Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4009,2,Mod(1,4009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4009, 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("4009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4009 = 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4009.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: | \(32.0120261703\) |
Analytic rank: | \(0\) |
Dimension: | \(82\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 4009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.71228 | −1.91787 | −0.958937 | − | 0.283621i | \(-0.908464\pi\) | ||||
−0.958937 | + | 0.283621i | \(0.908464\pi\) | |||||||
\(3\) | −0.799829 | −0.461781 | −0.230891 | − | 0.972980i | \(-0.574164\pi\) | ||||
−0.230891 | + | 0.972980i | \(0.574164\pi\) | |||||||
\(4\) | 5.35647 | 2.67824 | ||||||||
\(5\) | 2.45685 | 1.09874 | 0.549369 | − | 0.835580i | \(-0.314868\pi\) | ||||
0.549369 | + | 0.835580i | \(0.314868\pi\) | |||||||
\(6\) | 2.16936 | 0.885638 | ||||||||
\(7\) | −1.47623 | −0.557964 | −0.278982 | − | 0.960296i | \(-0.589997\pi\) | ||||
−0.278982 | + | 0.960296i | \(0.589997\pi\) | |||||||
\(8\) | −9.10370 | −3.21865 | ||||||||
\(9\) | −2.36027 | −0.786758 | ||||||||
\(10\) | −6.66368 | −2.10724 | ||||||||
\(11\) | −3.67530 | −1.10815 | −0.554073 | − | 0.832468i | \(-0.686927\pi\) | ||||
−0.554073 | + | 0.832468i | \(0.686927\pi\) | |||||||
\(12\) | −4.28426 | −1.23676 | ||||||||
\(13\) | −0.840855 | −0.233211 | −0.116606 | − | 0.993178i | \(-0.537201\pi\) | ||||
−0.116606 | + | 0.993178i | \(0.537201\pi\) | |||||||
\(14\) | 4.00396 | 1.07010 | ||||||||
\(15\) | −1.96506 | −0.507377 | ||||||||
\(16\) | 13.9789 | 3.49472 | ||||||||
\(17\) | −2.83991 | −0.688779 | −0.344390 | − | 0.938827i | \(-0.611914\pi\) | ||||
−0.344390 | + | 0.938827i | \(0.611914\pi\) | |||||||
\(18\) | 6.40173 | 1.50890 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 13.1601 | 2.94268 | ||||||||
\(21\) | 1.18073 | 0.257657 | ||||||||
\(22\) | 9.96846 | 2.12528 | ||||||||
\(23\) | 1.26199 | 0.263143 | 0.131572 | − | 0.991307i | \(-0.457998\pi\) | ||||
0.131572 | + | 0.991307i | \(0.457998\pi\) | |||||||
\(24\) | 7.28140 | 1.48631 | ||||||||
\(25\) | 1.03613 | 0.207226 | ||||||||
\(26\) | 2.28064 | 0.447270 | ||||||||
\(27\) | 4.28730 | 0.825091 | ||||||||
\(28\) | −7.90740 | −1.49436 | ||||||||
\(29\) | 1.56159 | 0.289980 | 0.144990 | − | 0.989433i | \(-0.453685\pi\) | ||||
0.144990 | + | 0.989433i | \(0.453685\pi\) | |||||||
\(30\) | 5.32980 | 0.973084 | ||||||||
\(31\) | −5.90829 | −1.06116 | −0.530580 | − | 0.847635i | \(-0.678026\pi\) | ||||
−0.530580 | + | 0.847635i | \(0.678026\pi\) | |||||||
\(32\) | −19.7072 | −3.48378 | ||||||||
\(33\) | 2.93961 | 0.511721 | ||||||||
\(34\) | 7.70264 | 1.32099 | ||||||||
\(35\) | −3.62689 | −0.613056 | ||||||||
\(36\) | −12.6427 | −2.10712 | ||||||||
\(37\) | −9.30121 | −1.52911 | −0.764555 | − | 0.644559i | \(-0.777041\pi\) | ||||
−0.764555 | + | 0.644559i | \(0.777041\pi\) | |||||||
\(38\) | −2.71228 | −0.439990 | ||||||||
\(39\) | 0.672540 | 0.107693 | ||||||||
\(40\) | −22.3665 | −3.53645 | ||||||||
\(41\) | 5.99792 | 0.936718 | 0.468359 | − | 0.883538i | \(-0.344845\pi\) | ||||
0.468359 | + | 0.883538i | \(0.344845\pi\) | |||||||
\(42\) | −3.20248 | −0.494154 | ||||||||
\(43\) | −9.15103 | −1.39552 | −0.697760 | − | 0.716332i | \(-0.745820\pi\) | ||||
−0.697760 | + | 0.716332i | \(0.745820\pi\) | |||||||
\(44\) | −19.6867 | −2.96788 | ||||||||
\(45\) | −5.79885 | −0.864441 | ||||||||
\(46\) | −3.42287 | −0.504675 | ||||||||
\(47\) | −9.32102 | −1.35961 | −0.679805 | − | 0.733393i | \(-0.737936\pi\) | ||||
−0.679805 | + | 0.733393i | \(0.737936\pi\) | |||||||
\(48\) | −11.1807 | −1.61379 | ||||||||
\(49\) | −4.82074 | −0.688677 | ||||||||
\(50\) | −2.81027 | −0.397432 | ||||||||
\(51\) | 2.27144 | 0.318065 | ||||||||
\(52\) | −4.50402 | −0.624595 | ||||||||
\(53\) | 6.66269 | 0.915191 | 0.457595 | − | 0.889161i | \(-0.348711\pi\) | ||||
0.457595 | + | 0.889161i | \(0.348711\pi\) | |||||||
\(54\) | −11.6284 | −1.58242 | ||||||||
\(55\) | −9.02968 | −1.21756 | ||||||||
\(56\) | 13.4392 | 1.79589 | ||||||||
\(57\) | −0.799829 | −0.105940 | ||||||||
\(58\) | −4.23547 | −0.556145 | ||||||||
\(59\) | 11.7356 | 1.52784 | 0.763921 | − | 0.645310i | \(-0.223272\pi\) | ||||
0.763921 | + | 0.645310i | \(0.223272\pi\) | |||||||
\(60\) | −10.5258 | −1.35888 | ||||||||
\(61\) | −1.48915 | −0.190667 | −0.0953334 | − | 0.995445i | \(-0.530392\pi\) | ||||
−0.0953334 | + | 0.995445i | \(0.530392\pi\) | |||||||
\(62\) | 16.0249 | 2.03517 | ||||||||
\(63\) | 3.48431 | 0.438982 | ||||||||
\(64\) | 25.4938 | 3.18673 | ||||||||
\(65\) | −2.06586 | −0.256238 | ||||||||
\(66\) | −7.97306 | −0.981416 | ||||||||
\(67\) | 7.67269 | 0.937368 | 0.468684 | − | 0.883366i | \(-0.344728\pi\) | ||||
0.468684 | + | 0.883366i | \(0.344728\pi\) | |||||||
\(68\) | −15.2119 | −1.84471 | ||||||||
\(69\) | −1.00938 | −0.121515 | ||||||||
\(70\) | 9.83714 | 1.17576 | ||||||||
\(71\) | 13.8293 | 1.64123 | 0.820616 | − | 0.571480i | \(-0.193631\pi\) | ||||
0.820616 | + | 0.571480i | \(0.193631\pi\) | |||||||
\(72\) | 21.4872 | 2.53230 | ||||||||
\(73\) | 6.37179 | 0.745762 | 0.372881 | − | 0.927879i | \(-0.378370\pi\) | ||||
0.372881 | + | 0.927879i | \(0.378370\pi\) | |||||||
\(74\) | 25.2275 | 2.93264 | ||||||||
\(75\) | −0.828725 | −0.0956929 | ||||||||
\(76\) | 5.35647 | 0.614430 | ||||||||
\(77\) | 5.42561 | 0.618305 | ||||||||
\(78\) | −1.82412 | −0.206541 | ||||||||
\(79\) | −1.59842 | −0.179836 | −0.0899182 | − | 0.995949i | \(-0.528661\pi\) | ||||
−0.0899182 | + | 0.995949i | \(0.528661\pi\) | |||||||
\(80\) | 34.3440 | 3.83978 | ||||||||
\(81\) | 3.65172 | 0.405746 | ||||||||
\(82\) | −16.2681 | −1.79651 | ||||||||
\(83\) | 6.54855 | 0.718797 | 0.359399 | − | 0.933184i | \(-0.382982\pi\) | ||||
0.359399 | + | 0.933184i | \(0.382982\pi\) | |||||||
\(84\) | 6.32457 | 0.690067 | ||||||||
\(85\) | −6.97724 | −0.756788 | ||||||||
\(86\) | 24.8202 | 2.67643 | ||||||||
\(87\) | −1.24900 | −0.133907 | ||||||||
\(88\) | 33.4589 | 3.56673 | ||||||||
\(89\) | −12.9084 | −1.36829 | −0.684146 | − | 0.729345i | \(-0.739825\pi\) | ||||
−0.684146 | + | 0.729345i | \(0.739825\pi\) | |||||||
\(90\) | 15.7281 | 1.65789 | ||||||||
\(91\) | 1.24130 | 0.130123 | ||||||||
\(92\) | 6.75982 | 0.704760 | ||||||||
\(93\) | 4.72562 | 0.490024 | ||||||||
\(94\) | 25.2812 | 2.60756 | ||||||||
\(95\) | 2.45685 | 0.252068 | ||||||||
\(96\) | 15.7624 | 1.60874 | ||||||||
\(97\) | −12.3544 | −1.25440 | −0.627198 | − | 0.778859i | \(-0.715799\pi\) | ||||
−0.627198 | + | 0.778859i | \(0.715799\pi\) | |||||||
\(98\) | 13.0752 | 1.32079 | ||||||||
\(99\) | 8.67473 | 0.871843 | ||||||||
\(100\) | 5.54999 | 0.554999 | ||||||||
\(101\) | −10.5379 | −1.04856 | −0.524279 | − | 0.851547i | \(-0.675665\pi\) | ||||
−0.524279 | + | 0.851547i | \(0.675665\pi\) | |||||||
\(102\) | −6.16079 | −0.610009 | ||||||||
\(103\) | −10.5142 | −1.03599 | −0.517995 | − | 0.855383i | \(-0.673322\pi\) | ||||
−0.517995 | + | 0.855383i | \(0.673322\pi\) | |||||||
\(104\) | 7.65490 | 0.750624 | ||||||||
\(105\) | 2.90089 | 0.283098 | ||||||||
