Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2541,2,Mod(1,2541)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2541, 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("2541.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2541 = 3 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2541.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: | \(20.2899871536\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.7488.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.05896\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2541.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.32691 | −0.938266 | −0.469133 | − | 0.883128i | \(-0.655434\pi\) | ||||
−0.469133 | + | 0.883128i | \(0.655434\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.239314 | −0.119657 | ||||||||
\(5\) | 2.32691 | 1.04063 | 0.520313 | − | 0.853976i | \(-0.325815\pi\) | ||||
0.520313 | + | 0.853976i | \(0.325815\pi\) | |||||||
\(6\) | 1.32691 | 0.541708 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.97136 | 1.05054 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.08759 | −0.976383 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.239314 | 0.0690839 | ||||||||
\(13\) | −4.53759 | −1.25850 | −0.629250 | − | 0.777203i | \(-0.716638\pi\) | ||||
−0.629250 | + | 0.777203i | \(0.716638\pi\) | |||||||
\(14\) | 1.32691 | 0.354631 | ||||||||
\(15\) | −2.32691 | −0.600805 | ||||||||
\(16\) | −3.46410 | −0.866025 | ||||||||
\(17\) | 3.29827 | 0.799949 | 0.399974 | − | 0.916526i | \(-0.369019\pi\) | ||||
0.399974 | + | 0.916526i | \(0.369019\pi\) | |||||||
\(18\) | −1.32691 | −0.312755 | ||||||||
\(19\) | −1.08759 | −0.249511 | −0.124756 | − | 0.992187i | \(-0.539815\pi\) | ||||
−0.124756 | + | 0.992187i | \(0.539815\pi\) | |||||||
\(20\) | −0.556861 | −0.124518 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.29827 | 1.31328 | 0.656640 | − | 0.754204i | \(-0.271977\pi\) | ||||
0.656640 | + | 0.754204i | \(0.271977\pi\) | |||||||
\(24\) | −2.97136 | −0.606527 | ||||||||
\(25\) | 0.414503 | 0.0829007 | ||||||||
\(26\) | 6.02096 | 1.18081 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.239314 | 0.0452260 | ||||||||
\(29\) | −3.16583 | −0.587880 | −0.293940 | − | 0.955824i | \(-0.594967\pi\) | ||||
−0.293940 | + | 0.955824i | \(0.594967\pi\) | |||||||
\(30\) | 3.08759 | 0.563715 | ||||||||
\(31\) | −2.97136 | −0.533673 | −0.266836 | − | 0.963742i | \(-0.585978\pi\) | ||||
−0.266836 | + | 0.963742i | \(0.585978\pi\) | |||||||
\(32\) | −1.34618 | −0.237974 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.37651 | −0.750565 | ||||||||
\(35\) | −2.32691 | −0.393319 | ||||||||
\(36\) | −0.239314 | −0.0398856 | ||||||||
\(37\) | 1.70342 | 0.280040 | 0.140020 | − | 0.990149i | \(-0.455283\pi\) | ||||
0.140020 | + | 0.990149i | \(0.455283\pi\) | |||||||
\(38\) | 1.44314 | 0.234108 | ||||||||
\(39\) | 4.53759 | 0.726595 | ||||||||
\(40\) | 6.91409 | 1.09321 | ||||||||
\(41\) | −4.90724 | −0.766382 | −0.383191 | − | 0.923669i | \(-0.625175\pi\) | ||||
−0.383191 | + | 0.923669i | \(0.625175\pi\) | |||||||
\(42\) | −1.32691 | −0.204746 | ||||||||
\(43\) | −8.38587 | −1.27883 | −0.639416 | − | 0.768861i | \(-0.720824\pi\) | ||||
−0.639416 | + | 0.768861i | \(0.720824\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.32691 | 0.346875 | ||||||||
\(46\) | −8.35723 | −1.23221 | ||||||||
\(47\) | −4.69825 | −0.685310 | −0.342655 | − | 0.939461i | \(-0.611326\pi\) | ||||
−0.342655 | + | 0.939461i | \(0.611326\pi\) | |||||||
\(48\) | 3.46410 | 0.500000 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −0.550008 | −0.0777829 | ||||||||
\(51\) | −3.29827 | −0.461851 | ||||||||
\(52\) | 1.08591 | 0.150588 | ||||||||
\(53\) | −4.98547 | −0.684808 | −0.342404 | − | 0.939553i | \(-0.611241\pi\) | ||||
−0.342404 | + | 0.939553i | \(0.611241\pi\) | |||||||
\(54\) | 1.32691 | 0.180569 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.97136 | −0.397065 | ||||||||
\(57\) | 1.08759 | 0.144055 | ||||||||
\(58\) | 4.20077 | 0.551587 | ||||||||
\(59\) | 10.0654 | 1.31040 | 0.655201 | − | 0.755454i | \(-0.272584\pi\) | ||||
0.655201 | + | 0.755454i | \(0.272584\pi\) | |||||||
\(60\) | 0.556861 | 0.0718905 | ||||||||
\(61\) | −1.74141 | −0.222965 | −0.111482 | − | 0.993766i | \(-0.535560\pi\) | ||||
−0.111482 | + | 0.993766i | \(0.535560\pi\) | |||||||
\(62\) | 3.94273 | 0.500727 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 8.71446 | 1.08931 | ||||||||
\(65\) | −10.5585 | −1.30963 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.44958 | −1.15445 | −0.577225 | − | 0.816585i | \(-0.695864\pi\) | ||||
−0.577225 | + | 0.816585i | \(0.695864\pi\) | |||||||
\(68\) | −0.789322 | −0.0957193 | ||||||||
\(69\) | −6.29827 | −0.758223 | ||||||||
\(70\) | 3.08759 | 0.369038 | ||||||||
\(71\) | 16.1593 | 1.91776 | 0.958878 | − | 0.283820i | \(-0.0916018\pi\) | ||||
0.958878 | + | 0.283820i | \(0.0916018\pi\) | |||||||
\(72\) | 2.97136 | 0.350179 | ||||||||
\(73\) | 14.4700 | 1.69358 | 0.846792 | − | 0.531924i | \(-0.178531\pi\) | ||||
0.846792 | + | 0.531924i | \(0.178531\pi\) | |||||||
\(74\) | −2.26028 | −0.262752 | ||||||||
\(75\) | −0.414503 | −0.0478627 | ||||||||
\(76\) | 0.260276 | 0.0298557 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.02096 | −0.681740 | ||||||||
\(79\) | −12.8359 | −1.44415 | −0.722074 | − | 0.691816i | \(-0.756811\pi\) | ||||
−0.722074 | + | 0.691816i | \(0.756811\pi\) | |||||||
\(80\) | −8.06065 | −0.901208 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.51146 | 0.719070 | ||||||||
\(83\) | 0.205514 | 0.0225581 | 0.0112790 | − | 0.999936i | \(-0.496410\pi\) | ||||
0.0112790 | + | 0.999936i | \(0.496410\pi\) | |||||||
\(84\) | −0.239314 | −0.0261113 | ||||||||
\(85\) | 7.67478 | 0.832447 | ||||||||
\(86\) | 11.1273 | 1.19989 | ||||||||
\(87\) | 3.16583 | 0.339412 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.93798 | 0.417425 | 0.208713 | − | 0.977977i | \(-0.433073\pi\) | ||||
0.208713 | + | 0.977977i | \(0.433073\pi\) | |||||||
\(90\) | −3.08759 | −0.325461 | ||||||||
\(91\) | 4.53759 | 0.475668 | ||||||||
\(92\) | −1.50726 | −0.157143 | ||||||||
\(93\) | 2.97136 | 0.308116 | ||||||||
\(94\) | 6.23415 | 0.643003 | ||||||||
\(95\) | −2.53073 | −0.259648 | ||||||||
\(96\) | 1.34618 | 0.137394 | ||||||||
\(97\) | 13.0444 | 1.32446 | 0.662231 | − | 0.749300i | \(-0.269610\pi\) | ||||
0.662231 | + | 0.749300i | \(0.269610\pi\) | |||||||
\(98\) | −1.32691 | −0.134038 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.0991963 | −0.00991963 | ||||||||
\(101\) | −7.01580 | −0.698098 | −0.349049 | − | 0.937104i | \(-0.613495\pi\) | ||||
−0.349049 | + | 0.937104i | \(0.613495\pi\) | |||||||
\(102\) | 4.37651 | 0.433339 | ||||||||
\(103\) | 7.36659 | 0.725852 | 0.362926 | − | 0.931818i | \(-0.381778\pi\) | ||||
0.362926 | + | 0.931818i | \(0.381778\pi\) | |||||||
\(104\) | −13.4828 | −1.32210 | ||||||||
\(105\) | 2.32691 | 0.227083 | ||||||||
\(106\) | 6.61527 | 0.642532 | ||||||||
\(107\) | −1.20899 | −0.116877 | −0.0584387 | − | 0.998291i | \(-0.518612\pi\) | ||||
−0.0584387 | + | 0.998291i | \(0.518612\pi\) | |||||||
