Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8021,2,Mod(1,8021)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8021, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8021.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8021 = 13 \cdot 617 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8021.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: | \(64.0480074613\) |
Analytic rank: | \(1\) |
Dimension: | \(134\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 8021.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.26323 | −1.60035 | −0.800173 | − | 0.599769i | \(-0.795259\pi\) | ||||
−0.800173 | + | 0.599769i | \(0.795259\pi\) | |||||||
\(3\) | 2.87488 | 1.65981 | 0.829907 | − | 0.557902i | \(-0.188394\pi\) | ||||
0.829907 | + | 0.557902i | \(0.188394\pi\) | |||||||
\(4\) | 3.12222 | 1.56111 | ||||||||
\(5\) | 0.727126 | 0.325181 | 0.162590 | − | 0.986694i | \(-0.448015\pi\) | ||||
0.162590 | + | 0.986694i | \(0.448015\pi\) | |||||||
\(6\) | −6.50652 | −2.65628 | ||||||||
\(7\) | 0.231070 | 0.0873361 | 0.0436680 | − | 0.999046i | \(-0.486096\pi\) | ||||
0.0436680 | + | 0.999046i | \(0.486096\pi\) | |||||||
\(8\) | −2.53984 | −0.897968 | ||||||||
\(9\) | 5.26494 | 1.75498 | ||||||||
\(10\) | −1.64565 | −0.520402 | ||||||||
\(11\) | −3.33792 | −1.00642 | −0.503210 | − | 0.864164i | \(-0.667848\pi\) | ||||
−0.503210 | + | 0.864164i | \(0.667848\pi\) | |||||||
\(12\) | 8.97600 | 2.59115 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −0.522964 | −0.139768 | ||||||||
\(15\) | 2.09040 | 0.539739 | ||||||||
\(16\) | −0.496194 | −0.124049 | ||||||||
\(17\) | −3.22094 | −0.781194 | −0.390597 | − | 0.920562i | \(-0.627731\pi\) | ||||
−0.390597 | + | 0.920562i | \(0.627731\pi\) | |||||||
\(18\) | −11.9158 | −2.80858 | ||||||||
\(19\) | 6.87412 | 1.57703 | 0.788516 | − | 0.615015i | \(-0.210850\pi\) | ||||
0.788516 | + | 0.615015i | \(0.210850\pi\) | |||||||
\(20\) | 2.27025 | 0.507642 | ||||||||
\(21\) | 0.664297 | 0.144962 | ||||||||
\(22\) | 7.55448 | 1.61062 | ||||||||
\(23\) | 5.68451 | 1.18530 | 0.592652 | − | 0.805459i | \(-0.298081\pi\) | ||||
0.592652 | + | 0.805459i | \(0.298081\pi\) | |||||||
\(24\) | −7.30173 | −1.49046 | ||||||||
\(25\) | −4.47129 | −0.894258 | ||||||||
\(26\) | −2.26323 | −0.443856 | ||||||||
\(27\) | 6.51144 | 1.25313 | ||||||||
\(28\) | 0.721449 | 0.136341 | ||||||||
\(29\) | −4.07676 | −0.757036 | −0.378518 | − | 0.925594i | \(-0.623566\pi\) | ||||
−0.378518 | + | 0.925594i | \(0.623566\pi\) | |||||||
\(30\) | −4.73106 | −0.863770 | ||||||||
\(31\) | −7.88925 | −1.41695 | −0.708476 | − | 0.705735i | \(-0.750617\pi\) | ||||
−0.708476 | + | 0.705735i | \(0.750617\pi\) | |||||||
\(32\) | 6.20268 | 1.09649 | ||||||||
\(33\) | −9.59611 | −1.67047 | ||||||||
\(34\) | 7.28974 | 1.25018 | ||||||||
\(35\) | 0.168017 | 0.0284000 | ||||||||
\(36\) | 16.4383 | 2.73972 | ||||||||
\(37\) | −0.678172 | −0.111491 | −0.0557454 | − | 0.998445i | \(-0.517754\pi\) | ||||
−0.0557454 | + | 0.998445i | \(0.517754\pi\) | |||||||
\(38\) | −15.5577 | −2.52380 | ||||||||
\(39\) | 2.87488 | 0.460349 | ||||||||
\(40\) | −1.84678 | −0.292002 | ||||||||
\(41\) | −1.78071 | −0.278100 | −0.139050 | − | 0.990285i | \(-0.544405\pi\) | ||||
−0.139050 | + | 0.990285i | \(0.544405\pi\) | |||||||
\(42\) | −1.50346 | −0.231989 | ||||||||
\(43\) | −10.7329 | −1.63676 | −0.818379 | − | 0.574679i | \(-0.805127\pi\) | ||||
−0.818379 | + | 0.574679i | \(0.805127\pi\) | |||||||
\(44\) | −10.4217 | −1.57113 | ||||||||
\(45\) | 3.82828 | 0.570686 | ||||||||
\(46\) | −12.8654 | −1.89690 | ||||||||
\(47\) | −6.89821 | −1.00621 | −0.503103 | − | 0.864226i | \(-0.667809\pi\) | ||||
−0.503103 | + | 0.864226i | \(0.667809\pi\) | |||||||
\(48\) | −1.42650 | −0.205898 | ||||||||
\(49\) | −6.94661 | −0.992372 | ||||||||
\(50\) | 10.1196 | 1.43112 | ||||||||
\(51\) | −9.25983 | −1.29664 | ||||||||
\(52\) | 3.12222 | 0.432974 | ||||||||
\(53\) | −13.4534 | −1.84796 | −0.923981 | − | 0.382439i | \(-0.875084\pi\) | ||||
−0.923981 | + | 0.382439i | \(0.875084\pi\) | |||||||
\(54\) | −14.7369 | −2.00544 | ||||||||
\(55\) | −2.42709 | −0.327268 | ||||||||
\(56\) | −0.586879 | −0.0784250 | ||||||||
\(57\) | 19.7623 | 2.61758 | ||||||||
\(58\) | 9.22666 | 1.21152 | ||||||||
\(59\) | 3.71415 | 0.483541 | 0.241771 | − | 0.970333i | \(-0.422272\pi\) | ||||
0.241771 | + | 0.970333i | \(0.422272\pi\) | |||||||
\(60\) | 6.52669 | 0.842592 | ||||||||
\(61\) | −11.1669 | −1.42978 | −0.714888 | − | 0.699239i | \(-0.753522\pi\) | ||||
−0.714888 | + | 0.699239i | \(0.753522\pi\) | |||||||
\(62\) | 17.8552 | 2.26761 | ||||||||
\(63\) | 1.21657 | 0.153273 | ||||||||
\(64\) | −13.0457 | −1.63071 | ||||||||
\(65\) | 0.727126 | 0.0901889 | ||||||||
\(66\) | 21.7182 | 2.67333 | ||||||||
\(67\) | −2.94515 | −0.359807 | −0.179904 | − | 0.983684i | \(-0.557579\pi\) | ||||
−0.179904 | + | 0.983684i | \(0.557579\pi\) | |||||||
\(68\) | −10.0565 | −1.21953 | ||||||||
\(69\) | 16.3423 | 1.96738 | ||||||||
\(70\) | −0.380261 | −0.0454498 | ||||||||
\(71\) | 4.67416 | 0.554720 | 0.277360 | − | 0.960766i | \(-0.410540\pi\) | ||||
0.277360 | + | 0.960766i | \(0.410540\pi\) | |||||||
\(72\) | −13.3721 | −1.57592 | ||||||||
\(73\) | −9.34443 | −1.09368 | −0.546841 | − | 0.837236i | \(-0.684170\pi\) | ||||
−0.546841 | + | 0.837236i | \(0.684170\pi\) | |||||||
\(74\) | 1.53486 | 0.178424 | ||||||||
\(75\) | −12.8544 | −1.48430 | ||||||||
\(76\) | 21.4625 | 2.46192 | ||||||||
\(77\) | −0.771291 | −0.0878967 | ||||||||
\(78\) | −6.50652 | −0.736719 | ||||||||
\(79\) | −10.8175 | −1.21707 | −0.608534 | − | 0.793527i | \(-0.708242\pi\) | ||||
−0.608534 | + | 0.793527i | \(0.708242\pi\) | |||||||
\(80\) | −0.360796 | −0.0403382 | ||||||||
\(81\) | 2.92479 | 0.324977 | ||||||||
\(82\) | 4.03016 | 0.445057 | ||||||||
\(83\) | 1.49211 | 0.163780 | 0.0818902 | − | 0.996641i | \(-0.473904\pi\) | ||||
0.0818902 | + | 0.996641i | \(0.473904\pi\) | |||||||
\(84\) | 2.07408 | 0.226301 | ||||||||
\(85\) | −2.34203 | −0.254029 | ||||||||
\(86\) | 24.2911 | 2.61938 | ||||||||
\(87\) | −11.7202 | −1.25654 | ||||||||
\(88\) | 8.47776 | 0.903733 | ||||||||
\(89\) | −7.30224 | −0.774036 | −0.387018 | − | 0.922072i | \(-0.626495\pi\) | ||||
−0.387018 | + | 0.922072i | \(0.626495\pi\) | |||||||
\(90\) | −8.66428 | −0.913295 | ||||||||
\(91\) | 0.231070 | 0.0242227 | ||||||||
\(92\) | 17.7483 | 1.85039 | ||||||||
\(93\) | −22.6807 | −2.35187 | ||||||||
\(94\) | 15.6122 | 1.61028 | ||||||||
\(95\) | 4.99835 | 0.512820 | ||||||||
\(96\) | 17.8320 | 1.81997 | ||||||||
\(97\) | 5.41826 | 0.550141 | 0.275070 | − | 0.961424i | \(-0.411299\pi\) | ||||
0.275070 | + | 0.961424i | \(0.411299\pi\) | |||||||
\(98\) | 15.7218 | 1.58814 | ||||||||
\(99\) | −17.5739 | −1.76625 | ||||||||
\(100\) | −13.9603 | −1.39603 | ||||||||
\(101\) | 10.0455 | 0.999565 | 0.499782 | − | 0.866151i | \(-0.333413\pi\) | ||||
0.499782 | + | 0.866151i | \(0.333413\pi\) | |||||||
\(102\) | 20.9571 | 2.07507 | ||||||||
\(103\) | 12.4191 | 1.22369 | 0.611844 | − | 0.790979i | \(-0.290428\pi\) | ||||
0.611844 | + | 0.790979i | \(0.290428\pi\) | |||||||
\(104\) | −2.53984 | −0.249052 | ||||||||
\(105\) | 0.483028 | 0.0471387 | ||||||||
