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: | \(0\) |
Dimension: | \(67\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.94503 | −1.37534 | −0.687671 | − | 0.726022i | \(-0.741367\pi\) | ||||
−0.687671 | + | 0.726022i | \(0.741367\pi\) | |||||||
\(3\) | 2.18285 | 1.26027 | 0.630135 | − | 0.776486i | \(-0.283000\pi\) | ||||
0.630135 | + | 0.776486i | \(0.283000\pi\) | |||||||
\(4\) | 1.78313 | 0.891567 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −4.24571 | −1.73330 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0.421811 | 0.149133 | ||||||||
\(9\) | 1.76484 | 0.588279 | ||||||||
\(10\) | −1.94503 | −0.615072 | ||||||||
\(11\) | 6.09451 | 1.83756 | 0.918782 | − | 0.394766i | \(-0.129174\pi\) | ||||
0.918782 | + | 0.394766i | \(0.129174\pi\) | |||||||
\(12\) | 3.89231 | 1.12361 | ||||||||
\(13\) | 3.26846 | 0.906507 | 0.453253 | − | 0.891382i | \(-0.350263\pi\) | ||||
0.453253 | + | 0.891382i | \(0.350263\pi\) | |||||||
\(14\) | 1.94503 | 0.519831 | ||||||||
\(15\) | 2.18285 | 0.563610 | ||||||||
\(16\) | −4.38670 | −1.09668 | ||||||||
\(17\) | −5.66347 | −1.37359 | −0.686797 | − | 0.726850i | \(-0.740984\pi\) | ||||
−0.686797 | + | 0.726850i | \(0.740984\pi\) | |||||||
\(18\) | −3.43266 | −0.809085 | ||||||||
\(19\) | 7.89079 | 1.81027 | 0.905135 | − | 0.425124i | \(-0.139769\pi\) | ||||
0.905135 | + | 0.425124i | \(0.139769\pi\) | |||||||
\(20\) | 1.78313 | 0.398721 | ||||||||
\(21\) | −2.18285 | −0.476337 | ||||||||
\(22\) | −11.8540 | −2.52728 | ||||||||
\(23\) | −3.46719 | −0.722960 | −0.361480 | − | 0.932380i | \(-0.617728\pi\) | ||||
−0.361480 | + | 0.932380i | \(0.617728\pi\) | |||||||
\(24\) | 0.920750 | 0.187947 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −6.35724 | −1.24676 | ||||||||
\(27\) | −2.69618 | −0.518880 | ||||||||
\(28\) | −1.78313 | −0.336981 | ||||||||
\(29\) | 6.35413 | 1.17993 | 0.589966 | − | 0.807428i | \(-0.299141\pi\) | ||||
0.589966 | + | 0.807428i | \(0.299141\pi\) | |||||||
\(30\) | −4.24571 | −0.775156 | ||||||||
\(31\) | −4.38922 | −0.788327 | −0.394163 | − | 0.919040i | \(-0.628966\pi\) | ||||
−0.394163 | + | 0.919040i | \(0.628966\pi\) | |||||||
\(32\) | 7.68864 | 1.35917 | ||||||||
\(33\) | 13.3034 | 2.31582 | ||||||||
\(34\) | 11.0156 | 1.88916 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 3.14694 | 0.524490 | ||||||||
\(37\) | −5.29552 | −0.870579 | −0.435289 | − | 0.900291i | \(-0.643354\pi\) | ||||
−0.435289 | + | 0.900291i | \(0.643354\pi\) | |||||||
\(38\) | −15.3478 | −2.48974 | ||||||||
\(39\) | 7.13455 | 1.14244 | ||||||||
\(40\) | 0.421811 | 0.0666942 | ||||||||
\(41\) | −1.38738 | −0.216672 | −0.108336 | − | 0.994114i | \(-0.534552\pi\) | ||||
−0.108336 | + | 0.994114i | \(0.534552\pi\) | |||||||
\(42\) | 4.24571 | 0.655127 | ||||||||
\(43\) | 6.06975 | 0.925629 | 0.462814 | − | 0.886455i | \(-0.346840\pi\) | ||||
0.462814 | + | 0.886455i | \(0.346840\pi\) | |||||||
\(44\) | 10.8673 | 1.63831 | ||||||||
\(45\) | 1.76484 | 0.263086 | ||||||||
\(46\) | 6.74379 | 0.994317 | ||||||||
\(47\) | −5.49249 | −0.801162 | −0.400581 | − | 0.916261i | \(-0.631192\pi\) | ||||
−0.400581 | + | 0.916261i | \(0.631192\pi\) | |||||||
\(48\) | −9.57551 | −1.38211 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.94503 | −0.275068 | ||||||||
