) | |||||||
\(48\) | −2.50354 | −0.361354 | ||||||||
\(49\) | −0.889369 | −0.127053 | ||||||||
\(50\) | 9.03728 | 1.27806 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 2.10958 | 0.292547 | ||||||||
\(53\) | 6.97068 | 0.957497 | 0.478748 | − | 0.877952i | \(-0.341091\pi\) | ||||
0.478748 | + | 0.877952i | \(0.341091\pi\) | |||||||
\(54\) | −2.14010 | −0.291230 | ||||||||
\(55\) | 3.87628 | 0.522677 | ||||||||
\(56\) | 3.06845 | 0.410040 | ||||||||
\(57\) | −5.73800 | −0.760017 | ||||||||
\(58\) | −13.5944 | −1.78503 | ||||||||
\(59\) | −0.253239 | −0.0329690 | −0.0164845 | − | 0.999864i | \(-0.505247\pi\) | ||||
−0.0164845 | + | 0.999864i | \(0.505247\pi\) | |||||||
\(60\) | −2.27447 | −0.293633 | ||||||||
\(61\) | −0.406403 | −0.0520346 | −0.0260173 | − | 0.999661i | \(-0.508282\pi\) | ||||
−0.0260173 | + | 0.999661i | \(0.508282\pi\) | |||||||
\(62\) | −7.77740 | −0.987731 | ||||||||
\(63\) | −2.47197 | −0.311439 | ||||||||
\(64\) | −11.7722 | −1.47152 | ||||||||
\(65\) | −0.720826 | −0.0894075 | ||||||||
\(66\) | 9.41004 | 1.15830 | ||||||||
\(67\) | −13.9141 | −1.69987 | −0.849936 | − | 0.526886i | \(-0.823360\pi\) | ||||
−0.849936 | + | 0.526886i | \(0.823360\pi\) | |||||||
\(68\) | −2.58002 | −0.312873 | ||||||||
\(69\) | −3.68733 | −0.443903 | ||||||||
\(70\) | −4.66373 | −0.557422 | ||||||||
\(71\) | 1.26017 | 0.149555 | 0.0747775 | − | 0.997200i | \(-0.476175\pi\) | ||||
0.0747775 | + | 0.997200i | \(0.476175\pi\) | |||||||
\(72\) | −1.24130 | −0.146289 | ||||||||
\(73\) | 2.46325 | 0.288301 | 0.144151 | − | 0.989556i | \(-0.453955\pi\) | ||||
0.144151 | + | 0.989556i | \(0.453955\pi\) | |||||||
\(74\) | −2.23183 | −0.259445 | ||||||||
\(75\) | −4.22283 | −0.487611 | ||||||||
\(76\) | −14.8042 | −1.69815 | ||||||||
\(77\) | 10.8693 | 1.23867 | ||||||||
\(78\) | −1.74988 | −0.198134 | ||||||||
\(79\) | −12.2775 | −1.38133 | −0.690664 | − | 0.723176i | \(-0.742682\pi\) | ||||
−0.690664 | + | 0.723176i | \(0.742682\pi\) | |||||||
\(80\) | 2.20704 | 0.246755 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 21.3741 | 2.36038 | ||||||||
\(83\) | 12.3191 | 1.35220 | 0.676098 | − | 0.736812i | \(-0.263670\pi\) | ||||
0.676098 | + | 0.736812i | \(0.263670\pi\) | |||||||
\(84\) | −6.37773 | −0.695867 | ||||||||
\(85\) | 0.881570 | 0.0956197 | ||||||||
\(86\) | 15.3905 | 1.65960 | ||||||||
\(87\) | 6.35222 | 0.681029 | ||||||||
\(88\) | 5.45801 | 0.581826 | ||||||||
\(89\) | −0.0913787 | −0.00968613 | −0.00484306 | − | 0.999988i | \(-0.501542\pi\) | ||||
−0.00484306 | + | 0.999988i | \(0.501542\pi\) | |||||||
\(90\) | 1.88665 | 0.198870 | ||||||||
\(91\) | −2.02123 | −0.211883 | ||||||||
\(92\) | −9.51339 | −0.991840 | ||||||||
\(93\) | 3.63413 | 0.376842 | ||||||||
\(94\) | 14.2864 | 1.47353 | ||||||||
\(95\) | 5.05845 | 0.518986 | ||||||||
\(96\) | 7.84041 | 0.800209 | ||||||||
\(97\) | 0.121846 | 0.0123716 | 0.00618579 | − | 0.999981i | \(-0.498031\pi\) | ||||
0.00618579 | + | 0.999981i | \(0.498031\pi\) | |||||||
\(98\) | 1.90334 | 0.192266 | ||||||||
\(99\) | −4.39701 | −0.441917 | ||||||||
\(100\) | −10.8950 | −1.08950 | ||||||||
\(101\) | 8.36778 | 0.832625 | 0.416313 | − | 0.909222i | \(-0.363322\pi\) | ||||
0.416313 | + | 0.909222i | \(0.363322\pi\) | |||||||
\(102\) | 2.14010 | 0.211901 | ||||||||
\(103\) | 4.62450 | 0.455665 | 0.227833 | − | 0.973700i | \(-0.426836\pi\) | ||||
0.227833 | + | 0.973700i | \(0.426836\pi\) | |||||||
\(104\) | −1.01496 | −0.0995253 | ||||||||
\(105\) | 2.17921 | 0.212669 | ||||||||
\(106\) | −14.9179 | −1.44896 | ||||||||
\(107\) | −8.59293 | −0.830710 | −0.415355 | − | 0.909659i | \(-0.636343\pi\) | ||||
−0.415355 | + | 0.909659i | \(0.636343\pi\) | |||||||
\(108\) | 2.58002 | 0.248263 | ||||||||
\(109\) | 9.75288 | 0.934157 | 0.467078 | − | 0.884216i | \(-0.345307\pi\) | ||||
0.467078 | + | 0.884216i | \(0.345307\pi\) | |||||||
\(110\) | −8.29561 | −0.790955 | ||||||||
\(111\) | 1.04286 | 0.0989843 | ||||||||
\(112\) | 6.18867 | 0.584774 | ||||||||
\(113\) | −12.1553 | −1.14347 | −0.571737 | − | 0.820437i | \(-0.693730\pi\) | ||||
−0.571737 | + | 0.820437i | \(0.693730\pi\) | |||||||
\(114\) | 12.2799 | 1.15012 | ||||||||
\(115\) | 3.25064 | 0.303124 | ||||||||
\(116\) | 16.3888 | 1.52167 | ||||||||
\(117\) | 0.817662 | 0.0755929 | ||||||||
\(118\) | 0.541957 | 0.0498912 | ||||||||
\(119\) | 2.47197 | 0.226605 | ||||||||
\(120\) | 1.09429 | 0.0998948 | ||||||||
\(121\) | 8.33373 | 0.757612 | ||||||||
\(122\) | 0.869743 | 0.0787428 | ||||||||
\(123\) | −9.98744 | −0.900537 | ||||||||
\(124\) | 9.37614 | 0.842002 | ||||||||
\(125\) | 8.13057 | 0.727221 | ||||||||
\(126\) | 5.29026 | 0.471293 | ||||||||
\(127\) | −17.8509 | −1.58401 | −0.792004 | − | 0.610516i | \(-0.790962\pi\) | ||||
−0.792004 | + | 0.610516i | \(0.790962\pi\) | |||||||
\(128\) | 9.51280 | 0.840820 | ||||||||
\(129\) | −7.19149 | −0.633176 | ||||||||
\(130\) | 1.54264 | 0.135298 | ||||||||
\(131\) | 0.501756 | 0.0438386 | 0.0219193 | − | 0.999760i | \(-0.493022\pi\) | ||||
0.0219193 | + | 0.999760i | \(0.493022\pi\) | |||||||
\(132\) | −11.3444 | −0.987402 | ||||||||
\(133\) | 14.1842 | 1.22992 | ||||||||
\(134\) | 29.7774 | 2.57238 | ||||||||
\(135\) | −0.881570 | −0.0758735 | ||||||||
\(136\) | 1.24130 | 0.106441 | ||||||||
\(137\) | −2.97320 | −0.254017 | −0.127009 | − | 0.991902i | \(-0.540538\pi\) | ||||
−0.127009 | + | 0.991902i | \(0.540538\pi\) | |||||||
\(138\) | 7.89125 | 0.671748 | ||||||||
\(139\) | 1.70852 | 0.144915 | 0.0724574 | − | 0.997372i | \(-0.476916\pi\) | ||||
0.0724574 | + | 0.997372i | \(0.476916\pi\) | |||||||
\(140\) | 5.62241 | 0.475181 | ||||||||
\(141\) | −6.67559 | −0.562186 | ||||||||
\(142\) | −2.69689 | −0.226318 | ||||||||
\(143\) | −3.59527 | −0.300652 | ||||||||
\(144\) | −2.50354 | −0.208628 | ||||||||
\(145\) | −5.59992 | −0.465048 | ||||||||
\(146\) | −5.27159 | −0.436280 | ||||||||
\(147\) | −0.889369 | −0.0733539 | ||||||||
\(148\) | 2.69061 | 0.221167 | ||||||||
\(149\) | 6.03429 | 0.494348 | 0.247174 | − | 0.968971i | \(-0.420498\pi\) | ||||
0.247174 | + | 0.968971i | \(0.420498\pi\) | |||||||
\(150\) | 9.03728 | 0.737891 | ||||||||
\(151\) | −6.84081 | −0.556698 | −0.278349 | − | 0.960480i | \(-0.589787\pi\) | ||||
−0.278349 | + | 0.960480i | \(0.589787\pi\) | |||||||
\(152\) | 7.12258 | 0.577718 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −23.2613 | −1.87445 | ||||||||
\(155\) | −3.20374 | −0.257331 | ||||||||
\(156\) | 2.10958 | 0.168902 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | 26.2751 | 2.09033 | ||||||||
\(159\) | 6.97068 | 0.552811 | ||||||||
\(160\) | −6.91187 | −0.546431 | ||||||||
\(161\) | 9.11497 | 0.718360 | ||||||||
\(162\) | −2.14010 | −0.168142 | ||||||||
\(163\) | 4.97205 | 0.389441 | 0.194721 | − | 0.980859i | \(-0.437620\pi\) | ||||