\(108\) | 0.239314 | 0.0230280 | ||||||||
\(109\) | 15.8465 | 1.51782 | 0.758909 | − | 0.651196i | \(-0.225733\pi\) | ||||
0.758909 | + | 0.651196i | \(0.225733\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.70342 | −0.161681 | ||||||||
\(112\) | 3.46410 | 0.327327 | ||||||||
\(113\) | −18.4717 | −1.73767 | −0.868835 | − | 0.495103i | \(-0.835130\pi\) | ||||
−0.868835 | + | 0.495103i | \(0.835130\pi\) | |||||||
\(114\) | −1.44314 | −0.135162 | ||||||||
\(115\) | 14.6555 | 1.36663 | ||||||||
\(116\) | 0.757626 | 0.0703438 | ||||||||
\(117\) | −4.53759 | −0.419500 | ||||||||
\(118\) | −13.3559 | −1.22951 | ||||||||
\(119\) | −3.29827 | −0.302352 | ||||||||
\(120\) | −6.91409 | −0.631167 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 2.31069 | 0.209200 | ||||||||
\(123\) | 4.90724 | 0.442471 | ||||||||
\(124\) | 0.711088 | 0.0638576 | ||||||||
\(125\) | −10.6700 | −0.954357 | ||||||||
\(126\) | 1.32691 | 0.118210 | ||||||||
\(127\) | −16.0576 | −1.42488 | −0.712440 | − | 0.701733i | \(-0.752410\pi\) | ||||
−0.712440 | + | 0.701733i | \(0.752410\pi\) | |||||||
\(128\) | −8.87093 | −0.784087 | ||||||||
\(129\) | 8.38587 | 0.738335 | ||||||||
\(130\) | 14.0102 | 1.22878 | ||||||||
\(131\) | −19.2597 | −1.68273 | −0.841365 | − | 0.540467i | \(-0.818247\pi\) | ||||
−0.841365 | + | 0.540467i | \(0.818247\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.08759 | 0.0943064 | ||||||||
\(134\) | 12.5387 | 1.08318 | ||||||||
\(135\) | −2.32691 | −0.200268 | ||||||||
\(136\) | 9.80037 | 0.840375 | ||||||||
\(137\) | 5.24059 | 0.447733 | 0.223867 | − | 0.974620i | \(-0.428132\pi\) | ||||
0.223867 | + | 0.974620i | \(0.428132\pi\) | |||||||
\(138\) | 8.35723 | 0.711415 | ||||||||
\(139\) | −22.9872 | −1.94975 | −0.974873 | − | 0.222762i | \(-0.928493\pi\) | ||||
−0.974873 | + | 0.222762i | \(0.928493\pi\) | |||||||
\(140\) | 0.556861 | 0.0470633 | ||||||||
\(141\) | 4.69825 | 0.395664 | ||||||||
\(142\) | −21.4419 | −1.79936 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −3.46410 | −0.288675 | ||||||||
\(145\) | −7.36659 | −0.611762 | ||||||||
\(146\) | −19.2003 | −1.58903 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −0.407651 | −0.0335087 | ||||||||
\(149\) | 3.47305 | 0.284523 | 0.142262 | − | 0.989829i | \(-0.454563\pi\) | ||||
0.142262 | + | 0.989829i | \(0.454563\pi\) | |||||||
\(150\) | 0.550008 | 0.0449080 | ||||||||
\(151\) | 3.15760 | 0.256962 | 0.128481 | − | 0.991712i | \(-0.458990\pi\) | ||||
0.128481 | + | 0.991712i | \(0.458990\pi\) | |||||||
\(152\) | −3.23164 | −0.262121 | ||||||||
\(153\) | 3.29827 | 0.266650 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.91409 | −0.555353 | ||||||||
\(156\) | −1.08591 | −0.0869421 | ||||||||
\(157\) | 7.50726 | 0.599145 | 0.299572 | − | 0.954074i | \(-0.403156\pi\) | ||||
0.299572 | + | 0.954074i | \(0.403156\pi\) | |||||||
\(158\) | 17.0320 | 1.35499 | ||||||||
\(159\) | 4.98547 | 0.395374 | ||||||||
\(160\) | −3.13244 | −0.247641 | ||||||||
\(161\) | −6.29827 | −0.496373 | ||||||||
\(162\) | −1.32691 | −0.104252 | ||||||||
\(163\) | −14.3187 | −1.12153 | −0.560763 | − | 0.827976i | \(-0.689492\pi\) | ||||
−0.560763 | + | 0.827976i | \(0.689492\pi\) | |||||||
\(164\) | 1.17437 | 0.0917029 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.272698 | −0.0211655 | ||||||||
\(167\) | −13.1628 | −1.01857 | −0.509283 | − | 0.860599i | \(-0.670089\pi\) | ||||
−0.509283 | + | 0.860599i | \(0.670089\pi\) | |||||||
\(168\) | 2.97136 | 0.229246 | ||||||||
\(169\) | 7.58969 | 0.583823 | ||||||||
\(170\) | −10.1837 | −0.781057 | ||||||||
\(171\) | −1.08759 | −0.0831705 | ||||||||
\(172\) | 2.00685 | 0.153021 | ||||||||
\(173\) | −12.9479 | −0.984410 | −0.492205 | − | 0.870479i | \(-0.663809\pi\) | ||||
−0.492205 | + | 0.870479i | \(0.663809\pi\) | |||||||
\(174\) | −4.20077 | −0.318459 | ||||||||
\(175\) | −0.414503 | −0.0313335 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.0654 | −0.756562 | ||||||||
\(178\) | −5.22534 | −0.391656 | ||||||||
\(179\) | −18.7751 | −1.40332 | −0.701659 | − | 0.712513i | \(-0.747557\pi\) | ||||
−0.701659 | + | 0.712513i | \(0.747557\pi\) | |||||||
\(180\) | −0.556861 | −0.0415060 | ||||||||
\(181\) | −7.59696 | −0.564678 | −0.282339 | − | 0.959315i | \(-0.591110\pi\) | ||||
−0.282339 | + | 0.959315i | \(0.591110\pi\) | |||||||
\(182\) | −6.02096 | −0.446303 | ||||||||
\(183\) | 1.74141 | 0.128729 | ||||||||
\(184\) | 18.7145 | 1.37965 | ||||||||
\(185\) | 3.96369 | 0.291416 | ||||||||
\(186\) | −3.94273 | −0.289095 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1.12436 | 0.0820021 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 3.35805 | 0.243619 | ||||||||
\(191\) | −21.6059 | −1.56335 | −0.781674 | − | 0.623687i | \(-0.785634\pi\) | ||||
−0.781674 | + | 0.623687i | \(0.785634\pi\) | |||||||
\(192\) | −8.71446 | −0.628912 | ||||||||
\(193\) | −25.3968 | −1.82810 | −0.914051 | − | 0.405598i | \(-0.867063\pi\) | ||||
−0.914051 | + | 0.405598i | \(0.867063\pi\) | |||||||
\(194\) | −17.3088 | −1.24270 | ||||||||
\(195\) | 10.5585 | 0.756113 | ||||||||
\(196\) | −0.239314 | −0.0170938 | ||||||||
\(197\) | 6.79617 | 0.484207 | 0.242104 | − | 0.970250i | \(-0.422163\pi\) | ||||
0.242104 | + | 0.970250i | \(0.422163\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.2276 | −1.36301 | −0.681505 | − | 0.731814i | \(-0.738674\pi\) | ||||
−0.681505 | + | 0.731814i | \(0.738674\pi\) | |||||||
\(200\) | 1.23164 | 0.0870902 | ||||||||
\(201\) | 9.44958 | 0.666522 | ||||||||
\(202\) | 9.30932 | 0.655002 | ||||||||
\(203\) | 3.16583 | 0.222198 | ||||||||
\(204\) | 0.789322 | 0.0552636 | ||||||||
\(205\) | −11.4187 | −0.797517 | ||||||||
\(206\) | −9.77480 | −0.681042 | ||||||||
\(207\) | 6.29827 | 0.437760 | ||||||||
\(208\) | 15.7187 | 1.08989 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −3.08759 | −0.213064 | ||||||||
\(211\) | 12.1499 | 0.836436 | 0.418218 | − | 0.908347i | \(-0.362655\pi\) | ||||
0.418218 | + | 0.908347i | \(0.362655\pi\) | |||||||
\(212\) | 1.19309 | 0.0819419 | ||||||||
\(213\) | −16.1593 | −1.10722 | ||||||||
\(214\) | 1.60422 | 0.109662 | ||||||||
\(215\) | −19.5131 | −1.33079 | ||||||||
\(216\) | −2.97136 | −0.202176 | ||||||||
\(217\) | 2.97136 | 0.201709 | ||||||||
\(218\) | −21.0268 | −1.42412 | ||||||||
\(219\) | −14.4700 | −0.977791 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.9662 | −1.00674 | ||||||||
\(222\) | 2.26028 | 0.151700 | ||||||||
\(223\) | 13.9217 | 0.932264 | 0.466132 | − | 0.884715i | \(-0.345647\pi\) | ||||
0.466132 | + | 0.884715i | \(0.345647\pi\) | |||||||
\(224\) | 1.34618 | 0.0899456 | ||||||||
\(225\) | 0.414503 | 0.0276336 | ||||||||
\(226\) | 24.5102 | 1.63040 | ||||||||
\(227\) | 10.5593 | 0.700843 | 0.350422 | − | 0.936592i | \(-0.386038\pi\) | ||||
0.350422 | + | 0.936592i | \(0.386038\pi\) | |||||||
\(228\) | −0.260276 | −0.0172372 | ||||||||
\(229\) | −28.9118 | −1.91054 | −0.955271 | − | 0.295731i | \(-0.904437\pi\) | ||||
−0.955271 | + | 0.295731i | \(0.904437\pi\) | |||||||
\(230\) | −19.4465 | −1.28227 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.40683 | −0.617589 | ||||||||