\(106\) | 30.4481 | 2.95738 | ||||||||
\(107\) | −14.9574 | −1.44598 | −0.722992 | − | 0.690857i | \(-0.757234\pi\) | ||||
−0.722992 | + | 0.690857i | \(0.757234\pi\) | |||||||
\(108\) | 20.3301 | 1.95627 | ||||||||
\(109\) | −4.23403 | −0.405546 | −0.202773 | − | 0.979226i | \(-0.564995\pi\) | ||||
−0.202773 | + | 0.979226i | \(0.564995\pi\) | |||||||
\(110\) | 5.49306 | 0.523742 | ||||||||
\(111\) | −1.94966 | −0.185054 | ||||||||
\(112\) | −0.114655 | −0.0108339 | ||||||||
\(113\) | 15.7265 | 1.47943 | 0.739713 | − | 0.672922i | \(-0.234961\pi\) | ||||
0.739713 | + | 0.672922i | \(0.234961\pi\) | |||||||
\(114\) | −44.7266 | −4.18903 | ||||||||
\(115\) | 4.13336 | 0.385438 | ||||||||
\(116\) | −12.7285 | −1.18182 | ||||||||
\(117\) | 5.26494 | 0.486744 | ||||||||
\(118\) | −8.40599 | −0.773834 | ||||||||
\(119\) | −0.744262 | −0.0682264 | ||||||||
\(120\) | −5.30928 | −0.484669 | ||||||||
\(121\) | 0.141686 | 0.0128805 | ||||||||
\(122\) | 25.2733 | 2.28814 | ||||||||
\(123\) | −5.11934 | −0.461595 | ||||||||
\(124\) | −24.6320 | −2.21201 | ||||||||
\(125\) | −6.88682 | −0.615976 | ||||||||
\(126\) | −2.75337 | −0.245290 | ||||||||
\(127\) | −17.2316 | −1.52906 | −0.764529 | − | 0.644589i | \(-0.777028\pi\) | ||||
−0.764529 | + | 0.644589i | \(0.777028\pi\) | |||||||
\(128\) | 17.1201 | 1.51322 | ||||||||
\(129\) | −30.8559 | −2.71671 | ||||||||
\(130\) | −1.64565 | −0.144333 | ||||||||
\(131\) | 21.0173 | 1.83629 | 0.918147 | − | 0.396240i | \(-0.129685\pi\) | ||||
0.918147 | + | 0.396240i | \(0.129685\pi\) | |||||||
\(132\) | −29.9611 | −2.60778 | ||||||||
\(133\) | 1.58840 | 0.137732 | ||||||||
\(134\) | 6.66556 | 0.575816 | ||||||||
\(135\) | 4.73464 | 0.407493 | ||||||||
\(136\) | 8.18067 | 0.701487 | ||||||||
\(137\) | 4.18841 | 0.357840 | 0.178920 | − | 0.983864i | \(-0.442740\pi\) | ||||
0.178920 | + | 0.983864i | \(0.442740\pi\) | |||||||
\(138\) | −36.9864 | −3.14849 | ||||||||
\(139\) | −1.64264 | −0.139327 | −0.0696636 | − | 0.997571i | \(-0.522193\pi\) | ||||
−0.0696636 | + | 0.997571i | \(0.522193\pi\) | |||||||
\(140\) | 0.524585 | 0.0443355 | ||||||||
\(141\) | −19.8315 | −1.67012 | ||||||||
\(142\) | −10.5787 | −0.887745 | ||||||||
\(143\) | −3.33792 | −0.279131 | ||||||||
\(144\) | −2.61243 | −0.217703 | ||||||||
\(145\) | −2.96432 | −0.246173 | ||||||||
\(146\) | 21.1486 | 1.75027 | ||||||||
\(147\) | −19.9707 | −1.64715 | ||||||||
\(148\) | −2.11740 | −0.174049 | ||||||||
\(149\) | 0.782707 | 0.0641219 | 0.0320609 | − | 0.999486i | \(-0.489793\pi\) | ||||
0.0320609 | + | 0.999486i | \(0.489793\pi\) | |||||||
\(150\) | 29.0925 | 2.37540 | ||||||||
\(151\) | 8.82419 | 0.718102 | 0.359051 | − | 0.933318i | \(-0.383100\pi\) | ||||
0.359051 | + | 0.933318i | \(0.383100\pi\) | |||||||
\(152\) | −17.4591 | −1.41612 | ||||||||
\(153\) | −16.9581 | −1.37098 | ||||||||
\(154\) | 1.74561 | 0.140665 | ||||||||
\(155\) | −5.73648 | −0.460765 | ||||||||
\(156\) | 8.97600 | 0.718655 | ||||||||
\(157\) | −10.5723 | −0.843763 | −0.421882 | − | 0.906651i | \(-0.638630\pi\) | ||||
−0.421882 | + | 0.906651i | \(0.638630\pi\) | |||||||
\(158\) | 24.4826 | 1.94773 | ||||||||
\(159\) | −38.6768 | −3.06727 | ||||||||
\(160\) | 4.51013 | 0.356557 | ||||||||
\(161\) | 1.31352 | 0.103520 | ||||||||
\(162\) | −6.61948 | −0.520075 | ||||||||
\(163\) | 4.52550 | 0.354464 | 0.177232 | − | 0.984169i | \(-0.443286\pi\) | ||||
0.177232 | + | 0.984169i | \(0.443286\pi\) | |||||||
\(164\) | −5.55977 | −0.434145 | ||||||||
\(165\) | −6.97758 | −0.543204 | ||||||||
\(166\) | −3.37699 | −0.262105 | ||||||||
\(167\) | 23.7812 | 1.84024 | 0.920122 | − | 0.391632i | \(-0.128089\pi\) | ||||
0.920122 | + | 0.391632i | \(0.128089\pi\) | |||||||
\(168\) | −1.68721 | −0.130171 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 5.30056 | 0.406535 | ||||||||
\(171\) | 36.1919 | 2.76766 | ||||||||
\(172\) | −33.5106 | −2.55516 | ||||||||
\(173\) | 8.48460 | 0.645072 | 0.322536 | − | 0.946557i | \(-0.395465\pi\) | ||||
0.322536 | + | 0.946557i | \(0.395465\pi\) | |||||||
\(174\) | 26.5255 | 2.01090 | ||||||||
\(175\) | −1.03318 | −0.0781009 | ||||||||
\(176\) | 1.65626 | 0.124845 | ||||||||
\(177\) | 10.6777 | 0.802589 | ||||||||
\(178\) | 16.5267 | 1.23873 | ||||||||
\(179\) | −3.70508 | −0.276931 | −0.138465 | − | 0.990367i | \(-0.544217\pi\) | ||||
−0.138465 | + | 0.990367i | \(0.544217\pi\) | |||||||
\(180\) | 11.9527 | 0.890902 | ||||||||
\(181\) | 20.9145 | 1.55456 | 0.777281 | − | 0.629154i | \(-0.216598\pi\) | ||||
0.777281 | + | 0.629154i | \(0.216598\pi\) | |||||||
\(182\) | −0.522964 | −0.0387647 | ||||||||
\(183\) | −32.1035 | −2.37316 | ||||||||
\(184\) | −14.4377 | −1.06436 | ||||||||
\(185\) | −0.493116 | −0.0362546 | ||||||||
\(186\) | 51.3316 | 3.76381 | ||||||||
\(187\) | 10.7512 | 0.786209 | ||||||||
\(188\) | −21.5377 | −1.57080 | ||||||||
\(189\) | 1.50460 | 0.109443 | ||||||||
\(190\) | −11.3124 | −0.820690 | ||||||||
\(191\) | −9.99153 | −0.722962 | −0.361481 | − | 0.932380i | \(-0.617729\pi\) | ||||
−0.361481 | + | 0.932380i | \(0.617729\pi\) | |||||||
\(192\) | −37.5049 | −2.70668 | ||||||||
\(193\) | 19.9574 | 1.43656 | 0.718282 | − | 0.695752i | \(-0.244929\pi\) | ||||
0.718282 | + | 0.695752i | \(0.244929\pi\) | |||||||
\(194\) | −12.2628 | −0.880416 | ||||||||
\(195\) | 2.09040 | 0.149697 | ||||||||
\(196\) | −21.6888 | −1.54920 | ||||||||
\(197\) | 11.2148 | 0.799023 | 0.399512 | − | 0.916728i | \(-0.369180\pi\) | ||||
0.399512 | + | 0.916728i | \(0.369180\pi\) | |||||||
\(198\) | 39.7739 | 2.82661 | ||||||||
\(199\) | 4.80276 | 0.340459 | 0.170229 | − | 0.985404i | \(-0.445549\pi\) | ||||
0.170229 | + | 0.985404i | \(0.445549\pi\) | |||||||
\(200\) | 11.3563 | 0.803015 | ||||||||
\(201\) | −8.46696 | −0.597213 | ||||||||
\(202\) | −22.7353 | −1.59965 | ||||||||
\(203\) | −0.942016 | −0.0661165 | ||||||||
\(204\) | −28.9112 | −2.02419 | ||||||||
\(205\) | −1.29480 | −0.0904329 | ||||||||
\(206\) | −28.1072 | −1.95832 | ||||||||
\(207\) | 29.9286 | 2.08018 | ||||||||
\(208\) | −0.496194 | −0.0344049 | ||||||||
\(209\) | −22.9452 | −1.58716 | ||||||||
\(210\) | −1.09320 | −0.0754383 | ||||||||
\(211\) | −6.46430 | −0.445021 | −0.222510 | − | 0.974930i | \(-0.571425\pi\) | ||||
−0.222510 | + | 0.974930i | \(0.571425\pi\) | |||||||
\(212\) | −42.0043 | −2.88487 | ||||||||
\(213\) | 13.4376 | 0.920732 | ||||||||
\(214\) | 33.8520 | 2.31407 | ||||||||
\(215\) | −7.80420 | −0.532242 | ||||||||
\(216\) | −16.5380 | −1.12527 | ||||||||
\(217\) | −1.82297 | −0.123751 | ||||||||
\(218\) | 9.58258 | 0.649015 | ||||||||
\(219\) | −26.8641 | −1.81531 | ||||||||
\(220\) | −7.57789 | −0.510901 | ||||||||
\(221\) | −3.22094 | −0.216664 | ||||||||
\(222\) | 4.41254 | 0.296150 | ||||||||
\(223\) | −1.79459 | −0.120175 | −0.0600874 | − | 0.998193i | \(-0.519138\pi\) | ||||
−0.0600874 | + | 0.998193i | \(0.519138\pi\) | |||||||
\(224\) | 1.43325 | 0.0957630 | ||||||||
\(225\) | −23.5411 | −1.56940 | ||||||||
\(226\) | −35.5928 | −2.36760 | ||||||||
\(227\) | 9.79583 | 0.650172 | 0.325086 | − | 0.945684i | \(-0.394607\pi\) | ||||
0.325086 | + | 0.945684i | \(0.394607\pi\) | |||||||
\(228\) | 61.7021 | 4.08632 | ||||||||
