Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [945,2,Mod(1,945)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(945, 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("945.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 945 = 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 945.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: | \(7.54586299101\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
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 | \(2.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 945.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.30278 | 1.62831 | 0.814154 | − | 0.580649i | \(-0.197201\pi\) | ||||
0.814154 | + | 0.580649i | \(0.197201\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.30278 | 1.65139 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 3.00000 | 1.06066 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.30278 | 0.728202 | ||||||||
\(11\) | 3.00000 | 0.904534 | 0.452267 | − | 0.891883i | \(-0.350615\pi\) | ||||
0.452267 | + | 0.891883i | \(0.350615\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.30278 | 0.361325 | 0.180662 | − | 0.983545i | \(-0.442176\pi\) | ||||
0.180662 | + | 0.983545i | \(0.442176\pi\) | |||||||
\(14\) | 2.30278 | 0.615443 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.302776 | 0.0756939 | ||||||||
\(17\) | −2.30278 | −0.558505 | −0.279253 | − | 0.960218i | \(-0.590087\pi\) | ||||
−0.279253 | + | 0.960218i | \(0.590087\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.30278 | −0.757709 | −0.378854 | − | 0.925456i | \(-0.623682\pi\) | ||||
−0.378854 | + | 0.925456i | \(0.623682\pi\) | |||||||
\(20\) | 3.30278 | 0.738523 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.90833 | 1.47286 | ||||||||
\(23\) | 0.697224 | 0.145381 | 0.0726907 | − | 0.997355i | \(-0.476841\pi\) | ||||
0.0726907 | + | 0.997355i | \(0.476841\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.00000 | 0.588348 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.30278 | 0.624166 | ||||||||
\(29\) | 5.30278 | 0.984701 | 0.492350 | − | 0.870397i | \(-0.336138\pi\) | ||||
0.492350 | + | 0.870397i | \(0.336138\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.39445 | −0.430056 | −0.215028 | − | 0.976608i | \(-0.568984\pi\) | ||||
−0.215028 | + | 0.976608i | \(0.568984\pi\) | |||||||
\(32\) | −5.30278 | −0.937407 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.30278 | −0.909419 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.60555 | 0.592749 | 0.296374 | − | 0.955072i | \(-0.404222\pi\) | ||||
0.296374 | + | 0.955072i | \(0.404222\pi\) | |||||||
\(38\) | −7.60555 | −1.23378 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.00000 | 0.474342 | ||||||||
\(41\) | −6.90833 | −1.07890 | −0.539450 | − | 0.842018i | \(-0.681368\pi\) | ||||
−0.539450 | + | 0.842018i | \(0.681368\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.21110 | −0.642187 | −0.321094 | − | 0.947047i | \(-0.604050\pi\) | ||||
−0.321094 | + | 0.947047i | \(0.604050\pi\) | |||||||
\(44\) | 9.90833 | 1.49374 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.60555 | 0.236726 | ||||||||
\(47\) | 7.60555 | 1.10938 | 0.554692 | − | 0.832056i | \(-0.312836\pi\) | ||||
0.554692 | + | 0.832056i | \(0.312836\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.30278 | 0.325662 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.30278 | 0.596688 | ||||||||
\(53\) | −5.51388 | −0.757389 | −0.378695 | − | 0.925522i | \(-0.623627\pi\) | ||||
−0.378695 | + | 0.925522i | \(0.623627\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.00000 | 0.404520 | ||||||||
\(56\) | 3.00000 | 0.400892 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 12.2111 | 1.60340 | ||||||||
\(59\) | 6.21110 | 0.808617 | 0.404308 | − | 0.914623i | \(-0.367512\pi\) | ||||
0.404308 | + | 0.914623i | \(0.367512\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.1194 | −1.42370 | −0.711849 | − | 0.702333i | \(-0.752142\pi\) | ||||
−0.711849 | + | 0.702333i | \(0.752142\pi\) | |||||||
\(62\) | −5.51388 | −0.700263 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.8167 | −1.60208 | ||||||||
\(65\) | 1.30278 | 0.161589 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.5139 | 1.65098 | 0.825491 | − | 0.564415i | \(-0.190898\pi\) | ||||
0.825491 | + | 0.564415i | \(0.190898\pi\) | |||||||
\(68\) | −7.60555 | −0.922309 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.30278 | 0.275234 | ||||||||
\(71\) | 2.09167 | 0.248236 | 0.124118 | − | 0.992267i | \(-0.460390\pi\) | ||||
0.124118 | + | 0.992267i | \(0.460390\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.2111 | −1.19512 | −0.597560 | − | 0.801825i | \(-0.703863\pi\) | ||||
−0.597560 | + | 0.801825i | \(0.703863\pi\) | |||||||
\(74\) | 8.30278 | 0.965178 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.9083 | −1.25127 | ||||||||
\(77\) | 3.00000 | 0.341882 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.9083 | −1.90234 | −0.951168 | − | 0.308675i | \(-0.900115\pi\) | ||||
−0.951168 | + | 0.308675i | \(0.900115\pi\) | |||||||
\(80\) | 0.302776 | 0.0338513 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −15.9083 | −1.75678 | ||||||||
\(83\) | −12.2111 | −1.34034 | −0.670171 | − | 0.742206i | \(-0.733779\pi\) | ||||
−0.670171 | + | 0.742206i | \(0.733779\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.30278 | −0.249771 | ||||||||
\(86\) | −9.69722 | −1.04568 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.00000 | 0.959403 | ||||||||
\(89\) | 10.8167 | 1.14656 | 0.573282 | − | 0.819358i | \(-0.305670\pi\) | ||||
0.573282 | + | 0.819358i | \(0.305670\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.30278 | 0.136568 | ||||||||
\(92\) | 2.30278 | 0.240081 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 17.5139 | 1.80642 | ||||||||
\(95\) | −3.30278 | −0.338858 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.51388 | −0.965988 | −0.482994 | − | 0.875624i | \(-0.660451\pi\) | ||||
−0.482994 | + | 0.875624i | \(0.660451\pi\) | |||||||
\(98\) | 2.30278 | 0.232615 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.30278 | 0.330278 | ||||||||
\(101\) | −9.21110 | −0.916539 | −0.458269 | − | 0.888813i | \(-0.651531\pi\) | ||||
−0.458269 | + | 0.888813i | \(0.651531\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.7250 | −1.54943 | −0.774714 | − | 0.632312i | \(-0.782106\pi\) | ||||
−0.774714 | + | 0.632312i | \(0.782106\pi\) | |||||||
\(104\) | 3.90833 | 0.383243 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.6972 | −1.23326 | ||||||||
\(107\) | 15.0000 | 1.45010 | 0.725052 | − | 0.688694i | \(-0.241816\pi\) | ||||
