Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.38255 | −0.977608 | −0.488804 | − | 0.872394i | \(-0.662567\pi\) | ||||
−0.488804 | + | 0.872394i | \(0.662567\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.0885651 | −0.0442825 | ||||||||
\(5\) | 2.12725 | 0.951337 | 0.475668 | − | 0.879625i | \(-0.342206\pi\) | ||||
0.475668 | + | 0.879625i | \(0.342206\pi\) | |||||||
\(6\) | 1.38255 | 0.564422 | ||||||||
\(7\) | −0.203962 | −0.0770903 | −0.0385451 | − | 0.999257i | \(-0.512272\pi\) | ||||
−0.0385451 | + | 0.999257i | \(0.512272\pi\) | |||||||
\(8\) | 2.88754 | 1.02090 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.94103 | −0.930035 | ||||||||
\(11\) | −1.88271 | −0.567658 | −0.283829 | − | 0.958875i | \(-0.591605\pi\) | ||||
−0.283829 | + | 0.958875i | \(0.591605\pi\) | |||||||
\(12\) | 0.0885651 | 0.0255665 | ||||||||
\(13\) | 3.56447 | 0.988605 | 0.494302 | − | 0.869290i | \(-0.335424\pi\) | ||||
0.494302 | + | 0.869290i | \(0.335424\pi\) | |||||||
\(14\) | 0.281986 | 0.0753641 | ||||||||
\(15\) | −2.12725 | −0.549255 | ||||||||
\(16\) | −3.81503 | −0.953757 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.38255 | −0.325869 | ||||||||
\(19\) | −0.0124475 | −0.00285564 | −0.00142782 | − | 0.999999i | \(-0.500454\pi\) | ||||
−0.00142782 | + | 0.999999i | \(0.500454\pi\) | |||||||
\(20\) | −0.188400 | −0.0421276 | ||||||||
\(21\) | 0.203962 | 0.0445081 | ||||||||
\(22\) | 2.60293 | 0.554947 | ||||||||
\(23\) | 6.58314 | 1.37268 | 0.686340 | − | 0.727281i | \(-0.259216\pi\) | ||||
0.686340 | + | 0.727281i | \(0.259216\pi\) | |||||||
\(24\) | −2.88754 | −0.589416 | ||||||||
\(25\) | −0.474791 | −0.0949582 | ||||||||
\(26\) | −4.92804 | −0.966468 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.0180639 | 0.00341375 | ||||||||
\(29\) | 0.647363 | 0.120212 | 0.0601062 | − | 0.998192i | \(-0.480856\pi\) | ||||
0.0601062 | + | 0.998192i | \(0.480856\pi\) | |||||||
\(30\) | 2.94103 | 0.536956 | ||||||||
\(31\) | 0.398581 | 0.0715873 | 0.0357936 | − | 0.999359i | \(-0.488604\pi\) | ||||
0.0357936 | + | 0.999359i | \(0.488604\pi\) | |||||||
\(32\) | −0.500626 | −0.0884990 | ||||||||
\(33\) | 1.88271 | 0.327738 | ||||||||
\(34\) | 1.38255 | 0.237105 | ||||||||
\(35\) | −0.433878 | −0.0733388 | ||||||||
\(36\) | −0.0885651 | −0.0147608 | ||||||||
\(37\) | 4.09354 | 0.672974 | 0.336487 | − | 0.941688i | \(-0.390761\pi\) | ||||
0.336487 | + | 0.941688i | \(0.390761\pi\) | |||||||
\(38\) | 0.0172092 | 0.00279170 | ||||||||
\(39\) | −3.56447 | −0.570771 | ||||||||
\(40\) | 6.14253 | 0.971219 | ||||||||
\(41\) | −12.2874 | −1.91897 | −0.959486 | − | 0.281756i | \(-0.909083\pi\) | ||||
−0.959486 | + | 0.281756i | \(0.909083\pi\) | |||||||
\(42\) | −0.281986 | −0.0435115 | ||||||||
\(43\) | −8.80499 | −1.34275 | −0.671374 | − | 0.741118i | \(-0.734296\pi\) | ||||
−0.671374 | + | 0.741118i | \(0.734296\pi\) | |||||||
\(44\) | 0.166742 | 0.0251374 | ||||||||
\(45\) | 2.12725 | 0.317112 | ||||||||
\(46\) | −9.10150 | −1.34194 | ||||||||
\(47\) | 5.83223 | 0.850718 | 0.425359 | − | 0.905025i | \(-0.360148\pi\) | ||||
0.425359 | + | 0.905025i | \(0.360148\pi\) | |||||||
\(48\) | 3.81503 | 0.550652 | ||||||||
\(49\) | −6.95840 | −0.994057 | ||||||||
\(50\) | 0.656421 | 0.0928319 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −0.315687 | −0.0437779 | ||||||||
\(53\) | −1.05821 | −0.145356 | −0.0726778 | − | 0.997355i | \(-0.523154\pi\) | ||||
−0.0726778 | + | 0.997355i | \(0.523154\pi\) | |||||||
\(54\) | 1.38255 | 0.188141 | ||||||||
\(55\) | −4.00500 | −0.540034 | ||||||||
\(56\) | −0.588947 | −0.0787014 | ||||||||
\(57\) | 0.0124475 | 0.00164871 | ||||||||
\(58\) | −0.895010 | −0.117521 | ||||||||
\(59\) | −14.7742 | −1.92344 | −0.961720 | − | 0.274034i | \(-0.911642\pi\) | ||||
−0.961720 | + | 0.274034i | \(0.911642\pi\) | |||||||
\(60\) | 0.188400 | 0.0243224 | ||||||||
\(61\) | 2.57004 | 0.329060 | 0.164530 | − | 0.986372i | \(-0.447389\pi\) | ||||
0.164530 | + | 0.986372i | \(0.447389\pi\) | |||||||
\(62\) | −0.551057 | −0.0699843 | ||||||||
\(63\) | −0.203962 | −0.0256968 | ||||||||
\(64\) | 8.32219 | 1.04027 | ||||||||
\(65\) | 7.58252 | 0.940496 | ||||||||
\(66\) | −2.60293 | −0.320399 | ||||||||
\(67\) | 6.56955 | 0.802598 | 0.401299 | − | 0.915947i | \(-0.368559\pi\) | ||||
0.401299 | + | 0.915947i | \(0.368559\pi\) | |||||||
\(68\) | 0.0885651 | 0.0107401 | ||||||||
\(69\) | −6.58314 | −0.792517 | ||||||||
\(70\) | 0.599857 | 0.0716966 | ||||||||
\(71\) | 3.69245 | 0.438214 | 0.219107 | − | 0.975701i | \(-0.429686\pi\) | ||||
0.219107 | + | 0.975701i | \(0.429686\pi\) | |||||||
\(72\) | 2.88754 | 0.340300 | ||||||||
\(73\) | 0.453140 | 0.0530360 | 0.0265180 | − | 0.999648i | \(-0.491558\pi\) | ||||
0.0265180 | + | 0.999648i | \(0.491558\pi\) | |||||||
\(74\) | −5.65951 | −0.657905 | ||||||||
\(75\) | 0.474791 | 0.0548241 | ||||||||
\(76\) | 0.00110241 | 0.000126455 0 | ||||||||
\(77\) | 0.384001 | 0.0437609 | ||||||||
\(78\) | 4.92804 | 0.557991 | ||||||||
\(79\) | −2.56543 | −0.288634 | −0.144317 | − | 0.989532i | \(-0.546098\pi\) | ||||
−0.144317 | + | 0.989532i | \(0.546098\pi\) | |||||||
\(80\) | −8.11553 | −0.907344 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 16.9879 | 1.87600 | ||||||||
\(83\) | 8.30907 | 0.912039 | 0.456020 | − | 0.889970i | \(-0.349275\pi\) | ||||
0.456020 | + | 0.889970i | \(0.349275\pi\) | |||||||
\(84\) | −0.0180639 | −0.00197093 | ||||||||
\(85\) | −2.12725 | −0.230733 | ||||||||
\(86\) | 12.1733 | 1.31268 | ||||||||
\(87\) | −0.647363 | −0.0694046 | ||||||||
\(88\) | −5.43640 | −0.579522 | ||||||||
\(89\) | −15.5694 | −1.65035 | −0.825175 | − | 0.564877i | \(-0.808924\pi\) | ||||
−0.825175 | + | 0.564877i | \(0.808924\pi\) | |||||||
\(90\) | −2.94103 | −0.310012 | ||||||||
\(91\) | −0.727014 | −0.0762118 | ||||||||
\(92\) | −0.583036 | −0.0607857 | ||||||||
\(93\) | −0.398581 | −0.0413309 | ||||||||
\(94\) | −8.06333 | −0.831669 | ||||||||
\(95\) | −0.0264789 | −0.00271668 | ||||||||
\(96\) | 0.500626 | 0.0510949 | ||||||||
\(97\) | −12.1019 | −1.22876 | −0.614380 | − | 0.789010i | \(-0.710594\pi\) | ||||
−0.614380 | + | 0.789010i | \(0.710594\pi\) | |||||||
\(98\) | 9.62031 | 0.971798 | ||||||||
\(99\) | −1.88271 | −0.189219 | ||||||||
\(100\) | 0.0420499 | 0.00420499 | ||||||||
\(101\) | −3.19743 | −0.318157 | −0.159078 | − | 0.987266i | \(-0.550852\pi\) | ||||
−0.159078 | + | 0.987266i | \(0.550852\pi\) | |||||||
\(102\) | −1.38255 | −0.136893 | ||||||||
\(103\) | 10.5170 | 1.03628 | 0.518138 | − | 0.855297i | \(-0.326625\pi\) | ||||
0.518138 | + | 0.855297i | \(0.326625\pi\) | |||||||
\(104\) | 10.2925 | 1.00927 | ||||||||
\(105\) | 0.433878 | 0.0423422 | ||||||||
\(106\) | 1.46302 | 0.142101 | ||||||||
\(107\) | −1.18955 | −0.114998 | −0.0574988 | − | 0.998346i | \(-0.518313\pi\) | ||||
−0.0574988 | + | 0.998346i | \(0.518313\pi\) | |||||||
\(108\) | 0.0885651 | 0.00852218 | ||||||||
\(109\) | −0.401268 | −0.0384345 | −0.0192173 | − | 0.999815i | \(-0.506117\pi\) | ||||
−0.0192173 | + | 0.999815i | \(0.506117\pi\) | |||||||
\(110\) | 5.53710 | 0.527942 | ||||||||
\(111\) | −4.09354 | −0.388542 | ||||||||
\(112\) | 0.778119 | 0.0735253 | ||||||||
\(113\) | 2.21505 | 0.208375 | 0.104187 | − | 0.994558i | \(-0.466776\pi\) | ||||