\(229\) | −19.8591 | −1.31232 | −0.656162 | − | 0.754620i | \(-0.727821\pi\) | ||||
−0.656162 | + | 0.754620i | \(0.727821\pi\) | |||||||
\(230\) | −9.35475 | −0.616834 | ||||||||
\(231\) | −2.21737 | −0.145892 | ||||||||
\(232\) | 10.3543 | 0.679794 | ||||||||
\(233\) | −21.0746 | −1.38064 | −0.690322 | − | 0.723502i | \(-0.742531\pi\) | ||||
−0.690322 | + | 0.723502i | \(0.742531\pi\) | |||||||
\(234\) | −11.9158 | −0.778959 | ||||||||
\(235\) | −5.01587 | −0.327199 | ||||||||
\(236\) | 11.5964 | 0.754861 | ||||||||
\(237\) | −31.0992 | −2.02011 | ||||||||
\(238\) | 1.68444 | 0.109186 | ||||||||
\(239\) | 29.6582 | 1.91843 | 0.959213 | − | 0.282684i | \(-0.0912247\pi\) | ||||
0.959213 | + | 0.282684i | \(0.0912247\pi\) | |||||||
\(240\) | −1.03725 | −0.0669539 | ||||||||
\(241\) | 5.26925 | 0.339422 | 0.169711 | − | 0.985494i | \(-0.445717\pi\) | ||||
0.169711 | + | 0.985494i | \(0.445717\pi\) | |||||||
\(242\) | −0.320668 | −0.0206133 | ||||||||
\(243\) | −11.1259 | −0.713727 | ||||||||
\(244\) | −34.8655 | −2.23203 | ||||||||
\(245\) | −5.05106 | −0.322700 | ||||||||
\(246\) | 11.5862 | 0.738712 | ||||||||
\(247\) | 6.87412 | 0.437390 | ||||||||
\(248\) | 20.0374 | 1.27238 | ||||||||
\(249\) | 4.28964 | 0.271845 | ||||||||
\(250\) | 15.5865 | 0.985775 | ||||||||
\(251\) | 6.16806 | 0.389324 | 0.194662 | − | 0.980870i | \(-0.437639\pi\) | ||||
0.194662 | + | 0.980870i | \(0.437639\pi\) | |||||||
\(252\) | 3.79839 | 0.239276 | ||||||||
\(253\) | −18.9744 | −1.19291 | ||||||||
\(254\) | 38.9991 | 2.44702 | ||||||||
\(255\) | −6.73306 | −0.421641 | ||||||||
\(256\) | −12.6553 | −0.790959 | ||||||||
\(257\) | −3.02385 | −0.188623 | −0.0943113 | − | 0.995543i | \(-0.530065\pi\) | ||||
−0.0943113 | + | 0.995543i | \(0.530065\pi\) | |||||||
\(258\) | 69.8341 | 4.34768 | ||||||||
\(259\) | −0.156705 | −0.00973716 | ||||||||
\(260\) | 2.27025 | 0.140795 | ||||||||
\(261\) | −21.4639 | −1.32858 | ||||||||
\(262\) | −47.5671 | −2.93871 | ||||||||
\(263\) | 12.9573 | 0.798984 | 0.399492 | − | 0.916737i | \(-0.369187\pi\) | ||||
0.399492 | + | 0.916737i | \(0.369187\pi\) | |||||||
\(264\) | 24.3726 | 1.50003 | ||||||||
\(265\) | −9.78229 | −0.600921 | ||||||||
\(266\) | −3.59492 | −0.220419 | ||||||||
\(267\) | −20.9931 | −1.28476 | ||||||||
\(268\) | −9.19540 | −0.561698 | ||||||||
\(269\) | −5.52691 | −0.336982 | −0.168491 | − | 0.985703i | \(-0.553889\pi\) | ||||
−0.168491 | + | 0.985703i | \(0.553889\pi\) | |||||||
\(270\) | −10.7156 | −0.652129 | ||||||||
\(271\) | −4.95257 | −0.300847 | −0.150424 | − | 0.988622i | \(-0.548064\pi\) | ||||
−0.150424 | + | 0.988622i | \(0.548064\pi\) | |||||||
\(272\) | 1.59821 | 0.0969060 | ||||||||
\(273\) | 0.664297 | 0.0402051 | ||||||||
\(274\) | −9.47935 | −0.572668 | ||||||||
\(275\) | 14.9248 | 0.899998 | ||||||||
\(276\) | 51.0242 | 3.07130 | ||||||||
\(277\) | −10.4964 | −0.630670 | −0.315335 | − | 0.948980i | \(-0.602117\pi\) | ||||
−0.315335 | + | 0.948980i | \(0.602117\pi\) | |||||||
\(278\) | 3.71768 | 0.222972 | ||||||||
\(279\) | −41.5365 | −2.48672 | ||||||||
\(280\) | −0.426735 | −0.0255023 | ||||||||
\(281\) | 10.4408 | 0.622846 | 0.311423 | − | 0.950271i | \(-0.399194\pi\) | ||||
0.311423 | + | 0.950271i | \(0.399194\pi\) | |||||||
\(282\) | 44.8833 | 2.67276 | ||||||||
\(283\) | 13.5942 | 0.808094 | 0.404047 | − | 0.914738i | \(-0.367603\pi\) | ||||
0.404047 | + | 0.914738i | \(0.367603\pi\) | |||||||
\(284\) | 14.5937 | 0.865979 | ||||||||
\(285\) | 14.3697 | 0.851186 | ||||||||
\(286\) | 7.55448 | 0.446706 | ||||||||
\(287\) | −0.411468 | −0.0242882 | ||||||||
\(288\) | 32.6567 | 1.92432 | ||||||||
\(289\) | −6.62552 | −0.389736 | ||||||||
\(290\) | 6.70894 | 0.393963 | ||||||||
\(291\) | 15.5769 | 0.913131 | ||||||||
\(292\) | −29.1753 | −1.70736 | ||||||||
\(293\) | −17.8775 | −1.04441 | −0.522207 | − | 0.852818i | \(-0.674891\pi\) | ||||
−0.522207 | + | 0.852818i | \(0.674891\pi\) | |||||||
\(294\) | 45.1983 | 2.63602 | ||||||||
\(295\) | 2.70066 | 0.157238 | ||||||||
\(296\) | 1.72245 | 0.100115 | ||||||||
\(297\) | −21.7346 | −1.26117 | ||||||||
\(298\) | −1.77145 | −0.102617 | ||||||||
\(299\) | 5.68451 | 0.328744 | ||||||||
\(300\) | −40.1343 | −2.31715 | ||||||||
\(301\) | −2.48005 | −0.142948 | ||||||||
\(302\) | −19.9712 | −1.14921 | ||||||||
\(303\) | 28.8796 | 1.65909 | ||||||||
\(304\) | −3.41090 | −0.195629 | ||||||||
\(305\) | −8.11974 | −0.464935 | ||||||||
\(306\) | 38.3801 | 2.19404 | ||||||||
\(307\) | −8.81980 | −0.503372 | −0.251686 | − | 0.967809i | \(-0.580985\pi\) | ||||
−0.251686 | + | 0.967809i | \(0.580985\pi\) | |||||||
\(308\) | −2.40814 | −0.137216 | ||||||||
\(309\) | 35.7033 | 2.03109 | ||||||||
\(310\) | 12.9830 | 0.737384 | ||||||||
\(311\) | 12.7692 | 0.724074 | 0.362037 | − | 0.932164i | \(-0.382081\pi\) | ||||
0.362037 | + | 0.932164i | \(0.382081\pi\) | |||||||
\(312\) | −7.30173 | −0.413379 | ||||||||
\(313\) | −15.3799 | −0.869323 | −0.434662 | − | 0.900594i | \(-0.643132\pi\) | ||||
−0.434662 | + | 0.900594i | \(0.643132\pi\) | |||||||
\(314\) | 23.9276 | 1.35031 | ||||||||
\(315\) | 0.884598 | 0.0498415 | ||||||||
\(316\) | −33.7747 | −1.89998 | ||||||||
\(317\) | −25.1672 | −1.41353 | −0.706764 | − | 0.707449i | \(-0.749846\pi\) | ||||
−0.706764 | + | 0.707449i | \(0.749846\pi\) | |||||||
\(318\) | 87.5346 | 4.90870 | ||||||||
\(319\) | 13.6079 | 0.761896 | ||||||||
\(320\) | −9.48587 | −0.530276 | ||||||||
\(321\) | −43.0007 | −2.40006 | ||||||||
\(322\) | −2.97280 | −0.165667 | ||||||||
\(323\) | −22.1412 | −1.23197 | ||||||||
\(324\) | 9.13183 | 0.507324 | ||||||||
\(325\) | −4.47129 | −0.248022 | ||||||||
\(326\) | −10.2423 | −0.567266 | ||||||||
\(327\) | −12.1723 | −0.673131 | ||||||||
\(328\) | 4.52272 | 0.249725 | ||||||||
\(329\) | −1.59397 | −0.0878782 | ||||||||
\(330\) | 15.7919 | 0.869315 | ||||||||
\(331\) | −6.56601 | −0.360901 | −0.180450 | − | 0.983584i | \(-0.557756\pi\) | ||||
−0.180450 | + | 0.983584i | \(0.557756\pi\) | |||||||
\(332\) | 4.65869 | 0.255679 | ||||||||
\(333\) | −3.57053 | −0.195664 | ||||||||
\(334\) | −53.8223 | −2.94503 | ||||||||
\(335\) | −2.14150 | −0.117002 | ||||||||
\(336\) | −0.329621 | −0.0179823 | ||||||||
\(337\) | −5.94918 | −0.324072 | −0.162036 | − | 0.986785i | \(-0.551806\pi\) | ||||
−0.162036 | + | 0.986785i | \(0.551806\pi\) | |||||||
\(338\) | −2.26323 | −0.123104 | ||||||||
\(339\) | 45.2119 | 2.45557 | ||||||||
\(340\) | −7.31233 | −0.396567 | ||||||||
\(341\) | 26.3337 | 1.42605 | ||||||||
\(342\) | −81.9105 | −4.42921 | ||||||||
\(343\) | −3.22264 | −0.174006 | ||||||||
\(344\) | 27.2599 | 1.46976 | ||||||||
\(345\) | 11.8829 | 0.639755 | ||||||||
\(346\) | −19.2026 | −1.03234 | ||||||||
\(347\) | −10.7969 | −0.579610 | −0.289805 | − | 0.957086i | \(-0.593590\pi\) | ||||
−0.289805 | + | 0.957086i | \(0.593590\pi\) | |||||||
\(348\) | −36.5930 | −1.96159 | ||||||||
\(349\) | 6.09456 | 0.326234 | 0.163117 | − | 0.986607i | \(-0.447845\pi\) | ||||
0.163117 | + | 0.986607i | \(0.447845\pi\) | |||||||
\(350\) | 2.33832 | 0.124989 | ||||||||
\(351\) | 6.51144 | 0.347555 | ||||||||
\(352\) | −20.7040 | −1.10353 | ||||||||
\(353\) | −14.3485 | −0.763693 | −0.381846 | − | 0.924226i | \(-0.624712\pi\) | ||||