0.194721 | + | 0.980859i | \(0.437620\pi\) | |||||||
\(164\) | −25.7678 | −2.01213 | ||||||||
\(165\) | 3.87628 | 0.301768 | ||||||||
\(166\) | −26.3640 | −2.04625 | ||||||||
\(167\) | 2.72951 | 0.211216 | 0.105608 | − | 0.994408i | \(-0.466321\pi\) | ||||
0.105608 | + | 0.994408i | \(0.466321\pi\) | |||||||
\(168\) | 3.06845 | 0.236736 | ||||||||
\(169\) | −12.3314 | −0.948571 | ||||||||
\(170\) | −1.88665 | −0.144699 | ||||||||
\(171\) | −5.73800 | −0.438796 | ||||||||
\(172\) | −18.5542 | −1.41474 | ||||||||
\(173\) | 8.88822 | 0.675759 | 0.337879 | − | 0.941189i | \(-0.390290\pi\) | ||||
0.337879 | + | 0.941189i | \(0.390290\pi\) | |||||||
\(174\) | −13.5944 | −1.03059 | ||||||||
\(175\) | 10.4387 | 0.789093 | ||||||||
\(176\) | 11.0081 | 0.829766 | ||||||||
\(177\) | −0.253239 | −0.0190346 | ||||||||
\(178\) | 0.195559 | 0.0146578 | ||||||||
\(179\) | 2.12366 | 0.158730 | 0.0793649 | − | 0.996846i | \(-0.474711\pi\) | ||||
0.0793649 | + | 0.996846i | \(0.474711\pi\) | |||||||
\(180\) | −2.27447 | −0.169529 | ||||||||
\(181\) | −0.390811 | −0.0290487 | −0.0145244 | − | 0.999895i | \(-0.504623\pi\) | ||||
−0.0145244 | + | 0.999895i | \(0.504623\pi\) | |||||||
\(182\) | 4.32564 | 0.320638 | ||||||||
\(183\) | −0.406403 | −0.0300422 | ||||||||
\(184\) | 4.57709 | 0.337427 | ||||||||
\(185\) | −0.919358 | −0.0675925 | ||||||||
\(186\) | −7.77740 | −0.570267 | ||||||||
\(187\) | 4.39701 | 0.321542 | ||||||||
\(188\) | −17.2232 | −1.25613 | ||||||||
\(189\) | −2.47197 | −0.179809 | ||||||||
\(190\) | −10.8256 | −0.785370 | ||||||||
\(191\) | 18.7735 | 1.35840 | 0.679200 | − | 0.733954i | \(-0.262327\pi\) | ||||
0.679200 | + | 0.733954i | \(0.262327\pi\) | |||||||
\(192\) | −11.7722 | −0.849584 | ||||||||
\(193\) | 15.0657 | 1.08445 | 0.542225 | − | 0.840233i | \(-0.317582\pi\) | ||||
0.542225 | + | 0.840233i | \(0.317582\pi\) | |||||||
\(194\) | −0.260762 | −0.0187216 | ||||||||
\(195\) | −0.720826 | −0.0516194 | ||||||||
\(196\) | −2.29459 | −0.163899 | ||||||||
\(197\) | −24.8741 | −1.77221 | −0.886105 | − | 0.463485i | \(-0.846599\pi\) | ||||
−0.886105 | + | 0.463485i | \(0.846599\pi\) | |||||||
\(198\) | 9.41004 | 0.668743 | ||||||||
\(199\) | 13.4451 | 0.953098 | 0.476549 | − | 0.879148i | \(-0.341887\pi\) | ||||
0.476549 | + | 0.879148i | \(0.341887\pi\) | |||||||
\(200\) | 5.24180 | 0.370652 | ||||||||
\(201\) | −13.9141 | −0.981422 | ||||||||
\(202\) | −17.9079 | −1.25999 | ||||||||
\(203\) | −15.7025 | −1.10210 | ||||||||
\(204\) | −2.58002 | −0.180638 | ||||||||
\(205\) | 8.80463 | 0.614942 | ||||||||
\(206\) | −9.89688 | −0.689548 | ||||||||
\(207\) | −3.68733 | −0.256287 | ||||||||
\(208\) | −2.04705 | −0.141937 | ||||||||
\(209\) | 25.2301 | 1.74520 | ||||||||
\(210\) | −4.66373 | −0.321828 | ||||||||
\(211\) | −15.3455 | −1.05643 | −0.528214 | − | 0.849111i | \(-0.677138\pi\) | ||||
−0.528214 | + | 0.849111i | \(0.677138\pi\) | |||||||
\(212\) | 17.9845 | 1.23518 | ||||||||
\(213\) | 1.26017 | 0.0863456 | ||||||||
\(214\) | 18.3897 | 1.25710 | ||||||||
\(215\) | 6.33980 | 0.432371 | ||||||||
\(216\) | −1.24130 | −0.0844598 | ||||||||
\(217\) | −8.98346 | −0.609837 | ||||||||
\(218\) | −20.8721 | −1.41364 | ||||||||
\(219\) | 2.46325 | 0.166451 | ||||||||
\(220\) | 10.0009 | 0.674258 | ||||||||
\(221\) | −0.817662 | −0.0550019 | ||||||||
\(222\) | −2.23183 | −0.149791 | ||||||||
\(223\) | −3.33836 | −0.223553 | −0.111777 | − | 0.993733i | \(-0.535654\pi\) | ||||
−0.111777 | + | 0.993733i | \(0.535654\pi\) | |||||||
\(224\) | −19.3813 | −1.29496 | ||||||||
\(225\) | −4.22283 | −0.281522 | ||||||||
\(226\) | 26.0135 | 1.73039 | ||||||||
\(227\) | 1.51252 | 0.100390 | 0.0501948 | − | 0.998739i | \(-0.484016\pi\) | ||||
0.0501948 | + | 0.998739i | \(0.484016\pi\) | |||||||
\(228\) | −14.8042 | −0.980429 | ||||||||
\(229\) | 3.65826 | 0.241745 | 0.120872 | − | 0.992668i | \(-0.461431\pi\) | ||||
0.120872 | + | 0.992668i | \(0.461431\pi\) | |||||||
\(230\) | −6.95669 | −0.458711 | ||||||||
\(231\) | 10.8693 | 0.715146 | ||||||||
\(232\) | −7.88500 | −0.517676 | ||||||||
\(233\) | −1.12286 | −0.0735610 | −0.0367805 | − | 0.999323i | \(-0.511710\pi\) | ||||
−0.0367805 | + | 0.999323i | \(0.511710\pi\) | |||||||
\(234\) | −1.74988 | −0.114393 | ||||||||
\(235\) | 5.88500 | 0.383895 | ||||||||
\(236\) | −0.653363 | −0.0425303 | ||||||||
\(237\) | −12.2775 | −0.797510 | ||||||||
\(238\) | −5.29026 | −0.342916 | ||||||||
\(239\) | 2.05527 | 0.132944 | 0.0664720 | − | 0.997788i | \(-0.478826\pi\) | ||||
0.0664720 | + | 0.997788i | \(0.478826\pi\) | |||||||
\(240\) | 2.20704 | 0.142464 | ||||||||
\(241\) | −9.03883 | −0.582242 | −0.291121 | − | 0.956686i | \(-0.594028\pi\) | ||||
−0.291121 | + | 0.956686i | \(0.594028\pi\) | |||||||
\(242\) | −17.8350 | −1.14648 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −1.04853 | −0.0671252 | ||||||||
\(245\) | 0.784041 | 0.0500905 | ||||||||
\(246\) | 21.3741 | 1.36276 | ||||||||
\(247\) | −4.69174 | −0.298529 | ||||||||
\(248\) | −4.51105 | −0.286452 | ||||||||
\(249\) | 12.3191 | 0.780690 | ||||||||
\(250\) | −17.4002 | −1.10049 | ||||||||
\(251\) | −4.94002 | −0.311811 | −0.155906 | − | 0.987772i | \(-0.549830\pi\) | ||||
−0.155906 | + | 0.987772i | \(0.549830\pi\) | |||||||
\(252\) | −6.37773 | −0.401759 | ||||||||
\(253\) | 16.2133 | 1.01932 | ||||||||
\(254\) | 38.2026 | 2.39704 | ||||||||
\(255\) | 0.881570 | 0.0552060 | ||||||||
\(256\) | 3.18605 | 0.199128 | ||||||||
\(257\) | 24.1712 | 1.50776 | 0.753880 | − | 0.657012i | \(-0.228180\pi\) | ||||
0.753880 | + | 0.657012i | \(0.228180\pi\) | |||||||
\(258\) | 15.3905 | 0.958171 | ||||||||
\(259\) | −2.57793 | −0.160185 | ||||||||
\(260\) | −1.85975 | −0.115337 | ||||||||
\(261\) | 6.35222 | 0.393192 | ||||||||
\(262\) | −1.07381 | −0.0663400 | ||||||||
\(263\) | 19.7946 | 1.22059 | 0.610293 | − | 0.792176i | \(-0.291052\pi\) | ||||
0.610293 | + | 0.792176i | \(0.291052\pi\) | |||||||
\(264\) | 5.45801 | 0.335917 | ||||||||
\(265\) | −6.14514 | −0.377493 | ||||||||
\(266\) | −30.3555 | −1.86121 | ||||||||
\(267\) | −0.0913787 | −0.00559229 | ||||||||
\(268\) | −35.8985 | −2.19285 | ||||||||
\(269\) | 32.5751 | 1.98614 | 0.993068 | − | 0.117542i | \(-0.0375013\pi\) | ||||
0.993068 | + | 0.117542i | \(0.0375013\pi\) | |||||||
\(270\) | 1.88665 | 0.114818 | ||||||||
\(271\) | 21.5603 | 1.30970 | 0.654848 | − | 0.755760i | \(-0.272733\pi\) | ||||
0.654848 | + | 0.755760i | \(0.272733\pi\) | |||||||
\(272\) | 2.50354 | 0.151799 | ||||||||
\(273\) | −2.02123 | −0.122331 | ||||||||
\(274\) | 6.36294 | 0.384399 | ||||||||
\(275\) | 18.5679 | 1.11968 | ||||||||
\(276\) | −9.51339 | −0.572639 | ||||||||
\(277\) | −27.0378 | −1.62454 | −0.812271 | − | 0.583280i | \(-0.801769\pi\) | ||||