0.104187 | + | 0.994558i | \(0.466776\pi\) | |||||||
\(114\) | −0.0172092 | −0.00161179 | ||||||||
\(115\) | 14.0040 | 1.30588 | ||||||||
\(116\) | −0.0573338 | −0.00532331 | ||||||||
\(117\) | 3.56447 | 0.329535 | ||||||||
\(118\) | 20.4260 | 1.88037 | ||||||||
\(119\) | 0.203962 | 0.0186971 | ||||||||
\(120\) | −6.14253 | −0.560733 | ||||||||
\(121\) | −7.45540 | −0.677764 | ||||||||
\(122\) | −3.55320 | −0.321692 | ||||||||
\(123\) | 12.2874 | 1.10792 | ||||||||
\(124\) | −0.0353004 | −0.00317007 | ||||||||
\(125\) | −11.6463 | −1.04167 | ||||||||
\(126\) | 0.281986 | 0.0251214 | ||||||||
\(127\) | −14.0283 | −1.24481 | −0.622404 | − | 0.782696i | \(-0.713844\pi\) | ||||
−0.622404 | + | 0.782696i | \(0.713844\pi\) | |||||||
\(128\) | −10.5046 | −0.928481 | ||||||||
\(129\) | 8.80499 | 0.775236 | ||||||||
\(130\) | −10.4832 | −0.919437 | ||||||||
\(131\) | −12.8106 | −1.11926 | −0.559632 | − | 0.828741i | \(-0.689058\pi\) | ||||
−0.559632 | + | 0.828741i | \(0.689058\pi\) | |||||||
\(132\) | −0.166742 | −0.0145131 | ||||||||
\(133\) | 0.00253880 | 0.000220142 0 | ||||||||
\(134\) | −9.08271 | −0.784626 | ||||||||
\(135\) | −2.12725 | −0.183085 | ||||||||
\(136\) | −2.88754 | −0.247604 | ||||||||
\(137\) | −9.88512 | −0.844543 | −0.422272 | − | 0.906469i | \(-0.638767\pi\) | ||||
−0.422272 | + | 0.906469i | \(0.638767\pi\) | |||||||
\(138\) | 9.10150 | 0.774771 | ||||||||
\(139\) | −18.5865 | −1.57649 | −0.788245 | − | 0.615362i | \(-0.789010\pi\) | ||||
−0.788245 | + | 0.615362i | \(0.789010\pi\) | |||||||
\(140\) | 0.0384265 | 0.00324763 | ||||||||
\(141\) | −5.83223 | −0.491162 | ||||||||
\(142\) | −5.10499 | −0.428401 | ||||||||
\(143\) | −6.71086 | −0.561190 | ||||||||
\(144\) | −3.81503 | −0.317919 | ||||||||
\(145\) | 1.37711 | 0.114362 | ||||||||
\(146\) | −0.626487 | −0.0518484 | ||||||||
\(147\) | 6.95840 | 0.573919 | ||||||||
\(148\) | −0.362545 | −0.0298010 | ||||||||
\(149\) | 4.36739 | 0.357791 | 0.178895 | − | 0.983868i | \(-0.442748\pi\) | ||||
0.178895 | + | 0.983868i | \(0.442748\pi\) | |||||||
\(150\) | −0.656421 | −0.0535965 | ||||||||
\(151\) | −3.13523 | −0.255142 | −0.127571 | − | 0.991829i | \(-0.540718\pi\) | ||||
−0.127571 | + | 0.991829i | \(0.540718\pi\) | |||||||
\(152\) | −0.0359425 | −0.00291532 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −0.530899 | −0.0427810 | ||||||||
\(155\) | 0.847883 | 0.0681036 | ||||||||
\(156\) | 0.315687 | 0.0252752 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | 3.54683 | 0.282171 | ||||||||
\(159\) | 1.05821 | 0.0839211 | ||||||||
\(160\) | −1.06496 | −0.0841923 | ||||||||
\(161\) | −1.34271 | −0.105820 | ||||||||
\(162\) | −1.38255 | −0.108623 | ||||||||
\(163\) | 2.29919 | 0.180086 | 0.0900432 | − | 0.995938i | \(-0.471299\pi\) | ||||
0.0900432 | + | 0.995938i | \(0.471299\pi\) | |||||||
\(164\) | 1.08824 | 0.0849770 | ||||||||
\(165\) | 4.00500 | 0.311789 | ||||||||
\(166\) | −11.4877 | −0.891617 | ||||||||
\(167\) | 16.6030 | 1.28478 | 0.642388 | − | 0.766380i | \(-0.277944\pi\) | ||||
0.642388 | + | 0.766380i | \(0.277944\pi\) | |||||||
\(168\) | 0.588947 | 0.0454383 | ||||||||
\(169\) | −0.294584 | −0.0226603 | ||||||||
\(170\) | 2.94103 | 0.225567 | ||||||||
\(171\) | −0.0124475 | −0.000951881 0 | ||||||||
\(172\) | 0.779815 | 0.0594603 | ||||||||
\(173\) | −5.74478 | −0.436767 | −0.218384 | − | 0.975863i | \(-0.570078\pi\) | ||||
−0.218384 | + | 0.975863i | \(0.570078\pi\) | |||||||
\(174\) | 0.895010 | 0.0678505 | ||||||||
\(175\) | 0.0968392 | 0.00732035 | ||||||||
\(176\) | 7.18259 | 0.541408 | ||||||||
\(177\) | 14.7742 | 1.11050 | ||||||||
\(178\) | 21.5254 | 1.61340 | ||||||||
\(179\) | 7.63031 | 0.570316 | 0.285158 | − | 0.958480i | \(-0.407954\pi\) | ||||
0.285158 | + | 0.958480i | \(0.407954\pi\) | |||||||
\(180\) | −0.188400 | −0.0140425 | ||||||||
\(181\) | 8.05234 | 0.598525 | 0.299263 | − | 0.954171i | \(-0.403259\pi\) | ||||
0.299263 | + | 0.954171i | \(0.403259\pi\) | |||||||
\(182\) | 1.00513 | 0.0745053 | ||||||||
\(183\) | −2.57004 | −0.189983 | ||||||||
\(184\) | 19.0091 | 1.40137 | ||||||||
\(185\) | 8.70800 | 0.640225 | ||||||||
\(186\) | 0.551057 | 0.0404055 | ||||||||
\(187\) | 1.88271 | 0.137677 | ||||||||
\(188\) | −0.516532 | −0.0376719 | ||||||||
\(189\) | 0.203962 | 0.0148360 | ||||||||
\(190\) | 0.0366083 | 0.00265585 | ||||||||
\(191\) | −4.14413 | −0.299859 | −0.149930 | − | 0.988697i | \(-0.547905\pi\) | ||||
−0.149930 | + | 0.988697i | \(0.547905\pi\) | |||||||
\(192\) | −8.32219 | −0.600602 | ||||||||
\(193\) | 10.1962 | 0.733937 | 0.366969 | − | 0.930233i | \(-0.380396\pi\) | ||||
0.366969 | + | 0.930233i | \(0.380396\pi\) | |||||||
\(194\) | 16.7314 | 1.20125 | ||||||||
\(195\) | −7.58252 | −0.542996 | ||||||||
\(196\) | 0.616271 | 0.0440194 | ||||||||
\(197\) | −7.93699 | −0.565487 | −0.282744 | − | 0.959196i | \(-0.591245\pi\) | ||||
−0.282744 | + | 0.959196i | \(0.591245\pi\) | |||||||
\(198\) | 2.60293 | 0.184982 | ||||||||
\(199\) | −1.58998 | −0.112711 | −0.0563553 | − | 0.998411i | \(-0.517948\pi\) | ||||
−0.0563553 | + | 0.998411i | \(0.517948\pi\) | |||||||
\(200\) | −1.37098 | −0.0969427 | ||||||||
\(201\) | −6.56955 | −0.463380 | ||||||||
\(202\) | 4.42060 | 0.311032 | ||||||||
\(203\) | −0.132037 | −0.00926720 | ||||||||
\(204\) | −0.0885651 | −0.00620080 | ||||||||
\(205\) | −26.1385 | −1.82559 | ||||||||
\(206\) | −14.5403 | −1.01307 | ||||||||
\(207\) | 6.58314 | 0.457560 | ||||||||
\(208\) | −13.5985 | −0.942888 | ||||||||
\(209\) | 0.0234350 | 0.00162103 | ||||||||
\(210\) | −0.599857 | −0.0413941 | ||||||||
\(211\) | −0.650575 | −0.0447874 | −0.0223937 | − | 0.999749i | \(-0.507129\pi\) | ||||
−0.0223937 | + | 0.999749i | \(0.507129\pi\) | |||||||
\(212\) | 0.0937200 | 0.00643672 | ||||||||
\(213\) | −3.69245 | −0.253003 | ||||||||
\(214\) | 1.64460 | 0.112423 | ||||||||
\(215\) | −18.7305 | −1.27741 | ||||||||
\(216\) | −2.88754 | −0.196472 | ||||||||
\(217\) | −0.0812953 | −0.00551868 | ||||||||
\(218\) | 0.554772 | 0.0375739 | ||||||||
\(219\) | −0.453140 | −0.0306204 | ||||||||
\(220\) | 0.354703 | 0.0239141 | ||||||||
\(221\) | −3.56447 | −0.239772 | ||||||||
\(222\) | 5.65951 | 0.379842 | ||||||||
\(223\) | −10.6846 | −0.715491 | −0.357745 | − | 0.933819i | \(-0.616454\pi\) | ||||
−0.357745 | + | 0.933819i | \(0.616454\pi\) | |||||||
\(224\) | 0.102108 | 0.00682241 | ||||||||
\(225\) | −0.474791 | −0.0316527 | ||||||||
\(226\) | −3.06241 | −0.203709 | ||||||||
\(227\) | 14.6258 | 0.970751 | 0.485375 | − | 0.874306i | \(-0.338683\pi\) | ||||
0.485375 | + | 0.874306i | \(0.338683\pi\) | |||||||
\(228\) | −0.00110241 | −7.30089e−5 0 | ||||||||
\(229\) | 0.419946 | 0.0277508 | 0.0138754 | − | 0.999904i | \(-0.495583\pi\) | ||||
0.0138754 | + | 0.999904i | \(0.495583\pi\) | |||||||
\(230\) | −19.3612 | −1.27664 | ||||||||
\(231\) | −0.384001 | −0.0252654 | ||||||||
\(232\) | 1.86929 | 0.122725 | ||||||||
\(233\) | 21.0978 | 1.38216 | 0.691080 | − | 0.722778i | \(-0.257135\pi\) | ||||
0.691080 | + | 0.722778i | \(0.257135\pi\) | |||||||
\(234\) | −4.92804 | −0.322156 | ||||||||
\(235\) | 12.4066 | 0.809319 | ||||||||
\(236\) | 1.30848 | 0.0851748 | ||||||||
\(237\) | 2.56543 | 0.166643 | ||||||||