−0.381846 | + | 0.924226i | \(0.624712\pi\) | |||||||
\(354\) | −24.1662 | −1.28442 | ||||||||
\(355\) | 3.39870 | 0.180384 | ||||||||
\(356\) | −22.7992 | −1.20835 | ||||||||
\(357\) | −2.13967 | −0.113243 | ||||||||
\(358\) | 8.38546 | 0.443185 | ||||||||
\(359\) | −7.22186 | −0.381155 | −0.190578 | − | 0.981672i | \(-0.561036\pi\) | ||||
−0.190578 | + | 0.981672i | \(0.561036\pi\) | |||||||
\(360\) | −9.72320 | −0.512458 | ||||||||
\(361\) | 28.2535 | 1.48703 | ||||||||
\(362\) | −47.3343 | −2.48784 | ||||||||
\(363\) | 0.407330 | 0.0213793 | ||||||||
\(364\) | 0.721449 | 0.0378142 | ||||||||
\(365\) | −6.79458 | −0.355644 | ||||||||
\(366\) | 72.6577 | 3.79788 | ||||||||
\(367\) | 24.6065 | 1.28445 | 0.642224 | − | 0.766517i | \(-0.278012\pi\) | ||||
0.642224 | + | 0.766517i | \(0.278012\pi\) | |||||||
\(368\) | −2.82062 | −0.147035 | ||||||||
\(369\) | −9.37535 | −0.488061 | ||||||||
\(370\) | 1.11604 | 0.0580200 | ||||||||
\(371\) | −3.10866 | −0.161394 | ||||||||
\(372\) | −70.8139 | −3.67153 | ||||||||
\(373\) | 15.4082 | 0.797806 | 0.398903 | − | 0.916993i | \(-0.369391\pi\) | ||||
0.398903 | + | 0.916993i | \(0.369391\pi\) | |||||||
\(374\) | −24.3326 | −1.25821 | ||||||||
\(375\) | −19.7988 | −1.02241 | ||||||||
\(376\) | 17.5203 | 0.903542 | ||||||||
\(377\) | −4.07676 | −0.209964 | ||||||||
\(378\) | −3.40525 | −0.175147 | ||||||||
\(379\) | 16.8279 | 0.864391 | 0.432195 | − | 0.901780i | \(-0.357739\pi\) | ||||
0.432195 | + | 0.901780i | \(0.357739\pi\) | |||||||
\(380\) | 15.6059 | 0.800568 | ||||||||
\(381\) | −49.5388 | −2.53795 | ||||||||
\(382\) | 22.6131 | 1.15699 | ||||||||
\(383\) | 1.67797 | 0.0857405 | 0.0428702 | − | 0.999081i | \(-0.486350\pi\) | ||||
0.0428702 | + | 0.999081i | \(0.486350\pi\) | |||||||
\(384\) | 49.2183 | 2.51166 | ||||||||
\(385\) | −0.560826 | −0.0285823 | ||||||||
\(386\) | −45.1682 | −2.29900 | ||||||||
\(387\) | −56.5083 | −2.87248 | ||||||||
\(388\) | 16.9170 | 0.858830 | ||||||||
\(389\) | 4.70040 | 0.238320 | 0.119160 | − | 0.992875i | \(-0.461980\pi\) | ||||
0.119160 | + | 0.992875i | \(0.461980\pi\) | |||||||
\(390\) | −4.73106 | −0.239567 | ||||||||
\(391\) | −18.3095 | −0.925951 | ||||||||
\(392\) | 17.6433 | 0.891119 | ||||||||
\(393\) | 60.4224 | 3.04791 | ||||||||
\(394\) | −25.3818 | −1.27871 | ||||||||
\(395\) | −7.86572 | −0.395767 | ||||||||
\(396\) | −54.8696 | −2.75730 | ||||||||
\(397\) | −11.8147 | −0.592965 | −0.296482 | − | 0.955038i | \(-0.595814\pi\) | ||||
−0.296482 | + | 0.955038i | \(0.595814\pi\) | |||||||
\(398\) | −10.8698 | −0.544852 | ||||||||
\(399\) | 4.56646 | 0.228609 | ||||||||
\(400\) | 2.21863 | 0.110931 | ||||||||
\(401\) | −28.4064 | −1.41855 | −0.709273 | − | 0.704934i | \(-0.750977\pi\) | ||||
−0.709273 | + | 0.704934i | \(0.750977\pi\) | |||||||
\(402\) | 19.1627 | 0.955748 | ||||||||
\(403\) | −7.88925 | −0.392992 | ||||||||
\(404\) | 31.3642 | 1.56043 | ||||||||
\(405\) | 2.12669 | 0.105676 | ||||||||
\(406\) | 2.13200 | 0.105809 | ||||||||
\(407\) | 2.26368 | 0.112206 | ||||||||
\(408\) | 23.5185 | 1.16434 | ||||||||
\(409\) | −6.04617 | −0.298964 | −0.149482 | − | 0.988764i | \(-0.547761\pi\) | ||||
−0.149482 | + | 0.988764i | \(0.547761\pi\) | |||||||
\(410\) | 2.93044 | 0.144724 | ||||||||
\(411\) | 12.0412 | 0.593948 | ||||||||
\(412\) | 38.7750 | 1.91031 | ||||||||
\(413\) | 0.858227 | 0.0422306 | ||||||||
\(414\) | −67.7354 | −3.32902 | ||||||||
\(415\) | 1.08495 | 0.0532582 | ||||||||
\(416\) | 6.20268 | 0.304111 | ||||||||
\(417\) | −4.72240 | −0.231257 | ||||||||
\(418\) | 51.9304 | 2.54000 | ||||||||
\(419\) | −29.6068 | −1.44639 | −0.723194 | − | 0.690644i | \(-0.757327\pi\) | ||||
−0.723194 | + | 0.690644i | \(0.757327\pi\) | |||||||
\(420\) | 1.50812 | 0.0735886 | ||||||||
\(421\) | 5.27427 | 0.257052 | 0.128526 | − | 0.991706i | \(-0.458975\pi\) | ||||
0.128526 | + | 0.991706i | \(0.458975\pi\) | |||||||
\(422\) | 14.6302 | 0.712188 | ||||||||
\(423\) | −36.3187 | −1.76587 | ||||||||
\(424\) | 34.1694 | 1.65941 | ||||||||
\(425\) | 14.4018 | 0.698588 | ||||||||
\(426\) | −30.4125 | −1.47349 | ||||||||
\(427\) | −2.58033 | −0.124871 | ||||||||
\(428\) | −46.7002 | −2.25734 | ||||||||
\(429\) | −9.59611 | −0.463305 | ||||||||
\(430\) | 17.6627 | 0.851771 | ||||||||
\(431\) | 2.20419 | 0.106172 | 0.0530859 | − | 0.998590i | \(-0.483094\pi\) | ||||
0.0530859 | + | 0.998590i | \(0.483094\pi\) | |||||||
\(432\) | −3.23094 | −0.155449 | ||||||||
\(433\) | −30.8102 | −1.48064 | −0.740322 | − | 0.672252i | \(-0.765327\pi\) | ||||
−0.740322 | + | 0.672252i | \(0.765327\pi\) | |||||||
\(434\) | 4.12579 | 0.198044 | ||||||||
\(435\) | −8.52207 | −0.408602 | ||||||||
\(436\) | −13.2196 | −0.633102 | ||||||||
\(437\) | 39.0760 | 1.86926 | ||||||||
\(438\) | 60.7997 | 2.90512 | ||||||||
\(439\) | −1.74225 | −0.0831531 | −0.0415766 | − | 0.999135i | \(-0.513238\pi\) | ||||
−0.0415766 | + | 0.999135i | \(0.513238\pi\) | |||||||
\(440\) | 6.16440 | 0.293876 | ||||||||
\(441\) | −36.5735 | −1.74159 | ||||||||
\(442\) | 7.28974 | 0.346738 | ||||||||
\(443\) | −7.07615 | −0.336198 | −0.168099 | − | 0.985770i | \(-0.553763\pi\) | ||||
−0.168099 | + | 0.985770i | \(0.553763\pi\) | |||||||
\(444\) | −6.08727 | −0.288889 | ||||||||
\(445\) | −5.30965 | −0.251702 | ||||||||
\(446\) | 4.06158 | 0.192321 | ||||||||
\(447\) | 2.25019 | 0.106430 | ||||||||
\(448\) | −3.01447 | −0.142420 | ||||||||
\(449\) | 3.08120 | 0.145411 | 0.0727054 | − | 0.997353i | \(-0.476837\pi\) | ||||
0.0727054 | + | 0.997353i | \(0.476837\pi\) | |||||||
\(450\) | 53.2789 | 2.51159 | ||||||||
\(451\) | 5.94387 | 0.279886 | ||||||||
\(452\) | 49.1016 | 2.30955 | ||||||||
\(453\) | 25.3685 | 1.19192 | ||||||||
\(454\) | −22.1702 | −1.04050 | ||||||||
\(455\) | 0.168017 | 0.00787674 | ||||||||
\(456\) | −50.1930 | −2.35050 | ||||||||
\(457\) | 29.2582 | 1.36864 | 0.684321 | − | 0.729181i | \(-0.260099\pi\) | ||||
0.684321 | + | 0.729181i | \(0.260099\pi\) | |||||||
\(458\) | 44.9457 | 2.10017 | ||||||||
\(459\) | −20.9730 | −0.978935 | ||||||||
\(460\) | 12.9052 | 0.601710 | ||||||||
\(461\) | −21.4103 | −0.997177 | −0.498589 | − | 0.866839i | \(-0.666148\pi\) | ||||
−0.498589 | + | 0.866839i | \(0.666148\pi\) | |||||||
\(462\) | 5.01842 | 0.233478 | ||||||||
\(463\) | −0.171564 | −0.00797325 | −0.00398662 | − | 0.999992i | \(-0.501269\pi\) | ||||
−0.00398662 | + | 0.999992i | \(0.501269\pi\) | |||||||
\(464\) | 2.02287 | 0.0939092 | ||||||||
\(465\) | −16.4917 | −0.764784 | ||||||||
\(466\) | 47.6967 | 2.20951 | ||||||||
\(467\) | 0.438115 | 0.0202736 | 0.0101368 | − | 0.999949i | \(-0.496773\pi\) | ||||
0.0101368 | + | 0.999949i | \(0.496773\pi\) | |||||||
\(468\) | 16.4383 | 0.759860 | ||||||||
\(469\) | −0.680534 | −0.0314242 | ||||||||
\(470\) | 11.3521 | 0.523632 | ||||||||
\(471\) | −30.3942 | −1.40049 | ||||||||
\(472\) | −9.43334 | −0.434205 | ||||||||
\(473\) | 35.8256 | 1.64726 | ||||||||
\(474\) | 70.3846 | 3.23287 | ||||||||
\(475\) | −30.7362 | −1.41027 | ||||||||
\(476\) | −2.32375 | −0.106509 | ||||||||
\(477\) | −70.8312 | −3.24314 | ||||||||
\(478\) | −67.1233 | −3.07015 | ||||||||
\(479\) | 22.0409 | 1.00707 | 0.503537 | − | 0.863973i | \(-0.332032\pi\) | ||||