0.725052 | + | 0.688694i | \(0.241816\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.69722 | −0.162565 | −0.0812823 | − | 0.996691i | \(-0.525902\pi\) | ||||
−0.0812823 | + | 0.996691i | \(0.525902\pi\) | |||||||
\(110\) | 6.90833 | 0.658683 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.302776 | 0.0286096 | ||||||||
\(113\) | 15.9083 | 1.49653 | 0.748265 | − | 0.663400i | \(-0.230887\pi\) | ||||
0.748265 | + | 0.663400i | \(0.230887\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.697224 | 0.0650165 | ||||||||
\(116\) | 17.5139 | 1.62612 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 14.3028 | 1.31668 | ||||||||
\(119\) | −2.30278 | −0.211095 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | −25.6056 | −2.31822 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.90833 | −0.710189 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.7250 | −1.66157 | −0.830787 | − | 0.556591i | \(-0.812109\pi\) | ||||
−0.830787 | + | 0.556591i | \(0.812109\pi\) | |||||||
\(128\) | −18.9083 | −1.67128 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.00000 | 0.263117 | ||||||||
\(131\) | −8.30278 | −0.725417 | −0.362708 | − | 0.931903i | \(-0.618148\pi\) | ||||
−0.362708 | + | 0.931903i | \(0.618148\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.30278 | −0.286387 | ||||||||
\(134\) | 31.1194 | 2.68831 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.90833 | −0.592384 | ||||||||
\(137\) | 18.4222 | 1.57392 | 0.786958 | − | 0.617007i | \(-0.211655\pi\) | ||||
0.786958 | + | 0.617007i | \(0.211655\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.60555 | −0.475457 | −0.237728 | − | 0.971332i | \(-0.576403\pi\) | ||||
−0.237728 | + | 0.971332i | \(0.576403\pi\) | |||||||
\(140\) | 3.30278 | 0.279135 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.81665 | 0.404205 | ||||||||
\(143\) | 3.90833 | 0.326831 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.30278 | 0.440372 | ||||||||
\(146\) | −23.5139 | −1.94602 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.9083 | 0.978858 | ||||||||
\(149\) | 5.51388 | 0.451715 | 0.225857 | − | 0.974160i | \(-0.427482\pi\) | ||||
0.225857 | + | 0.974160i | \(0.427482\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.00000 | −0.0813788 | −0.0406894 | − | 0.999172i | \(-0.512955\pi\) | ||||
−0.0406894 | + | 0.999172i | \(0.512955\pi\) | |||||||
\(152\) | −9.90833 | −0.803671 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.90833 | 0.556689 | ||||||||
\(155\) | −2.39445 | −0.192327 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.60555 | 0.527180 | 0.263590 | − | 0.964635i | \(-0.415093\pi\) | ||||
0.263590 | + | 0.964635i | \(0.415093\pi\) | |||||||
\(158\) | −38.9361 | −3.09759 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.30278 | −0.419221 | ||||||||
\(161\) | 0.697224 | 0.0549490 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.2111 | 1.81803 | 0.909017 | − | 0.416759i | \(-0.136834\pi\) | ||||
0.909017 | + | 0.416759i | \(0.136834\pi\) | |||||||
\(164\) | −22.8167 | −1.78168 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −28.1194 | −2.18249 | ||||||||
\(167\) | 19.6056 | 1.51712 | 0.758562 | − | 0.651601i | \(-0.225902\pi\) | ||||
0.758562 | + | 0.651601i | \(0.225902\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.3028 | −0.869444 | ||||||||
\(170\) | −5.30278 | −0.406704 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −13.9083 | −1.06050 | ||||||||
\(173\) | −16.8167 | −1.27855 | −0.639273 | − | 0.768980i | \(-0.720765\pi\) | ||||
−0.639273 | + | 0.768980i | \(0.720765\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0.908327 | 0.0684677 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 24.9083 | 1.86696 | ||||||||
\(179\) | 16.8167 | 1.25694 | 0.628468 | − | 0.777836i | \(-0.283682\pi\) | ||||
0.628468 | + | 0.777836i | \(0.283682\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.4222 | 1.29498 | 0.647491 | − | 0.762073i | \(-0.275818\pi\) | ||||
0.647491 | + | 0.762073i | \(0.275818\pi\) | |||||||
\(182\) | 3.00000 | 0.222375 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.09167 | 0.154200 | ||||||||
\(185\) | 3.60555 | 0.265085 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.90833 | −0.505187 | ||||||||
\(188\) | 25.1194 | 1.83202 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.60555 | −0.551765 | ||||||||
\(191\) | −6.69722 | −0.484594 | −0.242297 | − | 0.970202i | \(-0.577901\pi\) | ||||
−0.242297 | + | 0.970202i | \(0.577901\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.11943 | 0.440486 | 0.220243 | − | 0.975445i | \(-0.429315\pi\) | ||||
0.220243 | + | 0.975445i | \(0.429315\pi\) | |||||||
\(194\) | −21.9083 | −1.57293 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.30278 | 0.235913 | ||||||||
\(197\) | −22.8167 | −1.62562 | −0.812810 | − | 0.582529i | \(-0.802063\pi\) | ||||
−0.812810 | + | 0.582529i | \(0.802063\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.7250 | 1.61093 | 0.805466 | − | 0.592643i | \(-0.201915\pi\) | ||||
0.805466 | + | 0.592643i | \(0.201915\pi\) | |||||||
\(200\) | 3.00000 | 0.212132 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −21.2111 | −1.49241 | ||||||||
\(203\) | 5.30278 | 0.372182 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.90833 | −0.482498 | ||||||||
\(206\) | −36.2111 | −2.52295 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.394449 | 0.0273501 | ||||||||
\(209\) | −9.90833 | −0.685373 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.3944 | −0.784426 | −0.392213 | − | 0.919874i | \(-0.628290\pi\) | ||||
−0.392213 | + | 0.919874i | \(0.628290\pi\) | |||||||
\(212\) | −18.2111 | −1.25074 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 34.5416 | 2.36122 | ||||||||
\(215\) | −4.21110 | −0.287195 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.39445 | −0.162546 | ||||||||
\(218\) | −3.90833 | −0.264705 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9.90833 | 0.668019 | ||||||||
\(221\) | −3.00000 | −0.201802 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.2111 | 1.35344 | 0.676718 | − | 0.736243i | \(-0.263402\pi\) | ||||
0.676718 | + | 0.736243i | \(0.263402\pi\) | |||||||
\(224\) | −5.30278 | −0.354307 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 36.6333 | 2.43681 | ||||||||
\(227\) | −6.48612 | −0.430499 | −0.215250 | − | 0.976559i | \(-0.569056\pi\) | ||||
−0.215250 | + | 0.976559i | \(0.569056\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.78890 | 0.118214 | 0.0591068 | − | 0.998252i | \(-0.481175\pi\) | ||||
0.0591068 | + | 0.998252i | \(0.481175\pi\) | |||||||
\(230\) | 1.60555 | 0.105867 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 15.9083 | 1.04443 | ||||||||
\(233\) | −9.90833 | −0.649116 | −0.324558 | − | 0.945866i | \(-0.605216\pi\) | ||||