\(106\) | −18.0711 | −1.75522 | ||||||||
\(107\) | 9.67234 | 0.935060 | 0.467530 | − | 0.883977i | \(-0.345144\pi\) | ||||
0.467530 | + | 0.883977i | \(0.345144\pi\) | |||||||
\(108\) | 22.9648 | 2.20979 | ||||||||
\(109\) | 6.15033 | 0.589095 | 0.294547 | − | 0.955637i | \(-0.404831\pi\) | ||||
0.294547 | + | 0.955637i | \(0.404831\pi\) | |||||||
\(110\) | 24.4911 | 2.33513 | ||||||||
\(111\) | 7.43937 | 0.706114 | ||||||||
\(112\) | −20.6361 | −1.94992 | ||||||||
\(113\) | −3.07916 | −0.289663 | −0.144832 | − | 0.989456i | \(-0.546264\pi\) | ||||
−0.144832 | + | 0.989456i | \(0.546264\pi\) | |||||||
\(114\) | 2.16936 | 0.203179 | ||||||||
\(115\) | 3.10053 | 0.289125 | ||||||||
\(116\) | 8.36462 | 0.776635 | ||||||||
\(117\) | 1.98465 | 0.183481 | ||||||||
\(118\) | −31.8302 | −2.93021 | ||||||||
\(119\) | 4.19237 | 0.384314 | ||||||||
\(120\) | 17.8893 | 1.63307 | ||||||||
\(121\) | 2.50786 | 0.227988 | ||||||||
\(122\) | 4.03901 | 0.365675 | ||||||||
\(123\) | −4.79731 | −0.432559 | ||||||||
\(124\) | −31.6476 | −2.84204 | ||||||||
\(125\) | −9.73865 | −0.871051 | ||||||||
\(126\) | −9.45044 | −0.841912 | ||||||||
\(127\) | 12.3594 | 1.09672 | 0.548362 | − | 0.836241i | \(-0.315252\pi\) | ||||
0.548362 | + | 0.836241i | \(0.315252\pi\) | |||||||
\(128\) | −29.7320 | −2.62796 | ||||||||
\(129\) | 7.31926 | 0.644425 | ||||||||
\(130\) | 5.60319 | 0.491432 | ||||||||
\(131\) | 6.51070 | 0.568842 | 0.284421 | − | 0.958699i | \(-0.408199\pi\) | ||||
0.284421 | + | 0.958699i | \(0.408199\pi\) | |||||||
\(132\) | 15.7460 | 1.37051 | ||||||||
\(133\) | −1.47623 | −0.128006 | ||||||||
\(134\) | −20.8105 | −1.79775 | ||||||||
\(135\) | 10.5333 | 0.906559 | ||||||||
\(136\) | 25.8537 | 2.21694 | ||||||||
\(137\) | −17.9528 | −1.53381 | −0.766906 | − | 0.641759i | \(-0.778205\pi\) | ||||
−0.766906 | + | 0.641759i | \(0.778205\pi\) | |||||||
\(138\) | 2.73771 | 0.233050 | ||||||||
\(139\) | 15.1380 | 1.28399 | 0.641996 | − | 0.766708i | \(-0.278106\pi\) | ||||
0.641996 | + | 0.766708i | \(0.278106\pi\) | |||||||
\(140\) | −19.4273 | −1.64191 | ||||||||
\(141\) | 7.45522 | 0.627842 | ||||||||
\(142\) | −37.5089 | −3.14767 | ||||||||
\(143\) | 3.09040 | 0.258432 | ||||||||
\(144\) | −32.9940 | −2.74950 | ||||||||
\(145\) | 3.83660 | 0.318612 | ||||||||
\(146\) | −17.2821 | −1.43028 | ||||||||
\(147\) | 3.85576 | 0.318018 | ||||||||
\(148\) | −49.8217 | −4.09532 | ||||||||
\(149\) | 10.1271 | 0.829641 | 0.414820 | − | 0.909903i | \(-0.363844\pi\) | ||||
0.414820 | + | 0.909903i | \(0.363844\pi\) | |||||||
\(150\) | 2.24774 | 0.183527 | ||||||||
\(151\) | 19.6867 | 1.60208 | 0.801039 | − | 0.598612i | \(-0.204281\pi\) | ||||
0.801039 | + | 0.598612i | \(0.204281\pi\) | |||||||
\(152\) | −9.10370 | −0.738408 | ||||||||
\(153\) | 6.70297 | 0.541903 | ||||||||
\(154\) | −14.7158 | −1.18583 | ||||||||
\(155\) | −14.5158 | −1.16594 | ||||||||
\(156\) | 3.60244 | 0.288426 | ||||||||
\(157\) | 15.7539 | 1.25729 | 0.628647 | − | 0.777690i | \(-0.283609\pi\) | ||||
0.628647 | + | 0.777690i | \(0.283609\pi\) | |||||||
\(158\) | 4.33537 | 0.344903 | ||||||||
\(159\) | −5.32901 | −0.422618 | ||||||||
\(160\) | −48.4178 | −3.82776 | ||||||||
\(161\) | −1.86299 | −0.146824 | ||||||||
\(162\) | −9.90449 | −0.778170 | ||||||||
\(163\) | 1.98798 | 0.155711 | 0.0778554 | − | 0.996965i | \(-0.475193\pi\) | ||||
0.0778554 | + | 0.996965i | \(0.475193\pi\) | |||||||
\(164\) | 32.1277 | 2.50875 | ||||||||
\(165\) | 7.22220 | 0.562247 | ||||||||
\(166\) | −17.7615 | −1.37856 | ||||||||
\(167\) | 4.97328 | 0.384844 | 0.192422 | − | 0.981312i | \(-0.438366\pi\) | ||||
0.192422 | + | 0.981312i | \(0.438366\pi\) | |||||||
\(168\) | −10.7490 | −0.829307 | ||||||||
\(169\) | −12.2930 | −0.945613 | ||||||||
\(170\) | 18.9242 | 1.45142 | ||||||||
\(171\) | −2.36027 | −0.180495 | ||||||||
\(172\) | −49.0173 | −3.73753 | ||||||||
\(173\) | 14.4357 | 1.09752 | 0.548762 | − | 0.835979i | \(-0.315099\pi\) | ||||
0.548762 | + | 0.835979i | \(0.315099\pi\) | |||||||
\(174\) | 3.38765 | 0.256817 | ||||||||
\(175\) | −1.52957 | −0.115624 | ||||||||
\(176\) | −51.3766 | −3.87266 | ||||||||
\(177\) | −9.38644 | −0.705528 | ||||||||
\(178\) | 35.0113 | 2.62421 | ||||||||
\(179\) | 14.3611 | 1.07340 | 0.536701 | − | 0.843773i | \(-0.319670\pi\) | ||||
0.536701 | + | 0.843773i | \(0.319670\pi\) | |||||||
\(180\) | −31.0614 | −2.31518 | ||||||||
\(181\) | −14.9618 | −1.11210 | −0.556050 | − | 0.831149i | \(-0.687684\pi\) | ||||
−0.556050 | + | 0.831149i | \(0.687684\pi\) | |||||||
\(182\) | −3.36675 | −0.249560 | ||||||||
\(183\) | 1.19107 | 0.0880463 | ||||||||
\(184\) | −11.4888 | −0.846965 | ||||||||
\(185\) | −22.8517 | −1.68009 | ||||||||
\(186\) | −12.8172 | −0.939804 | ||||||||
\(187\) | 10.4375 | 0.763268 | ||||||||
\(188\) | −49.9278 | −3.64136 | ||||||||
\(189\) | −6.32905 | −0.460371 | ||||||||
\(190\) | −6.66368 | −0.483434 | ||||||||
\(191\) | 22.9058 | 1.65740 | 0.828702 | − | 0.559690i | \(-0.189080\pi\) | ||||
0.828702 | + | 0.559690i | \(0.189080\pi\) | |||||||
\(192\) | −20.3907 | −1.47157 | ||||||||
\(193\) | 9.77008 | 0.703266 | 0.351633 | − | 0.936138i | \(-0.385627\pi\) | ||||
0.351633 | + | 0.936138i | \(0.385627\pi\) | |||||||
\(194\) | 33.5086 | 2.40577 | ||||||||
\(195\) | 1.65233 | 0.118326 | ||||||||
\(196\) | −25.8221 | −1.84444 | ||||||||
\(197\) | 3.30108 | 0.235192 | 0.117596 | − | 0.993062i | \(-0.462481\pi\) | ||||
0.117596 | + | 0.993062i | \(0.462481\pi\) | |||||||
\(198\) | −23.5283 | −1.67208 | ||||||||
\(199\) | 4.77708 | 0.338638 | 0.169319 | − | 0.985561i | \(-0.445843\pi\) | ||||
0.169319 | + | 0.985561i | \(0.445843\pi\) | |||||||
\(200\) | −9.43260 | −0.666986 | ||||||||
\(201\) | −6.13684 | −0.432859 | ||||||||
\(202\) | 28.5817 | 2.01100 | ||||||||
\(203\) | −2.30527 | −0.161798 | ||||||||
\(204\) | 12.1669 | 0.851854 | ||||||||
\(205\) | 14.7360 | 1.02921 | ||||||||
\(206\) | 28.5174 | 1.98690 | ||||||||
\(207\) | −2.97864 | −0.207030 | ||||||||
\(208\) | −11.7542 | −0.815007 | ||||||||
\(209\) | −3.67530 | −0.254226 | ||||||||
\(210\) | −7.86803 | −0.542946 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | 35.6885 | 2.45110 | ||||||||
\(213\) | −11.0610 | −0.757890 | ||||||||
\(214\) | −26.2341 | −1.79333 | ||||||||
\(215\) | −22.4827 | −1.53331 | ||||||||
\(216\) | −39.0303 | −2.65568 | ||||||||
\(217\) | 8.72201 | 0.592089 | ||||||||
\(218\) | −16.6814 | −1.12981 | ||||||||
\(219\) | −5.09634 | −0.344379 | ||||||||
\(220\) | −48.3673 | −3.26092 | ||||||||
\(221\) | 2.38795 | 0.160631 | ||||||||
\(222\) | −20.1777 | −1.35424 | ||||||||
\(223\) | −1.56503 | −0.104802 | −0.0524012 | − | 0.998626i | \(-0.516687\pi\) | ||||
−0.0524012 | + | 0.998626i | \(0.516687\pi\) | |||||||
\(224\) | 29.0924 | 1.94382 | ||||||||
\(225\) | −2.44555 | −0.163036 | ||||||||
\(226\) | 8.35156 | 0.555537 | ||||||||
\(227\) | −25.5881 | −1.69834 | −0.849171 | − | 0.528118i | \(-0.822898\pi\) | ||||
−0.849171 | + | 0.528118i | \(0.822898\pi\) | |||||||
\(228\) | −4.28426 | −0.283732 | ||||||||
\(229\) | 10.2025 | 0.674200 | 0.337100 | − | 0.941469i | \(-0.390554\pi\) | ||||
0.337100 | + | 0.941469i | \(0.390554\pi\) | |||||||