−0.812271 | + | 0.583280i | \(0.801769\pi\) | |||||||
\(278\) | −3.65640 | −0.219296 | ||||||||
\(279\) | 3.63413 | 0.217570 | ||||||||
\(280\) | −2.70506 | −0.161658 | ||||||||
\(281\) | −26.2192 | −1.56410 | −0.782052 | − | 0.623213i | \(-0.785827\pi\) | ||||
−0.782052 | + | 0.623213i | \(0.785827\pi\) | |||||||
\(282\) | 14.2864 | 0.850744 | ||||||||
\(283\) | 19.1415 | 1.13784 | 0.568921 | − | 0.822392i | \(-0.307361\pi\) | ||||
0.568921 | + | 0.822392i | \(0.307361\pi\) | |||||||
\(284\) | 3.25127 | 0.192927 | ||||||||
\(285\) | 5.05845 | 0.299637 | ||||||||
\(286\) | 7.69423 | 0.454969 | ||||||||
\(287\) | 24.6886 | 1.45732 | ||||||||
\(288\) | 7.84041 | 0.462001 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 11.9844 | 0.703747 | ||||||||
\(291\) | 0.121846 | 0.00714274 | ||||||||
\(292\) | 6.35523 | 0.371912 | ||||||||
\(293\) | 27.8120 | 1.62479 | 0.812397 | − | 0.583105i | \(-0.198162\pi\) | ||||
0.812397 | + | 0.583105i | \(0.198162\pi\) | |||||||
\(294\) | 1.90334 | 0.111005 | ||||||||
\(295\) | 0.223248 | 0.0129980 | ||||||||
\(296\) | −1.29451 | −0.0752417 | ||||||||
\(297\) | −4.39701 | −0.255141 | ||||||||
\(298\) | −12.9140 | −0.748086 | ||||||||
\(299\) | −3.01499 | −0.174361 | ||||||||
\(300\) | −10.8950 | −0.629023 | ||||||||
\(301\) | 17.7772 | 1.02466 | ||||||||
\(302\) | 14.6400 | 0.842438 | ||||||||
\(303\) | 8.36778 | 0.480716 | ||||||||
\(304\) | 14.3653 | 0.823906 | ||||||||
\(305\) | 0.358273 | 0.0205146 | ||||||||
\(306\) | 2.14010 | 0.122341 | ||||||||
\(307\) | −17.0193 | −0.971346 | −0.485673 | − | 0.874141i | \(-0.661425\pi\) | ||||
−0.485673 | + | 0.874141i | \(0.661425\pi\) | |||||||
\(308\) | 28.0430 | 1.59790 | ||||||||
\(309\) | 4.62450 | 0.263078 | ||||||||
\(310\) | 6.85632 | 0.389413 | ||||||||
\(311\) | 7.70438 | 0.436875 | 0.218438 | − | 0.975851i | \(-0.429904\pi\) | ||||
0.218438 | + | 0.975851i | \(0.429904\pi\) | |||||||
\(312\) | −1.01496 | −0.0574610 | ||||||||
\(313\) | −12.6441 | −0.714689 | −0.357344 | − | 0.933973i | \(-0.616318\pi\) | ||||
−0.357344 | + | 0.933973i | \(0.616318\pi\) | |||||||
\(314\) | 2.14010 | 0.120773 | ||||||||
\(315\) | 2.17921 | 0.122785 | ||||||||
\(316\) | −31.6762 | −1.78193 | ||||||||
\(317\) | 14.5346 | 0.816343 | 0.408171 | − | 0.912905i | \(-0.366167\pi\) | ||||
0.408171 | + | 0.912905i | \(0.366167\pi\) | |||||||
\(318\) | −14.9179 | −0.836557 | ||||||||
\(319\) | −27.9308 | −1.56382 | ||||||||
\(320\) | 10.3780 | 0.580148 | ||||||||
\(321\) | −8.59293 | −0.479611 | ||||||||
\(322\) | −19.5069 | −1.08708 | ||||||||
\(323\) | 5.73800 | 0.319271 | ||||||||
\(324\) | 2.58002 | 0.143334 | ||||||||
\(325\) | −3.45285 | −0.191530 | ||||||||
\(326\) | −10.6407 | −0.589333 | ||||||||
\(327\) | 9.75288 | 0.539336 | ||||||||
\(328\) | 12.3974 | 0.684532 | ||||||||
\(329\) | 16.5019 | 0.909777 | ||||||||
\(330\) | −8.29561 | −0.456658 | ||||||||
\(331\) | −11.9795 | −0.658455 | −0.329227 | − | 0.944251i | \(-0.606788\pi\) | ||||
−0.329227 | + | 0.944251i | \(0.606788\pi\) | |||||||
\(332\) | 31.7835 | 1.74435 | ||||||||
\(333\) | 1.04286 | 0.0571486 | ||||||||
\(334\) | −5.84143 | −0.319629 | ||||||||
\(335\) | 12.2662 | 0.670175 | ||||||||
\(336\) | 6.18867 | 0.337619 | ||||||||
\(337\) | −4.54589 | −0.247631 | −0.123815 | − | 0.992305i | \(-0.539513\pi\) | ||||
−0.123815 | + | 0.992305i | \(0.539513\pi\) | |||||||
\(338\) | 26.3905 | 1.43545 | ||||||||
\(339\) | −12.1553 | −0.660185 | ||||||||
\(340\) | 2.27447 | 0.123350 | ||||||||
\(341\) | −15.9793 | −0.865329 | ||||||||
\(342\) | 12.2799 | 0.664020 | ||||||||
\(343\) | 19.5023 | 1.05302 | ||||||||
\(344\) | 8.92680 | 0.481301 | ||||||||
\(345\) | 3.25064 | 0.175009 | ||||||||
\(346\) | −19.0217 | −1.02261 | ||||||||
\(347\) | 12.4071 | 0.666050 | 0.333025 | − | 0.942918i | \(-0.391931\pi\) | ||||
0.333025 | + | 0.942918i | \(0.391931\pi\) | |||||||
\(348\) | 16.3888 | 0.878534 | ||||||||
\(349\) | 10.4827 | 0.561125 | 0.280563 | − | 0.959836i | \(-0.409479\pi\) | ||||
0.280563 | + | 0.959836i | \(0.409479\pi\) | |||||||
\(350\) | −22.3399 | −1.19412 | ||||||||
\(351\) | 0.817662 | 0.0436436 | ||||||||
\(352\) | −34.4744 | −1.83749 | ||||||||
\(353\) | −19.4023 | −1.03268 | −0.516341 | − | 0.856383i | \(-0.672706\pi\) | ||||
−0.516341 | + | 0.856383i | \(0.672706\pi\) | |||||||
\(354\) | 0.541957 | 0.0288047 | ||||||||
\(355\) | −1.11093 | −0.0589620 | ||||||||
\(356\) | −0.235759 | −0.0124952 | ||||||||
\(357\) | 2.47197 | 0.130830 | ||||||||
\(358\) | −4.54484 | −0.240202 | ||||||||
\(359\) | −1.00055 | −0.0528070 | −0.0264035 | − | 0.999651i | \(-0.508405\pi\) | ||||
−0.0264035 | + | 0.999651i | \(0.508405\pi\) | |||||||
\(360\) | 1.09429 | 0.0576743 | ||||||||
\(361\) | 13.9247 | 0.732877 | ||||||||
\(362\) | 0.836373 | 0.0439588 | ||||||||
\(363\) | 8.33373 | 0.437408 | ||||||||
\(364\) | −5.21483 | −0.273331 | ||||||||
\(365\) | −2.17152 | −0.113663 | ||||||||
\(366\) | 0.869743 | 0.0454622 | ||||||||
\(367\) | −24.5915 | −1.28367 | −0.641834 | − | 0.766843i | \(-0.721826\pi\) | ||||
−0.641834 | + | 0.766843i | \(0.721826\pi\) | |||||||
\(368\) | 9.23137 | 0.481219 | ||||||||
\(369\) | −9.98744 | −0.519925 | ||||||||
\(370\) | 1.96752 | 0.102286 | ||||||||
\(371\) | −17.2313 | −0.894605 | ||||||||
\(372\) | 9.37614 | 0.486130 | ||||||||
\(373\) | 16.9231 | 0.876246 | 0.438123 | − | 0.898915i | \(-0.355643\pi\) | ||||
0.438123 | + | 0.898915i | \(0.355643\pi\) | |||||||
\(374\) | −9.41004 | −0.486582 | ||||||||
\(375\) | 8.13057 | 0.419861 | ||||||||
\(376\) | 8.28641 | 0.427339 | ||||||||
\(377\) | 5.19396 | 0.267503 | ||||||||
\(378\) | 5.29026 | 0.272101 | ||||||||
\(379\) | −37.3918 | −1.92069 | −0.960343 | − | 0.278822i | \(-0.910056\pi\) | ||||
−0.960343 | + | 0.278822i | \(0.910056\pi\) | |||||||
\(380\) | 13.0509 | 0.669497 | ||||||||
\(381\) | −17.8509 | −0.914527 | ||||||||
\(382\) | −40.1770 | −2.05564 | ||||||||
\(383\) | −10.5461 | −0.538881 | −0.269441 | − | 0.963017i | \(-0.586839\pi\) | ||||
−0.269441 | + | 0.963017i | \(0.586839\pi\) | |||||||
\(384\) | 9.51280 | 0.485448 | ||||||||
\(385\) | −9.58203 | −0.488346 | ||||||||
\(386\) | −32.2420 | −1.64107 | ||||||||
\(387\) | −7.19149 | −0.365564 | ||||||||
\(388\) | 0.314365 | 0.0159595 | ||||||||
\(389\) | −5.03436 | −0.255252 | −0.127626 | − | 0.991822i | \(-0.540736\pi\) | ||||
−0.127626 | + | 0.991822i | \(0.540736\pi\) | |||||||
\(390\) | 1.54264 | 0.0781145 | ||||||||
\(391\) | 3.68733 | 0.186476 | ||||||||
\(392\) | 1.10397 | 0.0557591 | ||||||||
\(393\) | 0.501756 | 0.0253102 | ||||||||
\(394\) | 53.2331 | 2.68185 | ||||||||
\(395\) | 10.8235 | 0.544588 | ||||||||
\(396\) | −11.3444 | −0.570077 | ||||||||
\(397\) | 30.5986 | 1.53570 | 0.767850 | − | 0.640630i | \(-0.221327\pi\) | ||||
