Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, 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("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0000972201\) |
Analytic rank: | \(1\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.66719 | −1.17888 | −0.589441 | − | 0.807811i | \(-0.700652\pi\) | ||||
−0.589441 | + | 0.807811i | \(0.700652\pi\) | |||||||
\(3\) | 2.43876 | 1.40802 | 0.704010 | − | 0.710190i | \(-0.251391\pi\) | ||||
0.704010 | + | 0.710190i | \(0.251391\pi\) | |||||||
\(4\) | 0.779527 | 0.389763 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −4.06588 | −1.65989 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.03476 | 0.719397 | ||||||||
\(9\) | 2.94756 | 0.982519 | ||||||||
\(10\) | −1.66719 | −0.527212 | ||||||||
\(11\) | 3.17175 | 0.956320 | 0.478160 | − | 0.878273i | \(-0.341304\pi\) | ||||
0.478160 | + | 0.878273i | \(0.341304\pi\) | |||||||
\(12\) | 1.90108 | 0.548794 | ||||||||
\(13\) | −2.08978 | −0.579600 | −0.289800 | − | 0.957087i | \(-0.593589\pi\) | ||||
−0.289800 | + | 0.957087i | \(0.593589\pi\) | |||||||
\(14\) | −1.66719 | −0.445576 | ||||||||
\(15\) | 2.43876 | 0.629685 | ||||||||
\(16\) | −4.95139 | −1.23785 | ||||||||
\(17\) | −2.91545 | −0.707100 | −0.353550 | − | 0.935416i | \(-0.615026\pi\) | ||||
−0.353550 | + | 0.935416i | \(0.615026\pi\) | |||||||
\(18\) | −4.91414 | −1.15827 | ||||||||
\(19\) | −5.66999 | −1.30079 | −0.650393 | − | 0.759598i | \(-0.725396\pi\) | ||||
−0.650393 | + | 0.759598i | \(0.725396\pi\) | |||||||
\(20\) | 0.779527 | 0.174307 | ||||||||
\(21\) | 2.43876 | 0.532181 | ||||||||
\(22\) | −5.28792 | −1.12739 | ||||||||
\(23\) | −1.71652 | −0.357920 | −0.178960 | − | 0.983856i | \(-0.557273\pi\) | ||||
−0.178960 | + | 0.983856i | \(0.557273\pi\) | |||||||
\(24\) | 4.96230 | 1.01293 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.48406 | 0.683280 | ||||||||
\(27\) | −0.127896 | −0.0246136 | ||||||||
\(28\) | 0.779527 | 0.147317 | ||||||||
\(29\) | −5.05955 | −0.939534 | −0.469767 | − | 0.882790i | \(-0.655662\pi\) | ||||
−0.469767 | + | 0.882790i | \(0.655662\pi\) | |||||||
\(30\) | −4.06588 | −0.742325 | ||||||||
\(31\) | −3.30922 | −0.594354 | −0.297177 | − | 0.954822i | \(-0.596045\pi\) | ||||
−0.297177 | + | 0.954822i | \(0.596045\pi\) | |||||||
\(32\) | 4.18539 | 0.739880 | ||||||||
\(33\) | 7.73515 | 1.34652 | ||||||||
\(34\) | 4.86061 | 0.833588 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 2.29770 | 0.382950 | ||||||||
\(37\) | −3.21787 | −0.529015 | −0.264507 | − | 0.964384i | \(-0.585209\pi\) | ||||
−0.264507 | + | 0.964384i | \(0.585209\pi\) | |||||||
\(38\) | 9.45296 | 1.53347 | ||||||||
\(39\) | −5.09647 | −0.816088 | ||||||||
\(40\) | 2.03476 | 0.321724 | ||||||||
\(41\) | 3.49213 | 0.545380 | 0.272690 | − | 0.962102i | \(-0.412087\pi\) | ||||
0.272690 | + | 0.962102i | \(0.412087\pi\) | |||||||
\(42\) | −4.06588 | −0.627379 | ||||||||
\(43\) | 2.26663 | 0.345658 | 0.172829 | − | 0.984952i | \(-0.444709\pi\) | ||||
0.172829 | + | 0.984952i | \(0.444709\pi\) | |||||||
\(44\) | 2.47247 | 0.372738 | ||||||||
\(45\) | 2.94756 | 0.439396 | ||||||||
\(46\) | 2.86177 | 0.421945 | ||||||||
\(47\) | −1.59980 | −0.233355 | −0.116677 | − | 0.993170i | \(-0.537224\pi\) | ||||
−0.116677 | + | 0.993170i | \(0.537224\pi\) | |||||||
\(48\) | −12.0753 | −1.74291 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.66719 | −0.235776 | ||||||||
\(51\) | −7.11009 | −0.995611 | ||||||||
\(52\) | −1.62904 | −0.225907 | ||||||||
\(53\) | −0.825739 | −0.113424 | −0.0567120 | − | 0.998391i | \(-0.518062\pi\) | ||||
−0.0567120 | + | 0.998391i | \(0.518062\pi\) | |||||||
\(54\) | 0.213227 | 0.0290165 | ||||||||
\(55\) | 3.17175 | 0.427679 | ||||||||
\(56\) | 2.03476 | 0.271907 | ||||||||
\(57\) | −13.8278 | −1.83153 | ||||||||
\(58\) | 8.43523 | 1.10760 | ||||||||
\(59\) | −11.8583 | −1.54382 | −0.771911 | − | 0.635730i | \(-0.780699\pi\) | ||||
−0.771911 | + | 0.635730i | \(0.780699\pi\) | |||||||
\(60\) | 1.90108 | 0.245428 | ||||||||
\(61\) | 8.83426 | 1.13111 | 0.565556 | − | 0.824710i | \(-0.308662\pi\) | ||||
0.565556 | + | 0.824710i | \(0.308662\pi\) | |||||||
\(62\) | 5.51711 | 0.700673 | ||||||||
\(63\) | 2.94756 | 0.371357 | ||||||||
\(64\) | 2.92493 | 0.365617 | ||||||||
\(65\) | −2.08978 | −0.259205 | ||||||||
\(66\) | −12.8960 | −1.58738 | ||||||||
\(67\) | 0.605036 | 0.0739169 | 0.0369585 | − | 0.999317i | \(-0.488233\pi\) | ||||
0.0369585 | + | 0.999317i | \(0.488233\pi\) | |||||||
\(68\) | −2.27267 | −0.275602 | ||||||||
\(69\) | −4.18619 | −0.503958 | ||||||||
\(70\) | −1.66719 | −0.199267 | ||||||||
\(71\) | −6.38393 | −0.757633 | −0.378816 | − | 0.925472i | \(-0.623669\pi\) | ||||
−0.378816 | + | 0.925472i | \(0.623669\pi\) | |||||||
\(72\) | 5.99758 | 0.706821 | ||||||||
\(73\) | −8.89810 | −1.04144 | −0.520722 | − | 0.853726i | \(-0.674337\pi\) | ||||
−0.520722 | + | 0.853726i | \(0.674337\pi\) | |||||||
\(74\) | 5.36480 | 0.623646 | ||||||||
\(75\) | 2.43876 | 0.281604 | ||||||||
\(76\) | −4.41991 | −0.506998 | ||||||||
\(77\) | 3.17175 | 0.361455 | ||||||||
\(78\) | 8.49678 | 0.962071 | ||||||||
\(79\) | 8.19199 | 0.921671 | 0.460835 | − | 0.887486i | \(-0.347550\pi\) | ||||
0.460835 | + | 0.887486i | \(0.347550\pi\) | |||||||
\(80\) | −4.95139 | −0.553582 | ||||||||
\(81\) | −9.15458 | −1.01718 | ||||||||
\(82\) | −5.82205 | −0.642938 | ||||||||
\(83\) | −4.56508 | −0.501083 | −0.250541 | − | 0.968106i | \(-0.580609\pi\) | ||||
−0.250541 | + | 0.968106i | \(0.580609\pi\) | |||||||
\(84\) | 1.90108 | 0.207425 | ||||||||
\(85\) | −2.91545 | −0.316225 | ||||||||
\(86\) | −3.77890 | −0.407490 | ||||||||
\(87\) | −12.3390 | −1.32288 | ||||||||
\(88\) | 6.45377 | 0.687974 | ||||||||
\(89\) | −6.31868 | −0.669779 | −0.334889 | − | 0.942257i | \(-0.608699\pi\) | ||||
−0.334889 | + | 0.942257i | \(0.608699\pi\) | |||||||
\(90\) | −4.91414 | −0.517996 | ||||||||
\(91\) | −2.08978 | −0.219068 | ||||||||
\(92\) | −1.33808 | −0.139504 | ||||||||
\(93\) | −8.07040 | −0.836862 | ||||||||
\(94\) | 2.66717 | 0.275098 | ||||||||
\(95\) | −5.66999 | −0.581729 | ||||||||
\(96\) | 10.2072 | 1.04177 | ||||||||
\(97\) | 9.41996 | 0.956452 | 0.478226 | − | 0.878237i | \(-0.341280\pi\) | ||||
0.478226 | + | 0.878237i | \(0.341280\pi\) | |||||||
\(98\) | −1.66719 | −0.168412 | ||||||||
\(99\) | 9.34893 | 0.939602 | ||||||||
\(100\) | 0.779527 | 0.0779527 | ||||||||
\(101\) | −16.3968 | −1.63155 | −0.815773 | − | 0.578373i | \(-0.803688\pi\) | ||||
−0.815773 | + | 0.578373i | \(0.803688\pi\) | |||||||
\(102\) | 11.8539 | 1.17371 | ||||||||
\(103\) | −17.8785 | −1.76163 | −0.880813 | − | 0.473464i | \(-0.843003\pi\) | ||||
−0.880813 | + | 0.473464i | \(0.843003\pi\) | |||||||
\(104\) | −4.25220 | −0.416962 | ||||||||
\(105\) | 2.43876 | 0.237999 | ||||||||
\(106\) | 1.37667 | 0.133714 | ||||||||
\(107\) | −1.83151 | −0.177059 | −0.0885295 | − | 0.996074i | \(-0.528217\pi\) | ||||
−0.0885295 | + | 0.996074i | \(0.528217\pi\) | |||||||
\(108\) | −0.0996983 | −0.00959347 | ||||||||
\(109\) | −15.5569 | −1.49008 | −0.745042 | − | 0.667018i | \(-0.767570\pi\) | ||||
−0.745042 | + | 0.667018i | \(0.767570\pi\) | |||||||