−0.324558 | + | 0.945866i | \(0.605216\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.60555 | 0.496131 | ||||||||
\(236\) | 20.5139 | 1.33534 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.30278 | −0.343728 | ||||||||
\(239\) | 5.78890 | 0.374453 | 0.187226 | − | 0.982317i | \(-0.440050\pi\) | ||||
0.187226 | + | 0.982317i | \(0.440050\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.119429 | 0.00769313 | 0.00384656 | − | 0.999993i | \(-0.498776\pi\) | ||||
0.00384656 | + | 0.999993i | \(0.498776\pi\) | |||||||
\(242\) | −4.60555 | −0.296056 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −36.7250 | −2.35108 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.30278 | −0.273779 | ||||||||
\(248\) | −7.18335 | −0.456143 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.30278 | 0.145640 | ||||||||
\(251\) | 4.18335 | 0.264050 | 0.132025 | − | 0.991246i | \(-0.457852\pi\) | ||||
0.132025 | + | 0.991246i | \(0.457852\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.09167 | 0.131502 | ||||||||
\(254\) | −43.1194 | −2.70555 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −17.9083 | −1.11927 | ||||||||
\(257\) | −12.0000 | −0.748539 | −0.374270 | − | 0.927320i | \(-0.622107\pi\) | ||||
−0.374270 | + | 0.927320i | \(0.622107\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.60555 | 0.224038 | ||||||||
\(260\) | 4.30278 | 0.266847 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −19.1194 | −1.18120 | ||||||||
\(263\) | 12.4861 | 0.769927 | 0.384964 | − | 0.922932i | \(-0.374214\pi\) | ||||
0.384964 | + | 0.922932i | \(0.374214\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.51388 | −0.338715 | ||||||||
\(266\) | −7.60555 | −0.466326 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 44.6333 | 2.72641 | ||||||||
\(269\) | 9.42221 | 0.574482 | 0.287241 | − | 0.957858i | \(-0.407262\pi\) | ||||
0.287241 | + | 0.957858i | \(0.407262\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.1194 | 0.736203 | 0.368101 | − | 0.929786i | \(-0.380008\pi\) | ||||
0.368101 | + | 0.929786i | \(0.380008\pi\) | |||||||
\(272\) | −0.697224 | −0.0422754 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 42.4222 | 2.56282 | ||||||||
\(275\) | 3.00000 | 0.180907 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.09167 | −0.185761 | −0.0928803 | − | 0.995677i | \(-0.529607\pi\) | ||||
−0.0928803 | + | 0.995677i | \(0.529607\pi\) | |||||||
\(278\) | −12.9083 | −0.774190 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.00000 | 0.179284 | ||||||||
\(281\) | −20.7250 | −1.23635 | −0.618174 | − | 0.786041i | \(-0.712127\pi\) | ||||
−0.618174 | + | 0.786041i | \(0.712127\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.90833 | 0.172882 | 0.0864410 | − | 0.996257i | \(-0.472451\pi\) | ||||
0.0864410 | + | 0.996257i | \(0.472451\pi\) | |||||||
\(284\) | 6.90833 | 0.409934 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.00000 | 0.532181 | ||||||||
\(287\) | −6.90833 | −0.407786 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.6972 | −0.688072 | ||||||||
\(290\) | 12.2111 | 0.717061 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −33.7250 | −1.97361 | ||||||||
\(293\) | 20.2389 | 1.18237 | 0.591183 | − | 0.806537i | \(-0.298661\pi\) | ||||
0.591183 | + | 0.806537i | \(0.298661\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.21110 | 0.361624 | ||||||||
\(296\) | 10.8167 | 0.628705 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.6972 | 0.735530 | ||||||||
\(299\) | 0.908327 | 0.0525299 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.21110 | −0.242724 | ||||||||
\(302\) | −2.30278 | −0.132510 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −11.1194 | −0.636697 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.8444 | 1.87453 | 0.937265 | − | 0.348618i | \(-0.113349\pi\) | ||||
0.937265 | + | 0.348618i | \(0.113349\pi\) | |||||||
\(308\) | 9.90833 | 0.564579 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.51388 | −0.313167 | ||||||||
\(311\) | 14.0917 | 0.799065 | 0.399533 | − | 0.916719i | \(-0.369172\pi\) | ||||
0.399533 | + | 0.916719i | \(0.369172\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.8167 | −0.837487 | −0.418743 | − | 0.908105i | \(-0.637529\pi\) | ||||
−0.418743 | + | 0.908105i | \(0.637529\pi\) | |||||||
\(314\) | 15.2111 | 0.858412 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −55.8444 | −3.14149 | ||||||||
\(317\) | 17.2389 | 0.968231 | 0.484115 | − | 0.875004i | \(-0.339141\pi\) | ||||
0.484115 | + | 0.875004i | \(0.339141\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.9083 | 0.890695 | ||||||||
\(320\) | −12.8167 | −0.716473 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.60555 | 0.0894739 | ||||||||
\(323\) | 7.60555 | 0.423184 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.30278 | 0.0722650 | ||||||||
\(326\) | 53.4500 | 2.96032 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −20.7250 | −1.14435 | ||||||||
\(329\) | 7.60555 | 0.419308 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.3028 | 0.731187 | 0.365593 | − | 0.930775i | \(-0.380866\pi\) | ||||
0.365593 | + | 0.930775i | \(0.380866\pi\) | |||||||
\(332\) | −40.3305 | −2.21343 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 45.1472 | 2.47034 | ||||||||
\(335\) | 13.5139 | 0.738342 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.69722 | 0.473768 | 0.236884 | − | 0.971538i | \(-0.423874\pi\) | ||||
0.236884 | + | 0.971538i | \(0.423874\pi\) | |||||||
\(338\) | −26.0278 | −1.41572 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.60555 | −0.412469 | ||||||||
\(341\) | −7.18335 | −0.389000 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −12.6333 | −0.681142 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −38.7250 | −2.08187 | ||||||||
\(347\) | 19.3944 | 1.04115 | 0.520574 | − | 0.853816i | \(-0.325718\pi\) | ||||
0.520574 | + | 0.853816i | \(0.325718\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.6333 | 1.42565 | 0.712824 | − | 0.701343i | \(-0.247416\pi\) | ||||
0.712824 | + | 0.701343i | \(0.247416\pi\) | |||||||
\(350\) | 2.30278 | 0.123089 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −15.9083 | −0.847917 | ||||||||
\(353\) | 23.7250 | 1.26275 | 0.631377 | − | 0.775476i | \(-0.282490\pi\) | ||||
0.631377 | + | 0.775476i | \(0.282490\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.09167 | 0.111014 | ||||||||
\(356\) | 35.7250 | 1.89342 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 38.7250 | 2.04668 | ||||||||
\(359\) | 1.18335 | 0.0624546 | 0.0312273 | − | 0.999512i | \(-0.490058\pi\) | ||||
0.0312273 | + | 0.999512i | \(0.490058\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.09167 | −0.425878 | ||||||||