0.767850 | + | 0.640630i | \(0.221327\pi\) | |||||||
\(398\) | −28.7738 | −1.44230 | ||||||||
\(399\) | 14.1842 | 0.710096 | ||||||||
\(400\) | 10.5720 | 0.528601 | ||||||||
\(401\) | 21.9887 | 1.09806 | 0.549031 | − | 0.835802i | \(-0.314997\pi\) | ||||
0.549031 | + | 0.835802i | \(0.314997\pi\) | |||||||
\(402\) | 29.7774 | 1.48516 | ||||||||
\(403\) | 2.97149 | 0.148021 | ||||||||
\(404\) | 21.5890 | 1.07409 | ||||||||
\(405\) | −0.881570 | −0.0438056 | ||||||||
\(406\) | 33.6048 | 1.66778 | ||||||||
\(407\) | −4.58549 | −0.227294 | ||||||||
\(408\) | 1.24130 | 0.0614535 | ||||||||
\(409\) | 27.9598 | 1.38253 | 0.691263 | − | 0.722603i | \(-0.257055\pi\) | ||||
0.691263 | + | 0.722603i | \(0.257055\pi\) | |||||||
\(410\) | −18.8428 | −0.930578 | ||||||||
\(411\) | −2.97320 | −0.146657 | ||||||||
\(412\) | 11.9313 | 0.587813 | ||||||||
\(413\) | 0.626000 | 0.0308035 | ||||||||
\(414\) | 7.89125 | 0.387834 | ||||||||
\(415\) | −10.8601 | −0.533103 | ||||||||
\(416\) | 6.41081 | 0.314316 | ||||||||
\(417\) | 1.70852 | 0.0836666 | ||||||||
\(418\) | −53.9948 | −2.64097 | ||||||||
\(419\) | 33.8540 | 1.65388 | 0.826938 | − | 0.562293i | \(-0.190081\pi\) | ||||
0.826938 | + | 0.562293i | \(0.190081\pi\) | |||||||
\(420\) | 5.62241 | 0.274346 | ||||||||
\(421\) | −32.8232 | −1.59971 | −0.799853 | − | 0.600196i | \(-0.795089\pi\) | ||||
−0.799853 | + | 0.600196i | \(0.795089\pi\) | |||||||
\(422\) | 32.8409 | 1.59867 | ||||||||
\(423\) | −6.67559 | −0.324578 | ||||||||
\(424\) | −8.65271 | −0.420213 | ||||||||
\(425\) | 4.22283 | 0.204838 | ||||||||
\(426\) | −2.69689 | −0.130665 | ||||||||
\(427\) | 1.00462 | 0.0486168 | ||||||||
\(428\) | −22.1699 | −1.07162 | ||||||||
\(429\) | −3.59527 | −0.173581 | ||||||||
\(430\) | −13.5678 | −0.654298 | ||||||||
\(431\) | −38.5361 | −1.85622 | −0.928109 | − | 0.372309i | \(-0.878566\pi\) | ||||
−0.928109 | + | 0.372309i | \(0.878566\pi\) | |||||||
\(432\) | −2.50354 | −0.120451 | ||||||||
\(433\) | 12.6145 | 0.606217 | 0.303108 | − | 0.952956i | \(-0.401976\pi\) | ||||
0.303108 | + | 0.952956i | \(0.401976\pi\) | |||||||
\(434\) | 19.2255 | 0.922853 | ||||||||
\(435\) | −5.59992 | −0.268496 | ||||||||
\(436\) | 25.1626 | 1.20507 | ||||||||
\(437\) | 21.1579 | 1.01212 | ||||||||
\(438\) | −5.27159 | −0.251886 | ||||||||
\(439\) | −7.91175 | −0.377607 | −0.188804 | − | 0.982015i | \(-0.560461\pi\) | ||||
−0.188804 | + | 0.982015i | \(0.560461\pi\) | |||||||
\(440\) | −4.81162 | −0.229385 | ||||||||
\(441\) | −0.889369 | −0.0423509 | ||||||||
\(442\) | 1.74988 | 0.0832331 | ||||||||
\(443\) | 17.9207 | 0.851440 | 0.425720 | − | 0.904855i | \(-0.360021\pi\) | ||||
0.425720 | + | 0.904855i | \(0.360021\pi\) | |||||||
\(444\) | 2.69061 | 0.127691 | ||||||||
\(445\) | 0.0805567 | 0.00381876 | ||||||||
\(446\) | 7.14442 | 0.338298 | ||||||||
\(447\) | 6.03429 | 0.285412 | ||||||||
\(448\) | 29.1005 | 1.37487 | ||||||||
\(449\) | −12.5869 | −0.594015 | −0.297007 | − | 0.954875i | \(-0.595989\pi\) | ||||
−0.297007 | + | 0.954875i | \(0.595989\pi\) | |||||||
\(450\) | 9.03728 | 0.426021 | ||||||||
\(451\) | 43.9149 | 2.06787 | ||||||||
\(452\) | −31.3609 | −1.47509 | ||||||||
\(453\) | −6.84081 | −0.321410 | ||||||||
\(454\) | −3.23694 | −0.151917 | ||||||||
\(455\) | 1.78186 | 0.0835349 | ||||||||
\(456\) | 7.12258 | 0.333545 | ||||||||
\(457\) | −24.0733 | −1.12610 | −0.563050 | − | 0.826423i | \(-0.690372\pi\) | ||||
−0.563050 | + | 0.826423i | \(0.690372\pi\) | |||||||
\(458\) | −7.82904 | −0.365827 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 8.38672 | 0.391033 | ||||||||
\(461\) | 9.04092 | 0.421077 | 0.210539 | − | 0.977586i | \(-0.432478\pi\) | ||||
0.210539 | + | 0.977586i | \(0.432478\pi\) | |||||||
\(462\) | −23.2613 | −1.08222 | ||||||||
\(463\) | −25.4948 | −1.18484 | −0.592421 | − | 0.805628i | \(-0.701828\pi\) | ||||
−0.592421 | + | 0.805628i | \(0.701828\pi\) | |||||||
\(464\) | −15.9030 | −0.738278 | ||||||||
\(465\) | −3.20374 | −0.148570 | ||||||||
\(466\) | 2.40303 | 0.111318 | ||||||||
\(467\) | 16.8833 | 0.781264 | 0.390632 | − | 0.920547i | \(-0.372257\pi\) | ||||
0.390632 | + | 0.920547i | \(0.372257\pi\) | |||||||
\(468\) | 2.10958 | 0.0975155 | ||||||||
\(469\) | 34.3951 | 1.58822 | ||||||||
\(470\) | −12.5945 | −0.580940 | ||||||||
\(471\) | −1.00000 | −0.0460776 | ||||||||
\(472\) | 0.314346 | 0.0144690 | ||||||||
\(473\) | 31.6211 | 1.45394 | ||||||||
\(474\) | 26.2751 | 1.20685 | ||||||||
\(475\) | 24.2306 | 1.11178 | ||||||||
\(476\) | 6.37773 | 0.292323 | ||||||||
\(477\) | 6.97068 | 0.319166 | ||||||||
\(478\) | −4.39847 | −0.201181 | ||||||||
\(479\) | −42.2849 | −1.93205 | −0.966024 | − | 0.258452i | \(-0.916788\pi\) | ||||
−0.966024 | + | 0.258452i | \(0.916788\pi\) | |||||||
\(480\) | −6.91187 | −0.315482 | ||||||||
\(481\) | 0.852710 | 0.0388802 | ||||||||
\(482\) | 19.3440 | 0.881094 | ||||||||
\(483\) | 9.11497 | 0.414746 | ||||||||
\(484\) | 21.5012 | 0.977327 | ||||||||
\(485\) | −0.107416 | −0.00487750 | ||||||||
\(486\) | −2.14010 | −0.0970768 | ||||||||
\(487\) | 9.54387 | 0.432474 | 0.216237 | − | 0.976341i | \(-0.430622\pi\) | ||||
0.216237 | + | 0.976341i | \(0.430622\pi\) | |||||||
\(488\) | 0.504468 | 0.0228362 | ||||||||
\(489\) | 4.97205 | 0.224844 | ||||||||
\(490\) | −1.67792 | −0.0758009 | ||||||||
\(491\) | −12.3188 | −0.555938 | −0.277969 | − | 0.960590i | \(-0.589661\pi\) | ||||
−0.277969 | + | 0.960590i | \(0.589661\pi\) | |||||||
\(492\) | −25.7678 | −1.16170 | ||||||||
\(493\) | −6.35222 | −0.286089 | ||||||||
\(494\) | 10.0408 | 0.451757 | ||||||||
\(495\) | 3.87628 | 0.174226 | ||||||||
\(496\) | −9.09818 | −0.408521 | ||||||||
\(497\) | −3.11511 | −0.139732 | ||||||||
\(498\) | −26.3640 | −1.18140 | ||||||||
\(499\) | −20.0980 | −0.899709 | −0.449855 | − | 0.893102i | \(-0.648524\pi\) | ||||
−0.449855 | + | 0.893102i | \(0.648524\pi\) | |||||||
\(500\) | 20.9770 | 0.938122 | ||||||||
\(501\) | 2.72951 | 0.121946 | ||||||||
\(502\) | 10.5721 | 0.471857 | ||||||||
\(503\) | −30.0728 | −1.34088 | −0.670441 | − | 0.741963i | \(-0.733895\pi\) | ||||
−0.670441 | + | 0.741963i | \(0.733895\pi\) | |||||||
\(504\) | 3.06845 | 0.136680 | ||||||||
\(505\) | −7.37678 | −0.328262 | ||||||||
\(506\) | −34.6980 | −1.54251 | ||||||||
\(507\) | −12.3314 | −0.547658 | ||||||||
\(508\) | −46.0556 | −2.04339 | ||||||||
\(509\) | 31.1843 | 1.38222 | 0.691110 | − | 0.722750i | \(-0.257122\pi\) | ||||
0.691110 | + | 0.722750i | \(0.257122\pi\) | |||||||
\(510\) | −1.88665 | −0.0835421 | ||||||||
\(511\) | −6.08907 | −0.269365 | ||||||||
\(512\) | −25.8440 | −1.14216 | ||||||||
\(513\) | −5.73800 | −0.253339 | ||||||||
\(514\) | −51.7288 | −2.28166 | ||||||||
\(515\) | −4.07682 | −0.179646 | ||||||||