\(51\) | −12.3625 | −1.73110 | ||||||||
\(52\) | 5.82810 | 0.808211 | ||||||||
\(53\) | −11.7735 | −1.61722 | −0.808611 | − | 0.588344i | \(-0.799780\pi\) | ||||
−0.808611 | + | 0.588344i | \(0.799780\pi\) | |||||||
\(54\) | 5.24414 | 0.713637 | ||||||||
\(55\) | 6.09451 | 0.821783 | ||||||||
\(56\) | −0.421811 | −0.0563669 | ||||||||
\(57\) | 17.2244 | 2.28143 | ||||||||
\(58\) | −12.3590 | −1.62281 | ||||||||
\(59\) | 11.9506 | 1.55584 | 0.777919 | − | 0.628365i | \(-0.216276\pi\) | ||||
0.777919 | + | 0.628365i | \(0.216276\pi\) | |||||||
\(60\) | 3.89231 | 0.502496 | ||||||||
\(61\) | 7.00385 | 0.896751 | 0.448375 | − | 0.893845i | \(-0.352003\pi\) | ||||
0.448375 | + | 0.893845i | \(0.352003\pi\) | |||||||
\(62\) | 8.53715 | 1.08422 | ||||||||
\(63\) | −1.76484 | −0.222348 | ||||||||
\(64\) | −6.18121 | −0.772651 | ||||||||
\(65\) | 3.26846 | 0.405402 | ||||||||
\(66\) | −25.8755 | −3.18505 | ||||||||
\(67\) | 8.63416 | 1.05483 | 0.527415 | − | 0.849608i | \(-0.323161\pi\) | ||||
0.527415 | + | 0.849608i | \(0.323161\pi\) | |||||||
\(68\) | −10.0987 | −1.22465 | ||||||||
\(69\) | −7.56836 | −0.911124 | ||||||||
\(70\) | 1.94503 | 0.232475 | ||||||||
\(71\) | 14.7022 | 1.74483 | 0.872414 | − | 0.488767i | \(-0.162553\pi\) | ||||
0.872414 | + | 0.488767i | \(0.162553\pi\) | |||||||
\(72\) | 0.744427 | 0.0877316 | ||||||||
\(73\) | 4.02309 | 0.470867 | 0.235434 | − | 0.971890i | \(-0.424349\pi\) | ||||
0.235434 | + | 0.971890i | \(0.424349\pi\) | |||||||
\(74\) | 10.2999 | 1.19734 | ||||||||
\(75\) | 2.18285 | 0.252054 | ||||||||
\(76\) | 14.0703 | 1.61398 | ||||||||
\(77\) | −6.09451 | −0.694534 | ||||||||
\(78\) | −13.8769 | −1.57125 | ||||||||
\(79\) | 4.96540 | 0.558651 | 0.279326 | − | 0.960196i | \(-0.409889\pi\) | ||||
0.279326 | + | 0.960196i | \(0.409889\pi\) | |||||||
\(80\) | −4.38670 | −0.490448 | ||||||||
\(81\) | −11.1799 | −1.24221 | ||||||||
\(82\) | 2.69848 | 0.297998 | ||||||||
\(83\) | 0.709802 | 0.0779109 | 0.0389554 | − | 0.999241i | \(-0.487597\pi\) | ||||
0.0389554 | + | 0.999241i | \(0.487597\pi\) | |||||||
\(84\) | −3.89231 | −0.424686 | ||||||||
\(85\) | −5.66347 | −0.614290 | ||||||||
\(86\) | −11.8058 | −1.27306 | ||||||||
\(87\) | 13.8701 | 1.48703 | ||||||||
\(88\) | 2.57073 | 0.274041 | ||||||||
\(89\) | 14.7952 | 1.56829 | 0.784145 | − | 0.620577i | \(-0.213102\pi\) | ||||
0.784145 | + | 0.620577i | \(0.213102\pi\) | |||||||
\(90\) | −3.43266 | −0.361834 | ||||||||
\(91\) | −3.26846 | −0.342627 | ||||||||
\(92\) | −6.18247 | −0.644567 | ||||||||
\(93\) | −9.58101 | −0.993504 | ||||||||
\(94\) | 10.6830 | 1.10187 | ||||||||
\(95\) | 7.89079 | 0.809578 | ||||||||
\(96\) | 16.7831 | 1.71292 | ||||||||
\(97\) | −7.08866 | −0.719744 | −0.359872 | − | 0.933002i | \(-0.617180\pi\) | ||||
−0.359872 | + | 0.933002i | \(0.617180\pi\) | |||||||
\(98\) | −1.94503 | −0.196477 | ||||||||
\(99\) | 10.7558 | 1.08100 | ||||||||
\(100\) | 1.78313 | 0.178313 | ||||||||
\(101\) | −5.16388 | −0.513826 | −0.256913 | − | 0.966435i | \(-0.582705\pi\) | ||||
−0.256913 | + | 0.966435i | \(0.582705\pi\) | |||||||
\(102\) | 24.0454 | 2.38085 | ||||||||
\(103\) | 6.94975 | 0.684779 | 0.342390 | − | 0.939558i | \(-0.388764\pi\) | ||||
0.342390 | + | 0.939558i | \(0.388764\pi\) | |||||||
\(104\) | 1.37867 | 0.135190 | ||||||||
