Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, 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("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.13298000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 10x^{4} + 3x^{3} + 26x^{2} + 13x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 770) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.42266\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.17142 | 0.676320 | 0.338160 | − | 0.941089i | \(-0.390195\pi\) | ||||
0.338160 | + | 0.941089i | \(0.390195\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.17142 | −0.478231 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.62777 | −0.542591 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.17142 | 0.338160 | ||||||||
\(13\) | −2.71483 | −0.752958 | −0.376479 | − | 0.926425i | \(-0.622865\pi\) | ||||
−0.376479 | + | 0.926425i | \(0.622865\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 1.17142 | 0.302460 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.34260 | 1.29577 | 0.647885 | − | 0.761738i | \(-0.275654\pi\) | ||||
0.647885 | + | 0.761738i | \(0.275654\pi\) | |||||||
\(18\) | 1.62777 | 0.383670 | ||||||||
\(19\) | −3.97605 | −0.912167 | −0.456084 | − | 0.889937i | \(-0.650748\pi\) | ||||
−0.456084 | + | 0.889937i | \(0.650748\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −1.17142 | −0.255625 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.49704 | 1.14621 | 0.573106 | − | 0.819481i | \(-0.305738\pi\) | ||||
0.573106 | + | 0.819481i | \(0.305738\pi\) | |||||||
\(24\) | −1.17142 | −0.239115 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.71483 | 0.532422 | ||||||||
\(27\) | −5.42107 | −1.04329 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 4.99939 | 0.928364 | 0.464182 | − | 0.885740i | \(-0.346348\pi\) | ||||
0.464182 | + | 0.885740i | \(0.346348\pi\) | |||||||
\(30\) | −1.17142 | −0.213871 | ||||||||
\(31\) | −2.87010 | −0.515485 | −0.257743 | − | 0.966214i | \(-0.582979\pi\) | ||||
−0.257743 | + | 0.966214i | \(0.582979\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.34260 | −0.916248 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −1.62777 | −0.271295 | ||||||||
\(37\) | 0.0405417 | 0.00666501 | 0.00333251 | − | 0.999994i | \(-0.498939\pi\) | ||||
0.00333251 | + | 0.999994i | \(0.498939\pi\) | |||||||
\(38\) | 3.97605 | 0.645000 | ||||||||
\(39\) | −3.18021 | −0.509241 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −5.13012 | −0.801191 | −0.400595 | − | 0.916255i | \(-0.631197\pi\) | ||||
−0.400595 | + | 0.916255i | \(0.631197\pi\) | |||||||
\(42\) | 1.17142 | 0.180754 | ||||||||
\(43\) | −12.2705 | −1.87123 | −0.935617 | − | 0.353017i | \(-0.885156\pi\) | ||||
−0.935617 | + | 0.353017i | \(0.885156\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.62777 | −0.242654 | ||||||||
\(46\) | −5.49704 | −0.810495 | ||||||||
\(47\) | 9.89983 | 1.44404 | 0.722019 | − | 0.691873i | \(-0.243214\pi\) | ||||
0.722019 | + | 0.691873i | \(0.243214\pi\) | |||||||
\(48\) | 1.17142 | 0.169080 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 6.25844 | 0.876356 | ||||||||
\(52\) | −2.71483 | −0.376479 | ||||||||
\(53\) | 4.55880 | 0.626199 | 0.313100 | − | 0.949720i | \(-0.398633\pi\) | ||||
0.313100 | + | 0.949720i | \(0.398633\pi\) | |||||||
\(54\) | 5.42107 | 0.737714 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −4.65762 | −0.616917 | ||||||||
\(58\) | −4.99939 | −0.656453 | ||||||||
\(59\) | −0.584705 | −0.0761221 | −0.0380610 | − | 0.999275i | \(-0.512118\pi\) | ||||
−0.0380610 | + | 0.999275i | \(0.512118\pi\) | |||||||
\(60\) | 1.17142 | 0.151230 | ||||||||
\(61\) | −7.25963 | −0.929500 | −0.464750 | − | 0.885442i | \(-0.653856\pi\) | ||||
−0.464750 | + | 0.885442i | \(0.653856\pi\) | |||||||
\(62\) | 2.87010 | 0.364503 | ||||||||
\(63\) | 1.62777 | 0.205080 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.71483 | −0.336733 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.4148 | −1.76105 | −0.880526 | − | 0.473998i | \(-0.842811\pi\) | ||||
−0.880526 | + | 0.473998i | \(0.842811\pi\) | |||||||
\(68\) | 5.34260 | 0.647885 | ||||||||
\(69\) | 6.43935 | 0.775207 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | 8.20815 | 0.974128 | 0.487064 | − | 0.873366i | \(-0.338068\pi\) | ||||
0.487064 | + | 0.873366i | \(0.338068\pi\) | |||||||
\(72\) | 1.62777 | 0.191835 | ||||||||
\(73\) | −14.5897 | −1.70760 | −0.853801 | − | 0.520600i | \(-0.825708\pi\) | ||||
−0.853801 | + | 0.520600i | \(0.825708\pi\) | |||||||
\(74\) | −0.0405417 | −0.00471288 | ||||||||
\(75\) | 1.17142 | 0.135264 | ||||||||
\(76\) | −3.97605 | −0.456084 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.18021 | 0.360088 | ||||||||
\(79\) | −6.75342 | −0.759819 | −0.379910 | − | 0.925024i | \(-0.624045\pi\) | ||||
−0.379910 | + | 0.925024i | \(0.624045\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −1.46704 | −0.163005 | ||||||||
\(82\) | 5.13012 | 0.566527 | ||||||||
\(83\) | 15.5794 | 1.71006 | 0.855031 | − | 0.518577i | \(-0.173538\pi\) | ||||
0.855031 | + | 0.518577i | \(0.173538\pi\) | |||||||
\(84\) | −1.17142 | −0.127813 | ||||||||
\(85\) | 5.34260 | 0.579486 | ||||||||
\(86\) | 12.2705 | 1.32316 | ||||||||
\(87\) | 5.85640 | 0.627872 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.73408 | 0.289812 | 0.144906 | − | 0.989445i | \(-0.453712\pi\) | ||||
0.144906 | + | 0.989445i | \(0.453712\pi\) | |||||||
\(90\) | 1.62777 | 0.171582 | ||||||||
\(91\) | 2.71483 | 0.284591 | ||||||||
\(92\) | 5.49704 | 0.573106 | ||||||||
\(93\) | −3.36210 | −0.348633 | ||||||||
\(94\) | −9.89983 | −1.02109 | ||||||||
\(95\) | −3.97605 | −0.407934 | ||||||||
\(96\) | −1.17142 | −0.119558 | ||||||||
\(97\) | −1.32780 | −0.134818 | −0.0674088 | − | 0.997725i | \(-0.521473\pi\) | ||||
−0.0674088 | + | 0.997725i | \(0.521473\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −12.9533 | −1.28890 | −0.644449 | − | 0.764647i | \(-0.722913\pi\) | ||||
−0.644449 | + | 0.764647i | \(0.722913\pi\) | |||||||
\(102\) | −6.25844 | −0.619678 | ||||||||
\(103\) | 9.24014 | 0.910458 | 0.455229 | − | 0.890374i | \(-0.349557\pi\) | ||||
0.455229 | + | 0.890374i | \(0.349557\pi\) | |||||||
\(104\) | 2.71483 | 0.266211 | ||||||||
\(105\) | −1.17142 | −0.114319 | ||||||||
\(106\) | −4.55880 | −0.442790 | ||||||||
\(107\) | −10.0022 | −0.966947 | −0.483473 | − | 0.875359i | \(-0.660625\pi\) | ||||
−0.483473 | + | 0.875359i | \(0.660625\pi\) | |||||||
\(108\) | −5.42107 | −0.521643 | ||||||||
\(109\) | 0.535064 | 0.0512498 | 0.0256249 | − | 0.999672i | \(-0.491842\pi\) | ||||
0.0256249 | + | 0.999672i | \(0.491842\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.0474914 | 0.00450768 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −1.55217 | −0.146016 | −0.0730078 | − | 0.997331i | \(-0.523260\pi\) | ||||
−0.0730078 | + | 0.997331i | \(0.523260\pi\) | |||||||
\(114\) | 4.65762 | 0.436226 | ||||||||
\(115\) | 5.49704 | 0.512602 | ||||||||
\(116\) | 4.99939 | 0.464182 | ||||||||