\(516\) | −18.5542 | −0.816803 | ||||||||
\(517\) | 29.3527 | 1.29093 | ||||||||
\(518\) | 5.51702 | 0.242404 | ||||||||
\(519\) | 8.88822 | 0.390150 | ||||||||
\(520\) | 0.894761 | 0.0392379 | ||||||||
\(521\) | −32.7773 | −1.43600 | −0.718001 | − | 0.696042i | \(-0.754943\pi\) | ||||
−0.718001 | + | 0.696042i | \(0.754943\pi\) | |||||||
\(522\) | −13.5944 | −0.595009 | ||||||||
\(523\) | 44.5046 | 1.94605 | 0.973026 | − | 0.230697i | \(-0.0741006\pi\) | ||||
0.973026 | + | 0.230697i | \(0.0741006\pi\) | |||||||
\(524\) | 1.29454 | 0.0565523 | ||||||||
\(525\) | 10.4387 | 0.455583 | ||||||||
\(526\) | −42.3623 | −1.84708 | ||||||||
\(527\) | −3.63413 | −0.158305 | ||||||||
\(528\) | 11.0081 | 0.479065 | ||||||||
\(529\) | −9.40358 | −0.408851 | ||||||||
\(530\) | 13.1512 | 0.571252 | ||||||||
\(531\) | −0.253239 | −0.0109897 | ||||||||
\(532\) | 36.5954 | 1.58661 | ||||||||
\(533\) | −8.16635 | −0.353724 | ||||||||
\(534\) | 0.195559 | 0.00846268 | ||||||||
\(535\) | 7.57527 | 0.327507 | ||||||||
\(536\) | 17.2715 | 0.746016 | ||||||||
\(537\) | 2.12366 | 0.0916427 | ||||||||
\(538\) | −69.7138 | −3.00558 | ||||||||
\(539\) | 3.91057 | 0.168440 | ||||||||
\(540\) | −2.27447 | −0.0978775 | ||||||||
\(541\) | 3.91343 | 0.168251 | 0.0841257 | − | 0.996455i | \(-0.473190\pi\) | ||||
0.0841257 | + | 0.996455i | \(0.473190\pi\) | |||||||
\(542\) | −46.1412 | −1.98193 | ||||||||
\(543\) | −0.390811 | −0.0167713 | ||||||||
\(544\) | −7.84041 | −0.336155 | ||||||||
\(545\) | −8.59785 | −0.368291 | ||||||||
\(546\) | 4.32564 | 0.185120 | ||||||||
\(547\) | −41.9736 | −1.79466 | −0.897330 | − | 0.441360i | \(-0.854496\pi\) | ||||
−0.897330 | + | 0.441360i | \(0.854496\pi\) | |||||||
\(548\) | −7.67091 | −0.327685 | ||||||||
\(549\) | −0.406403 | −0.0173449 | ||||||||
\(550\) | −39.7371 | −1.69439 | ||||||||
\(551\) | −36.4490 | −1.55278 | ||||||||
\(552\) | 4.57709 | 0.194814 | ||||||||
\(553\) | 30.3496 | 1.29060 | ||||||||
\(554\) | 57.8635 | 2.45838 | ||||||||
\(555\) | −0.919358 | −0.0390246 | ||||||||
\(556\) | 4.40802 | 0.186942 | ||||||||
\(557\) | 29.7339 | 1.25986 | 0.629932 | − | 0.776650i | \(-0.283083\pi\) | ||||
0.629932 | + | 0.776650i | \(0.283083\pi\) | |||||||
\(558\) | −7.77740 | −0.329244 | ||||||||
\(559\) | −5.88021 | −0.248706 | ||||||||
\(560\) | −5.45574 | −0.230547 | ||||||||
\(561\) | 4.39701 | 0.185642 | ||||||||
\(562\) | 56.1116 | 2.36692 | ||||||||
\(563\) | 35.5038 | 1.49631 | 0.748154 | − | 0.663525i | \(-0.230940\pi\) | ||||
0.748154 | + | 0.663525i | \(0.230940\pi\) | |||||||
\(564\) | −17.2232 | −0.725226 | ||||||||
\(565\) | 10.7157 | 0.450815 | ||||||||
\(566\) | −40.9646 | −1.72187 | ||||||||
\(567\) | −2.47197 | −0.103813 | ||||||||
\(568\) | −1.56425 | −0.0656345 | ||||||||
\(569\) | 31.0450 | 1.30147 | 0.650736 | − | 0.759304i | \(-0.274460\pi\) | ||||
0.650736 | + | 0.759304i | \(0.274460\pi\) | |||||||
\(570\) | −10.8256 | −0.453434 | ||||||||
\(571\) | 20.7759 | 0.869445 | 0.434723 | − | 0.900564i | \(-0.356846\pi\) | ||||
0.434723 | + | 0.900564i | \(0.356846\pi\) | |||||||
\(572\) | −9.27587 | −0.387844 | ||||||||
\(573\) | 18.7735 | 0.784272 | ||||||||
\(574\) | −52.8361 | −2.20534 | ||||||||
\(575\) | 15.5710 | 0.649355 | ||||||||
\(576\) | −11.7722 | −0.490508 | ||||||||
\(577\) | −14.5922 | −0.607480 | −0.303740 | − | 0.952755i | \(-0.598235\pi\) | ||||
−0.303740 | + | 0.952755i | \(0.598235\pi\) | |||||||
\(578\) | −2.14010 | −0.0890163 | ||||||||
\(579\) | 15.0657 | 0.626107 | ||||||||
\(580\) | −14.4479 | −0.599917 | ||||||||
\(581\) | −30.4524 | −1.26338 | ||||||||
\(582\) | −0.260762 | −0.0108089 | ||||||||
\(583\) | −30.6502 | −1.26940 | ||||||||
\(584\) | −3.05763 | −0.126526 | ||||||||
\(585\) | −0.720826 | −0.0298025 | ||||||||
\(586\) | −59.5204 | −2.45876 | ||||||||
\(587\) | −33.4816 | −1.38193 | −0.690967 | − | 0.722886i | \(-0.742815\pi\) | ||||
−0.690967 | + | 0.722886i | \(0.742815\pi\) | |||||||
\(588\) | −2.29459 | −0.0946273 | ||||||||
\(589\) | −20.8527 | −0.859219 | ||||||||
\(590\) | −0.477773 | −0.0196696 | ||||||||
\(591\) | −24.8741 | −1.02319 | ||||||||
\(592\) | −2.61085 | −0.107305 | ||||||||
\(593\) | −18.8359 | −0.773496 | −0.386748 | − | 0.922185i | \(-0.626402\pi\) | ||||
−0.386748 | + | 0.922185i | \(0.626402\pi\) | |||||||
\(594\) | 9.41004 | 0.386099 | ||||||||
\(595\) | −2.17921 | −0.0893390 | ||||||||
\(596\) | 15.5686 | 0.637714 | ||||||||
\(597\) | 13.4451 | 0.550271 | ||||||||
\(598\) | 6.45238 | 0.263857 | ||||||||
\(599\) | −32.0153 | −1.30811 | −0.654055 | − | 0.756447i | \(-0.726934\pi\) | ||||
−0.654055 | + | 0.756447i | \(0.726934\pi\) | |||||||
\(600\) | 5.24180 | 0.213996 | ||||||||
\(601\) | −2.33741 | −0.0953451 | −0.0476725 | − | 0.998863i | \(-0.515180\pi\) | ||||
−0.0476725 | + | 0.998863i | \(0.515180\pi\) | |||||||
\(602\) | −38.0448 | −1.55059 | ||||||||
\(603\) | −13.9141 | −0.566624 | ||||||||
\(604\) | −17.6494 | −0.718145 | ||||||||
\(605\) | −7.34677 | −0.298689 | ||||||||
\(606\) | −17.9079 | −0.727457 | ||||||||
\(607\) | 18.4430 | 0.748580 | 0.374290 | − | 0.927312i | \(-0.377886\pi\) | ||||
0.374290 | + | 0.927312i | \(0.377886\pi\) | |||||||
\(608\) | −44.9883 | −1.82452 | ||||||||
\(609\) | −15.7025 | −0.636297 | ||||||||
\(610\) | −0.766739 | −0.0310444 | ||||||||
\(611\) | −5.45838 | −0.220822 | ||||||||
\(612\) | −2.58002 | −0.104291 | ||||||||
\(613\) | −6.22344 | −0.251362 | −0.125681 | − | 0.992071i | \(-0.540112\pi\) | ||||
−0.125681 | + | 0.992071i | \(0.540112\pi\) | |||||||
\(614\) | 36.4231 | 1.46992 | ||||||||
\(615\) | 8.80463 | 0.355037 | ||||||||
\(616\) | −13.4920 | −0.543610 | ||||||||
\(617\) | 29.8564 | 1.20197 | 0.600986 | − | 0.799260i | \(-0.294775\pi\) | ||||
0.600986 | + | 0.799260i | \(0.294775\pi\) | |||||||
\(618\) | −9.89688 | −0.398111 | ||||||||
\(619\) | 14.0071 | 0.562992 | 0.281496 | − | 0.959562i | \(-0.409169\pi\) | ||||
0.281496 | + | 0.959562i | \(0.409169\pi\) | |||||||
\(620\) | −8.26572 | −0.331959 | ||||||||
\(621\) | −3.68733 | −0.147968 | ||||||||
\(622\) | −16.4881 | −0.661114 | ||||||||
\(623\) | 0.225885 | 0.00904991 | ||||||||
\(624\) | −2.04705 | −0.0819474 | ||||||||
\(625\) | 13.9465 | 0.557860 | ||||||||
\(626\) | 27.0597 | 1.08152 | ||||||||
\(627\) | 25.2301 | 1.00759 | ||||||||
\(628\) | −2.58002 | −0.102954 | ||||||||
\(629\) | −1.04286 | −0.0415817 | ||||||||
\(630\) | −4.66373 | −0.185807 | ||||||||
\(631\) | 32.0368 | 1.27537 | 0.637683 | − | 0.770299i | \(-0.279893\pi\) | ||||
0.637683 | + | 0.770299i | \(0.279893\pi\) | |||||||
\(632\) | 15.2401 | 0.606217 | ||||||||
\(633\) | −15.3455 | −0.609929 | ||||||||
\(634\) | −31.1054 | −1.23535 | ||||||||
\(635\) | 15.7368 | 0.624495 | ||||||||
\(636\) | 17.9845 | 0.713132 | ||||||||