\(105\) | −2.18285 | −0.213024 | ||||||||
\(106\) | 22.8999 | 2.22423 | ||||||||
\(107\) | 18.0290 | 1.74293 | 0.871464 | − | 0.490460i | \(-0.163171\pi\) | ||||
0.871464 | + | 0.490460i | \(0.163171\pi\) | |||||||
\(108\) | −4.80765 | −0.462616 | ||||||||
\(109\) | −13.0278 | −1.24784 | −0.623918 | − | 0.781490i | \(-0.714460\pi\) | ||||
−0.623918 | + | 0.781490i | \(0.714460\pi\) | |||||||
\(110\) | −11.8540 | −1.13023 | ||||||||
\(111\) | −11.5593 | −1.09716 | ||||||||
\(112\) | 4.38670 | 0.414504 | ||||||||
\(113\) | −6.68878 | −0.629228 | −0.314614 | − | 0.949220i | \(-0.601875\pi\) | ||||
−0.314614 | + | 0.949220i | \(0.601875\pi\) | |||||||
\(114\) | −33.5020 | −3.13775 | ||||||||
\(115\) | −3.46719 | −0.323317 | ||||||||
\(116\) | 11.3303 | 1.05199 | ||||||||
\(117\) | 5.76829 | 0.533279 | ||||||||
\(118\) | −23.2443 | −2.13981 | ||||||||
\(119\) | 5.66347 | 0.519169 | ||||||||
\(120\) | 0.920750 | 0.0840526 | ||||||||
\(121\) | 26.1430 | 2.37664 | ||||||||
\(122\) | −13.6227 | −1.23334 | ||||||||
\(123\) | −3.02843 | −0.273065 | ||||||||
\(124\) | −7.82656 | −0.702846 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 3.43266 | 0.305805 | ||||||||
\(127\) | 15.7252 | 1.39539 | 0.697695 | − | 0.716395i | \(-0.254209\pi\) | ||||
0.697695 | + | 0.716395i | \(0.254209\pi\) | |||||||
\(128\) | −3.35465 | −0.296512 | ||||||||
\(129\) | 13.2494 | 1.16654 | ||||||||
\(130\) | −6.35724 | −0.557567 | ||||||||
\(131\) | 9.24702 | 0.807916 | 0.403958 | − | 0.914777i | \(-0.367634\pi\) | ||||
0.403958 | + | 0.914777i | \(0.367634\pi\) | |||||||
\(132\) | 23.7217 | 2.06471 | ||||||||
\(133\) | −7.89079 | −0.684218 | ||||||||
\(134\) | −16.7937 | −1.45075 | ||||||||
\(135\) | −2.69618 | −0.232050 | ||||||||
\(136\) | −2.38891 | −0.204848 | ||||||||
\(137\) | −6.76591 | −0.578051 | −0.289025 | − | 0.957321i | \(-0.593331\pi\) | ||||
−0.289025 | + | 0.957321i | \(0.593331\pi\) | |||||||
\(138\) | 14.7207 | 1.25311 | ||||||||
\(139\) | 3.08504 | 0.261670 | 0.130835 | − | 0.991404i | \(-0.458234\pi\) | ||||
0.130835 | + | 0.991404i | \(0.458234\pi\) | |||||||
\(140\) | −1.78313 | −0.150702 | ||||||||
\(141\) | −11.9893 | −1.00968 | ||||||||
\(142\) | −28.5962 | −2.39974 | ||||||||
\(143\) | 19.9196 | 1.66576 | ||||||||
\(144\) | −7.74181 | −0.645151 | ||||||||
\(145\) | 6.35413 | 0.527681 | ||||||||
\(146\) | −7.82503 | −0.647604 | ||||||||
\(147\) | 2.18285 | 0.180038 | ||||||||
\(148\) | −9.44263 | −0.776179 | ||||||||
\(149\) | −8.33305 | −0.682670 | −0.341335 | − | 0.939942i | \(-0.610879\pi\) | ||||
−0.341335 | + | 0.939942i | \(0.610879\pi\) | |||||||
\(150\) | −4.24571 | −0.346660 | ||||||||
\(151\) | 2.27792 | 0.185374 | 0.0926872 | − | 0.995695i | \(-0.470454\pi\) | ||||
0.0926872 | + | 0.995695i | \(0.470454\pi\) | |||||||
\(152\) | 3.32842 | 0.269971 | ||||||||
\(153\) | −9.99509 | −0.808055 | ||||||||
\(154\) | 11.8540 | 0.955222 | ||||||||
\(155\) | −4.38922 | −0.352550 | ||||||||
\(156\) | 12.7219 | 1.01856 | ||||||||
\(157\) | −22.9011 | −1.82771 | −0.913853 | − | 0.406044i | \(-0.866908\pi\) | ||||
−0.913853 | + | 0.406044i | \(0.866908\pi\) | |||||||
\(158\) | −9.65785 | −0.768337 | ||||||||
\(159\) | −25.6999 | −2.03813 | ||||||||
\(160\) | 7.68864 | 0.607840 | ||||||||
\(161\) | 3.46719 | 0.273253 | ||||||||
\(162\) | 21.7451 | 1.70846 | ||||||||