\(233\) | 18.2551 | 1.19593 | 0.597966 | − | 0.801521i | \(-0.295976\pi\) | ||||
0.597966 | + | 0.801521i | \(0.295976\pi\) | |||||||
\(234\) | 6.02096 | 0.393603 | ||||||||
\(235\) | −10.9324 | −0.713151 | ||||||||
\(236\) | −2.40879 | −0.156799 | ||||||||
\(237\) | 12.8359 | 0.833779 | ||||||||
\(238\) | 4.37651 | 0.283687 | ||||||||
\(239\) | 2.03621 | 0.131711 | 0.0658557 | − | 0.997829i | \(-0.479022\pi\) | ||||
0.0658557 | + | 0.997829i | \(0.479022\pi\) | |||||||
\(240\) | 8.06065 | 0.520313 | ||||||||
\(241\) | 28.9345 | 1.86384 | 0.931918 | − | 0.362670i | \(-0.118135\pi\) | ||||
0.931918 | + | 0.362670i | \(0.118135\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0.416744 | 0.0266793 | ||||||||
\(245\) | 2.32691 | 0.148661 | ||||||||
\(246\) | −6.51146 | −0.415155 | ||||||||
\(247\) | 4.93506 | 0.314010 | ||||||||
\(248\) | −8.82901 | −0.560642 | ||||||||
\(249\) | −0.205514 | −0.0130239 | ||||||||
\(250\) | 14.1582 | 0.895440 | ||||||||
\(251\) | −27.7896 | −1.75407 | −0.877033 | − | 0.480430i | \(-0.840481\pi\) | ||||
−0.877033 | + | 0.480430i | \(0.840481\pi\) | |||||||
\(252\) | 0.239314 | 0.0150753 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 21.3070 | 1.33692 | ||||||||
\(255\) | −7.67478 | −0.480613 | ||||||||
\(256\) | −5.65801 | −0.353626 | ||||||||
\(257\) | 12.8265 | 0.800095 | 0.400047 | − | 0.916494i | \(-0.368994\pi\) | ||||
0.400047 | + | 0.916494i | \(0.368994\pi\) | |||||||
\(258\) | −11.1273 | −0.692754 | ||||||||
\(259\) | −1.70342 | −0.105845 | ||||||||
\(260\) | 2.52681 | 0.156706 | ||||||||
\(261\) | −3.16583 | −0.195960 | ||||||||
\(262\) | 25.5559 | 1.57885 | ||||||||
\(263\) | 2.55283 | 0.157414 | 0.0787072 | − | 0.996898i | \(-0.474921\pi\) | ||||
0.0787072 | + | 0.996898i | \(0.474921\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.6007 | −0.712628 | ||||||||
\(266\) | −1.44314 | −0.0884845 | ||||||||
\(267\) | −3.93798 | −0.241000 | ||||||||
\(268\) | 2.26141 | 0.138138 | ||||||||
\(269\) | 19.0274 | 1.16012 | 0.580061 | − | 0.814573i | \(-0.303029\pi\) | ||||
0.580061 | + | 0.814573i | \(0.303029\pi\) | |||||||
\(270\) | 3.08759 | 0.187905 | ||||||||
\(271\) | −10.3268 | −0.627307 | −0.313653 | − | 0.949538i | \(-0.601553\pi\) | ||||
−0.313653 | + | 0.949538i | \(0.601553\pi\) | |||||||
\(272\) | −11.4256 | −0.692776 | ||||||||
\(273\) | −4.53759 | −0.274627 | ||||||||
\(274\) | −6.95378 | −0.420093 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.50726 | 0.0907266 | ||||||||
\(277\) | −2.89957 | −0.174218 | −0.0871091 | − | 0.996199i | \(-0.527763\pi\) | ||||
−0.0871091 | + | 0.996199i | \(0.527763\pi\) | |||||||
\(278\) | 30.5019 | 1.82938 | ||||||||
\(279\) | −2.97136 | −0.177891 | ||||||||
\(280\) | −6.91409 | −0.413196 | ||||||||
\(281\) | −17.4209 | −1.03925 | −0.519623 | − | 0.854396i | \(-0.673928\pi\) | ||||
−0.519623 | + | 0.854396i | \(0.673928\pi\) | |||||||
\(282\) | −6.23415 | −0.371238 | ||||||||
\(283\) | −9.49232 | −0.564260 | −0.282130 | − | 0.959376i | \(-0.591041\pi\) | ||||
−0.282130 | + | 0.959376i | \(0.591041\pi\) | |||||||
\(284\) | −3.86714 | −0.229473 | ||||||||
\(285\) | 2.53073 | 0.149908 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.90724 | 0.289665 | ||||||||
\(288\) | −1.34618 | −0.0793246 | ||||||||
\(289\) | −6.12139 | −0.360082 | ||||||||
\(290\) | 9.77480 | 0.573996 | ||||||||
\(291\) | −13.0444 | −0.764678 | ||||||||
\(292\) | −3.46287 | −0.202649 | ||||||||
\(293\) | −3.27005 | −0.191039 | −0.0955193 | − | 0.995428i | \(-0.530451\pi\) | ||||
−0.0955193 | + | 0.995428i | \(0.530451\pi\) | |||||||
\(294\) | 1.32691 | 0.0773869 | ||||||||
\(295\) | 23.4213 | 1.36364 | ||||||||
\(296\) | 5.06147 | 0.294192 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.60842 | −0.266958 | ||||||||
\(299\) | −28.5790 | −1.65276 | ||||||||
\(300\) | 0.0991963 | 0.00572710 | ||||||||
\(301\) | 8.38587 | 0.483353 | ||||||||
\(302\) | −4.18985 | −0.241099 | ||||||||
\(303\) | 7.01580 | 0.403047 | ||||||||
\(304\) | 3.76754 | 0.216083 | ||||||||
\(305\) | −4.05211 | −0.232023 | ||||||||
\(306\) | −4.37651 | −0.250188 | ||||||||
\(307\) | 16.5841 | 0.946506 | 0.473253 | − | 0.880927i | \(-0.343080\pi\) | ||||
0.473253 | + | 0.880927i | \(0.343080\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.36659 | −0.419071 | ||||||||
\(310\) | 9.17437 | 0.521069 | ||||||||
\(311\) | −6.64098 | −0.376575 | −0.188288 | − | 0.982114i | \(-0.560294\pi\) | ||||
−0.188288 | + | 0.982114i | \(0.560294\pi\) | |||||||
\(312\) | 13.4828 | 0.763315 | ||||||||
\(313\) | −3.58663 | −0.202728 | −0.101364 | − | 0.994849i | \(-0.532321\pi\) | ||||
−0.101364 | + | 0.994849i | \(0.532321\pi\) | |||||||
\(314\) | −9.96145 | −0.562157 | ||||||||
\(315\) | −2.32691 | −0.131106 | ||||||||
\(316\) | 3.07180 | 0.172802 | ||||||||
\(317\) | −11.4017 | −0.640381 | −0.320191 | − | 0.947353i | \(-0.603747\pi\) | ||||
−0.320191 | + | 0.947353i | \(0.603747\pi\) | |||||||
\(318\) | −6.61527 | −0.370966 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 20.2778 | 1.13356 | ||||||||
\(321\) | 1.20899 | 0.0674792 | ||||||||
\(322\) | 8.35723 | 0.465730 | ||||||||
\(323\) | −3.58718 | −0.199596 | ||||||||
\(324\) | −0.239314 | −0.0132952 | ||||||||
\(325\) | −1.88085 | −0.104331 | ||||||||
\(326\) | 18.9996 | 1.05229 | ||||||||
\(327\) | −15.8465 | −0.876313 | ||||||||
\(328\) | −14.5812 | −0.805112 | ||||||||
\(329\) | 4.69825 | 0.259023 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.84006 | −0.375964 | −0.187982 | − | 0.982173i | \(-0.560195\pi\) | ||||
−0.187982 | + | 0.982173i | \(0.560195\pi\) | |||||||
\(332\) | −0.0491822 | −0.00269922 | ||||||||
\(333\) | 1.70342 | 0.0933466 | ||||||||
\(334\) | 17.4658 | 0.955686 | ||||||||
\(335\) | −21.9883 | −1.20135 | ||||||||
\(336\) | −3.46410 | −0.188982 | ||||||||
\(337\) | 8.40501 | 0.457850 | 0.228925 | − | 0.973444i | \(-0.426479\pi\) | ||||
0.228925 | + | 0.973444i | \(0.426479\pi\) | |||||||
\(338\) | −10.0708 | −0.547781 | ||||||||
\(339\) | 18.4717 | 1.00324 | ||||||||
\(340\) | −1.83668 | −0.0996079 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 1.44314 | 0.0780360 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −24.9175 | −1.34346 | ||||||||
\(345\) | −14.6555 | −0.789026 | ||||||||
\(346\) | 17.1807 | 0.923639 | ||||||||
\(347\) | −8.47346 | −0.454879 | −0.227440 | − | 0.973792i | \(-0.573035\pi\) | ||||
−0.227440 | + | 0.973792i | \(0.573035\pi\) | |||||||
\(348\) | −0.757626 | −0.0406130 | ||||||||
\(349\) | −16.0748 | −0.860462 | −0.430231 | − | 0.902719i | \(-0.641568\pi\) | ||||
−0.430231 | + | 0.902719i | \(0.641568\pi\) | |||||||
\(350\) | 0.550008 | 0.0293992 | ||||||||
\(351\) | 4.53759 | 0.242198 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.3786 | −0.712072 | −0.356036 | − | 0.934472i | \(-0.615872\pi\) | ||||
−0.356036 | + | 0.934472i | \(0.615872\pi\) | |||||||
\(354\) | 13.3559 | 0.709856 | ||||||||
\(355\) | 37.6012 | 1.99566 | ||||||||
\(356\) | −0.942413 | −0.0499478 | ||||||||
\(357\) | 3.29827 | 0.174563 | ||||||||
\(358\) | 24.9129 | 1.31669 | ||||||||