\(110\) | −5.28792 | −0.504183 | ||||||||
\(111\) | −7.84762 | −0.744863 | ||||||||
\(112\) | −4.95139 | −0.467863 | ||||||||
\(113\) | −6.33363 | −0.595818 | −0.297909 | − | 0.954594i | \(-0.596289\pi\) | ||||
−0.297909 | + | 0.954594i | \(0.596289\pi\) | |||||||
\(114\) | 23.0535 | 2.15916 | ||||||||
\(115\) | −1.71652 | −0.160067 | ||||||||
\(116\) | −3.94405 | −0.366196 | ||||||||
\(117\) | −6.15974 | −0.569468 | ||||||||
\(118\) | 19.7701 | 1.81998 | ||||||||
\(119\) | −2.91545 | −0.267259 | ||||||||
\(120\) | 4.96230 | 0.452994 | ||||||||
\(121\) | −0.939978 | −0.0854525 | ||||||||
\(122\) | −14.7284 | −1.33345 | ||||||||
\(123\) | 8.51648 | 0.767905 | ||||||||
\(124\) | −2.57963 | −0.231657 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −4.91414 | −0.437786 | ||||||||
\(127\) | −10.4074 | −0.923510 | −0.461755 | − | 0.887008i | \(-0.652780\pi\) | ||||
−0.461755 | + | 0.887008i | \(0.652780\pi\) | |||||||
\(128\) | −13.2472 | −1.17090 | ||||||||
\(129\) | 5.52777 | 0.486693 | ||||||||
\(130\) | 3.48406 | 0.305572 | ||||||||
\(131\) | 3.86535 | 0.337717 | 0.168859 | − | 0.985640i | \(-0.445992\pi\) | ||||
0.168859 | + | 0.985640i | \(0.445992\pi\) | |||||||
\(132\) | 6.02976 | 0.524823 | ||||||||
\(133\) | −5.66999 | −0.491651 | ||||||||
\(134\) | −1.00871 | −0.0871394 | ||||||||
\(135\) | −0.127896 | −0.0110075 | ||||||||
\(136\) | −5.93225 | −0.508686 | ||||||||
\(137\) | −1.29536 | −0.110670 | −0.0553349 | − | 0.998468i | \(-0.517623\pi\) | ||||
−0.0553349 | + | 0.998468i | \(0.517623\pi\) | |||||||
\(138\) | 6.97918 | 0.594107 | ||||||||
\(139\) | −6.80695 | −0.577358 | −0.288679 | − | 0.957426i | \(-0.593216\pi\) | ||||
−0.288679 | + | 0.957426i | \(0.593216\pi\) | |||||||
\(140\) | 0.779527 | 0.0658820 | ||||||||
\(141\) | −3.90153 | −0.328568 | ||||||||
\(142\) | 10.6432 | 0.893160 | ||||||||
\(143\) | −6.62826 | −0.554283 | ||||||||
\(144\) | −14.5945 | −1.21621 | ||||||||
\(145\) | −5.05955 | −0.420173 | ||||||||
\(146\) | 14.8348 | 1.22774 | ||||||||
\(147\) | 2.43876 | 0.201146 | ||||||||
\(148\) | −2.50842 | −0.206190 | ||||||||
\(149\) | −1.79556 | −0.147098 | −0.0735488 | − | 0.997292i | \(-0.523432\pi\) | ||||
−0.0735488 | + | 0.997292i | \(0.523432\pi\) | |||||||
\(150\) | −4.06588 | −0.331978 | ||||||||
\(151\) | 20.7823 | 1.69124 | 0.845619 | − | 0.533787i | \(-0.179232\pi\) | ||||
0.845619 | + | 0.533787i | \(0.179232\pi\) | |||||||
\(152\) | −11.5371 | −0.935781 | ||||||||
\(153\) | −8.59345 | −0.694740 | ||||||||
\(154\) | −5.28792 | −0.426113 | ||||||||
\(155\) | −3.30922 | −0.265803 | ||||||||
\(156\) | −3.97283 | −0.318081 | ||||||||
\(157\) | −4.31404 | −0.344298 | −0.172149 | − | 0.985071i | \(-0.555071\pi\) | ||||
−0.172149 | + | 0.985071i | \(0.555071\pi\) | |||||||
\(158\) | −13.6576 | −1.08654 | ||||||||
\(159\) | −2.01378 | −0.159703 | ||||||||
\(160\) | 4.18539 | 0.330884 | ||||||||
\(161\) | −1.71652 | −0.135281 | ||||||||
\(162\) | 15.2624 | 1.19913 | ||||||||
\(163\) | 24.7220 | 1.93637 | 0.968187 | − | 0.250227i | \(-0.0805054\pi\) | ||||
0.968187 | + | 0.250227i | \(0.0805054\pi\) | |||||||
\(164\) | 2.72221 | 0.212569 | ||||||||
\(165\) | 7.73515 | 0.602181 | ||||||||
\(166\) | 7.61086 | 0.590718 | ||||||||
\(167\) | −5.97506 | −0.462364 | −0.231182 | − | 0.972911i | \(-0.574259\pi\) | ||||
−0.231182 | + | 0.972911i | \(0.574259\pi\) | |||||||
\(168\) | 4.96230 | 0.382850 | ||||||||
\(169\) | −8.63283 | −0.664064 | ||||||||
\(170\) | 4.86061 | 0.372792 | ||||||||
\(171\) | −16.7126 | −1.27805 | ||||||||
\(172\) | 1.76690 | 0.134725 | ||||||||
\(173\) | 16.8489 | 1.28100 | 0.640500 | − | 0.767958i | \(-0.278727\pi\) | ||||
0.640500 | + | 0.767958i | \(0.278727\pi\) | |||||||
\(174\) | 20.5715 | 1.55952 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | −15.7046 | −1.18378 | ||||||||
\(177\) | −28.9196 | −2.17373 | ||||||||
\(178\) | 10.5345 | 0.789590 | ||||||||
\(179\) | 1.22054 | 0.0912276 | 0.0456138 | − | 0.998959i | \(-0.485476\pi\) | ||||
0.0456138 | + | 0.998959i | \(0.485476\pi\) | |||||||
\(180\) | 2.29770 | 0.171260 | ||||||||
\(181\) | 19.3567 | 1.43877 | 0.719387 | − | 0.694610i | \(-0.244423\pi\) | ||||
0.719387 | + | 0.694610i | \(0.244423\pi\) | |||||||
\(182\) | 3.48406 | 0.258255 | ||||||||
\(183\) | 21.5447 | 1.59263 | ||||||||
\(184\) | −3.49272 | −0.257487 | ||||||||
\(185\) | −3.21787 | −0.236583 | ||||||||
\(186\) | 13.4549 | 0.986561 | ||||||||
\(187\) | −9.24709 | −0.676214 | ||||||||
\(188\) | −1.24709 | −0.0909530 | ||||||||
\(189\) | −0.127896 | −0.00930306 | ||||||||
\(190\) | 9.45296 | 0.685790 | ||||||||
\(191\) | 10.9970 | 0.795713 | 0.397857 | − | 0.917448i | \(-0.369754\pi\) | ||||
0.397857 | + | 0.917448i | \(0.369754\pi\) | |||||||
\(192\) | 7.13322 | 0.514796 | ||||||||
\(193\) | −7.19974 | −0.518249 | −0.259124 | − | 0.965844i | \(-0.583434\pi\) | ||||
−0.259124 | + | 0.965844i | \(0.583434\pi\) | |||||||
\(194\) | −15.7049 | −1.12754 | ||||||||
\(195\) | −5.09647 | −0.364966 | ||||||||
\(196\) | 0.779527 | 0.0556805 | ||||||||
\(197\) | −0.491967 | −0.0350512 | −0.0175256 | − | 0.999846i | \(-0.505579\pi\) | ||||
−0.0175256 | + | 0.999846i | \(0.505579\pi\) | |||||||
\(198\) | −15.5864 | −1.10768 | ||||||||
\(199\) | 1.47755 | 0.104740 | 0.0523702 | − | 0.998628i | \(-0.483322\pi\) | ||||
0.0523702 | + | 0.998628i | \(0.483322\pi\) | |||||||
\(200\) | 2.03476 | 0.143879 | ||||||||
\(201\) | 1.47554 | 0.104076 | ||||||||
\(202\) | 27.3366 | 1.92340 | ||||||||
\(203\) | −5.05955 | −0.355111 | ||||||||
\(204\) | −5.54250 | −0.388053 | ||||||||
\(205\) | 3.49213 | 0.243901 | ||||||||
\(206\) | 29.8070 | 2.07675 | ||||||||
\(207\) | −5.05955 | −0.351663 | ||||||||
\(208\) | 10.3473 | 0.717456 | ||||||||
\(209\) | −17.9838 | −1.24397 | ||||||||
\(210\) | −4.06588 | −0.280572 | ||||||||
\(211\) | −5.31971 | −0.366224 | −0.183112 | − | 0.983092i | \(-0.558617\pi\) | ||||
−0.183112 | + | 0.983092i | \(0.558617\pi\) | |||||||
\(212\) | −0.643686 | −0.0442085 | ||||||||
\(213\) | −15.5689 | −1.06676 | ||||||||
\(214\) | 3.05348 | 0.208732 | ||||||||
\(215\) | 2.26663 | 0.154583 | ||||||||
\(216\) | −0.260238 | −0.0177069 | ||||||||
\(217\) | −3.30922 | −0.224645 | ||||||||
\(218\) | 25.9364 | 1.75663 | ||||||||
\(219\) | −21.7003 | −1.46637 | ||||||||
\(220\) | 2.47247 | 0.166694 | ||||||||
\(221\) | 6.09264 | 0.409835 | ||||||||
\(222\) | 13.0835 | 0.878106 | ||||||||
\(223\) | 15.9044 | 1.06504 | 0.532519 | − | 0.846418i | \(-0.321245\pi\) | ||||
0.532519 | + | 0.846418i | \(0.321245\pi\) | |||||||
\(224\) | 4.18539 | 0.279648 | ||||||||
\(225\) | 2.94756 | 0.196504 | ||||||||
\(226\) | 10.5594 | 0.702399 | ||||||||
\(227\) | −6.38175 | −0.423571 | −0.211786 | − | 0.977316i | \(-0.567928\pi\) | ||||
−0.211786 | + | 0.977316i | \(0.567928\pi\) | |||||||
\(228\) | −10.7791 | −0.713864 | ||||||||
\(229\) | −1.00000 | −0.0660819 | ||||||||
\(230\) | 2.86177 | 0.188700 | ||||||||
\(231\) | 7.73515 | 0.508936 | ||||||||
\(232\) | −10.2950 | −0.675898 | ||||||||
\(233\) | 20.3234 | 1.33143 | 0.665714 | − | 0.746207i | \(-0.268127\pi\) | ||||
0.665714 | + | 0.746207i | \(0.268127\pi\) | |||||||
\(234\) | 10.2695 | 0.671335 | ||||||||