\(230\) | −8.40950 | −0.554506 | ||||||||
\(231\) | −4.33955 | −0.285522 | ||||||||
\(232\) | −14.2163 | −0.933343 | ||||||||
\(233\) | 2.03950 | 0.133612 | 0.0668060 | − | 0.997766i | \(-0.478719\pi\) | ||||
0.0668060 | + | 0.997766i | \(0.478719\pi\) | |||||||
\(234\) | −5.38293 | −0.351893 | ||||||||
\(235\) | −22.9004 | −1.49386 | ||||||||
\(236\) | 62.8613 | 4.09192 | ||||||||
\(237\) | 1.27846 | 0.0830451 | ||||||||
\(238\) | −11.3709 | −0.737065 | ||||||||
\(239\) | 14.6027 | 0.944567 | 0.472284 | − | 0.881447i | \(-0.343430\pi\) | ||||
0.472284 | + | 0.881447i | \(0.343430\pi\) | |||||||
\(240\) | −27.4693 | −1.77314 | ||||||||
\(241\) | 10.4529 | 0.673329 | 0.336665 | − | 0.941625i | \(-0.390701\pi\) | ||||
0.336665 | + | 0.941625i | \(0.390701\pi\) | |||||||
\(242\) | −6.80203 | −0.437251 | ||||||||
\(243\) | −15.7826 | −1.01246 | ||||||||
\(244\) | −7.97662 | −0.510651 | ||||||||
\(245\) | −11.8438 | −0.756675 | ||||||||
\(246\) | 13.0117 | 0.829593 | ||||||||
\(247\) | −0.840855 | −0.0535023 | ||||||||
\(248\) | 53.7873 | 3.41550 | ||||||||
\(249\) | −5.23772 | −0.331927 | ||||||||
\(250\) | 26.4140 | 1.67057 | ||||||||
\(251\) | −1.05763 | −0.0667570 | −0.0333785 | − | 0.999443i | \(-0.510627\pi\) | ||||
−0.0333785 | + | 0.999443i | \(0.510627\pi\) | |||||||
\(252\) | 18.6636 | 1.17570 | ||||||||
\(253\) | −4.63820 | −0.291601 | ||||||||
\(254\) | −33.5223 | −2.10338 | ||||||||
\(255\) | 5.58060 | 0.349471 | ||||||||
\(256\) | 29.6538 | 1.85336 | ||||||||
\(257\) | −22.3386 | −1.39344 | −0.696721 | − | 0.717342i | \(-0.745359\pi\) | ||||
−0.696721 | + | 0.717342i | \(0.745359\pi\) | |||||||
\(258\) | −19.8519 | −1.23592 | ||||||||
\(259\) | 13.7308 | 0.853187 | ||||||||
\(260\) | −11.0657 | −0.686266 | ||||||||
\(261\) | −3.68578 | −0.228144 | ||||||||
\(262\) | −17.6589 | −1.09097 | ||||||||
\(263\) | −9.96838 | −0.614676 | −0.307338 | − | 0.951600i | \(-0.599438\pi\) | ||||
−0.307338 | + | 0.951600i | \(0.599438\pi\) | |||||||
\(264\) | −26.7614 | −1.64705 | ||||||||
\(265\) | 16.3692 | 1.00555 | ||||||||
\(266\) | 4.00396 | 0.245499 | ||||||||
\(267\) | 10.3245 | 0.631852 | ||||||||
\(268\) | 41.0986 | 2.51049 | ||||||||
\(269\) | 2.48959 | 0.151793 | 0.0758966 | − | 0.997116i | \(-0.475818\pi\) | ||||
0.0758966 | + | 0.997116i | \(0.475818\pi\) | |||||||
\(270\) | −28.5692 | −1.73867 | ||||||||
\(271\) | −17.6039 | −1.06936 | −0.534680 | − | 0.845054i | \(-0.679568\pi\) | ||||
−0.534680 | + | 0.845054i | \(0.679568\pi\) | |||||||
\(272\) | −39.6987 | −2.40709 | ||||||||
\(273\) | −0.992826 | −0.0600885 | ||||||||
\(274\) | 48.6931 | 2.94166 | ||||||||
\(275\) | −3.80809 | −0.229636 | ||||||||
\(276\) | −5.40670 | −0.325445 | ||||||||
\(277\) | −29.7323 | −1.78644 | −0.893220 | − | 0.449620i | \(-0.851560\pi\) | ||||
−0.893220 | + | 0.449620i | \(0.851560\pi\) | |||||||
\(278\) | −41.0587 | −2.46253 | ||||||||
\(279\) | 13.9452 | 0.834876 | ||||||||
\(280\) | 33.0181 | 1.97321 | ||||||||
\(281\) | 24.9925 | 1.49092 | 0.745462 | − | 0.666548i | \(-0.232229\pi\) | ||||
0.745462 | + | 0.666548i | \(0.232229\pi\) | |||||||
\(282\) | −20.2206 | −1.20412 | ||||||||
\(283\) | −10.8391 | −0.644319 | −0.322160 | − | 0.946685i | \(-0.604409\pi\) | ||||
−0.322160 | + | 0.946685i | \(0.604409\pi\) | |||||||
\(284\) | 74.0761 | 4.39561 | ||||||||
\(285\) | −1.96506 | −0.116400 | ||||||||
\(286\) | −8.38203 | −0.495640 | ||||||||
\(287\) | −8.85433 | −0.522654 | ||||||||
\(288\) | 46.5144 | 2.74089 | ||||||||
\(289\) | −8.93491 | −0.525583 | ||||||||
\(290\) | −10.4059 | −0.611058 | ||||||||
\(291\) | 9.88138 | 0.579257 | ||||||||
\(292\) | 34.1304 | 1.99733 | ||||||||
\(293\) | 12.5011 | 0.730321 | 0.365161 | − | 0.930945i | \(-0.381014\pi\) | ||||
0.365161 | + | 0.930945i | \(0.381014\pi\) | |||||||
\(294\) | −10.4579 | −0.609918 | ||||||||
\(295\) | 28.8326 | 1.67870 | ||||||||
\(296\) | 84.6755 | 4.92166 | ||||||||
\(297\) | −15.7571 | −0.914322 | ||||||||
\(298\) | −27.4674 | −1.59115 | ||||||||
\(299\) | −1.06115 | −0.0613679 | ||||||||
\(300\) | −4.43904 | −0.256288 | ||||||||
\(301\) | 13.5091 | 0.778649 | ||||||||
\(302\) | −53.3958 | −3.07258 | ||||||||
\(303\) | 8.42850 | 0.484204 | ||||||||
\(304\) | 13.9789 | 0.801743 | ||||||||
\(305\) | −3.65863 | −0.209493 | ||||||||
\(306\) | −18.1803 | −1.03930 | ||||||||
\(307\) | −5.90705 | −0.337133 | −0.168567 | − | 0.985690i | \(-0.553914\pi\) | ||||
−0.168567 | + | 0.985690i | \(0.553914\pi\) | |||||||
\(308\) | 29.0621 | 1.65597 | ||||||||
\(309\) | 8.40952 | 0.478401 | ||||||||
\(310\) | 39.3709 | 2.23612 | ||||||||
\(311\) | −7.38585 | −0.418813 | −0.209406 | − | 0.977829i | \(-0.567153\pi\) | ||||
−0.209406 | + | 0.977829i | \(0.567153\pi\) | |||||||
\(312\) | −6.12260 | −0.346624 | ||||||||
\(313\) | 9.50913 | 0.537488 | 0.268744 | − | 0.963212i | \(-0.413391\pi\) | ||||
0.268744 | + | 0.963212i | \(0.413391\pi\) | |||||||
\(314\) | −42.7289 | −2.41133 | ||||||||
\(315\) | 8.56045 | 0.482327 | ||||||||
\(316\) | −8.56190 | −0.481644 | ||||||||
\(317\) | 22.6673 | 1.27312 | 0.636562 | − | 0.771225i | \(-0.280356\pi\) | ||||
0.636562 | + | 0.771225i | \(0.280356\pi\) | |||||||
\(318\) | 14.4538 | 0.810527 | ||||||||
\(319\) | −5.73932 | −0.321340 | ||||||||
\(320\) | 62.6345 | 3.50138 | ||||||||
\(321\) | −7.73621 | −0.431793 | ||||||||
\(322\) | 5.05296 | 0.281590 | ||||||||
\(323\) | −2.83991 | −0.158017 | ||||||||
\(324\) | 19.5603 | 1.08668 | ||||||||
\(325\) | −0.871234 | −0.0483273 | ||||||||
\(326\) | −5.39197 | −0.298633 | ||||||||
\(327\) | −4.91921 | −0.272033 | ||||||||
\(328\) | −54.6033 | −3.01496 | ||||||||
\(329\) | 13.7600 | 0.758613 | ||||||||
\(330\) | −19.5886 | −1.07832 | ||||||||
\(331\) | 4.83227 | 0.265605 | 0.132803 | − | 0.991142i | \(-0.457602\pi\) | ||||
0.132803 | + | 0.991142i | \(0.457602\pi\) | |||||||
\(332\) | 35.0772 | 1.92511 | ||||||||
\(333\) | 21.9534 | 1.20304 | ||||||||
\(334\) | −13.4889 | −0.738082 | ||||||||
\(335\) | 18.8507 | 1.02992 | ||||||||
\(336\) | 16.5053 | 0.900439 | ||||||||
\(337\) | −14.7426 | −0.803082 | −0.401541 | − | 0.915841i | \(-0.631525\pi\) | ||||
−0.401541 | + | 0.915841i | \(0.631525\pi\) | |||||||
\(338\) | 33.3420 | 1.81356 | ||||||||
\(339\) | 2.46280 | 0.133761 | ||||||||
\(340\) | −37.3734 | −2.02686 | ||||||||
\(341\) | 21.7148 | 1.17592 | ||||||||
\(342\) | 6.40173 | 0.346166 | ||||||||
\(343\) | 17.4502 | 0.942220 | ||||||||
\(344\) | 83.3083 | 4.49168 | ||||||||
\(345\) | −2.47989 | −0.133513 | ||||||||
\(346\) | −39.1536 | −2.10491 | ||||||||
\(347\) | 26.6494 | 1.43062 | 0.715308 | − | 0.698810i | \(-0.246287\pi\) | ||||
0.715308 | + | 0.698810i | \(0.246287\pi\) | |||||||
\(348\) | −6.69026 | −0.358636 | ||||||||
\(349\) | 11.3757 | 0.608930 | 0.304465 | − | 0.952524i | \(-0.401522\pi\) | ||||
0.304465 | + | 0.952524i | \(0.401522\pi\) | |||||||
\(350\) | 4.14862 | 0.221753 | ||||||||
\(351\) | −3.60500 | −0.192421 | ||||||||
\(352\) | 72.4300 | 3.86053 | ||||||||
\(353\) | −12.1480 | −0.646571 | −0.323286 | − | 0.946301i | \(-0.604787\pi\) | ||||
−0.323286 | + | 0.946301i | \(0.604787\pi\) | |||||||
\(354\) | 25.4587 | 1.35311 | ||||||||
\(355\) | 33.9765 | 1.80328 | ||||||||