\(238\) | −0.281986 | −0.0182785 | ||||||||
\(239\) | 22.6592 | 1.46570 | 0.732851 | − | 0.680389i | \(-0.238189\pi\) | ||||
0.732851 | + | 0.680389i | \(0.238189\pi\) | |||||||
\(240\) | 8.11553 | 0.523855 | ||||||||
\(241\) | 25.3959 | 1.63590 | 0.817948 | − | 0.575292i | \(-0.195112\pi\) | ||||
0.817948 | + | 0.575292i | \(0.195112\pi\) | |||||||
\(242\) | 10.3074 | 0.662587 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −0.227616 | −0.0145716 | ||||||||
\(245\) | −14.8023 | −0.945683 | ||||||||
\(246\) | −16.9879 | −1.08311 | ||||||||
\(247\) | −0.0443685 | −0.00282310 | ||||||||
\(248\) | 1.15092 | 0.0730834 | ||||||||
\(249\) | −8.30907 | −0.526566 | ||||||||
\(250\) | 16.1015 | 1.01835 | ||||||||
\(251\) | 1.76138 | 0.111178 | 0.0555888 | − | 0.998454i | \(-0.482296\pi\) | ||||
0.0555888 | + | 0.998454i | \(0.482296\pi\) | |||||||
\(252\) | 0.0180639 | 0.00113792 | ||||||||
\(253\) | −12.3941 | −0.779213 | ||||||||
\(254\) | 19.3947 | 1.21693 | ||||||||
\(255\) | 2.12725 | 0.133214 | ||||||||
\(256\) | −2.12133 | −0.132583 | ||||||||
\(257\) | 8.52815 | 0.531971 | 0.265986 | − | 0.963977i | \(-0.414303\pi\) | ||||
0.265986 | + | 0.963977i | \(0.414303\pi\) | |||||||
\(258\) | −12.1733 | −0.757877 | ||||||||
\(259\) | −0.834925 | −0.0518797 | ||||||||
\(260\) | −0.671547 | −0.0416476 | ||||||||
\(261\) | 0.647363 | 0.0400708 | ||||||||
\(262\) | 17.7112 | 1.09420 | ||||||||
\(263\) | 9.05067 | 0.558088 | 0.279044 | − | 0.960278i | \(-0.409982\pi\) | ||||
0.279044 | + | 0.960278i | \(0.409982\pi\) | |||||||
\(264\) | 5.43640 | 0.334587 | ||||||||
\(265\) | −2.25107 | −0.138282 | ||||||||
\(266\) | −0.00351001 | −0.000215213 0 | ||||||||
\(267\) | 15.5694 | 0.952830 | ||||||||
\(268\) | −0.581832 | −0.0355411 | ||||||||
\(269\) | 10.5853 | 0.645399 | 0.322699 | − | 0.946502i | \(-0.395410\pi\) | ||||
0.322699 | + | 0.946502i | \(0.395410\pi\) | |||||||
\(270\) | 2.94103 | 0.178985 | ||||||||
\(271\) | 9.18533 | 0.557969 | 0.278984 | − | 0.960296i | \(-0.410002\pi\) | ||||
0.278984 | + | 0.960296i | \(0.410002\pi\) | |||||||
\(272\) | 3.81503 | 0.231320 | ||||||||
\(273\) | 0.727014 | 0.0440009 | ||||||||
\(274\) | 13.6666 | 0.825632 | ||||||||
\(275\) | 0.893894 | 0.0539038 | ||||||||
\(276\) | 0.583036 | 0.0350947 | ||||||||
\(277\) | −4.83846 | −0.290715 | −0.145358 | − | 0.989379i | \(-0.546433\pi\) | ||||
−0.145358 | + | 0.989379i | \(0.546433\pi\) | |||||||
\(278\) | 25.6968 | 1.54119 | ||||||||
\(279\) | 0.398581 | 0.0238624 | ||||||||
\(280\) | −1.25284 | −0.0748715 | ||||||||
\(281\) | −16.5815 | −0.989171 | −0.494585 | − | 0.869129i | \(-0.664680\pi\) | ||||
−0.494585 | + | 0.869129i | \(0.664680\pi\) | |||||||
\(282\) | 8.06333 | 0.480164 | ||||||||
\(283\) | 19.2054 | 1.14164 | 0.570820 | − | 0.821075i | \(-0.306625\pi\) | ||||
0.570820 | + | 0.821075i | \(0.306625\pi\) | |||||||
\(284\) | −0.327022 | −0.0194052 | ||||||||
\(285\) | 0.0264789 | 0.00156847 | ||||||||
\(286\) | 9.27807 | 0.548624 | ||||||||
\(287\) | 2.50616 | 0.147934 | ||||||||
\(288\) | −0.500626 | −0.0294997 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −1.90391 | −0.111802 | ||||||||
\(291\) | 12.1019 | 0.709425 | ||||||||
\(292\) | −0.0401324 | −0.00234857 | ||||||||
\(293\) | −21.3155 | −1.24527 | −0.622633 | − | 0.782514i | \(-0.713937\pi\) | ||||
−0.622633 | + | 0.782514i | \(0.713937\pi\) | |||||||
\(294\) | −9.62031 | −0.561068 | ||||||||
\(295\) | −31.4285 | −1.82984 | ||||||||
\(296\) | 11.8203 | 0.687039 | ||||||||
\(297\) | 1.88271 | 0.109246 | ||||||||
\(298\) | −6.03812 | −0.349779 | ||||||||
\(299\) | 23.4654 | 1.35704 | ||||||||
\(300\) | −0.0420499 | −0.00242775 | ||||||||
\(301\) | 1.79588 | 0.103513 | ||||||||
\(302\) | 4.33461 | 0.249429 | ||||||||
\(303\) | 3.19743 | 0.183688 | ||||||||
\(304\) | 0.0474874 | 0.00272359 | ||||||||
\(305\) | 5.46713 | 0.313047 | ||||||||
\(306\) | 1.38255 | 0.0790349 | ||||||||
\(307\) | 16.5041 | 0.941939 | 0.470970 | − | 0.882149i | \(-0.343904\pi\) | ||||
0.470970 | + | 0.882149i | \(0.343904\pi\) | |||||||
\(308\) | −0.0340091 | −0.00193785 | ||||||||
\(309\) | −10.5170 | −0.598294 | ||||||||
\(310\) | −1.17224 | −0.0665787 | ||||||||
\(311\) | 0.315638 | 0.0178982 | 0.00894909 | − | 0.999960i | \(-0.497151\pi\) | ||||
0.00894909 | + | 0.999960i | \(0.497151\pi\) | |||||||
\(312\) | −10.2925 | −0.582700 | ||||||||
\(313\) | 30.8499 | 1.74374 | 0.871870 | − | 0.489738i | \(-0.162907\pi\) | ||||
0.871870 | + | 0.489738i | \(0.162907\pi\) | |||||||
\(314\) | 1.38255 | 0.0780216 | ||||||||
\(315\) | −0.433878 | −0.0244463 | ||||||||
\(316\) | 0.227208 | 0.0127814 | ||||||||
\(317\) | −10.5058 | −0.590066 | −0.295033 | − | 0.955487i | \(-0.595331\pi\) | ||||
−0.295033 | + | 0.955487i | \(0.595331\pi\) | |||||||
\(318\) | −1.46302 | −0.0820420 | ||||||||
\(319\) | −1.21880 | −0.0682395 | ||||||||
\(320\) | 17.7034 | 0.989651 | ||||||||
\(321\) | 1.18955 | 0.0663939 | ||||||||
\(322\) | 1.85636 | 0.103451 | ||||||||
\(323\) | 0.0124475 | 0.000692595 0 | ||||||||
\(324\) | −0.0885651 | −0.00492028 | ||||||||
\(325\) | −1.69238 | −0.0938761 | ||||||||
\(326\) | −3.17874 | −0.176054 | ||||||||
\(327\) | 0.401268 | 0.0221902 | ||||||||
\(328\) | −35.4804 | −1.95908 | ||||||||
\(329\) | −1.18955 | −0.0655821 | ||||||||
\(330\) | −5.53710 | −0.304807 | ||||||||
\(331\) | −33.7794 | −1.85668 | −0.928342 | − | 0.371728i | \(-0.878765\pi\) | ||||
−0.928342 | + | 0.371728i | \(0.878765\pi\) | |||||||
\(332\) | −0.735894 | −0.0403874 | ||||||||
\(333\) | 4.09354 | 0.224325 | ||||||||
\(334\) | −22.9544 | −1.25601 | ||||||||
\(335\) | 13.9751 | 0.763541 | ||||||||
\(336\) | −0.778119 | −0.0424499 | ||||||||
\(337\) | −35.5128 | −1.93450 | −0.967252 | − | 0.253819i | \(-0.918313\pi\) | ||||
−0.967252 | + | 0.253819i | \(0.918313\pi\) | |||||||
\(338\) | 0.407276 | 0.0221529 | ||||||||
\(339\) | −2.21505 | −0.120305 | ||||||||
\(340\) | 0.188400 | 0.0102174 | ||||||||
\(341\) | −0.750413 | −0.0406371 | ||||||||
\(342\) | 0.0172092 | 0.000930566 0 | ||||||||
\(343\) | 2.84698 | 0.153722 | ||||||||
\(344\) | −25.4248 | −1.37081 | ||||||||
\(345\) | −14.0040 | −0.753951 | ||||||||
\(346\) | 7.94242 | 0.426987 | ||||||||
\(347\) | 9.64863 | 0.517966 | 0.258983 | − | 0.965882i | \(-0.416613\pi\) | ||||
0.258983 | + | 0.965882i | \(0.416613\pi\) | |||||||
\(348\) | 0.0573338 | 0.00307341 | ||||||||
\(349\) | −20.8693 | −1.11711 | −0.558553 | − | 0.829469i | \(-0.688643\pi\) | ||||
−0.558553 | + | 0.829469i | \(0.688643\pi\) | |||||||
\(350\) | −0.133885 | −0.00715644 | ||||||||
\(351\) | −3.56447 | −0.190257 | ||||||||
\(352\) | 0.942533 | 0.0502372 | ||||||||
\(353\) | −18.8427 | −1.00290 | −0.501448 | − | 0.865188i | \(-0.667199\pi\) | ||||
−0.501448 | + | 0.865188i | \(0.667199\pi\) | |||||||
\(354\) | −20.4260 | −1.08563 | ||||||||
\(355\) | 7.85478 | 0.416889 | ||||||||
\(356\) | 1.37890 | 0.0730817 | ||||||||
\(357\) | −0.203962 | −0.0107948 | ||||||||
\(358\) | −10.5493 | −0.557546 | ||||||||
\(359\) | −8.50792 | −0.449031 | −0.224515 | − | 0.974471i | \(-0.572080\pi\) | ||||
−0.224515 | + | 0.974471i | \(0.572080\pi\) | |||||||
\(360\) | 6.14253 | 0.323740 | ||||||||
\(361\) | −18.9998 | −0.999992 | ||||||||
\(362\) | −11.1327 | −0.585123 | ||||||||