\(637\) | −0.727203 | −0.0288128 | ||||||||
\(638\) | 59.7746 | 2.36650 | ||||||||
\(639\) | 1.26017 | 0.0498516 | ||||||||
\(640\) | −8.38619 | −0.331493 | ||||||||
\(641\) | 4.57156 | 0.180566 | 0.0902830 | − | 0.995916i | \(-0.471223\pi\) | ||||
0.0902830 | + | 0.995916i | \(0.471223\pi\) | |||||||
\(642\) | 18.3897 | 0.725784 | ||||||||
\(643\) | 17.4894 | 0.689715 | 0.344857 | − | 0.938655i | \(-0.387927\pi\) | ||||
0.344857 | + | 0.938655i | \(0.387927\pi\) | |||||||
\(644\) | 23.5168 | 0.926692 | ||||||||
\(645\) | 6.33980 | 0.249630 | ||||||||
\(646\) | −12.2799 | −0.483146 | ||||||||
\(647\) | 20.7390 | 0.815333 | 0.407666 | − | 0.913131i | \(-0.366343\pi\) | ||||
0.407666 | + | 0.913131i | \(0.366343\pi\) | |||||||
\(648\) | −1.24130 | −0.0487629 | ||||||||
\(649\) | 1.11350 | 0.0437086 | ||||||||
\(650\) | 7.38944 | 0.289838 | ||||||||
\(651\) | −8.98346 | −0.352090 | ||||||||
\(652\) | 12.8280 | 0.502383 | ||||||||
\(653\) | 16.1630 | 0.632505 | 0.316253 | − | 0.948675i | \(-0.397575\pi\) | ||||
0.316253 | + | 0.948675i | \(0.397575\pi\) | |||||||
\(654\) | −20.8721 | −0.816165 | ||||||||
\(655\) | −0.442333 | −0.0172834 | ||||||||
\(656\) | 25.0039 | 0.976239 | ||||||||
\(657\) | 2.46325 | 0.0961004 | ||||||||
\(658\) | −35.3156 | −1.37674 | ||||||||
\(659\) | 1.39224 | 0.0542338 | 0.0271169 | − | 0.999632i | \(-0.491367\pi\) | ||||
0.0271169 | + | 0.999632i | \(0.491367\pi\) | |||||||
\(660\) | 10.0009 | 0.389283 | ||||||||
\(661\) | 25.6166 | 0.996370 | 0.498185 | − | 0.867071i | \(-0.334000\pi\) | ||||
0.498185 | + | 0.867071i | \(0.334000\pi\) | |||||||
\(662\) | 25.6374 | 0.996425 | ||||||||
\(663\) | −0.817662 | −0.0317554 | ||||||||
\(664\) | −15.2917 | −0.593432 | ||||||||
\(665\) | −12.5043 | −0.484897 | ||||||||
\(666\) | −2.23183 | −0.0864817 | ||||||||
\(667\) | −23.4227 | −0.906932 | ||||||||
\(668\) | 7.04220 | 0.272471 | ||||||||
\(669\) | −3.33836 | −0.129069 | ||||||||
\(670\) | −26.2509 | −1.01416 | ||||||||
\(671\) | 1.78696 | 0.0689849 | ||||||||
\(672\) | −19.3813 | −0.747648 | ||||||||
\(673\) | 46.9033 | 1.80799 | 0.903994 | − | 0.427545i | \(-0.140621\pi\) | ||||
0.903994 | + | 0.427545i | \(0.140621\pi\) | |||||||
\(674\) | 9.72866 | 0.374734 | ||||||||
\(675\) | −4.22283 | −0.162537 | ||||||||
\(676\) | −31.8153 | −1.22367 | ||||||||
\(677\) | 6.16514 | 0.236946 | 0.118473 | − | 0.992957i | \(-0.462200\pi\) | ||||
0.118473 | + | 0.992957i | \(0.462200\pi\) | |||||||
\(678\) | 26.0135 | 0.999044 | ||||||||
\(679\) | −0.301199 | −0.0115590 | ||||||||
\(680\) | −1.09429 | −0.0419642 | ||||||||
\(681\) | 1.51252 | 0.0579600 | ||||||||
\(682\) | 34.1973 | 1.30948 | ||||||||
\(683\) | 26.1733 | 1.00149 | 0.500747 | − | 0.865593i | \(-0.333059\pi\) | ||||
0.500747 | + | 0.865593i | \(0.333059\pi\) | |||||||
\(684\) | −14.8042 | −0.566051 | ||||||||
\(685\) | 2.62108 | 0.100146 | ||||||||
\(686\) | −41.7368 | −1.59352 | ||||||||
\(687\) | 3.65826 | 0.139571 | ||||||||
\(688\) | 18.0042 | 0.686403 | ||||||||
\(689\) | 5.69966 | 0.217140 | ||||||||
\(690\) | −6.95669 | −0.264837 | ||||||||
\(691\) | −18.0459 | −0.686497 | −0.343248 | − | 0.939245i | \(-0.611527\pi\) | ||||
−0.343248 | + | 0.939245i | \(0.611527\pi\) | |||||||
\(692\) | 22.9318 | 0.871736 | ||||||||
\(693\) | 10.8693 | 0.412890 | ||||||||
\(694\) | −26.5525 | −1.00792 | ||||||||
\(695\) | −1.50618 | −0.0571327 | ||||||||
\(696\) | −7.88500 | −0.298880 | ||||||||
\(697\) | 9.98744 | 0.378301 | ||||||||
\(698\) | −22.4340 | −0.849138 | ||||||||
\(699\) | −1.12286 | −0.0424704 | ||||||||
\(700\) | 26.9321 | 1.01794 | ||||||||
\(701\) | 22.6827 | 0.856713 | 0.428357 | − | 0.903610i | \(-0.359093\pi\) | ||||
0.428357 | + | 0.903610i | \(0.359093\pi\) | |||||||
\(702\) | −1.74988 | −0.0660448 | ||||||||
\(703\) | −5.98396 | −0.225689 | ||||||||
\(704\) | 51.7624 | 1.95087 | ||||||||
\(705\) | 5.88500 | 0.221642 | ||||||||
\(706\) | 41.5229 | 1.56273 | ||||||||
\(707\) | −20.6849 | −0.777935 | ||||||||
\(708\) | −0.653363 | −0.0245549 | ||||||||
\(709\) | 47.1433 | 1.77051 | 0.885253 | − | 0.465110i | \(-0.153985\pi\) | ||||
0.885253 | + | 0.465110i | \(0.153985\pi\) | |||||||
\(710\) | 2.37750 | 0.0892259 | ||||||||
\(711\) | −12.2775 | −0.460443 | ||||||||
\(712\) | 0.113428 | 0.00425091 | ||||||||
\(713\) | −13.4003 | −0.501844 | ||||||||
\(714\) | −5.29026 | −0.197983 | ||||||||
\(715\) | 3.16948 | 0.118532 | ||||||||
\(716\) | 5.47909 | 0.204763 | ||||||||
\(717\) | 2.05527 | 0.0767553 | ||||||||
\(718\) | 2.14128 | 0.0799117 | ||||||||
\(719\) | 3.26137 | 0.121629 | 0.0608143 | − | 0.998149i | \(-0.480630\pi\) | ||||
0.0608143 | + | 0.998149i | \(0.480630\pi\) | |||||||
\(720\) | 2.20704 | 0.0822516 | ||||||||
\(721\) | −11.4316 | −0.425736 | ||||||||
\(722\) | −29.8001 | −1.10905 | ||||||||
\(723\) | −9.03883 | −0.336158 | ||||||||
\(724\) | −1.00830 | −0.0374732 | ||||||||
\(725\) | −26.8244 | −0.996232 | ||||||||
\(726\) | −17.8350 | −0.661919 | ||||||||
\(727\) | 6.26372 | 0.232309 | 0.116154 | − | 0.993231i | \(-0.462943\pi\) | ||||
0.116154 | + | 0.993231i | \(0.462943\pi\) | |||||||
\(728\) | 2.50896 | 0.0929882 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 4.64728 | 0.172003 | ||||||||
\(731\) | 7.19149 | 0.265987 | ||||||||
\(732\) | −1.04853 | −0.0387547 | ||||||||
\(733\) | −34.9714 | −1.29170 | −0.645849 | − | 0.763465i | \(-0.723497\pi\) | ||||
−0.645849 | + | 0.763465i | \(0.723497\pi\) | |||||||
\(734\) | 52.6283 | 1.94255 | ||||||||
\(735\) | 0.784041 | 0.0289198 | ||||||||
\(736\) | −28.9102 | −1.06564 | ||||||||
\(737\) | 61.1803 | 2.25361 | ||||||||
\(738\) | 21.3741 | 0.786792 | ||||||||
\(739\) | −20.0758 | −0.738501 | −0.369250 | − | 0.929330i | \(-0.620386\pi\) | ||||
−0.369250 | + | 0.929330i | \(0.620386\pi\) | |||||||
\(740\) | −2.37196 | −0.0871950 | ||||||||
\(741\) | −4.69174 | −0.172356 | ||||||||
\(742\) | 36.8767 | 1.35379 | ||||||||
\(743\) | −8.89429 | −0.326300 | −0.163150 | − | 0.986601i | \(-0.552165\pi\) | ||||
−0.163150 | + | 0.986601i | \(0.552165\pi\) | |||||||
\(744\) | −4.51105 | −0.165383 | ||||||||
\(745\) | −5.31965 | −0.194897 | ||||||||
\(746\) | −36.2171 | −1.32600 | ||||||||
\(747\) | 12.3191 | 0.450732 | ||||||||
\(748\) | 11.3444 | 0.414792 | ||||||||
\(749\) | 21.2415 | 0.776146 | ||||||||
\(750\) | −17.4002 | −0.635366 | ||||||||
\(751\) | 22.2596 | 0.812264 | 0.406132 | − | 0.913814i | \(-0.366877\pi\) | ||||
0.406132 | + | 0.913814i | \(0.366877\pi\) | |||||||
\(752\) | 16.7126 | 0.609445 | ||||||||
\(753\) | −4.94002 | −0.180024 | ||||||||
\(754\) | −11.1156 | −0.404806 | ||||||||
\(755\) | 6.03066 | 0.219478 | ||||||||
\(756\) | −6.37773 | −0.231956 | ||||||||
\(757\) | 11.8905 | 0.432169 | 0.216084 | − | 0.976375i | \(-0.430671\pi\) | ||||