\(359\) | −27.1016 | −1.43037 | −0.715184 | − | 0.698936i | \(-0.753657\pi\) | ||||
−0.715184 | + | 0.698936i | \(0.753657\pi\) | |||||||
\(360\) | 6.91409 | 0.364405 | ||||||||
\(361\) | −17.8171 | −0.937744 | ||||||||
\(362\) | 10.0805 | 0.529818 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.08591 | −0.0569170 | ||||||||
\(365\) | 33.6703 | 1.76239 | ||||||||
\(366\) | −2.31069 | −0.120782 | ||||||||
\(367\) | −0.0252953 | −0.00132040 | −0.000660202 | − | 1.00000i | \(-0.500210\pi\) | ||||
−0.000660202 | 1.00000i | \(0.500210\pi\) | ||||||||
\(368\) | −21.8179 | −1.13733 | ||||||||
\(369\) | −4.90724 | −0.255461 | ||||||||
\(370\) | −5.25946 | −0.273426 | ||||||||
\(371\) | 4.98547 | 0.258833 | ||||||||
\(372\) | −0.711088 | −0.0368682 | ||||||||
\(373\) | 23.7038 | 1.22734 | 0.613669 | − | 0.789563i | \(-0.289693\pi\) | ||||
0.613669 | + | 0.789563i | \(0.289693\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.6700 | 0.550998 | ||||||||
\(376\) | −13.9602 | −0.719943 | ||||||||
\(377\) | 14.3652 | 0.739847 | ||||||||
\(378\) | −1.32691 | −0.0682488 | ||||||||
\(379\) | −29.0675 | −1.49310 | −0.746549 | − | 0.665331i | \(-0.768290\pi\) | ||||
−0.746549 | + | 0.665331i | \(0.768290\pi\) | |||||||
\(380\) | 0.605639 | 0.0310686 | ||||||||
\(381\) | 16.0576 | 0.822655 | ||||||||
\(382\) | 28.6691 | 1.46684 | ||||||||
\(383\) | 16.8650 | 0.861764 | 0.430882 | − | 0.902408i | \(-0.358203\pi\) | ||||
0.430882 | + | 0.902408i | \(0.358203\pi\) | |||||||
\(384\) | 8.87093 | 0.452693 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 33.6993 | 1.71525 | ||||||||
\(387\) | −8.38587 | −0.426278 | ||||||||
\(388\) | −3.12171 | −0.158481 | ||||||||
\(389\) | 13.0752 | 0.662938 | 0.331469 | − | 0.943466i | \(-0.392456\pi\) | ||||
0.331469 | + | 0.943466i | \(0.392456\pi\) | |||||||
\(390\) | −14.0102 | −0.709436 | ||||||||
\(391\) | 20.7734 | 1.05056 | ||||||||
\(392\) | 2.97136 | 0.150077 | ||||||||
\(393\) | 19.2597 | 0.971525 | ||||||||
\(394\) | −9.01790 | −0.454315 | ||||||||
\(395\) | −29.8679 | −1.50282 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.28891 | 0.0646886 | 0.0323443 | − | 0.999477i | \(-0.489703\pi\) | ||||
0.0323443 | + | 0.999477i | \(0.489703\pi\) | |||||||
\(398\) | 25.5133 | 1.27887 | ||||||||
\(399\) | −1.08759 | −0.0544478 | ||||||||
\(400\) | −1.43588 | −0.0717941 | ||||||||
\(401\) | 7.50643 | 0.374853 | 0.187427 | − | 0.982279i | \(-0.439985\pi\) | ||||
0.187427 | + | 0.982279i | \(0.439985\pi\) | |||||||
\(402\) | −12.5387 | −0.625375 | ||||||||
\(403\) | 13.4828 | 0.671627 | ||||||||
\(404\) | 1.67898 | 0.0835322 | ||||||||
\(405\) | 2.32691 | 0.115625 | ||||||||
\(406\) | −4.20077 | −0.208480 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −9.80037 | −0.485191 | ||||||||
\(409\) | 37.3746 | 1.84805 | 0.924027 | − | 0.382327i | \(-0.124877\pi\) | ||||
0.924027 | + | 0.382327i | \(0.124877\pi\) | |||||||
\(410\) | 15.1516 | 0.748283 | ||||||||
\(411\) | −5.24059 | −0.258499 | ||||||||
\(412\) | −1.76293 | −0.0868532 | ||||||||
\(413\) | −10.0654 | −0.495286 | ||||||||
\(414\) | −8.35723 | −0.410736 | ||||||||
\(415\) | 0.478211 | 0.0234745 | ||||||||
\(416\) | 6.10842 | 0.299490 | ||||||||
\(417\) | 22.9872 | 1.12569 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.0696 | 0.638491 | 0.319246 | − | 0.947672i | \(-0.396570\pi\) | ||||
0.319246 | + | 0.947672i | \(0.396570\pi\) | |||||||
\(420\) | −0.556861 | −0.0271720 | ||||||||
\(421\) | −21.3443 | −1.04026 | −0.520128 | − | 0.854088i | \(-0.674116\pi\) | ||||
−0.520128 | + | 0.854088i | \(0.674116\pi\) | |||||||
\(422\) | −16.1218 | −0.784799 | ||||||||
\(423\) | −4.69825 | −0.228437 | ||||||||
\(424\) | −14.8137 | −0.719415 | ||||||||
\(425\) | 1.36715 | 0.0663163 | ||||||||
\(426\) | 21.4419 | 1.03886 | ||||||||
\(427\) | 1.74141 | 0.0842728 | ||||||||
\(428\) | 0.289328 | 0.0139852 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 25.8922 | 1.24863 | ||||||||
\(431\) | 24.8042 | 1.19477 | 0.597387 | − | 0.801953i | \(-0.296206\pi\) | ||||
0.597387 | + | 0.801953i | \(0.296206\pi\) | |||||||
\(432\) | 3.46410 | 0.166667 | ||||||||
\(433\) | −25.9947 | −1.24923 | −0.624614 | − | 0.780934i | \(-0.714744\pi\) | ||||
−0.624614 | + | 0.780934i | \(0.714744\pi\) | |||||||
\(434\) | −3.94273 | −0.189257 | ||||||||
\(435\) | 7.36659 | 0.353201 | ||||||||
\(436\) | −3.79228 | −0.181617 | ||||||||
\(437\) | −6.84997 | −0.327678 | ||||||||
\(438\) | 19.2003 | 0.917428 | ||||||||
\(439\) | 0.615268 | 0.0293652 | 0.0146826 | − | 0.999892i | \(-0.495326\pi\) | ||||
0.0146826 | + | 0.999892i | \(0.495326\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 19.8588 | 0.944586 | ||||||||
\(443\) | −36.3307 | −1.72612 | −0.863062 | − | 0.505098i | \(-0.831456\pi\) | ||||
−0.863062 | + | 0.505098i | \(0.831456\pi\) | |||||||
\(444\) | 0.407651 | 0.0193462 | ||||||||
\(445\) | 9.16332 | 0.434383 | ||||||||
\(446\) | −18.4728 | −0.874711 | ||||||||
\(447\) | −3.47305 | −0.164269 | ||||||||
\(448\) | −8.71446 | −0.411720 | ||||||||
\(449\) | 28.5858 | 1.34905 | 0.674524 | − | 0.738253i | \(-0.264349\pi\) | ||||
0.674524 | + | 0.738253i | \(0.264349\pi\) | |||||||
\(450\) | −0.550008 | −0.0259276 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 4.42052 | 0.207924 | ||||||||
\(453\) | −3.15760 | −0.148357 | ||||||||
\(454\) | −14.0112 | −0.657578 | ||||||||
\(455\) | 10.5585 | 0.494992 | ||||||||
\(456\) | 3.23164 | 0.151335 | ||||||||
\(457\) | 39.2884 | 1.83783 | 0.918917 | − | 0.394451i | \(-0.129065\pi\) | ||||
0.918917 | + | 0.394451i | \(0.129065\pi\) | |||||||
\(458\) | 38.3633 | 1.79260 | ||||||||
\(459\) | −3.29827 | −0.153950 | ||||||||
\(460\) | −3.50726 | −0.163527 | ||||||||
\(461\) | −0.411163 | −0.0191498 | −0.00957489 | − | 0.999954i | \(-0.503048\pi\) | ||||
−0.00957489 | + | 0.999954i | \(0.503048\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.6179 | −0.818774 | −0.409387 | − | 0.912361i | \(-0.634257\pi\) | ||||
−0.409387 | + | 0.912361i | \(0.634257\pi\) | |||||||
\(464\) | 10.9668 | 0.509119 | ||||||||
\(465\) | 6.91409 | 0.320633 | ||||||||
\(466\) | −24.2229 | −1.12210 | ||||||||
\(467\) | −7.61248 | −0.352264 | −0.176132 | − | 0.984367i | \(-0.556358\pi\) | ||||
−0.176132 | + | 0.984367i | \(0.556358\pi\) | |||||||
\(468\) | 1.08591 | 0.0501960 | ||||||||
\(469\) | 9.44958 | 0.436341 | ||||||||
\(470\) | 14.5063 | 0.669125 | ||||||||
\(471\) | −7.50726 | −0.345916 | ||||||||
\(472\) | 29.9080 | 1.37663 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −17.0320 | −0.782306 | ||||||||
\(475\) | −0.450812 | −0.0206847 | ||||||||
\(476\) | 0.789322 | 0.0361785 | ||||||||
\(477\) | −4.98547 | −0.228269 | ||||||||
\(478\) | −2.70186 | −0.123580 | ||||||||
\(479\) | −34.7448 | −1.58753 | −0.793765 | − | 0.608225i | \(-0.791882\pi\) | ||||
−0.793765 | + | 0.608225i | \(0.791882\pi\) | |||||||
\(480\) | 3.13244 | 0.142976 | ||||||||
\(481\) | −7.72939 | −0.352430 | ||||||||
\(482\) | −38.3934 | −1.74877 | ||||||||
\(483\) | 6.29827 | 0.286581 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 30.3532 | 1.37827 | ||||||||
\(486\) | 1.32691 | 0.0601898 | ||||||||
