Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 4x^{5} + 14x^{4} + 3x^{3} - 12x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.16681\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.61702 | −1.17037 | −0.585184 | − | 0.810900i | \(-0.698978\pi\) | ||||
−0.585184 | + | 0.810900i | \(0.698978\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −0.977840 | −0.369589 | −0.184794 | − | 0.982777i | \(-0.559162\pi\) | ||||
−0.184794 | + | 0.982777i | \(0.559162\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.61702 | 0.827576 | ||||||||
\(11\) | −0.240785 | −0.0725993 | −0.0362997 | − | 0.999341i | \(-0.511557\pi\) | ||||
−0.0362997 | + | 0.999341i | \(0.511557\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0.977840 | 0.261339 | ||||||||
\(15\) | 2.61702 | 0.675713 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.91508 | −1.19208 | −0.596041 | − | 0.802954i | \(-0.703261\pi\) | ||||
−0.596041 | + | 0.802954i | \(0.703261\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.97784 | −0.453748 | −0.226874 | − | 0.973924i | \(-0.572851\pi\) | ||||
−0.226874 | + | 0.973924i | \(0.572851\pi\) | |||||||
\(20\) | −2.61702 | −0.585184 | ||||||||
\(21\) | 0.977840 | 0.213382 | ||||||||
\(22\) | 0.240785 | 0.0513355 | ||||||||
\(23\) | −0.244868 | −0.0510585 | −0.0255292 | − | 0.999674i | \(-0.508127\pi\) | ||||
−0.0255292 | + | 0.999674i | \(0.508127\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.84882 | 0.369763 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.977840 | −0.184794 | ||||||||
\(29\) | 8.09791 | 1.50374 | 0.751872 | − | 0.659309i | \(-0.229151\pi\) | ||||
0.751872 | + | 0.659309i | \(0.229151\pi\) | |||||||
\(30\) | −2.61702 | −0.477801 | ||||||||
\(31\) | −7.15427 | −1.28494 | −0.642472 | − | 0.766309i | \(-0.722091\pi\) | ||||
−0.642472 | + | 0.766309i | \(0.722091\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.240785 | 0.0419152 | ||||||||
\(34\) | 4.91508 | 0.842930 | ||||||||
\(35\) | 2.55903 | 0.432555 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 5.41686 | 0.890526 | 0.445263 | − | 0.895400i | \(-0.353110\pi\) | ||||
0.445263 | + | 0.895400i | \(0.353110\pi\) | |||||||
\(38\) | 1.97784 | 0.320848 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 2.61702 | 0.413788 | ||||||||
\(41\) | 10.7554 | 1.67971 | 0.839855 | − | 0.542811i | \(-0.182640\pi\) | ||||
0.839855 | + | 0.542811i | \(0.182640\pi\) | |||||||
\(42\) | −0.977840 | −0.150884 | ||||||||
\(43\) | −5.03820 | −0.768318 | −0.384159 | − | 0.923267i | \(-0.625509\pi\) | ||||
−0.384159 | + | 0.923267i | \(0.625509\pi\) | |||||||
\(44\) | −0.240785 | −0.0362997 | ||||||||
\(45\) | −2.61702 | −0.390123 | ||||||||
\(46\) | 0.244868 | 0.0361038 | ||||||||
\(47\) | 9.26343 | 1.35121 | 0.675605 | − | 0.737264i | \(-0.263882\pi\) | ||||
0.675605 | + | 0.737264i | \(0.263882\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.04383 | −0.863404 | ||||||||
\(50\) | −1.84882 | −0.261462 | ||||||||
\(51\) | 4.91508 | 0.688249 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 9.79000 | 1.34476 | 0.672380 | − | 0.740206i | \(-0.265272\pi\) | ||||
0.672380 | + | 0.740206i | \(0.265272\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0.630140 | 0.0849680 | ||||||||
\(56\) | 0.977840 | 0.130669 | ||||||||
\(57\) | 1.97784 | 0.261971 | ||||||||
\(58\) | −8.09791 | −1.06331 | ||||||||
\(59\) | −7.05375 | −0.918320 | −0.459160 | − | 0.888353i | \(-0.651850\pi\) | ||||
−0.459160 | + | 0.888353i | \(0.651850\pi\) | |||||||
\(60\) | 2.61702 | 0.337856 | ||||||||
\(61\) | 3.55737 | 0.455474 | 0.227737 | − | 0.973723i | \(-0.426867\pi\) | ||||
0.227737 | + | 0.973723i | \(0.426867\pi\) | |||||||
\(62\) | 7.15427 | 0.908593 | ||||||||
\(63\) | −0.977840 | −0.123196 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.61702 | −0.324602 | ||||||||
\(66\) | −0.240785 | −0.0296386 | ||||||||
\(67\) | −14.2272 | −1.73813 | −0.869067 | − | 0.494694i | \(-0.835280\pi\) | ||||
−0.869067 | + | 0.494694i | \(0.835280\pi\) | |||||||
\(68\) | −4.91508 | −0.596041 | ||||||||
\(69\) | 0.244868 | 0.0294786 | ||||||||
\(70\) | −2.55903 | −0.305863 | ||||||||
\(71\) | 9.42409 | 1.11843 | 0.559217 | − | 0.829021i | \(-0.311102\pi\) | ||||
0.559217 | + | 0.829021i | \(0.311102\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 0.976521 | 0.114293 | 0.0571466 | − | 0.998366i | \(-0.481800\pi\) | ||||
0.0571466 | + | 0.998366i | \(0.481800\pi\) | |||||||
\(74\) | −5.41686 | −0.629697 | ||||||||
\(75\) | −1.84882 | −0.213483 | ||||||||
\(76\) | −1.97784 | −0.226874 | ||||||||
\(77\) | 0.235449 | 0.0268319 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | −8.87366 | −0.998365 | −0.499182 | − | 0.866497i | \(-0.666366\pi\) | ||||
−0.499182 | + | 0.866497i | \(0.666366\pi\) | |||||||
\(80\) | −2.61702 | −0.292592 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −10.7554 | −1.18773 | ||||||||
\(83\) | 13.3970 | 1.47051 | 0.735253 | − | 0.677792i | \(-0.237063\pi\) | ||||
0.735253 | + | 0.677792i | \(0.237063\pi\) | |||||||
\(84\) | 0.977840 | 0.106691 | ||||||||
\(85\) | 12.8629 | 1.39518 | ||||||||
\(86\) | 5.03820 | 0.543283 | ||||||||
\(87\) | −8.09791 | −0.868187 | ||||||||
\(88\) | 0.240785 | 0.0256677 | ||||||||
\(89\) | −0.490697 | −0.0520138 | −0.0260069 | − | 0.999662i | \(-0.508279\pi\) | ||||
−0.0260069 | + | 0.999662i | \(0.508279\pi\) | |||||||
\(90\) | 2.61702 | 0.275859 | ||||||||
\(91\) | −0.977840 | −0.102506 | ||||||||
\(92\) | −0.244868 | −0.0255292 | ||||||||
\(93\) | 7.15427 | 0.741863 | ||||||||
\(94\) | −9.26343 | −0.955450 | ||||||||
\(95\) | 5.17606 | 0.531052 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 14.7754 | 1.50021 | 0.750107 | − | 0.661317i | \(-0.230002\pi\) | ||||
0.750107 | + | 0.661317i | \(0.230002\pi\) | |||||||
\(98\) | 6.04383 | 0.610519 | ||||||||
\(99\) | −0.240785 | −0.0241998 | ||||||||
\(100\) | 1.84882 | 0.184882 | ||||||||
\(101\) | −10.7141 | −1.06609 | −0.533045 | − | 0.846087i | \(-0.678953\pi\) | ||||
−0.533045 | + | 0.846087i | \(0.678953\pi\) | |||||||
\(102\) | −4.91508 | −0.486666 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | −2.55903 | −0.249736 | ||||||||
\(106\) | −9.79000 | −0.950889 | ||||||||
\(107\) | −12.2317 | −1.18248 | −0.591241 | − | 0.806495i | \(-0.701362\pi\) | ||||
−0.591241 | + | 0.806495i | \(0.701362\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −15.0495 | −1.44148 | −0.720740 | − | 0.693206i | \(-0.756198\pi\) | ||||
−0.720740 | + | 0.693206i | \(0.756198\pi\) | |||||||
\(110\) | −0.630140 | −0.0600814 | ||||||||
\(111\) | −5.41686 | −0.514145 | ||||||||
\(112\) | −0.977840 | −0.0923972 | ||||||||
\(113\) | 15.2767 | 1.43711 | 0.718557 | − | 0.695468i | \(-0.244803\pi\) | ||||
0.718557 | + | 0.695468i | \(0.244803\pi\) | |||||||
\(114\) | −1.97784 | −0.185242 | ||||||||
\(115\) | 0.640825 | 0.0597572 | ||||||||
\(116\) | 8.09791 | 0.751872 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 7.05375 | 0.649351 | ||||||||
\(119\) | 4.80617 | 0.440581 | ||||||||
\(120\) | −2.61702 | −0.238901 | ||||||||
\(121\) | −10.9420 | −0.994729 | ||||||||