\(356\) | −69.1437 | −3.66461 | ||||||||
\(357\) | −3.35318 | −0.177469 | ||||||||
\(358\) | −38.9514 | −2.05865 | ||||||||
\(359\) | −17.9251 | −0.946049 | −0.473025 | − | 0.881049i | \(-0.656838\pi\) | ||||
−0.473025 | + | 0.881049i | \(0.656838\pi\) | |||||||
\(360\) | 52.7910 | 2.78233 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 40.5806 | 2.13287 | ||||||||
\(363\) | −2.00586 | −0.105280 | ||||||||
\(364\) | 6.64898 | 0.348501 | ||||||||
\(365\) | 15.6546 | 0.819397 | ||||||||
\(366\) | −3.23051 | −0.168862 | ||||||||
\(367\) | 0.144009 | 0.00751719 | 0.00375860 | − | 0.999993i | \(-0.498804\pi\) | ||||
0.00375860 | + | 0.999993i | \(0.498804\pi\) | |||||||
\(368\) | 17.6412 | 0.919611 | ||||||||
\(369\) | −14.1567 | −0.736970 | ||||||||
\(370\) | 61.9803 | 3.22220 | ||||||||
\(371\) | −9.83568 | −0.510643 | ||||||||
\(372\) | 25.3127 | 1.31240 | ||||||||
\(373\) | 9.72792 | 0.503693 | 0.251846 | − | 0.967767i | \(-0.418962\pi\) | ||||
0.251846 | + | 0.967767i | \(0.418962\pi\) | |||||||
\(374\) | −28.3095 | −1.46385 | ||||||||
\(375\) | 7.78925 | 0.402235 | ||||||||
\(376\) | 84.8558 | 4.37610 | ||||||||
\(377\) | −1.31307 | −0.0676266 | ||||||||
\(378\) | 17.1662 | 0.882933 | ||||||||
\(379\) | −25.2656 | −1.29781 | −0.648903 | − | 0.760871i | \(-0.724772\pi\) | ||||
−0.648903 | + | 0.760871i | \(0.724772\pi\) | |||||||
\(380\) | 13.1601 | 0.675097 | ||||||||
\(381\) | −9.88544 | −0.506446 | ||||||||
\(382\) | −62.1269 | −3.17869 | ||||||||
\(383\) | 20.0775 | 1.02591 | 0.512957 | − | 0.858414i | \(-0.328550\pi\) | ||||
0.512957 | + | 0.858414i | \(0.328550\pi\) | |||||||
\(384\) | 23.7805 | 1.21354 | ||||||||
\(385\) | 13.3299 | 0.679356 | ||||||||
\(386\) | −26.4992 | −1.34877 | ||||||||
\(387\) | 21.5989 | 1.09794 | ||||||||
\(388\) | −66.1759 | −3.35957 | ||||||||
\(389\) | 4.75914 | 0.241298 | 0.120649 | − | 0.992695i | \(-0.461502\pi\) | ||||
0.120649 | + | 0.992695i | \(0.461502\pi\) | |||||||
\(390\) | −4.48159 | −0.226934 | ||||||||
\(391\) | −3.58394 | −0.181248 | ||||||||
\(392\) | 43.8866 | 2.21661 | ||||||||
\(393\) | −5.20744 | −0.262681 | ||||||||
\(394\) | −8.95345 | −0.451069 | ||||||||
\(395\) | −3.92708 | −0.197593 | ||||||||
\(396\) | 46.4659 | 2.33500 | ||||||||
\(397\) | −21.0468 | −1.05631 | −0.528153 | − | 0.849149i | \(-0.677115\pi\) | ||||
−0.528153 | + | 0.849149i | \(0.677115\pi\) | |||||||
\(398\) | −12.9568 | −0.649465 | ||||||||
\(399\) | 1.18073 | 0.0591106 | ||||||||
\(400\) | 14.4839 | 0.724195 | ||||||||
\(401\) | 25.1820 | 1.25753 | 0.628763 | − | 0.777597i | \(-0.283561\pi\) | ||||
0.628763 | + | 0.777597i | \(0.283561\pi\) | |||||||
\(402\) | 16.6448 | 0.830169 | ||||||||
\(403\) | 4.96802 | 0.247474 | ||||||||
\(404\) | −56.4459 | −2.80829 | ||||||||
\(405\) | 8.97173 | 0.445809 | ||||||||
\(406\) | 6.25255 | 0.310309 | ||||||||
\(407\) | 34.1848 | 1.69448 | ||||||||
\(408\) | −20.6785 | −1.02374 | ||||||||
\(409\) | 19.8929 | 0.983639 | 0.491820 | − | 0.870697i | \(-0.336332\pi\) | ||||
0.491820 | + | 0.870697i | \(0.336332\pi\) | |||||||
\(410\) | −39.9682 | −1.97389 | ||||||||
\(411\) | 14.3592 | 0.708286 | ||||||||
\(412\) | −56.3188 | −2.77463 | ||||||||
\(413\) | −17.3244 | −0.852480 | ||||||||
\(414\) | 8.07892 | 0.397057 | ||||||||
\(415\) | 16.0888 | 0.789770 | ||||||||
\(416\) | 16.5709 | 0.812456 | ||||||||
\(417\) | −12.1078 | −0.592924 | ||||||||
\(418\) | 9.96846 | 0.487573 | ||||||||
\(419\) | −7.81583 | −0.381828 | −0.190914 | − | 0.981607i | \(-0.561145\pi\) | ||||
−0.190914 | + | 0.981607i | \(0.561145\pi\) | |||||||
\(420\) | 15.5385 | 0.758203 | ||||||||
\(421\) | 15.1876 | 0.740199 | 0.370100 | − | 0.928992i | \(-0.379324\pi\) | ||||
0.370100 | + | 0.928992i | \(0.379324\pi\) | |||||||
\(422\) | 2.71228 | 0.132032 | ||||||||
\(423\) | 22.0002 | 1.06968 | ||||||||
\(424\) | −60.6551 | −2.94567 | ||||||||
\(425\) | −2.94251 | −0.142733 | ||||||||
\(426\) | 30.0007 | 1.45354 | ||||||||
\(427\) | 2.19834 | 0.106385 | ||||||||
\(428\) | 51.8096 | 2.50431 | ||||||||
\(429\) | −2.47179 | −0.119339 | ||||||||
\(430\) | 60.9795 | 2.94069 | ||||||||
\(431\) | −10.0020 | −0.481778 | −0.240889 | − | 0.970553i | \(-0.577439\pi\) | ||||
−0.240889 | + | 0.970553i | \(0.577439\pi\) | |||||||
\(432\) | 59.9316 | 2.88346 | ||||||||
\(433\) | 6.48340 | 0.311572 | 0.155786 | − | 0.987791i | \(-0.450209\pi\) | ||||
0.155786 | + | 0.987791i | \(0.450209\pi\) | |||||||
\(434\) | −23.6566 | −1.13555 | ||||||||
\(435\) | −3.06862 | −0.147129 | ||||||||
\(436\) | 32.9441 | 1.57774 | ||||||||
\(437\) | 1.26199 | 0.0603692 | ||||||||
\(438\) | 13.8227 | 0.660475 | ||||||||
\(439\) | 8.62375 | 0.411589 | 0.205795 | − | 0.978595i | \(-0.434022\pi\) | ||||
0.205795 | + | 0.978595i | \(0.434022\pi\) | |||||||
\(440\) | 82.2036 | 3.91890 | ||||||||
\(441\) | 11.3783 | 0.541822 | ||||||||
\(442\) | −6.47680 | −0.308070 | ||||||||
\(443\) | 5.30205 | 0.251908 | 0.125954 | − | 0.992036i | \(-0.459801\pi\) | ||||
0.125954 | + | 0.992036i | \(0.459801\pi\) | |||||||
\(444\) | 39.8488 | 1.89114 | ||||||||
\(445\) | −31.7141 | −1.50339 | ||||||||
\(446\) | 4.24481 | 0.200998 | ||||||||
\(447\) | −8.09991 | −0.383112 | ||||||||
\(448\) | −37.6348 | −1.77808 | ||||||||
\(449\) | −9.04103 | −0.426672 | −0.213336 | − | 0.976979i | \(-0.568433\pi\) | ||||
−0.213336 | + | 0.976979i | \(0.568433\pi\) | |||||||
\(450\) | 6.63301 | 0.312683 | ||||||||
\(451\) | −22.0442 | −1.03802 | ||||||||
\(452\) | −16.4935 | −0.775787 | ||||||||
\(453\) | −15.7460 | −0.739810 | ||||||||
\(454\) | 69.4021 | 3.25720 | ||||||||
\(455\) | 3.04969 | 0.142972 | ||||||||
\(456\) | 7.28140 | 0.340983 | ||||||||
\(457\) | 12.7837 | 0.597998 | 0.298999 | − | 0.954253i | \(-0.403347\pi\) | ||||
0.298999 | + | 0.954253i | \(0.403347\pi\) | |||||||
\(458\) | −27.6721 | −1.29303 | ||||||||
\(459\) | −12.1755 | −0.568306 | ||||||||
\(460\) | 16.6079 | 0.774347 | ||||||||
\(461\) | 11.1578 | 0.519671 | 0.259836 | − | 0.965653i | \(-0.416332\pi\) | ||||
0.259836 | + | 0.965653i | \(0.416332\pi\) | |||||||
\(462\) | 11.7701 | 0.547594 | ||||||||
\(463\) | −40.5434 | −1.88421 | −0.942106 | − | 0.335316i | \(-0.891157\pi\) | ||||
−0.942106 | + | 0.335316i | \(0.891157\pi\) | |||||||
\(464\) | 21.8293 | 1.01340 | ||||||||
\(465\) | 11.6102 | 0.538408 | ||||||||
\(466\) | −5.53170 | −0.256251 | ||||||||
\(467\) | 30.3092 | 1.40254 | 0.701271 | − | 0.712895i | \(-0.252616\pi\) | ||||
0.701271 | + | 0.712895i | \(0.252616\pi\) | |||||||
\(468\) | 10.6307 | 0.491405 | ||||||||
\(469\) | −11.3267 | −0.523017 | ||||||||
\(470\) | 62.1123 | 2.86503 | ||||||||
\(471\) | −12.6004 | −0.580595 | ||||||||
\(472\) | −106.837 | −4.91758 | ||||||||
\(473\) | 33.6328 | 1.54644 | ||||||||
\(474\) | −3.46755 | −0.159270 | ||||||||
\(475\) | 1.03613 | 0.0475408 | ||||||||
\(476\) | 22.4563 | 1.02928 | ||||||||
\(477\) | −15.7258 | −0.720034 | ||||||||
\(478\) | −39.6065 | −1.81156 | ||||||||
\(479\) | 31.9210 | 1.45851 | 0.729255 | − | 0.684242i | \(-0.239867\pi\) | ||||
0.729255 | + | 0.684242i | \(0.239867\pi\) | |||||||
\(480\) | 38.7259 | 1.76759 | ||||||||
\(481\) | 7.82097 | 0.356605 | ||||||||