\(117\) | 4.41912 | 0.408548 | ||||||||
\(118\) | 0.584705 | 0.0538264 | ||||||||
\(119\) | −5.34260 | −0.489755 | ||||||||
\(120\) | −1.17142 | −0.106936 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 7.25963 | 0.657256 | ||||||||
\(123\) | −6.00954 | −0.541862 | ||||||||
\(124\) | −2.87010 | −0.257743 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.62777 | −0.145013 | ||||||||
\(127\) | 17.2777 | 1.53315 | 0.766575 | − | 0.642155i | \(-0.221959\pi\) | ||||
0.766575 | + | 0.642155i | \(0.221959\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −14.3739 | −1.26555 | ||||||||
\(130\) | 2.71483 | 0.238106 | ||||||||
\(131\) | −11.0180 | −0.962651 | −0.481325 | − | 0.876542i | \(-0.659844\pi\) | ||||
−0.481325 | + | 0.876542i | \(0.659844\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.97605 | 0.344767 | ||||||||
\(134\) | 14.4148 | 1.24525 | ||||||||
\(135\) | −5.42107 | −0.466572 | ||||||||
\(136\) | −5.34260 | −0.458124 | ||||||||
\(137\) | 9.48971 | 0.810760 | 0.405380 | − | 0.914148i | \(-0.367139\pi\) | ||||
0.405380 | + | 0.914148i | \(0.367139\pi\) | |||||||
\(138\) | −6.43935 | −0.548154 | ||||||||
\(139\) | 10.8603 | 0.921162 | 0.460581 | − | 0.887618i | \(-0.347641\pi\) | ||||
0.460581 | + | 0.887618i | \(0.347641\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | 11.5969 | 0.976633 | ||||||||
\(142\) | −8.20815 | −0.688813 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.62777 | −0.135648 | ||||||||
\(145\) | 4.99939 | 0.415177 | ||||||||
\(146\) | 14.5897 | 1.20746 | ||||||||
\(147\) | 1.17142 | 0.0966172 | ||||||||
\(148\) | 0.0405417 | 0.00333251 | ||||||||
\(149\) | −12.3315 | −1.01024 | −0.505118 | − | 0.863050i | \(-0.668551\pi\) | ||||
−0.505118 | + | 0.863050i | \(0.668551\pi\) | |||||||
\(150\) | −1.17142 | −0.0956462 | ||||||||
\(151\) | 8.70759 | 0.708613 | 0.354307 | − | 0.935129i | \(-0.384717\pi\) | ||||
0.354307 | + | 0.935129i | \(0.384717\pi\) | |||||||
\(152\) | 3.97605 | 0.322500 | ||||||||
\(153\) | −8.69653 | −0.703073 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.87010 | −0.230532 | ||||||||
\(156\) | −3.18021 | −0.254620 | ||||||||
\(157\) | −19.1275 | −1.52654 | −0.763269 | − | 0.646081i | \(-0.776407\pi\) | ||||
−0.763269 | + | 0.646081i | \(0.776407\pi\) | |||||||
\(158\) | 6.75342 | 0.537273 | ||||||||
\(159\) | 5.34028 | 0.423511 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −5.49704 | −0.433228 | ||||||||
\(162\) | 1.46704 | 0.115262 | ||||||||
\(163\) | −18.6244 | −1.45878 | −0.729389 | − | 0.684099i | \(-0.760195\pi\) | ||||
−0.729389 | + | 0.684099i | \(0.760195\pi\) | |||||||
\(164\) | −5.13012 | −0.400595 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.5794 | −1.20920 | ||||||||
\(167\) | −1.66091 | −0.128525 | −0.0642624 | − | 0.997933i | \(-0.520469\pi\) | ||||
−0.0642624 | + | 0.997933i | \(0.520469\pi\) | |||||||
\(168\) | 1.17142 | 0.0903771 | ||||||||
\(169\) | −5.62971 | −0.433054 | ||||||||
\(170\) | −5.34260 | −0.409759 | ||||||||
\(171\) | 6.47209 | 0.494933 | ||||||||
\(172\) | −12.2705 | −0.935617 | ||||||||
\(173\) | 10.4055 | 0.791115 | 0.395557 | − | 0.918441i | \(-0.370551\pi\) | ||||
0.395557 | + | 0.918441i | \(0.370551\pi\) | |||||||
\(174\) | −5.85640 | −0.443972 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.684935 | −0.0514829 | ||||||||
\(178\) | −2.73408 | −0.204928 | ||||||||
\(179\) | −25.4215 | −1.90010 | −0.950048 | − | 0.312104i | \(-0.898966\pi\) | ||||
−0.950048 | + | 0.312104i | \(0.898966\pi\) | |||||||
\(180\) | −1.62777 | −0.121327 | ||||||||
\(181\) | −9.34641 | −0.694713 | −0.347357 | − | 0.937733i | \(-0.612921\pi\) | ||||
−0.347357 | + | 0.937733i | \(0.612921\pi\) | |||||||
\(182\) | −2.71483 | −0.201236 | ||||||||
\(183\) | −8.50409 | −0.628640 | ||||||||
\(184\) | −5.49704 | −0.405247 | ||||||||
\(185\) | 0.0405417 | 0.00298068 | ||||||||
\(186\) | 3.36210 | 0.246521 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 9.89983 | 0.722019 | ||||||||
\(189\) | 5.42107 | 0.394325 | ||||||||
\(190\) | 3.97605 | 0.288453 | ||||||||
\(191\) | 4.55912 | 0.329886 | 0.164943 | − | 0.986303i | \(-0.447256\pi\) | ||||
0.164943 | + | 0.986303i | \(0.447256\pi\) | |||||||
\(192\) | 1.17142 | 0.0845401 | ||||||||
\(193\) | −15.8146 | −1.13836 | −0.569181 | − | 0.822212i | \(-0.692740\pi\) | ||||
−0.569181 | + | 0.822212i | \(0.692740\pi\) | |||||||
\(194\) | 1.32780 | 0.0953304 | ||||||||
\(195\) | −3.18021 | −0.227739 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −14.6162 | −1.04136 | −0.520679 | − | 0.853753i | \(-0.674321\pi\) | ||||
−0.520679 | + | 0.853753i | \(0.674321\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.4255 | 1.16438 | 0.582188 | − | 0.813054i | \(-0.302197\pi\) | ||||
0.582188 | + | 0.813054i | \(0.302197\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −16.8858 | −1.19104 | ||||||||
\(202\) | 12.9533 | 0.911389 | ||||||||
\(203\) | −4.99939 | −0.350889 | ||||||||
\(204\) | 6.25844 | 0.438178 | ||||||||
\(205\) | −5.13012 | −0.358303 | ||||||||
\(206\) | −9.24014 | −0.643791 | ||||||||
\(207\) | −8.94793 | −0.621924 | ||||||||
\(208\) | −2.71483 | −0.188239 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.17142 | 0.0808358 | ||||||||
\(211\) | 4.78958 | 0.329728 | 0.164864 | − | 0.986316i | \(-0.447281\pi\) | ||||
0.164864 | + | 0.986316i | \(0.447281\pi\) | |||||||
\(212\) | 4.55880 | 0.313100 | ||||||||
\(213\) | 9.61520 | 0.658823 | ||||||||
\(214\) | 10.0022 | 0.683735 | ||||||||
\(215\) | −12.2705 | −0.836841 | ||||||||
\(216\) | 5.42107 | 0.368857 | ||||||||
\(217\) | 2.87010 | 0.194835 | ||||||||
\(218\) | −0.535064 | −0.0362391 | ||||||||
\(219\) | −17.0907 | −1.15489 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.5042 | −0.975661 | ||||||||
\(222\) | −0.0474914 | −0.00318741 | ||||||||
\(223\) | −23.2488 | −1.55685 | −0.778426 | − | 0.627737i | \(-0.783981\pi\) | ||||
−0.778426 | + | 0.627737i | \(0.783981\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −1.62777 | −0.108518 | ||||||||
\(226\) | 1.55217 | 0.103249 | ||||||||
\(227\) | 17.0503 | 1.13167 | 0.565834 | − | 0.824519i | \(-0.308554\pi\) | ||||
0.565834 | + | 0.824519i | \(0.308554\pi\) | |||||||
\(228\) | −4.65762 | −0.308459 | ||||||||
\(229\) | 10.5051 | 0.694196 | 0.347098 | − | 0.937829i | \(-0.387167\pi\) | ||||
0.347098 | + | 0.937829i | \(0.387167\pi\) | |||||||
\(230\) | −5.49704 | −0.362464 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.99939 | −0.328226 | ||||||||
\(233\) | −21.0739 | −1.38060 | −0.690300 | − | 0.723523i | \(-0.742521\pi\) | ||||
−0.690300 | + | 0.723523i | \(0.742521\pi\) | |||||||
\(234\) | −4.41912 | −0.288887 | ||||||||
\(235\) | 9.89983 | 0.645794 | ||||||||
\(236\) | −0.584705 | −0.0380610 | ||||||||
\(237\) | −7.91110 | −0.513881 | ||||||||
\(238\) | 5.34260 | 0.346309 | ||||||||
\(239\) | −1.21833 | −0.0788074 | −0.0394037 | − | 0.999223i | \(-0.512546\pi\) | ||||
−0.0394037 | + | 0.999223i | \(0.512546\pi\) | |||||||
\(240\) | 1.17142 | 0.0756149 | ||||||||