\(363\) | 7.45540 | 0.391307 | ||||||||
\(364\) | 0.0643881 | 0.00337485 | ||||||||
\(365\) | 0.963943 | 0.0504551 | ||||||||
\(366\) | 3.55320 | 0.185729 | ||||||||
\(367\) | 26.1719 | 1.36616 | 0.683081 | − | 0.730343i | \(-0.260640\pi\) | ||||
0.683081 | + | 0.730343i | \(0.260640\pi\) | |||||||
\(368\) | −25.1149 | −1.30920 | ||||||||
\(369\) | −12.2874 | −0.639657 | ||||||||
\(370\) | −12.0392 | −0.625889 | ||||||||
\(371\) | 0.215833 | 0.0112055 | ||||||||
\(372\) | 0.0353004 | 0.00183024 | ||||||||
\(373\) | 25.9925 | 1.34584 | 0.672921 | − | 0.739714i | \(-0.265039\pi\) | ||||
0.672921 | + | 0.739714i | \(0.265039\pi\) | |||||||
\(374\) | −2.60293 | −0.134595 | ||||||||
\(375\) | 11.6463 | 0.601411 | ||||||||
\(376\) | 16.8408 | 0.868497 | ||||||||
\(377\) | 2.30750 | 0.118842 | ||||||||
\(378\) | −0.281986 | −0.0145038 | ||||||||
\(379\) | −24.8000 | −1.27389 | −0.636944 | − | 0.770910i | \(-0.719802\pi\) | ||||
−0.636944 | + | 0.770910i | \(0.719802\pi\) | |||||||
\(380\) | 0.00234511 | 0.000120301 0 | ||||||||
\(381\) | 14.0283 | 0.718690 | ||||||||
\(382\) | 5.72946 | 0.293145 | ||||||||
\(383\) | 28.0135 | 1.43142 | 0.715712 | − | 0.698395i | \(-0.246102\pi\) | ||||
0.715712 | + | 0.698395i | \(0.246102\pi\) | |||||||
\(384\) | 10.5046 | 0.536059 | ||||||||
\(385\) | 0.816867 | 0.0416314 | ||||||||
\(386\) | −14.0967 | −0.717503 | ||||||||
\(387\) | −8.80499 | −0.447583 | ||||||||
\(388\) | 1.07180 | 0.0544126 | ||||||||
\(389\) | −27.4137 | −1.38993 | −0.694965 | − | 0.719043i | \(-0.744580\pi\) | ||||
−0.694965 | + | 0.719043i | \(0.744580\pi\) | |||||||
\(390\) | 10.4832 | 0.530837 | ||||||||
\(391\) | −6.58314 | −0.332924 | ||||||||
\(392\) | −20.0926 | −1.01483 | ||||||||
\(393\) | 12.8106 | 0.646208 | ||||||||
\(394\) | 10.9733 | 0.552825 | ||||||||
\(395\) | −5.45733 | −0.274588 | ||||||||
\(396\) | 0.166742 | 0.00837912 | ||||||||
\(397\) | −31.1240 | −1.56207 | −0.781034 | − | 0.624489i | \(-0.785307\pi\) | ||||
−0.781034 | + | 0.624489i | \(0.785307\pi\) | |||||||
\(398\) | 2.19822 | 0.110187 | ||||||||
\(399\) | −0.00253880 | −0.000127099 0 | ||||||||
\(400\) | 1.81134 | 0.0905670 | ||||||||
\(401\) | 37.7419 | 1.88474 | 0.942369 | − | 0.334574i | \(-0.108593\pi\) | ||||
0.942369 | + | 0.334574i | \(0.108593\pi\) | |||||||
\(402\) | 9.08271 | 0.453004 | ||||||||
\(403\) | 1.42073 | 0.0707716 | ||||||||
\(404\) | 0.283181 | 0.0140888 | ||||||||
\(405\) | 2.12725 | 0.105704 | ||||||||
\(406\) | 0.182548 | 0.00905969 | ||||||||
\(407\) | −7.70695 | −0.382019 | ||||||||
\(408\) | 2.88754 | 0.142954 | ||||||||
\(409\) | −20.7562 | −1.02633 | −0.513165 | − | 0.858290i | \(-0.671527\pi\) | ||||
−0.513165 | + | 0.858290i | \(0.671527\pi\) | |||||||
\(410\) | 36.1376 | 1.78471 | ||||||||
\(411\) | 9.88512 | 0.487597 | ||||||||
\(412\) | −0.931443 | −0.0458889 | ||||||||
\(413\) | 3.01337 | 0.148278 | ||||||||
\(414\) | −9.10150 | −0.447314 | ||||||||
\(415\) | 17.6755 | 0.867656 | ||||||||
\(416\) | −1.78446 | −0.0874905 | ||||||||
\(417\) | 18.5865 | 0.910187 | ||||||||
\(418\) | −0.0323999 | −0.00158473 | ||||||||
\(419\) | −3.11619 | −0.152236 | −0.0761179 | − | 0.997099i | \(-0.524253\pi\) | ||||
−0.0761179 | + | 0.997099i | \(0.524253\pi\) | |||||||
\(420\) | −0.0384265 | −0.00187502 | ||||||||
\(421\) | 10.8003 | 0.526374 | 0.263187 | − | 0.964745i | \(-0.415226\pi\) | ||||
0.263187 | + | 0.964745i | \(0.415226\pi\) | |||||||
\(422\) | 0.899450 | 0.0437846 | ||||||||
\(423\) | 5.83223 | 0.283573 | ||||||||
\(424\) | −3.05561 | −0.148393 | ||||||||
\(425\) | 0.474791 | 0.0230307 | ||||||||
\(426\) | 5.10499 | 0.247337 | ||||||||
\(427\) | −0.524190 | −0.0253673 | ||||||||
\(428\) | 0.105352 | 0.00509239 | ||||||||
\(429\) | 6.71086 | 0.324003 | ||||||||
\(430\) | 25.8957 | 1.24880 | ||||||||
\(431\) | 4.07885 | 0.196471 | 0.0982357 | − | 0.995163i | \(-0.468680\pi\) | ||||
0.0982357 | + | 0.995163i | \(0.468680\pi\) | |||||||
\(432\) | 3.81503 | 0.183551 | ||||||||
\(433\) | −28.1269 | −1.35169 | −0.675845 | − | 0.737043i | \(-0.736221\pi\) | ||||
−0.675845 | + | 0.737043i | \(0.736221\pi\) | |||||||
\(434\) | 0.112395 | 0.00539511 | ||||||||
\(435\) | −1.37711 | −0.0660272 | ||||||||
\(436\) | 0.0355383 | 0.00170198 | ||||||||
\(437\) | −0.0819434 | −0.00391988 | ||||||||
\(438\) | 0.626487 | 0.0299347 | ||||||||
\(439\) | −26.1788 | −1.24944 | −0.624722 | − | 0.780847i | \(-0.714788\pi\) | ||||
−0.624722 | + | 0.780847i | \(0.714788\pi\) | |||||||
\(440\) | −11.5646 | −0.551321 | ||||||||
\(441\) | −6.95840 | −0.331352 | ||||||||
\(442\) | 4.92804 | 0.234403 | ||||||||
\(443\) | −18.6227 | −0.884790 | −0.442395 | − | 0.896820i | \(-0.645871\pi\) | ||||
−0.442395 | + | 0.896820i | \(0.645871\pi\) | |||||||
\(444\) | 0.362545 | 0.0172056 | ||||||||
\(445\) | −33.1200 | −1.57004 | ||||||||
\(446\) | 14.7719 | 0.699470 | ||||||||
\(447\) | −4.36739 | −0.206570 | ||||||||
\(448\) | −1.69741 | −0.0801950 | ||||||||
\(449\) | 16.9928 | 0.801941 | 0.400971 | − | 0.916091i | \(-0.368673\pi\) | ||||
0.400971 | + | 0.916091i | \(0.368673\pi\) | |||||||
\(450\) | 0.656421 | 0.0309440 | ||||||||
\(451\) | 23.1336 | 1.08932 | ||||||||
\(452\) | −0.196176 | −0.00922735 | ||||||||
\(453\) | 3.13523 | 0.147306 | ||||||||
\(454\) | −20.2209 | −0.949014 | ||||||||
\(455\) | −1.54654 | −0.0725031 | ||||||||
\(456\) | 0.0359425 | 0.00168316 | ||||||||
\(457\) | −30.4744 | −1.42553 | −0.712765 | − | 0.701403i | \(-0.752557\pi\) | ||||
−0.712765 | + | 0.701403i | \(0.752557\pi\) | |||||||
\(458\) | −0.580596 | −0.0271294 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −1.24027 | −0.0578277 | ||||||||
\(461\) | 14.7883 | 0.688762 | 0.344381 | − | 0.938830i | \(-0.388089\pi\) | ||||
0.344381 | + | 0.938830i | \(0.388089\pi\) | |||||||
\(462\) | 0.530899 | 0.0246996 | ||||||||
\(463\) | 22.7388 | 1.05676 | 0.528382 | − | 0.849007i | \(-0.322799\pi\) | ||||
0.528382 | + | 0.849007i | \(0.322799\pi\) | |||||||
\(464\) | −2.46971 | −0.114653 | ||||||||
\(465\) | −0.847883 | −0.0393197 | ||||||||
\(466\) | −29.1686 | −1.35121 | ||||||||
\(467\) | 22.5443 | 1.04323 | 0.521613 | − | 0.853182i | \(-0.325330\pi\) | ||||
0.521613 | + | 0.853182i | \(0.325330\pi\) | |||||||
\(468\) | −0.315687 | −0.0145926 | ||||||||
\(469\) | −1.33994 | −0.0618725 | ||||||||
\(470\) | −17.1527 | −0.791197 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | −42.6611 | −1.96364 | ||||||||
\(473\) | 16.5772 | 0.762223 | ||||||||
\(474\) | −3.54683 | −0.162911 | ||||||||
\(475\) | 0.00590994 | 0.000271167 0 | ||||||||
\(476\) | −0.0180639 | −0.000827957 0 | ||||||||
\(477\) | −1.05821 | −0.0484519 | ||||||||
\(478\) | −31.3274 | −1.43288 | ||||||||
\(479\) | −16.4861 | −0.753269 | −0.376635 | − | 0.926362i | \(-0.622919\pi\) | ||||
−0.376635 | + | 0.926362i | \(0.622919\pi\) | |||||||
\(480\) | 1.06496 | 0.0486085 | ||||||||
\(481\) | 14.5913 | 0.665305 | ||||||||
\(482\) | −35.1111 | −1.59927 | ||||||||
\(483\) | 1.34271 | 0.0610953 | ||||||||
\(484\) | 0.660288 | 0.0300131 | ||||||||
\(485\) | −25.7438 | −1.16896 | ||||||||
\(486\) | 1.38255 | 0.0627136 | ||||||||
\(487\) | −38.4656 | −1.74304 | −0.871521 | − | 0.490357i | \(-0.836866\pi\) | ||||
−0.871521 | + | 0.490357i | \(0.836866\pi\) | |||||||