\(362\) | 40.1194 | 2.10863 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.30278 | 0.225527 | ||||||||
\(365\) | −10.2111 | −0.534474 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.30278 | −0.329002 | −0.164501 | − | 0.986377i | \(-0.552601\pi\) | ||||
−0.164501 | + | 0.986377i | \(0.552601\pi\) | |||||||
\(368\) | 0.211103 | 0.0110045 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.30278 | 0.431641 | ||||||||
\(371\) | −5.51388 | −0.286266 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.90833 | −0.0988094 | −0.0494047 | − | 0.998779i | \(-0.515732\pi\) | ||||
−0.0494047 | + | 0.998779i | \(0.515732\pi\) | |||||||
\(374\) | −15.9083 | −0.822600 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 22.8167 | 1.17668 | ||||||||
\(377\) | 6.90833 | 0.355797 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.6333 | −1.31669 | −0.658347 | − | 0.752714i | \(-0.728744\pi\) | ||||
−0.658347 | + | 0.752714i | \(0.728744\pi\) | |||||||
\(380\) | −10.9083 | −0.559585 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −15.4222 | −0.789069 | ||||||||
\(383\) | 0.211103 | 0.0107868 | 0.00539342 | − | 0.999985i | \(-0.498283\pi\) | ||||
0.00539342 | + | 0.999985i | \(0.498283\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.00000 | 0.152894 | ||||||||
\(386\) | 14.0917 | 0.717247 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −31.4222 | −1.59522 | ||||||||
\(389\) | −8.72498 | −0.442374 | −0.221187 | − | 0.975231i | \(-0.570993\pi\) | ||||
−0.221187 | + | 0.975231i | \(0.570993\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.60555 | −0.0811962 | ||||||||
\(392\) | 3.00000 | 0.151523 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −52.5416 | −2.64701 | ||||||||
\(395\) | −16.9083 | −0.850750 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00000 | 0.100377 | 0.0501886 | − | 0.998740i | \(-0.484018\pi\) | ||||
0.0501886 | + | 0.998740i | \(0.484018\pi\) | |||||||
\(398\) | 52.3305 | 2.62309 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.302776 | 0.0151388 | ||||||||
\(401\) | −5.72498 | −0.285892 | −0.142946 | − | 0.989730i | \(-0.545658\pi\) | ||||
−0.142946 | + | 0.989730i | \(0.545658\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.11943 | −0.155390 | ||||||||
\(404\) | −30.4222 | −1.51356 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.2111 | 0.606027 | ||||||||
\(407\) | 10.8167 | 0.536162 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.0000 | 0.692255 | 0.346128 | − | 0.938187i | \(-0.387496\pi\) | ||||
0.346128 | + | 0.938187i | \(0.387496\pi\) | |||||||
\(410\) | −15.9083 | −0.785656 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −51.9361 | −2.55871 | ||||||||
\(413\) | 6.21110 | 0.305628 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.2111 | −0.599419 | ||||||||
\(416\) | −6.90833 | −0.338709 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −22.8167 | −1.11600 | ||||||||
\(419\) | 13.1833 | 0.644049 | 0.322024 | − | 0.946731i | \(-0.395637\pi\) | ||||
0.322024 | + | 0.946731i | \(0.395637\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.69722 | 0.131455 | 0.0657273 | − | 0.997838i | \(-0.479063\pi\) | ||||
0.0657273 | + | 0.997838i | \(0.479063\pi\) | |||||||
\(422\) | −26.2389 | −1.27729 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −16.5416 | −0.803333 | ||||||||
\(425\) | −2.30278 | −0.111701 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.1194 | −0.538107 | ||||||||
\(428\) | 49.5416 | 2.39469 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.69722 | −0.467642 | ||||||||
\(431\) | 35.9361 | 1.73098 | 0.865490 | − | 0.500926i | \(-0.167007\pi\) | ||||
0.865490 | + | 0.500926i | \(0.167007\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.3305 | 0.736738 | 0.368369 | − | 0.929680i | \(-0.379916\pi\) | ||||
0.368369 | + | 0.929680i | \(0.379916\pi\) | |||||||
\(434\) | −5.51388 | −0.264675 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.60555 | −0.268457 | ||||||||
\(437\) | −2.30278 | −0.110157 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.3944 | −1.25974 | −0.629869 | − | 0.776701i | \(-0.716891\pi\) | ||||
−0.629869 | + | 0.776701i | \(0.716891\pi\) | |||||||
\(440\) | 9.00000 | 0.429058 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.90833 | −0.328596 | ||||||||
\(443\) | −0.275019 | −0.0130666 | −0.00653328 | − | 0.999979i | \(-0.502080\pi\) | ||||
−0.00653328 | + | 0.999979i | \(0.502080\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.8167 | 0.512759 | ||||||||
\(446\) | 46.5416 | 2.20381 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −12.8167 | −0.605530 | ||||||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.7250 | −0.975901 | ||||||||
\(452\) | 52.5416 | 2.47135 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −14.9361 | −0.700985 | ||||||||
\(455\) | 1.30278 | 0.0610751 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.3028 | 1.04328 | 0.521640 | − | 0.853166i | \(-0.325320\pi\) | ||||
0.521640 | + | 0.853166i | \(0.325320\pi\) | |||||||
\(458\) | 4.11943 | 0.192488 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.30278 | 0.107367 | ||||||||
\(461\) | −26.5139 | −1.23487 | −0.617437 | − | 0.786620i | \(-0.711829\pi\) | ||||
−0.617437 | + | 0.786620i | \(0.711829\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.9361 | 0.508243 | 0.254121 | − | 0.967172i | \(-0.418214\pi\) | ||||
0.254121 | + | 0.967172i | \(0.418214\pi\) | |||||||
\(464\) | 1.60555 | 0.0745358 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −22.8167 | −1.05696 | ||||||||
\(467\) | 9.21110 | 0.426239 | 0.213119 | − | 0.977026i | \(-0.431638\pi\) | ||||
0.213119 | + | 0.977026i | \(0.431638\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.5139 | 0.624013 | ||||||||
\(470\) | 17.5139 | 0.807855 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 18.6333 | 0.857668 | ||||||||
\(473\) | −12.6333 | −0.580880 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.30278 | −0.151542 | ||||||||
\(476\) | −7.60555 | −0.348600 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 13.3305 | 0.609724 | ||||||||
\(479\) | −11.9361 | −0.545374 | −0.272687 | − | 0.962103i | \(-0.587912\pi\) | ||||
−0.272687 | + | 0.962103i | \(0.587912\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.69722 | 0.214175 | ||||||||
\(482\) | 0.275019 | 0.0125268 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.60555 | −0.300252 | ||||||||
\(485\) | −9.51388 | −0.432003 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.0000 | 1.72194 | 0.860972 | − | 0.508652i | \(-0.169856\pi\) | ||||
0.860972 | + | 0.508652i | \(0.169856\pi\) | |||||||
\(488\) | −33.3583 | −1.51006 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.30278 | 0.104029 | ||||||||