\(241\) | 1.70364 | 0.109741 | 0.0548706 | − | 0.998493i | \(-0.482525\pi\) | ||||
0.0548706 | + | 0.998493i | \(0.482525\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.5447 | 0.933042 | ||||||||
\(244\) | −7.25963 | −0.464750 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 6.00954 | 0.383154 | ||||||||
\(247\) | 10.7943 | 0.686824 | ||||||||
\(248\) | 2.87010 | 0.182252 | ||||||||
\(249\) | 18.2500 | 1.15655 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −19.2825 | −1.21710 | −0.608551 | − | 0.793515i | \(-0.708249\pi\) | ||||
−0.608551 | + | 0.793515i | \(0.708249\pi\) | |||||||
\(252\) | 1.62777 | 0.102540 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −17.2777 | −1.08410 | ||||||||
\(255\) | 6.25844 | 0.391918 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.96978 | −0.621898 | −0.310949 | − | 0.950427i | \(-0.600647\pi\) | ||||
−0.310949 | + | 0.950427i | \(0.600647\pi\) | |||||||
\(258\) | 14.3739 | 0.894881 | ||||||||
\(259\) | −0.0405417 | −0.00251914 | ||||||||
\(260\) | −2.71483 | −0.168367 | ||||||||
\(261\) | −8.13787 | −0.503722 | ||||||||
\(262\) | 11.0180 | 0.680697 | ||||||||
\(263\) | −15.3900 | −0.948985 | −0.474493 | − | 0.880260i | \(-0.657368\pi\) | ||||
−0.474493 | + | 0.880260i | \(0.657368\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.55880 | 0.280045 | ||||||||
\(266\) | −3.97605 | −0.243787 | ||||||||
\(267\) | 3.20276 | 0.196006 | ||||||||
\(268\) | −14.4148 | −0.880526 | ||||||||
\(269\) | −16.6521 | −1.01530 | −0.507649 | − | 0.861564i | \(-0.669485\pi\) | ||||
−0.507649 | + | 0.861564i | \(0.669485\pi\) | |||||||
\(270\) | 5.42107 | 0.329916 | ||||||||
\(271\) | 2.85449 | 0.173398 | 0.0866989 | − | 0.996235i | \(-0.472368\pi\) | ||||
0.0866989 | + | 0.996235i | \(0.472368\pi\) | |||||||
\(272\) | 5.34260 | 0.323943 | ||||||||
\(273\) | 3.18021 | 0.192475 | ||||||||
\(274\) | −9.48971 | −0.573294 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.43935 | 0.387603 | ||||||||
\(277\) | −25.0469 | −1.50492 | −0.752462 | − | 0.658636i | \(-0.771134\pi\) | ||||
−0.752462 | + | 0.658636i | \(0.771134\pi\) | |||||||
\(278\) | −10.8603 | −0.651360 | ||||||||
\(279\) | 4.67187 | 0.279698 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | −4.37825 | −0.261184 | −0.130592 | − | 0.991436i | \(-0.541688\pi\) | ||||
−0.130592 | + | 0.991436i | \(0.541688\pi\) | |||||||
\(282\) | −11.5969 | −0.690584 | ||||||||
\(283\) | 7.46206 | 0.443573 | 0.221787 | − | 0.975095i | \(-0.428811\pi\) | ||||
0.221787 | + | 0.975095i | \(0.428811\pi\) | |||||||
\(284\) | 8.20815 | 0.487064 | ||||||||
\(285\) | −4.65762 | −0.275894 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.13012 | 0.302822 | ||||||||
\(288\) | 1.62777 | 0.0959174 | ||||||||
\(289\) | 11.5434 | 0.679022 | ||||||||
\(290\) | −4.99939 | −0.293575 | ||||||||
\(291\) | −1.55541 | −0.0911799 | ||||||||
\(292\) | −14.5897 | −0.853801 | ||||||||
\(293\) | −5.85672 | −0.342153 | −0.171077 | − | 0.985258i | \(-0.554725\pi\) | ||||
−0.171077 | + | 0.985258i | \(0.554725\pi\) | |||||||
\(294\) | −1.17142 | −0.0683187 | ||||||||
\(295\) | −0.584705 | −0.0340428 | ||||||||
\(296\) | −0.0405417 | −0.00235644 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.3315 | 0.714344 | ||||||||
\(299\) | −14.9235 | −0.863050 | ||||||||
\(300\) | 1.17142 | 0.0676320 | ||||||||
\(301\) | 12.2705 | 0.707260 | ||||||||
\(302\) | −8.70759 | −0.501065 | ||||||||
\(303\) | −15.1737 | −0.871709 | ||||||||
\(304\) | −3.97605 | −0.228042 | ||||||||
\(305\) | −7.25963 | −0.415685 | ||||||||
\(306\) | 8.69653 | 0.497148 | ||||||||
\(307\) | −34.7874 | −1.98542 | −0.992712 | − | 0.120513i | \(-0.961546\pi\) | ||||
−0.992712 | + | 0.120513i | \(0.961546\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.8241 | 0.615761 | ||||||||
\(310\) | 2.87010 | 0.163011 | ||||||||
\(311\) | 19.5779 | 1.11016 | 0.555082 | − | 0.831796i | \(-0.312687\pi\) | ||||
0.555082 | + | 0.831796i | \(0.312687\pi\) | |||||||
\(312\) | 3.18021 | 0.180044 | ||||||||
\(313\) | −12.3630 | −0.698796 | −0.349398 | − | 0.936974i | \(-0.613614\pi\) | ||||
−0.349398 | + | 0.936974i | \(0.613614\pi\) | |||||||
\(314\) | 19.1275 | 1.07942 | ||||||||
\(315\) | 1.62777 | 0.0917146 | ||||||||
\(316\) | −6.75342 | −0.379910 | ||||||||
\(317\) | 5.15560 | 0.289568 | 0.144784 | − | 0.989463i | \(-0.453751\pi\) | ||||
0.144784 | + | 0.989463i | \(0.453751\pi\) | |||||||
\(318\) | −5.34028 | −0.299468 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −11.7168 | −0.653966 | ||||||||
\(322\) | 5.49704 | 0.306338 | ||||||||
\(323\) | −21.2424 | −1.18196 | ||||||||
\(324\) | −1.46704 | −0.0815024 | ||||||||
\(325\) | −2.71483 | −0.150592 | ||||||||
\(326\) | 18.6244 | 1.03151 | ||||||||
\(327\) | 0.626785 | 0.0346613 | ||||||||
\(328\) | 5.13012 | 0.283264 | ||||||||
\(329\) | −9.89983 | −0.545795 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.5061 | −1.78670 | −0.893349 | − | 0.449364i | \(-0.851651\pi\) | ||||
−0.893349 | + | 0.449364i | \(0.851651\pi\) | |||||||
\(332\) | 15.5794 | 0.855031 | ||||||||
\(333\) | −0.0659926 | −0.00361637 | ||||||||
\(334\) | 1.66091 | 0.0908807 | ||||||||
\(335\) | −14.4148 | −0.787566 | ||||||||
\(336\) | −1.17142 | −0.0639063 | ||||||||
\(337\) | 27.1277 | 1.47774 | 0.738870 | − | 0.673848i | \(-0.235360\pi\) | ||||
0.738870 | + | 0.673848i | \(0.235360\pi\) | |||||||
\(338\) | 5.62971 | 0.306216 | ||||||||
\(339\) | −1.81824 | −0.0987534 | ||||||||
\(340\) | 5.34260 | 0.289743 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −6.47209 | −0.349971 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 12.2705 | 0.661581 | ||||||||
\(345\) | 6.43935 | 0.346683 | ||||||||
\(346\) | −10.4055 | −0.559403 | ||||||||
\(347\) | −11.1959 | −0.601027 | −0.300514 | − | 0.953778i | \(-0.597158\pi\) | ||||
−0.300514 | + | 0.953778i | \(0.597158\pi\) | |||||||
\(348\) | 5.85640 | 0.313936 | ||||||||
\(349\) | 28.5841 | 1.53007 | 0.765035 | − | 0.643989i | \(-0.222722\pi\) | ||||
0.765035 | + | 0.643989i | \(0.222722\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | 14.7173 | 0.785550 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.00343 | 0.213081 | 0.106541 | − | 0.994308i | \(-0.466023\pi\) | ||||
0.106541 | + | 0.994308i | \(0.466023\pi\) | |||||||
\(354\) | 0.684935 | 0.0364039 | ||||||||
\(355\) | 8.20815 | 0.435643 | ||||||||
\(356\) | 2.73408 | 0.144906 | ||||||||
\(357\) | −6.25844 | −0.331232 | ||||||||
\(358\) | 25.4215 | 1.34357 | ||||||||
\(359\) | 9.77677 | 0.515998 | 0.257999 | − | 0.966145i | \(-0.416937\pi\) | ||||
0.257999 | + | 0.966145i | \(0.416937\pi\) | |||||||
\(360\) | 1.62777 | 0.0857911 | ||||||||
\(361\) | −3.19107 | −0.167951 | ||||||||
\(362\) | 9.34641 | 0.491237 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.71483 | 0.142296 | ||||||||
\(365\) | −14.5897 | −0.763662 | ||||||||
\(366\) | 8.50409 | 0.444516 | ||||||||
\(367\) | −13.1201 | −0.684865 | −0.342432 | − | 0.939543i | \(-0.611251\pi\) | ||||