\(482\) | −28.3512 | −1.29136 | ||||||||
\(483\) | 1.49007 | 0.0678007 | ||||||||
\(484\) | 13.4333 | 0.610605 | ||||||||
\(485\) | −30.3529 | −1.37825 | ||||||||
\(486\) | 42.8070 | 1.94176 | ||||||||
\(487\) | −32.9994 | −1.49535 | −0.747673 | − | 0.664067i | \(-0.768829\pi\) | ||||
−0.747673 | + | 0.664067i | \(0.768829\pi\) | |||||||
\(488\) | 13.5568 | 0.613689 | ||||||||
\(489\) | −1.59004 | −0.0719043 | ||||||||
\(490\) | 32.1238 | 1.45121 | ||||||||
\(491\) | −15.1884 | −0.685443 | −0.342721 | − | 0.939437i | \(-0.611349\pi\) | ||||
−0.342721 | + | 0.939437i | \(0.611349\pi\) | |||||||
\(492\) | −25.6967 | −1.15849 | ||||||||
\(493\) | −4.43477 | −0.199732 | ||||||||
\(494\) | 2.28064 | 0.102611 | ||||||||
\(495\) | 21.3125 | 0.957927 | ||||||||
\(496\) | −82.5912 | −3.70845 | ||||||||
\(497\) | −20.4152 | −0.915748 | ||||||||
\(498\) | 14.2062 | 0.636594 | ||||||||
\(499\) | 19.5782 | 0.876441 | 0.438221 | − | 0.898867i | \(-0.355609\pi\) | ||||
0.438221 | + | 0.898867i | \(0.355609\pi\) | |||||||
\(500\) | −52.1648 | −2.33288 | ||||||||
\(501\) | −3.97777 | −0.177714 | ||||||||
\(502\) | 2.86859 | 0.128031 | ||||||||
\(503\) | 34.8193 | 1.55252 | 0.776259 | − | 0.630414i | \(-0.217115\pi\) | ||||
0.776259 | + | 0.630414i | \(0.217115\pi\) | |||||||
\(504\) | −31.7202 | −1.41293 | ||||||||
\(505\) | −25.8900 | −1.15209 | ||||||||
\(506\) | 12.5801 | 0.559254 | ||||||||
\(507\) | 9.83226 | 0.436666 | ||||||||
\(508\) | 66.2030 | 2.93728 | ||||||||
\(509\) | −20.5164 | −0.909375 | −0.454688 | − | 0.890651i | \(-0.650249\pi\) | ||||
−0.454688 | + | 0.890651i | \(0.650249\pi\) | |||||||
\(510\) | −15.1362 | −0.670240 | ||||||||
\(511\) | −9.40625 | −0.416108 | ||||||||
\(512\) | −20.9657 | −0.926560 | ||||||||
\(513\) | 4.28730 | 0.189289 | ||||||||
\(514\) | 60.5885 | 2.67245 | ||||||||
\(515\) | −25.8317 | −1.13828 | ||||||||
\(516\) | 39.2054 | 1.72592 | ||||||||
\(517\) | 34.2576 | 1.50665 | ||||||||
\(518\) | −37.2417 | −1.63630 | ||||||||
\(519\) | −11.5461 | −0.506816 | ||||||||
\(520\) | 18.8070 | 0.824740 | ||||||||
\(521\) | 23.5097 | 1.02998 | 0.514990 | − | 0.857196i | \(-0.327796\pi\) | ||||
0.514990 | + | 0.857196i | \(0.327796\pi\) | |||||||
\(522\) | 9.99688 | 0.437551 | ||||||||
\(523\) | 2.74665 | 0.120102 | 0.0600512 | − | 0.998195i | \(-0.480874\pi\) | ||||
0.0600512 | + | 0.998195i | \(0.480874\pi\) | |||||||
\(524\) | 34.8744 | 1.52349 | ||||||||
\(525\) | 1.22339 | 0.0533932 | ||||||||
\(526\) | 27.0370 | 1.17887 | ||||||||
\(527\) | 16.7790 | 0.730905 | ||||||||
\(528\) | 41.0925 | 1.78832 | ||||||||
\(529\) | −21.4074 | −0.930756 | ||||||||
\(530\) | −44.3980 | −1.92853 | ||||||||
\(531\) | −27.6992 | −1.20204 | ||||||||
\(532\) | −7.90740 | −0.342829 | ||||||||
\(533\) | −5.04338 | −0.218453 | ||||||||
\(534\) | −28.0031 | −1.21181 | ||||||||
\(535\) | 23.7635 | 1.02739 | ||||||||
\(536\) | −69.8499 | −3.01706 | ||||||||
\(537\) | −11.4864 | −0.495677 | ||||||||
\(538\) | −6.75248 | −0.291120 | ||||||||
\(539\) | 17.7177 | 0.763154 | ||||||||
\(540\) | 56.4212 | 2.42798 | ||||||||
\(541\) | 39.6647 | 1.70532 | 0.852659 | − | 0.522468i | \(-0.174989\pi\) | ||||
0.852659 | + | 0.522468i | \(0.174989\pi\) | |||||||
\(542\) | 47.7467 | 2.05090 | ||||||||
\(543\) | 11.9669 | 0.513547 | ||||||||
\(544\) | 55.9667 | 2.39955 | ||||||||
\(545\) | 15.1105 | 0.647261 | ||||||||
\(546\) | 2.69282 | 0.115242 | ||||||||
\(547\) | 21.0644 | 0.900649 | 0.450325 | − | 0.892865i | \(-0.351308\pi\) | ||||
0.450325 | + | 0.892865i | \(0.351308\pi\) | |||||||
\(548\) | −96.1638 | −4.10791 | ||||||||
\(549\) | 3.51481 | 0.150009 | ||||||||
\(550\) | 10.3286 | 0.440413 | ||||||||
\(551\) | 1.56159 | 0.0665260 | ||||||||
\(552\) | 9.18906 | 0.391112 | ||||||||
\(553\) | 2.35964 | 0.100342 | ||||||||
\(554\) | 80.6424 | 3.42617 | ||||||||
\(555\) | 18.2774 | 0.775834 | ||||||||
\(556\) | 81.0866 | 3.43884 | ||||||||
\(557\) | 17.0092 | 0.720704 | 0.360352 | − | 0.932816i | \(-0.382657\pi\) | ||||
0.360352 | + | 0.932816i | \(0.382657\pi\) | |||||||
\(558\) | −37.8233 | −1.60119 | ||||||||
\(559\) | 7.69469 | 0.325451 | ||||||||
\(560\) | −50.6998 | −2.14246 | ||||||||
\(561\) | −8.34824 | −0.352463 | ||||||||
\(562\) | −67.7866 | −2.85940 | ||||||||
\(563\) | 20.8209 | 0.877497 | 0.438748 | − | 0.898610i | \(-0.355422\pi\) | ||||
0.438748 | + | 0.898610i | \(0.355422\pi\) | |||||||
\(564\) | 39.9337 | 1.68151 | ||||||||
\(565\) | −7.56505 | −0.318264 | ||||||||
\(566\) | 29.3988 | 1.23572 | ||||||||
\(567\) | −5.39079 | −0.226392 | ||||||||
\(568\) | −125.898 | −5.28254 | ||||||||
\(569\) | 11.2418 | 0.471279 | 0.235639 | − | 0.971841i | \(-0.424282\pi\) | ||||
0.235639 | + | 0.971841i | \(0.424282\pi\) | |||||||
\(570\) | 5.32980 | 0.223241 | ||||||||
\(571\) | 4.51880 | 0.189106 | 0.0945529 | − | 0.995520i | \(-0.469858\pi\) | ||||
0.0945529 | + | 0.995520i | \(0.469858\pi\) | |||||||
\(572\) | 16.5536 | 0.692142 | ||||||||
\(573\) | −18.3207 | −0.765358 | ||||||||
\(574\) | 24.0154 | 1.00238 | ||||||||
\(575\) | 1.30758 | 0.0545300 | ||||||||
\(576\) | −60.1724 | −2.50718 | ||||||||
\(577\) | −0.364448 | −0.0151722 | −0.00758608 | − | 0.999971i | \(-0.502415\pi\) | ||||
−0.00758608 | + | 0.999971i | \(0.502415\pi\) | |||||||
\(578\) | 24.2340 | 1.00800 | ||||||||
\(579\) | −7.81439 | −0.324755 | ||||||||
\(580\) | 20.5506 | 0.853319 | ||||||||
\(581\) | −9.66719 | −0.401063 | ||||||||
\(582\) | −26.8011 | −1.11094 | ||||||||
\(583\) | −24.4874 | −1.01416 | ||||||||
\(584\) | −58.0069 | −2.40034 | ||||||||
\(585\) | 4.87599 | 0.201597 | ||||||||
\(586\) | −33.9065 | −1.40066 | ||||||||
\(587\) | −3.41227 | −0.140839 | −0.0704197 | − | 0.997517i | \(-0.522434\pi\) | ||||
−0.0704197 | + | 0.997517i | \(0.522434\pi\) | |||||||
\(588\) | 20.6533 | 0.851727 | ||||||||
\(589\) | −5.90829 | −0.243447 | ||||||||
\(590\) | −78.2021 | −3.21953 | ||||||||
\(591\) | −2.64030 | −0.108607 | ||||||||
\(592\) | −130.020 | −5.34380 | ||||||||
\(593\) | −30.6507 | −1.25867 | −0.629336 | − | 0.777133i | \(-0.716673\pi\) | ||||
−0.629336 | + | 0.777133i | \(0.716673\pi\) | |||||||
\(594\) | 42.7378 | 1.75355 | ||||||||
\(595\) | 10.3000 | 0.422260 | ||||||||
\(596\) | 54.2453 | 2.22197 | ||||||||
\(597\) | −3.82085 | −0.156377 | ||||||||
\(598\) | 2.87814 | 0.117696 | ||||||||
\(599\) | −0.285237 | −0.0116545 | −0.00582723 | − | 0.999983i | \(-0.501855\pi\) | ||||
−0.00582723 | + | 0.999983i | \(0.501855\pi\) | |||||||
\(600\) | 7.54447 | 0.308002 | ||||||||
\(601\) | −7.08967 | −0.289194 | −0.144597 | − | 0.989491i | \(-0.546189\pi\) | ||||
−0.144597 | + | 0.989491i | \(0.546189\pi\) | |||||||
\(602\) | −36.6404 | −1.49335 | ||||||||
\(603\) | −18.1097 | −0.737482 | ||||||||
\(604\) | 105.451 | 4.29075 | ||||||||
\(605\) | 6.16145 | 0.250499 | ||||||||
\(606\) | −22.8605 | −0.928643 | ||||||||
\(607\) | −41.2577 | −1.67460 | −0.837299 | − | 0.546745i | \(-0.815867\pi\) | ||||
−0.837299 | + | 0.546745i | \(0.815867\pi\) | |||||||
\(608\) | −19.7072 | −0.799233 | ||||||||
\(609\) | 1.84382 | 0.0747154 | ||||||||
\(610\) | 9.92325 | 0.401781 | ||||||||
\(611\) | 7.83762 | 0.317076 | ||||||||
\(612\) | 35.9043 | 1.45134 | ||||||||