\(491\) | −20.7250 | −0.935305 | −0.467653 | − | 0.883912i | \(-0.654900\pi\) | ||||
−0.467653 | + | 0.883912i | \(0.654900\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.2111 | −0.549960 | ||||||||
\(494\) | −9.90833 | −0.445797 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.724981 | −0.0325526 | ||||||||
\(497\) | 2.09167 | 0.0938244 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −40.6333 | −1.81900 | −0.909498 | − | 0.415708i | \(-0.863534\pi\) | ||||
−0.909498 | + | 0.415708i | \(0.863534\pi\) | |||||||
\(500\) | 3.30278 | 0.147705 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.63331 | 0.429956 | ||||||||
\(503\) | 19.1194 | 0.852493 | 0.426247 | − | 0.904607i | \(-0.359836\pi\) | ||||
0.426247 | + | 0.904607i | \(0.359836\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.21110 | −0.409889 | ||||||||
\(506\) | 4.81665 | 0.214126 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −61.8444 | −2.74390 | ||||||||
\(509\) | −23.2389 | −1.03004 | −0.515022 | − | 0.857177i | \(-0.672216\pi\) | ||||
−0.515022 | + | 0.857177i | \(0.672216\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.2111 | −0.451713 | ||||||||
\(512\) | −3.42221 | −0.151242 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −27.6333 | −1.21885 | ||||||||
\(515\) | −15.7250 | −0.692925 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.8167 | 1.00348 | ||||||||
\(518\) | 8.30278 | 0.364803 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.90833 | 0.171391 | ||||||||
\(521\) | −43.6056 | −1.91039 | −0.955197 | − | 0.295971i | \(-0.904357\pi\) | ||||
−0.955197 | + | 0.295971i | \(0.904357\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.7250 | 0.600152 | 0.300076 | − | 0.953915i | \(-0.402988\pi\) | ||||
0.300076 | + | 0.953915i | \(0.402988\pi\) | |||||||
\(524\) | −27.4222 | −1.19794 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 28.7527 | 1.25368 | ||||||||
\(527\) | 5.51388 | 0.240188 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.5139 | −0.978864 | ||||||||
\(530\) | −12.6972 | −0.551532 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −10.9083 | −0.472936 | ||||||||
\(533\) | −9.00000 | −0.389833 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.0000 | 0.648507 | ||||||||
\(536\) | 40.5416 | 1.75113 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 21.6972 | 0.935434 | ||||||||
\(539\) | 3.00000 | 0.129219 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.5139 | −0.666994 | −0.333497 | − | 0.942751i | \(-0.608229\pi\) | ||||
−0.333497 | + | 0.942751i | \(0.608229\pi\) | |||||||
\(542\) | 27.9083 | 1.19877 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 12.2111 | 0.523547 | ||||||||
\(545\) | −1.69722 | −0.0727011 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.2111 | 1.63379 | 0.816894 | − | 0.576787i | \(-0.195694\pi\) | ||||
0.816894 | + | 0.576787i | \(0.195694\pi\) | |||||||
\(548\) | 60.8444 | 2.59914 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.90833 | 0.294572 | ||||||||
\(551\) | −17.5139 | −0.746116 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.9083 | −0.719015 | ||||||||
\(554\) | −7.11943 | −0.302476 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −18.5139 | −0.785163 | ||||||||
\(557\) | −15.4861 | −0.656168 | −0.328084 | − | 0.944649i | \(-0.606403\pi\) | ||||
−0.328084 | + | 0.944649i | \(0.606403\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.48612 | −0.232038 | ||||||||
\(560\) | 0.302776 | 0.0127946 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −47.7250 | −2.01316 | ||||||||
\(563\) | 35.9361 | 1.51453 | 0.757263 | − | 0.653110i | \(-0.226536\pi\) | ||||
0.757263 | + | 0.653110i | \(0.226536\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.9083 | 0.669268 | ||||||||
\(566\) | 6.69722 | 0.281505 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.27502 | 0.263294 | ||||||||
\(569\) | −30.6333 | −1.28422 | −0.642108 | − | 0.766615i | \(-0.721940\pi\) | ||||
−0.642108 | + | 0.766615i | \(0.721940\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.9361 | 0.834299 | 0.417150 | − | 0.908838i | \(-0.363029\pi\) | ||||
0.417150 | + | 0.908838i | \(0.363029\pi\) | |||||||
\(572\) | 12.9083 | 0.539724 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −15.9083 | −0.664001 | ||||||||
\(575\) | 0.697224 | 0.0290763 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.6056 | 1.64880 | 0.824400 | − | 0.566007i | \(-0.191513\pi\) | ||||
0.824400 | + | 0.566007i | \(0.191513\pi\) | |||||||
\(578\) | −26.9361 | −1.12039 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 17.5139 | 0.727224 | ||||||||
\(581\) | −12.2111 | −0.506602 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.5416 | −0.685085 | ||||||||
\(584\) | −30.6333 | −1.26762 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 46.6056 | 1.92526 | ||||||||
\(587\) | −2.09167 | −0.0863326 | −0.0431663 | − | 0.999068i | \(-0.513745\pi\) | ||||
−0.0431663 | + | 0.999068i | \(0.513745\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.90833 | 0.325857 | ||||||||
\(590\) | 14.3028 | 0.588836 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.09167 | 0.0448675 | ||||||||
\(593\) | −34.8167 | −1.42975 | −0.714874 | − | 0.699253i | \(-0.753516\pi\) | ||||
−0.714874 | + | 0.699253i | \(0.753516\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.30278 | −0.0944046 | ||||||||
\(596\) | 18.2111 | 0.745956 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.09167 | 0.0855349 | ||||||||
\(599\) | 36.4222 | 1.48817 | 0.744085 | − | 0.668084i | \(-0.232886\pi\) | ||||
0.744085 | + | 0.668084i | \(0.232886\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 45.1194 | 1.84046 | 0.920230 | − | 0.391378i | \(-0.128002\pi\) | ||||
0.920230 | + | 0.391378i | \(0.128002\pi\) | |||||||
\(602\) | −9.69722 | −0.395229 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.30278 | −0.134388 | ||||||||
\(605\) | −2.00000 | −0.0813116 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.6333 | 0.593948 | 0.296974 | − | 0.954886i | \(-0.404023\pi\) | ||||
0.296974 | + | 0.954886i | \(0.404023\pi\) | |||||||
\(608\) | 17.5139 | 0.710282 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −25.6056 | −1.03674 | ||||||||
\(611\) | 9.90833 | 0.400848 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.2389 | −1.10017 | −0.550084 | − | 0.835110i | \(-0.685404\pi\) | ||||
−0.550084 | + | 0.835110i | \(0.685404\pi\) | |||||||
\(614\) | 75.6333 | 3.05231 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.00000 | 0.362620 | ||||||||
\(617\) | 42.9083 | 1.72742 | 0.863712 | − | 0.503986i | \(-0.168134\pi\) | ||||