0.503537 | + | 0.863973i | \(0.332032\pi\) | |||||||
\(480\) | 12.9661 | 0.591818 | ||||||||
\(481\) | −0.678172 | −0.0309220 | ||||||||
\(482\) | −11.9255 | −0.543193 | ||||||||
\(483\) | 3.77621 | 0.171823 | ||||||||
\(484\) | 0.442374 | 0.0201079 | ||||||||
\(485\) | 3.93976 | 0.178895 | ||||||||
\(486\) | 25.1805 | 1.14221 | ||||||||
\(487\) | 3.21183 | 0.145542 | 0.0727709 | − | 0.997349i | \(-0.476816\pi\) | ||||
0.0727709 | + | 0.997349i | \(0.476816\pi\) | |||||||
\(488\) | 28.3621 | 1.28389 | ||||||||
\(489\) | 13.0103 | 0.588345 | ||||||||
\(490\) | 11.4317 | 0.516432 | ||||||||
\(491\) | 39.8075 | 1.79649 | 0.898243 | − | 0.439500i | \(-0.144844\pi\) | ||||
0.898243 | + | 0.439500i | \(0.144844\pi\) | |||||||
\(492\) | −15.9837 | −0.720600 | ||||||||
\(493\) | 13.1310 | 0.591392 | ||||||||
\(494\) | −15.5577 | −0.699975 | ||||||||
\(495\) | −12.7785 | −0.574349 | ||||||||
\(496\) | 3.91460 | 0.175771 | ||||||||
\(497\) | 1.08006 | 0.0484471 | ||||||||
\(498\) | −9.70845 | −0.435046 | ||||||||
\(499\) | −20.5000 | −0.917708 | −0.458854 | − | 0.888512i | \(-0.651740\pi\) | ||||
−0.458854 | + | 0.888512i | \(0.651740\pi\) | |||||||
\(500\) | −21.5021 | −0.961605 | ||||||||
\(501\) | 68.3681 | 3.05446 | ||||||||
\(502\) | −13.9597 | −0.623054 | ||||||||
\(503\) | 38.2808 | 1.70686 | 0.853429 | − | 0.521209i | \(-0.174519\pi\) | ||||
0.853429 | + | 0.521209i | \(0.174519\pi\) | |||||||
\(504\) | −3.08988 | −0.137634 | ||||||||
\(505\) | 7.30435 | 0.325039 | ||||||||
\(506\) | 42.9435 | 1.90907 | ||||||||
\(507\) | 2.87488 | 0.127678 | ||||||||
\(508\) | −53.8008 | −2.38703 | ||||||||
\(509\) | 9.77141 | 0.433110 | 0.216555 | − | 0.976270i | \(-0.430518\pi\) | ||||
0.216555 | + | 0.976270i | \(0.430518\pi\) | |||||||
\(510\) | 15.2385 | 0.674771 | ||||||||
\(511\) | −2.15921 | −0.0955179 | ||||||||
\(512\) | −5.59824 | −0.247410 | ||||||||
\(513\) | 44.7604 | 1.97622 | ||||||||
\(514\) | 6.84367 | 0.301862 | ||||||||
\(515\) | 9.03023 | 0.397919 | ||||||||
\(516\) | −96.3389 | −4.24108 | ||||||||
\(517\) | 23.0256 | 1.01267 | ||||||||
\(518\) | 0.354659 | 0.0155828 | ||||||||
\(519\) | 24.3922 | 1.07070 | ||||||||
\(520\) | −1.84678 | −0.0809867 | ||||||||
\(521\) | 7.79097 | 0.341328 | 0.170664 | − | 0.985329i | \(-0.445409\pi\) | ||||
0.170664 | + | 0.985329i | \(0.445409\pi\) | |||||||
\(522\) | 48.5778 | 2.12619 | ||||||||
\(523\) | −10.7245 | −0.468947 | −0.234474 | − | 0.972122i | \(-0.575337\pi\) | ||||
−0.234474 | + | 0.972122i | \(0.575337\pi\) | |||||||
\(524\) | 65.6207 | 2.86665 | ||||||||
\(525\) | −2.97027 | −0.129633 | ||||||||
\(526\) | −29.3255 | −1.27865 | ||||||||
\(527\) | 25.4108 | 1.10691 | ||||||||
\(528\) | 4.76154 | 0.207219 | ||||||||
\(529\) | 9.31370 | 0.404943 | ||||||||
\(530\) | 22.1396 | 0.961682 | ||||||||
\(531\) | 19.5548 | 0.848606 | ||||||||
\(532\) | 4.95933 | 0.215014 | ||||||||
\(533\) | −1.78071 | −0.0771312 | ||||||||
\(534\) | 47.5122 | 2.05605 | ||||||||
\(535\) | −10.8759 | −0.470206 | ||||||||
\(536\) | 7.48020 | 0.323096 | ||||||||
\(537\) | −10.6517 | −0.459654 | ||||||||
\(538\) | 12.5087 | 0.539288 | ||||||||
\(539\) | 23.1872 | 0.998743 | ||||||||
\(540\) | 14.7826 | 0.636140 | ||||||||
\(541\) | 38.4437 | 1.65282 | 0.826411 | − | 0.563067i | \(-0.190379\pi\) | ||||
0.826411 | + | 0.563067i | \(0.190379\pi\) | |||||||
\(542\) | 11.2088 | 0.481460 | ||||||||
\(543\) | 60.1267 | 2.58028 | ||||||||
\(544\) | −19.9785 | −0.856570 | ||||||||
\(545\) | −3.07867 | −0.131876 | ||||||||
\(546\) | −1.50346 | −0.0643421 | ||||||||
\(547\) | 0.255008 | 0.0109034 | 0.00545168 | − | 0.999985i | \(-0.498265\pi\) | ||||
0.00545168 | + | 0.999985i | \(0.498265\pi\) | |||||||
\(548\) | 13.0771 | 0.558627 | ||||||||
\(549\) | −58.7931 | −2.50923 | ||||||||
\(550\) | −33.7782 | −1.44031 | ||||||||
\(551\) | −28.0242 | −1.19387 | ||||||||
\(552\) | −41.5068 | −1.76665 | ||||||||
\(553\) | −2.49961 | −0.106294 | ||||||||
\(554\) | 23.7559 | 1.00929 | ||||||||
\(555\) | −1.41765 | −0.0601759 | ||||||||
\(556\) | −5.12869 | −0.217505 | ||||||||
\(557\) | −3.93264 | −0.166631 | −0.0833157 | − | 0.996523i | \(-0.526551\pi\) | ||||
−0.0833157 | + | 0.996523i | \(0.526551\pi\) | |||||||
\(558\) | 94.0066 | 3.97962 | ||||||||
\(559\) | −10.7329 | −0.453955 | ||||||||
\(560\) | −0.0833689 | −0.00352298 | ||||||||
\(561\) | 30.9085 | 1.30496 | ||||||||
\(562\) | −23.6300 | −0.996770 | ||||||||
\(563\) | −5.44011 | −0.229274 | −0.114637 | − | 0.993407i | \(-0.536570\pi\) | ||||
−0.114637 | + | 0.993407i | \(0.536570\pi\) | |||||||
\(564\) | −61.9183 | −2.60723 | ||||||||
\(565\) | 11.4352 | 0.481081 | ||||||||
\(566\) | −30.7669 | −1.29323 | ||||||||
\(567\) | 0.675830 | 0.0283822 | ||||||||
\(568\) | −11.8716 | −0.498121 | ||||||||
\(569\) | 13.0844 | 0.548528 | 0.274264 | − | 0.961654i | \(-0.411566\pi\) | ||||
0.274264 | + | 0.961654i | \(0.411566\pi\) | |||||||
\(570\) | −32.5219 | −1.36219 | ||||||||
\(571\) | 35.9286 | 1.50356 | 0.751782 | − | 0.659412i | \(-0.229195\pi\) | ||||
0.751782 | + | 0.659412i | \(0.229195\pi\) | |||||||
\(572\) | −10.4217 | −0.435753 | ||||||||
\(573\) | −28.7245 | −1.19998 | ||||||||
\(574\) | 0.931248 | 0.0388695 | ||||||||
\(575\) | −25.4171 | −1.05997 | ||||||||
\(576\) | −68.6849 | −2.86187 | ||||||||
\(577\) | −34.1241 | −1.42060 | −0.710302 | − | 0.703897i | \(-0.751441\pi\) | ||||
−0.710302 | + | 0.703897i | \(0.751441\pi\) | |||||||
\(578\) | 14.9951 | 0.623713 | ||||||||
\(579\) | 57.3751 | 2.38443 | ||||||||
\(580\) | −9.25525 | −0.384303 | ||||||||
\(581\) | 0.344781 | 0.0143039 | ||||||||
\(582\) | −35.2540 | −1.46133 | ||||||||
\(583\) | 44.9062 | 1.85982 | ||||||||
\(584\) | 23.7333 | 0.982092 | ||||||||
\(585\) | 3.82828 | 0.158280 | ||||||||
\(586\) | 40.4609 | 1.67143 | ||||||||
\(587\) | 18.9242 | 0.781087 | 0.390543 | − | 0.920584i | \(-0.372287\pi\) | ||||
0.390543 | + | 0.920584i | \(0.372287\pi\) | |||||||
\(588\) | −62.3528 | −2.57138 | ||||||||
\(589\) | −54.2317 | −2.23458 | ||||||||
\(590\) | −6.11221 | −0.251636 | ||||||||
\(591\) | 32.2413 | 1.32623 | ||||||||
\(592\) | 0.336505 | 0.0138303 | ||||||||
\(593\) | 32.0440 | 1.31589 | 0.657944 | − | 0.753067i | \(-0.271426\pi\) | ||||
0.657944 | + | 0.753067i | \(0.271426\pi\) | |||||||
\(594\) | 49.1905 | 2.01831 | ||||||||
\(595\) | −0.541172 | −0.0221859 | ||||||||
\(596\) | 2.44378 | 0.100101 | ||||||||
\(597\) | 13.8074 | 0.565098 | ||||||||
\(598\) | −12.8654 | −0.526104 | ||||||||
\(599\) | −43.6287 | −1.78262 | −0.891311 | − | 0.453393i | \(-0.850213\pi\) | ||||
−0.891311 | + | 0.453393i | \(0.850213\pi\) | |||||||
\(600\) | 32.6481 | 1.33285 | ||||||||
\(601\) | 21.5082 | 0.877339 | 0.438670 | − | 0.898648i | \(-0.355450\pi\) | ||||
0.438670 | + | 0.898648i | \(0.355450\pi\) | |||||||
\(602\) | 5.61294 | 0.228766 | ||||||||
\(603\) | −15.5060 | −0.631455 | ||||||||
\(604\) | 27.5510 | 1.12104 | ||||||||
\(605\) | 0.103024 | 0.00418850 | ||||||||
\(606\) | −65.3613 | −2.65512 | ||||||||
\(607\) | −43.7596 | −1.77615 | −0.888073 | − | 0.459702i | \(-0.847956\pi\) | ||||
−0.888073 | + | 0.459702i | \(0.847956\pi\) | |||||||
\(608\) | 42.6380 | 1.72920 | ||||||||
\(609\) | −2.70818 | −0.109741 | ||||||||