\(235\) | −1.59980 | −0.104359 | ||||||||
\(236\) | −9.24388 | −0.601725 | ||||||||
\(237\) | 19.9783 | 1.29773 | ||||||||
\(238\) | 4.86061 | 0.315067 | ||||||||
\(239\) | 4.74198 | 0.306733 | 0.153366 | − | 0.988169i | \(-0.450988\pi\) | ||||
0.153366 | + | 0.988169i | \(0.450988\pi\) | |||||||
\(240\) | −12.0753 | −0.779455 | ||||||||
\(241\) | 4.51309 | 0.290714 | 0.145357 | − | 0.989379i | \(-0.453567\pi\) | ||||
0.145357 | + | 0.989379i | \(0.453567\pi\) | |||||||
\(242\) | 1.56712 | 0.100738 | ||||||||
\(243\) | −21.9421 | −1.40759 | ||||||||
\(244\) | 6.88654 | 0.440866 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −14.1986 | −0.905270 | ||||||||
\(247\) | 11.8490 | 0.753935 | ||||||||
\(248\) | −6.73348 | −0.427576 | ||||||||
\(249\) | −11.1331 | −0.705534 | ||||||||
\(250\) | −1.66719 | −0.105442 | ||||||||
\(251\) | 7.19621 | 0.454221 | 0.227110 | − | 0.973869i | \(-0.427072\pi\) | ||||
0.227110 | + | 0.973869i | \(0.427072\pi\) | |||||||
\(252\) | 2.29770 | 0.144741 | ||||||||
\(253\) | −5.44439 | −0.342286 | ||||||||
\(254\) | 17.3512 | 1.08871 | ||||||||
\(255\) | −7.11009 | −0.445251 | ||||||||
\(256\) | 16.2358 | 1.01474 | ||||||||
\(257\) | 15.4803 | 0.965632 | 0.482816 | − | 0.875722i | \(-0.339614\pi\) | ||||
0.482816 | + | 0.875722i | \(0.339614\pi\) | |||||||
\(258\) | −9.21585 | −0.573754 | ||||||||
\(259\) | −3.21787 | −0.199949 | ||||||||
\(260\) | −1.62904 | −0.101029 | ||||||||
\(261\) | −14.9133 | −0.923110 | ||||||||
\(262\) | −6.44428 | −0.398129 | ||||||||
\(263\) | −0.0244229 | −0.00150598 | −0.000752992 | − | 1.00000i | \(-0.500240\pi\) | ||||
−0.000752992 | 1.00000i | \(0.500240\pi\) | ||||||||
\(264\) | 15.7392 | 0.968680 | ||||||||
\(265\) | −0.825739 | −0.0507248 | ||||||||
\(266\) | 9.45296 | 0.579598 | ||||||||
\(267\) | −15.4098 | −0.943062 | ||||||||
\(268\) | 0.471642 | 0.0288101 | ||||||||
\(269\) | 9.70154 | 0.591513 | 0.295757 | − | 0.955263i | \(-0.404428\pi\) | ||||
0.295757 | + | 0.955263i | \(0.404428\pi\) | |||||||
\(270\) | 0.213227 | 0.0129766 | ||||||||
\(271\) | 27.2886 | 1.65767 | 0.828833 | − | 0.559496i | \(-0.189005\pi\) | ||||
0.828833 | + | 0.559496i | \(0.189005\pi\) | |||||||
\(272\) | 14.4355 | 0.875283 | ||||||||
\(273\) | −5.09647 | −0.308452 | ||||||||
\(274\) | 2.15961 | 0.130467 | ||||||||
\(275\) | 3.17175 | 0.191264 | ||||||||
\(276\) | −3.26325 | −0.196424 | ||||||||
\(277\) | −24.3353 | −1.46217 | −0.731083 | − | 0.682289i | \(-0.760985\pi\) | ||||
−0.731083 | + | 0.682289i | \(0.760985\pi\) | |||||||
\(278\) | 11.3485 | 0.680637 | ||||||||
\(279\) | −9.75412 | −0.583964 | ||||||||
\(280\) | 2.03476 | 0.121600 | ||||||||
\(281\) | −10.6345 | −0.634401 | −0.317200 | − | 0.948359i | \(-0.602743\pi\) | ||||
−0.317200 | + | 0.948359i | \(0.602743\pi\) | |||||||
\(282\) | 6.50459 | 0.387343 | ||||||||
\(283\) | 0.0230340 | 0.00136923 | 0.000684613 | − | 1.00000i | \(-0.499782\pi\) | ||||
0.000684613 | 1.00000i | \(0.499782\pi\) | ||||||||
\(284\) | −4.97644 | −0.295297 | ||||||||
\(285\) | −13.8278 | −0.819086 | ||||||||
\(286\) | 11.0506 | 0.653434 | ||||||||
\(287\) | 3.49213 | 0.206134 | ||||||||
\(288\) | 12.3367 | 0.726946 | ||||||||
\(289\) | −8.50015 | −0.500009 | ||||||||
\(290\) | 8.43523 | 0.495334 | ||||||||
\(291\) | 22.9730 | 1.34670 | ||||||||
\(292\) | −6.93631 | −0.405917 | ||||||||
\(293\) | −2.21751 | −0.129548 | −0.0647740 | − | 0.997900i | \(-0.520633\pi\) | ||||
−0.0647740 | + | 0.997900i | \(0.520633\pi\) | |||||||
\(294\) | −4.06588 | −0.237127 | ||||||||
\(295\) | −11.8583 | −0.690418 | ||||||||
\(296\) | −6.54760 | −0.380572 | ||||||||
\(297\) | −0.405654 | −0.0235385 | ||||||||
\(298\) | 2.99353 | 0.173411 | ||||||||
\(299\) | 3.58715 | 0.207450 | ||||||||
\(300\) | 1.90108 | 0.109759 | ||||||||
\(301\) | 2.26663 | 0.130646 | ||||||||
\(302\) | −34.6480 | −1.99377 | ||||||||
\(303\) | −39.9879 | −2.29725 | ||||||||
\(304\) | 28.0743 | 1.61017 | ||||||||
\(305\) | 8.83426 | 0.505848 | ||||||||
\(306\) | 14.3269 | 0.819016 | ||||||||
\(307\) | −17.2889 | −0.986728 | −0.493364 | − | 0.869823i | \(-0.664233\pi\) | ||||
−0.493364 | + | 0.869823i | \(0.664233\pi\) | |||||||
\(308\) | 2.47247 | 0.140882 | ||||||||
\(309\) | −43.6015 | −2.48040 | ||||||||
\(310\) | 5.51711 | 0.313351 | ||||||||
\(311\) | 14.1869 | 0.804468 | 0.402234 | − | 0.915537i | \(-0.368234\pi\) | ||||
0.402234 | + | 0.915537i | \(0.368234\pi\) | |||||||
\(312\) | −10.3701 | −0.587091 | ||||||||
\(313\) | 29.0571 | 1.64241 | 0.821203 | − | 0.570636i | \(-0.193303\pi\) | ||||
0.821203 | + | 0.570636i | \(0.193303\pi\) | |||||||
\(314\) | 7.19232 | 0.405886 | ||||||||
\(315\) | 2.94756 | 0.166076 | ||||||||
\(316\) | 6.38587 | 0.359233 | ||||||||
\(317\) | 0.640357 | 0.0359660 | 0.0179830 | − | 0.999838i | \(-0.494276\pi\) | ||||
0.0179830 | + | 0.999838i | \(0.494276\pi\) | |||||||
\(318\) | 3.35736 | 0.188271 | ||||||||
\(319\) | −16.0476 | −0.898495 | ||||||||
\(320\) | 2.92493 | 0.163509 | ||||||||
\(321\) | −4.46662 | −0.249303 | ||||||||
\(322\) | 2.86177 | 0.159480 | ||||||||
\(323\) | 16.5306 | 0.919786 | ||||||||
\(324\) | −7.13624 | −0.396458 | ||||||||
\(325\) | −2.08978 | −0.115920 | ||||||||
\(326\) | −41.2163 | −2.28276 | ||||||||
\(327\) | −37.9396 | −2.09807 | ||||||||
\(328\) | 7.10566 | 0.392345 | ||||||||
\(329\) | −1.59980 | −0.0881997 | ||||||||
\(330\) | −12.8960 | −0.709900 | ||||||||
\(331\) | −9.08622 | −0.499424 | −0.249712 | − | 0.968320i | \(-0.580336\pi\) | ||||
−0.249712 | + | 0.968320i | \(0.580336\pi\) | |||||||
\(332\) | −3.55860 | −0.195304 | ||||||||
\(333\) | −9.48486 | −0.519767 | ||||||||
\(334\) | 9.96156 | 0.545072 | ||||||||
\(335\) | 0.605036 | 0.0330567 | ||||||||
\(336\) | −12.0753 | −0.658760 | ||||||||
\(337\) | −15.6644 | −0.853295 | −0.426648 | − | 0.904418i | \(-0.640306\pi\) | ||||
−0.426648 | + | 0.904418i | \(0.640306\pi\) | |||||||
\(338\) | 14.3926 | 0.782853 | ||||||||
\(339\) | −15.4462 | −0.838923 | ||||||||
\(340\) | −2.27267 | −0.123253 | ||||||||
\(341\) | −10.4960 | −0.568392 | ||||||||
\(342\) | 27.8631 | 1.50667 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 4.61205 | 0.248665 | ||||||||
\(345\) | −4.18619 | −0.225377 | ||||||||
\(346\) | −28.0904 | −1.51015 | ||||||||
\(347\) | −7.07806 | −0.379970 | −0.189985 | − | 0.981787i | \(-0.560844\pi\) | ||||
−0.189985 | + | 0.981787i | \(0.560844\pi\) | |||||||
\(348\) | −9.61860 | −0.515611 | ||||||||
\(349\) | 13.0009 | 0.695924 | 0.347962 | − | 0.937509i | \(-0.386874\pi\) | ||||
0.347962 | + | 0.937509i | \(0.386874\pi\) | |||||||
\(350\) | −1.66719 | −0.0891151 | ||||||||
\(351\) | 0.267274 | 0.0142660 | ||||||||
\(352\) | 13.2750 | 0.707562 | ||||||||
\(353\) | −7.87559 | −0.419176 | −0.209588 | − | 0.977790i | \(-0.567212\pi\) | ||||
−0.209588 | + | 0.977790i | \(0.567212\pi\) | |||||||
\(354\) | 48.2145 | 2.56257 | ||||||||
\(355\) | −6.38393 | −0.338824 | ||||||||
\(356\) | −4.92558 | −0.261055 | ||||||||
\(357\) | −7.11009 | −0.376306 | ||||||||
\(358\) | −2.03488 | −0.107547 | ||||||||
\(359\) | 15.9735 | 0.843050 | 0.421525 | − | 0.906817i | \(-0.361495\pi\) | ||||
0.421525 | + | 0.906817i | \(0.361495\pi\) | |||||||