0.863712 | + | 0.503986i | \(0.168134\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.0278 | 0.644210 | 0.322105 | − | 0.946704i | \(-0.395610\pi\) | ||||
0.322105 | + | 0.946704i | \(0.395610\pi\) | |||||||
\(620\) | −7.90833 | −0.317606 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 32.4500 | 1.30112 | ||||||||
\(623\) | 10.8167 | 0.433360 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −34.1194 | −1.36369 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 21.8167 | 0.870579 | ||||||||
\(629\) | −8.30278 | −0.331053 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.7889 | −1.22569 | −0.612843 | − | 0.790204i | \(-0.709974\pi\) | ||||
−0.612843 | + | 0.790204i | \(0.709974\pi\) | |||||||
\(632\) | −50.7250 | −2.01773 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 39.6972 | 1.57658 | ||||||||
\(635\) | −18.7250 | −0.743078 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.30278 | 0.0516179 | ||||||||
\(638\) | 36.6333 | 1.45033 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −18.9083 | −0.747417 | ||||||||
\(641\) | 5.72498 | 0.226123 | 0.113062 | − | 0.993588i | \(-0.463934\pi\) | ||||
0.113062 | + | 0.993588i | \(0.463934\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.4861 | −0.531841 | −0.265920 | − | 0.963995i | \(-0.585676\pi\) | ||||
−0.265920 | + | 0.963995i | \(0.585676\pi\) | |||||||
\(644\) | 2.30278 | 0.0907421 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 17.5139 | 0.689074 | ||||||||
\(647\) | 30.0000 | 1.17942 | 0.589711 | − | 0.807614i | \(-0.299242\pi\) | ||||
0.589711 | + | 0.807614i | \(0.299242\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.6333 | 0.731421 | ||||||||
\(650\) | 3.00000 | 0.117670 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 76.6611 | 3.00228 | ||||||||
\(653\) | 4.88057 | 0.190991 | 0.0954957 | − | 0.995430i | \(-0.469556\pi\) | ||||
0.0954957 | + | 0.995430i | \(0.469556\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.30278 | −0.324416 | ||||||||
\(656\) | −2.09167 | −0.0816661 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 17.5139 | 0.682762 | ||||||||
\(659\) | −22.1833 | −0.864140 | −0.432070 | − | 0.901840i | \(-0.642217\pi\) | ||||
−0.432070 | + | 0.901840i | \(0.642217\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.72498 | 0.300467 | 0.150233 | − | 0.988651i | \(-0.451997\pi\) | ||||
0.150233 | + | 0.988651i | \(0.451997\pi\) | |||||||
\(662\) | 30.6333 | 1.19060 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −36.6333 | −1.42165 | ||||||||
\(665\) | −3.30278 | −0.128076 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.69722 | 0.143157 | ||||||||
\(668\) | 64.7527 | 2.50536 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 31.1194 | 1.20225 | ||||||||
\(671\) | −33.3583 | −1.28778 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.0000 | −1.07932 | −0.539660 | − | 0.841883i | \(-0.681447\pi\) | ||||
−0.539660 | + | 0.841883i | \(0.681447\pi\) | |||||||
\(674\) | 20.0278 | 0.771440 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −37.3305 | −1.43579 | ||||||||
\(677\) | −17.7889 | −0.683683 | −0.341841 | − | 0.939758i | \(-0.611051\pi\) | ||||
−0.341841 | + | 0.939758i | \(0.611051\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.51388 | −0.365109 | ||||||||
\(680\) | −6.90833 | −0.264922 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −16.5416 | −0.633412 | ||||||||
\(683\) | −45.3583 | −1.73559 | −0.867793 | − | 0.496925i | \(-0.834462\pi\) | ||||
−0.867793 | + | 0.496925i | \(0.834462\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.4222 | 0.703876 | ||||||||
\(686\) | 2.30278 | 0.0879204 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.27502 | −0.0486097 | ||||||||
\(689\) | −7.18335 | −0.273664 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.42221 | −0.282354 | −0.141177 | − | 0.989984i | \(-0.545089\pi\) | ||||
−0.141177 | + | 0.989984i | \(0.545089\pi\) | |||||||
\(692\) | −55.5416 | −2.11138 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 44.6611 | 1.69531 | ||||||||
\(695\) | −5.60555 | −0.212631 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.9083 | 0.602571 | ||||||||
\(698\) | 61.3305 | 2.32139 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.30278 | 0.124833 | ||||||||
\(701\) | 26.0278 | 0.983055 | 0.491527 | − | 0.870862i | \(-0.336439\pi\) | ||||
0.491527 | + | 0.870862i | \(0.336439\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.9083 | −0.449131 | ||||||||
\(704\) | −38.4500 | −1.44914 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 54.6333 | 2.05615 | ||||||||
\(707\) | −9.21110 | −0.346419 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −45.0278 | −1.69105 | −0.845526 | − | 0.533934i | \(-0.820713\pi\) | ||||
−0.845526 | + | 0.533934i | \(0.820713\pi\) | |||||||
\(710\) | 4.81665 | 0.180766 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 32.4500 | 1.21611 | ||||||||
\(713\) | −1.66947 | −0.0625221 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.90833 | 0.146163 | ||||||||
\(716\) | 55.5416 | 2.07569 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.72498 | 0.101695 | ||||||||
\(719\) | 19.3305 | 0.720907 | 0.360454 | − | 0.932777i | \(-0.382622\pi\) | ||||
0.360454 | + | 0.932777i | \(0.382622\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.7250 | −0.585629 | ||||||||
\(722\) | −18.6333 | −0.693460 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 57.5416 | 2.13852 | ||||||||
\(725\) | 5.30278 | 0.196940 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.4861 | −0.722700 | −0.361350 | − | 0.932430i | \(-0.617684\pi\) | ||||
−0.361350 | + | 0.932430i | \(0.617684\pi\) | |||||||
\(728\) | 3.90833 | 0.144852 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −23.5139 | −0.870288 | ||||||||
\(731\) | 9.69722 | 0.358665 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.5416 | 0.463236 | 0.231618 | − | 0.972807i | \(-0.425598\pi\) | ||||
0.231618 | + | 0.972807i | \(0.425598\pi\) | |||||||
\(734\) | −14.5139 | −0.535717 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.69722 | −0.136281 | ||||||||
\(737\) | 40.5416 | 1.49337 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.1833 | −0.742456 | −0.371228 | − | 0.928542i | \(-0.621063\pi\) | ||||
−0.371228 | + | 0.928542i | \(0.621063\pi\) | |||||||
\(740\) | 11.9083 | 0.437759 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12.6972 | −0.466130 | ||||||||
\(743\) | 34.5416 | 1.26721 | 0.633605 | − | 0.773657i | \(-0.281575\pi\) | ||||
0.633605 | + | 0.773657i | \(0.281575\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.51388 | 0.202013 | ||||||||
\(746\) | −4.39445 | −0.160892 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −22.8167 | −0.834259 | ||||||||