\(610\) | 18.3769 | 0.744057 | ||||||||
\(611\) | −6.89821 | −0.279072 | ||||||||
\(612\) | −52.9468 | −2.14025 | ||||||||
\(613\) | −40.7041 | −1.64402 | −0.822012 | − | 0.569471i | \(-0.807148\pi\) | ||||
−0.822012 | + | 0.569471i | \(0.807148\pi\) | |||||||
\(614\) | 19.9612 | 0.805570 | ||||||||
\(615\) | −3.72240 | −0.150102 | ||||||||
\(616\) | 1.95895 | 0.0789285 | ||||||||
\(617\) | 1.00000 | 0.0402585 | ||||||||
\(618\) | −80.8049 | −3.25045 | ||||||||
\(619\) | −11.0672 | −0.444828 | −0.222414 | − | 0.974952i | \(-0.571394\pi\) | ||||
−0.222414 | + | 0.974952i | \(0.571394\pi\) | |||||||
\(620\) | −17.9105 | −0.719304 | ||||||||
\(621\) | 37.0144 | 1.48534 | ||||||||
\(622\) | −28.8996 | −1.15877 | ||||||||
\(623\) | −1.68733 | −0.0676013 | ||||||||
\(624\) | −1.42650 | −0.0571057 | ||||||||
\(625\) | 17.3489 | 0.693954 | ||||||||
\(626\) | 34.8083 | 1.39122 | ||||||||
\(627\) | −65.9648 | −2.63438 | ||||||||
\(628\) | −33.0091 | −1.31721 | ||||||||
\(629\) | 2.18435 | 0.0870958 | ||||||||
\(630\) | −2.00205 | −0.0797636 | ||||||||
\(631\) | 42.4297 | 1.68910 | 0.844550 | − | 0.535477i | \(-0.179868\pi\) | ||||
0.844550 | + | 0.535477i | \(0.179868\pi\) | |||||||
\(632\) | 27.4748 | 1.09289 | ||||||||
\(633\) | −18.5841 | −0.738652 | ||||||||
\(634\) | 56.9591 | 2.26213 | ||||||||
\(635\) | −12.5295 | −0.497220 | ||||||||
\(636\) | −120.757 | −4.78834 | ||||||||
\(637\) | −6.94661 | −0.275235 | ||||||||
\(638\) | −30.7978 | −1.21930 | ||||||||
\(639\) | 24.6092 | 0.973523 | ||||||||
\(640\) | 12.4485 | 0.492069 | ||||||||
\(641\) | 30.2692 | 1.19556 | 0.597782 | − | 0.801659i | \(-0.296049\pi\) | ||||
0.597782 | + | 0.801659i | \(0.296049\pi\) | |||||||
\(642\) | 97.3205 | 3.84093 | ||||||||
\(643\) | 41.8938 | 1.65213 | 0.826065 | − | 0.563575i | \(-0.190574\pi\) | ||||
0.826065 | + | 0.563575i | \(0.190574\pi\) | |||||||
\(644\) | 4.10109 | 0.161606 | ||||||||
\(645\) | −22.4361 | −0.883422 | ||||||||
\(646\) | 50.1106 | 1.97157 | ||||||||
\(647\) | 22.0340 | 0.866246 | 0.433123 | − | 0.901335i | \(-0.357412\pi\) | ||||
0.433123 | + | 0.901335i | \(0.357412\pi\) | |||||||
\(648\) | −7.42849 | −0.291819 | ||||||||
\(649\) | −12.3975 | −0.486646 | ||||||||
\(650\) | 10.1196 | 0.396922 | ||||||||
\(651\) | −5.24081 | −0.205404 | ||||||||
\(652\) | 14.1296 | 0.553358 | ||||||||
\(653\) | −40.6267 | −1.58985 | −0.794923 | − | 0.606710i | \(-0.792489\pi\) | ||||
−0.794923 | + | 0.606710i | \(0.792489\pi\) | |||||||
\(654\) | 27.5488 | 1.07724 | ||||||||
\(655\) | 15.2823 | 0.597127 | ||||||||
\(656\) | 0.883579 | 0.0344980 | ||||||||
\(657\) | −49.1979 | −1.91939 | ||||||||
\(658\) | 3.60751 | 0.140636 | ||||||||
\(659\) | −29.4560 | −1.14744 | −0.573721 | − | 0.819051i | \(-0.694501\pi\) | ||||
−0.573721 | + | 0.819051i | \(0.694501\pi\) | |||||||
\(660\) | −21.7855 | −0.848001 | ||||||||
\(661\) | −19.2038 | −0.746940 | −0.373470 | − | 0.927642i | \(-0.621832\pi\) | ||||
−0.373470 | + | 0.927642i | \(0.621832\pi\) | |||||||
\(662\) | 14.8604 | 0.577566 | ||||||||
\(663\) | −9.25983 | −0.359622 | ||||||||
\(664\) | −3.78972 | −0.147070 | ||||||||
\(665\) | 1.15497 | 0.0447877 | ||||||||
\(666\) | 8.08095 | 0.313130 | ||||||||
\(667\) | −23.1744 | −0.897317 | ||||||||
\(668\) | 74.2500 | 2.87282 | ||||||||
\(669\) | −5.15924 | −0.199468 | ||||||||
\(670\) | 4.84670 | 0.187244 | ||||||||
\(671\) | 37.2742 | 1.43895 | ||||||||
\(672\) | 4.12042 | 0.158949 | ||||||||
\(673\) | 24.0230 | 0.926018 | 0.463009 | − | 0.886353i | \(-0.346770\pi\) | ||||
0.463009 | + | 0.886353i | \(0.346770\pi\) | |||||||
\(674\) | 13.4644 | 0.518628 | ||||||||
\(675\) | −29.1145 | −1.12062 | ||||||||
\(676\) | 3.12222 | 0.120085 | ||||||||
\(677\) | −31.2762 | −1.20204 | −0.601022 | − | 0.799233i | \(-0.705240\pi\) | ||||
−0.601022 | + | 0.799233i | \(0.705240\pi\) | |||||||
\(678\) | −102.325 | −3.92977 | ||||||||
\(679\) | 1.25199 | 0.0480471 | ||||||||
\(680\) | 5.94838 | 0.228110 | ||||||||
\(681\) | 28.1618 | 1.07916 | ||||||||
\(682\) | −59.5992 | −2.28217 | ||||||||
\(683\) | 27.7739 | 1.06274 | 0.531368 | − | 0.847141i | \(-0.321678\pi\) | ||||
0.531368 | + | 0.847141i | \(0.321678\pi\) | |||||||
\(684\) | 112.999 | 4.32062 | ||||||||
\(685\) | 3.04550 | 0.116363 | ||||||||
\(686\) | 7.29357 | 0.278470 | ||||||||
\(687\) | −57.0925 | −2.17821 | ||||||||
\(688\) | 5.32562 | 0.203037 | ||||||||
\(689\) | −13.4534 | −0.512532 | ||||||||
\(690\) | −26.8938 | −1.02383 | ||||||||
\(691\) | 17.4490 | 0.663791 | 0.331896 | − | 0.943316i | \(-0.392312\pi\) | ||||
0.331896 | + | 0.943316i | \(0.392312\pi\) | |||||||
\(692\) | 26.4908 | 1.00703 | ||||||||
\(693\) | −4.06080 | −0.154257 | ||||||||
\(694\) | 24.4360 | 0.927576 | ||||||||
\(695\) | −1.19441 | −0.0453065 | ||||||||
\(696\) | 29.7674 | 1.12833 | ||||||||
\(697\) | 5.73557 | 0.217250 | ||||||||
\(698\) | −13.7934 | −0.522088 | ||||||||
\(699\) | −60.5870 | −2.29161 | ||||||||
\(700\) | −3.22581 | −0.121924 | ||||||||
\(701\) | 34.0334 | 1.28542 | 0.642712 | − | 0.766108i | \(-0.277809\pi\) | ||||
0.642712 | + | 0.766108i | \(0.277809\pi\) | |||||||
\(702\) | −14.7369 | −0.556208 | ||||||||
\(703\) | −4.66183 | −0.175824 | ||||||||
\(704\) | 43.5455 | 1.64118 | ||||||||
\(705\) | −14.4200 | −0.543089 | ||||||||
\(706\) | 32.4740 | 1.22217 | ||||||||
\(707\) | 2.32121 | 0.0872981 | ||||||||
\(708\) | 33.3382 | 1.25293 | ||||||||
\(709\) | −9.92587 | −0.372774 | −0.186387 | − | 0.982476i | \(-0.559678\pi\) | ||||
−0.186387 | + | 0.982476i | \(0.559678\pi\) | |||||||
\(710\) | −7.69205 | −0.288677 | ||||||||
\(711\) | −56.9537 | −2.13593 | ||||||||
\(712\) | 18.5465 | 0.695060 | ||||||||
\(713\) | −44.8466 | −1.67952 | ||||||||
\(714\) | 4.84256 | 0.181228 | ||||||||
\(715\) | −2.42709 | −0.0907679 | ||||||||
\(716\) | −11.5681 | −0.432319 | ||||||||
\(717\) | 85.2637 | 3.18423 | ||||||||
\(718\) | 16.3447 | 0.609980 | ||||||||
\(719\) | −22.7950 | −0.850110 | −0.425055 | − | 0.905168i | \(-0.639745\pi\) | ||||
−0.425055 | + | 0.905168i | \(0.639745\pi\) | |||||||
\(720\) | −1.89957 | −0.0707928 | ||||||||
\(721\) | 2.86967 | 0.106872 | ||||||||
\(722\) | −63.9443 | −2.37976 | ||||||||
\(723\) | 15.1485 | 0.563377 | ||||||||
\(724\) | 65.2996 | 2.42684 | ||||||||
\(725\) | 18.2284 | 0.676985 | ||||||||
\(726\) | −0.921883 | −0.0342143 | ||||||||
\(727\) | 12.8379 | 0.476132 | 0.238066 | − | 0.971249i | \(-0.423487\pi\) | ||||
0.238066 | + | 0.971249i | \(0.423487\pi\) | |||||||
\(728\) | −0.586879 | −0.0217512 | ||||||||
\(729\) | −40.7600 | −1.50963 | ||||||||
\(730\) | 15.3777 | 0.569154 | ||||||||
\(731\) | 34.5702 | 1.27862 | ||||||||
\(732\) | −100.234 | −3.70476 | ||||||||
\(733\) | 31.0559 | 1.14708 | 0.573539 | − | 0.819178i | \(-0.305570\pi\) | ||||
0.573539 | + | 0.819178i | \(0.305570\pi\) | |||||||
\(734\) | −55.6901 | −2.05556 | ||||||||
\(735\) | −14.5212 | −0.535622 | ||||||||
\(736\) | 35.2592 | 1.29967 | ||||||||
\(737\) | 9.83066 | 0.362117 | ||||||||
\(738\) | 21.2186 | 0.781067 | ||||||||
\(739\) | −19.5811 | −0.720302 | −0.360151 | − | 0.932894i | \(-0.617275\pi\) | ||||
−0.360151 | + | 0.932894i | \(0.617275\pi\) | |||||||
\(740\) | −1.53962 | −0.0565974 | ||||||||