\(122\) | −3.55737 | −0.322069 | ||||||||
\(123\) | −10.7554 | −0.969781 | ||||||||
\(124\) | −7.15427 | −0.642472 | ||||||||
\(125\) | 8.24672 | 0.737609 | ||||||||
\(126\) | 0.977840 | 0.0871129 | ||||||||
\(127\) | −5.61363 | −0.498129 | −0.249065 | − | 0.968487i | \(-0.580123\pi\) | ||||
−0.249065 | + | 0.968487i | \(0.580123\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 5.03820 | 0.443589 | ||||||||
\(130\) | 2.61702 | 0.229528 | ||||||||
\(131\) | 3.87103 | 0.338214 | 0.169107 | − | 0.985598i | \(-0.445912\pi\) | ||||
0.169107 | + | 0.985598i | \(0.445912\pi\) | |||||||
\(132\) | 0.240785 | 0.0209576 | ||||||||
\(133\) | 1.93401 | 0.167700 | ||||||||
\(134\) | 14.2272 | 1.22905 | ||||||||
\(135\) | 2.61702 | 0.225238 | ||||||||
\(136\) | 4.91508 | 0.421465 | ||||||||
\(137\) | 8.32317 | 0.711097 | 0.355548 | − | 0.934658i | \(-0.384294\pi\) | ||||
0.355548 | + | 0.934658i | \(0.384294\pi\) | |||||||
\(138\) | −0.244868 | −0.0208445 | ||||||||
\(139\) | 1.62532 | 0.137857 | 0.0689287 | − | 0.997622i | \(-0.478042\pi\) | ||||
0.0689287 | + | 0.997622i | \(0.478042\pi\) | |||||||
\(140\) | 2.55903 | 0.216278 | ||||||||
\(141\) | −9.26343 | −0.780122 | ||||||||
\(142\) | −9.42409 | −0.790852 | ||||||||
\(143\) | −0.240785 | −0.0201354 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −21.1924 | −1.75994 | ||||||||
\(146\) | −0.976521 | −0.0808174 | ||||||||
\(147\) | 6.04383 | 0.498487 | ||||||||
\(148\) | 5.41686 | 0.445263 | ||||||||
\(149\) | −6.63099 | −0.543232 | −0.271616 | − | 0.962406i | \(-0.587558\pi\) | ||||
−0.271616 | + | 0.962406i | \(0.587558\pi\) | |||||||
\(150\) | 1.84882 | 0.150955 | ||||||||
\(151\) | 7.91264 | 0.643922 | 0.321961 | − | 0.946753i | \(-0.395658\pi\) | ||||
0.321961 | + | 0.946753i | \(0.395658\pi\) | |||||||
\(152\) | 1.97784 | 0.160424 | ||||||||
\(153\) | −4.91508 | −0.397361 | ||||||||
\(154\) | −0.235449 | −0.0189730 | ||||||||
\(155\) | 18.7229 | 1.50386 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | 5.70092 | 0.454983 | 0.227492 | − | 0.973780i | \(-0.426948\pi\) | ||||
0.227492 | + | 0.973780i | \(0.426948\pi\) | |||||||
\(158\) | 8.87366 | 0.705950 | ||||||||
\(159\) | −9.79000 | −0.776398 | ||||||||
\(160\) | 2.61702 | 0.206894 | ||||||||
\(161\) | 0.239442 | 0.0188706 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 11.8922 | 0.931469 | 0.465734 | − | 0.884925i | \(-0.345790\pi\) | ||||
0.465734 | + | 0.884925i | \(0.345790\pi\) | |||||||
\(164\) | 10.7554 | 0.839855 | ||||||||
\(165\) | −0.630140 | −0.0490563 | ||||||||
\(166\) | −13.3970 | −1.03981 | ||||||||
\(167\) | 7.73384 | 0.598462 | 0.299231 | − | 0.954181i | \(-0.403270\pi\) | ||||
0.299231 | + | 0.954181i | \(0.403270\pi\) | |||||||
\(168\) | −0.977840 | −0.0754420 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −12.8629 | −0.986539 | ||||||||
\(171\) | −1.97784 | −0.151249 | ||||||||
\(172\) | −5.03820 | −0.384159 | ||||||||
\(173\) | 0.659015 | 0.0501040 | 0.0250520 | − | 0.999686i | \(-0.492025\pi\) | ||||
0.0250520 | + | 0.999686i | \(0.492025\pi\) | |||||||
\(174\) | 8.09791 | 0.613901 | ||||||||
\(175\) | −1.80785 | −0.136660 | ||||||||
\(176\) | −0.240785 | −0.0181498 | ||||||||
\(177\) | 7.05375 | 0.530193 | ||||||||
\(178\) | 0.490697 | 0.0367793 | ||||||||
\(179\) | 20.3333 | 1.51978 | 0.759891 | − | 0.650051i | \(-0.225253\pi\) | ||||
0.759891 | + | 0.650051i | \(0.225253\pi\) | |||||||
\(180\) | −2.61702 | −0.195061 | ||||||||
\(181\) | 11.7556 | 0.873786 | 0.436893 | − | 0.899514i | \(-0.356079\pi\) | ||||
0.436893 | + | 0.899514i | \(0.356079\pi\) | |||||||
\(182\) | 0.977840 | 0.0724823 | ||||||||
\(183\) | −3.55737 | −0.262968 | ||||||||
\(184\) | 0.244868 | 0.0180519 | ||||||||
\(185\) | −14.1760 | −1.04224 | ||||||||
\(186\) | −7.15427 | −0.524576 | ||||||||
\(187\) | 1.18348 | 0.0865444 | ||||||||
\(188\) | 9.26343 | 0.675605 | ||||||||
\(189\) | 0.977840 | 0.0711274 | ||||||||
\(190\) | −5.17606 | −0.375511 | ||||||||
\(191\) | 6.63399 | 0.480019 | 0.240009 | − | 0.970771i | \(-0.422849\pi\) | ||||
0.240009 | + | 0.970771i | \(0.422849\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 7.61732 | 0.548306 | 0.274153 | − | 0.961686i | \(-0.411602\pi\) | ||||
0.274153 | + | 0.961686i | \(0.411602\pi\) | |||||||
\(194\) | −14.7754 | −1.06081 | ||||||||
\(195\) | 2.61702 | 0.187409 | ||||||||
\(196\) | −6.04383 | −0.431702 | ||||||||
\(197\) | −5.85181 | −0.416924 | −0.208462 | − | 0.978030i | \(-0.566846\pi\) | ||||
−0.208462 | + | 0.978030i | \(0.566846\pi\) | |||||||
\(198\) | 0.240785 | 0.0171118 | ||||||||
\(199\) | −1.15345 | −0.0817656 | −0.0408828 | − | 0.999164i | \(-0.513017\pi\) | ||||
−0.0408828 | + | 0.999164i | \(0.513017\pi\) | |||||||
\(200\) | −1.84882 | −0.130731 | ||||||||
\(201\) | 14.2272 | 1.00351 | ||||||||
\(202\) | 10.7141 | 0.753840 | ||||||||
\(203\) | −7.91847 | −0.555767 | ||||||||
\(204\) | 4.91508 | 0.344125 | ||||||||
\(205\) | −28.1471 | −1.96588 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | −0.244868 | −0.0170195 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 0.476234 | 0.0329418 | ||||||||
\(210\) | 2.55903 | 0.176590 | ||||||||
\(211\) | 0.706007 | 0.0486035 | 0.0243018 | − | 0.999705i | \(-0.492264\pi\) | ||||
0.0243018 | + | 0.999705i | \(0.492264\pi\) | |||||||
\(212\) | 9.79000 | 0.672380 | ||||||||
\(213\) | −9.42409 | −0.645728 | ||||||||
\(214\) | 12.2317 | 0.836141 | ||||||||
\(215\) | 13.1851 | 0.899216 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 6.99573 | 0.474901 | ||||||||
\(218\) | 15.0495 | 1.01928 | ||||||||
\(219\) | −0.976521 | −0.0659872 | ||||||||
\(220\) | 0.630140 | 0.0424840 | ||||||||
\(221\) | −4.91508 | −0.330624 | ||||||||
\(222\) | 5.41686 | 0.363556 | ||||||||
\(223\) | 14.3345 | 0.959906 | 0.479953 | − | 0.877294i | \(-0.340654\pi\) | ||||
0.479953 | + | 0.877294i | \(0.340654\pi\) | |||||||
\(224\) | 0.977840 | 0.0653347 | ||||||||
\(225\) | 1.84882 | 0.123254 | ||||||||
\(226\) | −15.2767 | −1.01619 | ||||||||
\(227\) | 12.2428 | 0.812586 | 0.406293 | − | 0.913743i | \(-0.366821\pi\) | ||||
0.406293 | + | 0.913743i | \(0.366821\pi\) | |||||||
\(228\) | 1.97784 | 0.130986 | ||||||||
\(229\) | 26.8538 | 1.77455 | 0.887274 | − | 0.461242i | \(-0.152596\pi\) | ||||
0.887274 | + | 0.461242i | \(0.152596\pi\) | |||||||
\(230\) | −0.640825 | −0.0422547 | ||||||||
\(231\) | −0.235449 | −0.0154914 | ||||||||
\(232\) | −8.09791 | −0.531654 | ||||||||
\(233\) | −11.9179 | −0.780769 | −0.390384 | − | 0.920652i | \(-0.627658\pi\) | ||||
−0.390384 | + | 0.920652i | \(0.627658\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | −24.2426 | −1.58141 | ||||||||
\(236\) | −7.05375 | −0.459160 | ||||||||
\(237\) | 8.87366 | 0.576406 | ||||||||
\(238\) | −4.80617 | −0.311538 | ||||||||
\(239\) | −8.42147 | −0.544739 | −0.272370 | − | 0.962193i | \(-0.587807\pi\) | ||||
−0.272370 | + | 0.962193i | \(0.587807\pi\) | |||||||
\(240\) | 2.61702 | 0.168928 | ||||||||
\(241\) | 4.39928 | 0.283382 | 0.141691 | − | 0.989911i | \(-0.454746\pi\) | ||||
0.141691 | + | 0.989911i | \(0.454746\pi\) | |||||||