0.216084 | + | 0.976375i | \(0.430671\pi\) | |||||||
\(758\) | 80.0220 | 2.90653 | ||||||||
\(759\) | 16.2133 | 0.588504 | ||||||||
\(760\) | −6.27905 | −0.227765 | ||||||||
\(761\) | −0.466621 | −0.0169150 | −0.00845749 | − | 0.999964i | \(-0.502692\pi\) | ||||
−0.00845749 | + | 0.999964i | \(0.502692\pi\) | |||||||
\(762\) | 38.2026 | 1.38393 | ||||||||
\(763\) | −24.1088 | −0.872798 | ||||||||
\(764\) | 48.4359 | 1.75235 | ||||||||
\(765\) | 0.881570 | 0.0318732 | ||||||||
\(766\) | 22.5697 | 0.815477 | ||||||||
\(767\) | −0.207064 | −0.00747666 | ||||||||
\(768\) | 3.18605 | 0.114967 | ||||||||
\(769\) | −2.40136 | −0.0865952 | −0.0432976 | − | 0.999062i | \(-0.513786\pi\) | ||||
−0.0432976 | + | 0.999062i | \(0.513786\pi\) | |||||||
\(770\) | 20.5065 | 0.739003 | ||||||||
\(771\) | 24.1712 | 0.870506 | ||||||||
\(772\) | 38.8697 | 1.39895 | ||||||||
\(773\) | −8.47913 | −0.304973 | −0.152487 | − | 0.988306i | \(-0.548728\pi\) | ||||
−0.152487 | + | 0.988306i | \(0.548728\pi\) | |||||||
\(774\) | 15.3905 | 0.553200 | ||||||||
\(775\) | −15.3463 | −0.551257 | ||||||||
\(776\) | −0.151247 | −0.00542946 | ||||||||
\(777\) | −2.57793 | −0.0924827 | ||||||||
\(778\) | 10.7740 | 0.386268 | ||||||||
\(779\) | 57.3080 | 2.05327 | ||||||||
\(780\) | −1.85975 | −0.0665896 | ||||||||
\(781\) | −5.54100 | −0.198272 | ||||||||
\(782\) | −7.89125 | −0.282191 | ||||||||
\(783\) | 6.35222 | 0.227010 | ||||||||
\(784\) | 2.22657 | 0.0795203 | ||||||||
\(785\) | 0.881570 | 0.0314646 | ||||||||
\(786\) | −1.07381 | −0.0383014 | ||||||||
\(787\) | −17.7224 | −0.631734 | −0.315867 | − | 0.948804i | \(-0.602295\pi\) | ||||
−0.315867 | + | 0.948804i | \(0.602295\pi\) | |||||||
\(788\) | −64.1758 | −2.28617 | ||||||||
\(789\) | 19.7946 | 0.704705 | ||||||||
\(790\) | −23.1633 | −0.824114 | ||||||||
\(791\) | 30.0475 | 1.06837 | ||||||||
\(792\) | 5.45801 | 0.193942 | ||||||||
\(793\) | −0.332300 | −0.0118003 | ||||||||
\(794\) | −65.4840 | −2.32394 | ||||||||
\(795\) | −6.14514 | −0.217946 | ||||||||
\(796\) | 34.6886 | 1.22951 | ||||||||
\(797\) | 0.472084 | 0.0167221 | 0.00836104 | − | 0.999965i | \(-0.497339\pi\) | ||||
0.00836104 | + | 0.999965i | \(0.497339\pi\) | |||||||
\(798\) | −30.3555 | −1.07457 | ||||||||
\(799\) | 6.67559 | 0.236165 | ||||||||
\(800\) | −33.1088 | −1.17057 | ||||||||
\(801\) | −0.0913787 | −0.00322871 | ||||||||
\(802\) | −47.0579 | −1.66167 | ||||||||
\(803\) | −10.8309 | −0.382215 | ||||||||
\(804\) | −35.8985 | −1.26604 | ||||||||
\(805\) | −8.03548 | −0.283214 | ||||||||
\(806\) | −6.35928 | −0.223996 | ||||||||
\(807\) | 32.5751 | 1.14670 | ||||||||
\(808\) | −10.3869 | −0.365411 | ||||||||
\(809\) | −4.08901 | −0.143762 | −0.0718810 | − | 0.997413i | \(-0.522900\pi\) | ||||
−0.0718810 | + | 0.997413i | \(0.522900\pi\) | |||||||
\(810\) | 1.88665 | 0.0662900 | ||||||||
\(811\) | −38.6292 | −1.35645 | −0.678227 | − | 0.734853i | \(-0.737251\pi\) | ||||
−0.678227 | + | 0.734853i | \(0.737251\pi\) | |||||||
\(812\) | −40.5127 | −1.42172 | ||||||||
\(813\) | 21.5603 | 0.756154 | ||||||||
\(814\) | 9.81340 | 0.343959 | ||||||||
\(815\) | −4.38321 | −0.153537 | ||||||||
\(816\) | 2.50354 | 0.0876413 | ||||||||
\(817\) | 41.2648 | 1.44367 | ||||||||
\(818\) | −59.8368 | −2.09215 | ||||||||
\(819\) | −2.02123 | −0.0706276 | ||||||||
\(820\) | 22.7161 | 0.793281 | ||||||||
\(821\) | −16.4600 | −0.574457 | −0.287228 | − | 0.957862i | \(-0.592734\pi\) | ||||
−0.287228 | + | 0.957862i | \(0.592734\pi\) | |||||||
\(822\) | 6.36294 | 0.221933 | ||||||||
\(823\) | 35.9421 | 1.25286 | 0.626431 | − | 0.779477i | \(-0.284515\pi\) | ||||
0.626431 | + | 0.779477i | \(0.284515\pi\) | |||||||
\(824\) | −5.74039 | −0.199976 | ||||||||
\(825\) | 18.5679 | 0.646450 | ||||||||
\(826\) | −1.33970 | −0.0466142 | ||||||||
\(827\) | −27.3981 | −0.952725 | −0.476362 | − | 0.879249i | \(-0.658045\pi\) | ||||
−0.476362 | + | 0.879249i | \(0.658045\pi\) | |||||||
\(828\) | −9.51339 | −0.330613 | ||||||||
\(829\) | −1.58689 | −0.0551149 | −0.0275575 | − | 0.999620i | \(-0.508773\pi\) | ||||
−0.0275575 | + | 0.999620i | \(0.508773\pi\) | |||||||
\(830\) | 23.2417 | 0.806733 | ||||||||
\(831\) | −27.0378 | −0.937930 | ||||||||
\(832\) | −9.62566 | −0.333710 | ||||||||
\(833\) | 0.889369 | 0.0308148 | ||||||||
\(834\) | −3.65640 | −0.126611 | ||||||||
\(835\) | −2.40626 | −0.0832719 | ||||||||
\(836\) | 65.0941 | 2.25133 | ||||||||
\(837\) | 3.63413 | 0.125614 | ||||||||
\(838\) | −72.4509 | −2.50277 | ||||||||
\(839\) | 45.5689 | 1.57321 | 0.786607 | − | 0.617454i | \(-0.211836\pi\) | ||||
0.786607 | + | 0.617454i | \(0.211836\pi\) | |||||||
\(840\) | −2.70506 | −0.0933333 | ||||||||
\(841\) | 11.3506 | 0.391401 | ||||||||
\(842\) | 70.2449 | 2.42080 | ||||||||
\(843\) | −26.2192 | −0.903036 | ||||||||
\(844\) | −39.5917 | −1.36280 | ||||||||
\(845\) | 10.8710 | 0.373974 | ||||||||
\(846\) | 14.2864 | 0.491177 | ||||||||
\(847\) | −20.6007 | −0.707849 | ||||||||
\(848\) | −17.4514 | −0.599282 | ||||||||
\(849\) | 19.1415 | 0.656934 | ||||||||
\(850\) | −9.03728 | −0.309976 | ||||||||
\(851\) | −3.84539 | −0.131818 | ||||||||
\(852\) | 3.25127 | 0.111387 | ||||||||
\(853\) | −15.1494 | −0.518705 | −0.259353 | − | 0.965783i | \(-0.583509\pi\) | ||||
−0.259353 | + | 0.965783i | \(0.583509\pi\) | |||||||
\(854\) | −2.14998 | −0.0735707 | ||||||||
\(855\) | 5.05845 | 0.172995 | ||||||||
\(856\) | 10.6664 | 0.364570 | ||||||||
\(857\) | 7.98397 | 0.272727 | 0.136364 | − | 0.990659i | \(-0.456458\pi\) | ||||
0.136364 | + | 0.990659i | \(0.456458\pi\) | |||||||
\(858\) | 7.69423 | 0.262677 | ||||||||
\(859\) | 10.7793 | 0.367783 | 0.183892 | − | 0.982947i | \(-0.441130\pi\) | ||||
0.183892 | + | 0.982947i | \(0.441130\pi\) | |||||||
\(860\) | 16.3568 | 0.557763 | ||||||||
\(861\) | 24.6886 | 0.841387 | ||||||||
\(862\) | 82.4710 | 2.80897 | ||||||||
\(863\) | −10.2889 | −0.350237 | −0.175119 | − | 0.984547i | \(-0.556031\pi\) | ||||
−0.175119 | + | 0.984547i | \(0.556031\pi\) | |||||||
\(864\) | 7.84041 | 0.266736 | ||||||||
\(865\) | −7.83559 | −0.266418 | ||||||||
\(866\) | −26.9964 | −0.917374 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −23.1775 | −0.786696 | ||||||||
\(869\) | 53.9844 | 1.83129 | ||||||||
\(870\) | 11.9844 | 0.406309 | ||||||||
\(871\) | −11.3770 | −0.385495 | ||||||||
\(872\) | −12.1063 | −0.409969 | ||||||||
\(873\) | 0.121846 | 0.00412386 | ||||||||
\(874\) | −45.2800 | −1.53162 | ||||||||
\(875\) | −20.0985 | −0.679454 | ||||||||
\(876\) | 6.35523 | 0.214723 | ||||||||
\(877\) | −44.0032 | −1.48588 | −0.742942 | − | 0.669356i | \(-0.766570\pi\) | ||||
−0.742942 | + | 0.669356i | \(0.766570\pi\) | |||||||
\(878\) | 16.9319 | 0.571425 | ||||||||
\(879\) | 27.8120 | 0.938075 | ||||||||