\(163\) | −3.83777 | −0.300597 | −0.150299 | − | 0.988641i | \(-0.548024\pi\) | ||||
−0.150299 | + | 0.988641i | \(0.548024\pi\) | |||||||
\(164\) | −2.47388 | −0.193177 | ||||||||
\(165\) | 13.3034 | 1.03567 | ||||||||
\(166\) | −1.38058 | −0.107154 | ||||||||
\(167\) | −5.22631 | −0.404424 | −0.202212 | − | 0.979342i | \(-0.564813\pi\) | ||||
−0.202212 | + | 0.979342i | \(0.564813\pi\) | |||||||
\(168\) | −0.920750 | −0.0710374 | ||||||||
\(169\) | −2.31719 | −0.178245 | ||||||||
\(170\) | 11.0156 | 0.844858 | ||||||||
\(171\) | 13.9259 | 1.06494 | ||||||||
\(172\) | 10.8232 | 0.825260 | ||||||||
\(173\) | 4.83749 | 0.367788 | 0.183894 | − | 0.982946i | \(-0.441130\pi\) | ||||
0.183894 | + | 0.982946i | \(0.441130\pi\) | |||||||
\(174\) | −26.9777 | −2.04518 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | −26.7348 | −2.01521 | ||||||||
\(177\) | 26.0864 | 1.96077 | ||||||||
\(178\) | −28.7771 | −2.15694 | ||||||||
\(179\) | −6.15653 | −0.460161 | −0.230080 | − | 0.973172i | \(-0.573899\pi\) | ||||
−0.230080 | + | 0.973172i | \(0.573899\pi\) | |||||||
\(180\) | 3.14694 | 0.234559 | ||||||||
\(181\) | −14.0167 | −1.04185 | −0.520926 | − | 0.853602i | \(-0.674413\pi\) | ||||
−0.520926 | + | 0.853602i | \(0.674413\pi\) | |||||||
\(182\) | 6.35724 | 0.471230 | ||||||||
\(183\) | 15.2884 | 1.13015 | ||||||||
\(184\) | −1.46250 | −0.107817 | ||||||||
\(185\) | −5.29552 | −0.389335 | ||||||||
\(186\) | 18.6353 | 1.36641 | ||||||||
\(187\) | −34.5161 | −2.52406 | ||||||||
\(188\) | −9.79385 | −0.714290 | ||||||||
\(189\) | 2.69618 | 0.196118 | ||||||||
\(190\) | −15.3478 | −1.11345 | ||||||||
\(191\) | 0.0806972 | 0.00583905 | 0.00291952 | − | 0.999996i | \(-0.499071\pi\) | ||||
0.00291952 | + | 0.999996i | \(0.499071\pi\) | |||||||
\(192\) | −13.4927 | −0.973748 | ||||||||
\(193\) | −2.01661 | −0.145159 | −0.0725794 | − | 0.997363i | \(-0.523123\pi\) | ||||
−0.0725794 | + | 0.997363i | \(0.523123\pi\) | |||||||
\(194\) | 13.7876 | 0.989895 | ||||||||
\(195\) | 7.13455 | 0.510916 | ||||||||
\(196\) | 1.78313 | 0.127367 | ||||||||
\(197\) | −1.09518 | −0.0780286 | −0.0390143 | − | 0.999239i | \(-0.512422\pi\) | ||||
−0.0390143 | + | 0.999239i | \(0.512422\pi\) | |||||||
\(198\) | −20.9203 | −1.48674 | ||||||||
\(199\) | −10.5428 | −0.747358 | −0.373679 | − | 0.927558i | \(-0.621904\pi\) | ||||
−0.373679 | + | 0.927558i | \(0.621904\pi\) | |||||||
\(200\) | 0.421811 | 0.0298265 | ||||||||
\(201\) | 18.8471 | 1.32937 | ||||||||
\(202\) | 10.0439 | 0.706686 | ||||||||
\(203\) | −6.35413 | −0.445972 | ||||||||
\(204\) | −22.0440 | −1.54339 | ||||||||
\(205\) | −1.38738 | −0.0968985 | ||||||||
\(206\) | −13.5175 | −0.941806 | ||||||||
\(207\) | −6.11903 | −0.425302 | ||||||||
\(208\) | −14.3377 | −0.994144 | ||||||||
\(209\) | 48.0905 | 3.32649 | ||||||||
\(210\) | 4.24571 | 0.292981 | ||||||||
\(211\) | −13.0622 | −0.899237 | −0.449618 | − | 0.893221i | \(-0.648440\pi\) | ||||
−0.449618 | + | 0.893221i | \(0.648440\pi\) | |||||||
\(212\) | −20.9938 | −1.44186 | ||||||||
\(213\) | 32.0927 | 2.19895 | ||||||||
\(214\) | −35.0669 | −2.39712 | ||||||||
\(215\) | 6.06975 | 0.413954 | ||||||||
\(216\) | −1.13728 | −0.0773819 | ||||||||
\(217\) | 4.38922 | 0.297960 | ||||||||
\(218\) | 25.3394 | 1.71620 | ||||||||