\(242\) | 10.9420 | 0.703380 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 3.55737 | 0.227737 | ||||||||
\(245\) | 15.8168 | 1.01050 | ||||||||
\(246\) | 10.7554 | 0.685739 | ||||||||
\(247\) | −1.97784 | −0.125847 | ||||||||
\(248\) | 7.15427 | 0.454297 | ||||||||
\(249\) | −13.3970 | −0.848997 | ||||||||
\(250\) | −8.24672 | −0.521569 | ||||||||
\(251\) | −22.7613 | −1.43668 | −0.718339 | − | 0.695693i | \(-0.755097\pi\) | ||||
−0.718339 | + | 0.695693i | \(0.755097\pi\) | |||||||
\(252\) | −0.977840 | −0.0615982 | ||||||||
\(253\) | 0.0589604 | 0.00370681 | ||||||||
\(254\) | 5.61363 | 0.352230 | ||||||||
\(255\) | −12.8629 | −0.805506 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −29.1047 | −1.81550 | −0.907752 | − | 0.419507i | \(-0.862203\pi\) | ||||
−0.907752 | + | 0.419507i | \(0.862203\pi\) | |||||||
\(258\) | −5.03820 | −0.313665 | ||||||||
\(259\) | −5.29682 | −0.329128 | ||||||||
\(260\) | −2.61702 | −0.162301 | ||||||||
\(261\) | 8.09791 | 0.501248 | ||||||||
\(262\) | −3.87103 | −0.239153 | ||||||||
\(263\) | −6.72826 | −0.414882 | −0.207441 | − | 0.978247i | \(-0.566514\pi\) | ||||
−0.207441 | + | 0.978247i | \(0.566514\pi\) | |||||||
\(264\) | −0.240785 | −0.0148193 | ||||||||
\(265\) | −25.6207 | −1.57387 | ||||||||
\(266\) | −1.93401 | −0.118582 | ||||||||
\(267\) | 0.490697 | 0.0300302 | ||||||||
\(268\) | −14.2272 | −0.869067 | ||||||||
\(269\) | −14.7972 | −0.902204 | −0.451102 | − | 0.892472i | \(-0.648969\pi\) | ||||
−0.451102 | + | 0.892472i | \(0.648969\pi\) | |||||||
\(270\) | −2.61702 | −0.159267 | ||||||||
\(271\) | −1.96999 | −0.119669 | −0.0598343 | − | 0.998208i | \(-0.519057\pi\) | ||||
−0.0598343 | + | 0.998208i | \(0.519057\pi\) | |||||||
\(272\) | −4.91508 | −0.298021 | ||||||||
\(273\) | 0.977840 | 0.0591816 | ||||||||
\(274\) | −8.32317 | −0.502821 | ||||||||
\(275\) | −0.445167 | −0.0268446 | ||||||||
\(276\) | 0.244868 | 0.0147393 | ||||||||
\(277\) | −16.6946 | −1.00308 | −0.501541 | − | 0.865134i | \(-0.667233\pi\) | ||||
−0.501541 | + | 0.865134i | \(0.667233\pi\) | |||||||
\(278\) | −1.62532 | −0.0974800 | ||||||||
\(279\) | −7.15427 | −0.428315 | ||||||||
\(280\) | −2.55903 | −0.152931 | ||||||||
\(281\) | −27.9085 | −1.66488 | −0.832440 | − | 0.554115i | \(-0.813057\pi\) | ||||
−0.832440 | + | 0.554115i | \(0.813057\pi\) | |||||||
\(282\) | 9.26343 | 0.551629 | ||||||||
\(283\) | −0.449681 | −0.0267307 | −0.0133654 | − | 0.999911i | \(-0.504254\pi\) | ||||
−0.0133654 | + | 0.999911i | \(0.504254\pi\) | |||||||
\(284\) | 9.42409 | 0.559217 | ||||||||
\(285\) | −5.17606 | −0.306603 | ||||||||
\(286\) | 0.240785 | 0.0142379 | ||||||||
\(287\) | −10.5171 | −0.620802 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 7.15805 | 0.421062 | ||||||||
\(290\) | 21.1924 | 1.24446 | ||||||||
\(291\) | −14.7754 | −0.866149 | ||||||||
\(292\) | 0.976521 | 0.0571466 | ||||||||
\(293\) | 2.83914 | 0.165864 | 0.0829322 | − | 0.996555i | \(-0.473572\pi\) | ||||
0.0829322 | + | 0.996555i | \(0.473572\pi\) | |||||||
\(294\) | −6.04383 | −0.352483 | ||||||||
\(295\) | 18.4598 | 1.07477 | ||||||||
\(296\) | −5.41686 | −0.314848 | ||||||||
\(297\) | 0.240785 | 0.0139717 | ||||||||
\(298\) | 6.63099 | 0.384123 | ||||||||
\(299\) | −0.244868 | −0.0141611 | ||||||||
\(300\) | −1.84882 | −0.106741 | ||||||||
\(301\) | 4.92655 | 0.283962 | ||||||||
\(302\) | −7.91264 | −0.455321 | ||||||||
\(303\) | 10.7141 | 0.615508 | ||||||||
\(304\) | −1.97784 | −0.113437 | ||||||||
\(305\) | −9.30972 | −0.533073 | ||||||||
\(306\) | 4.91508 | 0.280977 | ||||||||
\(307\) | 22.4489 | 1.28123 | 0.640614 | − | 0.767863i | \(-0.278680\pi\) | ||||
0.640614 | + | 0.767863i | \(0.278680\pi\) | |||||||
\(308\) | 0.235449 | 0.0134160 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | −18.7229 | −1.06339 | ||||||||
\(311\) | −4.91789 | −0.278868 | −0.139434 | − | 0.990231i | \(-0.544528\pi\) | ||||
−0.139434 | + | 0.990231i | \(0.544528\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 14.2027 | 0.802781 | 0.401391 | − | 0.915907i | \(-0.368527\pi\) | ||||
0.401391 | + | 0.915907i | \(0.368527\pi\) | |||||||
\(314\) | −5.70092 | −0.321722 | ||||||||
\(315\) | 2.55903 | 0.144185 | ||||||||
\(316\) | −8.87366 | −0.499182 | ||||||||
\(317\) | 1.83459 | 0.103041 | 0.0515205 | − | 0.998672i | \(-0.483593\pi\) | ||||
0.0515205 | + | 0.998672i | \(0.483593\pi\) | |||||||
\(318\) | 9.79000 | 0.548996 | ||||||||
\(319\) | −1.94985 | −0.109171 | ||||||||
\(320\) | −2.61702 | −0.146296 | ||||||||
\(321\) | 12.2317 | 0.682706 | ||||||||
\(322\) | −0.239442 | −0.0133436 | ||||||||
\(323\) | 9.72125 | 0.540905 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 1.84882 | 0.102554 | ||||||||
\(326\) | −11.8922 | −0.658648 | ||||||||
\(327\) | 15.0495 | 0.832239 | ||||||||
\(328\) | −10.7554 | −0.593867 | ||||||||
\(329\) | −9.05816 | −0.499392 | ||||||||
\(330\) | 0.630140 | 0.0346880 | ||||||||
\(331\) | −22.7353 | −1.24965 | −0.624823 | − | 0.780767i | \(-0.714829\pi\) | ||||
−0.624823 | + | 0.780767i | \(0.714829\pi\) | |||||||
\(332\) | 13.3970 | 0.735253 | ||||||||
\(333\) | 5.41686 | 0.296842 | ||||||||
\(334\) | −7.73384 | −0.423177 | ||||||||
\(335\) | 37.2330 | 2.03426 | ||||||||
\(336\) | 0.977840 | 0.0533456 | ||||||||
\(337\) | 1.40532 | 0.0765528 | 0.0382764 | − | 0.999267i | \(-0.487813\pi\) | ||||
0.0382764 | + | 0.999267i | \(0.487813\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | −15.2767 | −0.829718 | ||||||||
\(340\) | 12.8629 | 0.697588 | ||||||||
\(341\) | 1.72264 | 0.0932861 | ||||||||
\(342\) | 1.97784 | 0.106949 | ||||||||
\(343\) | 12.7548 | 0.688693 | ||||||||
\(344\) | 5.03820 | 0.271641 | ||||||||
\(345\) | −0.640825 | −0.0345008 | ||||||||
\(346\) | −0.659015 | −0.0354289 | ||||||||
\(347\) | −28.8724 | −1.54995 | −0.774977 | − | 0.631989i | \(-0.782239\pi\) | ||||
−0.774977 | + | 0.631989i | \(0.782239\pi\) | |||||||
\(348\) | −8.09791 | −0.434094 | ||||||||
\(349\) | −22.1867 | −1.18763 | −0.593813 | − | 0.804603i | \(-0.702378\pi\) | ||||
−0.593813 | + | 0.804603i | \(0.702378\pi\) | |||||||
\(350\) | 1.80785 | 0.0966335 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0.240785 | 0.0128339 | ||||||||
\(353\) | −5.73114 | −0.305038 | −0.152519 | − | 0.988301i | \(-0.548738\pi\) | ||||
−0.152519 | + | 0.988301i | \(0.548738\pi\) | |||||||
\(354\) | −7.05375 | −0.374903 | ||||||||
\(355\) | −24.6631 | −1.30898 | ||||||||
\(356\) | −0.490697 | −0.0260069 | ||||||||
\(357\) | −4.80617 | −0.254369 | ||||||||
\(358\) | −20.3333 | −1.07465 | ||||||||
\(359\) | −16.9988 | −0.897164 | −0.448582 | − | 0.893742i | \(-0.648071\pi\) | ||||
−0.448582 | + | 0.893742i | \(0.648071\pi\) | |||||||
\(360\) | 2.61702 | 0.137929 | ||||||||
\(361\) | −15.0881 | −0.794113 | ||||||||
\(362\) | −11.7556 | −0.617860 | ||||||||
\(363\) | 10.9420 | 0.574307 | ||||||||
\(364\) | −0.977840 | −0.0512528 | ||||||||
\(365\) | −2.55558 | −0.133765 | ||||||||
\(366\) | 3.55737 | 0.185947 | ||||||||
\(367\) | −8.06954 | −0.421226 | −0.210613 | − | 0.977569i | \(-0.567546\pi\) | ||||