\(749\) | 15.0000 | 0.548088 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.0000 | 0.510867 | 0.255434 | − | 0.966827i | \(-0.417782\pi\) | ||||
0.255434 | + | 0.966827i | \(0.417782\pi\) | |||||||
\(752\) | 2.30278 | 0.0839736 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 15.9083 | 0.579347 | ||||||||
\(755\) | −1.00000 | −0.0363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.5416 | −0.528525 | −0.264262 | − | 0.964451i | \(-0.585128\pi\) | ||||
−0.264262 | + | 0.964451i | \(0.585128\pi\) | |||||||
\(758\) | −59.0278 | −2.14398 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −9.90833 | −0.359413 | ||||||||
\(761\) | 13.5416 | 0.490884 | 0.245442 | − | 0.969411i | \(-0.421067\pi\) | ||||
0.245442 | + | 0.969411i | \(0.421067\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.69722 | −0.0614436 | ||||||||
\(764\) | −22.1194 | −0.800253 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.486122 | 0.0175643 | ||||||||
\(767\) | 8.09167 | 0.292173 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.8167 | −0.967033 | −0.483517 | − | 0.875335i | \(-0.660641\pi\) | ||||
−0.483517 | + | 0.875335i | \(0.660641\pi\) | |||||||
\(770\) | 6.90833 | 0.248959 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 20.2111 | 0.727413 | ||||||||
\(773\) | 1.54163 | 0.0554487 | 0.0277244 | − | 0.999616i | \(-0.491174\pi\) | ||||
0.0277244 | + | 0.999616i | \(0.491174\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.39445 | −0.0860111 | ||||||||
\(776\) | −28.5416 | −1.02458 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20.0917 | −0.720321 | ||||||||
\(779\) | 22.8167 | 0.817491 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.27502 | 0.224538 | ||||||||
\(782\) | −3.69722 | −0.132212 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.302776 | 0.0108134 | ||||||||
\(785\) | 6.60555 | 0.235762 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.02776 | −0.107928 | −0.0539639 | − | 0.998543i | \(-0.517186\pi\) | ||||
−0.0539639 | + | 0.998543i | \(0.517186\pi\) | |||||||
\(788\) | −75.3583 | −2.68453 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −38.9361 | −1.38528 | ||||||||
\(791\) | 15.9083 | 0.565635 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.4861 | −0.514417 | ||||||||
\(794\) | 4.60555 | 0.163445 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 75.0555 | 2.66027 | ||||||||
\(797\) | −42.9083 | −1.51989 | −0.759945 | − | 0.649987i | \(-0.774774\pi\) | ||||
−0.759945 | + | 0.649987i | \(0.774774\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.5139 | −0.619596 | ||||||||
\(800\) | −5.30278 | −0.187481 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −13.1833 | −0.465520 | ||||||||
\(803\) | −30.6333 | −1.08103 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.697224 | 0.0245739 | ||||||||
\(806\) | −7.18335 | −0.253023 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −27.6333 | −0.972136 | ||||||||
\(809\) | −19.1833 | −0.674451 | −0.337225 | − | 0.941424i | \(-0.609488\pi\) | ||||
−0.337225 | + | 0.941424i | \(0.609488\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.5139 | −0.860799 | −0.430399 | − | 0.902639i | \(-0.641627\pi\) | ||||
−0.430399 | + | 0.902639i | \(0.641627\pi\) | |||||||
\(812\) | 17.5139 | 0.614617 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 24.9083 | 0.873036 | ||||||||
\(815\) | 23.2111 | 0.813049 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.9083 | 0.486591 | ||||||||
\(818\) | 32.2389 | 1.12721 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −22.8167 | −0.796792 | ||||||||
\(821\) | 10.8167 | 0.377504 | 0.188752 | − | 0.982025i | \(-0.439556\pi\) | ||||
0.188752 | + | 0.982025i | \(0.439556\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.6333 | 1.13753 | 0.568763 | − | 0.822502i | \(-0.307422\pi\) | ||||
0.568763 | + | 0.822502i | \(0.307422\pi\) | |||||||
\(824\) | −47.1749 | −1.64342 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.3028 | 0.497657 | ||||||||
\(827\) | 0.633308 | 0.0220223 | 0.0110111 | − | 0.999939i | \(-0.496495\pi\) | ||||
0.0110111 | + | 0.999939i | \(0.496495\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.0555 | −0.800751 | −0.400376 | − | 0.916351i | \(-0.631120\pi\) | ||||
−0.400376 | + | 0.916351i | \(0.631120\pi\) | |||||||
\(830\) | −28.1194 | −0.976040 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −16.6972 | −0.578872 | ||||||||
\(833\) | −2.30278 | −0.0797864 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.6056 | 0.678478 | ||||||||
\(836\) | −32.7250 | −1.13182 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 30.3583 | 1.04871 | ||||||||
\(839\) | −11.0917 | −0.382927 | −0.191464 | − | 0.981500i | \(-0.561323\pi\) | ||||
−0.191464 | + | 0.981500i | \(0.561323\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.880571 | −0.0303645 | ||||||||
\(842\) | 6.21110 | 0.214049 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −37.6333 | −1.29539 | ||||||||
\(845\) | −11.3028 | −0.388827 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.00000 | −0.0687208 | ||||||||
\(848\) | −1.66947 | −0.0573298 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.30278 | −0.181884 | ||||||||
\(851\) | 2.51388 | 0.0861746 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.8444 | 1.02185 | 0.510927 | − | 0.859624i | \(-0.329302\pi\) | ||||
0.510927 | + | 0.859624i | \(0.329302\pi\) | |||||||
\(854\) | −25.6056 | −0.876204 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 45.0000 | 1.53807 | ||||||||
\(857\) | −34.2666 | −1.17053 | −0.585263 | − | 0.810844i | \(-0.699009\pi\) | ||||
−0.585263 | + | 0.810844i | \(0.699009\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.8167 | 0.949092 | 0.474546 | − | 0.880231i | \(-0.342612\pi\) | ||||
0.474546 | + | 0.880231i | \(0.342612\pi\) | |||||||
\(860\) | −13.9083 | −0.474270 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 82.7527 | 2.81857 | ||||||||
\(863\) | −31.2666 | −1.06433 | −0.532164 | − | 0.846641i | \(-0.678621\pi\) | ||||
−0.532164 | + | 0.846641i | \(0.678621\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.8167 | −0.571783 | ||||||||
\(866\) | 35.3028 | 1.19964 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.90833 | −0.268426 | ||||||||
\(869\) | −50.7250 | −1.72073 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.6056 | 0.596541 | ||||||||
\(872\) | −5.09167 | −0.172426 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.30278 | −0.179369 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.6333 | −0.764272 | −0.382136 | − | 0.924106i | \(-0.624811\pi\) | ||||
−0.382136 | + | 0.924106i | \(0.624811\pi\) | |||||||
\(878\) | −60.7805 | −2.05124 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.908327 | 0.0306197 | ||||||||