\(487\) | 21.6667 | 0.981811 | 0.490906 | − | 0.871213i | \(-0.336666\pi\) | ||||
0.490906 | + | 0.871213i | \(0.336666\pi\) | |||||||
\(488\) | −5.17437 | −0.234233 | ||||||||
\(489\) | 14.3187 | 0.647513 | ||||||||
\(490\) | −3.08759 | −0.139483 | ||||||||
\(491\) | −13.3539 | −0.602653 | −0.301326 | − | 0.953521i | \(-0.597429\pi\) | ||||
−0.301326 | + | 0.953521i | \(0.597429\pi\) | |||||||
\(492\) | −1.17437 | −0.0529447 | ||||||||
\(493\) | −10.4418 | −0.470274 | ||||||||
\(494\) | −6.54837 | −0.294625 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.2931 | 0.462174 | ||||||||
\(497\) | −16.1593 | −0.724843 | ||||||||
\(498\) | 0.272698 | 0.0122199 | ||||||||
\(499\) | −19.5813 | −0.876579 | −0.438290 | − | 0.898834i | \(-0.644416\pi\) | ||||
−0.438290 | + | 0.898834i | \(0.644416\pi\) | |||||||
\(500\) | 2.55348 | 0.114195 | ||||||||
\(501\) | 13.1628 | 0.588069 | ||||||||
\(502\) | 36.8743 | 1.64578 | ||||||||
\(503\) | 16.7345 | 0.746153 | 0.373076 | − | 0.927801i | \(-0.378303\pi\) | ||||
0.373076 | + | 0.927801i | \(0.378303\pi\) | |||||||
\(504\) | −2.97136 | −0.132355 | ||||||||
\(505\) | −16.3251 | −0.726458 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.58969 | −0.337070 | ||||||||
\(508\) | 3.84280 | 0.170497 | ||||||||
\(509\) | −4.40431 | −0.195218 | −0.0976088 | − | 0.995225i | \(-0.531119\pi\) | ||||
−0.0976088 | + | 0.995225i | \(0.531119\pi\) | |||||||
\(510\) | 10.1837 | 0.450943 | ||||||||
\(511\) | −14.4700 | −0.640115 | ||||||||
\(512\) | 25.2495 | 1.11588 | ||||||||
\(513\) | 1.08759 | 0.0480185 | ||||||||
\(514\) | −17.0196 | −0.750702 | ||||||||
\(515\) | 17.1414 | 0.755340 | ||||||||
\(516\) | −2.00685 | −0.0883468 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 2.26028 | 0.0993108 | ||||||||
\(519\) | 12.9479 | 0.568349 | ||||||||
\(520\) | −31.3733 | −1.37581 | ||||||||
\(521\) | −42.9199 | −1.88035 | −0.940177 | − | 0.340686i | \(-0.889341\pi\) | ||||
−0.940177 | + | 0.340686i | \(0.889341\pi\) | |||||||
\(522\) | 4.20077 | 0.183862 | ||||||||
\(523\) | 9.54178 | 0.417233 | 0.208617 | − | 0.977998i | \(-0.433104\pi\) | ||||
0.208617 | + | 0.977998i | \(0.433104\pi\) | |||||||
\(524\) | 4.60912 | 0.201350 | ||||||||
\(525\) | 0.414503 | 0.0180904 | ||||||||
\(526\) | −3.38738 | −0.147697 | ||||||||
\(527\) | −9.80037 | −0.426911 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.6682 | 0.724706 | ||||||||
\(530\) | 15.3931 | 0.668635 | ||||||||
\(531\) | 10.0654 | 0.436801 | ||||||||
\(532\) | −0.260276 | −0.0112844 | ||||||||
\(533\) | 22.2670 | 0.964492 | ||||||||
\(534\) | 5.22534 | 0.226123 | ||||||||
\(535\) | −2.81321 | −0.121626 | ||||||||
\(536\) | −28.0781 | −1.21279 | ||||||||
\(537\) | 18.7751 | 0.810206 | ||||||||
\(538\) | −25.2476 | −1.08850 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.556861 | 0.0239635 | ||||||||
\(541\) | 12.3576 | 0.531297 | 0.265648 | − | 0.964070i | \(-0.414414\pi\) | ||||
0.265648 | + | 0.964070i | \(0.414414\pi\) | |||||||
\(542\) | 13.7027 | 0.588581 | ||||||||
\(543\) | 7.59696 | 0.326017 | ||||||||
\(544\) | −4.44008 | −0.190367 | ||||||||
\(545\) | 36.8733 | 1.57948 | ||||||||
\(546\) | 6.02096 | 0.257673 | ||||||||
\(547\) | 10.6187 | 0.454025 | 0.227012 | − | 0.973892i | \(-0.427104\pi\) | ||||
0.227012 | + | 0.973892i | \(0.427104\pi\) | |||||||
\(548\) | −1.25414 | −0.0535744 | ||||||||
\(549\) | −1.74141 | −0.0743217 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.44314 | 0.146683 | ||||||||
\(552\) | −18.7145 | −0.796541 | ||||||||
\(553\) | 12.8359 | 0.545836 | ||||||||
\(554\) | 3.84746 | 0.163463 | ||||||||
\(555\) | −3.96369 | −0.168249 | ||||||||
\(556\) | 5.50114 | 0.233300 | ||||||||
\(557\) | 17.2434 | 0.730627 | 0.365313 | − | 0.930885i | \(-0.380962\pi\) | ||||
0.365313 | + | 0.930885i | \(0.380962\pi\) | |||||||
\(558\) | 3.94273 | 0.166909 | ||||||||
\(559\) | 38.0516 | 1.60941 | ||||||||
\(560\) | 8.06065 | 0.340625 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 23.1160 | 0.975089 | ||||||||
\(563\) | −18.3349 | −0.772724 | −0.386362 | − | 0.922347i | \(-0.626268\pi\) | ||||
−0.386362 | + | 0.922347i | \(0.626268\pi\) | |||||||
\(564\) | −1.12436 | −0.0473439 | ||||||||
\(565\) | −42.9819 | −1.80826 | ||||||||
\(566\) | 12.5954 | 0.529426 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 48.0151 | 2.01467 | ||||||||
\(569\) | −13.3639 | −0.560246 | −0.280123 | − | 0.959964i | \(-0.590375\pi\) | ||||
−0.280123 | + | 0.959964i | \(0.590375\pi\) | |||||||
\(570\) | −3.35805 | −0.140653 | ||||||||
\(571\) | −8.21601 | −0.343829 | −0.171915 | − | 0.985112i | \(-0.554995\pi\) | ||||
−0.171915 | + | 0.985112i | \(0.554995\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.6059 | 0.902600 | ||||||||
\(574\) | −6.51146 | −0.271783 | ||||||||
\(575\) | 2.61066 | 0.108872 | ||||||||
\(576\) | 8.71446 | 0.363103 | ||||||||
\(577\) | 33.8566 | 1.40947 | 0.704734 | − | 0.709472i | \(-0.251066\pi\) | ||||
0.704734 | + | 0.709472i | \(0.251066\pi\) | |||||||
\(578\) | 8.12253 | 0.337853 | ||||||||
\(579\) | 25.3968 | 1.05546 | ||||||||
\(580\) | 1.76293 | 0.0732015 | ||||||||
\(581\) | −0.205514 | −0.00852614 | ||||||||
\(582\) | 17.3088 | 0.717472 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 42.9956 | 1.77917 | ||||||||
\(585\) | −10.5585 | −0.436542 | ||||||||
\(586\) | 4.33906 | 0.179245 | ||||||||
\(587\) | −2.51243 | −0.103699 | −0.0518495 | − | 0.998655i | \(-0.516512\pi\) | ||||
−0.0518495 | + | 0.998655i | \(0.516512\pi\) | |||||||
\(588\) | 0.239314 | 0.00986913 | ||||||||
\(589\) | 3.23164 | 0.133157 | ||||||||
\(590\) | −31.0779 | −1.27946 | ||||||||
\(591\) | −6.79617 | −0.279557 | ||||||||
\(592\) | −5.90080 | −0.242522 | ||||||||
\(593\) | 24.5112 | 1.00655 | 0.503277 | − | 0.864125i | \(-0.332128\pi\) | ||||
0.503277 | + | 0.864125i | \(0.332128\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.67478 | −0.314635 | ||||||||
\(596\) | −0.831148 | −0.0340451 | ||||||||
\(597\) | 19.2276 | 0.786934 | ||||||||
\(598\) | 37.9217 | 1.55073 | ||||||||
\(599\) | 32.2579 | 1.31802 | 0.659012 | − | 0.752133i | \(-0.270975\pi\) | ||||
0.659012 | + | 0.752133i | \(0.270975\pi\) | |||||||
\(600\) | −1.23164 | −0.0502815 | ||||||||
\(601\) | −34.3485 | −1.40110 | −0.700552 | − | 0.713601i | \(-0.747063\pi\) | ||||
−0.700552 | + | 0.713601i | \(0.747063\pi\) | |||||||
\(602\) | −11.1273 | −0.453514 | ||||||||
\(603\) | −9.44958 | −0.384816 | ||||||||
\(604\) | −0.755658 | −0.0307473 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9.30932 | −0.378165 | ||||||||
\(607\) | −16.6066 | −0.674042 | −0.337021 | − | 0.941497i | \(-0.609419\pi\) | ||||
−0.337021 | + | 0.941497i | \(0.609419\pi\) | |||||||
\(608\) | 1.46410 | 0.0593772 | ||||||||
\(609\) | −3.16583 | −0.128286 | ||||||||
\(610\) | 5.37677 | 0.217699 | ||||||||
\(611\) | 21.3187 | 0.862463 | ||||||||
\(612\) | −0.789322 | −0.0319064 | ||||||||
\(613\) | 12.8483 | 0.518939 | 0.259469 | − | 0.965751i | \(-0.416452\pi\) | ||||
0.259469 | + | 0.965751i | \(0.416452\pi\) | |||||||
\(614\) | −22.0056 | −0.888074 | ||||||||