\(219\) | 8.78181 | 0.593420 | ||||||||
\(220\) | 10.8673 | 0.732675 | ||||||||
\(221\) | −18.5108 | −1.24517 | ||||||||
\(222\) | 22.4832 | 1.50898 | ||||||||
\(223\) | −2.70168 | −0.180918 | −0.0904589 | − | 0.995900i | \(-0.528833\pi\) | ||||
−0.0904589 | + | 0.995900i | \(0.528833\pi\) | |||||||
\(224\) | −7.68864 | −0.513719 | ||||||||
\(225\) | 1.76484 | 0.117656 | ||||||||
\(226\) | 13.0099 | 0.865403 | ||||||||
\(227\) | −20.0411 | −1.33018 | −0.665088 | − | 0.746765i | \(-0.731606\pi\) | ||||
−0.665088 | + | 0.746765i | \(0.731606\pi\) | |||||||
\(228\) | 30.7134 | 2.03405 | ||||||||
\(229\) | −1.00000 | −0.0660819 | ||||||||
\(230\) | 6.74379 | 0.444672 | ||||||||
\(231\) | −13.3034 | −0.875299 | ||||||||
\(232\) | 2.68024 | 0.175966 | ||||||||
\(233\) | 24.1462 | 1.58187 | 0.790936 | − | 0.611899i | \(-0.209594\pi\) | ||||
0.790936 | + | 0.611899i | \(0.209594\pi\) | |||||||
\(234\) | −11.2195 | −0.733441 | ||||||||
\(235\) | −5.49249 | −0.358291 | ||||||||
\(236\) | 21.3095 | 1.38713 | ||||||||
\(237\) | 10.8387 | 0.704051 | ||||||||
\(238\) | −11.0156 | −0.714036 | ||||||||
\(239\) | 8.77862 | 0.567841 | 0.283921 | − | 0.958848i | \(-0.408365\pi\) | ||||
0.283921 | + | 0.958848i | \(0.408365\pi\) | |||||||
\(240\) | −9.57551 | −0.618097 | ||||||||
\(241\) | 5.29756 | 0.341246 | 0.170623 | − | 0.985336i | \(-0.445422\pi\) | ||||
0.170623 | + | 0.985336i | \(0.445422\pi\) | |||||||
\(242\) | −50.8489 | −3.26869 | ||||||||
\(243\) | −16.3154 | −1.04664 | ||||||||
\(244\) | 12.4888 | 0.799513 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 5.89039 | 0.375557 | ||||||||
\(247\) | 25.7907 | 1.64102 | ||||||||
\(248\) | −1.85142 | −0.117565 | ||||||||
\(249\) | 1.54939 | 0.0981887 | ||||||||
\(250\) | −1.94503 | −0.123014 | ||||||||
\(251\) | −8.70336 | −0.549351 | −0.274676 | − | 0.961537i | \(-0.588570\pi\) | ||||
−0.274676 | + | 0.961537i | \(0.588570\pi\) | |||||||
\(252\) | −3.14694 | −0.198238 | ||||||||
\(253\) | −21.1308 | −1.32848 | ||||||||
\(254\) | −30.5860 | −1.91914 | ||||||||
\(255\) | −12.3625 | −0.774170 | ||||||||
\(256\) | 18.8873 | 1.18046 | ||||||||
\(257\) | 29.3730 | 1.83224 | 0.916120 | − | 0.400905i | \(-0.131304\pi\) | ||||
0.916120 | + | 0.400905i | \(0.131304\pi\) | |||||||
\(258\) | −25.7704 | −1.60439 | ||||||||
\(259\) | 5.29552 | 0.329048 | ||||||||
\(260\) | 5.82810 | 0.361443 | ||||||||
\(261\) | 11.2140 | 0.694128 | ||||||||
\(262\) | −17.9857 | −1.11116 | ||||||||
\(263\) | 14.1841 | 0.874631 | 0.437315 | − | 0.899308i | \(-0.355929\pi\) | ||||
0.437315 | + | 0.899308i | \(0.355929\pi\) | |||||||
\(264\) | 5.61152 | 0.345365 | ||||||||
\(265\) | −11.7735 | −0.723243 | ||||||||
\(266\) | 15.3478 | 0.941034 | ||||||||
\(267\) | 32.2958 | 1.97647 | ||||||||
\(268\) | 15.3959 | 0.940452 | ||||||||
\(269\) | 13.3952 | 0.816719 | 0.408359 | − | 0.912821i | \(-0.366101\pi\) | ||||
0.408359 | + | 0.912821i | \(0.366101\pi\) | |||||||
\(270\) | 5.24414 | 0.319148 | ||||||||
\(271\) | 5.97771 | 0.363120 | 0.181560 | − | 0.983380i | \(-0.441885\pi\) | ||||
0.181560 | + | 0.983380i | \(0.441885\pi\) | |||||||
\(272\) | 24.8440 | 1.50639 | ||||||||
\(273\) | −7.13455 | −0.431803 | ||||||||
\(274\) | 13.1599 | 0.795018 | ||||||||
\(275\) | 6.09451 | 0.367513 | ||||||||
\(276\) | −13.4954 | −0.812328 | ||||||||