−0.342432 | + | 0.939543i | \(0.611251\pi\) | |||||||
\(368\) | 5.49704 | 0.286553 | ||||||||
\(369\) | 8.35067 | 0.434719 | ||||||||
\(370\) | −0.0405417 | −0.00210766 | ||||||||
\(371\) | −4.55880 | −0.236681 | ||||||||
\(372\) | −3.36210 | −0.174317 | ||||||||
\(373\) | 15.2552 | 0.789886 | 0.394943 | − | 0.918706i | \(-0.370764\pi\) | ||||
0.394943 | + | 0.918706i | \(0.370764\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.17142 | 0.0604919 | ||||||||
\(376\) | −9.89983 | −0.510545 | ||||||||
\(377\) | −13.5725 | −0.699019 | ||||||||
\(378\) | −5.42107 | −0.278830 | ||||||||
\(379\) | 26.6376 | 1.36828 | 0.684141 | − | 0.729349i | \(-0.260177\pi\) | ||||
0.684141 | + | 0.729349i | \(0.260177\pi\) | |||||||
\(380\) | −3.97605 | −0.203967 | ||||||||
\(381\) | 20.2395 | 1.03690 | ||||||||
\(382\) | −4.55912 | −0.233265 | ||||||||
\(383\) | 6.81998 | 0.348485 | 0.174242 | − | 0.984703i | \(-0.444252\pi\) | ||||
0.174242 | + | 0.984703i | \(0.444252\pi\) | |||||||
\(384\) | −1.17142 | −0.0597788 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 15.8146 | 0.804944 | ||||||||
\(387\) | 19.9736 | 1.01531 | ||||||||
\(388\) | −1.32780 | −0.0674088 | ||||||||
\(389\) | 23.0806 | 1.17023 | 0.585117 | − | 0.810949i | \(-0.301048\pi\) | ||||
0.585117 | + | 0.810949i | \(0.301048\pi\) | |||||||
\(390\) | 3.18021 | 0.161036 | ||||||||
\(391\) | 29.3685 | 1.48523 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −12.9068 | −0.651060 | ||||||||
\(394\) | 14.6162 | 0.736351 | ||||||||
\(395\) | −6.75342 | −0.339801 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.6435 | −0.785123 | −0.392561 | − | 0.919726i | \(-0.628411\pi\) | ||||
−0.392561 | + | 0.919726i | \(0.628411\pi\) | |||||||
\(398\) | −16.4255 | −0.823338 | ||||||||
\(399\) | 4.65762 | 0.233173 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −1.51369 | −0.0755900 | −0.0377950 | − | 0.999286i | \(-0.512033\pi\) | ||||
−0.0377950 | + | 0.999286i | \(0.512033\pi\) | |||||||
\(402\) | 16.8858 | 0.842189 | ||||||||
\(403\) | 7.79183 | 0.388139 | ||||||||
\(404\) | −12.9533 | −0.644449 | ||||||||
\(405\) | −1.46704 | −0.0728980 | ||||||||
\(406\) | 4.99939 | 0.248116 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −6.25844 | −0.309839 | ||||||||
\(409\) | 14.2110 | 0.702689 | 0.351345 | − | 0.936246i | \(-0.385725\pi\) | ||||
0.351345 | + | 0.936246i | \(0.385725\pi\) | |||||||
\(410\) | 5.13012 | 0.253359 | ||||||||
\(411\) | 11.1164 | 0.548334 | ||||||||
\(412\) | 9.24014 | 0.455229 | ||||||||
\(413\) | 0.584705 | 0.0287714 | ||||||||
\(414\) | 8.94793 | 0.439767 | ||||||||
\(415\) | 15.5794 | 0.764763 | ||||||||
\(416\) | 2.71483 | 0.133105 | ||||||||
\(417\) | 12.7220 | 0.623001 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.61451 | 0.323140 | 0.161570 | − | 0.986861i | \(-0.448344\pi\) | ||||
0.161570 | + | 0.986861i | \(0.448344\pi\) | |||||||
\(420\) | −1.17142 | −0.0571595 | ||||||||
\(421\) | −38.2913 | −1.86620 | −0.933101 | − | 0.359614i | \(-0.882908\pi\) | ||||
−0.933101 | + | 0.359614i | \(0.882908\pi\) | |||||||
\(422\) | −4.78958 | −0.233153 | ||||||||
\(423\) | −16.1147 | −0.783522 | ||||||||
\(424\) | −4.55880 | −0.221395 | ||||||||
\(425\) | 5.34260 | 0.259154 | ||||||||
\(426\) | −9.61520 | −0.465858 | ||||||||
\(427\) | 7.25963 | 0.351318 | ||||||||
\(428\) | −10.0022 | −0.483473 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.2705 | 0.591736 | ||||||||
\(431\) | −6.73123 | −0.324232 | −0.162116 | − | 0.986772i | \(-0.551832\pi\) | ||||
−0.162116 | + | 0.986772i | \(0.551832\pi\) | |||||||
\(432\) | −5.42107 | −0.260821 | ||||||||
\(433\) | −25.7699 | −1.23842 | −0.619212 | − | 0.785224i | \(-0.712548\pi\) | ||||
−0.619212 | + | 0.785224i | \(0.712548\pi\) | |||||||
\(434\) | −2.87010 | −0.137769 | ||||||||
\(435\) | 5.85640 | 0.280793 | ||||||||
\(436\) | 0.535064 | 0.0256249 | ||||||||
\(437\) | −21.8565 | −1.04554 | ||||||||
\(438\) | 17.0907 | 0.816627 | ||||||||
\(439\) | −13.8131 | −0.659262 | −0.329631 | − | 0.944110i | \(-0.606924\pi\) | ||||
−0.329631 | + | 0.944110i | \(0.606924\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.62777 | −0.0775129 | ||||||||
\(442\) | 14.5042 | 0.689896 | ||||||||
\(443\) | −28.1206 | −1.33605 | −0.668025 | − | 0.744139i | \(-0.732860\pi\) | ||||
−0.668025 | + | 0.744139i | \(0.732860\pi\) | |||||||
\(444\) | 0.0474914 | 0.00225384 | ||||||||
\(445\) | 2.73408 | 0.129608 | ||||||||
\(446\) | 23.2488 | 1.10086 | ||||||||
\(447\) | −14.4454 | −0.683243 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 27.8576 | 1.31468 | 0.657341 | − | 0.753593i | \(-0.271681\pi\) | ||||
0.657341 | + | 0.753593i | \(0.271681\pi\) | |||||||
\(450\) | 1.62777 | 0.0767339 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −1.55217 | −0.0730078 | ||||||||
\(453\) | 10.2003 | 0.479250 | ||||||||
\(454\) | −17.0503 | −0.800210 | ||||||||
\(455\) | 2.71483 | 0.127273 | ||||||||
\(456\) | 4.65762 | 0.218113 | ||||||||
\(457\) | 38.0839 | 1.78149 | 0.890745 | − | 0.454504i | \(-0.150183\pi\) | ||||
0.890745 | + | 0.454504i | \(0.150183\pi\) | |||||||
\(458\) | −10.5051 | −0.490871 | ||||||||
\(459\) | −28.9626 | −1.35186 | ||||||||
\(460\) | 5.49704 | 0.256301 | ||||||||
\(461\) | −13.9251 | −0.648556 | −0.324278 | − | 0.945962i | \(-0.605121\pi\) | ||||
−0.324278 | + | 0.945962i | \(0.605121\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.93872 | −0.136574 | −0.0682870 | − | 0.997666i | \(-0.521753\pi\) | ||||
−0.0682870 | + | 0.997666i | \(0.521753\pi\) | |||||||
\(464\) | 4.99939 | 0.232091 | ||||||||
\(465\) | −3.36210 | −0.155914 | ||||||||
\(466\) | 21.0739 | 0.976231 | ||||||||
\(467\) | −31.8095 | −1.47197 | −0.735985 | − | 0.676998i | \(-0.763280\pi\) | ||||
−0.735985 | + | 0.676998i | \(0.763280\pi\) | |||||||
\(468\) | 4.41912 | 0.204274 | ||||||||
\(469\) | 14.4148 | 0.665615 | ||||||||
\(470\) | −9.89983 | −0.456645 | ||||||||
\(471\) | −22.4063 | −1.03243 | ||||||||
\(472\) | 0.584705 | 0.0269132 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 7.91110 | 0.363369 | ||||||||
\(475\) | −3.97605 | −0.182433 | ||||||||
\(476\) | −5.34260 | −0.244878 | ||||||||
\(477\) | −7.42069 | −0.339770 | ||||||||
\(478\) | 1.21833 | 0.0557252 | ||||||||
\(479\) | −37.7725 | −1.72587 | −0.862936 | − | 0.505314i | \(-0.831377\pi\) | ||||
−0.862936 | + | 0.505314i | \(0.831377\pi\) | |||||||
\(480\) | −1.17142 | −0.0534678 | ||||||||
\(481\) | −0.110064 | −0.00501847 | ||||||||
\(482\) | −1.70364 | −0.0775988 | ||||||||
\(483\) | −6.43935 | −0.293001 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.32780 | −0.0602922 | ||||||||
\(486\) | −14.5447 | −0.659760 | ||||||||
\(487\) | −9.53146 | −0.431912 | −0.215956 | − | 0.976403i | \(-0.569287\pi\) | ||||
−0.215956 | + | 0.976403i | \(0.569287\pi\) | |||||||
\(488\) | 7.25963 | 0.328628 | ||||||||
\(489\) | −21.8170 | −0.986601 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | 22.2193 | 1.00274 | 0.501371 | − | 0.865232i | \(-0.332829\pi\) | ||||