−0.210613 | + | 0.977569i | \(0.567546\pi\) | |||||||
\(368\) | −0.244868 | −0.0127646 | ||||||||
\(369\) | 10.7554 | 0.559903 | ||||||||
\(370\) | 14.1760 | 0.736978 | ||||||||
\(371\) | −9.57306 | −0.497008 | ||||||||
\(372\) | 7.15427 | 0.370932 | ||||||||
\(373\) | −9.23667 | −0.478257 | −0.239128 | − | 0.970988i | \(-0.576862\pi\) | ||||
−0.239128 | + | 0.970988i | \(0.576862\pi\) | |||||||
\(374\) | −1.18348 | −0.0611962 | ||||||||
\(375\) | −8.24672 | −0.425859 | ||||||||
\(376\) | −9.26343 | −0.477725 | ||||||||
\(377\) | 8.09791 | 0.417064 | ||||||||
\(378\) | −0.977840 | −0.0502947 | ||||||||
\(379\) | −16.8755 | −0.866834 | −0.433417 | − | 0.901193i | \(-0.642692\pi\) | ||||
−0.433417 | + | 0.901193i | \(0.642692\pi\) | |||||||
\(380\) | 5.17606 | 0.265526 | ||||||||
\(381\) | 5.61363 | 0.287595 | ||||||||
\(382\) | −6.63399 | −0.339425 | ||||||||
\(383\) | −10.8901 | −0.556460 | −0.278230 | − | 0.960514i | \(-0.589748\pi\) | ||||
−0.278230 | + | 0.960514i | \(0.589748\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −0.616176 | −0.0314032 | ||||||||
\(386\) | −7.61732 | −0.387711 | ||||||||
\(387\) | −5.03820 | −0.256106 | ||||||||
\(388\) | 14.7754 | 0.750107 | ||||||||
\(389\) | 23.2979 | 1.18125 | 0.590626 | − | 0.806945i | \(-0.298881\pi\) | ||||
0.590626 | + | 0.806945i | \(0.298881\pi\) | |||||||
\(390\) | −2.61702 | −0.132518 | ||||||||
\(391\) | 1.20355 | 0.0608659 | ||||||||
\(392\) | 6.04383 | 0.305259 | ||||||||
\(393\) | −3.87103 | −0.195268 | ||||||||
\(394\) | 5.85181 | 0.294810 | ||||||||
\(395\) | 23.2226 | 1.16845 | ||||||||
\(396\) | −0.240785 | −0.0120999 | ||||||||
\(397\) | 12.2264 | 0.613624 | 0.306812 | − | 0.951770i | \(-0.400738\pi\) | ||||
0.306812 | + | 0.951770i | \(0.400738\pi\) | |||||||
\(398\) | 1.15345 | 0.0578170 | ||||||||
\(399\) | −1.93401 | −0.0968217 | ||||||||
\(400\) | 1.84882 | 0.0924408 | ||||||||
\(401\) | 8.14554 | 0.406769 | 0.203385 | − | 0.979099i | \(-0.434806\pi\) | ||||
0.203385 | + | 0.979099i | \(0.434806\pi\) | |||||||
\(402\) | −14.2272 | −0.709590 | ||||||||
\(403\) | −7.15427 | −0.356380 | ||||||||
\(404\) | −10.7141 | −0.533045 | ||||||||
\(405\) | −2.61702 | −0.130041 | ||||||||
\(406\) | 7.91847 | 0.392987 | ||||||||
\(407\) | −1.30430 | −0.0646516 | ||||||||
\(408\) | −4.91508 | −0.243333 | ||||||||
\(409\) | −23.0045 | −1.13750 | −0.568749 | − | 0.822511i | \(-0.692572\pi\) | ||||
−0.568749 | + | 0.822511i | \(0.692572\pi\) | |||||||
\(410\) | 28.1471 | 1.39009 | ||||||||
\(411\) | −8.32317 | −0.410552 | ||||||||
\(412\) | 1.00000 | 0.0492665 | ||||||||
\(413\) | 6.89744 | 0.339401 | ||||||||
\(414\) | 0.244868 | 0.0120346 | ||||||||
\(415\) | −35.0602 | −1.72104 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −1.62532 | −0.0795921 | ||||||||
\(418\) | −0.476234 | −0.0232934 | ||||||||
\(419\) | 17.7485 | 0.867070 | 0.433535 | − | 0.901137i | \(-0.357266\pi\) | ||||
0.433535 | + | 0.901137i | \(0.357266\pi\) | |||||||
\(420\) | −2.55903 | −0.124868 | ||||||||
\(421\) | 9.92884 | 0.483902 | 0.241951 | − | 0.970288i | \(-0.422213\pi\) | ||||
0.241951 | + | 0.970288i | \(0.422213\pi\) | |||||||
\(422\) | −0.706007 | −0.0343679 | ||||||||
\(423\) | 9.26343 | 0.450403 | ||||||||
\(424\) | −9.79000 | −0.475445 | ||||||||
\(425\) | −9.08709 | −0.440788 | ||||||||
\(426\) | 9.42409 | 0.456599 | ||||||||
\(427\) | −3.47854 | −0.168338 | ||||||||
\(428\) | −12.2317 | −0.591241 | ||||||||
\(429\) | 0.240785 | 0.0116252 | ||||||||
\(430\) | −13.1851 | −0.635841 | ||||||||
\(431\) | 7.53987 | 0.363183 | 0.181591 | − | 0.983374i | \(-0.441875\pi\) | ||||
0.181591 | + | 0.983374i | \(0.441875\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −9.84043 | −0.472901 | −0.236451 | − | 0.971644i | \(-0.575984\pi\) | ||||
−0.236451 | + | 0.971644i | \(0.575984\pi\) | |||||||
\(434\) | −6.99573 | −0.335806 | ||||||||
\(435\) | 21.1924 | 1.01610 | ||||||||
\(436\) | −15.0495 | −0.720740 | ||||||||
\(437\) | 0.484309 | 0.0231677 | ||||||||
\(438\) | 0.976521 | 0.0466600 | ||||||||
\(439\) | −18.5120 | −0.883528 | −0.441764 | − | 0.897131i | \(-0.645647\pi\) | ||||
−0.441764 | + | 0.897131i | \(0.645647\pi\) | |||||||
\(440\) | −0.630140 | −0.0300407 | ||||||||
\(441\) | −6.04383 | −0.287801 | ||||||||
\(442\) | 4.91508 | 0.233787 | ||||||||
\(443\) | −19.4535 | −0.924264 | −0.462132 | − | 0.886811i | \(-0.652915\pi\) | ||||
−0.462132 | + | 0.886811i | \(0.652915\pi\) | |||||||
\(444\) | −5.41686 | −0.257073 | ||||||||
\(445\) | 1.28417 | 0.0608753 | ||||||||
\(446\) | −14.3345 | −0.678756 | ||||||||
\(447\) | 6.63099 | 0.313635 | ||||||||
\(448\) | −0.977840 | −0.0461986 | ||||||||
\(449\) | −42.1339 | −1.98842 | −0.994211 | − | 0.107445i | \(-0.965733\pi\) | ||||
−0.994211 | + | 0.107445i | \(0.965733\pi\) | |||||||
\(450\) | −1.84882 | −0.0871540 | ||||||||
\(451\) | −2.58973 | −0.121946 | ||||||||
\(452\) | 15.2767 | 0.718557 | ||||||||
\(453\) | −7.91264 | −0.371768 | ||||||||
\(454\) | −12.2428 | −0.574585 | ||||||||
\(455\) | 2.55903 | 0.119969 | ||||||||
\(456\) | −1.97784 | −0.0926209 | ||||||||
\(457\) | 22.9184 | 1.07208 | 0.536038 | − | 0.844194i | \(-0.319920\pi\) | ||||
0.536038 | + | 0.844194i | \(0.319920\pi\) | |||||||
\(458\) | −26.8538 | −1.25480 | ||||||||
\(459\) | 4.91508 | 0.229416 | ||||||||
\(460\) | 0.640825 | 0.0298786 | ||||||||
\(461\) | −6.85452 | −0.319247 | −0.159623 | − | 0.987178i | \(-0.551028\pi\) | ||||
−0.159623 | + | 0.987178i | \(0.551028\pi\) | |||||||
\(462\) | 0.235449 | 0.0109541 | ||||||||
\(463\) | −20.9881 | −0.975399 | −0.487699 | − | 0.873012i | \(-0.662164\pi\) | ||||
−0.487699 | + | 0.873012i | \(0.662164\pi\) | |||||||
\(464\) | 8.09791 | 0.375936 | ||||||||
\(465\) | −18.7229 | −0.868254 | ||||||||
\(466\) | 11.9179 | 0.552087 | ||||||||
\(467\) | 25.5979 | 1.18453 | 0.592264 | − | 0.805744i | \(-0.298234\pi\) | ||||
0.592264 | + | 0.805744i | \(0.298234\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | 13.9120 | 0.642395 | ||||||||
\(470\) | 24.2426 | 1.11823 | ||||||||
\(471\) | −5.70092 | −0.262685 | ||||||||
\(472\) | 7.05375 | 0.324675 | ||||||||
\(473\) | 1.21312 | 0.0557794 | ||||||||
\(474\) | −8.87366 | −0.407581 | ||||||||
\(475\) | −3.65666 | −0.167779 | ||||||||
\(476\) | 4.80617 | 0.220290 | ||||||||
\(477\) | 9.79000 | 0.448253 | ||||||||
\(478\) | 8.42147 | 0.385189 | ||||||||
\(479\) | −27.7457 | −1.26773 | −0.633867 | − | 0.773442i | \(-0.718533\pi\) | ||||
−0.633867 | + | 0.773442i | \(0.718533\pi\) | |||||||
\(480\) | −2.61702 | −0.119450 | ||||||||
\(481\) | 5.41686 | 0.246987 | ||||||||
\(482\) | −4.39928 | −0.200382 | ||||||||
\(483\) | −0.239442 | −0.0108950 | ||||||||
\(484\) | −10.9420 | −0.497365 | ||||||||
\(485\) | −38.6676 | −1.75580 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 20.8544 | 0.945004 | 0.472502 | − | 0.881330i | \(-0.343351\pi\) | ||||
0.472502 | + | 0.881330i | \(0.343351\pi\) | |||||||
\(488\) | −3.55737 | −0.161034 | ||||||||
\(489\) | −11.8922 | −0.537784 | ||||||||
\(490\) | −15.8168 | −0.714532 | ||||||||
\(491\) | −29.1552 | −1.31576 | −0.657879 | − | 0.753124i | \(-0.728546\pi\) | ||||