\(741\) | 19.7623 | 0.725986 | ||||||||
\(742\) | 7.03562 | 0.258286 | ||||||||
\(743\) | 20.3408 | 0.746232 | 0.373116 | − | 0.927785i | \(-0.378289\pi\) | ||||
0.373116 | + | 0.927785i | \(0.378289\pi\) | |||||||
\(744\) | 57.6052 | 2.11191 | ||||||||
\(745\) | 0.569127 | 0.0208512 | ||||||||
\(746\) | −34.8723 | −1.27677 | ||||||||
\(747\) | 7.85588 | 0.287432 | ||||||||
\(748\) | 33.5677 | 1.22736 | ||||||||
\(749\) | −3.45619 | −0.126287 | ||||||||
\(750\) | 44.8092 | 1.63620 | ||||||||
\(751\) | −25.8205 | −0.942204 | −0.471102 | − | 0.882079i | \(-0.656144\pi\) | ||||
−0.471102 | + | 0.882079i | \(0.656144\pi\) | |||||||
\(752\) | 3.42285 | 0.124819 | ||||||||
\(753\) | 17.7324 | 0.646206 | ||||||||
\(754\) | 9.22666 | 0.336015 | ||||||||
\(755\) | 6.41630 | 0.233513 | ||||||||
\(756\) | 4.69767 | 0.170853 | ||||||||
\(757\) | 38.1845 | 1.38784 | 0.693920 | − | 0.720052i | \(-0.255882\pi\) | ||||
0.693920 | + | 0.720052i | \(0.255882\pi\) | |||||||
\(758\) | −38.0854 | −1.38332 | ||||||||
\(759\) | −54.5492 | −1.98001 | ||||||||
\(760\) | −12.6950 | −0.460496 | ||||||||
\(761\) | −18.3843 | −0.666432 | −0.333216 | − | 0.942851i | \(-0.608134\pi\) | ||||
−0.333216 | + | 0.942851i | \(0.608134\pi\) | |||||||
\(762\) | 112.118 | 4.06160 | ||||||||
\(763\) | −0.978355 | −0.0354188 | ||||||||
\(764\) | −31.1957 | −1.12862 | ||||||||
\(765\) | −12.3307 | −0.445816 | ||||||||
\(766\) | −3.79764 | −0.137214 | ||||||||
\(767\) | 3.71415 | 0.134110 | ||||||||
\(768\) | −36.3826 | −1.31284 | ||||||||
\(769\) | −41.9478 | −1.51268 | −0.756339 | − | 0.654180i | \(-0.773014\pi\) | ||||
−0.756339 | + | 0.654180i | \(0.773014\pi\) | |||||||
\(770\) | 1.26928 | 0.0457416 | ||||||||
\(771\) | −8.69321 | −0.313078 | ||||||||
\(772\) | 62.3113 | 2.24263 | ||||||||
\(773\) | −2.88745 | −0.103854 | −0.0519272 | − | 0.998651i | \(-0.516536\pi\) | ||||
−0.0519272 | + | 0.998651i | \(0.516536\pi\) | |||||||
\(774\) | 127.891 | 4.59696 | ||||||||
\(775\) | 35.2751 | 1.26712 | ||||||||
\(776\) | −13.7615 | −0.494009 | ||||||||
\(777\) | −0.450508 | −0.0161619 | ||||||||
\(778\) | −10.6381 | −0.381394 | ||||||||
\(779\) | −12.2408 | −0.438573 | ||||||||
\(780\) | 6.52669 | 0.233693 | ||||||||
\(781\) | −15.6019 | −0.558281 | ||||||||
\(782\) | 41.4386 | 1.48184 | ||||||||
\(783\) | −26.5456 | −0.948662 | ||||||||
\(784\) | 3.44687 | 0.123102 | ||||||||
\(785\) | −7.68741 | −0.274375 | ||||||||
\(786\) | −136.750 | −4.87770 | ||||||||
\(787\) | −40.8556 | −1.45634 | −0.728172 | − | 0.685394i | \(-0.759630\pi\) | ||||
−0.728172 | + | 0.685394i | \(0.759630\pi\) | |||||||
\(788\) | 35.0151 | 1.24736 | ||||||||
\(789\) | 37.2508 | 1.32616 | ||||||||
\(790\) | 17.8019 | 0.633365 | ||||||||
\(791\) | 3.63392 | 0.129207 | ||||||||
\(792\) | 44.6349 | 1.58603 | ||||||||
\(793\) | −11.1669 | −0.396548 | ||||||||
\(794\) | 26.7395 | 0.948949 | ||||||||
\(795\) | −28.1229 | −0.997417 | ||||||||
\(796\) | 14.9953 | 0.531493 | ||||||||
\(797\) | −2.94119 | −0.104182 | −0.0520911 | − | 0.998642i | \(-0.516589\pi\) | ||||
−0.0520911 | + | 0.998642i | \(0.516589\pi\) | |||||||
\(798\) | −10.3350 | −0.365854 | ||||||||
\(799\) | 22.2187 | 0.786043 | ||||||||
\(800\) | −27.7340 | −0.980543 | ||||||||
\(801\) | −38.4459 | −1.35842 | ||||||||
\(802\) | 64.2902 | 2.27017 | ||||||||
\(803\) | 31.1909 | 1.10070 | ||||||||
\(804\) | −26.4357 | −0.932314 | ||||||||
\(805\) | 0.955093 | 0.0336626 | ||||||||
\(806\) | 17.8552 | 0.628923 | ||||||||
\(807\) | −15.8892 | −0.559327 | ||||||||
\(808\) | −25.5139 | −0.897577 | ||||||||
\(809\) | −36.1523 | −1.27105 | −0.635523 | − | 0.772082i | \(-0.719215\pi\) | ||||
−0.635523 | + | 0.772082i | \(0.719215\pi\) | |||||||
\(810\) | −4.81319 | −0.169118 | ||||||||
\(811\) | 15.1272 | 0.531187 | 0.265593 | − | 0.964085i | \(-0.414432\pi\) | ||||
0.265593 | + | 0.964085i | \(0.414432\pi\) | |||||||
\(812\) | −2.94118 | −0.103215 | ||||||||
\(813\) | −14.2381 | −0.499350 | ||||||||
\(814\) | −5.12323 | −0.179569 | ||||||||
\(815\) | 3.29061 | 0.115265 | ||||||||
\(816\) | 4.59468 | 0.160846 | ||||||||
\(817\) | −73.7795 | −2.58122 | ||||||||
\(818\) | 13.6839 | 0.478446 | ||||||||
\(819\) | 1.21657 | 0.0425103 | ||||||||
\(820\) | −4.04265 | −0.141176 | ||||||||
\(821\) | −53.7149 | −1.87466 | −0.937331 | − | 0.348440i | \(-0.886711\pi\) | ||||
−0.937331 | + | 0.348440i | \(0.886711\pi\) | |||||||
\(822\) | −27.2520 | −0.950523 | ||||||||
\(823\) | −16.5464 | −0.576771 | −0.288385 | − | 0.957514i | \(-0.593118\pi\) | ||||
−0.288385 | + | 0.957514i | \(0.593118\pi\) | |||||||
\(824\) | −31.5424 | −1.09883 | ||||||||
\(825\) | 42.9070 | 1.49383 | ||||||||
\(826\) | −1.94237 | −0.0675836 | ||||||||
\(827\) | 32.1477 | 1.11788 | 0.558942 | − | 0.829207i | \(-0.311208\pi\) | ||||
0.558942 | + | 0.829207i | \(0.311208\pi\) | |||||||
\(828\) | 93.4437 | 3.24739 | ||||||||
\(829\) | 36.6747 | 1.27376 | 0.636882 | − | 0.770961i | \(-0.280224\pi\) | ||||
0.636882 | + | 0.770961i | \(0.280224\pi\) | |||||||
\(830\) | −2.45550 | −0.0852316 | ||||||||
\(831\) | −30.1760 | −1.04679 | ||||||||
\(832\) | −13.0457 | −0.452278 | ||||||||
\(833\) | 22.3746 | 0.775235 | ||||||||
\(834\) | 10.6879 | 0.370091 | ||||||||
\(835\) | 17.2919 | 0.598412 | ||||||||
\(836\) | −71.6400 | −2.47772 | ||||||||
\(837\) | −51.3704 | −1.77562 | ||||||||
\(838\) | 67.0071 | 2.31472 | ||||||||
\(839\) | −24.5399 | −0.847212 | −0.423606 | − | 0.905846i | \(-0.639236\pi\) | ||||
−0.423606 | + | 0.905846i | \(0.639236\pi\) | |||||||
\(840\) | −1.22681 | −0.0423291 | ||||||||
\(841\) | −12.3800 | −0.426897 | ||||||||
\(842\) | −11.9369 | −0.411372 | ||||||||
\(843\) | 30.0161 | 1.03381 | ||||||||
\(844\) | −20.1830 | −0.694726 | ||||||||
\(845\) | 0.727126 | 0.0250139 | ||||||||
\(846\) | 82.1975 | 2.82601 | ||||||||
\(847\) | 0.0327393 | 0.00112494 | ||||||||
\(848\) | 6.67548 | 0.229237 | ||||||||
\(849\) | 39.0818 | 1.34129 | ||||||||
\(850\) | −32.5945 | −1.11798 | ||||||||
\(851\) | −3.85508 | −0.132150 | ||||||||
\(852\) | 41.9552 | 1.43736 | ||||||||
\(853\) | −47.5215 | −1.62710 | −0.813552 | − | 0.581492i | \(-0.802469\pi\) | ||||
−0.813552 | + | 0.581492i | \(0.802469\pi\) | |||||||
\(854\) | 5.83989 | 0.199837 | ||||||||
\(855\) | 26.3160 | 0.899989 | ||||||||
\(856\) | 37.9893 | 1.29845 | ||||||||
\(857\) | 56.4179 | 1.92720 | 0.963600 | − | 0.267349i | \(-0.0861476\pi\) | ||||
0.963600 | + | 0.267349i | \(0.0861476\pi\) | |||||||
\(858\) | 21.7182 | 0.741448 | ||||||||
\(859\) | −31.8299 | −1.08602 | −0.543011 | − | 0.839726i | \(-0.682716\pi\) | ||||
−0.543011 | + | 0.839726i | \(0.682716\pi\) | |||||||
\(860\) | −24.3664 | −0.830887 | ||||||||
\(861\) | −1.18292 | −0.0403139 | ||||||||
\(862\) | −4.98858 | −0.169912 | ||||||||
\(863\) | −20.4909 | −0.697518 | −0.348759 | − | 0.937212i | \(-0.613397\pi\) | ||||
−0.348759 | + | 0.937212i | \(0.613397\pi\) | |||||||
\(864\) | 40.3884 | 1.37404 | ||||||||
\(865\) | 6.16937 | 0.209765 | ||||||||
\(866\) | 69.7306 | 2.36954 | ||||||||
\(867\) | −19.0476 | −0.646890 | ||||||||
\(868\) | −5.69169 | −0.193189 | ||||||||
\(869\) | 36.1081 | 1.22488 | ||||||||
\(870\) | 19.2874 | 0.653905 | ||||||||
\(871\) | −2.94515 | −0.0997926 | ||||||||