0.501371 | + | 0.865232i | \(0.332829\pi\) | |||||||
\(492\) | −6.00954 | −0.270931 | ||||||||
\(493\) | 26.7098 | 1.20295 | ||||||||
\(494\) | −10.7943 | −0.485658 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.87010 | −0.128871 | ||||||||
\(497\) | −8.20815 | −0.368186 | ||||||||
\(498\) | −18.2500 | −0.817804 | ||||||||
\(499\) | −10.8366 | −0.485112 | −0.242556 | − | 0.970137i | \(-0.577986\pi\) | ||||
−0.242556 | + | 0.970137i | \(0.577986\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −1.94562 | −0.0869239 | ||||||||
\(502\) | 19.2825 | 0.860621 | ||||||||
\(503\) | 12.2494 | 0.546173 | 0.273087 | − | 0.961989i | \(-0.411955\pi\) | ||||
0.273087 | + | 0.961989i | \(0.411955\pi\) | |||||||
\(504\) | −1.62777 | −0.0725067 | ||||||||
\(505\) | −12.9533 | −0.576413 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.59476 | −0.292884 | ||||||||
\(508\) | 17.2777 | 0.766575 | ||||||||
\(509\) | −0.295071 | −0.0130788 | −0.00653939 | − | 0.999979i | \(-0.502082\pi\) | ||||
−0.00653939 | + | 0.999979i | \(0.502082\pi\) | |||||||
\(510\) | −6.25844 | −0.277128 | ||||||||
\(511\) | 14.5897 | 0.645413 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 21.5544 | 0.951651 | ||||||||
\(514\) | 9.96978 | 0.439748 | ||||||||
\(515\) | 9.24014 | 0.407169 | ||||||||
\(516\) | −14.3739 | −0.632777 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0.0405417 | 0.00178130 | ||||||||
\(519\) | 12.1892 | 0.535047 | ||||||||
\(520\) | 2.71483 | 0.119053 | ||||||||
\(521\) | 27.5697 | 1.20785 | 0.603925 | − | 0.797041i | \(-0.293603\pi\) | ||||
0.603925 | + | 0.797041i | \(0.293603\pi\) | |||||||
\(522\) | 8.13787 | 0.356185 | ||||||||
\(523\) | −24.2495 | −1.06036 | −0.530178 | − | 0.847887i | \(-0.677875\pi\) | ||||
−0.530178 | + | 0.847887i | \(0.677875\pi\) | |||||||
\(524\) | −11.0180 | −0.481325 | ||||||||
\(525\) | −1.17142 | −0.0511250 | ||||||||
\(526\) | 15.3900 | 0.671034 | ||||||||
\(527\) | −15.3338 | −0.667951 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.21747 | 0.313803 | ||||||||
\(530\) | −4.55880 | −0.198022 | ||||||||
\(531\) | 0.951766 | 0.0413031 | ||||||||
\(532\) | 3.97605 | 0.172383 | ||||||||
\(533\) | 13.9274 | 0.603263 | ||||||||
\(534\) | −3.20276 | −0.138597 | ||||||||
\(535\) | −10.0022 | −0.432432 | ||||||||
\(536\) | 14.4148 | 0.622626 | ||||||||
\(537\) | −29.7793 | −1.28507 | ||||||||
\(538\) | 16.6521 | 0.717924 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.42107 | −0.233286 | ||||||||
\(541\) | −19.6382 | −0.844310 | −0.422155 | − | 0.906524i | \(-0.638726\pi\) | ||||
−0.422155 | + | 0.906524i | \(0.638726\pi\) | |||||||
\(542\) | −2.85449 | −0.122611 | ||||||||
\(543\) | −10.9486 | −0.469849 | ||||||||
\(544\) | −5.34260 | −0.229062 | ||||||||
\(545\) | 0.535064 | 0.0229196 | ||||||||
\(546\) | −3.18021 | −0.136100 | ||||||||
\(547\) | 0.502119 | 0.0214691 | 0.0107345 | − | 0.999942i | \(-0.496583\pi\) | ||||
0.0107345 | + | 0.999942i | \(0.496583\pi\) | |||||||
\(548\) | 9.48971 | 0.405380 | ||||||||
\(549\) | 11.8170 | 0.504338 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.8778 | −0.846823 | ||||||||
\(552\) | −6.43935 | −0.274077 | ||||||||
\(553\) | 6.75342 | 0.287185 | ||||||||
\(554\) | 25.0469 | 1.06414 | ||||||||
\(555\) | 0.0474914 | 0.00201590 | ||||||||
\(556\) | 10.8603 | 0.460581 | ||||||||
\(557\) | −2.50897 | −0.106308 | −0.0531541 | − | 0.998586i | \(-0.516927\pi\) | ||||
−0.0531541 | + | 0.998586i | \(0.516927\pi\) | |||||||
\(558\) | −4.67187 | −0.197776 | ||||||||
\(559\) | 33.3123 | 1.40896 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.37825 | 0.184685 | ||||||||
\(563\) | 17.3706 | 0.732086 | 0.366043 | − | 0.930598i | \(-0.380712\pi\) | ||||
0.366043 | + | 0.930598i | \(0.380712\pi\) | |||||||
\(564\) | 11.5969 | 0.488317 | ||||||||
\(565\) | −1.55217 | −0.0653002 | ||||||||
\(566\) | −7.46206 | −0.313654 | ||||||||
\(567\) | 1.46704 | 0.0616100 | ||||||||
\(568\) | −8.20815 | −0.344406 | ||||||||
\(569\) | 31.7612 | 1.33150 | 0.665750 | − | 0.746175i | \(-0.268112\pi\) | ||||
0.665750 | + | 0.746175i | \(0.268112\pi\) | |||||||
\(570\) | 4.65762 | 0.195086 | ||||||||
\(571\) | −7.43290 | −0.311057 | −0.155529 | − | 0.987831i | \(-0.549708\pi\) | ||||
−0.155529 | + | 0.987831i | \(0.549708\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.34065 | 0.223109 | ||||||||
\(574\) | −5.13012 | −0.214127 | ||||||||
\(575\) | 5.49704 | 0.229243 | ||||||||
\(576\) | −1.62777 | −0.0678238 | ||||||||
\(577\) | −18.4342 | −0.767426 | −0.383713 | − | 0.923452i | \(-0.625355\pi\) | ||||
−0.383713 | + | 0.923452i | \(0.625355\pi\) | |||||||
\(578\) | −11.5434 | −0.480141 | ||||||||
\(579\) | −18.5256 | −0.769898 | ||||||||
\(580\) | 4.99939 | 0.207589 | ||||||||
\(581\) | −15.5794 | −0.646343 | ||||||||
\(582\) | 1.55541 | 0.0644739 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 14.5897 | 0.603728 | ||||||||
\(585\) | 4.41912 | 0.182708 | ||||||||
\(586\) | 5.85672 | 0.241939 | ||||||||
\(587\) | 10.1616 | 0.419413 | 0.209707 | − | 0.977764i | \(-0.432749\pi\) | ||||
0.209707 | + | 0.977764i | \(0.432749\pi\) | |||||||
\(588\) | 1.17142 | 0.0483086 | ||||||||
\(589\) | 11.4117 | 0.470209 | ||||||||
\(590\) | 0.584705 | 0.0240719 | ||||||||
\(591\) | −17.1217 | −0.704292 | ||||||||
\(592\) | 0.0405417 | 0.00166625 | ||||||||
\(593\) | 22.2216 | 0.912532 | 0.456266 | − | 0.889844i | \(-0.349187\pi\) | ||||
0.456266 | + | 0.889844i | \(0.349187\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.34260 | −0.219025 | ||||||||
\(596\) | −12.3315 | −0.505118 | ||||||||
\(597\) | 19.2412 | 0.787491 | ||||||||
\(598\) | 14.9235 | 0.610268 | ||||||||
\(599\) | 9.45290 | 0.386235 | 0.193117 | − | 0.981176i | \(-0.438140\pi\) | ||||
0.193117 | + | 0.981176i | \(0.438140\pi\) | |||||||
\(600\) | −1.17142 | −0.0478231 | ||||||||
\(601\) | −26.9039 | −1.09743 | −0.548716 | − | 0.836009i | \(-0.684883\pi\) | ||||
−0.548716 | + | 0.836009i | \(0.684883\pi\) | |||||||
\(602\) | −12.2705 | −0.500108 | ||||||||
\(603\) | 23.4641 | 0.955530 | ||||||||
\(604\) | 8.70759 | 0.354307 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 15.1737 | 0.616391 | ||||||||
\(607\) | 17.1534 | 0.696237 | 0.348118 | − | 0.937451i | \(-0.386821\pi\) | ||||
0.348118 | + | 0.937451i | \(0.386821\pi\) | |||||||
\(608\) | 3.97605 | 0.161250 | ||||||||
\(609\) | −5.85640 | −0.237313 | ||||||||
\(610\) | 7.25963 | 0.293934 | ||||||||
\(611\) | −26.8763 | −1.08730 | ||||||||
\(612\) | −8.69653 | −0.351537 | ||||||||
\(613\) | −37.6479 | −1.52059 | −0.760293 | − | 0.649580i | \(-0.774945\pi\) | ||||
−0.760293 | + | 0.649580i | \(0.774945\pi\) | |||||||
\(614\) | 34.7874 | 1.40391 | ||||||||
\(615\) | −6.00954 | −0.242328 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.0199 | 0.886488 | 0.443244 | − | 0.896401i | \(-0.353828\pi\) | ||||
0.443244 | + | 0.896401i | \(0.353828\pi\) | |||||||
\(618\) | −10.8241 | −0.435409 | ||||||||
\(619\) | 30.3761 | 1.22092 | 0.610459 | − | 0.792047i | \(-0.290985\pi\) | ||||