−0.657879 | + | 0.753124i | \(0.728546\pi\) | |||||||
\(492\) | −10.7554 | −0.484891 | ||||||||
\(493\) | −39.8019 | −1.79259 | ||||||||
\(494\) | 1.97784 | 0.0889872 | ||||||||
\(495\) | 0.630140 | 0.0283227 | ||||||||
\(496\) | −7.15427 | −0.321236 | ||||||||
\(497\) | −9.21526 | −0.413361 | ||||||||
\(498\) | 13.3970 | 0.600332 | ||||||||
\(499\) | −22.6831 | −1.01543 | −0.507717 | − | 0.861524i | \(-0.669511\pi\) | ||||
−0.507717 | + | 0.861524i | \(0.669511\pi\) | |||||||
\(500\) | 8.24672 | 0.368805 | ||||||||
\(501\) | −7.73384 | −0.345522 | ||||||||
\(502\) | 22.7613 | 1.01588 | ||||||||
\(503\) | −8.39406 | −0.374272 | −0.187136 | − | 0.982334i | \(-0.559921\pi\) | ||||
−0.187136 | + | 0.982334i | \(0.559921\pi\) | |||||||
\(504\) | 0.977840 | 0.0435565 | ||||||||
\(505\) | 28.0390 | 1.24772 | ||||||||
\(506\) | −0.0589604 | −0.00262111 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −5.61363 | −0.249065 | ||||||||
\(509\) | 15.2631 | 0.676526 | 0.338263 | − | 0.941052i | \(-0.390161\pi\) | ||||
0.338263 | + | 0.941052i | \(0.390161\pi\) | |||||||
\(510\) | 12.8629 | 0.569579 | ||||||||
\(511\) | −0.954881 | −0.0422415 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.97784 | 0.0873238 | ||||||||
\(514\) | 29.1047 | 1.28376 | ||||||||
\(515\) | −2.61702 | −0.115320 | ||||||||
\(516\) | 5.03820 | 0.221794 | ||||||||
\(517\) | −2.23049 | −0.0980970 | ||||||||
\(518\) | 5.29682 | 0.232729 | ||||||||
\(519\) | −0.659015 | −0.0289275 | ||||||||
\(520\) | 2.61702 | 0.114764 | ||||||||
\(521\) | 13.5364 | 0.593041 | 0.296521 | − | 0.955026i | \(-0.404174\pi\) | ||||
0.296521 | + | 0.955026i | \(0.404174\pi\) | |||||||
\(522\) | −8.09791 | −0.354436 | ||||||||
\(523\) | −14.4599 | −0.632288 | −0.316144 | − | 0.948711i | \(-0.602388\pi\) | ||||
−0.316144 | + | 0.948711i | \(0.602388\pi\) | |||||||
\(524\) | 3.87103 | 0.169107 | ||||||||
\(525\) | 1.80785 | 0.0789009 | ||||||||
\(526\) | 6.72826 | 0.293366 | ||||||||
\(527\) | 35.1638 | 1.53176 | ||||||||
\(528\) | 0.240785 | 0.0104788 | ||||||||
\(529\) | −22.9400 | −0.997393 | ||||||||
\(530\) | 25.6207 | 1.11289 | ||||||||
\(531\) | −7.05375 | −0.306107 | ||||||||
\(532\) | 1.93401 | 0.0838501 | ||||||||
\(533\) | 10.7554 | 0.465868 | ||||||||
\(534\) | −0.490697 | −0.0212345 | ||||||||
\(535\) | 32.0106 | 1.38394 | ||||||||
\(536\) | 14.2272 | 0.614523 | ||||||||
\(537\) | −20.3333 | −0.877446 | ||||||||
\(538\) | 14.7972 | 0.637954 | ||||||||
\(539\) | 1.45526 | 0.0626826 | ||||||||
\(540\) | 2.61702 | 0.112619 | ||||||||
\(541\) | −34.3574 | −1.47714 | −0.738571 | − | 0.674176i | \(-0.764499\pi\) | ||||
−0.738571 | + | 0.674176i | \(0.764499\pi\) | |||||||
\(542\) | 1.96999 | 0.0846185 | ||||||||
\(543\) | −11.7556 | −0.504480 | ||||||||
\(544\) | 4.91508 | 0.210732 | ||||||||
\(545\) | 39.3849 | 1.68706 | ||||||||
\(546\) | −0.977840 | −0.0418477 | ||||||||
\(547\) | −7.44242 | −0.318215 | −0.159107 | − | 0.987261i | \(-0.550862\pi\) | ||||
−0.159107 | + | 0.987261i | \(0.550862\pi\) | |||||||
\(548\) | 8.32317 | 0.355548 | ||||||||
\(549\) | 3.55737 | 0.151825 | ||||||||
\(550\) | 0.445167 | 0.0189820 | ||||||||
\(551\) | −16.0164 | −0.682321 | ||||||||
\(552\) | −0.244868 | −0.0104223 | ||||||||
\(553\) | 8.67702 | 0.368984 | ||||||||
\(554\) | 16.6946 | 0.709286 | ||||||||
\(555\) | 14.1760 | 0.601740 | ||||||||
\(556\) | 1.62532 | 0.0689287 | ||||||||
\(557\) | 19.7550 | 0.837045 | 0.418522 | − | 0.908207i | \(-0.362548\pi\) | ||||
0.418522 | + | 0.908207i | \(0.362548\pi\) | |||||||
\(558\) | 7.15427 | 0.302864 | ||||||||
\(559\) | −5.03820 | −0.213093 | ||||||||
\(560\) | 2.55903 | 0.108139 | ||||||||
\(561\) | −1.18348 | −0.0499664 | ||||||||
\(562\) | 27.9085 | 1.17725 | ||||||||
\(563\) | −12.0479 | −0.507757 | −0.253878 | − | 0.967236i | \(-0.581706\pi\) | ||||
−0.253878 | + | 0.967236i | \(0.581706\pi\) | |||||||
\(564\) | −9.26343 | −0.390061 | ||||||||
\(565\) | −39.9796 | −1.68195 | ||||||||
\(566\) | 0.449681 | 0.0189015 | ||||||||
\(567\) | −0.977840 | −0.0410654 | ||||||||
\(568\) | −9.42409 | −0.395426 | ||||||||
\(569\) | −5.93297 | −0.248723 | −0.124362 | − | 0.992237i | \(-0.539688\pi\) | ||||
−0.124362 | + | 0.992237i | \(0.539688\pi\) | |||||||
\(570\) | 5.17606 | 0.216801 | ||||||||
\(571\) | −5.79958 | −0.242705 | −0.121352 | − | 0.992609i | \(-0.538723\pi\) | ||||
−0.121352 | + | 0.992609i | \(0.538723\pi\) | |||||||
\(572\) | −0.240785 | −0.0100677 | ||||||||
\(573\) | −6.63399 | −0.277139 | ||||||||
\(574\) | 10.5171 | 0.438973 | ||||||||
\(575\) | −0.452715 | −0.0188795 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 3.70002 | 0.154034 | 0.0770169 | − | 0.997030i | \(-0.475460\pi\) | ||||
0.0770169 | + | 0.997030i | \(0.475460\pi\) | |||||||
\(578\) | −7.15805 | −0.297736 | ||||||||
\(579\) | −7.61732 | −0.316565 | ||||||||
\(580\) | −21.1924 | −0.879968 | ||||||||
\(581\) | −13.1001 | −0.543483 | ||||||||
\(582\) | 14.7754 | 0.612460 | ||||||||
\(583\) | −2.35728 | −0.0976287 | ||||||||
\(584\) | −0.976521 | −0.0404087 | ||||||||
\(585\) | −2.61702 | −0.108201 | ||||||||
\(586\) | −2.83914 | −0.117284 | ||||||||
\(587\) | 18.7108 | 0.772278 | 0.386139 | − | 0.922441i | \(-0.373808\pi\) | ||||
0.386139 | + | 0.922441i | \(0.373808\pi\) | |||||||
\(588\) | 6.04383 | 0.249243 | ||||||||
\(589\) | 14.1500 | 0.583041 | ||||||||
\(590\) | −18.4598 | −0.759980 | ||||||||
\(591\) | 5.85181 | 0.240711 | ||||||||
\(592\) | 5.41686 | 0.222631 | ||||||||
\(593\) | −23.9001 | −0.981460 | −0.490730 | − | 0.871312i | \(-0.663270\pi\) | ||||
−0.490730 | + | 0.871312i | \(0.663270\pi\) | |||||||
\(594\) | −0.240785 | −0.00987952 | ||||||||
\(595\) | −12.5779 | −0.515642 | ||||||||
\(596\) | −6.63099 | −0.271616 | ||||||||
\(597\) | 1.15345 | 0.0472074 | ||||||||
\(598\) | 0.244868 | 0.0100134 | ||||||||
\(599\) | 12.7785 | 0.522114 | 0.261057 | − | 0.965323i | \(-0.415929\pi\) | ||||
0.261057 | + | 0.965323i | \(0.415929\pi\) | |||||||
\(600\) | 1.84882 | 0.0754776 | ||||||||
\(601\) | −2.45569 | −0.100170 | −0.0500848 | − | 0.998745i | \(-0.515949\pi\) | ||||
−0.0500848 | + | 0.998745i | \(0.515949\pi\) | |||||||
\(602\) | −4.92655 | −0.200791 | ||||||||
\(603\) | −14.2272 | −0.579378 | ||||||||
\(604\) | 7.91264 | 0.321961 | ||||||||
\(605\) | 28.6355 | 1.16420 | ||||||||
\(606\) | −10.7141 | −0.435230 | ||||||||
\(607\) | 37.5049 | 1.52228 | 0.761138 | − | 0.648590i | \(-0.224641\pi\) | ||||
0.761138 | + | 0.648590i | \(0.224641\pi\) | |||||||
\(608\) | 1.97784 | 0.0802120 | ||||||||
\(609\) | 7.91847 | 0.320872 | ||||||||
\(610\) | 9.30972 | 0.376939 | ||||||||
\(611\) | 9.26343 | 0.374758 | ||||||||
\(612\) | −4.91508 | −0.198680 | ||||||||
\(613\) | 21.6188 | 0.873176 | 0.436588 | − | 0.899662i | \(-0.356187\pi\) | ||||
0.436588 | + | 0.899662i | \(0.356187\pi\) | |||||||
\(614\) | −22.4489 | −0.905964 | ||||||||
\(615\) | 28.1471 | 1.13500 | ||||||||
\(616\) | −0.235449 | −0.00948651 | ||||||||
\(617\) | −7.98471 | −0.321452 | −0.160726 | − | 0.986999i | \(-0.551384\pi\) | ||||