\(615\) | 11.4187 | 0.460446 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.5521 | −0.746881 | −0.373441 | − | 0.927654i | \(-0.621822\pi\) | ||||
−0.373441 | + | 0.927654i | \(0.621822\pi\) | |||||||
\(618\) | 9.77480 | 0.393200 | ||||||||
\(619\) | 24.5919 | 0.988433 | 0.494217 | − | 0.869339i | \(-0.335455\pi\) | ||||
0.494217 | + | 0.869339i | \(0.335455\pi\) | |||||||
\(620\) | 1.65464 | 0.0664518 | ||||||||
\(621\) | −6.29827 | −0.252741 | ||||||||
\(622\) | 8.81197 | 0.353328 | ||||||||
\(623\) | −3.93798 | −0.157772 | ||||||||
\(624\) | −15.7187 | −0.629250 | ||||||||
\(625\) | −26.9007 | −1.07603 | ||||||||
\(626\) | 4.75913 | 0.190213 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.79659 | −0.0716918 | ||||||||
\(629\) | 5.61833 | 0.224017 | ||||||||
\(630\) | 3.08759 | 0.123013 | ||||||||
\(631\) | −41.8792 | −1.66719 | −0.833593 | − | 0.552379i | \(-0.813720\pi\) | ||||
−0.833593 | + | 0.552379i | \(0.813720\pi\) | |||||||
\(632\) | −38.1400 | −1.51713 | ||||||||
\(633\) | −12.1499 | −0.482916 | ||||||||
\(634\) | 15.1290 | 0.600848 | ||||||||
\(635\) | −37.3645 | −1.48277 | ||||||||
\(636\) | −1.19309 | −0.0473092 | ||||||||
\(637\) | −4.53759 | −0.179786 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 16.1593 | 0.639252 | ||||||||
\(640\) | −20.6418 | −0.815941 | ||||||||
\(641\) | −2.23529 | −0.0882885 | −0.0441442 | − | 0.999025i | \(-0.514056\pi\) | ||||
−0.0441442 | + | 0.999025i | \(0.514056\pi\) | |||||||
\(642\) | −1.60422 | −0.0633135 | ||||||||
\(643\) | −13.8690 | −0.546940 | −0.273470 | − | 0.961880i | \(-0.588171\pi\) | ||||
−0.273470 | + | 0.961880i | \(0.588171\pi\) | |||||||
\(644\) | 1.50726 | 0.0593945 | ||||||||
\(645\) | 19.5131 | 0.768329 | ||||||||
\(646\) | 4.75987 | 0.187274 | ||||||||
\(647\) | −8.04106 | −0.316127 | −0.158063 | − | 0.987429i | \(-0.550525\pi\) | ||||
−0.158063 | + | 0.987429i | \(0.550525\pi\) | |||||||
\(648\) | 2.97136 | 0.116726 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.49571 | 0.0978898 | ||||||||
\(651\) | −2.97136 | −0.116457 | ||||||||
\(652\) | 3.42666 | 0.134198 | ||||||||
\(653\) | −2.75480 | −0.107804 | −0.0539019 | − | 0.998546i | \(-0.517166\pi\) | ||||
−0.0539019 | + | 0.998546i | \(0.517166\pi\) | |||||||
\(654\) | 21.0268 | 0.822215 | ||||||||
\(655\) | −44.8156 | −1.75109 | ||||||||
\(656\) | 16.9992 | 0.663706 | ||||||||
\(657\) | 14.4700 | 0.564528 | ||||||||
\(658\) | −6.23415 | −0.243032 | ||||||||
\(659\) | 37.1797 | 1.44832 | 0.724159 | − | 0.689634i | \(-0.242228\pi\) | ||||
0.724159 | + | 0.689634i | \(0.242228\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.19963 | −0.0855556 | −0.0427778 | − | 0.999085i | \(-0.513621\pi\) | ||||
−0.0427778 | + | 0.999085i | \(0.513621\pi\) | |||||||
\(662\) | 9.07613 | 0.352754 | ||||||||
\(663\) | 14.9662 | 0.581239 | ||||||||
\(664\) | 0.610656 | 0.0236980 | ||||||||
\(665\) | 2.53073 | 0.0981376 | ||||||||
\(666\) | −2.26028 | −0.0875839 | ||||||||
\(667\) | −19.9393 | −0.772051 | ||||||||
\(668\) | 3.15003 | 0.121878 | ||||||||
\(669\) | −13.9217 | −0.538243 | ||||||||
\(670\) | 29.1765 | 1.12719 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1.34618 | −0.0519301 | ||||||||
\(673\) | 28.2877 | 1.09041 | 0.545205 | − | 0.838303i | \(-0.316452\pi\) | ||||
0.545205 | + | 0.838303i | \(0.316452\pi\) | |||||||
\(674\) | −11.1527 | −0.429585 | ||||||||
\(675\) | −0.414503 | −0.0159542 | ||||||||
\(676\) | −1.81632 | −0.0698584 | ||||||||
\(677\) | 11.1440 | 0.428300 | 0.214150 | − | 0.976801i | \(-0.431302\pi\) | ||||
0.214150 | + | 0.976801i | \(0.431302\pi\) | |||||||
\(678\) | −24.5102 | −0.941309 | ||||||||
\(679\) | −13.0444 | −0.500599 | ||||||||
\(680\) | 22.8046 | 0.874515 | ||||||||
\(681\) | −10.5593 | −0.404632 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 45.6300 | 1.74598 | 0.872992 | − | 0.487735i | \(-0.162177\pi\) | ||||
0.872992 | + | 0.487735i | \(0.162177\pi\) | |||||||
\(684\) | 0.260276 | 0.00995191 | ||||||||
\(685\) | 12.1944 | 0.465923 | ||||||||
\(686\) | 1.32691 | 0.0506616 | ||||||||
\(687\) | 28.9118 | 1.10305 | ||||||||
\(688\) | 29.0495 | 1.10750 | ||||||||
\(689\) | 22.6220 | 0.861830 | ||||||||
\(690\) | 19.4465 | 0.740316 | ||||||||
\(691\) | 11.1889 | 0.425645 | 0.212823 | − | 0.977091i | \(-0.431734\pi\) | ||||
0.212823 | + | 0.977091i | \(0.431734\pi\) | |||||||
\(692\) | 3.09861 | 0.117791 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.2435 | 0.426798 | ||||||||
\(695\) | −53.4890 | −2.02895 | ||||||||
\(696\) | 9.40683 | 0.356565 | ||||||||
\(697\) | −16.1854 | −0.613066 | ||||||||
\(698\) | 21.3297 | 0.807342 | ||||||||
\(699\) | −18.2551 | −0.690472 | ||||||||
\(700\) | 0.0991963 | 0.00374927 | ||||||||
\(701\) | −1.02581 | −0.0387443 | −0.0193722 | − | 0.999812i | \(-0.506167\pi\) | ||||
−0.0193722 | + | 0.999812i | \(0.506167\pi\) | |||||||
\(702\) | −6.02096 | −0.227247 | ||||||||
\(703\) | −1.85263 | −0.0698731 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.9324 | 0.411738 | ||||||||
\(706\) | 17.7522 | 0.668113 | ||||||||
\(707\) | 7.01580 | 0.263856 | ||||||||
\(708\) | 2.40879 | 0.0905278 | ||||||||
\(709\) | −20.4828 | −0.769249 | −0.384624 | − | 0.923073i | \(-0.625669\pi\) | ||||
−0.384624 | + | 0.923073i | \(0.625669\pi\) | |||||||
\(710\) | −49.8933 | −1.87246 | ||||||||
\(711\) | −12.8359 | −0.481382 | ||||||||
\(712\) | 11.7012 | 0.438520 | ||||||||
\(713\) | −18.7145 | −0.700862 | ||||||||
\(714\) | −4.37651 | −0.163787 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.49314 | 0.167917 | ||||||||
\(717\) | −2.03621 | −0.0760436 | ||||||||
\(718\) | 35.9614 | 1.34207 | ||||||||
\(719\) | 32.9187 | 1.22766 | 0.613830 | − | 0.789438i | \(-0.289628\pi\) | ||||
0.613830 | + | 0.789438i | \(0.289628\pi\) | |||||||
\(720\) | −8.06065 | −0.300403 | ||||||||
\(721\) | −7.36659 | −0.274346 | ||||||||
\(722\) | 23.6417 | 0.879853 | ||||||||
\(723\) | −28.9345 | −1.07609 | ||||||||
\(724\) | 1.81806 | 0.0675676 | ||||||||
\(725\) | −1.31225 | −0.0487356 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.1632 | 1.15578 | 0.577889 | − | 0.816115i | \(-0.303877\pi\) | ||||
0.577889 | + | 0.816115i | \(0.303877\pi\) | |||||||
\(728\) | 13.4828 | 0.499707 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −44.6775 | −1.65359 | ||||||||
\(731\) | −27.6589 | −1.02300 | ||||||||
\(732\) | −0.416744 | −0.0154033 | ||||||||
\(733\) | −9.48073 | −0.350179 | −0.175089 | − | 0.984553i | \(-0.556021\pi\) | ||||
−0.175089 | + | 0.984553i | \(0.556021\pi\) | |||||||
\(734\) | 0.0335645 | 0.00123889 | ||||||||
\(735\) | −2.32691 | −0.0858293 | ||||||||
\(736\) | −8.47863 | −0.312526 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 6.51146 | 0.239690 | ||||||||
\(739\) | −37.9205 | −1.39493 | −0.697465 | − | 0.716619i | \(-0.745689\pi\) | ||||
−0.697465 | + | 0.716619i | \(0.745689\pi\) | |||||||
\(740\) | −0.948566 | −0.0348700 | ||||||||
\(741\) | −4.93506 | −0.181294 | ||||||||
\(742\) | −6.61527 | −0.242854 | ||||||||
\(743\) | −21.0795 | −0.773332 | −0.386666 | − | 0.922220i | \(-0.626373\pi\) | ||||
−0.386666 | + | 0.922220i | \(0.626373\pi\) | |||||||