\(880\) | −9.70440 | −0.327135 | ||||||||
\(881\) | 4.27019 | 0.143866 | 0.0719331 | − | 0.997409i | \(-0.477083\pi\) | ||||
0.0719331 | + | 0.997409i | \(0.477083\pi\) | |||||||
\(882\) | 1.90334 | 0.0640887 | ||||||||
\(883\) | 16.6413 | 0.560025 | 0.280013 | − | 0.959996i | \(-0.409661\pi\) | ||||
0.280013 | + | 0.959996i | \(0.409661\pi\) | |||||||
\(884\) | −2.10958 | −0.0709530 | ||||||||
\(885\) | 0.223248 | 0.00750441 | ||||||||
\(886\) | −38.3522 | −1.28847 | ||||||||
\(887\) | 25.3148 | 0.849989 | 0.424994 | − | 0.905196i | \(-0.360276\pi\) | ||||
0.424994 | + | 0.905196i | \(0.360276\pi\) | |||||||
\(888\) | −1.29451 | −0.0434408 | ||||||||
\(889\) | 44.1268 | 1.47996 | ||||||||
\(890\) | −0.172399 | −0.00577884 | ||||||||
\(891\) | −4.39701 | −0.147306 | ||||||||
\(892\) | −8.61304 | −0.288386 | ||||||||
\(893\) | 38.3045 | 1.28181 | ||||||||
\(894\) | −12.9140 | −0.431908 | ||||||||
\(895\) | −1.87215 | −0.0625792 | ||||||||
\(896\) | −23.5153 | −0.785592 | ||||||||
\(897\) | −3.01499 | −0.100668 | ||||||||
\(898\) | 26.9373 | 0.898909 | ||||||||
\(899\) | 23.0848 | 0.769921 | ||||||||
\(900\) | −10.8950 | −0.363167 | ||||||||
\(901\) | −6.97068 | −0.232227 | ||||||||
\(902\) | −93.9823 | −3.12927 | ||||||||
\(903\) | 17.7772 | 0.591587 | ||||||||
\(904\) | 15.0884 | 0.501832 | ||||||||
\(905\) | 0.344527 | 0.0114525 | ||||||||
\(906\) | 14.6400 | 0.486382 | ||||||||
\(907\) | 41.6481 | 1.38290 | 0.691450 | − | 0.722424i | \(-0.256972\pi\) | ||||
0.691450 | + | 0.722424i | \(0.256972\pi\) | |||||||
\(908\) | 3.90234 | 0.129504 | ||||||||
\(909\) | 8.36778 | 0.277542 | ||||||||
\(910\) | −3.81335 | −0.126411 | ||||||||
\(911\) | 26.5065 | 0.878200 | 0.439100 | − | 0.898438i | \(-0.355297\pi\) | ||||
0.439100 | + | 0.898438i | \(0.355297\pi\) | |||||||
\(912\) | 14.3653 | 0.475683 | ||||||||
\(913\) | −54.1672 | −1.79267 | ||||||||
\(914\) | 51.5191 | 1.70410 | ||||||||
\(915\) | 0.358273 | 0.0118441 | ||||||||
\(916\) | 9.43839 | 0.311853 | ||||||||
\(917\) | −1.24033 | −0.0409592 | ||||||||
\(918\) | 2.14010 | 0.0706338 | ||||||||
\(919\) | 12.7801 | 0.421577 | 0.210789 | − | 0.977532i | \(-0.432397\pi\) | ||||
0.210789 | + | 0.977532i | \(0.432397\pi\) | |||||||
\(920\) | −4.03502 | −0.133031 | ||||||||
\(921\) | −17.0193 | −0.560807 | ||||||||
\(922\) | −19.3485 | −0.637207 | ||||||||
\(923\) | 1.03039 | 0.0339159 | ||||||||
\(924\) | 28.0430 | 0.922546 | ||||||||
\(925\) | −4.40384 | −0.144798 | ||||||||
\(926\) | 54.5613 | 1.79300 | ||||||||
\(927\) | 4.62450 | 0.151888 | ||||||||
\(928\) | 49.8040 | 1.63490 | ||||||||
\(929\) | −14.5892 | −0.478657 | −0.239328 | − | 0.970939i | \(-0.576927\pi\) | ||||
−0.239328 | + | 0.970939i | \(0.576927\pi\) | |||||||
\(930\) | 6.85632 | 0.224828 | ||||||||
\(931\) | 5.10320 | 0.167251 | ||||||||
\(932\) | −2.89700 | −0.0948944 | ||||||||
\(933\) | 7.70438 | 0.252230 | ||||||||
\(934\) | −36.1318 | −1.18227 | ||||||||
\(935\) | −3.87628 | −0.126768 | ||||||||
\(936\) | −1.01496 | −0.0331751 | ||||||||
\(937\) | 25.0496 | 0.818333 | 0.409167 | − | 0.912460i | \(-0.365819\pi\) | ||||
0.409167 | + | 0.912460i | \(0.365819\pi\) | |||||||
\(938\) | −73.6089 | −2.40342 | ||||||||
\(939\) | −12.6441 | −0.412626 | ||||||||
\(940\) | 15.1834 | 0.495228 | ||||||||
\(941\) | 56.2836 | 1.83479 | 0.917396 | − | 0.397975i | \(-0.130287\pi\) | ||||
0.917396 | + | 0.397975i | \(0.130287\pi\) | |||||||
\(942\) | 2.14010 | 0.0697282 | ||||||||
\(943\) | 36.8270 | 1.19925 | ||||||||
\(944\) | 0.633994 | 0.0206348 | ||||||||
\(945\) | 2.17921 | 0.0708898 | ||||||||
\(946\) | −67.6723 | −2.20021 | ||||||||
\(947\) | −51.8711 | −1.68558 | −0.842792 | − | 0.538239i | \(-0.819090\pi\) | ||||
−0.842792 | + | 0.538239i | \(0.819090\pi\) | |||||||
\(948\) | −31.6762 | −1.02880 | ||||||||
\(949\) | 2.01410 | 0.0653806 | ||||||||
\(950\) | −51.8559 | −1.68243 | ||||||||
\(951\) | 14.5346 | 0.471316 | ||||||||
\(952\) | −3.06845 | −0.0994492 | ||||||||
\(953\) | 0.455325 | 0.0147494 | 0.00737472 | − | 0.999973i | \(-0.497653\pi\) | ||||
0.00737472 | + | 0.999973i | \(0.497653\pi\) | |||||||
\(954\) | −14.9179 | −0.482986 | ||||||||
\(955\) | −16.5501 | −0.535549 | ||||||||
\(956\) | 5.30263 | 0.171499 | ||||||||
\(957\) | −27.9308 | −0.902874 | ||||||||
\(958\) | 90.4939 | 2.92373 | ||||||||
\(959\) | 7.34965 | 0.237333 | ||||||||
\(960\) | 10.3780 | 0.334949 | ||||||||
\(961\) | −17.7931 | −0.573970 | ||||||||
\(962\) | −1.82488 | −0.0588366 | ||||||||
\(963\) | −8.59293 | −0.276903 | ||||||||
\(964\) | −23.3204 | −0.751098 | ||||||||
\(965\) | −13.2814 | −0.427544 | ||||||||
\(966\) | −19.5069 | −0.627625 | ||||||||
\(967\) | −3.46648 | −0.111474 | −0.0557372 | − | 0.998445i | \(-0.517751\pi\) | ||||
−0.0557372 | + | 0.998445i | \(0.517751\pi\) | |||||||
\(968\) | −10.3447 | −0.332490 | ||||||||
\(969\) | 5.73800 | 0.184331 | ||||||||
\(970\) | 0.229880 | 0.00738101 | ||||||||
\(971\) | 7.41569 | 0.237981 | 0.118990 | − | 0.992895i | \(-0.462034\pi\) | ||||
0.118990 | + | 0.992895i | \(0.462034\pi\) | |||||||
\(972\) | 2.58002 | 0.0827542 | ||||||||
\(973\) | −4.22341 | −0.135396 | ||||||||
\(974\) | −20.4248 | −0.654453 | ||||||||
\(975\) | −3.45285 | −0.110580 | ||||||||
\(976\) | 1.01745 | 0.0325676 | ||||||||
\(977\) | 32.7096 | 1.04647 | 0.523236 | − | 0.852188i | \(-0.324725\pi\) | ||||
0.523236 | + | 0.852188i | \(0.324725\pi\) | |||||||
\(978\) | −10.6407 | −0.340252 | ||||||||
\(979\) | 0.401794 | 0.0128414 | ||||||||
\(980\) | 2.02284 | 0.0646173 | ||||||||
\(981\) | 9.75288 | 0.311386 | ||||||||
\(982\) | 26.3634 | 0.841288 | ||||||||
\(983\) | −0.185502 | −0.00591659 | −0.00295829 | − | 0.999996i | \(-0.500942\pi\) | ||||
−0.00295829 | + | 0.999996i | \(0.500942\pi\) | |||||||
\(984\) | 12.3974 | 0.395215 | ||||||||
\(985\) | 21.9283 | 0.698694 | ||||||||
\(986\) | 13.5944 | 0.432933 | ||||||||
\(987\) | 16.5019 | 0.525260 | ||||||||
\(988\) | −12.1048 | −0.385105 | ||||||||
\(989\) | 26.5174 | 0.843205 | ||||||||
\(990\) | −8.29561 | −0.263652 | ||||||||
\(991\) | 30.0728 | 0.955295 | 0.477648 | − | 0.878551i | \(-0.341490\pi\) | ||||
0.477648 | + | 0.878551i | \(0.341490\pi\) | |||||||
\(992\) | 28.4931 | 0.904657 | ||||||||
\(993\) | −11.9795 | −0.380159 | ||||||||
\(994\) | 6.66663 | 0.211453 | ||||||||
\(995\) | −11.8528 | −0.375759 | ||||||||
\(996\) | 31.7835 | 1.00710 | ||||||||
\(997\) | 28.7287 | 0.909848 | 0.454924 | − | 0.890530i | \(-0.349666\pi\) | ||||
0.454924 | + | 0.890530i | \(0.349666\pi\) | |||||||
\(998\) | 43.0116 | 1.36151 | ||||||||
\(999\) | 1.04286 | 0.0329948 |
(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 | 8007.2.a.h.1.8 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.h.1.8 | ✓ | 56 | 1.1 | even | 1 | trivial |