\(872\) | 10.7537 | 0.364168 | ||||||||
\(873\) | 28.5268 | 0.965487 | ||||||||
\(874\) | −88.4381 | −2.99146 | ||||||||
\(875\) | −1.59133 | −0.0537969 | ||||||||
\(876\) | −83.8756 | −2.83389 | ||||||||
\(877\) | −12.5402 | −0.423452 | −0.211726 | − | 0.977329i | \(-0.567908\pi\) | ||||
−0.211726 | + | 0.977329i | \(0.567908\pi\) | |||||||
\(878\) | 3.94312 | 0.133074 | ||||||||
\(879\) | −51.3957 | −1.73353 | ||||||||
\(880\) | 1.20431 | 0.0405972 | ||||||||
\(881\) | −7.60706 | −0.256288 | −0.128144 | − | 0.991756i | \(-0.540902\pi\) | ||||
−0.128144 | + | 0.991756i | \(0.540902\pi\) | |||||||
\(882\) | 82.7743 | 2.78715 | ||||||||
\(883\) | −38.5940 | −1.29879 | −0.649396 | − | 0.760450i | \(-0.724978\pi\) | ||||
−0.649396 | + | 0.760450i | \(0.724978\pi\) | |||||||
\(884\) | −10.0565 | −0.338236 | ||||||||
\(885\) | 7.76407 | 0.260986 | ||||||||
\(886\) | 16.0150 | 0.538034 | ||||||||
\(887\) | −43.4524 | −1.45899 | −0.729495 | − | 0.683986i | \(-0.760245\pi\) | ||||
−0.729495 | + | 0.683986i | \(0.760245\pi\) | |||||||
\(888\) | 4.95183 | 0.166172 | ||||||||
\(889\) | −3.98170 | −0.133542 | ||||||||
\(890\) | 12.0170 | 0.402810 | ||||||||
\(891\) | −9.76270 | −0.327063 | ||||||||
\(892\) | −5.60311 | −0.187606 | ||||||||
\(893\) | −47.4191 | −1.58682 | ||||||||
\(894\) | −5.09270 | −0.170325 | ||||||||
\(895\) | −2.69406 | −0.0900526 | ||||||||
\(896\) | 3.95593 | 0.132158 | ||||||||
\(897\) | 16.3423 | 0.545654 | ||||||||
\(898\) | −6.97347 | −0.232708 | ||||||||
\(899\) | 32.1626 | 1.07268 | ||||||||
\(900\) | −73.5003 | −2.45001 | ||||||||
\(901\) | 43.3325 | 1.44362 | ||||||||
\(902\) | −13.4523 | −0.447914 | ||||||||
\(903\) | −7.12986 | −0.237267 | ||||||||
\(904\) | −39.9428 | −1.32848 | ||||||||
\(905\) | 15.2075 | 0.505514 | ||||||||
\(906\) | −57.4148 | −1.90748 | ||||||||
\(907\) | −4.21894 | −0.140088 | −0.0700439 | − | 0.997544i | \(-0.522314\pi\) | ||||
−0.0700439 | + | 0.997544i | \(0.522314\pi\) | |||||||
\(908\) | 30.5847 | 1.01499 | ||||||||
\(909\) | 52.8890 | 1.75422 | ||||||||
\(910\) | −0.380261 | −0.0126055 | ||||||||
\(911\) | −29.4628 | −0.976147 | −0.488073 | − | 0.872803i | \(-0.662300\pi\) | ||||
−0.488073 | + | 0.872803i | \(0.662300\pi\) | |||||||
\(912\) | −9.80593 | −0.324707 | ||||||||
\(913\) | −4.98054 | −0.164832 | ||||||||
\(914\) | −66.2181 | −2.19030 | ||||||||
\(915\) | −23.3433 | −0.771706 | ||||||||
\(916\) | −62.0044 | −2.04868 | ||||||||
\(917\) | 4.85647 | 0.160375 | ||||||||
\(918\) | 47.4667 | 1.56664 | ||||||||
\(919\) | −23.8998 | −0.788382 | −0.394191 | − | 0.919029i | \(-0.628975\pi\) | ||||
−0.394191 | + | 0.919029i | \(0.628975\pi\) | |||||||
\(920\) | −10.4981 | −0.346111 | ||||||||
\(921\) | −25.3559 | −0.835504 | ||||||||
\(922\) | 48.4565 | 1.59583 | ||||||||
\(923\) | 4.67416 | 0.153852 | ||||||||
\(924\) | −6.92311 | −0.227754 | ||||||||
\(925\) | 3.03230 | 0.0997014 | ||||||||
\(926\) | 0.388289 | 0.0127600 | ||||||||
\(927\) | 65.3857 | 2.14755 | ||||||||
\(928\) | −25.2868 | −0.830081 | ||||||||
\(929\) | 45.3090 | 1.48654 | 0.743271 | − | 0.668991i | \(-0.233274\pi\) | ||||
0.743271 | + | 0.668991i | \(0.233274\pi\) | |||||||
\(930\) | 37.3245 | 1.22392 | ||||||||
\(931\) | −47.7518 | −1.56500 | ||||||||
\(932\) | −65.7995 | −2.15533 | ||||||||
\(933\) | 36.7099 | 1.20183 | ||||||||
\(934\) | −0.991557 | −0.0324447 | ||||||||
\(935\) | 7.81751 | 0.255660 | ||||||||
\(936\) | −13.3721 | −0.437081 | ||||||||
\(937\) | −7.03101 | −0.229693 | −0.114847 | − | 0.993383i | \(-0.536638\pi\) | ||||
−0.114847 | + | 0.993383i | \(0.536638\pi\) | |||||||
\(938\) | 1.54021 | 0.0502895 | ||||||||
\(939\) | −44.2154 | −1.44291 | ||||||||
\(940\) | −15.6606 | −0.510793 | ||||||||
\(941\) | 45.0322 | 1.46801 | 0.734004 | − | 0.679146i | \(-0.237650\pi\) | ||||
0.734004 | + | 0.679146i | \(0.237650\pi\) | |||||||
\(942\) | 68.7890 | 2.24127 | ||||||||
\(943\) | −10.1225 | −0.329633 | ||||||||
\(944\) | −1.84294 | −0.0599826 | ||||||||
\(945\) | 1.09403 | 0.0355888 | ||||||||
\(946\) | −81.0817 | −2.63619 | ||||||||
\(947\) | 16.5944 | 0.539246 | 0.269623 | − | 0.962966i | \(-0.413101\pi\) | ||||
0.269623 | + | 0.962966i | \(0.413101\pi\) | |||||||
\(948\) | −97.0983 | −3.15361 | ||||||||
\(949\) | −9.34443 | −0.303333 | ||||||||
\(950\) | 69.5631 | 2.25692 | ||||||||
\(951\) | −72.3526 | −2.34619 | ||||||||
\(952\) | 1.89030 | 0.0612651 | ||||||||
\(953\) | −6.82136 | −0.220965 | −0.110483 | − | 0.993878i | \(-0.535240\pi\) | ||||
−0.110483 | + | 0.993878i | \(0.535240\pi\) | |||||||
\(954\) | 160.307 | 5.19014 | ||||||||
\(955\) | −7.26510 | −0.235093 | ||||||||
\(956\) | 92.5992 | 2.99487 | ||||||||
\(957\) | 39.1211 | 1.26460 | ||||||||
\(958\) | −49.8837 | −1.61167 | ||||||||
\(959\) | 0.967815 | 0.0312524 | ||||||||
\(960\) | −27.2708 | −0.880160 | ||||||||
\(961\) | 31.2403 | 1.00775 | ||||||||
\(962\) | 1.53486 | 0.0494859 | ||||||||
\(963\) | −78.7497 | −2.53767 | ||||||||
\(964\) | 16.4517 | 0.529874 | ||||||||
\(965\) | 14.5115 | 0.467143 | ||||||||
\(966\) | −8.54643 | −0.274977 | ||||||||
\(967\) | −11.8405 | −0.380764 | −0.190382 | − | 0.981710i | \(-0.560973\pi\) | ||||
−0.190382 | + | 0.981710i | \(0.560973\pi\) | |||||||
\(968\) | −0.359859 | −0.0115663 | ||||||||
\(969\) | −63.6532 | −2.04484 | ||||||||
\(970\) | −8.91658 | −0.286294 | ||||||||
\(971\) | −21.0574 | −0.675764 | −0.337882 | − | 0.941189i | \(-0.609710\pi\) | ||||
−0.337882 | + | 0.941189i | \(0.609710\pi\) | |||||||
\(972\) | −34.7375 | −1.11420 | ||||||||
\(973\) | −0.379565 | −0.0121683 | ||||||||
\(974\) | −7.26910 | −0.232917 | ||||||||
\(975\) | −12.8544 | −0.411671 | ||||||||
\(976\) | 5.54095 | 0.177362 | ||||||||
\(977\) | −26.8184 | −0.857996 | −0.428998 | − | 0.903305i | \(-0.641133\pi\) | ||||
−0.428998 | + | 0.903305i | \(0.641133\pi\) | |||||||
\(978\) | −29.4453 | −0.941556 | ||||||||
\(979\) | 24.3743 | 0.779005 | ||||||||
\(980\) | −15.7705 | −0.503770 | ||||||||
\(981\) | −22.2919 | −0.711726 | ||||||||
\(982\) | −90.0935 | −2.87500 | ||||||||
\(983\) | −10.5295 | −0.335839 | −0.167920 | − | 0.985801i | \(-0.553705\pi\) | ||||
−0.167920 | + | 0.985801i | \(0.553705\pi\) | |||||||
\(984\) | 13.0023 | 0.414497 | ||||||||
\(985\) | 8.15459 | 0.259827 | ||||||||
\(986\) | −29.7186 | −0.946431 | ||||||||
\(987\) | −4.58246 | −0.145861 | ||||||||
\(988\) | 21.4625 | 0.682813 | ||||||||
\(989\) | −61.0115 | −1.94005 | ||||||||
\(990\) | 28.9206 | 0.919158 | ||||||||
\(991\) | −1.12636 | −0.0357799 | −0.0178900 | − | 0.999840i | \(-0.505695\pi\) | ||||
−0.0178900 | + | 0.999840i | \(0.505695\pi\) | |||||||
\(992\) | −48.9345 | −1.55367 | ||||||||
\(993\) | −18.8765 | −0.599028 | ||||||||
\(994\) | −2.44441 | −0.0775321 | ||||||||
\(995\) | 3.49222 | 0.110711 | ||||||||
\(996\) | 13.3932 | 0.424380 | ||||||||
\(997\) | 28.5834 | 0.905247 | 0.452623 | − | 0.891702i | \(-0.350488\pi\) | ||||
0.452623 | + | 0.891702i | \(0.350488\pi\) | |||||||
\(998\) | 46.3964 | 1.46865 | ||||||||
\(999\) | −4.41587 | −0.139712 |
(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 | 8021.2.a.a.1.15 | ✓ | 134 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8021.2.a.a.1.15 | ✓ | 134 | 1.1 | even | 1 | trivial |