\(277\) | 8.87570 | 0.533289 | 0.266645 | − | 0.963795i | \(-0.414085\pi\) | ||||
0.266645 | + | 0.963795i | \(0.414085\pi\) | |||||||
\(278\) | −6.00050 | −0.359886 | ||||||||
\(279\) | −7.74625 | −0.463756 | ||||||||
\(280\) | −0.421811 | −0.0252080 | ||||||||
\(281\) | −22.1107 | −1.31902 | −0.659508 | − | 0.751697i | \(-0.729235\pi\) | ||||
−0.659508 | + | 0.751697i | \(0.729235\pi\) | |||||||
\(282\) | 23.3195 | 1.38866 | ||||||||
\(283\) | 2.35505 | 0.139993 | 0.0699966 | − | 0.997547i | \(-0.477701\pi\) | ||||
0.0699966 | + | 0.997547i | \(0.477701\pi\) | |||||||
\(284\) | 26.2160 | 1.55563 | ||||||||
\(285\) | 17.2244 | 1.02029 | ||||||||
\(286\) | −38.7442 | −2.29100 | ||||||||
\(287\) | 1.38738 | 0.0818942 | ||||||||
\(288\) | 13.5692 | 0.799572 | ||||||||
\(289\) | 15.0749 | 0.886758 | ||||||||
\(290\) | −12.3590 | −0.725743 | ||||||||
\(291\) | −15.4735 | −0.907071 | ||||||||
\(292\) | 7.17371 | 0.419810 | ||||||||
\(293\) | −3.36842 | −0.196785 | −0.0983926 | − | 0.995148i | \(-0.531370\pi\) | ||||
−0.0983926 | + | 0.995148i | \(0.531370\pi\) | |||||||
\(294\) | −4.24571 | −0.247615 | ||||||||
\(295\) | 11.9506 | 0.695791 | ||||||||
\(296\) | −2.23371 | −0.129832 | ||||||||
\(297\) | −16.4319 | −0.953474 | ||||||||
\(298\) | 16.2080 | 0.938905 | ||||||||
\(299\) | −11.3324 | −0.655368 | ||||||||
\(300\) | 3.89231 | 0.224723 | ||||||||
\(301\) | −6.06975 | −0.349855 | ||||||||
\(302\) | −4.43061 | −0.254953 | ||||||||
\(303\) | −11.2720 | −0.647559 | ||||||||
\(304\) | −34.6145 | −1.98528 | ||||||||
\(305\) | 7.00385 | 0.401039 | ||||||||
\(306\) | 19.4407 | 1.11135 | ||||||||
\(307\) | 17.5637 | 1.00241 | 0.501206 | − | 0.865328i | \(-0.332890\pi\) | ||||
0.501206 | + | 0.865328i | \(0.332890\pi\) | |||||||
\(308\) | −10.8673 | −0.619223 | ||||||||
\(309\) | 15.1703 | 0.863006 | ||||||||
\(310\) | 8.53715 | 0.484878 | ||||||||
\(311\) | 1.86503 | 0.105756 | 0.0528780 | − | 0.998601i | \(-0.483161\pi\) | ||||
0.0528780 | + | 0.998601i | \(0.483161\pi\) | |||||||
\(312\) | 3.00943 | 0.170376 | ||||||||
\(313\) | 25.7982 | 1.45820 | 0.729099 | − | 0.684408i | \(-0.239939\pi\) | ||||
0.729099 | + | 0.684408i | \(0.239939\pi\) | |||||||
\(314\) | 44.5433 | 2.51372 | ||||||||
\(315\) | −1.76484 | −0.0994372 | ||||||||
\(316\) | 8.85398 | 0.498075 | ||||||||
\(317\) | 7.33811 | 0.412149 | 0.206075 | − | 0.978536i | \(-0.433931\pi\) | ||||
0.206075 | + | 0.978536i | \(0.433931\pi\) | |||||||
\(318\) | 49.9870 | 2.80313 | ||||||||
\(319\) | 38.7253 | 2.16820 | ||||||||
\(320\) | −6.18121 | −0.345540 | ||||||||
\(321\) | 39.3546 | 2.19656 | ||||||||
\(322\) | −6.74379 | −0.375817 | ||||||||
\(323\) | −44.6892 | −2.48658 | ||||||||
\(324\) | −19.9352 | −1.10751 | ||||||||
\(325\) | 3.26846 | 0.181301 | ||||||||
\(326\) | 7.46457 | 0.413424 | ||||||||
\(327\) | −28.4377 | −1.57261 | ||||||||
\(328\) | −0.585210 | −0.0323128 | ||||||||
\(329\) | 5.49249 | 0.302811 | ||||||||
\(330\) | −25.8755 | −1.42440 | ||||||||
\(331\) | 11.3771 | 0.625343 | 0.312672 | − | 0.949861i | \(-0.398776\pi\) | ||||
0.312672 | + | 0.949861i | \(0.398776\pi\) | |||||||
\(332\) | 1.26567 | 0.0694627 | ||||||||
\(333\) | −9.34573 | −0.512143 | ||||||||
\(334\) | 10.1653 | 0.556222 | ||||||||
\(335\) | 8.63416 | 0.471735 | ||||||||
\(336\) | 9.57551 | 0.522387 | ||||||||