\(881\) | −45.6333 | −1.53743 | −0.768713 | − | 0.639594i | \(-0.779102\pi\) | ||||
−0.768713 | + | 0.639594i | \(0.779102\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.02776 | −0.202850 | −0.101425 | − | 0.994843i | \(-0.532340\pi\) | ||||
−0.101425 | + | 0.994843i | \(0.532340\pi\) | |||||||
\(884\) | −9.90833 | −0.333253 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.633308 | −0.0212764 | ||||||||
\(887\) | −22.6056 | −0.759020 | −0.379510 | − | 0.925188i | \(-0.623907\pi\) | ||||
−0.379510 | + | 0.925188i | \(0.623907\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.7250 | −0.628016 | ||||||||
\(890\) | 24.9083 | 0.834929 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 66.7527 | 2.23505 | ||||||||
\(893\) | −25.1194 | −0.840590 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.8167 | 0.562119 | ||||||||
\(896\) | −18.9083 | −0.631683 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −41.4500 | −1.38320 | ||||||||
\(899\) | −12.6972 | −0.423476 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.6972 | 0.423006 | ||||||||
\(902\) | −47.7250 | −1.58907 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 47.7250 | 1.58731 | ||||||||
\(905\) | 17.4222 | 0.579134 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −52.5694 | −1.74554 | −0.872769 | − | 0.488133i | \(-0.837678\pi\) | ||||
−0.872769 | + | 0.488133i | \(0.837678\pi\) | |||||||
\(908\) | −21.4222 | −0.710921 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.00000 | 0.0994490 | ||||||||
\(911\) | −27.6333 | −0.915532 | −0.457766 | − | 0.889073i | \(-0.651350\pi\) | ||||
−0.457766 | + | 0.889073i | \(0.651350\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −36.6333 | −1.21239 | ||||||||
\(914\) | 51.3583 | 1.69878 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.90833 | 0.195217 | ||||||||
\(917\) | −8.30278 | −0.274182 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.48612 | 0.0820096 | 0.0410048 | − | 0.999159i | \(-0.486944\pi\) | ||||
0.0410048 | + | 0.999159i | \(0.486944\pi\) | |||||||
\(920\) | 2.09167 | 0.0689604 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −61.0555 | −2.01076 | ||||||||
\(923\) | 2.72498 | 0.0896938 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.60555 | 0.118550 | ||||||||
\(926\) | 25.1833 | 0.827576 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −28.1194 | −0.923065 | ||||||||
\(929\) | 39.5694 | 1.29823 | 0.649115 | − | 0.760690i | \(-0.275139\pi\) | ||||
0.649115 | + | 0.760690i | \(0.275139\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.30278 | −0.108244 | ||||||||
\(932\) | −32.7250 | −1.07194 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 21.2111 | 0.694048 | ||||||||
\(935\) | −6.90833 | −0.225926 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.4222 | 1.45121 | 0.725605 | − | 0.688111i | \(-0.241560\pi\) | ||||
0.725605 | + | 0.688111i | \(0.241560\pi\) | |||||||
\(938\) | 31.1194 | 1.01609 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 25.1194 | 0.819305 | ||||||||
\(941\) | −34.2666 | −1.11706 | −0.558530 | − | 0.829484i | \(-0.688634\pi\) | ||||
−0.558530 | + | 0.829484i | \(0.688634\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.81665 | −0.156852 | ||||||||
\(944\) | 1.88057 | 0.0612074 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −29.0917 | −0.945852 | ||||||||
\(947\) | 1.33053 | 0.0432365 | 0.0216182 | − | 0.999766i | \(-0.493118\pi\) | ||||
0.0216182 | + | 0.999766i | \(0.493118\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.3028 | −0.431826 | ||||||||
\(950\) | −7.60555 | −0.246757 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.90833 | −0.223900 | ||||||||
\(953\) | −51.4222 | −1.66573 | −0.832864 | − | 0.553477i | \(-0.813301\pi\) | ||||
−0.832864 | + | 0.553477i | \(0.813301\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.69722 | −0.216717 | ||||||||
\(956\) | 19.1194 | 0.618367 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −27.4861 | −0.888036 | ||||||||
\(959\) | 18.4222 | 0.594884 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.2666 | −0.815052 | ||||||||
\(962\) | 10.8167 | 0.348743 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.394449 | 0.0127043 | ||||||||
\(965\) | 6.11943 | 0.196991 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.8444 | −0.831100 | −0.415550 | − | 0.909570i | \(-0.636411\pi\) | ||||
−0.415550 | + | 0.909570i | \(0.636411\pi\) | |||||||
\(968\) | −6.00000 | −0.192847 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −21.9083 | −0.703434 | ||||||||
\(971\) | −5.57779 | −0.179000 | −0.0895000 | − | 0.995987i | \(-0.528527\pi\) | ||||
−0.0895000 | + | 0.995987i | \(0.528527\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.60555 | −0.179706 | ||||||||
\(974\) | 87.5055 | 2.80386 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.36669 | −0.107765 | ||||||||
\(977\) | 0.422205 | 0.0135075 | 0.00675377 | − | 0.999977i | \(-0.497850\pi\) | ||||
0.00675377 | + | 0.999977i | \(0.497850\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32.4500 | 1.03711 | ||||||||
\(980\) | 3.30278 | 0.105503 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −47.7250 | −1.52297 | ||||||||
\(983\) | 20.5139 | 0.654291 | 0.327146 | − | 0.944974i | \(-0.393913\pi\) | ||||
0.327146 | + | 0.944974i | \(0.393913\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.8167 | −0.726999 | ||||||||
\(986\) | −28.1194 | −0.895505 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −14.2111 | −0.452115 | ||||||||
\(989\) | −2.93608 | −0.0933620 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −59.0555 | −1.87596 | −0.937980 | − | 0.346689i | \(-0.887306\pi\) | ||||
−0.937980 | + | 0.346689i | \(0.887306\pi\) | |||||||
\(992\) | 12.6972 | 0.403137 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.81665 | 0.152775 | ||||||||
\(995\) | 22.7250 | 0.720430 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.8167 | −0.469248 | −0.234624 | − | 0.972086i | \(-0.575386\pi\) | ||||
−0.234624 | + | 0.972086i | \(0.575386\pi\) | |||||||
\(998\) | −93.5694 | −2.96189 | ||||||||
\(999\) | 0 | 0 |
(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 | 945.2.a.j.1.2 | yes | 2 | |
3.2 | odd | 2 | 945.2.a.f.1.1 | ✓ | 2 | ||
5.4 | even | 2 | 4725.2.a.z.1.1 | 2 | |||
7.6 | odd | 2 | 6615.2.a.u.1.2 | 2 | |||
15.14 | odd | 2 | 4725.2.a.bf.1.2 | 2 | |||
21.20 | even | 2 | 6615.2.a.q.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
945.2.a.f.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
945.2.a.j.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
4725.2.a.z.1.1 | 2 | 5.4 | even | 2 | |||
4725.2.a.bf.1.2 | 2 | 15.14 | odd | 2 | |||
6615.2.a.q.1.1 | 2 | 21.20 | even | 2 | |||
6615.2.a.u.1.2 | 2 | 7.6 | odd | 2 |