\(360\) | 5.99758 | 0.316100 | ||||||||
\(361\) | 13.1488 | 0.692042 | ||||||||
\(362\) | −32.2714 | −1.69615 | ||||||||
\(363\) | −2.29238 | −0.120319 | ||||||||
\(364\) | −1.62904 | −0.0853847 | ||||||||
\(365\) | −8.89810 | −0.465748 | ||||||||
\(366\) | −35.9191 | −1.87752 | ||||||||
\(367\) | −34.3708 | −1.79414 | −0.897071 | − | 0.441886i | \(-0.854309\pi\) | ||||
−0.897071 | + | 0.441886i | \(0.854309\pi\) | |||||||
\(368\) | 8.49918 | 0.443050 | ||||||||
\(369\) | 10.2933 | 0.535846 | ||||||||
\(370\) | 5.36480 | 0.278903 | ||||||||
\(371\) | −0.825739 | −0.0428702 | ||||||||
\(372\) | −6.29109 | −0.326178 | ||||||||
\(373\) | −9.23275 | −0.478053 | −0.239027 | − | 0.971013i | \(-0.576828\pi\) | ||||
−0.239027 | + | 0.971013i | \(0.576828\pi\) | |||||||
\(374\) | 15.4167 | 0.797177 | ||||||||
\(375\) | 2.43876 | 0.125937 | ||||||||
\(376\) | −3.25521 | −0.167875 | ||||||||
\(377\) | 10.5733 | 0.544554 | ||||||||
\(378\) | 0.213227 | 0.0109672 | ||||||||
\(379\) | −24.0056 | −1.23308 | −0.616542 | − | 0.787322i | \(-0.711467\pi\) | ||||
−0.616542 | + | 0.787322i | \(0.711467\pi\) | |||||||
\(380\) | −4.41991 | −0.226737 | ||||||||
\(381\) | −25.3812 | −1.30032 | ||||||||
\(382\) | −18.3341 | −0.938052 | ||||||||
\(383\) | 2.91243 | 0.148818 | 0.0744091 | − | 0.997228i | \(-0.476293\pi\) | ||||
0.0744091 | + | 0.997228i | \(0.476293\pi\) | |||||||
\(384\) | −32.3068 | −1.64865 | ||||||||
\(385\) | 3.17175 | 0.161648 | ||||||||
\(386\) | 12.0033 | 0.610954 | ||||||||
\(387\) | 6.68102 | 0.339615 | ||||||||
\(388\) | 7.34311 | 0.372790 | ||||||||
\(389\) | −10.2907 | −0.521760 | −0.260880 | − | 0.965371i | \(-0.584013\pi\) | ||||
−0.260880 | + | 0.965371i | \(0.584013\pi\) | |||||||
\(390\) | 8.49678 | 0.430251 | ||||||||
\(391\) | 5.00444 | 0.253085 | ||||||||
\(392\) | 2.03476 | 0.102771 | ||||||||
\(393\) | 9.42666 | 0.475512 | ||||||||
\(394\) | 0.820203 | 0.0413212 | ||||||||
\(395\) | 8.19199 | 0.412184 | ||||||||
\(396\) | 7.28774 | 0.366223 | ||||||||
\(397\) | 14.3226 | 0.718829 | 0.359415 | − | 0.933178i | \(-0.382976\pi\) | ||||
0.359415 | + | 0.933178i | \(0.382976\pi\) | |||||||
\(398\) | −2.46335 | −0.123477 | ||||||||
\(399\) | −13.8278 | −0.692254 | ||||||||
\(400\) | −4.95139 | −0.247570 | ||||||||
\(401\) | −0.831367 | −0.0415165 | −0.0207582 | − | 0.999785i | \(-0.506608\pi\) | ||||
−0.0207582 | + | 0.999785i | \(0.506608\pi\) | |||||||
\(402\) | −2.46001 | −0.122694 | ||||||||
\(403\) | 6.91553 | 0.344487 | ||||||||
\(404\) | −12.7818 | −0.635916 | ||||||||
\(405\) | −9.15458 | −0.454895 | ||||||||
\(406\) | 8.43523 | 0.418634 | ||||||||
\(407\) | −10.2063 | −0.505907 | ||||||||
\(408\) | −14.4673 | −0.716240 | ||||||||
\(409\) | 7.99114 | 0.395137 | 0.197568 | − | 0.980289i | \(-0.436696\pi\) | ||||
0.197568 | + | 0.980289i | \(0.436696\pi\) | |||||||
\(410\) | −5.82205 | −0.287531 | ||||||||
\(411\) | −3.15907 | −0.155825 | ||||||||
\(412\) | −13.9368 | −0.686617 | ||||||||
\(413\) | −11.8583 | −0.583510 | ||||||||
\(414\) | 8.43524 | 0.414569 | ||||||||
\(415\) | −4.56508 | −0.224091 | ||||||||
\(416\) | −8.74653 | −0.428834 | ||||||||
\(417\) | −16.6005 | −0.812931 | ||||||||
\(418\) | 29.9825 | 1.46649 | ||||||||
\(419\) | 25.6358 | 1.25239 | 0.626196 | − | 0.779666i | \(-0.284611\pi\) | ||||
0.626196 | + | 0.779666i | \(0.284611\pi\) | |||||||
\(420\) | 1.90108 | 0.0927632 | ||||||||
\(421\) | 3.89261 | 0.189714 | 0.0948571 | − | 0.995491i | \(-0.469761\pi\) | ||||
0.0948571 | + | 0.995491i | \(0.469761\pi\) | |||||||
\(422\) | 8.86898 | 0.431735 | ||||||||
\(423\) | −4.71550 | −0.229275 | ||||||||
\(424\) | −1.68018 | −0.0815969 | ||||||||
\(425\) | −2.91545 | −0.141420 | ||||||||
\(426\) | 25.9563 | 1.25759 | ||||||||
\(427\) | 8.83426 | 0.427520 | ||||||||
\(428\) | −1.42771 | −0.0690111 | ||||||||
\(429\) | −16.1647 | −0.780441 | ||||||||
\(430\) | −3.77890 | −0.182235 | ||||||||
\(431\) | −9.23599 | −0.444882 | −0.222441 | − | 0.974946i | \(-0.571402\pi\) | ||||
−0.222441 | + | 0.974946i | \(0.571402\pi\) | |||||||
\(432\) | 0.633263 | 0.0304679 | ||||||||
\(433\) | 9.36806 | 0.450200 | 0.225100 | − | 0.974336i | \(-0.427729\pi\) | ||||
0.225100 | + | 0.974336i | \(0.427729\pi\) | |||||||
\(434\) | 5.51711 | 0.264830 | ||||||||
\(435\) | −12.3390 | −0.591611 | ||||||||
\(436\) | −12.1270 | −0.580780 | ||||||||
\(437\) | 9.73267 | 0.465577 | ||||||||
\(438\) | 36.1786 | 1.72868 | ||||||||
\(439\) | 15.8432 | 0.756156 | 0.378078 | − | 0.925774i | \(-0.376585\pi\) | ||||
0.378078 | + | 0.925774i | \(0.376585\pi\) | |||||||
\(440\) | 6.45377 | 0.307671 | ||||||||
\(441\) | 2.94756 | 0.140360 | ||||||||
\(442\) | −10.1576 | −0.483147 | ||||||||
\(443\) | −19.6877 | −0.935390 | −0.467695 | − | 0.883890i | \(-0.654916\pi\) | ||||
−0.467695 | + | 0.883890i | \(0.654916\pi\) | |||||||
\(444\) | −6.11743 | −0.290320 | ||||||||
\(445\) | −6.31868 | −0.299534 | ||||||||
\(446\) | −26.5157 | −1.25555 | ||||||||
\(447\) | −4.37893 | −0.207116 | ||||||||
\(448\) | 2.92493 | 0.138190 | ||||||||
\(449\) | −15.1563 | −0.715271 | −0.357635 | − | 0.933861i | \(-0.616417\pi\) | ||||
−0.357635 | + | 0.933861i | \(0.616417\pi\) | |||||||
\(450\) | −4.91414 | −0.231655 | ||||||||
\(451\) | 11.0762 | 0.521557 | ||||||||
\(452\) | −4.93723 | −0.232228 | ||||||||
\(453\) | 50.6830 | 2.38130 | ||||||||
\(454\) | 10.6396 | 0.499341 | ||||||||
\(455\) | −2.08978 | −0.0979702 | ||||||||
\(456\) | −28.1362 | −1.31760 | ||||||||
\(457\) | −10.9152 | −0.510593 | −0.255297 | − | 0.966863i | \(-0.582173\pi\) | ||||
−0.255297 | + | 0.966863i | \(0.582173\pi\) | |||||||
\(458\) | 1.66719 | 0.0779027 | ||||||||
\(459\) | 0.372874 | 0.0174043 | ||||||||
\(460\) | −1.33808 | −0.0623881 | ||||||||
\(461\) | 7.32827 | 0.341311 | 0.170656 | − | 0.985331i | \(-0.445411\pi\) | ||||
0.170656 | + | 0.985331i | \(0.445411\pi\) | |||||||
\(462\) | −12.8960 | −0.599975 | ||||||||
\(463\) | −36.9367 | −1.71660 | −0.858298 | − | 0.513152i | \(-0.828478\pi\) | ||||
−0.858298 | + | 0.513152i | \(0.828478\pi\) | |||||||
\(464\) | 25.0518 | 1.16300 | ||||||||
\(465\) | −8.07040 | −0.374256 | ||||||||
\(466\) | −33.8829 | −1.56960 | ||||||||
\(467\) | 30.0042 | 1.38843 | 0.694214 | − | 0.719769i | \(-0.255752\pi\) | ||||
0.694214 | + | 0.719769i | \(0.255752\pi\) | |||||||
\(468\) | −4.80168 | −0.221958 | ||||||||
\(469\) | 0.605036 | 0.0279380 | ||||||||
\(470\) | 2.66717 | 0.123027 | ||||||||
\(471\) | −10.5209 | −0.484778 | ||||||||
\(472\) | −24.1289 | −1.11062 | ||||||||
\(473\) | 7.18919 | 0.330559 | ||||||||
\(474\) | −33.3077 | −1.52987 | ||||||||
\(475\) | −5.66999 | −0.260157 | ||||||||
\(476\) | −2.27267 | −0.104168 | ||||||||
\(477\) | −2.43391 | −0.111441 | ||||||||
\(478\) | −7.90578 | −0.361602 | ||||||||
\(479\) | 12.9333 | 0.590939 | 0.295470 | − | 0.955352i | \(-0.404524\pi\) | ||||
0.295470 | + | 0.955352i | \(0.404524\pi\) | |||||||
\(480\) | 10.2072 | 0.465891 | ||||||||
\(481\) | 6.72463 | 0.306617 | ||||||||
\(482\) | −7.52419 | −0.342717 | ||||||||
\(483\) | −4.18619 | −0.190478 | ||||||||
\(484\) | −0.732738 | −0.0333063 | ||||||||
\(485\) | 9.41996 | 0.427738 | ||||||||
\(486\) | 36.5818 | 1.65938 | ||||||||