\(337\) | −31.0498 | −1.69139 | −0.845696 | − | 0.533664i | \(-0.820815\pi\) | ||||
−0.845696 | + | 0.533664i | \(0.820815\pi\) | |||||||
\(338\) | 4.50700 | 0.245149 | ||||||||
\(339\) | −14.6006 | −0.792996 | ||||||||
\(340\) | −10.0987 | −0.547680 | ||||||||
\(341\) | −26.7501 | −1.44860 | ||||||||
\(342\) | −27.0864 | −1.46466 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 2.56029 | 0.138041 | ||||||||
\(345\) | −7.56836 | −0.407467 | ||||||||
\(346\) | −9.40905 | −0.505834 | ||||||||
\(347\) | 9.88075 | 0.530426 | 0.265213 | − | 0.964190i | \(-0.414558\pi\) | ||||
0.265213 | + | 0.964190i | \(0.414558\pi\) | |||||||
\(348\) | 24.7323 | 1.32579 | ||||||||
\(349\) | −17.6303 | −0.943726 | −0.471863 | − | 0.881672i | \(-0.656418\pi\) | ||||
−0.471863 | + | 0.881672i | \(0.656418\pi\) | |||||||
\(350\) | 1.94503 | 0.103966 | ||||||||
\(351\) | −8.81234 | −0.470368 | ||||||||
\(352\) | 46.8584 | 2.49756 | ||||||||
\(353\) | −21.1391 | −1.12512 | −0.562560 | − | 0.826757i | \(-0.690183\pi\) | ||||
−0.562560 | + | 0.826757i | \(0.690183\pi\) | |||||||
\(354\) | −50.7388 | −2.69674 | ||||||||
\(355\) | 14.7022 | 0.780311 | ||||||||
\(356\) | 26.3819 | 1.39824 | ||||||||
\(357\) | 12.3625 | 0.654293 | ||||||||
\(358\) | 11.9746 | 0.632879 | ||||||||
\(359\) | −27.9344 | −1.47432 | −0.737161 | − | 0.675717i | \(-0.763834\pi\) | ||||
−0.737161 | + | 0.675717i | \(0.763834\pi\) | |||||||
\(360\) | 0.744427 | 0.0392348 | ||||||||
\(361\) | 43.2645 | 2.27708 | ||||||||
\(362\) | 27.2629 | 1.43290 | ||||||||
\(363\) | 57.0663 | 2.99520 | ||||||||
\(364\) | −5.82810 | −0.305475 | ||||||||
\(365\) | 4.02309 | 0.210578 | ||||||||
\(366\) | −29.7363 | −1.55434 | ||||||||
\(367\) | 2.46148 | 0.128488 | 0.0642440 | − | 0.997934i | \(-0.479536\pi\) | ||||
0.0642440 | + | 0.997934i | \(0.479536\pi\) | |||||||
\(368\) | 15.2095 | 0.792852 | ||||||||
\(369\) | −2.44849 | −0.127463 | ||||||||
\(370\) | 10.2999 | 0.535468 | ||||||||
\(371\) | 11.7735 | 0.611252 | ||||||||
\(372\) | −17.0842 | −0.885775 | ||||||||
\(373\) | 31.3663 | 1.62409 | 0.812044 | − | 0.583597i | \(-0.198355\pi\) | ||||
0.812044 | + | 0.583597i | \(0.198355\pi\) | |||||||
\(374\) | 67.1347 | 3.47145 | ||||||||
\(375\) | 2.18285 | 0.112722 | ||||||||
\(376\) | −2.31679 | −0.119479 | ||||||||
\(377\) | 20.7682 | 1.06962 | ||||||||
\(378\) | −5.24414 | −0.269730 | ||||||||
\(379\) | 34.5706 | 1.77577 | 0.887886 | − | 0.460063i | \(-0.152173\pi\) | ||||
0.887886 | + | 0.460063i | \(0.152173\pi\) | |||||||
\(380\) | 14.0703 | 0.721793 | ||||||||
\(381\) | 34.3259 | 1.75857 | ||||||||
\(382\) | −0.156958 | −0.00803069 | ||||||||
\(383\) | 19.7372 | 1.00852 | 0.504261 | − | 0.863551i | \(-0.331765\pi\) | ||||
0.504261 | + | 0.863551i | \(0.331765\pi\) | |||||||
\(384\) | −7.32270 | −0.373685 | ||||||||
\(385\) | −6.09451 | −0.310605 | ||||||||
\(386\) | 3.92236 | 0.199643 | ||||||||
\(387\) | 10.7121 | 0.544528 | ||||||||
\(388\) | −12.6400 | −0.641700 | ||||||||
\(389\) | −28.9690 | −1.46879 | −0.734394 | − | 0.678723i | \(-0.762533\pi\) | ||||
−0.734394 | + | 0.678723i | \(0.762533\pi\) | |||||||
\(390\) | −13.8769 | −0.702684 | ||||||||
\(391\) | 19.6363 | 0.993052 | ||||||||
\(392\) | 0.421811 | 0.0213047 | ||||||||
\(393\) | 20.1849 | 1.01819 | ||||||||