\(613\) | −15.3921 | −0.621682 | −0.310841 | − | 0.950462i | \(-0.600611\pi\) | ||||
−0.310841 | + | 0.950462i | \(0.600611\pi\) | |||||||
\(614\) | 16.0216 | 0.646579 | ||||||||
\(615\) | −11.7863 | −0.475269 | ||||||||
\(616\) | −49.3931 | −1.99011 | ||||||||
\(617\) | 6.30336 | 0.253764 | 0.126882 | − | 0.991918i | \(-0.459503\pi\) | ||||
0.126882 | + | 0.991918i | \(0.459503\pi\) | |||||||
\(618\) | −22.8090 | −0.917512 | ||||||||
\(619\) | 47.2358 | 1.89857 | 0.949283 | − | 0.314423i | \(-0.101811\pi\) | ||||
0.949283 | + | 0.314423i | \(0.101811\pi\) | |||||||
\(620\) | −77.7535 | −3.12266 | ||||||||
\(621\) | 5.41053 | 0.217117 | ||||||||
\(622\) | 20.0325 | 0.803230 | ||||||||
\(623\) | 19.0559 | 0.763457 | ||||||||
\(624\) | 9.40135 | 0.376355 | ||||||||
\(625\) | −29.1071 | −1.16428 | ||||||||
\(626\) | −25.7914 | −1.03083 | ||||||||
\(627\) | 2.93961 | 0.117397 | ||||||||
\(628\) | 84.3851 | 3.36733 | ||||||||
\(629\) | 26.4146 | 1.05322 | ||||||||
\(630\) | −23.2184 | −0.925041 | ||||||||
\(631\) | −10.9022 | −0.434009 | −0.217005 | − | 0.976171i | \(-0.569629\pi\) | ||||
−0.217005 | + | 0.976171i | \(0.569629\pi\) | |||||||
\(632\) | 14.5515 | 0.578830 | ||||||||
\(633\) | 0.799829 | 0.0317903 | ||||||||
\(634\) | −61.4802 | −2.44169 | ||||||||
\(635\) | 30.3653 | 1.20501 | ||||||||
\(636\) | −28.5447 | −1.13187 | ||||||||
\(637\) | 4.05354 | 0.160607 | ||||||||
\(638\) | 15.5667 | 0.616290 | ||||||||
\(639\) | −32.6409 | −1.29125 | ||||||||
\(640\) | −73.0471 | −2.88744 | ||||||||
\(641\) | 42.2976 | 1.67065 | 0.835327 | − | 0.549753i | \(-0.185278\pi\) | ||||
0.835327 | + | 0.549753i | \(0.185278\pi\) | |||||||
\(642\) | 20.9828 | 0.828125 | ||||||||
\(643\) | 40.0207 | 1.57826 | 0.789131 | − | 0.614224i | \(-0.210531\pi\) | ||||
0.789131 | + | 0.614224i | \(0.210531\pi\) | |||||||
\(644\) | −9.97907 | −0.393230 | ||||||||
\(645\) | 17.9823 | 0.708054 | ||||||||
\(646\) | 7.70264 | 0.303056 | ||||||||
\(647\) | 39.5600 | 1.55527 | 0.777633 | − | 0.628719i | \(-0.216420\pi\) | ||||
0.777633 | + | 0.628719i | \(0.216420\pi\) | |||||||
\(648\) | −33.2442 | −1.30595 | ||||||||
\(649\) | −43.1318 | −1.69307 | ||||||||
\(650\) | 2.36303 | 0.0926857 | ||||||||
\(651\) | −6.97611 | −0.273415 | ||||||||
\(652\) | 10.6486 | 0.417030 | ||||||||
\(653\) | −42.0626 | −1.64604 | −0.823019 | − | 0.568014i | \(-0.807712\pi\) | ||||
−0.823019 | + | 0.568014i | \(0.807712\pi\) | |||||||
\(654\) | 13.3423 | 0.521725 | ||||||||
\(655\) | 15.9958 | 0.625009 | ||||||||
\(656\) | 83.8441 | 3.27356 | ||||||||
\(657\) | −15.0392 | −0.586734 | ||||||||
\(658\) | −37.3210 | −1.45492 | ||||||||
\(659\) | −30.2148 | −1.17700 | −0.588501 | − | 0.808497i | \(-0.700282\pi\) | ||||
−0.588501 | + | 0.808497i | \(0.700282\pi\) | |||||||
\(660\) | 38.6855 | 1.50583 | ||||||||
\(661\) | 27.5504 | 1.07158 | 0.535792 | − | 0.844350i | \(-0.320013\pi\) | ||||
0.535792 | + | 0.844350i | \(0.320013\pi\) | |||||||
\(662\) | −13.1065 | −0.509397 | ||||||||
\(663\) | −1.90995 | −0.0741764 | ||||||||
\(664\) | −59.6161 | −2.31355 | ||||||||
\(665\) | −3.62689 | −0.140645 | ||||||||
\(666\) | −59.5438 | −2.30728 | ||||||||
\(667\) | 1.97071 | 0.0763063 | ||||||||
\(668\) | 26.6393 | 1.03070 | ||||||||
\(669\) | 1.25176 | 0.0483958 | ||||||||
\(670\) | −51.1283 | −1.97526 | ||||||||
\(671\) | 5.47310 | 0.211287 | ||||||||
\(672\) | −23.2690 | −0.897620 | ||||||||
\(673\) | 6.75868 | 0.260528 | 0.130264 | − | 0.991479i | \(-0.458418\pi\) | ||||
0.130264 | + | 0.991479i | \(0.458418\pi\) | |||||||
\(674\) | 39.9862 | 1.54021 | ||||||||
\(675\) | 4.44219 | 0.170980 | ||||||||
\(676\) | −65.8469 | −2.53257 | ||||||||
\(677\) | −11.0544 | −0.424853 | −0.212427 | − | 0.977177i | \(-0.568137\pi\) | ||||
−0.212427 | + | 0.977177i | \(0.568137\pi\) | |||||||
\(678\) | −6.67982 | −0.256537 | ||||||||
\(679\) | 18.2379 | 0.699908 | ||||||||
\(680\) | 63.5187 | 2.43583 | ||||||||
\(681\) | 20.4661 | 0.784262 | ||||||||
\(682\) | −58.8966 | −2.25527 | ||||||||
\(683\) | −2.08758 | −0.0798791 | −0.0399396 | − | 0.999202i | \(-0.512717\pi\) | ||||
−0.0399396 | + | 0.999202i | \(0.512717\pi\) | |||||||
\(684\) | −12.6427 | −0.483408 | ||||||||
\(685\) | −44.1074 | −1.68526 | ||||||||
\(686\) | −47.3298 | −1.80706 | ||||||||
\(687\) | −8.16025 | −0.311333 | ||||||||
\(688\) | −127.921 | −4.87694 | ||||||||
\(689\) | −5.60235 | −0.213433 | ||||||||
\(690\) | 6.72616 | 0.256060 | ||||||||
\(691\) | 8.14697 | 0.309926 | 0.154963 | − | 0.987920i | \(-0.450474\pi\) | ||||
0.154963 | + | 0.987920i | \(0.450474\pi\) | |||||||
\(692\) | 77.3243 | 2.93943 | ||||||||
\(693\) | −12.8059 | −0.486457 | ||||||||
\(694\) | −72.2807 | −2.74374 | ||||||||
\(695\) | 37.1920 | 1.41077 | ||||||||
\(696\) | 11.3706 | 0.431000 | ||||||||
\(697\) | −17.0336 | −0.645192 | ||||||||
\(698\) | −30.8542 | −1.16785 | ||||||||
\(699\) | −1.63125 | −0.0616995 | ||||||||
\(700\) | −8.19308 | −0.309669 | ||||||||
\(701\) | 33.2624 | 1.25630 | 0.628152 | − | 0.778091i | \(-0.283812\pi\) | ||||
0.628152 | + | 0.778091i | \(0.283812\pi\) | |||||||
\(702\) | 9.77777 | 0.369038 | ||||||||
\(703\) | −9.30121 | −0.350802 | ||||||||
\(704\) | −93.6975 | −3.53136 | ||||||||
\(705\) | 18.3164 | 0.689835 | ||||||||
\(706\) | 32.9487 | 1.24004 | ||||||||
\(707\) | 15.5564 | 0.585057 | ||||||||
\(708\) | −50.2782 | −1.88957 | ||||||||
\(709\) | 9.89398 | 0.371576 | 0.185788 | − | 0.982590i | \(-0.440516\pi\) | ||||
0.185788 | + | 0.982590i | \(0.440516\pi\) | |||||||
\(710\) | −92.1538 | −3.45847 | ||||||||
\(711\) | 3.77271 | 0.141488 | ||||||||
\(712\) | 117.515 | 4.40405 | ||||||||
\(713\) | −7.45621 | −0.279237 | ||||||||
\(714\) | 9.09476 | 0.340363 | ||||||||
\(715\) | 7.59266 | 0.283949 | ||||||||
\(716\) | 76.9250 | 2.87482 | ||||||||
\(717\) | −11.6796 | −0.436183 | ||||||||
\(718\) | 48.6179 | 1.81440 | ||||||||
\(719\) | −42.2049 | −1.57398 | −0.786988 | − | 0.616968i | \(-0.788361\pi\) | ||||
−0.786988 | + | 0.616968i | \(0.788361\pi\) | |||||||
\(720\) | −81.0613 | −3.02098 | ||||||||
\(721\) | 15.5213 | 0.578045 | ||||||||
\(722\) | −2.71228 | −0.100941 | ||||||||
\(723\) | −8.36051 | −0.310931 | ||||||||
\(724\) | −80.1424 | −2.97847 | ||||||||
\(725\) | 1.61801 | 0.0600913 | ||||||||
\(726\) | 5.44046 | 0.201914 | ||||||||
\(727\) | −44.4926 | −1.65014 | −0.825069 | − | 0.565031i | \(-0.808864\pi\) | ||||
−0.825069 | + | 0.565031i | \(0.808864\pi\) | |||||||
\(728\) | −11.3004 | −0.418821 | ||||||||
\(729\) | 1.66826 | 0.0617875 | ||||||||
\(730\) | −42.4596 | −1.57150 | ||||||||
\(731\) | 25.9881 | 0.961205 | ||||||||
\(732\) | 6.37993 | 0.235809 | ||||||||
\(733\) | 7.53910 | 0.278463 | 0.139232 | − | 0.990260i | \(-0.455537\pi\) | ||||
0.139232 | + | 0.990260i | \(0.455537\pi\) | |||||||
\(734\) | −0.390592 | −0.0144170 | ||||||||
\(735\) | 9.47304 | 0.349418 | ||||||||
\(736\) | −24.8703 | −0.916732 | ||||||||
\(737\) | −28.1995 | −1.03874 | ||||||||
\(738\) | 38.3971 | 1.41342 | ||||||||
\(739\) | 36.9798 | 1.36032 | 0.680162 | − | 0.733062i | \(-0.261909\pi\) | ||||
0.680162 | + | 0.733062i | \(0.261909\pi\) | |||||||
\(740\) | −122.405 | −4.49968 | ||||||||