\(487\) | 15.4342 | 0.699392 | 0.349696 | − | 0.936863i | \(-0.386285\pi\) | ||||
0.349696 | + | 0.936863i | \(0.386285\pi\) | |||||||
\(488\) | 17.9756 | 0.813718 | ||||||||
\(489\) | 60.2910 | 2.72645 | ||||||||
\(490\) | −1.66719 | −0.0753160 | ||||||||
\(491\) | −11.1986 | −0.505386 | −0.252693 | − | 0.967546i | \(-0.581316\pi\) | ||||
−0.252693 | + | 0.967546i | \(0.581316\pi\) | |||||||
\(492\) | 6.63882 | 0.299301 | ||||||||
\(493\) | 14.7509 | 0.664345 | ||||||||
\(494\) | −19.7546 | −0.888800 | ||||||||
\(495\) | 9.34893 | 0.420203 | ||||||||
\(496\) | 16.3853 | 0.735720 | ||||||||
\(497\) | −6.38393 | −0.286358 | ||||||||
\(498\) | 18.5611 | 0.831742 | ||||||||
\(499\) | −14.6729 | −0.656850 | −0.328425 | − | 0.944530i | \(-0.606518\pi\) | ||||
−0.328425 | + | 0.944530i | \(0.606518\pi\) | |||||||
\(500\) | 0.779527 | 0.0348615 | ||||||||
\(501\) | −14.5717 | −0.651017 | ||||||||
\(502\) | −11.9975 | −0.535473 | ||||||||
\(503\) | −6.84700 | −0.305293 | −0.152646 | − | 0.988281i | \(-0.548780\pi\) | ||||
−0.152646 | + | 0.988281i | \(0.548780\pi\) | |||||||
\(504\) | 5.99758 | 0.267153 | ||||||||
\(505\) | −16.3968 | −0.729649 | ||||||||
\(506\) | 9.07684 | 0.403515 | ||||||||
\(507\) | −21.0534 | −0.935015 | ||||||||
\(508\) | −8.11287 | −0.359950 | ||||||||
\(509\) | −17.9549 | −0.795837 | −0.397919 | − | 0.917421i | \(-0.630267\pi\) | ||||
−0.397919 | + | 0.917421i | \(0.630267\pi\) | |||||||
\(510\) | 11.8539 | 0.524898 | ||||||||
\(511\) | −8.89810 | −0.393629 | ||||||||
\(512\) | −0.573701 | −0.0253542 | ||||||||
\(513\) | 0.725169 | 0.0320170 | ||||||||
\(514\) | −25.8085 | −1.13837 | ||||||||
\(515\) | −17.8785 | −0.787823 | ||||||||
\(516\) | 4.30904 | 0.189695 | ||||||||
\(517\) | −5.07417 | −0.223162 | ||||||||
\(518\) | 5.36480 | 0.235716 | ||||||||
\(519\) | 41.0905 | 1.80367 | ||||||||
\(520\) | −4.25220 | −0.186471 | ||||||||
\(521\) | −7.52954 | −0.329875 | −0.164938 | − | 0.986304i | \(-0.552742\pi\) | ||||
−0.164938 | + | 0.986304i | \(0.552742\pi\) | |||||||
\(522\) | 24.8633 | 1.08824 | ||||||||
\(523\) | −13.7576 | −0.601578 | −0.300789 | − | 0.953691i | \(-0.597250\pi\) | ||||
−0.300789 | + | 0.953691i | \(0.597250\pi\) | |||||||
\(524\) | 3.01314 | 0.131630 | ||||||||
\(525\) | 2.43876 | 0.106436 | ||||||||
\(526\) | 0.0407177 | 0.00177538 | ||||||||
\(527\) | 9.64787 | 0.420268 | ||||||||
\(528\) | −38.2998 | −1.66678 | ||||||||
\(529\) | −20.0535 | −0.871893 | ||||||||
\(530\) | 1.37667 | 0.0597985 | ||||||||
\(531\) | −34.9531 | −1.51683 | ||||||||
\(532\) | −4.41991 | −0.191627 | ||||||||
\(533\) | −7.29778 | −0.316102 | ||||||||
\(534\) | 25.6910 | 1.11176 | ||||||||
\(535\) | −1.83151 | −0.0791832 | ||||||||
\(536\) | 1.23110 | 0.0531756 | ||||||||
\(537\) | 2.97661 | 0.128450 | ||||||||
\(538\) | −16.1743 | −0.697325 | ||||||||
\(539\) | 3.17175 | 0.136617 | ||||||||
\(540\) | −0.0996983 | −0.00429033 | ||||||||
\(541\) | 20.5871 | 0.885108 | 0.442554 | − | 0.896742i | \(-0.354073\pi\) | ||||
0.442554 | + | 0.896742i | \(0.354073\pi\) | |||||||
\(542\) | −45.4954 | −1.95419 | ||||||||
\(543\) | 47.2064 | 2.02582 | ||||||||
\(544\) | −12.2023 | −0.523169 | ||||||||
\(545\) | −15.5569 | −0.666386 | ||||||||
\(546\) | 8.49678 | 0.363629 | ||||||||
\(547\) | 19.3715 | 0.828266 | 0.414133 | − | 0.910216i | \(-0.364085\pi\) | ||||
0.414133 | + | 0.910216i | \(0.364085\pi\) | |||||||
\(548\) | −1.00977 | −0.0431350 | ||||||||
\(549\) | 26.0395 | 1.11134 | ||||||||
\(550\) | −5.28792 | −0.225478 | ||||||||
\(551\) | 28.6876 | 1.22213 | ||||||||
\(552\) | −8.51791 | −0.362546 | ||||||||
\(553\) | 8.19199 | 0.348359 | ||||||||
\(554\) | 40.5716 | 1.72372 | ||||||||
\(555\) | −7.84762 | −0.333113 | ||||||||
\(556\) | −5.30620 | −0.225033 | ||||||||
\(557\) | 43.3532 | 1.83694 | 0.918468 | − | 0.395496i | \(-0.129427\pi\) | ||||
0.918468 | + | 0.395496i | \(0.129427\pi\) | |||||||
\(558\) | 16.2620 | 0.688425 | ||||||||
\(559\) | −4.73675 | −0.200343 | ||||||||
\(560\) | −4.95139 | −0.209234 | ||||||||
\(561\) | −22.5514 | −0.952123 | ||||||||
\(562\) | 17.7297 | 0.747884 | ||||||||
\(563\) | 28.1107 | 1.18472 | 0.592362 | − | 0.805672i | \(-0.298195\pi\) | ||||
0.592362 | + | 0.805672i | \(0.298195\pi\) | |||||||
\(564\) | −3.04134 | −0.128064 | ||||||||
\(565\) | −6.33363 | −0.266458 | ||||||||
\(566\) | −0.0384020 | −0.00161416 | ||||||||
\(567\) | −9.15458 | −0.384456 | ||||||||
\(568\) | −12.9898 | −0.545039 | ||||||||
\(569\) | −3.05925 | −0.128250 | −0.0641252 | − | 0.997942i | \(-0.520426\pi\) | ||||
−0.0641252 | + | 0.997942i | \(0.520426\pi\) | |||||||
\(570\) | 23.0535 | 0.965605 | ||||||||
\(571\) | −17.0220 | −0.712349 | −0.356174 | − | 0.934419i | \(-0.615919\pi\) | ||||
−0.356174 | + | 0.934419i | \(0.615919\pi\) | |||||||
\(572\) | −5.16690 | −0.216039 | ||||||||
\(573\) | 26.8190 | 1.12038 | ||||||||
\(574\) | −5.82205 | −0.243008 | ||||||||
\(575\) | −1.71652 | −0.0715840 | ||||||||
\(576\) | 8.62141 | 0.359226 | ||||||||
\(577\) | −24.5318 | −1.02127 | −0.510636 | − | 0.859797i | \(-0.670590\pi\) | ||||
−0.510636 | + | 0.859797i | \(0.670590\pi\) | |||||||
\(578\) | 14.1714 | 0.589452 | ||||||||
\(579\) | −17.5585 | −0.729704 | ||||||||
\(580\) | −3.94405 | −0.163768 | ||||||||
\(581\) | −4.56508 | −0.189392 | ||||||||
\(582\) | −38.3004 | −1.58760 | ||||||||
\(583\) | −2.61904 | −0.108470 | ||||||||
\(584\) | −18.1055 | −0.749212 | ||||||||
\(585\) | −6.15974 | −0.254674 | ||||||||
\(586\) | 3.69701 | 0.152722 | ||||||||
\(587\) | 1.78129 | 0.0735218 | 0.0367609 | − | 0.999324i | \(-0.488296\pi\) | ||||
0.0367609 | + | 0.999324i | \(0.488296\pi\) | |||||||
\(588\) | 1.90108 | 0.0783992 | ||||||||
\(589\) | 18.7633 | 0.773127 | ||||||||
\(590\) | 19.7701 | 0.813922 | ||||||||
\(591\) | −1.19979 | −0.0493528 | ||||||||
\(592\) | 15.9329 | 0.654840 | ||||||||
\(593\) | 37.9104 | 1.55680 | 0.778398 | − | 0.627771i | \(-0.216033\pi\) | ||||
0.778398 | + | 0.627771i | \(0.216033\pi\) | |||||||
\(594\) | 0.676304 | 0.0277491 | ||||||||
\(595\) | −2.91545 | −0.119522 | ||||||||
\(596\) | −1.39968 | −0.0573333 | ||||||||
\(597\) | 3.60338 | 0.147477 | ||||||||
\(598\) | −5.98047 | −0.244559 | ||||||||
\(599\) | −36.6172 | −1.49614 | −0.748070 | − | 0.663620i | \(-0.769019\pi\) | ||||
−0.748070 | + | 0.663620i | \(0.769019\pi\) | |||||||
\(600\) | 4.96230 | 0.202585 | ||||||||
\(601\) | 17.5314 | 0.715122 | 0.357561 | − | 0.933890i | \(-0.383608\pi\) | ||||
0.357561 | + | 0.933890i | \(0.383608\pi\) | |||||||
\(602\) | −3.77890 | −0.154017 | ||||||||
\(603\) | 1.78338 | 0.0726248 | ||||||||
\(604\) | 16.2003 | 0.659182 | ||||||||
\(605\) | −0.939978 | −0.0382155 | ||||||||
\(606\) | 66.6676 | 2.70818 | ||||||||
\(607\) | −43.3240 | −1.75847 | −0.879234 | − | 0.476391i | \(-0.841945\pi\) | ||||
−0.879234 | + | 0.476391i | \(0.841945\pi\) | |||||||
\(608\) | −23.7311 | −0.962425 | ||||||||
\(609\) | −12.3390 | −0.500003 | ||||||||
\(610\) | −14.7284 | −0.596336 | ||||||||
\(611\) | 3.34322 | 0.135252 | ||||||||
\(612\) | −6.69883 | −0.270784 | ||||||||
\(613\) | −22.1347 | −0.894013 | −0.447007 | − | 0.894531i | \(-0.647510\pi\) | ||||
−0.447007 | + | 0.894531i | \(0.647510\pi\) | |||||||