−0.160726 | + | 0.986999i | \(0.551384\pi\) | |||||||
\(618\) | 1.00000 | 0.0402259 | ||||||||
\(619\) | −15.5740 | −0.625972 | −0.312986 | − | 0.949758i | \(-0.601329\pi\) | ||||
−0.312986 | + | 0.949758i | \(0.601329\pi\) | |||||||
\(620\) | 18.7229 | 0.751930 | ||||||||
\(621\) | 0.244868 | 0.00982620 | ||||||||
\(622\) | 4.91789 | 0.197189 | ||||||||
\(623\) | 0.479823 | 0.0192237 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | −30.8260 | −1.23304 | ||||||||
\(626\) | −14.2027 | −0.567652 | ||||||||
\(627\) | −0.476234 | −0.0190189 | ||||||||
\(628\) | 5.70092 | 0.227492 | ||||||||
\(629\) | −26.6243 | −1.06158 | ||||||||
\(630\) | −2.55903 | −0.101954 | ||||||||
\(631\) | −19.6398 | −0.781847 | −0.390923 | − | 0.920423i | \(-0.627844\pi\) | ||||
−0.390923 | + | 0.920423i | \(0.627844\pi\) | |||||||
\(632\) | 8.87366 | 0.352975 | ||||||||
\(633\) | −0.706007 | −0.0280613 | ||||||||
\(634\) | −1.83459 | −0.0728609 | ||||||||
\(635\) | 14.6910 | 0.582995 | ||||||||
\(636\) | −9.79000 | −0.388199 | ||||||||
\(637\) | −6.04383 | −0.239465 | ||||||||
\(638\) | 1.94985 | 0.0771955 | ||||||||
\(639\) | 9.42409 | 0.372811 | ||||||||
\(640\) | 2.61702 | 0.103447 | ||||||||
\(641\) | −1.62764 | −0.0642879 | −0.0321439 | − | 0.999483i | \(-0.510233\pi\) | ||||
−0.0321439 | + | 0.999483i | \(0.510233\pi\) | |||||||
\(642\) | −12.2317 | −0.482746 | ||||||||
\(643\) | −29.8776 | −1.17826 | −0.589128 | − | 0.808040i | \(-0.700529\pi\) | ||||
−0.589128 | + | 0.808040i | \(0.700529\pi\) | |||||||
\(644\) | 0.239442 | 0.00943532 | ||||||||
\(645\) | −13.1851 | −0.519162 | ||||||||
\(646\) | −9.72125 | −0.382478 | ||||||||
\(647\) | −11.9039 | −0.467989 | −0.233995 | − | 0.972238i | \(-0.575180\pi\) | ||||
−0.233995 | + | 0.972238i | \(0.575180\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 1.69844 | 0.0666695 | ||||||||
\(650\) | −1.84882 | −0.0725165 | ||||||||
\(651\) | −6.99573 | −0.274184 | ||||||||
\(652\) | 11.8922 | 0.465734 | ||||||||
\(653\) | 13.2976 | 0.520374 | 0.260187 | − | 0.965558i | \(-0.416216\pi\) | ||||
0.260187 | + | 0.965558i | \(0.416216\pi\) | |||||||
\(654\) | −15.0495 | −0.588482 | ||||||||
\(655\) | −10.1306 | −0.395835 | ||||||||
\(656\) | 10.7554 | 0.419928 | ||||||||
\(657\) | 0.976521 | 0.0380977 | ||||||||
\(658\) | 9.05816 | 0.353124 | ||||||||
\(659\) | 0.0282496 | 0.00110045 | 0.000550223 | − | 1.00000i | \(-0.499825\pi\) | ||||
0.000550223 | 1.00000i | \(0.499825\pi\) | ||||||||
\(660\) | −0.630140 | −0.0245281 | ||||||||
\(661\) | 11.7375 | 0.456536 | 0.228268 | − | 0.973598i | \(-0.426694\pi\) | ||||
0.228268 | + | 0.973598i | \(0.426694\pi\) | |||||||
\(662\) | 22.7353 | 0.883633 | ||||||||
\(663\) | 4.91508 | 0.190886 | ||||||||
\(664\) | −13.3970 | −0.519903 | ||||||||
\(665\) | −5.06136 | −0.196271 | ||||||||
\(666\) | −5.41686 | −0.209899 | ||||||||
\(667\) | −1.98292 | −0.0767789 | ||||||||
\(668\) | 7.73384 | 0.299231 | ||||||||
\(669\) | −14.3345 | −0.554202 | ||||||||
\(670\) | −37.2330 | −1.43844 | ||||||||
\(671\) | −0.856560 | −0.0330671 | ||||||||
\(672\) | −0.977840 | −0.0377210 | ||||||||
\(673\) | −3.55254 | −0.136940 | −0.0684702 | − | 0.997653i | \(-0.521812\pi\) | ||||
−0.0684702 | + | 0.997653i | \(0.521812\pi\) | |||||||
\(674\) | −1.40532 | −0.0541310 | ||||||||
\(675\) | −1.84882 | −0.0711610 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −31.6198 | −1.21525 | −0.607623 | − | 0.794226i | \(-0.707877\pi\) | ||||
−0.607623 | + | 0.794226i | \(0.707877\pi\) | |||||||
\(678\) | 15.2767 | 0.586699 | ||||||||
\(679\) | −14.4480 | −0.554462 | ||||||||
\(680\) | −12.8629 | −0.493269 | ||||||||
\(681\) | −12.2428 | −0.469147 | ||||||||
\(682\) | −1.72264 | −0.0659633 | ||||||||
\(683\) | 10.8767 | 0.416184 | 0.208092 | − | 0.978109i | \(-0.433275\pi\) | ||||
0.208092 | + | 0.978109i | \(0.433275\pi\) | |||||||
\(684\) | −1.97784 | −0.0756246 | ||||||||
\(685\) | −21.7819 | −0.832245 | ||||||||
\(686\) | −12.7548 | −0.486980 | ||||||||
\(687\) | −26.8538 | −1.02454 | ||||||||
\(688\) | −5.03820 | −0.192080 | ||||||||
\(689\) | 9.79000 | 0.372969 | ||||||||
\(690\) | 0.640825 | 0.0243958 | ||||||||
\(691\) | 34.5054 | 1.31265 | 0.656324 | − | 0.754479i | \(-0.272110\pi\) | ||||
0.656324 | + | 0.754479i | \(0.272110\pi\) | |||||||
\(692\) | 0.659015 | 0.0250520 | ||||||||
\(693\) | 0.235449 | 0.00894397 | ||||||||
\(694\) | 28.8724 | 1.09598 | ||||||||
\(695\) | −4.25349 | −0.161344 | ||||||||
\(696\) | 8.09791 | 0.306951 | ||||||||
\(697\) | −52.8637 | −2.00235 | ||||||||
\(698\) | 22.1867 | 0.839778 | ||||||||
\(699\) | 11.9179 | 0.450777 | ||||||||
\(700\) | −1.80785 | −0.0683302 | ||||||||
\(701\) | −7.94945 | −0.300247 | −0.150123 | − | 0.988667i | \(-0.547967\pi\) | ||||
−0.150123 | + | 0.988667i | \(0.547967\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | −10.7137 | −0.404074 | ||||||||
\(704\) | −0.240785 | −0.00907492 | ||||||||
\(705\) | 24.2426 | 0.913030 | ||||||||
\(706\) | 5.73114 | 0.215694 | ||||||||
\(707\) | 10.4767 | 0.394015 | ||||||||
\(708\) | 7.05375 | 0.265096 | ||||||||
\(709\) | −38.7513 | −1.45534 | −0.727668 | − | 0.685930i | \(-0.759396\pi\) | ||||
−0.727668 | + | 0.685930i | \(0.759396\pi\) | |||||||
\(710\) | 24.6631 | 0.925589 | ||||||||
\(711\) | −8.87366 | −0.332788 | ||||||||
\(712\) | 0.490697 | 0.0183896 | ||||||||
\(713\) | 1.75185 | 0.0656073 | ||||||||
\(714\) | 4.80617 | 0.179866 | ||||||||
\(715\) | 0.630140 | 0.0235659 | ||||||||
\(716\) | 20.3333 | 0.759891 | ||||||||
\(717\) | 8.42147 | 0.314505 | ||||||||
\(718\) | 16.9988 | 0.634391 | ||||||||
\(719\) | 11.9026 | 0.443894 | 0.221947 | − | 0.975059i | \(-0.428759\pi\) | ||||
0.221947 | + | 0.975059i | \(0.428759\pi\) | |||||||
\(720\) | −2.61702 | −0.0975307 | ||||||||
\(721\) | −0.977840 | −0.0364167 | ||||||||
\(722\) | 15.0881 | 0.561523 | ||||||||
\(723\) | −4.39928 | −0.163611 | ||||||||
\(724\) | 11.7556 | 0.436893 | ||||||||
\(725\) | 14.9716 | 0.556030 | ||||||||
\(726\) | −10.9420 | −0.406097 | ||||||||
\(727\) | −20.3323 | −0.754082 | −0.377041 | − | 0.926197i | \(-0.623058\pi\) | ||||
−0.377041 | + | 0.926197i | \(0.623058\pi\) | |||||||
\(728\) | 0.977840 | 0.0362412 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.55558 | 0.0945862 | ||||||||
\(731\) | 24.7632 | 0.915899 | ||||||||
\(732\) | −3.55737 | −0.131484 | ||||||||
\(733\) | 44.3842 | 1.63937 | 0.819684 | − | 0.572816i | \(-0.194149\pi\) | ||||
0.819684 | + | 0.572816i | \(0.194149\pi\) | |||||||
\(734\) | 8.06954 | 0.297852 | ||||||||
\(735\) | −15.8168 | −0.583413 | ||||||||
\(736\) | 0.244868 | 0.00902594 | ||||||||
\(737\) | 3.42570 | 0.126187 | ||||||||
\(738\) | −10.7554 | −0.395911 | ||||||||
\(739\) | −47.1876 | −1.73582 | −0.867912 | − | 0.496718i | \(-0.834538\pi\) | ||||
−0.867912 | + | 0.496718i | \(0.834538\pi\) | |||||||
\(740\) | −14.1760 | −0.521122 | ||||||||
\(741\) | 1.97784 | 0.0726578 | ||||||||
\(742\) | 9.57306 | 0.351438 | ||||||||
\(743\) | −21.0148 | −0.770957 | −0.385478 | − | 0.922717i | \(-0.625964\pi\) | ||||
−0.385478 | + | 0.922717i | \(0.625964\pi\) | |||||||
\(744\) | −7.15427 | −0.262288 | ||||||||