\(741\) | 0.672540 | 0.0247064 | ||||||||
\(742\) | 26.6771 | 0.979349 | ||||||||
\(743\) | 45.9901 | 1.68721 | 0.843607 | − | 0.536961i | \(-0.180428\pi\) | ||||
0.843607 | + | 0.536961i | \(0.180428\pi\) | |||||||
\(744\) | −43.0206 | −1.57721 | ||||||||
\(745\) | 24.8807 | 0.911558 | ||||||||
\(746\) | −26.3849 | −0.966019 | ||||||||
\(747\) | −15.4564 | −0.565519 | ||||||||
\(748\) | 55.9084 | 2.04421 | ||||||||
\(749\) | −14.2786 | −0.521730 | ||||||||
\(750\) | −21.1266 | −0.771436 | ||||||||
\(751\) | 22.9971 | 0.839178 | 0.419589 | − | 0.907714i | \(-0.362174\pi\) | ||||
0.419589 | + | 0.907714i | \(0.362174\pi\) | |||||||
\(752\) | −130.297 | −4.75145 | ||||||||
\(753\) | 0.845923 | 0.0308271 | ||||||||
\(754\) | 3.56142 | 0.129699 | ||||||||
\(755\) | 48.3673 | 1.76027 | ||||||||
\(756\) | −33.9014 | −1.23298 | ||||||||
\(757\) | −32.2850 | −1.17342 | −0.586709 | − | 0.809798i | \(-0.699577\pi\) | ||||
−0.586709 | + | 0.809798i | \(0.699577\pi\) | |||||||
\(758\) | 68.5274 | 2.48903 | ||||||||
\(759\) | 3.70976 | 0.134656 | ||||||||
\(760\) | −22.3665 | −0.811317 | ||||||||
\(761\) | 0.697468 | 0.0252832 | 0.0126416 | − | 0.999920i | \(-0.495976\pi\) | ||||
0.0126416 | + | 0.999920i | \(0.495976\pi\) | |||||||
\(762\) | 26.8121 | 0.971300 | ||||||||
\(763\) | −9.07932 | −0.328694 | ||||||||
\(764\) | 122.694 | 4.43892 | ||||||||
\(765\) | 16.4682 | 0.595409 | ||||||||
\(766\) | −54.4560 | −1.96757 | ||||||||
\(767\) | −9.86791 | −0.356310 | ||||||||
\(768\) | −23.7180 | −0.855849 | ||||||||
\(769\) | −0.370782 | −0.0133707 | −0.00668537 | − | 0.999978i | \(-0.502128\pi\) | ||||
−0.00668537 | + | 0.999978i | \(0.502128\pi\) | |||||||
\(770\) | −36.1545 | −1.30292 | ||||||||
\(771\) | 17.8670 | 0.643466 | ||||||||
\(772\) | 52.3332 | 1.88351 | ||||||||
\(773\) | −12.6975 | −0.456696 | −0.228348 | − | 0.973580i | \(-0.573332\pi\) | ||||
−0.228348 | + | 0.973580i | \(0.573332\pi\) | |||||||
\(774\) | −58.5824 | −2.10570 | ||||||||
\(775\) | −6.12175 | −0.219900 | ||||||||
\(776\) | 112.471 | 4.03746 | ||||||||
\(777\) | −10.9822 | −0.393986 | ||||||||
\(778\) | −12.9081 | −0.462779 | ||||||||
\(779\) | 5.99792 | 0.214898 | ||||||||
\(780\) | 8.85067 | 0.316905 | ||||||||
\(781\) | −50.8268 | −1.81872 | ||||||||
\(782\) | 9.72065 | 0.347610 | ||||||||
\(783\) | 6.69501 | 0.239260 | ||||||||
\(784\) | −67.3884 | −2.40673 | ||||||||
\(785\) | 38.7049 | 1.38144 | ||||||||
\(786\) | 14.1241 | 0.503788 | ||||||||
\(787\) | 48.6276 | 1.73339 | 0.866693 | − | 0.498841i | \(-0.166241\pi\) | ||||
0.866693 | + | 0.498841i | \(0.166241\pi\) | |||||||
\(788\) | 17.6821 | 0.629900 | ||||||||
\(789\) | 7.97299 | 0.283846 | ||||||||
\(790\) | 10.6514 | 0.378958 | ||||||||
\(791\) | 4.54556 | 0.161622 | ||||||||
\(792\) | −78.9722 | −2.80615 | ||||||||
\(793\) | 1.25216 | 0.0444656 | ||||||||
\(794\) | 57.0847 | 2.02586 | ||||||||
\(795\) | −13.0926 | −0.464346 | ||||||||
\(796\) | 25.5883 | 0.906954 | ||||||||
\(797\) | −19.7509 | −0.699614 | −0.349807 | − | 0.936822i | \(-0.613753\pi\) | ||||
−0.349807 | + | 0.936822i | \(0.613753\pi\) | |||||||
\(798\) | −3.20248 | −0.113367 | ||||||||
\(799\) | 26.4708 | 0.936471 | ||||||||
\(800\) | −20.4192 | −0.721928 | ||||||||
\(801\) | 30.4675 | 1.07651 | ||||||||
\(802\) | −68.3006 | −2.41178 | ||||||||
\(803\) | −23.4183 | −0.826413 | ||||||||
\(804\) | −32.8718 | −1.15930 | ||||||||
\(805\) | −4.57710 | −0.161321 | ||||||||
\(806\) | −13.4747 | −0.474625 | ||||||||
\(807\) | −1.99125 | −0.0700953 | ||||||||
\(808\) | 95.9337 | 3.37494 | ||||||||
\(809\) | −22.6012 | −0.794617 | −0.397309 | − | 0.917685i | \(-0.630056\pi\) | ||||
−0.397309 | + | 0.917685i | \(0.630056\pi\) | |||||||
\(810\) | −24.3339 | −0.855005 | ||||||||
\(811\) | −40.1013 | −1.40815 | −0.704073 | − | 0.710128i | \(-0.748637\pi\) | ||||
−0.704073 | + | 0.710128i | \(0.748637\pi\) | |||||||
\(812\) | −12.3481 | −0.433334 | ||||||||
\(813\) | 14.0801 | 0.493811 | ||||||||
\(814\) | −92.7187 | −3.24979 | ||||||||
\(815\) | 4.88418 | 0.171085 | ||||||||
\(816\) | 31.7522 | 1.11155 | ||||||||
\(817\) | −9.15103 | −0.320154 | ||||||||
\(818\) | −53.9551 | −1.88650 | ||||||||
\(819\) | −2.92980 | −0.102376 | ||||||||
\(820\) | 78.9331 | 2.75646 | ||||||||
\(821\) | −25.1845 | −0.878945 | −0.439473 | − | 0.898256i | \(-0.644835\pi\) | ||||
−0.439473 | + | 0.898256i | \(0.644835\pi\) | |||||||
\(822\) | −38.9461 | −1.35840 | ||||||||
\(823\) | 54.4555 | 1.89820 | 0.949099 | − | 0.314978i | \(-0.101997\pi\) | ||||
0.949099 | + | 0.314978i | \(0.101997\pi\) | |||||||
\(824\) | 95.7178 | 3.33449 | ||||||||
\(825\) | 3.04582 | 0.106042 | ||||||||
\(826\) | 46.9888 | 1.63495 | ||||||||
\(827\) | −17.1538 | −0.596498 | −0.298249 | − | 0.954488i | \(-0.596403\pi\) | ||||
−0.298249 | + | 0.954488i | \(0.596403\pi\) | |||||||
\(828\) | −15.9550 | −0.554475 | ||||||||
\(829\) | 4.18673 | 0.145411 | 0.0727055 | − | 0.997353i | \(-0.476837\pi\) | ||||
0.0727055 | + | 0.997353i | \(0.476837\pi\) | |||||||
\(830\) | −43.6375 | −1.51468 | ||||||||
\(831\) | 23.7807 | 0.824945 | ||||||||
\(832\) | −21.4366 | −0.743180 | ||||||||
\(833\) | 13.6905 | 0.474346 | ||||||||
\(834\) | 32.8399 | 1.13715 | ||||||||
\(835\) | 12.2186 | 0.422843 | ||||||||
\(836\) | −19.6867 | −0.680878 | ||||||||
\(837\) | −25.3306 | −0.875554 | ||||||||
\(838\) | 21.1987 | 0.732298 | ||||||||
\(839\) | −15.8364 | −0.546732 | −0.273366 | − | 0.961910i | \(-0.588137\pi\) | ||||
−0.273366 | + | 0.961910i | \(0.588137\pi\) | |||||||
\(840\) | −26.4088 | −0.911191 | ||||||||
\(841\) | −26.5614 | −0.915912 | ||||||||
\(842\) | −41.1931 | −1.41961 | ||||||||
\(843\) | −19.9897 | −0.688481 | ||||||||
\(844\) | −5.35647 | −0.184377 | ||||||||
\(845\) | −30.2020 | −1.03898 | ||||||||
\(846\) | −59.6706 | −2.05152 | ||||||||
\(847\) | −3.70219 | −0.127209 | ||||||||
\(848\) | 93.1368 | 3.19833 | ||||||||
\(849\) | 8.66944 | 0.297535 | ||||||||
\(850\) | 7.98092 | 0.273743 | ||||||||
\(851\) | −11.7380 | −0.402375 | ||||||||
\(852\) | −59.2482 | −2.02981 | ||||||||
\(853\) | 25.5819 | 0.875908 | 0.437954 | − | 0.898997i | \(-0.355703\pi\) | ||||
0.437954 | + | 0.898997i | \(0.355703\pi\) | |||||||
\(854\) | −5.96252 | −0.204033 | ||||||||
\(855\) | −5.79885 | −0.198316 | ||||||||
\(856\) | −88.0541 | −3.00963 | ||||||||
\(857\) | 36.4245 | 1.24424 | 0.622118 | − | 0.782924i | \(-0.286272\pi\) | ||||
0.622118 | + | 0.782924i | \(0.286272\pi\) | |||||||
\(858\) | 6.70419 | 0.228877 | ||||||||
\(859\) | 33.6887 | 1.14944 | 0.574722 | − | 0.818349i | \(-0.305110\pi\) | ||||
0.574722 | + | 0.818349i | \(0.305110\pi\) | |||||||
\(860\) | −120.428 | −4.10657 | ||||||||
\(861\) | 7.08194 | 0.241352 | ||||||||
\(862\) | 27.1282 | 0.923989 | ||||||||
\(863\) | 17.5732 | 0.598197 | 0.299099 | − | 0.954222i | \(-0.403314\pi\) | ||||
0.299099 | + | 0.954222i | \(0.403314\pi\) | |||||||
\(864\) | −84.4908 | −2.87443 | ||||||||
\(865\) | 35.4663 | 1.20589 | ||||||||
\(866\) | −17.5848 | −0.597556 | ||||||||
\(867\) | 7.14640 | 0.242704 | ||||||||
\(868\) | 46.7192 | 1.58575 | ||||||||
\(869\) | 5.87468 | 0.199285 | ||||||||
\(870\) | 8.32297 | 0.282175 | ||||||||
\(871\) | −6.45162 | −0.218605 | ||||||||