\(614\) | 28.8238 | 1.16324 | ||||||||
\(615\) | 8.51648 | 0.343418 | ||||||||
\(616\) | 6.45377 | 0.260030 | ||||||||
\(617\) | 0.114211 | 0.00459797 | 0.00229898 | − | 0.999997i | \(-0.499268\pi\) | ||||
0.00229898 | + | 0.999997i | \(0.499268\pi\) | |||||||
\(618\) | 72.6921 | 2.92410 | ||||||||
\(619\) | −18.3523 | −0.737641 | −0.368820 | − | 0.929501i | \(-0.620238\pi\) | ||||
−0.368820 | + | 0.929501i | \(0.620238\pi\) | |||||||
\(620\) | −2.57963 | −0.103600 | ||||||||
\(621\) | 0.219536 | 0.00880969 | ||||||||
\(622\) | −23.6524 | −0.948373 | ||||||||
\(623\) | −6.31868 | −0.253153 | ||||||||
\(624\) | 25.2346 | 1.01019 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −48.4438 | −1.93620 | ||||||||
\(627\) | −43.8582 | −1.75153 | ||||||||
\(628\) | −3.36291 | −0.134195 | ||||||||
\(629\) | 9.38154 | 0.374066 | ||||||||
\(630\) | −4.91414 | −0.195784 | ||||||||
\(631\) | −17.0517 | −0.678817 | −0.339408 | − | 0.940639i | \(-0.610227\pi\) | ||||
−0.339408 | + | 0.940639i | \(0.610227\pi\) | |||||||
\(632\) | 16.6687 | 0.663047 | ||||||||
\(633\) | −12.9735 | −0.515651 | ||||||||
\(634\) | −1.06760 | −0.0423997 | ||||||||
\(635\) | −10.4074 | −0.413006 | ||||||||
\(636\) | −1.56980 | −0.0622465 | ||||||||
\(637\) | −2.08978 | −0.0828000 | ||||||||
\(638\) | 26.7545 | 1.05922 | ||||||||
\(639\) | −18.8170 | −0.744389 | ||||||||
\(640\) | −13.2472 | −0.523642 | ||||||||
\(641\) | −0.496602 | −0.0196146 | −0.00980731 | − | 0.999952i | \(-0.503122\pi\) | ||||
−0.00980731 | + | 0.999952i | \(0.503122\pi\) | |||||||
\(642\) | 7.44671 | 0.293898 | ||||||||
\(643\) | 10.4999 | 0.414075 | 0.207038 | − | 0.978333i | \(-0.433618\pi\) | ||||
0.207038 | + | 0.978333i | \(0.433618\pi\) | |||||||
\(644\) | −1.33808 | −0.0527276 | ||||||||
\(645\) | 5.52777 | 0.217656 | ||||||||
\(646\) | −27.5596 | −1.08432 | ||||||||
\(647\) | −13.3030 | −0.522996 | −0.261498 | − | 0.965204i | \(-0.584217\pi\) | ||||
−0.261498 | + | 0.965204i | \(0.584217\pi\) | |||||||
\(648\) | −18.6274 | −0.731753 | ||||||||
\(649\) | −37.6117 | −1.47639 | ||||||||
\(650\) | 3.48406 | 0.136656 | ||||||||
\(651\) | −8.07040 | −0.316304 | ||||||||
\(652\) | 19.2714 | 0.754728 | ||||||||
\(653\) | −7.51134 | −0.293942 | −0.146971 | − | 0.989141i | \(-0.546952\pi\) | ||||
−0.146971 | + | 0.989141i | \(0.546952\pi\) | |||||||
\(654\) | 63.2526 | 2.47337 | ||||||||
\(655\) | 3.86535 | 0.151032 | ||||||||
\(656\) | −17.2909 | −0.675097 | ||||||||
\(657\) | −26.2277 | −1.02324 | ||||||||
\(658\) | 2.66717 | 0.103977 | ||||||||
\(659\) | −16.9594 | −0.660646 | −0.330323 | − | 0.943868i | \(-0.607158\pi\) | ||||
−0.330323 | + | 0.943868i | \(0.607158\pi\) | |||||||
\(660\) | 6.02976 | 0.234708 | ||||||||
\(661\) | −27.2567 | −1.06016 | −0.530082 | − | 0.847946i | \(-0.677839\pi\) | ||||
−0.530082 | + | 0.847946i | \(0.677839\pi\) | |||||||
\(662\) | 15.1485 | 0.588762 | ||||||||
\(663\) | 14.8585 | 0.577056 | ||||||||
\(664\) | −9.28886 | −0.360478 | ||||||||
\(665\) | −5.66999 | −0.219873 | ||||||||
\(666\) | 15.8131 | 0.612744 | ||||||||
\(667\) | 8.68483 | 0.336278 | ||||||||
\(668\) | −4.65772 | −0.180212 | ||||||||
\(669\) | 38.7871 | 1.49959 | ||||||||
\(670\) | −1.00871 | −0.0389699 | ||||||||
\(671\) | 28.0201 | 1.08170 | ||||||||
\(672\) | 10.2072 | 0.393750 | ||||||||
\(673\) | 33.9613 | 1.30911 | 0.654556 | − | 0.756013i | \(-0.272855\pi\) | ||||
0.654556 | + | 0.756013i | \(0.272855\pi\) | |||||||
\(674\) | 26.1156 | 1.00593 | ||||||||
\(675\) | −0.127896 | −0.00492272 | ||||||||
\(676\) | −6.72952 | −0.258828 | ||||||||
\(677\) | 38.2594 | 1.47043 | 0.735214 | − | 0.677835i | \(-0.237082\pi\) | ||||
0.735214 | + | 0.677835i | \(0.237082\pi\) | |||||||
\(678\) | 25.7518 | 0.988991 | ||||||||
\(679\) | 9.41996 | 0.361505 | ||||||||
\(680\) | −5.93225 | −0.227491 | ||||||||
\(681\) | −15.5636 | −0.596397 | ||||||||
\(682\) | 17.4989 | 0.670068 | ||||||||
\(683\) | 24.4927 | 0.937188 | 0.468594 | − | 0.883414i | \(-0.344761\pi\) | ||||
0.468594 | + | 0.883414i | \(0.344761\pi\) | |||||||
\(684\) | −13.0279 | −0.498136 | ||||||||
\(685\) | −1.29536 | −0.0494930 | ||||||||
\(686\) | −1.66719 | −0.0636537 | ||||||||
\(687\) | −2.43876 | −0.0930445 | ||||||||
\(688\) | −11.2230 | −0.427872 | ||||||||
\(689\) | 1.72561 | 0.0657405 | ||||||||
\(690\) | 6.97918 | 0.265693 | ||||||||
\(691\) | −2.43951 | −0.0928033 | −0.0464016 | − | 0.998923i | \(-0.514775\pi\) | ||||
−0.0464016 | + | 0.998923i | \(0.514775\pi\) | |||||||
\(692\) | 13.1342 | 0.499287 | ||||||||
\(693\) | 9.34893 | 0.355136 | ||||||||
\(694\) | 11.8005 | 0.447940 | ||||||||
\(695\) | −6.80695 | −0.258202 | ||||||||
\(696\) | −25.1070 | −0.951678 | ||||||||
\(697\) | −10.1811 | −0.385638 | ||||||||
\(698\) | −21.6750 | −0.820412 | ||||||||
\(699\) | 49.5638 | 1.87468 | ||||||||
\(700\) | 0.779527 | 0.0294633 | ||||||||
\(701\) | −13.7058 | −0.517660 | −0.258830 | − | 0.965923i | \(-0.583337\pi\) | ||||
−0.258830 | + | 0.965923i | \(0.583337\pi\) | |||||||
\(702\) | −0.445597 | −0.0168180 | ||||||||
\(703\) | 18.2453 | 0.688134 | ||||||||
\(704\) | 9.27717 | 0.349647 | ||||||||
\(705\) | −3.90153 | −0.146940 | ||||||||
\(706\) | 13.1301 | 0.494159 | ||||||||
\(707\) | −16.3968 | −0.616666 | ||||||||
\(708\) | −22.5436 | −0.847241 | ||||||||
\(709\) | 14.6988 | 0.552027 | 0.276013 | − | 0.961154i | \(-0.410987\pi\) | ||||
0.276013 | + | 0.961154i | \(0.410987\pi\) | |||||||
\(710\) | 10.6432 | 0.399433 | ||||||||
\(711\) | 24.1464 | 0.905559 | ||||||||
\(712\) | −12.8570 | −0.481837 | ||||||||
\(713\) | 5.68036 | 0.212731 | ||||||||
\(714\) | 11.8539 | 0.443620 | ||||||||
\(715\) | −6.62826 | −0.247883 | ||||||||
\(716\) | 0.951445 | 0.0355572 | ||||||||
\(717\) | 11.5646 | 0.431886 | ||||||||
\(718\) | −26.6309 | −0.993856 | ||||||||
\(719\) | 27.2236 | 1.01527 | 0.507635 | − | 0.861572i | \(-0.330520\pi\) | ||||
0.507635 | + | 0.861572i | \(0.330520\pi\) | |||||||
\(720\) | −14.5945 | −0.543905 | ||||||||
\(721\) | −17.8785 | −0.665832 | ||||||||
\(722\) | −21.9216 | −0.815836 | ||||||||
\(723\) | 11.0064 | 0.409331 | ||||||||
\(724\) | 15.0891 | 0.560781 | ||||||||
\(725\) | −5.05955 | −0.187907 | ||||||||
\(726\) | 3.82184 | 0.141842 | ||||||||
\(727\) | −41.7627 | −1.54889 | −0.774447 | − | 0.632639i | \(-0.781972\pi\) | ||||
−0.774447 | + | 0.632639i | \(0.781972\pi\) | |||||||
\(728\) | −4.25220 | −0.157597 | ||||||||
\(729\) | −26.0479 | −0.964738 | ||||||||
\(730\) | 14.8348 | 0.549062 | ||||||||
\(731\) | −6.60824 | −0.244415 | ||||||||
\(732\) | 16.7946 | 0.620748 | ||||||||
\(733\) | 36.3783 | 1.34366 | 0.671832 | − | 0.740704i | \(-0.265508\pi\) | ||||
0.671832 | + | 0.740704i | \(0.265508\pi\) | |||||||
\(734\) | 57.3027 | 2.11508 | ||||||||
\(735\) | 2.43876 | 0.0899551 | ||||||||
\(736\) | −7.18432 | −0.264818 | ||||||||
\(737\) | 1.91903 | 0.0706882 | ||||||||
\(738\) | −17.1608 | −0.631699 | ||||||||
\(739\) | −38.1788 | −1.40443 | −0.702215 | − | 0.711965i | \(-0.747805\pi\) | ||||
−0.702215 | + | 0.711965i | \(0.747805\pi\) | |||||||
\(740\) | −2.50842 | −0.0922112 | ||||||||
\(741\) | 28.8969 | 1.06155 | ||||||||
\(742\) | 1.37667 | 0.0505390 | ||||||||