\(745\) | 17.3535 | 0.635782 | ||||||||
\(746\) | 9.23667 | 0.338179 | ||||||||
\(747\) | 13.3970 | 0.490169 | ||||||||
\(748\) | 1.18348 | 0.0432722 | ||||||||
\(749\) | 11.9606 | 0.437032 | ||||||||
\(750\) | 8.24672 | 0.301128 | ||||||||
\(751\) | 6.30191 | 0.229960 | 0.114980 | − | 0.993368i | \(-0.463320\pi\) | ||||
0.114980 | + | 0.993368i | \(0.463320\pi\) | |||||||
\(752\) | 9.26343 | 0.337803 | ||||||||
\(753\) | 22.7613 | 0.829467 | ||||||||
\(754\) | −8.09791 | −0.294909 | ||||||||
\(755\) | −20.7076 | −0.753626 | ||||||||
\(756\) | 0.977840 | 0.0355637 | ||||||||
\(757\) | 22.1721 | 0.805858 | 0.402929 | − | 0.915231i | \(-0.367992\pi\) | ||||
0.402929 | + | 0.915231i | \(0.367992\pi\) | |||||||
\(758\) | 16.8755 | 0.612945 | ||||||||
\(759\) | −0.0589604 | −0.00214013 | ||||||||
\(760\) | −5.17606 | −0.187755 | ||||||||
\(761\) | 11.4436 | 0.414830 | 0.207415 | − | 0.978253i | \(-0.433495\pi\) | ||||
0.207415 | + | 0.978253i | \(0.433495\pi\) | |||||||
\(762\) | −5.61363 | −0.203360 | ||||||||
\(763\) | 14.7160 | 0.532755 | ||||||||
\(764\) | 6.63399 | 0.240009 | ||||||||
\(765\) | 12.8629 | 0.465059 | ||||||||
\(766\) | 10.8901 | 0.393477 | ||||||||
\(767\) | −7.05375 | −0.254696 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 11.7434 | 0.423479 | 0.211739 | − | 0.977326i | \(-0.432087\pi\) | ||||
0.211739 | + | 0.977326i | \(0.432087\pi\) | |||||||
\(770\) | 0.616176 | 0.0222054 | ||||||||
\(771\) | 29.1047 | 1.04818 | ||||||||
\(772\) | 7.61732 | 0.274153 | ||||||||
\(773\) | −48.6889 | −1.75122 | −0.875608 | − | 0.483022i | \(-0.839539\pi\) | ||||
−0.875608 | + | 0.483022i | \(0.839539\pi\) | |||||||
\(774\) | 5.03820 | 0.181094 | ||||||||
\(775\) | −13.2269 | −0.475125 | ||||||||
\(776\) | −14.7754 | −0.530406 | ||||||||
\(777\) | 5.29682 | 0.190022 | ||||||||
\(778\) | −23.2979 | −0.835271 | ||||||||
\(779\) | −21.2724 | −0.762165 | ||||||||
\(780\) | 2.61702 | 0.0937045 | ||||||||
\(781\) | −2.26918 | −0.0811975 | ||||||||
\(782\) | −1.20355 | −0.0430387 | ||||||||
\(783\) | −8.09791 | −0.289396 | ||||||||
\(784\) | −6.04383 | −0.215851 | ||||||||
\(785\) | −14.9195 | −0.532498 | ||||||||
\(786\) | 3.87103 | 0.138075 | ||||||||
\(787\) | 46.3481 | 1.65213 | 0.826066 | − | 0.563574i | \(-0.190574\pi\) | ||||
0.826066 | + | 0.563574i | \(0.190574\pi\) | |||||||
\(788\) | −5.85181 | −0.208462 | ||||||||
\(789\) | 6.72826 | 0.239532 | ||||||||
\(790\) | −23.2226 | −0.826222 | ||||||||
\(791\) | −14.9382 | −0.531141 | ||||||||
\(792\) | 0.240785 | 0.00855591 | ||||||||
\(793\) | 3.55737 | 0.126326 | ||||||||
\(794\) | −12.2264 | −0.433898 | ||||||||
\(795\) | 25.6207 | 0.908672 | ||||||||
\(796\) | −1.15345 | −0.0408828 | ||||||||
\(797\) | −16.4711 | −0.583438 | −0.291719 | − | 0.956504i | \(-0.594227\pi\) | ||||
−0.291719 | + | 0.956504i | \(0.594227\pi\) | |||||||
\(798\) | 1.93401 | 0.0684633 | ||||||||
\(799\) | −45.5305 | −1.61075 | ||||||||
\(800\) | −1.84882 | −0.0653655 | ||||||||
\(801\) | −0.490697 | −0.0173379 | ||||||||
\(802\) | −8.14554 | −0.287629 | ||||||||
\(803\) | −0.235131 | −0.00829760 | ||||||||
\(804\) | 14.2272 | 0.501756 | ||||||||
\(805\) | −0.626624 | −0.0220856 | ||||||||
\(806\) | 7.15427 | 0.251998 | ||||||||
\(807\) | 14.7972 | 0.520888 | ||||||||
\(808\) | 10.7141 | 0.376920 | ||||||||
\(809\) | 23.2860 | 0.818692 | 0.409346 | − | 0.912379i | \(-0.365757\pi\) | ||||
0.409346 | + | 0.912379i | \(0.365757\pi\) | |||||||
\(810\) | 2.61702 | 0.0919529 | ||||||||
\(811\) | 2.52046 | 0.0885053 | 0.0442527 | − | 0.999020i | \(-0.485909\pi\) | ||||
0.0442527 | + | 0.999020i | \(0.485909\pi\) | |||||||
\(812\) | −7.91847 | −0.277884 | ||||||||
\(813\) | 1.96999 | 0.0690907 | ||||||||
\(814\) | 1.30430 | 0.0457156 | ||||||||
\(815\) | −31.1222 | −1.09016 | ||||||||
\(816\) | 4.91508 | 0.172062 | ||||||||
\(817\) | 9.96475 | 0.348623 | ||||||||
\(818\) | 23.0045 | 0.804333 | ||||||||
\(819\) | −0.977840 | −0.0341685 | ||||||||
\(820\) | −28.1471 | −0.982940 | ||||||||
\(821\) | 31.4193 | 1.09654 | 0.548270 | − | 0.836301i | \(-0.315287\pi\) | ||||
0.548270 | + | 0.836301i | \(0.315287\pi\) | |||||||
\(822\) | 8.32317 | 0.290304 | ||||||||
\(823\) | −36.9734 | −1.28881 | −0.644405 | − | 0.764684i | \(-0.722895\pi\) | ||||
−0.644405 | + | 0.764684i | \(0.722895\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | 0.445167 | 0.0154987 | ||||||||
\(826\) | −6.89744 | −0.239993 | ||||||||
\(827\) | −21.9835 | −0.764440 | −0.382220 | − | 0.924071i | \(-0.624840\pi\) | ||||
−0.382220 | + | 0.924071i | \(0.624840\pi\) | |||||||
\(828\) | −0.244868 | −0.00850974 | ||||||||
\(829\) | 30.7938 | 1.06951 | 0.534757 | − | 0.845006i | \(-0.320403\pi\) | ||||
0.534757 | + | 0.845006i | \(0.320403\pi\) | |||||||
\(830\) | 35.0602 | 1.21696 | ||||||||
\(831\) | 16.6946 | 0.579130 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 29.7059 | 1.02925 | ||||||||
\(834\) | 1.62532 | 0.0562801 | ||||||||
\(835\) | −20.2396 | −0.700422 | ||||||||
\(836\) | 0.476234 | 0.0164709 | ||||||||
\(837\) | 7.15427 | 0.247288 | ||||||||
\(838\) | −17.7485 | −0.613111 | ||||||||
\(839\) | −44.1131 | −1.52295 | −0.761477 | − | 0.648191i | \(-0.775526\pi\) | ||||
−0.761477 | + | 0.648191i | \(0.775526\pi\) | |||||||
\(840\) | 2.55903 | 0.0882950 | ||||||||
\(841\) | 36.5762 | 1.26125 | ||||||||
\(842\) | −9.92884 | −0.342170 | ||||||||
\(843\) | 27.9085 | 0.961219 | ||||||||
\(844\) | 0.706007 | 0.0243018 | ||||||||
\(845\) | −2.61702 | −0.0900284 | ||||||||
\(846\) | −9.26343 | −0.318483 | ||||||||
\(847\) | 10.6996 | 0.367641 | ||||||||
\(848\) | 9.79000 | 0.336190 | ||||||||
\(849\) | 0.449681 | 0.0154330 | ||||||||
\(850\) | 9.08709 | 0.311685 | ||||||||
\(851\) | −1.32641 | −0.0454689 | ||||||||
\(852\) | −9.42409 | −0.322864 | ||||||||
\(853\) | −14.4974 | −0.496381 | −0.248191 | − | 0.968711i | \(-0.579836\pi\) | ||||
−0.248191 | + | 0.968711i | \(0.579836\pi\) | |||||||
\(854\) | 3.47854 | 0.119033 | ||||||||
\(855\) | 5.17606 | 0.177017 | ||||||||
\(856\) | 12.2317 | 0.418071 | ||||||||
\(857\) | 4.24844 | 0.145124 | 0.0725620 | − | 0.997364i | \(-0.476882\pi\) | ||||
0.0725620 | + | 0.997364i | \(0.476882\pi\) | |||||||
\(858\) | −0.240785 | −0.00822026 | ||||||||
\(859\) | −15.3950 | −0.525271 | −0.262636 | − | 0.964895i | \(-0.584592\pi\) | ||||
−0.262636 | + | 0.964895i | \(0.584592\pi\) | |||||||
\(860\) | 13.1851 | 0.449608 | ||||||||
\(861\) | 10.5171 | 0.358420 | ||||||||
\(862\) | −7.53987 | −0.256809 | ||||||||
\(863\) | 24.2821 | 0.826573 | 0.413287 | − | 0.910601i | \(-0.364381\pi\) | ||||
0.413287 | + | 0.910601i | \(0.364381\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −1.72466 | −0.0586401 | ||||||||
\(866\) | 9.84043 | 0.334392 | ||||||||
\(867\) | −7.15805 | −0.243100 | ||||||||
\(868\) | 6.99573 | 0.237451 | ||||||||
\(869\) | 2.13664 | 0.0724806 | ||||||||
\(870\) | −21.1924 | −0.718491 | ||||||||
\(871\) | −14.2272 | −0.482072 | ||||||||
\(872\) | 15.0495 | 0.509640 | ||||||||
\(873\) | 14.7754 | 0.500071 | ||||||||
\(874\) | −0.484309 | −0.0163820 | ||||||||