\(488\) | 7.42109 | 0.335937 | ||||||||
\(489\) | −2.29919 | −0.103973 | ||||||||
\(490\) | 20.4648 | 0.924507 | ||||||||
\(491\) | 35.9939 | 1.62438 | 0.812191 | − | 0.583392i | \(-0.198275\pi\) | ||||
0.812191 | + | 0.583392i | \(0.198275\pi\) | |||||||
\(492\) | −1.08824 | −0.0490615 | ||||||||
\(493\) | −0.647363 | −0.0291558 | ||||||||
\(494\) | 0.0613416 | 0.00275989 | ||||||||
\(495\) | −4.00500 | −0.180011 | ||||||||
\(496\) | −1.52060 | −0.0682769 | ||||||||
\(497\) | −0.753119 | −0.0337820 | ||||||||
\(498\) | 11.4877 | 0.514775 | ||||||||
\(499\) | −3.18705 | −0.142672 | −0.0713359 | − | 0.997452i | \(-0.522726\pi\) | ||||
−0.0713359 | + | 0.997452i | \(0.522726\pi\) | |||||||
\(500\) | 1.03145 | 0.0461280 | ||||||||
\(501\) | −16.6030 | −0.741766 | ||||||||
\(502\) | −2.43519 | −0.108688 | ||||||||
\(503\) | −34.4157 | −1.53452 | −0.767260 | − | 0.641336i | \(-0.778380\pi\) | ||||
−0.767260 | + | 0.641336i | \(0.778380\pi\) | |||||||
\(504\) | −0.588947 | −0.0262338 | ||||||||
\(505\) | −6.80175 | −0.302674 | ||||||||
\(506\) | 17.1355 | 0.761765 | ||||||||
\(507\) | 0.294584 | 0.0130829 | ||||||||
\(508\) | 1.24242 | 0.0551233 | ||||||||
\(509\) | −5.63897 | −0.249943 | −0.124972 | − | 0.992160i | \(-0.539884\pi\) | ||||
−0.124972 | + | 0.992160i | \(0.539884\pi\) | |||||||
\(510\) | −2.94103 | −0.130231 | ||||||||
\(511\) | −0.0924232 | −0.00408856 | ||||||||
\(512\) | 23.9420 | 1.05810 | ||||||||
\(513\) | 0.0124475 | 0.000549569 0 | ||||||||
\(514\) | −11.7906 | −0.520059 | ||||||||
\(515\) | 22.3724 | 0.985847 | ||||||||
\(516\) | −0.779815 | −0.0343294 | ||||||||
\(517\) | −10.9804 | −0.482917 | ||||||||
\(518\) | 1.15432 | 0.0507181 | ||||||||
\(519\) | 5.74478 | 0.252168 | ||||||||
\(520\) | 21.8948 | 0.960152 | ||||||||
\(521\) | −6.52922 | −0.286051 | −0.143025 | − | 0.989719i | \(-0.545683\pi\) | ||||
−0.143025 | + | 0.989719i | \(0.545683\pi\) | |||||||
\(522\) | −0.895010 | −0.0391735 | ||||||||
\(523\) | 16.4664 | 0.720025 | 0.360012 | − | 0.932948i | \(-0.382772\pi\) | ||||
0.360012 | + | 0.932948i | \(0.382772\pi\) | |||||||
\(524\) | 1.13457 | 0.0495639 | ||||||||
\(525\) | −0.0968392 | −0.00422641 | ||||||||
\(526\) | −12.5130 | −0.545591 | ||||||||
\(527\) | −0.398581 | −0.0173625 | ||||||||
\(528\) | −7.18259 | −0.312582 | ||||||||
\(529\) | 20.3377 | 0.884249 | ||||||||
\(530\) | 3.11221 | 0.135186 | ||||||||
\(531\) | −14.7742 | −0.641147 | ||||||||
\(532\) | −0.000224849 0 | −9.74846e−6 0 | ||||||||
\(533\) | −43.7981 | −1.89711 | ||||||||
\(534\) | −21.5254 | −0.931495 | ||||||||
\(535\) | −2.53046 | −0.109402 | ||||||||
\(536\) | 18.9698 | 0.819371 | ||||||||
\(537\) | −7.63031 | −0.329272 | ||||||||
\(538\) | −14.6347 | −0.630947 | ||||||||
\(539\) | 13.1006 | 0.564285 | ||||||||
\(540\) | 0.188400 | 0.00810746 | ||||||||
\(541\) | −40.9238 | −1.75945 | −0.879726 | − | 0.475481i | \(-0.842274\pi\) | ||||
−0.879726 | + | 0.475481i | \(0.842274\pi\) | |||||||
\(542\) | −12.6991 | −0.545475 | ||||||||
\(543\) | −8.05234 | −0.345559 | ||||||||
\(544\) | 0.500626 | 0.0214642 | ||||||||
\(545\) | −0.853599 | −0.0365642 | ||||||||
\(546\) | −1.00513 | −0.0430156 | ||||||||
\(547\) | −36.0457 | −1.54120 | −0.770600 | − | 0.637319i | \(-0.780044\pi\) | ||||
−0.770600 | + | 0.637319i | \(0.780044\pi\) | |||||||
\(548\) | 0.875477 | 0.0373985 | ||||||||
\(549\) | 2.57004 | 0.109687 | ||||||||
\(550\) | −1.23585 | −0.0526968 | ||||||||
\(551\) | −0.00805802 | −0.000343283 0 | ||||||||
\(552\) | −19.0091 | −0.809080 | ||||||||
\(553\) | 0.523250 | 0.0222509 | ||||||||
\(554\) | 6.68940 | 0.284205 | ||||||||
\(555\) | −8.70800 | −0.369634 | ||||||||
\(556\) | 1.64612 | 0.0698110 | ||||||||
\(557\) | −1.03825 | −0.0439919 | −0.0219959 | − | 0.999758i | \(-0.507002\pi\) | ||||
−0.0219959 | + | 0.999758i | \(0.507002\pi\) | |||||||
\(558\) | −0.551057 | −0.0233281 | ||||||||
\(559\) | −31.3851 | −1.32745 | ||||||||
\(560\) | 1.65526 | 0.0699474 | ||||||||
\(561\) | −1.88271 | −0.0794881 | ||||||||
\(562\) | 22.9247 | 0.967021 | ||||||||
\(563\) | 9.70404 | 0.408976 | 0.204488 | − | 0.978869i | \(-0.434447\pi\) | ||||
0.204488 | + | 0.978869i | \(0.434447\pi\) | |||||||
\(564\) | 0.516532 | 0.0217499 | ||||||||
\(565\) | 4.71198 | 0.198234 | ||||||||
\(566\) | −26.5523 | −1.11608 | ||||||||
\(567\) | −0.203962 | −0.00856558 | ||||||||
\(568\) | 10.6621 | 0.447372 | ||||||||
\(569\) | 19.6552 | 0.823988 | 0.411994 | − | 0.911187i | \(-0.364832\pi\) | ||||
0.411994 | + | 0.911187i | \(0.364832\pi\) | |||||||
\(570\) | −0.0366083 | −0.00153335 | ||||||||
\(571\) | −11.3464 | −0.474833 | −0.237417 | − | 0.971408i | \(-0.576301\pi\) | ||||
−0.237417 | + | 0.971408i | \(0.576301\pi\) | |||||||
\(572\) | 0.594347 | 0.0248509 | ||||||||
\(573\) | 4.14413 | 0.173124 | ||||||||
\(574\) | −3.46489 | −0.144622 | ||||||||
\(575\) | −3.12562 | −0.130347 | ||||||||
\(576\) | 8.32219 | 0.346758 | ||||||||
\(577\) | −14.6785 | −0.611072 | −0.305536 | − | 0.952181i | \(-0.598836\pi\) | ||||
−0.305536 | + | 0.952181i | \(0.598836\pi\) | |||||||
\(578\) | −1.38255 | −0.0575064 | ||||||||
\(579\) | −10.1962 | −0.423739 | ||||||||
\(580\) | −0.121963 | −0.00506426 | ||||||||
\(581\) | −1.69473 | −0.0703093 | ||||||||
\(582\) | −16.7314 | −0.693539 | ||||||||
\(583\) | 1.99229 | 0.0825124 | ||||||||
\(584\) | 1.30846 | 0.0541444 | ||||||||
\(585\) | 7.58252 | 0.313499 | ||||||||
\(586\) | 29.4697 | 1.21738 | ||||||||
\(587\) | 23.0412 | 0.951014 | 0.475507 | − | 0.879712i | \(-0.342265\pi\) | ||||
0.475507 | + | 0.879712i | \(0.342265\pi\) | |||||||
\(588\) | −0.616271 | −0.0254146 | ||||||||
\(589\) | −0.00496132 | −0.000204428 0 | ||||||||
\(590\) | 43.4514 | 1.78887 | ||||||||
\(591\) | 7.93699 | 0.326484 | ||||||||
\(592\) | −15.6170 | −0.641853 | ||||||||
\(593\) | 13.6537 | 0.560689 | 0.280345 | − | 0.959899i | \(-0.409551\pi\) | ||||
0.280345 | + | 0.959899i | \(0.409551\pi\) | |||||||
\(594\) | −2.60293 | −0.106800 | ||||||||
\(595\) | 0.433878 | 0.0177873 | ||||||||
\(596\) | −0.386798 | −0.0158439 | ||||||||
\(597\) | 1.58998 | 0.0650735 | ||||||||
\(598\) | −32.4420 | −1.32665 | ||||||||
\(599\) | −11.5452 | −0.471724 | −0.235862 | − | 0.971787i | \(-0.575791\pi\) | ||||
−0.235862 | + | 0.971787i | \(0.575791\pi\) | |||||||
\(600\) | 1.37098 | 0.0559699 | ||||||||
\(601\) | −3.24584 | −0.132401 | −0.0662003 | − | 0.997806i | \(-0.521088\pi\) | ||||
−0.0662003 | + | 0.997806i | \(0.521088\pi\) | |||||||
\(602\) | −2.48289 | −0.101195 | ||||||||
\(603\) | 6.56955 | 0.267533 | ||||||||
\(604\) | 0.277672 | 0.0112983 | ||||||||
\(605\) | −15.8595 | −0.644782 | ||||||||
\(606\) | −4.42060 | −0.179575 | ||||||||
\(607\) | −31.7395 | −1.28827 | −0.644133 | − | 0.764913i | \(-0.722782\pi\) | ||||
−0.644133 | + | 0.764913i | \(0.722782\pi\) | |||||||
\(608\) | 0.00623152 | 0.000252721 0 | ||||||||
\(609\) | 0.132037 | 0.00535042 | ||||||||
\(610\) | −7.55856 | −0.306037 | ||||||||
\(611\) | 20.7888 | 0.841024 | ||||||||
\(612\) | 0.0885651 | 0.00358003 | ||||||||
\(613\) | −13.0712 | −0.527939 | −0.263969 | − | 0.964531i | \(-0.585032\pi\) | ||||
−0.263969 | + | 0.964531i | \(0.585032\pi\) | |||||||
\(614\) | −22.8177 | −0.920847 | ||||||||
\(615\) | 26.1385 | 1.05400 | ||||||||