0.610459 | + | 0.792047i | \(0.290985\pi\) | |||||||
\(620\) | −2.87010 | −0.115266 | ||||||||
\(621\) | −29.7999 | −1.19583 | ||||||||
\(622\) | −19.5779 | −0.785004 | ||||||||
\(623\) | −2.73408 | −0.109539 | ||||||||
\(624\) | −3.18021 | −0.127310 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 12.3630 | 0.494123 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −19.1275 | −0.763269 | ||||||||
\(629\) | 0.216598 | 0.00863633 | ||||||||
\(630\) | −1.62777 | −0.0648520 | ||||||||
\(631\) | 46.9052 | 1.86727 | 0.933634 | − | 0.358229i | \(-0.116619\pi\) | ||||
0.933634 | + | 0.358229i | \(0.116619\pi\) | |||||||
\(632\) | 6.75342 | 0.268637 | ||||||||
\(633\) | 5.61062 | 0.223002 | ||||||||
\(634\) | −5.15560 | −0.204755 | ||||||||
\(635\) | 17.2777 | 0.685645 | ||||||||
\(636\) | 5.34028 | 0.211756 | ||||||||
\(637\) | −2.71483 | −0.107565 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.3610 | −0.528553 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −25.1252 | −0.992385 | −0.496192 | − | 0.868213i | \(-0.665269\pi\) | ||||
−0.496192 | + | 0.868213i | \(0.665269\pi\) | |||||||
\(642\) | 11.7168 | 0.462424 | ||||||||
\(643\) | −24.8911 | −0.981608 | −0.490804 | − | 0.871270i | \(-0.663297\pi\) | ||||
−0.490804 | + | 0.871270i | \(0.663297\pi\) | |||||||
\(644\) | −5.49704 | −0.216614 | ||||||||
\(645\) | −14.3739 | −0.565973 | ||||||||
\(646\) | 21.2424 | 0.835772 | ||||||||
\(647\) | 40.7004 | 1.60010 | 0.800049 | − | 0.599934i | \(-0.204807\pi\) | ||||
0.800049 | + | 0.599934i | \(0.204807\pi\) | |||||||
\(648\) | 1.46704 | 0.0576309 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.71483 | 0.106484 | ||||||||
\(651\) | 3.36210 | 0.131771 | ||||||||
\(652\) | −18.6244 | −0.729389 | ||||||||
\(653\) | −13.3072 | −0.520752 | −0.260376 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260376 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(654\) | −0.626785 | −0.0245093 | ||||||||
\(655\) | −11.0180 | −0.430510 | ||||||||
\(656\) | −5.13012 | −0.200298 | ||||||||
\(657\) | 23.7488 | 0.926528 | ||||||||
\(658\) | 9.89983 | 0.385936 | ||||||||
\(659\) | 17.1669 | 0.668726 | 0.334363 | − | 0.942444i | \(-0.391479\pi\) | ||||
0.334363 | + | 0.942444i | \(0.391479\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.82979 | 0.0711705 | 0.0355853 | − | 0.999367i | \(-0.488670\pi\) | ||||
0.0355853 | + | 0.999367i | \(0.488670\pi\) | |||||||
\(662\) | 32.5061 | 1.26339 | ||||||||
\(663\) | −16.9906 | −0.659859 | ||||||||
\(664\) | −15.5794 | −0.604598 | ||||||||
\(665\) | 3.97605 | 0.154184 | ||||||||
\(666\) | 0.0659926 | 0.00255716 | ||||||||
\(667\) | 27.4819 | 1.06410 | ||||||||
\(668\) | −1.66091 | −0.0642624 | ||||||||
\(669\) | −27.2341 | −1.05293 | ||||||||
\(670\) | 14.4148 | 0.556894 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1.17142 | 0.0451886 | ||||||||
\(673\) | 19.8563 | 0.765402 | 0.382701 | − | 0.923872i | \(-0.374994\pi\) | ||||
0.382701 | + | 0.923872i | \(0.374994\pi\) | |||||||
\(674\) | −27.1277 | −1.04492 | ||||||||
\(675\) | −5.42107 | −0.208657 | ||||||||
\(676\) | −5.62971 | −0.216527 | ||||||||
\(677\) | 24.8180 | 0.953835 | 0.476918 | − | 0.878948i | \(-0.341754\pi\) | ||||
0.476918 | + | 0.878948i | \(0.341754\pi\) | |||||||
\(678\) | 1.81824 | 0.0698292 | ||||||||
\(679\) | 1.32780 | 0.0509562 | ||||||||
\(680\) | −5.34260 | −0.204879 | ||||||||
\(681\) | 19.9731 | 0.765370 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.25911 | 0.277762 | 0.138881 | − | 0.990309i | \(-0.455649\pi\) | ||||
0.138881 | + | 0.990309i | \(0.455649\pi\) | |||||||
\(684\) | 6.47209 | 0.247467 | ||||||||
\(685\) | 9.48971 | 0.362583 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 12.3059 | 0.469499 | ||||||||
\(688\) | −12.2705 | −0.467808 | ||||||||
\(689\) | −12.3764 | −0.471502 | ||||||||
\(690\) | −6.43935 | −0.245142 | ||||||||
\(691\) | −20.0175 | −0.761500 | −0.380750 | − | 0.924678i | \(-0.624334\pi\) | ||||
−0.380750 | + | 0.924678i | \(0.624334\pi\) | |||||||
\(692\) | 10.4055 | 0.395557 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.1959 | 0.424990 | ||||||||
\(695\) | 10.8603 | 0.411956 | ||||||||
\(696\) | −5.85640 | −0.221986 | ||||||||
\(697\) | −27.4082 | −1.03816 | ||||||||
\(698\) | −28.5841 | −1.08192 | ||||||||
\(699\) | −24.6865 | −0.933728 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | 41.0871 | 1.55184 | 0.775920 | − | 0.630831i | \(-0.217286\pi\) | ||||
0.775920 | + | 0.630831i | \(0.217286\pi\) | |||||||
\(702\) | −14.7173 | −0.555468 | ||||||||
\(703\) | −0.161196 | −0.00607961 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.5969 | 0.436764 | ||||||||
\(706\) | −4.00343 | −0.150671 | ||||||||
\(707\) | 12.9533 | 0.487158 | ||||||||
\(708\) | −0.684935 | −0.0257415 | ||||||||
\(709\) | −14.8981 | −0.559510 | −0.279755 | − | 0.960071i | \(-0.590253\pi\) | ||||
−0.279755 | + | 0.960071i | \(0.590253\pi\) | |||||||
\(710\) | −8.20815 | −0.308046 | ||||||||
\(711\) | 10.9930 | 0.412271 | ||||||||
\(712\) | −2.73408 | −0.102464 | ||||||||
\(713\) | −15.7771 | −0.590856 | ||||||||
\(714\) | 6.25844 | 0.234216 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −25.4215 | −0.950048 | ||||||||
\(717\) | −1.42718 | −0.0532990 | ||||||||
\(718\) | −9.77677 | −0.364866 | ||||||||
\(719\) | 35.3705 | 1.31910 | 0.659548 | − | 0.751662i | \(-0.270748\pi\) | ||||
0.659548 | + | 0.751662i | \(0.270748\pi\) | |||||||
\(720\) | −1.62777 | −0.0606635 | ||||||||
\(721\) | −9.24014 | −0.344121 | ||||||||
\(722\) | 3.19107 | 0.118759 | ||||||||
\(723\) | 1.99568 | 0.0742203 | ||||||||
\(724\) | −9.34641 | −0.347357 | ||||||||
\(725\) | 4.99939 | 0.185673 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.10139 | 0.0408482 | 0.0204241 | − | 0.999791i | \(-0.493498\pi\) | ||||
0.0204241 | + | 0.999791i | \(0.493498\pi\) | |||||||
\(728\) | −2.71483 | −0.100618 | ||||||||
\(729\) | 21.4391 | 0.794040 | ||||||||
\(730\) | 14.5897 | 0.539991 | ||||||||
\(731\) | −65.5564 | −2.42469 | ||||||||
\(732\) | −8.50409 | −0.314320 | ||||||||
\(733\) | −12.9270 | −0.477471 | −0.238735 | − | 0.971085i | \(-0.576733\pi\) | ||||
−0.238735 | + | 0.971085i | \(0.576733\pi\) | |||||||
\(734\) | 13.1201 | 0.484272 | ||||||||
\(735\) | 1.17142 | 0.0432085 | ||||||||
\(736\) | −5.49704 | −0.202624 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −8.35067 | −0.307392 | ||||||||
\(739\) | 32.1959 | 1.18435 | 0.592173 | − | 0.805810i | \(-0.298270\pi\) | ||||
0.592173 | + | 0.805810i | \(0.298270\pi\) | |||||||
\(740\) | 0.0405417 | 0.00149034 | ||||||||
\(741\) | 12.6447 | 0.464513 | ||||||||
\(742\) | 4.55880 | 0.167359 | ||||||||
\(743\) | −26.4833 | −0.971577 | −0.485788 | − | 0.874077i | \(-0.661467\pi\) | ||||
−0.485788 | + | 0.874077i | \(0.661467\pi\) | |||||||
\(744\) | 3.36210 | 0.123260 | ||||||||
\(745\) | −12.3315 | −0.451791 | ||||||||
\(746\) | −15.2552 | −0.558534 | ||||||||
\(747\) | −25.3597 | −0.927864 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.0022 | 0.365472 | ||||||||