\(875\) | −8.06398 | −0.272612 | ||||||||
\(876\) | −0.976521 | −0.0329936 | ||||||||
\(877\) | −1.83535 | −0.0619752 | −0.0309876 | − | 0.999520i | \(-0.509865\pi\) | ||||
−0.0309876 | + | 0.999520i | \(0.509865\pi\) | |||||||
\(878\) | 18.5120 | 0.624749 | ||||||||
\(879\) | −2.83914 | −0.0957618 | ||||||||
\(880\) | 0.630140 | 0.0212420 | ||||||||
\(881\) | −31.1530 | −1.04957 | −0.524785 | − | 0.851235i | \(-0.675854\pi\) | ||||
−0.524785 | + | 0.851235i | \(0.675854\pi\) | |||||||
\(882\) | 6.04383 | 0.203506 | ||||||||
\(883\) | −21.5055 | −0.723717 | −0.361859 | − | 0.932233i | \(-0.617858\pi\) | ||||
−0.361859 | + | 0.932233i | \(0.617858\pi\) | |||||||
\(884\) | −4.91508 | −0.165312 | ||||||||
\(885\) | −18.4598 | −0.620521 | ||||||||
\(886\) | 19.4535 | 0.653553 | ||||||||
\(887\) | −5.17151 | −0.173642 | −0.0868211 | − | 0.996224i | \(-0.527671\pi\) | ||||
−0.0868211 | + | 0.996224i | \(0.527671\pi\) | |||||||
\(888\) | 5.41686 | 0.181778 | ||||||||
\(889\) | 5.48923 | 0.184103 | ||||||||
\(890\) | −1.28417 | −0.0430453 | ||||||||
\(891\) | −0.240785 | −0.00806659 | ||||||||
\(892\) | 14.3345 | 0.479953 | ||||||||
\(893\) | −18.3216 | −0.613108 | ||||||||
\(894\) | −6.63099 | −0.221773 | ||||||||
\(895\) | −53.2127 | −1.77870 | ||||||||
\(896\) | 0.977840 | 0.0326674 | ||||||||
\(897\) | 0.244868 | 0.00817590 | ||||||||
\(898\) | 42.1339 | 1.40603 | ||||||||
\(899\) | −57.9346 | −1.93223 | ||||||||
\(900\) | 1.84882 | 0.0616272 | ||||||||
\(901\) | −48.1187 | −1.60307 | ||||||||
\(902\) | 2.58973 | 0.0862287 | ||||||||
\(903\) | −4.92655 | −0.163945 | ||||||||
\(904\) | −15.2767 | −0.508097 | ||||||||
\(905\) | −30.7647 | −1.02265 | ||||||||
\(906\) | 7.91264 | 0.262880 | ||||||||
\(907\) | −44.7207 | −1.48493 | −0.742464 | − | 0.669886i | \(-0.766343\pi\) | ||||
−0.742464 | + | 0.669886i | \(0.766343\pi\) | |||||||
\(908\) | 12.2428 | 0.406293 | ||||||||
\(909\) | −10.7141 | −0.355364 | ||||||||
\(910\) | −2.55903 | −0.0848311 | ||||||||
\(911\) | 11.8184 | 0.391560 | 0.195780 | − | 0.980648i | \(-0.437276\pi\) | ||||
0.195780 | + | 0.980648i | \(0.437276\pi\) | |||||||
\(912\) | 1.97784 | 0.0654928 | ||||||||
\(913\) | −3.22578 | −0.106758 | ||||||||
\(914\) | −22.9184 | −0.758073 | ||||||||
\(915\) | 9.30972 | 0.307770 | ||||||||
\(916\) | 26.8538 | 0.887274 | ||||||||
\(917\) | −3.78525 | −0.125000 | ||||||||
\(918\) | −4.91508 | −0.162222 | ||||||||
\(919\) | −5.92090 | −0.195313 | −0.0976563 | − | 0.995220i | \(-0.531135\pi\) | ||||
−0.0976563 | + | 0.995220i | \(0.531135\pi\) | |||||||
\(920\) | −0.640825 | −0.0211274 | ||||||||
\(921\) | −22.4489 | −0.739717 | ||||||||
\(922\) | 6.85452 | 0.225742 | ||||||||
\(923\) | 9.42409 | 0.310198 | ||||||||
\(924\) | −0.235449 | −0.00774570 | ||||||||
\(925\) | 10.0148 | 0.329284 | ||||||||
\(926\) | 20.9881 | 0.689711 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | −8.09791 | −0.265827 | ||||||||
\(929\) | 48.9683 | 1.60660 | 0.803299 | − | 0.595576i | \(-0.203076\pi\) | ||||
0.803299 | + | 0.595576i | \(0.203076\pi\) | |||||||
\(930\) | 18.7229 | 0.613948 | ||||||||
\(931\) | 11.9537 | 0.391768 | ||||||||
\(932\) | −11.9179 | −0.390384 | ||||||||
\(933\) | 4.91789 | 0.161004 | ||||||||
\(934\) | −25.5979 | −0.837588 | ||||||||
\(935\) | −3.09719 | −0.101289 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | −2.99171 | −0.0977350 | −0.0488675 | − | 0.998805i | \(-0.515561\pi\) | ||||
−0.0488675 | + | 0.998805i | \(0.515561\pi\) | |||||||
\(938\) | −13.9120 | −0.454242 | ||||||||
\(939\) | −14.2027 | −0.463486 | ||||||||
\(940\) | −24.2426 | −0.790707 | ||||||||
\(941\) | 53.2058 | 1.73446 | 0.867230 | − | 0.497908i | \(-0.165898\pi\) | ||||
0.867230 | + | 0.497908i | \(0.165898\pi\) | |||||||
\(942\) | 5.70092 | 0.185746 | ||||||||
\(943\) | −2.63365 | −0.0857634 | ||||||||
\(944\) | −7.05375 | −0.229580 | ||||||||
\(945\) | −2.55903 | −0.0832453 | ||||||||
\(946\) | −1.21312 | −0.0394420 | ||||||||
\(947\) | −37.0349 | −1.20347 | −0.601737 | − | 0.798694i | \(-0.705524\pi\) | ||||
−0.601737 | + | 0.798694i | \(0.705524\pi\) | |||||||
\(948\) | 8.87366 | 0.288203 | ||||||||
\(949\) | 0.976521 | 0.0316992 | ||||||||
\(950\) | 3.65666 | 0.118638 | ||||||||
\(951\) | −1.83459 | −0.0594907 | ||||||||
\(952\) | −4.80617 | −0.155769 | ||||||||
\(953\) | −6.97956 | −0.226090 | −0.113045 | − | 0.993590i | \(-0.536060\pi\) | ||||
−0.113045 | + | 0.993590i | \(0.536060\pi\) | |||||||
\(954\) | −9.79000 | −0.316963 | ||||||||
\(955\) | −17.3613 | −0.561799 | ||||||||
\(956\) | −8.42147 | −0.272370 | ||||||||
\(957\) | 1.94985 | 0.0630298 | ||||||||
\(958\) | 27.7457 | 0.896423 | ||||||||
\(959\) | −8.13873 | −0.262813 | ||||||||
\(960\) | 2.61702 | 0.0844641 | ||||||||
\(961\) | 20.1836 | 0.651083 | ||||||||
\(962\) | −5.41686 | −0.174646 | ||||||||
\(963\) | −12.2317 | −0.394161 | ||||||||
\(964\) | 4.39928 | 0.141691 | ||||||||
\(965\) | −19.9347 | −0.641721 | ||||||||
\(966\) | 0.239442 | 0.00770391 | ||||||||
\(967\) | −22.8451 | −0.734648 | −0.367324 | − | 0.930093i | \(-0.619726\pi\) | ||||
−0.367324 | + | 0.930093i | \(0.619726\pi\) | |||||||
\(968\) | 10.9420 | 0.351690 | ||||||||
\(969\) | −9.72125 | −0.312292 | ||||||||
\(970\) | 38.6676 | 1.24154 | ||||||||
\(971\) | −26.1693 | −0.839812 | −0.419906 | − | 0.907568i | \(-0.637937\pi\) | ||||
−0.419906 | + | 0.907568i | \(0.637937\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −1.58930 | −0.0509506 | ||||||||
\(974\) | −20.8544 | −0.668219 | ||||||||
\(975\) | −1.84882 | −0.0592095 | ||||||||
\(976\) | 3.55737 | 0.113869 | ||||||||
\(977\) | −13.8230 | −0.442235 | −0.221118 | − | 0.975247i | \(-0.570971\pi\) | ||||
−0.221118 | + | 0.975247i | \(0.570971\pi\) | |||||||
\(978\) | 11.8922 | 0.380270 | ||||||||
\(979\) | 0.118152 | 0.00377617 | ||||||||
\(980\) | 15.8168 | 0.505251 | ||||||||
\(981\) | −15.0495 | −0.480493 | ||||||||
\(982\) | 29.1552 | 0.930381 | ||||||||
\(983\) | −8.65886 | −0.276175 | −0.138087 | − | 0.990420i | \(-0.544095\pi\) | ||||
−0.138087 | + | 0.990420i | \(0.544095\pi\) | |||||||
\(984\) | 10.7554 | 0.342869 | ||||||||
\(985\) | 15.3143 | 0.487955 | ||||||||
\(986\) | 39.8019 | 1.26755 | ||||||||
\(987\) | 9.05816 | 0.288324 | ||||||||
\(988\) | −1.97784 | −0.0629235 | ||||||||
\(989\) | 1.23369 | 0.0392291 | ||||||||
\(990\) | −0.630140 | −0.0200271 | ||||||||
\(991\) | 4.05681 | 0.128869 | 0.0644344 | − | 0.997922i | \(-0.479476\pi\) | ||||
0.0644344 | + | 0.997922i | \(0.479476\pi\) | |||||||
\(992\) | 7.15427 | 0.227148 | ||||||||
\(993\) | 22.7353 | 0.721483 | ||||||||
\(994\) | 9.21526 | 0.292290 | ||||||||
\(995\) | 3.01859 | 0.0956959 | ||||||||
\(996\) | −13.3970 | −0.424499 | ||||||||
\(997\) | −40.8563 | −1.29393 | −0.646966 | − | 0.762519i | \(-0.723962\pi\) | ||||
−0.646966 | + | 0.762519i | \(0.723962\pi\) | |||||||
\(998\) | 22.6831 | 0.718021 | ||||||||
\(999\) | −5.41686 | −0.171382 |
(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 | 8034.2.a.o.1.2 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.o.1.2 | ✓ | 7 | 1.1 | even | 1 | trivial |