\(616\) | 1.10882 | 0.0446755 | ||||||||
\(617\) | −21.2147 | −0.854071 | −0.427036 | − | 0.904235i | \(-0.640442\pi\) | ||||
−0.427036 | + | 0.904235i | \(0.640442\pi\) | |||||||
\(618\) | 14.5403 | 0.584897 | ||||||||
\(619\) | −48.3407 | −1.94298 | −0.971488 | − | 0.237090i | \(-0.923806\pi\) | ||||
−0.971488 | + | 0.237090i | \(0.923806\pi\) | |||||||
\(620\) | −0.0750929 | −0.00301580 | ||||||||
\(621\) | −6.58314 | −0.264172 | ||||||||
\(622\) | −0.436384 | −0.0174974 | ||||||||
\(623\) | 3.17556 | 0.127226 | ||||||||
\(624\) | 13.5985 | 0.544377 | ||||||||
\(625\) | −22.4006 | −0.896025 | ||||||||
\(626\) | −42.6514 | −1.70469 | ||||||||
\(627\) | −0.0234350 | −0.000935902 0 | ||||||||
\(628\) | 0.0885651 | 0.00353413 | ||||||||
\(629\) | −4.09354 | −0.163220 | ||||||||
\(630\) | 0.599857 | 0.0238989 | ||||||||
\(631\) | −28.7219 | −1.14340 | −0.571700 | − | 0.820463i | \(-0.693716\pi\) | ||||
−0.571700 | + | 0.820463i | \(0.693716\pi\) | |||||||
\(632\) | −7.40779 | −0.294666 | ||||||||
\(633\) | 0.650575 | 0.0258580 | ||||||||
\(634\) | 14.5248 | 0.576853 | ||||||||
\(635\) | −29.8417 | −1.18423 | ||||||||
\(636\) | −0.0937200 | −0.00371624 | ||||||||
\(637\) | −24.8030 | −0.982730 | ||||||||
\(638\) | 1.68504 | 0.0667115 | ||||||||
\(639\) | 3.69245 | 0.146071 | ||||||||
\(640\) | −22.3459 | −0.883298 | ||||||||
\(641\) | 30.4386 | 1.20225 | 0.601126 | − | 0.799154i | \(-0.294719\pi\) | ||||
0.601126 | + | 0.799154i | \(0.294719\pi\) | |||||||
\(642\) | −1.64460 | −0.0649072 | ||||||||
\(643\) | 43.0852 | 1.69912 | 0.849558 | − | 0.527496i | \(-0.176869\pi\) | ||||
0.849558 | + | 0.527496i | \(0.176869\pi\) | |||||||
\(644\) | 0.118917 | 0.00468599 | ||||||||
\(645\) | 18.7305 | 0.737511 | ||||||||
\(646\) | −0.0172092 | −0.000677086 0 | ||||||||
\(647\) | 1.33198 | 0.0523656 | 0.0261828 | − | 0.999657i | \(-0.491665\pi\) | ||||
0.0261828 | + | 0.999657i | \(0.491665\pi\) | |||||||
\(648\) | 2.88754 | 0.113433 | ||||||||
\(649\) | 27.8156 | 1.09186 | ||||||||
\(650\) | 2.33979 | 0.0917741 | ||||||||
\(651\) | 0.0812953 | 0.00318621 | ||||||||
\(652\) | −0.203628 | −0.00797469 | ||||||||
\(653\) | −28.3679 | −1.11012 | −0.555061 | − | 0.831810i | \(-0.687305\pi\) | ||||
−0.555061 | + | 0.831810i | \(0.687305\pi\) | |||||||
\(654\) | −0.554772 | −0.0216933 | ||||||||
\(655\) | −27.2513 | −1.06480 | ||||||||
\(656\) | 46.8768 | 1.83023 | ||||||||
\(657\) | 0.453140 | 0.0176787 | ||||||||
\(658\) | 1.64461 | 0.0641136 | ||||||||
\(659\) | 34.9333 | 1.36081 | 0.680403 | − | 0.732838i | \(-0.261805\pi\) | ||||
0.680403 | + | 0.732838i | \(0.261805\pi\) | |||||||
\(660\) | −0.354703 | −0.0138068 | ||||||||
\(661\) | 47.8486 | 1.86109 | 0.930547 | − | 0.366173i | \(-0.119332\pi\) | ||||
0.930547 | + | 0.366173i | \(0.119332\pi\) | |||||||
\(662\) | 46.7016 | 1.81511 | ||||||||
\(663\) | 3.56447 | 0.138432 | ||||||||
\(664\) | 23.9928 | 0.931100 | ||||||||
\(665\) | 0.00540068 | 0.000209429 0 | ||||||||
\(666\) | −5.65951 | −0.219302 | ||||||||
\(667\) | 4.26168 | 0.165013 | ||||||||
\(668\) | −1.47044 | −0.0568931 | ||||||||
\(669\) | 10.6846 | 0.413089 | ||||||||
\(670\) | −19.3212 | −0.746444 | ||||||||
\(671\) | −4.83864 | −0.186794 | ||||||||
\(672\) | −0.102108 | −0.00393892 | ||||||||
\(673\) | −28.1217 | −1.08401 | −0.542007 | − | 0.840374i | \(-0.682335\pi\) | ||||
−0.542007 | + | 0.840374i | \(0.682335\pi\) | |||||||
\(674\) | 49.0980 | 1.89119 | ||||||||
\(675\) | 0.474791 | 0.0182747 | ||||||||
\(676\) | 0.0260899 | 0.00100346 | ||||||||
\(677\) | −50.6480 | −1.94656 | −0.973281 | − | 0.229618i | \(-0.926252\pi\) | ||||
−0.973281 | + | 0.229618i | \(0.926252\pi\) | |||||||
\(678\) | 3.06241 | 0.117611 | ||||||||
\(679\) | 2.46832 | 0.0947254 | ||||||||
\(680\) | −6.14253 | −0.235555 | ||||||||
\(681\) | −14.6258 | −0.560463 | ||||||||
\(682\) | 1.03748 | 0.0397272 | ||||||||
\(683\) | −26.7424 | −1.02327 | −0.511635 | − | 0.859203i | \(-0.670960\pi\) | ||||
−0.511635 | + | 0.859203i | \(0.670960\pi\) | |||||||
\(684\) | 0.00110241 | 4.21517e−5 0 | ||||||||
\(685\) | −21.0282 | −0.803445 | ||||||||
\(686\) | −3.93608 | −0.150280 | ||||||||
\(687\) | −0.419946 | −0.0160220 | ||||||||
\(688\) | 33.5913 | 1.28066 | ||||||||
\(689\) | −3.77194 | −0.143699 | ||||||||
\(690\) | 19.3612 | 0.737068 | ||||||||
\(691\) | −43.5596 | −1.65709 | −0.828543 | − | 0.559925i | \(-0.810830\pi\) | ||||
−0.828543 | + | 0.559925i | \(0.810830\pi\) | |||||||
\(692\) | 0.508786 | 0.0193412 | ||||||||
\(693\) | 0.384001 | 0.0145870 | ||||||||
\(694\) | −13.3397 | −0.506367 | ||||||||
\(695\) | −39.5383 | −1.49977 | ||||||||
\(696\) | −1.86929 | −0.0708551 | ||||||||
\(697\) | 12.2874 | 0.465419 | ||||||||
\(698\) | 28.8527 | 1.09209 | ||||||||
\(699\) | −21.0978 | −0.797991 | ||||||||
\(700\) | −0.00857657 | −0.000324164 0 | ||||||||
\(701\) | −15.9742 | −0.603337 | −0.301669 | − | 0.953413i | \(-0.597544\pi\) | ||||
−0.301669 | + | 0.953413i | \(0.597544\pi\) | |||||||
\(702\) | 4.92804 | 0.185997 | ||||||||
\(703\) | −0.0509542 | −0.00192177 | ||||||||
\(704\) | −15.6683 | −0.590520 | ||||||||
\(705\) | −12.4066 | −0.467261 | ||||||||
\(706\) | 26.0509 | 0.980439 | ||||||||
\(707\) | 0.652154 | 0.0245268 | ||||||||
\(708\) | −1.30848 | −0.0491757 | ||||||||
\(709\) | −44.6106 | −1.67539 | −0.837693 | − | 0.546142i | \(-0.816096\pi\) | ||||
−0.837693 | + | 0.546142i | \(0.816096\pi\) | |||||||
\(710\) | −10.8596 | −0.407554 | ||||||||
\(711\) | −2.56543 | −0.0962113 | ||||||||
\(712\) | −44.9572 | −1.68484 | ||||||||
\(713\) | 2.62392 | 0.0982664 | ||||||||
\(714\) | 0.281986 | 0.0105531 | ||||||||
\(715\) | −14.2757 | −0.533881 | ||||||||
\(716\) | −0.675779 | −0.0252551 | ||||||||
\(717\) | −22.6592 | −0.846224 | ||||||||
\(718\) | 11.7626 | 0.438976 | ||||||||
\(719\) | −23.9914 | −0.894729 | −0.447365 | − | 0.894352i | \(-0.647637\pi\) | ||||
−0.447365 | + | 0.894352i | \(0.647637\pi\) | |||||||
\(720\) | −8.11553 | −0.302448 | ||||||||
\(721\) | −2.14507 | −0.0798868 | ||||||||
\(722\) | 26.2682 | 0.977600 | ||||||||
\(723\) | −25.3959 | −0.944485 | ||||||||
\(724\) | −0.713156 | −0.0265042 | ||||||||
\(725\) | −0.307362 | −0.0114151 | ||||||||
\(726\) | −10.3074 | −0.382545 | ||||||||
\(727\) | −27.8456 | −1.03273 | −0.516367 | − | 0.856367i | \(-0.672716\pi\) | ||||
−0.516367 | + | 0.856367i | \(0.672716\pi\) | |||||||
\(728\) | −2.09928 | −0.0778046 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.33270 | −0.0493253 | ||||||||
\(731\) | 8.80499 | 0.325664 | ||||||||
\(732\) | 0.227616 | 0.00841292 | ||||||||
\(733\) | 36.3146 | 1.34131 | 0.670655 | − | 0.741769i | \(-0.266013\pi\) | ||||
0.670655 | + | 0.741769i | \(0.266013\pi\) | |||||||
\(734\) | −36.1838 | −1.33557 | ||||||||
\(735\) | 14.8023 | 0.545990 | ||||||||
\(736\) | −3.29569 | −0.121481 | ||||||||
\(737\) | −12.3686 | −0.455602 | ||||||||
\(738\) | 16.9879 | 0.625334 | ||||||||
\(739\) | 11.2275 | 0.413012 | 0.206506 | − | 0.978445i | \(-0.433791\pi\) | ||||
0.206506 | + | 0.978445i | \(0.433791\pi\) | |||||||
\(740\) | −0.771225 | −0.0283508 | ||||||||
\(741\) | 0.0443685 | 0.00162992 | ||||||||
\(742\) | −0.298400 | −0.0109546 | ||||||||
\(743\) | −5.17852 | −0.189982 | −0.0949908 | − | 0.995478i | \(-0.530282\pi\) | ||||