\(743\) | 21.0449 | 0.772061 | 0.386030 | − | 0.922486i | \(-0.373846\pi\) | ||||
0.386030 | + | 0.922486i | \(0.373846\pi\) | |||||||
\(744\) | −16.4214 | −0.602036 | ||||||||
\(745\) | −1.79556 | −0.0657841 | ||||||||
\(746\) | 15.3928 | 0.563569 | ||||||||
\(747\) | −13.4558 | −0.492323 | ||||||||
\(748\) | −7.20835 | −0.263563 | ||||||||
\(749\) | −1.83151 | −0.0669220 | ||||||||
\(750\) | −4.06588 | −0.148465 | ||||||||
\(751\) | 18.1076 | 0.660757 | 0.330379 | − | 0.943848i | \(-0.392824\pi\) | ||||
0.330379 | + | 0.943848i | \(0.392824\pi\) | |||||||
\(752\) | 7.92123 | 0.288857 | ||||||||
\(753\) | 17.5498 | 0.639552 | ||||||||
\(754\) | −17.6278 | −0.641965 | ||||||||
\(755\) | 20.7823 | 0.756344 | ||||||||
\(756\) | −0.0996983 | −0.00362599 | ||||||||
\(757\) | 31.5581 | 1.14700 | 0.573499 | − | 0.819207i | \(-0.305586\pi\) | ||||
0.573499 | + | 0.819207i | \(0.305586\pi\) | |||||||
\(758\) | 40.0219 | 1.45366 | ||||||||
\(759\) | −13.2776 | −0.481945 | ||||||||
\(760\) | −11.5371 | −0.418494 | ||||||||
\(761\) | −42.5852 | −1.54371 | −0.771856 | − | 0.635797i | \(-0.780671\pi\) | ||||
−0.771856 | + | 0.635797i | \(0.780671\pi\) | |||||||
\(762\) | 42.3154 | 1.53292 | ||||||||
\(763\) | −15.5569 | −0.563199 | ||||||||
\(764\) | 8.57244 | 0.310140 | ||||||||
\(765\) | −8.59345 | −0.310697 | ||||||||
\(766\) | −4.85557 | −0.175439 | ||||||||
\(767\) | 24.7812 | 0.894799 | ||||||||
\(768\) | 39.5951 | 1.42877 | ||||||||
\(769\) | 10.8966 | 0.392940 | 0.196470 | − | 0.980510i | \(-0.437052\pi\) | ||||
0.196470 | + | 0.980510i | \(0.437052\pi\) | |||||||
\(770\) | −5.28792 | −0.190563 | ||||||||
\(771\) | 37.7526 | 1.35963 | ||||||||
\(772\) | −5.61239 | −0.201994 | ||||||||
\(773\) | −5.52820 | −0.198835 | −0.0994177 | − | 0.995046i | \(-0.531698\pi\) | ||||
−0.0994177 | + | 0.995046i | \(0.531698\pi\) | |||||||
\(774\) | −11.1385 | −0.400366 | ||||||||
\(775\) | −3.30922 | −0.118871 | ||||||||
\(776\) | 19.1674 | 0.688069 | ||||||||
\(777\) | −7.84762 | −0.281532 | ||||||||
\(778\) | 17.1566 | 0.615094 | ||||||||
\(779\) | −19.8004 | −0.709422 | ||||||||
\(780\) | −3.97283 | −0.142250 | ||||||||
\(781\) | −20.2482 | −0.724539 | ||||||||
\(782\) | −8.34336 | −0.298358 | ||||||||
\(783\) | 0.647096 | 0.0231253 | ||||||||
\(784\) | −4.95139 | −0.176835 | ||||||||
\(785\) | −4.31404 | −0.153975 | ||||||||
\(786\) | −15.7160 | −0.560573 | ||||||||
\(787\) | 26.1952 | 0.933757 | 0.466879 | − | 0.884321i | \(-0.345378\pi\) | ||||
0.466879 | + | 0.884321i | \(0.345378\pi\) | |||||||
\(788\) | −0.383502 | −0.0136617 | ||||||||
\(789\) | −0.0595617 | −0.00212045 | ||||||||
\(790\) | −13.6576 | −0.485916 | ||||||||
\(791\) | −6.33363 | −0.225198 | ||||||||
\(792\) | 19.0228 | 0.675947 | ||||||||
\(793\) | −18.4616 | −0.655592 | ||||||||
\(794\) | −23.8785 | −0.847415 | ||||||||
\(795\) | −2.01378 | −0.0714214 | ||||||||
\(796\) | 1.15179 | 0.0408240 | ||||||||
\(797\) | 6.07751 | 0.215276 | 0.107638 | − | 0.994190i | \(-0.465671\pi\) | ||||
0.107638 | + | 0.994190i | \(0.465671\pi\) | |||||||
\(798\) | 23.0535 | 0.816085 | ||||||||
\(799\) | 4.66413 | 0.165005 | ||||||||
\(800\) | 4.18539 | 0.147976 | ||||||||
\(801\) | −18.6247 | −0.658071 | ||||||||
\(802\) | 1.38605 | 0.0489430 | ||||||||
\(803\) | −28.2226 | −0.995953 | ||||||||
\(804\) | 1.15022 | 0.0405652 | ||||||||
\(805\) | −1.71652 | −0.0604995 | ||||||||
\(806\) | −11.5295 | −0.406110 | ||||||||
\(807\) | 23.6597 | 0.832862 | ||||||||
\(808\) | −33.3636 | −1.17373 | ||||||||
\(809\) | −14.5431 | −0.511309 | −0.255655 | − | 0.966768i | \(-0.582291\pi\) | ||||
−0.255655 | + | 0.966768i | \(0.582291\pi\) | |||||||
\(810\) | 15.2624 | 0.536267 | ||||||||
\(811\) | 27.5081 | 0.965941 | 0.482970 | − | 0.875637i | \(-0.339558\pi\) | ||||
0.482970 | + | 0.875637i | \(0.339558\pi\) | |||||||
\(812\) | −3.94405 | −0.138409 | ||||||||
\(813\) | 66.5505 | 2.33403 | ||||||||
\(814\) | 17.0158 | 0.596405 | ||||||||
\(815\) | 24.7220 | 0.865973 | ||||||||
\(816\) | 35.2048 | 1.23242 | ||||||||
\(817\) | −12.8518 | −0.449626 | ||||||||
\(818\) | −13.3228 | −0.465820 | ||||||||
\(819\) | −6.15974 | −0.215239 | ||||||||
\(820\) | 2.72221 | 0.0950637 | ||||||||
\(821\) | 46.7674 | 1.63219 | 0.816097 | − | 0.577914i | \(-0.196133\pi\) | ||||
0.816097 | + | 0.577914i | \(0.196133\pi\) | |||||||
\(822\) | 5.26677 | 0.183700 | ||||||||
\(823\) | −21.9743 | −0.765975 | −0.382988 | − | 0.923753i | \(-0.625105\pi\) | ||||
−0.382988 | + | 0.923753i | \(0.625105\pi\) | |||||||
\(824\) | −36.3786 | −1.26731 | ||||||||
\(825\) | 7.73515 | 0.269303 | ||||||||
\(826\) | 19.7701 | 0.687890 | ||||||||
\(827\) | −33.5813 | −1.16774 | −0.583868 | − | 0.811848i | \(-0.698462\pi\) | ||||
−0.583868 | + | 0.811848i | \(0.698462\pi\) | |||||||
\(828\) | −3.94406 | −0.137065 | ||||||||
\(829\) | −4.04046 | −0.140331 | −0.0701655 | − | 0.997535i | \(-0.522353\pi\) | ||||
−0.0701655 | + | 0.997535i | \(0.522353\pi\) | |||||||
\(830\) | 7.61086 | 0.264177 | ||||||||
\(831\) | −59.3479 | −2.05876 | ||||||||
\(832\) | −6.11246 | −0.211911 | ||||||||
\(833\) | −2.91545 | −0.101014 | ||||||||
\(834\) | 27.6762 | 0.958350 | ||||||||
\(835\) | −5.97506 | −0.206775 | ||||||||
\(836\) | −14.0189 | −0.484853 | ||||||||
\(837\) | 0.423236 | 0.0146292 | ||||||||
\(838\) | −42.7398 | −1.47642 | ||||||||
\(839\) | 55.8314 | 1.92751 | 0.963756 | − | 0.266784i | \(-0.0859609\pi\) | ||||
0.963756 | + | 0.266784i | \(0.0859609\pi\) | |||||||
\(840\) | 4.96230 | 0.171216 | ||||||||
\(841\) | −3.40098 | −0.117275 | ||||||||
\(842\) | −6.48972 | −0.223651 | ||||||||
\(843\) | −25.9350 | −0.893249 | ||||||||
\(844\) | −4.14686 | −0.142741 | ||||||||
\(845\) | −8.63283 | −0.296979 | ||||||||
\(846\) | 7.86163 | 0.270289 | ||||||||
\(847\) | −0.939978 | −0.0322980 | ||||||||
\(848\) | 4.08856 | 0.140402 | ||||||||
\(849\) | 0.0561743 | 0.00192790 | ||||||||
\(850\) | 4.86061 | 0.166718 | ||||||||
\(851\) | 5.52355 | 0.189345 | ||||||||
\(852\) | −12.1364 | −0.415785 | ||||||||
\(853\) | 51.9975 | 1.78036 | 0.890181 | − | 0.455608i | \(-0.150578\pi\) | ||||
0.890181 | + | 0.455608i | \(0.150578\pi\) | |||||||
\(854\) | −14.7284 | −0.503996 | ||||||||
\(855\) | −16.7126 | −0.571560 | ||||||||
\(856\) | −3.72669 | −0.127376 | ||||||||
\(857\) | 10.8023 | 0.369000 | 0.184500 | − | 0.982832i | \(-0.440933\pi\) | ||||
0.184500 | + | 0.982832i | \(0.440933\pi\) | |||||||
\(858\) | 26.9497 | 0.920048 | ||||||||
\(859\) | −3.50191 | −0.119484 | −0.0597418 | − | 0.998214i | \(-0.519028\pi\) | ||||
−0.0597418 | + | 0.998214i | \(0.519028\pi\) | |||||||
\(860\) | 1.76690 | 0.0602507 | ||||||||
\(861\) | 8.51648 | 0.290241 | ||||||||
\(862\) | 15.3982 | 0.524463 | ||||||||
\(863\) | −32.4769 | −1.10553 | −0.552764 | − | 0.833338i | \(-0.686427\pi\) | ||||
−0.552764 | + | 0.833338i | \(0.686427\pi\) | |||||||
\(864\) | −0.535295 | −0.0182111 | ||||||||
\(865\) | 16.8489 | 0.572881 | ||||||||
\(866\) | −15.6184 | −0.530733 | ||||||||
\(867\) | −20.7298 | −0.704022 | ||||||||
\(868\) | −2.57963 | −0.0875582 | ||||||||
\(869\) | 25.9830 | 0.881412 | ||||||||
\(870\) | 20.5715 | 0.697440 | ||||||||
\(871\) | −1.26439 | −0.0428422 | ||||||||