\(750\) | −1.17142 | −0.0427743 | ||||||||
\(751\) | −38.6078 | −1.40882 | −0.704409 | − | 0.709795i | \(-0.748788\pi\) | ||||
−0.704409 | + | 0.709795i | \(0.748788\pi\) | |||||||
\(752\) | 9.89983 | 0.361010 | ||||||||
\(753\) | −22.5879 | −0.823151 | ||||||||
\(754\) | 13.5725 | 0.494281 | ||||||||
\(755\) | 8.70759 | 0.316902 | ||||||||
\(756\) | 5.42107 | 0.197162 | ||||||||
\(757\) | −38.9080 | −1.41413 | −0.707067 | − | 0.707146i | \(-0.749982\pi\) | ||||
−0.707067 | + | 0.707146i | \(0.749982\pi\) | |||||||
\(758\) | −26.6376 | −0.967522 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.97605 | 0.144226 | ||||||||
\(761\) | −9.88051 | −0.358168 | −0.179084 | − | 0.983834i | \(-0.557313\pi\) | ||||
−0.179084 | + | 0.983834i | \(0.557313\pi\) | |||||||
\(762\) | −20.2395 | −0.733199 | ||||||||
\(763\) | −0.535064 | −0.0193706 | ||||||||
\(764\) | 4.55912 | 0.164943 | ||||||||
\(765\) | −8.69653 | −0.314424 | ||||||||
\(766\) | −6.81998 | −0.246416 | ||||||||
\(767\) | 1.58737 | 0.0573167 | ||||||||
\(768\) | 1.17142 | 0.0422700 | ||||||||
\(769\) | 20.8801 | 0.752955 | 0.376478 | − | 0.926426i | \(-0.377135\pi\) | ||||
0.376478 | + | 0.926426i | \(0.377135\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.6788 | −0.420602 | ||||||||
\(772\) | −15.8146 | −0.569181 | ||||||||
\(773\) | −37.3833 | −1.34459 | −0.672293 | − | 0.740286i | \(-0.734690\pi\) | ||||
−0.672293 | + | 0.740286i | \(0.734690\pi\) | |||||||
\(774\) | −19.9736 | −0.717935 | ||||||||
\(775\) | −2.87010 | −0.103097 | ||||||||
\(776\) | 1.32780 | 0.0476652 | ||||||||
\(777\) | −0.0474914 | −0.00170374 | ||||||||
\(778\) | −23.0806 | −0.827481 | ||||||||
\(779\) | 20.3976 | 0.730820 | ||||||||
\(780\) | −3.18021 | −0.113870 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −29.3685 | −1.05022 | ||||||||
\(783\) | −27.1021 | −0.968549 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −19.1275 | −0.682688 | ||||||||
\(786\) | 12.9068 | 0.460369 | ||||||||
\(787\) | 16.4247 | 0.585477 | 0.292739 | − | 0.956193i | \(-0.405433\pi\) | ||||
0.292739 | + | 0.956193i | \(0.405433\pi\) | |||||||
\(788\) | −14.6162 | −0.520679 | ||||||||
\(789\) | −18.0281 | −0.641818 | ||||||||
\(790\) | 6.75342 | 0.240276 | ||||||||
\(791\) | 1.55217 | 0.0551887 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.7086 | 0.699875 | ||||||||
\(794\) | 15.6435 | 0.555166 | ||||||||
\(795\) | 5.34028 | 0.189400 | ||||||||
\(796\) | 16.4255 | 0.582188 | ||||||||
\(797\) | 31.5634 | 1.11803 | 0.559016 | − | 0.829157i | \(-0.311179\pi\) | ||||
0.559016 | + | 0.829157i | \(0.311179\pi\) | |||||||
\(798\) | −4.65762 | −0.164878 | ||||||||
\(799\) | 52.8908 | 1.87114 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −4.45046 | −0.157249 | ||||||||
\(802\) | 1.51369 | 0.0534502 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −16.8858 | −0.595518 | ||||||||
\(805\) | −5.49704 | −0.193745 | ||||||||
\(806\) | −7.79183 | −0.274456 | ||||||||
\(807\) | −19.5067 | −0.686667 | ||||||||
\(808\) | 12.9533 | 0.455695 | ||||||||
\(809\) | 6.30494 | 0.221670 | 0.110835 | − | 0.993839i | \(-0.464647\pi\) | ||||
0.110835 | + | 0.993839i | \(0.464647\pi\) | |||||||
\(810\) | 1.46704 | 0.0515466 | ||||||||
\(811\) | −28.7394 | −1.00918 | −0.504588 | − | 0.863361i | \(-0.668355\pi\) | ||||
−0.504588 | + | 0.863361i | \(0.668355\pi\) | |||||||
\(812\) | −4.99939 | −0.175444 | ||||||||
\(813\) | 3.34381 | 0.117273 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.6244 | −0.652385 | ||||||||
\(816\) | 6.25844 | 0.219089 | ||||||||
\(817\) | 48.7881 | 1.70688 | ||||||||
\(818\) | −14.2110 | −0.496876 | ||||||||
\(819\) | −4.41912 | −0.154417 | ||||||||
\(820\) | −5.13012 | −0.179152 | ||||||||
\(821\) | −40.1131 | −1.39996 | −0.699978 | − | 0.714165i | \(-0.746807\pi\) | ||||
−0.699978 | + | 0.714165i | \(0.746807\pi\) | |||||||
\(822\) | −11.1164 | −0.387731 | ||||||||
\(823\) | −16.7750 | −0.584739 | −0.292370 | − | 0.956305i | \(-0.594444\pi\) | ||||
−0.292370 | + | 0.956305i | \(0.594444\pi\) | |||||||
\(824\) | −9.24014 | −0.321895 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.584705 | −0.0203445 | ||||||||
\(827\) | −7.08065 | −0.246218 | −0.123109 | − | 0.992393i | \(-0.539287\pi\) | ||||
−0.123109 | + | 0.992393i | \(0.539287\pi\) | |||||||
\(828\) | −8.94793 | −0.310962 | ||||||||
\(829\) | −17.7789 | −0.617485 | −0.308743 | − | 0.951146i | \(-0.599908\pi\) | ||||
−0.308743 | + | 0.951146i | \(0.599908\pi\) | |||||||
\(830\) | −15.5794 | −0.540769 | ||||||||
\(831\) | −29.3405 | −1.01781 | ||||||||
\(832\) | −2.71483 | −0.0941197 | ||||||||
\(833\) | 5.34260 | 0.185110 | ||||||||
\(834\) | −12.7220 | −0.440528 | ||||||||
\(835\) | −1.66091 | −0.0574780 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15.5590 | 0.537798 | ||||||||
\(838\) | −6.61451 | −0.228494 | ||||||||
\(839\) | −7.03094 | −0.242735 | −0.121368 | − | 0.992608i | \(-0.538728\pi\) | ||||
−0.121368 | + | 0.992608i | \(0.538728\pi\) | |||||||
\(840\) | 1.17142 | 0.0404179 | ||||||||
\(841\) | −4.00606 | −0.138140 | ||||||||
\(842\) | 38.2913 | 1.31960 | ||||||||
\(843\) | −5.12877 | −0.176644 | ||||||||
\(844\) | 4.78958 | 0.164864 | ||||||||
\(845\) | −5.62971 | −0.193668 | ||||||||
\(846\) | 16.1147 | 0.554034 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.55880 | 0.156550 | ||||||||
\(849\) | 8.74121 | 0.299998 | ||||||||
\(850\) | −5.34260 | −0.183250 | ||||||||
\(851\) | 0.222859 | 0.00763952 | ||||||||
\(852\) | 9.61520 | 0.329411 | ||||||||
\(853\) | −48.2865 | −1.65330 | −0.826648 | − | 0.562719i | \(-0.809755\pi\) | ||||
−0.826648 | + | 0.562719i | \(0.809755\pi\) | |||||||
\(854\) | −7.25963 | −0.248419 | ||||||||
\(855\) | 6.47209 | 0.221341 | ||||||||
\(856\) | 10.0022 | 0.341867 | ||||||||
\(857\) | 30.6816 | 1.04806 | 0.524032 | − | 0.851699i | \(-0.324427\pi\) | ||||
0.524032 | + | 0.851699i | \(0.324427\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.1328 | 0.413965 | 0.206983 | − | 0.978345i | \(-0.433636\pi\) | ||||
0.206983 | + | 0.978345i | \(0.433636\pi\) | |||||||
\(860\) | −12.2705 | −0.418421 | ||||||||
\(861\) | 6.00954 | 0.204804 | ||||||||
\(862\) | 6.73123 | 0.229267 | ||||||||
\(863\) | −42.0830 | −1.43252 | −0.716261 | − | 0.697832i | \(-0.754148\pi\) | ||||
−0.716261 | + | 0.697832i | \(0.754148\pi\) | |||||||
\(864\) | 5.42107 | 0.184429 | ||||||||
\(865\) | 10.4055 | 0.353797 | ||||||||
\(866\) | 25.7699 | 0.875697 | ||||||||
\(867\) | 13.5222 | 0.459237 | ||||||||
\(868\) | 2.87010 | 0.0974176 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −5.85640 | −0.198550 | ||||||||
\(871\) | 39.1338 | 1.32600 | ||||||||
\(872\) | −0.535064 | −0.0181196 | ||||||||
\(873\) | 2.16135 | 0.0731507 | ||||||||
\(874\) | 21.8565 | 0.739307 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | −17.0907 | −0.577443 | ||||||||
\(877\) | 34.3045 | 1.15838 | 0.579190 | − | 0.815193i | \(-0.303369\pi\) | ||||