−0.0949908 | + | 0.995478i | \(0.530282\pi\) | |||||||
\(744\) | −1.15092 | −0.0421947 | ||||||||
\(745\) | 9.29055 | 0.340379 | ||||||||
\(746\) | −35.9359 | −1.31571 | ||||||||
\(747\) | 8.30907 | 0.304013 | ||||||||
\(748\) | −0.166742 | −0.00609670 | ||||||||
\(749\) | 0.242622 | 0.00886520 | ||||||||
\(750\) | −16.1015 | −0.587944 | ||||||||
\(751\) | 29.4141 | 1.07333 | 0.536667 | − | 0.843794i | \(-0.319683\pi\) | ||||
0.536667 | + | 0.843794i | \(0.319683\pi\) | |||||||
\(752\) | −22.2501 | −0.811378 | ||||||||
\(753\) | −1.76138 | −0.0641884 | ||||||||
\(754\) | −3.19023 | −0.116181 | ||||||||
\(755\) | −6.66944 | −0.242726 | ||||||||
\(756\) | −0.0180639 | −0.000656977 0 | ||||||||
\(757\) | −8.97631 | −0.326249 | −0.163125 | − | 0.986605i | \(-0.552157\pi\) | ||||
−0.163125 | + | 0.986605i | \(0.552157\pi\) | |||||||
\(758\) | 34.2871 | 1.24536 | ||||||||
\(759\) | 12.3941 | 0.449879 | ||||||||
\(760\) | −0.0764588 | −0.00277345 | ||||||||
\(761\) | −22.4232 | −0.812840 | −0.406420 | − | 0.913686i | \(-0.633223\pi\) | ||||
−0.406420 | + | 0.913686i | \(0.633223\pi\) | |||||||
\(762\) | −19.3947 | −0.702597 | ||||||||
\(763\) | 0.0818433 | 0.00296293 | ||||||||
\(764\) | 0.367026 | 0.0132785 | ||||||||
\(765\) | −2.12725 | −0.0769110 | ||||||||
\(766\) | −38.7300 | −1.39937 | ||||||||
\(767\) | −52.6622 | −1.90152 | ||||||||
\(768\) | 2.12133 | 0.0765470 | ||||||||
\(769\) | 26.6961 | 0.962686 | 0.481343 | − | 0.876532i | \(-0.340149\pi\) | ||||
0.481343 | + | 0.876532i | \(0.340149\pi\) | |||||||
\(770\) | −1.12936 | −0.0406992 | ||||||||
\(771\) | −8.52815 | −0.307134 | ||||||||
\(772\) | −0.903026 | −0.0325006 | ||||||||
\(773\) | −5.73569 | −0.206298 | −0.103149 | − | 0.994666i | \(-0.532892\pi\) | ||||
−0.103149 | + | 0.994666i | \(0.532892\pi\) | |||||||
\(774\) | 12.1733 | 0.437561 | ||||||||
\(775\) | −0.189243 | −0.00679780 | ||||||||
\(776\) | −34.9446 | −1.25444 | ||||||||
\(777\) | 0.834925 | 0.0299528 | ||||||||
\(778\) | 37.9007 | 1.35881 | ||||||||
\(779\) | 0.152947 | 0.00547990 | ||||||||
\(780\) | 0.671547 | 0.0240452 | ||||||||
\(781\) | −6.95182 | −0.248756 | ||||||||
\(782\) | 9.10150 | 0.325469 | ||||||||
\(783\) | −0.647363 | −0.0231349 | ||||||||
\(784\) | 26.5465 | 0.948088 | ||||||||
\(785\) | −2.12725 | −0.0759249 | ||||||||
\(786\) | −17.7112 | −0.631738 | ||||||||
\(787\) | 36.1386 | 1.28820 | 0.644101 | − | 0.764941i | \(-0.277232\pi\) | ||||
0.644101 | + | 0.764941i | \(0.277232\pi\) | |||||||
\(788\) | 0.702940 | 0.0250412 | ||||||||
\(789\) | −9.05067 | −0.322212 | ||||||||
\(790\) | 7.54501 | 0.268439 | ||||||||
\(791\) | −0.451786 | −0.0160636 | ||||||||
\(792\) | −5.43640 | −0.193174 | ||||||||
\(793\) | 9.16082 | 0.325310 | ||||||||
\(794\) | 43.0304 | 1.52709 | ||||||||
\(795\) | 2.25107 | 0.0798373 | ||||||||
\(796\) | 0.140816 | 0.00499111 | ||||||||
\(797\) | −30.4504 | −1.07861 | −0.539303 | − | 0.842112i | \(-0.681312\pi\) | ||||
−0.539303 | + | 0.842112i | \(0.681312\pi\) | |||||||
\(798\) | 0.00351001 | 0.000124253 0 | ||||||||
\(799\) | −5.83223 | −0.206329 | ||||||||
\(800\) | 0.237693 | 0.00840370 | ||||||||
\(801\) | −15.5694 | −0.550117 | ||||||||
\(802\) | −52.1799 | −1.84254 | ||||||||
\(803\) | −0.853131 | −0.0301063 | ||||||||
\(804\) | 0.581832 | 0.0205196 | ||||||||
\(805\) | −2.85628 | −0.100671 | ||||||||
\(806\) | −1.96422 | −0.0691868 | ||||||||
\(807\) | −10.5853 | −0.372621 | ||||||||
\(808\) | −9.23271 | −0.324806 | ||||||||
\(809\) | 52.2120 | 1.83568 | 0.917839 | − | 0.396953i | \(-0.129932\pi\) | ||||
0.917839 | + | 0.396953i | \(0.129932\pi\) | |||||||
\(810\) | −2.94103 | −0.103337 | ||||||||
\(811\) | −38.6079 | −1.35571 | −0.677854 | − | 0.735196i | \(-0.737090\pi\) | ||||
−0.677854 | + | 0.735196i | \(0.737090\pi\) | |||||||
\(812\) | 0.0116939 | 0.000410375 0 | ||||||||
\(813\) | −9.18533 | −0.322144 | ||||||||
\(814\) | 10.6552 | 0.373465 | ||||||||
\(815\) | 4.89096 | 0.171323 | ||||||||
\(816\) | −3.81503 | −0.133553 | ||||||||
\(817\) | 0.109600 | 0.00383441 | ||||||||
\(818\) | 28.6965 | 1.00335 | ||||||||
\(819\) | −0.727014 | −0.0254039 | ||||||||
\(820\) | 2.31495 | 0.0808417 | ||||||||
\(821\) | −32.4910 | −1.13394 | −0.566972 | − | 0.823737i | \(-0.691885\pi\) | ||||
−0.566972 | + | 0.823737i | \(0.691885\pi\) | |||||||
\(822\) | −13.6666 | −0.476679 | ||||||||
\(823\) | −30.8316 | −1.07472 | −0.537360 | − | 0.843353i | \(-0.680579\pi\) | ||||
−0.537360 | + | 0.843353i | \(0.680579\pi\) | |||||||
\(824\) | 30.3684 | 1.05793 | ||||||||
\(825\) | −0.893894 | −0.0311214 | ||||||||
\(826\) | −4.16613 | −0.144958 | ||||||||
\(827\) | 22.1948 | 0.771790 | 0.385895 | − | 0.922543i | \(-0.373893\pi\) | ||||
0.385895 | + | 0.922543i | \(0.373893\pi\) | |||||||
\(828\) | −0.583036 | −0.0202619 | ||||||||
\(829\) | −36.2820 | −1.26012 | −0.630062 | − | 0.776545i | \(-0.716971\pi\) | ||||
−0.630062 | + | 0.776545i | \(0.716971\pi\) | |||||||
\(830\) | −24.4372 | −0.848228 | ||||||||
\(831\) | 4.83846 | 0.167844 | ||||||||
\(832\) | 29.6642 | 1.02842 | ||||||||
\(833\) | 6.95840 | 0.241094 | ||||||||
\(834\) | −25.6968 | −0.889806 | ||||||||
\(835\) | 35.3187 | 1.22225 | ||||||||
\(836\) | −0.00207552 | −7.17833e−5 0 | ||||||||
\(837\) | −0.398581 | −0.0137770 | ||||||||
\(838\) | 4.30828 | 0.148827 | ||||||||
\(839\) | 39.9576 | 1.37949 | 0.689744 | − | 0.724053i | \(-0.257723\pi\) | ||||
0.689744 | + | 0.724053i | \(0.257723\pi\) | |||||||
\(840\) | 1.25284 | 0.0432271 | ||||||||
\(841\) | −28.5809 | −0.985549 | ||||||||
\(842\) | −14.9319 | −0.514587 | ||||||||
\(843\) | 16.5815 | 0.571098 | ||||||||
\(844\) | 0.0576182 | 0.00198330 | ||||||||
\(845\) | −0.626655 | −0.0215576 | ||||||||
\(846\) | −8.06333 | −0.277223 | ||||||||
\(847\) | 1.52062 | 0.0522490 | ||||||||
\(848\) | 4.03708 | 0.138634 | ||||||||
\(849\) | −19.2054 | −0.659126 | ||||||||
\(850\) | −0.656421 | −0.0225150 | ||||||||
\(851\) | 26.9484 | 0.923778 | ||||||||
\(852\) | 0.327022 | 0.0112036 | ||||||||
\(853\) | 11.3176 | 0.387507 | 0.193753 | − | 0.981050i | \(-0.437934\pi\) | ||||
0.193753 | + | 0.981050i | \(0.437934\pi\) | |||||||
\(854\) | 0.724717 | 0.0247993 | ||||||||
\(855\) | −0.0264789 | −0.000905559 0 | ||||||||
\(856\) | −3.43486 | −0.117401 | ||||||||
\(857\) | 30.1121 | 1.02861 | 0.514305 | − | 0.857607i | \(-0.328050\pi\) | ||||
0.514305 | + | 0.857607i | \(0.328050\pi\) | |||||||
\(858\) | −9.27807 | −0.316748 | ||||||||
\(859\) | −8.17691 | −0.278993 | −0.139496 | − | 0.990223i | \(-0.544548\pi\) | ||||
−0.139496 | + | 0.990223i | \(0.544548\pi\) | |||||||
\(860\) | 1.65886 | 0.0565668 | ||||||||
\(861\) | −2.50616 | −0.0854098 | ||||||||
\(862\) | −5.63920 | −0.192072 | ||||||||
\(863\) | 47.6091 | 1.62063 | 0.810317 | − | 0.585992i | \(-0.199295\pi\) | ||||
0.810317 | + | 0.585992i | \(0.199295\pi\) | |||||||
\(864\) | 0.500626 | 0.0170316 | ||||||||
\(865\) | −12.2206 | −0.415513 | ||||||||
\(866\) | 38.8867 | 1.32142 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 0.00719992 | 0.000244381 0 | ||||||||
\(869\) | 4.82997 | 0.163845 | ||||||||
\(870\) | 1.90391 | 0.0645487 | ||||||||
\(871\) | 23.4169 | 0.793452 | ||||||||
\(872\) | −1.15868 | −0.0392378 | ||||||||