\(744\) | 8.82901 | 0.323687 | ||||||||
\(745\) | 8.08146 | 0.296082 | ||||||||
\(746\) | −31.4528 | −1.15157 | ||||||||
\(747\) | 0.205514 | 0.00751935 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.20899 | 0.0441755 | ||||||||
\(750\) | −14.1582 | −0.516983 | ||||||||
\(751\) | −49.9699 | −1.82343 | −0.911713 | − | 0.410828i | \(-0.865240\pi\) | ||||
−0.911713 | + | 0.410828i | \(0.865240\pi\) | |||||||
\(752\) | 16.2752 | 0.593496 | ||||||||
\(753\) | 27.7896 | 1.01271 | ||||||||
\(754\) | −19.0613 | −0.694173 | ||||||||
\(755\) | 7.34746 | 0.267401 | ||||||||
\(756\) | −0.239314 | −0.00870375 | ||||||||
\(757\) | 33.8732 | 1.23114 | 0.615571 | − | 0.788081i | \(-0.288925\pi\) | ||||
0.615571 | + | 0.788081i | \(0.288925\pi\) | |||||||
\(758\) | 38.5699 | 1.40092 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.51973 | −0.272769 | ||||||||
\(761\) | −1.57878 | −0.0572307 | −0.0286154 | − | 0.999590i | \(-0.509110\pi\) | ||||
−0.0286154 | + | 0.999590i | \(0.509110\pi\) | |||||||
\(762\) | −21.3070 | −0.771869 | ||||||||
\(763\) | −15.8465 | −0.573682 | ||||||||
\(764\) | 5.17059 | 0.187065 | ||||||||
\(765\) | 7.67478 | 0.277482 | ||||||||
\(766\) | −22.3784 | −0.808564 | ||||||||
\(767\) | −45.6726 | −1.64914 | ||||||||
\(768\) | 5.65801 | 0.204166 | ||||||||
\(769\) | −17.0786 | −0.615868 | −0.307934 | − | 0.951408i | \(-0.599638\pi\) | ||||
−0.307934 | + | 0.951408i | \(0.599638\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.8265 | −0.461935 | ||||||||
\(772\) | 6.07781 | 0.218745 | ||||||||
\(773\) | 33.4826 | 1.20429 | 0.602143 | − | 0.798389i | \(-0.294314\pi\) | ||||
0.602143 | + | 0.798389i | \(0.294314\pi\) | |||||||
\(774\) | 11.1273 | 0.399962 | ||||||||
\(775\) | −1.23164 | −0.0442418 | ||||||||
\(776\) | 38.7598 | 1.39139 | ||||||||
\(777\) | 1.70342 | 0.0611097 | ||||||||
\(778\) | −17.3496 | −0.622012 | ||||||||
\(779\) | 5.33709 | 0.191221 | ||||||||
\(780\) | −2.52681 | −0.0904741 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −27.5644 | −0.985702 | ||||||||
\(783\) | 3.16583 | 0.113137 | ||||||||
\(784\) | −3.46410 | −0.123718 | ||||||||
\(785\) | 17.4687 | 0.623485 | ||||||||
\(786\) | −25.5559 | −0.911549 | ||||||||
\(787\) | 36.3779 | 1.29673 | 0.648366 | − | 0.761328i | \(-0.275452\pi\) | ||||
0.648366 | + | 0.761328i | \(0.275452\pi\) | |||||||
\(788\) | −1.62642 | −0.0579387 | ||||||||
\(789\) | −2.55283 | −0.0908833 | ||||||||
\(790\) | 39.6319 | 1.41004 | ||||||||
\(791\) | 18.4717 | 0.656777 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.90181 | 0.280601 | ||||||||
\(794\) | −1.71027 | −0.0606951 | ||||||||
\(795\) | 11.6007 | 0.411436 | ||||||||
\(796\) | 4.60143 | 0.163093 | ||||||||
\(797\) | 46.7424 | 1.65570 | 0.827851 | − | 0.560948i | \(-0.189563\pi\) | ||||
0.827851 | + | 0.560948i | \(0.189563\pi\) | |||||||
\(798\) | 1.44314 | 0.0510866 | ||||||||
\(799\) | −15.4961 | −0.548213 | ||||||||
\(800\) | −0.557997 | −0.0197282 | ||||||||
\(801\) | 3.93798 | 0.139142 | ||||||||
\(802\) | −9.96035 | −0.351712 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −2.26141 | −0.0797539 | ||||||||
\(805\) | −14.6555 | −0.516539 | ||||||||
\(806\) | −17.8905 | −0.630165 | ||||||||
\(807\) | −19.0274 | −0.669796 | ||||||||
\(808\) | −20.8465 | −0.733377 | ||||||||
\(809\) | −36.0260 | −1.26661 | −0.633304 | − | 0.773903i | \(-0.718302\pi\) | ||||
−0.633304 | + | 0.773903i | \(0.718302\pi\) | |||||||
\(810\) | −3.08759 | −0.108487 | ||||||||
\(811\) | 27.6340 | 0.970362 | 0.485181 | − | 0.874414i | \(-0.338754\pi\) | ||||
0.485181 | + | 0.874414i | \(0.338754\pi\) | |||||||
\(812\) | −0.757626 | −0.0265875 | ||||||||
\(813\) | 10.3268 | 0.362176 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −33.3183 | −1.16709 | ||||||||
\(816\) | 11.4256 | 0.399974 | ||||||||
\(817\) | 9.12043 | 0.319083 | ||||||||
\(818\) | −49.5927 | −1.73397 | ||||||||
\(819\) | 4.53759 | 0.158556 | ||||||||
\(820\) | 2.73265 | 0.0954283 | ||||||||
\(821\) | −32.1918 | −1.12350 | −0.561752 | − | 0.827306i | \(-0.689872\pi\) | ||||
−0.561752 | + | 0.827306i | \(0.689872\pi\) | |||||||
\(822\) | 6.95378 | 0.242541 | ||||||||
\(823\) | 19.4232 | 0.677050 | 0.338525 | − | 0.940957i | \(-0.390072\pi\) | ||||
0.338525 | + | 0.940957i | \(0.390072\pi\) | |||||||
\(824\) | 21.8888 | 0.762534 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.3559 | 0.464710 | ||||||||
\(827\) | −20.7586 | −0.721847 | −0.360923 | − | 0.932595i | \(-0.617538\pi\) | ||||
−0.360923 | + | 0.932595i | \(0.617538\pi\) | |||||||
\(828\) | −1.50726 | −0.0523810 | ||||||||
\(829\) | 54.3260 | 1.88682 | 0.943410 | − | 0.331629i | \(-0.107598\pi\) | ||||
0.943410 | + | 0.331629i | \(0.107598\pi\) | |||||||
\(830\) | −0.634543 | −0.0220253 | ||||||||
\(831\) | 2.89957 | 0.100585 | ||||||||
\(832\) | −39.5426 | −1.37089 | ||||||||
\(833\) | 3.29827 | 0.114278 | ||||||||
\(834\) | −30.5019 | −1.05619 | ||||||||
\(835\) | −30.6286 | −1.05994 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.97136 | 0.102705 | ||||||||
\(838\) | −17.3422 | −0.599075 | ||||||||
\(839\) | 14.2101 | 0.490588 | 0.245294 | − | 0.969449i | \(-0.421115\pi\) | ||||
0.245294 | + | 0.969449i | \(0.421115\pi\) | |||||||
\(840\) | 6.91409 | 0.238559 | ||||||||
\(841\) | −18.9775 | −0.654398 | ||||||||
\(842\) | 28.3219 | 0.976036 | ||||||||
\(843\) | 17.4209 | 0.600009 | ||||||||
\(844\) | −2.90764 | −0.100085 | ||||||||
\(845\) | 17.6605 | 0.607540 | ||||||||
\(846\) | 6.23415 | 0.214334 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 17.2702 | 0.593061 | ||||||||
\(849\) | 9.49232 | 0.325776 | ||||||||
\(850\) | −1.81408 | −0.0622223 | ||||||||
\(851\) | 10.7286 | 0.367771 | ||||||||
\(852\) | 3.86714 | 0.132486 | ||||||||
\(853\) | −19.5795 | −0.670388 | −0.335194 | − | 0.942149i | \(-0.608802\pi\) | ||||
−0.335194 | + | 0.942149i | \(0.608802\pi\) | |||||||
\(854\) | −2.31069 | −0.0790703 | ||||||||
\(855\) | −2.53073 | −0.0865493 | ||||||||
\(856\) | −3.59235 | −0.122784 | ||||||||
\(857\) | 18.8814 | 0.644977 | 0.322489 | − | 0.946573i | \(-0.395481\pi\) | ||||
0.322489 | + | 0.946573i | \(0.395481\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.77215 | −0.265182 | −0.132591 | − | 0.991171i | \(-0.542330\pi\) | ||||
−0.132591 | + | 0.991171i | \(0.542330\pi\) | |||||||
\(860\) | 4.66976 | 0.159238 | ||||||||
\(861\) | −4.90724 | −0.167238 | ||||||||
\(862\) | −32.9129 | −1.12102 | ||||||||
\(863\) | −7.94845 | −0.270568 | −0.135284 | − | 0.990807i | \(-0.543195\pi\) | ||||
−0.135284 | + | 0.990807i | \(0.543195\pi\) | |||||||
\(864\) | 1.34618 | 0.0457981 | ||||||||
\(865\) | −30.1286 | −1.02440 | ||||||||
\(866\) | 34.4926 | 1.17211 | ||||||||
\(867\) | 6.12139 | 0.207893 | ||||||||
\(868\) | −0.711088 | −0.0241359 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −9.77480 | −0.331397 | ||||||||
\(871\) | 42.8783 | 1.45287 | ||||||||
\(872\) | 47.0857 | 1.59452 | ||||||||
\(873\) | 13.0444 | 0.441487 | ||||||||
\(874\) | 9.08928 | 0.307450 | ||||||||
\(875\) | 10.6700 | 0.360713 | ||||||||
\(876\) | 3.46287 | 0.116999 | ||||||||