0.579190 | + | 0.815193i | \(0.303369\pi\) | |||||||
\(878\) | 13.8131 | 0.466169 | ||||||||
\(879\) | −6.86069 | −0.231405 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.874683 | 0.0294688 | 0.0147344 | − | 0.999891i | \(-0.495310\pi\) | ||||
0.0147344 | + | 0.999891i | \(0.495310\pi\) | |||||||
\(882\) | 1.62777 | 0.0548099 | ||||||||
\(883\) | 49.3208 | 1.65978 | 0.829888 | − | 0.557930i | \(-0.188404\pi\) | ||||
0.829888 | + | 0.557930i | \(0.188404\pi\) | |||||||
\(884\) | −14.5042 | −0.487830 | ||||||||
\(885\) | −0.684935 | −0.0230239 | ||||||||
\(886\) | 28.1206 | 0.944730 | ||||||||
\(887\) | −10.2517 | −0.344218 | −0.172109 | − | 0.985078i | \(-0.555058\pi\) | ||||
−0.172109 | + | 0.985078i | \(0.555058\pi\) | |||||||
\(888\) | −0.0474914 | −0.00159371 | ||||||||
\(889\) | −17.2777 | −0.579476 | ||||||||
\(890\) | −2.73408 | −0.0916466 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −23.2488 | −0.778426 | ||||||||
\(893\) | −39.3622 | −1.31721 | ||||||||
\(894\) | 14.4454 | 0.483126 | ||||||||
\(895\) | −25.4215 | −0.849749 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −17.4817 | −0.583698 | ||||||||
\(898\) | −27.8576 | −0.929621 | ||||||||
\(899\) | −14.3488 | −0.478558 | ||||||||
\(900\) | −1.62777 | −0.0542591 | ||||||||
\(901\) | 24.3558 | 0.811411 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.3739 | 0.478334 | ||||||||
\(904\) | 1.55217 | 0.0516243 | ||||||||
\(905\) | −9.34641 | −0.310685 | ||||||||
\(906\) | −10.2003 | −0.338881 | ||||||||
\(907\) | 54.0073 | 1.79328 | 0.896642 | − | 0.442757i | \(-0.146000\pi\) | ||||
0.896642 | + | 0.442757i | \(0.146000\pi\) | |||||||
\(908\) | 17.0503 | 0.565834 | ||||||||
\(909\) | 21.0850 | 0.699344 | ||||||||
\(910\) | −2.71483 | −0.0899957 | ||||||||
\(911\) | −21.9362 | −0.726779 | −0.363390 | − | 0.931637i | \(-0.618381\pi\) | ||||
−0.363390 | + | 0.931637i | \(0.618381\pi\) | |||||||
\(912\) | −4.65762 | −0.154229 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −38.0839 | −1.25970 | ||||||||
\(915\) | −8.50409 | −0.281136 | ||||||||
\(916\) | 10.5051 | 0.347098 | ||||||||
\(917\) | 11.0180 | 0.363848 | ||||||||
\(918\) | 28.9626 | 0.955909 | ||||||||
\(919\) | 32.5378 | 1.07332 | 0.536662 | − | 0.843798i | \(-0.319685\pi\) | ||||
0.536662 | + | 0.843798i | \(0.319685\pi\) | |||||||
\(920\) | −5.49704 | −0.181232 | ||||||||
\(921\) | −40.7507 | −1.34278 | ||||||||
\(922\) | 13.9251 | 0.458598 | ||||||||
\(923\) | −22.2837 | −0.733478 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.0405417 | 0.00133300 | ||||||||
\(926\) | 2.93872 | 0.0965725 | ||||||||
\(927\) | −15.0408 | −0.494006 | ||||||||
\(928\) | −4.99939 | −0.164113 | ||||||||
\(929\) | 1.52103 | 0.0499034 | 0.0249517 | − | 0.999689i | \(-0.492057\pi\) | ||||
0.0249517 | + | 0.999689i | \(0.492057\pi\) | |||||||
\(930\) | 3.36210 | 0.110248 | ||||||||
\(931\) | −3.97605 | −0.130310 | ||||||||
\(932\) | −21.0739 | −0.690300 | ||||||||
\(933\) | 22.9340 | 0.750826 | ||||||||
\(934\) | 31.8095 | 1.04084 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.41912 | −0.144443 | ||||||||
\(937\) | −35.3146 | −1.15368 | −0.576839 | − | 0.816858i | \(-0.695714\pi\) | ||||
−0.576839 | + | 0.816858i | \(0.695714\pi\) | |||||||
\(938\) | −14.4148 | −0.470661 | ||||||||
\(939\) | −14.4822 | −0.472610 | ||||||||
\(940\) | 9.89983 | 0.322897 | ||||||||
\(941\) | −17.8323 | −0.581316 | −0.290658 | − | 0.956827i | \(-0.593874\pi\) | ||||
−0.290658 | + | 0.956827i | \(0.593874\pi\) | |||||||
\(942\) | 22.4063 | 0.730037 | ||||||||
\(943\) | −28.2005 | −0.918335 | ||||||||
\(944\) | −0.584705 | −0.0190305 | ||||||||
\(945\) | 5.42107 | 0.176347 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.5867 | −0.863953 | −0.431977 | − | 0.901885i | \(-0.642184\pi\) | ||||
−0.431977 | + | 0.901885i | \(0.642184\pi\) | |||||||
\(948\) | −7.91110 | −0.256941 | ||||||||
\(949\) | 39.6087 | 1.28575 | ||||||||
\(950\) | 3.97605 | 0.129000 | ||||||||
\(951\) | 6.03939 | 0.195840 | ||||||||
\(952\) | 5.34260 | 0.173155 | ||||||||
\(953\) | −12.9284 | −0.418791 | −0.209396 | − | 0.977831i | \(-0.567150\pi\) | ||||
−0.209396 | + | 0.977831i | \(0.567150\pi\) | |||||||
\(954\) | 7.42069 | 0.240254 | ||||||||
\(955\) | 4.55912 | 0.147530 | ||||||||
\(956\) | −1.21833 | −0.0394037 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 37.7725 | 1.22038 | ||||||||
\(959\) | −9.48971 | −0.306439 | ||||||||
\(960\) | 1.17142 | 0.0378075 | ||||||||
\(961\) | −22.7625 | −0.734275 | ||||||||
\(962\) | 0.110064 | 0.00354860 | ||||||||
\(963\) | 16.2813 | 0.524656 | ||||||||
\(964\) | 1.70364 | 0.0548706 | ||||||||
\(965\) | −15.8146 | −0.509091 | ||||||||
\(966\) | 6.43935 | 0.207183 | ||||||||
\(967\) | −6.45564 | −0.207599 | −0.103800 | − | 0.994598i | \(-0.533100\pi\) | ||||
−0.103800 | + | 0.994598i | \(0.533100\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −24.8838 | −0.799384 | ||||||||
\(970\) | 1.32780 | 0.0426331 | ||||||||
\(971\) | 16.5435 | 0.530907 | 0.265454 | − | 0.964124i | \(-0.414478\pi\) | ||||
0.265454 | + | 0.964124i | \(0.414478\pi\) | |||||||
\(972\) | 14.5447 | 0.466521 | ||||||||
\(973\) | −10.8603 | −0.348167 | ||||||||
\(974\) | 9.53146 | 0.305408 | ||||||||
\(975\) | −3.18021 | −0.101848 | ||||||||
\(976\) | −7.25963 | −0.232375 | ||||||||
\(977\) | −24.7794 | −0.792762 | −0.396381 | − | 0.918086i | \(-0.629734\pi\) | ||||
−0.396381 | + | 0.918086i | \(0.629734\pi\) | |||||||
\(978\) | 21.8170 | 0.697632 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | −0.870962 | −0.0278077 | ||||||||
\(982\) | −22.2193 | −0.709046 | ||||||||
\(983\) | −46.4963 | −1.48300 | −0.741501 | − | 0.670952i | \(-0.765886\pi\) | ||||
−0.741501 | + | 0.670952i | \(0.765886\pi\) | |||||||
\(984\) | 6.00954 | 0.191577 | ||||||||
\(985\) | −14.6162 | −0.465709 | ||||||||
\(986\) | −26.7098 | −0.850612 | ||||||||
\(987\) | −11.5969 | −0.369133 | ||||||||
\(988\) | 10.7943 | 0.343412 | ||||||||
\(989\) | −67.4514 | −2.14483 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.0722 | 1.49530 | 0.747649 | − | 0.664094i | \(-0.231182\pi\) | ||||
0.747649 | + | 0.664094i | \(0.231182\pi\) | |||||||
\(992\) | 2.87010 | 0.0911258 | ||||||||
\(993\) | −38.0784 | −1.20838 | ||||||||
\(994\) | 8.20815 | 0.260347 | ||||||||
\(995\) | 16.4255 | 0.520725 | ||||||||
\(996\) | 18.2500 | 0.578275 | ||||||||
\(997\) | −56.2531 | −1.78155 | −0.890776 | − | 0.454442i | \(-0.849839\pi\) | ||||
−0.890776 | + | 0.454442i | \(0.849839\pi\) | |||||||
\(998\) | 10.8366 | 0.343026 | ||||||||
\(999\) | −0.219779 | −0.00695351 |
(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 | 8470.2.a.cy.1.4 | 6 | ||
11.2 | odd | 10 | 770.2.n.i.631.2 | yes | 12 | ||
11.6 | odd | 10 | 770.2.n.i.421.2 | ✓ | 12 | ||
11.10 | odd | 2 | 8470.2.a.de.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.i.421.2 | ✓ | 12 | 11.6 | odd | 10 | ||
770.2.n.i.631.2 | yes | 12 | 11.2 | odd | 10 | ||
8470.2.a.cy.1.4 | 6 | 1.1 | even | 1 | trivial | ||
8470.2.a.de.1.4 | 6 | 11.10 | odd | 2 |