\(872\) | −31.6547 | −1.07196 | ||||||||
\(873\) | 27.7659 | 0.939732 | ||||||||
\(874\) | −16.2262 | −0.548860 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −16.9160 | −0.571539 | ||||||||
\(877\) | −56.7011 | −1.91466 | −0.957331 | − | 0.288994i | \(-0.906679\pi\) | ||||
−0.957331 | + | 0.288994i | \(0.906679\pi\) | |||||||
\(878\) | −26.4137 | −0.891419 | ||||||||
\(879\) | −5.40797 | −0.182406 | ||||||||
\(880\) | −15.7046 | −0.529402 | ||||||||
\(881\) | 12.9094 | 0.434929 | 0.217464 | − | 0.976068i | \(-0.430221\pi\) | ||||
0.217464 | + | 0.976068i | \(0.430221\pi\) | |||||||
\(882\) | −4.91414 | −0.165468 | ||||||||
\(883\) | −16.0655 | −0.540647 | −0.270324 | − | 0.962770i | \(-0.587131\pi\) | ||||
−0.270324 | + | 0.962770i | \(0.587131\pi\) | |||||||
\(884\) | 4.74937 | 0.159739 | ||||||||
\(885\) | −28.9196 | −0.972123 | ||||||||
\(886\) | 32.8231 | 1.10272 | ||||||||
\(887\) | 25.2387 | 0.847434 | 0.423717 | − | 0.905795i | \(-0.360725\pi\) | ||||
0.423717 | + | 0.905795i | \(0.360725\pi\) | |||||||
\(888\) | −15.9680 | −0.535852 | ||||||||
\(889\) | −10.4074 | −0.349054 | ||||||||
\(890\) | 10.5345 | 0.353116 | ||||||||
\(891\) | −29.0361 | −0.972745 | ||||||||
\(892\) | 12.3979 | 0.415113 | ||||||||
\(893\) | 9.07084 | 0.303544 | ||||||||
\(894\) | 7.30052 | 0.244166 | ||||||||
\(895\) | 1.22054 | 0.0407982 | ||||||||
\(896\) | −13.2472 | −0.442558 | ||||||||
\(897\) | 8.74821 | 0.292094 | ||||||||
\(898\) | 25.2685 | 0.843220 | ||||||||
\(899\) | 16.7432 | 0.558416 | ||||||||
\(900\) | 2.29770 | 0.0765900 | ||||||||
\(901\) | 2.40740 | 0.0802022 | ||||||||
\(902\) | −18.4661 | −0.614855 | ||||||||
\(903\) | 5.52777 | 0.183953 | ||||||||
\(904\) | −12.8874 | −0.428630 | ||||||||
\(905\) | 19.3567 | 0.643439 | ||||||||
\(906\) | −84.4983 | −2.80727 | ||||||||
\(907\) | 39.3096 | 1.30525 | 0.652626 | − | 0.757680i | \(-0.273667\pi\) | ||||
0.652626 | + | 0.757680i | \(0.273667\pi\) | |||||||
\(908\) | −4.97474 | −0.165093 | ||||||||
\(909\) | −48.3306 | −1.60302 | ||||||||
\(910\) | 3.48406 | 0.115495 | ||||||||
\(911\) | −39.4741 | −1.30783 | −0.653917 | − | 0.756566i | \(-0.726876\pi\) | ||||
−0.653917 | + | 0.756566i | \(0.726876\pi\) | |||||||
\(912\) | 68.4666 | 2.26716 | ||||||||
\(913\) | −14.4793 | −0.479195 | ||||||||
\(914\) | 18.1978 | 0.601929 | ||||||||
\(915\) | 21.5447 | 0.712245 | ||||||||
\(916\) | −0.779527 | −0.0257563 | ||||||||
\(917\) | 3.86535 | 0.127645 | ||||||||
\(918\) | −0.621653 | −0.0205176 | ||||||||
\(919\) | −30.7682 | −1.01495 | −0.507475 | − | 0.861666i | \(-0.669421\pi\) | ||||
−0.507475 | + | 0.861666i | \(0.669421\pi\) | |||||||
\(920\) | −3.49272 | −0.115152 | ||||||||
\(921\) | −42.1634 | −1.38933 | ||||||||
\(922\) | −12.2176 | −0.402366 | ||||||||
\(923\) | 13.3410 | 0.439124 | ||||||||
\(924\) | 6.02976 | 0.198364 | ||||||||
\(925\) | −3.21787 | −0.105803 | ||||||||
\(926\) | 61.5806 | 2.02366 | ||||||||
\(927\) | −52.6980 | −1.73083 | ||||||||
\(928\) | −21.1762 | −0.695142 | ||||||||
\(929\) | 20.9931 | 0.688760 | 0.344380 | − | 0.938830i | \(-0.388089\pi\) | ||||
0.344380 | + | 0.938830i | \(0.388089\pi\) | |||||||
\(930\) | 13.4549 | 0.441204 | ||||||||
\(931\) | −5.66999 | −0.185826 | ||||||||
\(932\) | 15.8426 | 0.518942 | ||||||||
\(933\) | 34.5986 | 1.13271 | ||||||||
\(934\) | −50.0227 | −1.63679 | ||||||||
\(935\) | −9.24709 | −0.302412 | ||||||||
\(936\) | −12.5336 | −0.409673 | ||||||||
\(937\) | −1.56738 | −0.0512040 | −0.0256020 | − | 0.999672i | \(-0.508150\pi\) | ||||
−0.0256020 | + | 0.999672i | \(0.508150\pi\) | |||||||
\(938\) | −1.00871 | −0.0329356 | ||||||||
\(939\) | 70.8634 | 2.31254 | ||||||||
\(940\) | −1.24709 | −0.0406754 | ||||||||
\(941\) | −30.0695 | −0.980237 | −0.490118 | − | 0.871656i | \(-0.663046\pi\) | ||||
−0.490118 | + | 0.871656i | \(0.663046\pi\) | |||||||
\(942\) | 17.5404 | 0.571496 | ||||||||
\(943\) | −5.99433 | −0.195202 | ||||||||
\(944\) | 58.7152 | 1.91102 | ||||||||
\(945\) | −0.127896 | −0.00416046 | ||||||||
\(946\) | −11.9858 | −0.389691 | ||||||||
\(947\) | −46.5781 | −1.51358 | −0.756792 | − | 0.653656i | \(-0.773234\pi\) | ||||
−0.756792 | + | 0.653656i | \(0.773234\pi\) | |||||||
\(948\) | 15.5736 | 0.505808 | ||||||||
\(949\) | 18.5950 | 0.603621 | ||||||||
\(950\) | 9.45296 | 0.306695 | ||||||||
\(951\) | 1.56168 | 0.0506409 | ||||||||
\(952\) | −5.93225 | −0.192265 | ||||||||
\(953\) | 34.8143 | 1.12775 | 0.563873 | − | 0.825862i | \(-0.309311\pi\) | ||||
0.563873 | + | 0.825862i | \(0.309311\pi\) | |||||||
\(954\) | 4.05780 | 0.131376 | ||||||||
\(955\) | 10.9970 | 0.355854 | ||||||||
\(956\) | 3.69650 | 0.119553 | ||||||||
\(957\) | −39.1364 | −1.26510 | ||||||||
\(958\) | −21.5623 | −0.696648 | ||||||||
\(959\) | −1.29536 | −0.0418293 | ||||||||
\(960\) | 7.13322 | 0.230224 | ||||||||
\(961\) | −20.0490 | −0.646744 | ||||||||
\(962\) | −11.2112 | −0.361465 | ||||||||
\(963\) | −5.39849 | −0.173964 | ||||||||
\(964\) | 3.51807 | 0.113310 | ||||||||
\(965\) | −7.19974 | −0.231768 | ||||||||
\(966\) | 6.97918 | 0.224552 | ||||||||
\(967\) | 29.6580 | 0.953738 | 0.476869 | − | 0.878974i | \(-0.341772\pi\) | ||||
0.476869 | + | 0.878974i | \(0.341772\pi\) | |||||||
\(968\) | −1.91263 | −0.0614743 | ||||||||
\(969\) | 40.3141 | 1.29508 | ||||||||
\(970\) | −15.7049 | −0.504253 | ||||||||
\(971\) | −45.2029 | −1.45063 | −0.725316 | − | 0.688416i | \(-0.758306\pi\) | ||||
−0.725316 | + | 0.688416i | \(0.758306\pi\) | |||||||
\(972\) | −17.1045 | −0.548627 | ||||||||
\(973\) | −6.80695 | −0.218221 | ||||||||
\(974\) | −25.7318 | −0.824501 | ||||||||
\(975\) | −5.09647 | −0.163218 | ||||||||
\(976\) | −43.7419 | −1.40014 | ||||||||
\(977\) | 2.94679 | 0.0942763 | 0.0471382 | − | 0.998888i | \(-0.484990\pi\) | ||||
0.0471382 | + | 0.998888i | \(0.484990\pi\) | |||||||
\(978\) | −100.517 | −3.21417 | ||||||||
\(979\) | −20.0413 | −0.640523 | ||||||||
\(980\) | 0.779527 | 0.0249011 | ||||||||
\(981\) | −45.8549 | −1.46404 | ||||||||
\(982\) | 18.6702 | 0.595791 | ||||||||
\(983\) | −33.1113 | −1.05609 | −0.528044 | − | 0.849217i | \(-0.677074\pi\) | ||||
−0.528044 | + | 0.849217i | \(0.677074\pi\) | |||||||
\(984\) | 17.3290 | 0.552429 | ||||||||
\(985\) | −0.491967 | −0.0156754 | ||||||||
\(986\) | −24.5925 | −0.783185 | ||||||||
\(987\) | −3.90153 | −0.124187 | ||||||||
\(988\) | 9.23662 | 0.293856 | ||||||||
\(989\) | −3.89072 | −0.123718 | ||||||||
\(990\) | −15.5864 | −0.495370 | ||||||||
\(991\) | −36.6569 | −1.16444 | −0.582222 | − | 0.813030i | \(-0.697816\pi\) | ||||
−0.582222 | + | 0.813030i | \(0.697816\pi\) | |||||||
\(992\) | −13.8504 | −0.439750 | ||||||||
\(993\) | −22.1591 | −0.703198 | ||||||||
\(994\) | 10.6432 | 0.337583 | ||||||||
\(995\) | 1.47755 | 0.0468413 | ||||||||
\(996\) | −8.67858 | −0.274991 | ||||||||
\(997\) | −44.6807 | −1.41505 | −0.707525 | − | 0.706688i | \(-0.750188\pi\) | ||||
−0.707525 | + | 0.706688i | \(0.750188\pi\) | |||||||
\(998\) | 24.4625 | 0.774348 | ||||||||
\(999\) | 0.411553 | 0.0130209 |
(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 | 8015.2.a.h.1.11 | ✓ | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.h.1.11 | ✓ | 38 | 1.1 | even | 1 | trivial |