\(877\) | −19.7350 | −0.666404 | −0.333202 | − | 0.942855i | \(-0.608129\pi\) | ||||
−0.333202 | + | 0.942855i | \(0.608129\pi\) | |||||||
\(878\) | −0.816405 | −0.0275523 | ||||||||
\(879\) | 3.27005 | 0.110296 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.2300 | −1.08586 | −0.542928 | − | 0.839779i | \(-0.682684\pi\) | ||||
−0.542928 | + | 0.839779i | \(0.682684\pi\) | |||||||
\(882\) | −1.32691 | −0.0446793 | ||||||||
\(883\) | −18.6496 | −0.627610 | −0.313805 | − | 0.949488i | \(-0.601604\pi\) | ||||
−0.313805 | + | 0.949488i | \(0.601604\pi\) | |||||||
\(884\) | 3.58162 | 0.120463 | ||||||||
\(885\) | −23.4213 | −0.787297 | ||||||||
\(886\) | 48.2075 | 1.61956 | ||||||||
\(887\) | 37.6169 | 1.26305 | 0.631525 | − | 0.775355i | \(-0.282429\pi\) | ||||
0.631525 | + | 0.775355i | \(0.282429\pi\) | |||||||
\(888\) | −5.06147 | −0.169852 | ||||||||
\(889\) | 16.0576 | 0.538554 | ||||||||
\(890\) | −12.1589 | −0.407567 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.33165 | −0.111552 | ||||||||
\(893\) | 5.10979 | 0.170993 | ||||||||
\(894\) | 4.60842 | 0.154128 | ||||||||
\(895\) | −43.6880 | −1.46033 | ||||||||
\(896\) | 8.87093 | 0.296357 | ||||||||
\(897\) | 28.5790 | 0.954224 | ||||||||
\(898\) | −37.9308 | −1.26577 | ||||||||
\(899\) | 9.40683 | 0.313735 | ||||||||
\(900\) | −0.0991963 | −0.00330654 | ||||||||
\(901\) | −16.4435 | −0.547811 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.38587 | −0.279064 | ||||||||
\(904\) | −54.8861 | −1.82548 | ||||||||
\(905\) | −17.6774 | −0.587618 | ||||||||
\(906\) | 4.18985 | 0.139198 | ||||||||
\(907\) | −23.3358 | −0.774851 | −0.387426 | − | 0.921901i | \(-0.626636\pi\) | ||||
−0.387426 | + | 0.921901i | \(0.626636\pi\) | |||||||
\(908\) | −2.52698 | −0.0838607 | ||||||||
\(909\) | −7.01580 | −0.232699 | ||||||||
\(910\) | −14.0102 | −0.464435 | ||||||||
\(911\) | 39.8541 | 1.32042 | 0.660212 | − | 0.751079i | \(-0.270466\pi\) | ||||
0.660212 | + | 0.751079i | \(0.270466\pi\) | |||||||
\(912\) | −3.76754 | −0.124756 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −52.1321 | −1.72438 | ||||||||
\(915\) | 4.05211 | 0.133959 | ||||||||
\(916\) | 6.91898 | 0.228609 | ||||||||
\(917\) | 19.2597 | 0.636012 | ||||||||
\(918\) | 4.37651 | 0.144446 | ||||||||
\(919\) | 7.17929 | 0.236823 | 0.118411 | − | 0.992965i | \(-0.462220\pi\) | ||||
0.118411 | + | 0.992965i | \(0.462220\pi\) | |||||||
\(920\) | 43.5468 | 1.43570 | ||||||||
\(921\) | −16.5841 | −0.546465 | ||||||||
\(922\) | 0.545576 | 0.0179676 | ||||||||
\(923\) | −73.3242 | −2.41350 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.706072 | 0.0232155 | ||||||||
\(926\) | 23.3774 | 0.768228 | ||||||||
\(927\) | 7.36659 | 0.241951 | ||||||||
\(928\) | 4.26178 | 0.139900 | ||||||||
\(929\) | 15.3753 | 0.504446 | 0.252223 | − | 0.967669i | \(-0.418838\pi\) | ||||
0.252223 | + | 0.967669i | \(0.418838\pi\) | |||||||
\(930\) | −9.17437 | −0.300839 | ||||||||
\(931\) | −1.08759 | −0.0356445 | ||||||||
\(932\) | −4.36870 | −0.143101 | ||||||||
\(933\) | 6.64098 | 0.217416 | ||||||||
\(934\) | 10.1011 | 0.330517 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −13.4828 | −0.440700 | ||||||||
\(937\) | 34.8669 | 1.13905 | 0.569526 | − | 0.821973i | \(-0.307127\pi\) | ||||
0.569526 | + | 0.821973i | \(0.307127\pi\) | |||||||
\(938\) | −12.5387 | −0.409404 | ||||||||
\(939\) | 3.58663 | 0.117045 | ||||||||
\(940\) | 2.61627 | 0.0853334 | ||||||||
\(941\) | −11.1503 | −0.363491 | −0.181745 | − | 0.983346i | \(-0.558175\pi\) | ||||
−0.181745 | + | 0.983346i | \(0.558175\pi\) | |||||||
\(942\) | 9.96145 | 0.324562 | ||||||||
\(943\) | −30.9071 | −1.00647 | ||||||||
\(944\) | −34.8676 | −1.13484 | ||||||||
\(945\) | 2.32691 | 0.0756943 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.00144 | −0.260012 | −0.130006 | − | 0.991513i | \(-0.541500\pi\) | ||||
−0.130006 | + | 0.991513i | \(0.541500\pi\) | |||||||
\(948\) | −3.07180 | −0.0997673 | ||||||||
\(949\) | −65.6588 | −2.13138 | ||||||||
\(950\) | 0.598186 | 0.0194077 | ||||||||
\(951\) | 11.4017 | 0.369724 | ||||||||
\(952\) | −9.80037 | −0.317632 | ||||||||
\(953\) | −50.1472 | −1.62443 | −0.812213 | − | 0.583361i | \(-0.801737\pi\) | ||||
−0.812213 | + | 0.583361i | \(0.801737\pi\) | |||||||
\(954\) | 6.61527 | 0.214177 | ||||||||
\(955\) | −50.2750 | −1.62686 | ||||||||
\(956\) | −0.487293 | −0.0157602 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 46.1032 | 1.48953 | ||||||||
\(959\) | −5.24059 | −0.169227 | ||||||||
\(960\) | −20.2778 | −0.654462 | ||||||||
\(961\) | −22.1710 | −0.715193 | ||||||||
\(962\) | 10.2562 | 0.330673 | ||||||||
\(963\) | −1.20899 | −0.0389592 | ||||||||
\(964\) | −6.92442 | −0.223021 | ||||||||
\(965\) | −59.0961 | −1.90237 | ||||||||
\(966\) | −8.35723 | −0.268890 | ||||||||
\(967\) | 12.2748 | 0.394731 | 0.197366 | − | 0.980330i | \(-0.436761\pi\) | ||||
0.197366 | + | 0.980330i | \(0.436761\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.58718 | 0.115237 | ||||||||
\(970\) | −40.2759 | −1.29318 | ||||||||
\(971\) | 31.5666 | 1.01302 | 0.506511 | − | 0.862234i | \(-0.330935\pi\) | ||||
0.506511 | + | 0.862234i | \(0.330935\pi\) | |||||||
\(972\) | 0.239314 | 0.00767599 | ||||||||
\(973\) | 22.9872 | 0.736935 | ||||||||
\(974\) | −28.7497 | −0.921200 | ||||||||
\(975\) | 1.88085 | 0.0602353 | ||||||||
\(976\) | 6.03243 | 0.193093 | ||||||||
\(977\) | −12.1052 | −0.387279 | −0.193640 | − | 0.981073i | \(-0.562029\pi\) | ||||
−0.193640 | + | 0.981073i | \(0.562029\pi\) | |||||||
\(978\) | −18.9996 | −0.607540 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −0.556861 | −0.0177883 | ||||||||
\(981\) | 15.8465 | 0.505940 | ||||||||
\(982\) | 17.7194 | 0.565449 | ||||||||
\(983\) | −5.33084 | −0.170027 | −0.0850136 | − | 0.996380i | \(-0.527093\pi\) | ||||
−0.0850136 | + | 0.996380i | \(0.527093\pi\) | |||||||
\(984\) | 14.5812 | 0.464832 | ||||||||
\(985\) | 15.8141 | 0.503878 | ||||||||
\(986\) | 13.8553 | 0.441242 | ||||||||
\(987\) | −4.69825 | −0.149547 | ||||||||
\(988\) | −1.18103 | −0.0375735 | ||||||||
\(989\) | −52.8165 | −1.67947 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.1178 | 1.27438 | 0.637192 | − | 0.770705i | \(-0.280096\pi\) | ||||
0.637192 | + | 0.770705i | \(0.280096\pi\) | |||||||
\(992\) | 4.00000 | 0.127000 | ||||||||
\(993\) | 6.84006 | 0.217063 | ||||||||
\(994\) | 21.4419 | 0.680096 | ||||||||
\(995\) | −44.7409 | −1.41838 | ||||||||
\(996\) | 0.0491822 | 0.00155840 | ||||||||
\(997\) | 15.0344 | 0.476143 | 0.238071 | − | 0.971248i | \(-0.423485\pi\) | ||||
0.238071 | + | 0.971248i | \(0.423485\pi\) | |||||||
\(998\) | 25.9826 | 0.822465 | ||||||||
\(999\) | −1.70342 | −0.0538937 |
(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 | 2541.2.a.bk.1.2 | ✓ | 4 | |
3.2 | odd | 2 | 7623.2.a.cm.1.3 | 4 | |||
11.10 | odd | 2 | 2541.2.a.bo.1.3 | yes | 4 | ||
33.32 | even | 2 | 7623.2.a.cf.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2541.2.a.bk.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
2541.2.a.bo.1.3 | yes | 4 | 11.10 | odd | 2 | ||
7623.2.a.cf.1.2 | 4 | 33.32 | even | 2 | |||
7623.2.a.cm.1.3 | 4 | 3.2 | odd | 2 |