\(872\) | −55.9908 | −1.89609 | ||||||||
\(873\) | 29.1597 | 0.986907 | ||||||||
\(874\) | −3.42287 | −0.115780 | ||||||||
\(875\) | 14.3765 | 0.486015 | ||||||||
\(876\) | −27.2984 | −0.922329 | ||||||||
\(877\) | −37.4732 | −1.26538 | −0.632690 | − | 0.774405i | \(-0.718049\pi\) | ||||
−0.632690 | + | 0.774405i | \(0.718049\pi\) | |||||||
\(878\) | −23.3900 | −0.789376 | ||||||||
\(879\) | −9.99872 | −0.337249 | ||||||||
\(880\) | −126.225 | −4.25504 | ||||||||
\(881\) | 27.5202 | 0.927179 | 0.463589 | − | 0.886050i | \(-0.346561\pi\) | ||||
0.463589 | + | 0.886050i | \(0.346561\pi\) | |||||||
\(882\) | −30.8610 | −1.03915 | ||||||||
\(883\) | 20.5747 | 0.692393 | 0.346196 | − | 0.938162i | \(-0.387473\pi\) | ||||
0.346196 | + | 0.938162i | \(0.387473\pi\) | |||||||
\(884\) | 12.7910 | 0.430208 | ||||||||
\(885\) | −23.0611 | −0.775191 | ||||||||
\(886\) | −14.3807 | −0.483128 | ||||||||
\(887\) | −29.4657 | −0.989361 | −0.494680 | − | 0.869075i | \(-0.664715\pi\) | ||||
−0.494680 | + | 0.869075i | \(0.664715\pi\) | |||||||
\(888\) | −67.7258 | −2.27273 | ||||||||
\(889\) | −18.2454 | −0.611932 | ||||||||
\(890\) | 86.0177 | 2.88332 | ||||||||
\(891\) | −13.4212 | −0.449626 | ||||||||
\(892\) | −8.38306 | −0.280686 | ||||||||
\(893\) | −9.32102 | −0.311916 | ||||||||
\(894\) | 21.9692 | 0.734761 | ||||||||
\(895\) | 35.2832 | 1.17939 | ||||||||
\(896\) | 43.8913 | 1.46631 | ||||||||
\(897\) | 0.848739 | 0.0283386 | ||||||||
\(898\) | 24.5218 | 0.818304 | ||||||||
\(899\) | −9.22633 | −0.307715 | ||||||||
\(900\) | −13.0995 | −0.436650 | ||||||||
\(901\) | −18.9214 | −0.630364 | ||||||||
\(902\) | 59.7900 | 1.99079 | ||||||||
\(903\) | −10.8049 | −0.359566 | ||||||||
\(904\) | 28.0318 | 0.932323 | ||||||||
\(905\) | −36.7589 | −1.22191 | ||||||||
\(906\) | 42.7075 | 1.41886 | ||||||||
\(907\) | 6.74109 | 0.223834 | 0.111917 | − | 0.993718i | \(-0.464301\pi\) | ||||
0.111917 | + | 0.993718i | \(0.464301\pi\) | |||||||
\(908\) | −137.062 | −4.54856 | ||||||||
\(909\) | 24.8723 | 0.824961 | ||||||||
\(910\) | −8.27161 | −0.274201 | ||||||||
\(911\) | 8.41905 | 0.278936 | 0.139468 | − | 0.990227i | \(-0.455461\pi\) | ||||
0.139468 | + | 0.990227i | \(0.455461\pi\) | |||||||
\(912\) | −11.1807 | −0.370230 | ||||||||
\(913\) | −24.0679 | −0.796532 | ||||||||
\(914\) | −34.6731 | −1.14688 | ||||||||
\(915\) | 2.92628 | 0.0967398 | ||||||||
\(916\) | 54.6494 | 1.80567 | ||||||||
\(917\) | −9.61131 | −0.317393 | ||||||||
\(918\) | 33.0235 | 1.08994 | ||||||||
\(919\) | −26.9291 | −0.888310 | −0.444155 | − | 0.895950i | \(-0.646496\pi\) | ||||
−0.444155 | + | 0.895950i | \(0.646496\pi\) | |||||||
\(920\) | −28.2263 | −0.930592 | ||||||||
\(921\) | 4.72463 | 0.155682 | ||||||||
\(922\) | −30.2632 | −0.996664 | ||||||||
\(923\) | −11.6284 | −0.382754 | ||||||||
\(924\) | −23.2447 | −0.764695 | ||||||||
\(925\) | −9.63724 | −0.316871 | ||||||||
\(926\) | 109.965 | 3.61368 | ||||||||
\(927\) | 24.8163 | 0.815074 | ||||||||
\(928\) | −30.7746 | −1.01023 | ||||||||
\(929\) | −6.09447 | −0.199953 | −0.0999765 | − | 0.994990i | \(-0.531877\pi\) | ||||
−0.0999765 | + | 0.994990i | \(0.531877\pi\) | |||||||
\(930\) | −31.4900 | −1.03260 | ||||||||
\(931\) | −4.82074 | −0.157993 | ||||||||
\(932\) | 10.9245 | 0.357845 | ||||||||
\(933\) | 5.90741 | 0.193400 | ||||||||
\(934\) | −82.2071 | −2.68990 | ||||||||
\(935\) | 25.6435 | 0.838632 | ||||||||
\(936\) | −18.0677 | −0.590560 | ||||||||
\(937\) | −39.3441 | −1.28532 | −0.642658 | − | 0.766153i | \(-0.722168\pi\) | ||||
−0.642658 | + | 0.766153i | \(0.722168\pi\) | |||||||
\(938\) | 30.7211 | 1.00308 | ||||||||
\(939\) | −7.60567 | −0.248202 | ||||||||
\(940\) | −122.665 | −4.00090 | ||||||||
\(941\) | 7.71358 | 0.251455 | 0.125728 | − | 0.992065i | \(-0.459873\pi\) | ||||
0.125728 | + | 0.992065i | \(0.459873\pi\) | |||||||
\(942\) | 34.1758 | 1.11351 | ||||||||
\(943\) | 7.56932 | 0.246491 | ||||||||
\(944\) | 164.050 | 5.33937 | ||||||||
\(945\) | −15.5496 | −0.505827 | ||||||||
\(946\) | −91.2217 | −2.96587 | ||||||||
\(947\) | 18.3728 | 0.597037 | 0.298518 | − | 0.954404i | \(-0.403508\pi\) | ||||
0.298518 | + | 0.954404i | \(0.403508\pi\) | |||||||
\(948\) | 6.84805 | 0.222414 | ||||||||
\(949\) | −5.35776 | −0.173920 | ||||||||
\(950\) | −2.81027 | −0.0911773 | ||||||||
\(951\) | −18.1300 | −0.587905 | ||||||||
\(952\) | −38.1661 | −1.23697 | ||||||||
\(953\) | −31.7844 | −1.02960 | −0.514799 | − | 0.857311i | \(-0.672133\pi\) | ||||
−0.514799 | + | 0.857311i | \(0.672133\pi\) | |||||||
\(954\) | 42.6527 | 1.38093 | ||||||||
\(955\) | 56.2761 | 1.82105 | ||||||||
\(956\) | 78.2187 | 2.52978 | ||||||||
\(957\) | 4.59047 | 0.148389 | ||||||||
\(958\) | −86.5789 | −2.79724 | ||||||||
\(959\) | 26.5025 | 0.855812 | ||||||||
\(960\) | −50.0969 | −1.61687 | ||||||||
\(961\) | 3.90789 | 0.126061 | ||||||||
\(962\) | −21.2127 | −0.683924 | ||||||||
\(963\) | −22.8294 | −0.735666 | ||||||||
\(964\) | 55.9906 | 1.80334 | ||||||||
\(965\) | 24.0036 | 0.772705 | ||||||||
\(966\) | −4.04150 | −0.130033 | ||||||||
\(967\) | −4.79849 | −0.154309 | −0.0771546 | − | 0.997019i | \(-0.524583\pi\) | ||||
−0.0771546 | + | 0.997019i | \(0.524583\pi\) | |||||||
\(968\) | −22.8309 | −0.733811 | ||||||||
\(969\) | 2.27144 | 0.0729692 | ||||||||
\(970\) | 82.3256 | 2.64332 | ||||||||
\(971\) | 42.3773 | 1.35995 | 0.679976 | − | 0.733234i | \(-0.261990\pi\) | ||||
0.679976 | + | 0.733234i | \(0.261990\pi\) | |||||||
\(972\) | −84.5394 | −2.71160 | ||||||||
\(973\) | −22.3473 | −0.716421 | ||||||||
\(974\) | 89.5037 | 2.86788 | ||||||||
\(975\) | 0.696838 | 0.0223167 | ||||||||
\(976\) | −20.8167 | −0.666326 | ||||||||
\(977\) | 44.7260 | 1.43091 | 0.715456 | − | 0.698658i | \(-0.246219\pi\) | ||||
0.715456 | + | 0.698658i | \(0.246219\pi\) | |||||||
\(978\) | 4.31265 | 0.137903 | ||||||||
\(979\) | 47.4425 | 1.51627 | ||||||||
\(980\) | −63.4412 | −2.02656 | ||||||||
\(981\) | −14.5165 | −0.463475 | ||||||||
\(982\) | 41.1952 | 1.31459 | ||||||||
\(983\) | −44.3591 | −1.41484 | −0.707418 | − | 0.706795i | \(-0.750140\pi\) | ||||
−0.707418 | + | 0.706795i | \(0.750140\pi\) | |||||||
\(984\) | 43.6733 | 1.39225 | ||||||||
\(985\) | 8.11026 | 0.258415 | ||||||||
\(986\) | 12.0284 | 0.383061 | ||||||||
\(987\) | −11.0056 | −0.350313 | ||||||||
\(988\) | −4.50402 | −0.143292 | ||||||||
\(989\) | −11.5485 | −0.367221 | ||||||||
\(990\) | −57.8056 | −1.83718 | ||||||||
\(991\) | −46.5096 | −1.47743 | −0.738713 | − | 0.674020i | \(-0.764566\pi\) | ||||
−0.738713 | + | 0.674020i | \(0.764566\pi\) | |||||||
\(992\) | 116.436 | 3.69685 | ||||||||
\(993\) | −3.86499 | −0.122652 | ||||||||
\(994\) | 55.3718 | 1.75629 | ||||||||
\(995\) | 11.7366 | 0.372075 | ||||||||
\(996\) | −28.0557 | −0.888979 | ||||||||
\(997\) | 30.3045 | 0.959754 | 0.479877 | − | 0.877336i | \(-0.340681\pi\) | ||||
0.479877 | + | 0.877336i | \(0.340681\pi\) | |||||||
\(998\) | −53.1017 | −1.68090 | ||||||||
\(999\) | −39.8771 | −1.26165 |
(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 | 4009.2.a.e.1.1 | ✓ | 82 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4009.2.a.e.1.1 | ✓ | 82 | 1.1 | even | 1 | trivial |