\(873\) | −12.1019 | −0.409587 | ||||||||
\(874\) | 0.113291 | 0.00383211 | ||||||||
\(875\) | 2.37539 | 0.0803029 | ||||||||
\(876\) | 0.0401324 | 0.00135595 | ||||||||
\(877\) | 29.2718 | 0.988438 | 0.494219 | − | 0.869338i | \(-0.335454\pi\) | ||||
0.494219 | + | 0.869338i | \(0.335454\pi\) | |||||||
\(878\) | 36.1934 | 1.22147 | ||||||||
\(879\) | 21.3155 | 0.718955 | ||||||||
\(880\) | 15.2792 | 0.515061 | ||||||||
\(881\) | −18.7555 | −0.631890 | −0.315945 | − | 0.948777i | \(-0.602322\pi\) | ||||
−0.315945 | + | 0.948777i | \(0.602322\pi\) | |||||||
\(882\) | 9.62031 | 0.323933 | ||||||||
\(883\) | 17.7396 | 0.596986 | 0.298493 | − | 0.954412i | \(-0.403516\pi\) | ||||
0.298493 | + | 0.954412i | \(0.403516\pi\) | |||||||
\(884\) | 0.315687 | 0.0106177 | ||||||||
\(885\) | 31.4285 | 1.05646 | ||||||||
\(886\) | 25.7467 | 0.864978 | ||||||||
\(887\) | 35.7410 | 1.20006 | 0.600032 | − | 0.799976i | \(-0.295154\pi\) | ||||
0.600032 | + | 0.799976i | \(0.295154\pi\) | |||||||
\(888\) | −11.8203 | −0.396662 | ||||||||
\(889\) | 2.86123 | 0.0959626 | ||||||||
\(890\) | 45.7900 | 1.53488 | ||||||||
\(891\) | −1.88271 | −0.0630732 | ||||||||
\(892\) | 0.946279 | 0.0316838 | ||||||||
\(893\) | −0.0725964 | −0.00242935 | ||||||||
\(894\) | 6.03812 | 0.201945 | ||||||||
\(895\) | 16.2316 | 0.542563 | ||||||||
\(896\) | 2.14253 | 0.0715768 | ||||||||
\(897\) | −23.4654 | −0.783486 | ||||||||
\(898\) | −23.4934 | −0.783984 | ||||||||
\(899\) | 0.258027 | 0.00860567 | ||||||||
\(900\) | 0.0420499 | 0.00140166 | ||||||||
\(901\) | 1.05821 | 0.0352539 | ||||||||
\(902\) | −31.9833 | −1.06493 | ||||||||
\(903\) | −1.79588 | −0.0597632 | ||||||||
\(904\) | 6.39605 | 0.212729 | ||||||||
\(905\) | 17.1294 | 0.569399 | ||||||||
\(906\) | −4.33461 | −0.144008 | ||||||||
\(907\) | −48.8728 | −1.62280 | −0.811398 | − | 0.584494i | \(-0.801293\pi\) | ||||
−0.811398 | + | 0.584494i | \(0.801293\pi\) | |||||||
\(908\) | −1.29534 | −0.0429873 | ||||||||
\(909\) | −3.19743 | −0.106052 | ||||||||
\(910\) | 2.13817 | 0.0708796 | ||||||||
\(911\) | −30.3594 | −1.00585 | −0.502926 | − | 0.864329i | \(-0.667743\pi\) | ||||
−0.502926 | + | 0.864329i | \(0.667743\pi\) | |||||||
\(912\) | −0.0474874 | −0.00157246 | ||||||||
\(913\) | −15.6436 | −0.517727 | ||||||||
\(914\) | 42.1322 | 1.39361 | ||||||||
\(915\) | −5.46713 | −0.180738 | ||||||||
\(916\) | −0.0371926 | −0.00122888 | ||||||||
\(917\) | 2.61287 | 0.0862844 | ||||||||
\(918\) | −1.38255 | −0.0456308 | ||||||||
\(919\) | −39.7439 | −1.31103 | −0.655515 | − | 0.755182i | \(-0.727548\pi\) | ||||
−0.655515 | + | 0.755182i | \(0.727548\pi\) | |||||||
\(920\) | 40.4371 | 1.33317 | ||||||||
\(921\) | −16.5041 | −0.543829 | ||||||||
\(922\) | −20.4456 | −0.673339 | ||||||||
\(923\) | 13.1616 | 0.433220 | ||||||||
\(924\) | 0.0340091 | 0.00111882 | ||||||||
\(925\) | −1.94358 | −0.0639044 | ||||||||
\(926\) | −31.4375 | −1.03310 | ||||||||
\(927\) | 10.5170 | 0.345425 | ||||||||
\(928\) | −0.324087 | −0.0106387 | ||||||||
\(929\) | −7.96176 | −0.261217 | −0.130608 | − | 0.991434i | \(-0.541693\pi\) | ||||
−0.130608 | + | 0.991434i | \(0.541693\pi\) | |||||||
\(930\) | 1.17224 | 0.0384392 | ||||||||
\(931\) | 0.0866144 | 0.00283867 | ||||||||
\(932\) | −1.86852 | −0.0612056 | ||||||||
\(933\) | −0.315638 | −0.0103335 | ||||||||
\(934\) | −31.1686 | −1.01987 | ||||||||
\(935\) | 4.00500 | 0.130978 | ||||||||
\(936\) | 10.2925 | 0.336422 | ||||||||
\(937\) | 0.958798 | 0.0313226 | 0.0156613 | − | 0.999877i | \(-0.495015\pi\) | ||||
0.0156613 | + | 0.999877i | \(0.495015\pi\) | |||||||
\(938\) | 1.85252 | 0.0604870 | ||||||||
\(939\) | −30.8499 | −1.00675 | ||||||||
\(940\) | −1.09879 | −0.0358387 | ||||||||
\(941\) | −15.1533 | −0.493985 | −0.246992 | − | 0.969017i | \(-0.579442\pi\) | ||||
−0.246992 | + | 0.969017i | \(0.579442\pi\) | |||||||
\(942\) | −1.38255 | −0.0450458 | ||||||||
\(943\) | −80.8898 | −2.63413 | ||||||||
\(944\) | 56.3640 | 1.83449 | ||||||||
\(945\) | 0.433878 | 0.0141141 | ||||||||
\(946\) | −22.9188 | −0.745155 | ||||||||
\(947\) | 7.54635 | 0.245223 | 0.122612 | − | 0.992455i | \(-0.460873\pi\) | ||||
0.122612 | + | 0.992455i | \(0.460873\pi\) | |||||||
\(948\) | −0.227208 | −0.00737937 | ||||||||
\(949\) | 1.61520 | 0.0524317 | ||||||||
\(950\) | −0.00817077 | −0.000265095 0 | ||||||||
\(951\) | 10.5058 | 0.340675 | ||||||||
\(952\) | 0.588947 | 0.0190879 | ||||||||
\(953\) | −21.8241 | −0.706951 | −0.353475 | − | 0.935444i | \(-0.615000\pi\) | ||||
−0.353475 | + | 0.935444i | \(0.615000\pi\) | |||||||
\(954\) | 1.46302 | 0.0473670 | ||||||||
\(955\) | −8.81563 | −0.285267 | ||||||||
\(956\) | −2.00682 | −0.0649050 | ||||||||
\(957\) | 1.21880 | 0.0393981 | ||||||||
\(958\) | 22.7928 | 0.736402 | ||||||||
\(959\) | 2.01619 | 0.0651061 | ||||||||
\(960\) | −17.7034 | −0.571375 | ||||||||
\(961\) | −30.8411 | −0.994875 | ||||||||
\(962\) | −20.1731 | −0.650408 | ||||||||
\(963\) | −1.18955 | −0.0383326 | ||||||||
\(964\) | −2.24919 | −0.0724416 | ||||||||
\(965\) | 21.6899 | 0.698221 | ||||||||
\(966\) | −1.85636 | −0.0597273 | ||||||||
\(967\) | −28.6063 | −0.919916 | −0.459958 | − | 0.887941i | \(-0.652135\pi\) | ||||
−0.459958 | + | 0.887941i | \(0.652135\pi\) | |||||||
\(968\) | −21.5278 | −0.691928 | ||||||||
\(969\) | −0.0124475 | −0.000399870 0 | ||||||||
\(970\) | 35.5920 | 1.14279 | ||||||||
\(971\) | −11.0532 | −0.354714 | −0.177357 | − | 0.984147i | \(-0.556755\pi\) | ||||
−0.177357 | + | 0.984147i | \(0.556755\pi\) | |||||||
\(972\) | 0.0885651 | 0.00284073 | ||||||||
\(973\) | 3.79094 | 0.121532 | ||||||||
\(974\) | 53.1805 | 1.70401 | ||||||||
\(975\) | 1.69238 | 0.0541994 | ||||||||
\(976\) | −9.80477 | −0.313843 | ||||||||
\(977\) | −2.85988 | −0.0914956 | −0.0457478 | − | 0.998953i | \(-0.514567\pi\) | ||||
−0.0457478 | + | 0.998953i | \(0.514567\pi\) | |||||||
\(978\) | 3.17874 | 0.101645 | ||||||||
\(979\) | 29.3126 | 0.936835 | ||||||||
\(980\) | 1.31097 | 0.0418773 | ||||||||
\(981\) | −0.401268 | −0.0128115 | ||||||||
\(982\) | −49.7632 | −1.58801 | ||||||||
\(983\) | −12.8749 | −0.410647 | −0.205323 | − | 0.978694i | \(-0.565825\pi\) | ||||
−0.205323 | + | 0.978694i | \(0.565825\pi\) | |||||||
\(984\) | 35.4804 | 1.13107 | ||||||||
\(985\) | −16.8840 | −0.537969 | ||||||||
\(986\) | 0.895010 | 0.0285029 | ||||||||
\(987\) | 1.18955 | 0.0378638 | ||||||||
\(988\) | 0.00392950 | 0.000125014 0 | ||||||||
\(989\) | −57.9645 | −1.84316 | ||||||||
\(990\) | 5.53710 | 0.175981 | ||||||||
\(991\) | −1.74510 | −0.0554349 | −0.0277174 | − | 0.999616i | \(-0.508824\pi\) | ||||
−0.0277174 | + | 0.999616i | \(0.508824\pi\) | |||||||
\(992\) | −0.199540 | −0.00633540 | ||||||||
\(993\) | 33.7794 | 1.07196 | ||||||||
\(994\) | 1.04122 | 0.0330256 | ||||||||
\(995\) | −3.38229 | −0.107226 | ||||||||
\(996\) | 0.735894 | 0.0233177 | ||||||||
\(997\) | −3.28316 | −0.103979 | −0.0519894 | − | 0.998648i | \(-0.516556\pi\) | ||||
−0.0519894 | + | 0.998648i | \(0.516556\pi\) | |||||||
\(998\) | 4.40624 | 0.139477 | ||||||||
\(999\) | −4.09354 | −0.129514 |
(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 | 8007.2.a.f.1.15 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.f.1.15 | ✓ | 48 | 1.1 | even | 1 | trivial |