\(394\) | 2.13016 | 0.107316 | ||||||||
\(395\) | 4.96540 | 0.249836 | ||||||||
\(396\) | 19.1790 | 0.963783 | ||||||||
\(397\) | 26.0902 | 1.30943 | 0.654716 | − | 0.755875i | \(-0.272788\pi\) | ||||
0.654716 | + | 0.755875i | \(0.272788\pi\) | |||||||
\(398\) | 20.5060 | 1.02787 | ||||||||
\(399\) | −17.2244 | −0.862299 | ||||||||
\(400\) | −4.38670 | −0.219335 | ||||||||
\(401\) | −21.7214 | −1.08472 | −0.542359 | − | 0.840147i | \(-0.682469\pi\) | ||||
−0.542359 | + | 0.840147i | \(0.682469\pi\) | |||||||
\(402\) | −36.6581 | −1.82834 | ||||||||
\(403\) | −14.3460 | −0.714624 | ||||||||
\(404\) | −9.20790 | −0.458110 | ||||||||
\(405\) | −11.1799 | −0.555532 | ||||||||
\(406\) | 12.3590 | 0.613364 | ||||||||
\(407\) | −32.2736 | −1.59974 | ||||||||
\(408\) | −5.21464 | −0.258163 | ||||||||
\(409\) | 17.8012 | 0.880212 | 0.440106 | − | 0.897946i | \(-0.354941\pi\) | ||||
0.440106 | + | 0.897946i | \(0.354941\pi\) | |||||||
\(410\) | 2.69848 | 0.133269 | ||||||||
\(411\) | −14.7690 | −0.728500 | ||||||||
\(412\) | 12.3923 | 0.610527 | ||||||||
\(413\) | −11.9506 | −0.588051 | ||||||||
\(414\) | 11.9017 | 0.584935 | ||||||||
\(415\) | 0.709802 | 0.0348428 | ||||||||
\(416\) | 25.1300 | 1.23210 | ||||||||
\(417\) | 6.73419 | 0.329775 | ||||||||
\(418\) | −93.5373 | −4.57506 | ||||||||
\(419\) | 8.72315 | 0.426154 | 0.213077 | − | 0.977035i | \(-0.431652\pi\) | ||||
0.213077 | + | 0.977035i | \(0.431652\pi\) | |||||||
\(420\) | −3.89231 | −0.189925 | ||||||||
\(421\) | 4.72652 | 0.230356 | 0.115178 | − | 0.993345i | \(-0.463256\pi\) | ||||
0.115178 | + | 0.993345i | \(0.463256\pi\) | |||||||
\(422\) | 25.4063 | 1.23676 | ||||||||
\(423\) | −9.69335 | −0.471307 | ||||||||
\(424\) | −4.96621 | −0.241181 | ||||||||
\(425\) | −5.66347 | −0.274719 | ||||||||
\(426\) | −62.4212 | −3.02431 | ||||||||
\(427\) | −7.00385 | −0.338940 | ||||||||
\(428\) | 32.1481 | 1.55394 | ||||||||
\(429\) | 43.4816 | 2.09931 | ||||||||
\(430\) | −11.8058 | −0.569328 | ||||||||
\(431\) | −24.2116 | −1.16623 | −0.583116 | − | 0.812389i | \(-0.698167\pi\) | ||||
−0.583116 | + | 0.812389i | \(0.698167\pi\) | |||||||
\(432\) | 11.8273 | 0.569043 | ||||||||
\(433\) | −17.8543 | −0.858022 | −0.429011 | − | 0.903299i | \(-0.641138\pi\) | ||||
−0.429011 | + | 0.903299i | \(0.641138\pi\) | |||||||
\(434\) | −8.53715 | −0.409796 | ||||||||
\(435\) | 13.8701 | 0.665021 | ||||||||
\(436\) | −23.2303 | −1.11253 | ||||||||
\(437\) | −27.3589 | −1.30875 | ||||||||
\(438\) | −17.0809 | −0.816155 | ||||||||
\(439\) | 27.3246 | 1.30413 | 0.652065 | − | 0.758163i | \(-0.273903\pi\) | ||||
0.652065 | + | 0.758163i | \(0.273903\pi\) | |||||||
\(440\) | 2.57073 | 0.122555 | ||||||||
\(441\) | 1.76484 | 0.0840398 | ||||||||
\(442\) | 36.0040 | 1.71254 | ||||||||
\(443\) | 22.0902 | 1.04954 | 0.524768 | − | 0.851245i | \(-0.324152\pi\) | ||||
0.524768 | + | 0.851245i | \(0.324152\pi\) | |||||||
\(444\) | −20.6118 | −0.978195 | ||||||||
\(445\) | 14.7952 | 0.701361 | ||||||||
\(446\) | 5.25484 | 0.248824 | ||||||||
\(447\) | −18.1898 | −0.860348 | ||||||||
\(448\) | 6.18121 | 0.292035 | ||||||||
\(449\) | −33.0520 | −1.55982 | −0.779909 | − | 0.625893i | \(-0.784735\pi\) | ||||
−0.779909 | + | 0.625893i | \(0.784735\pi\) | |||||||
\(450\) | −3.43266 | −0.161817 | ||||||||
\(451\) | −8.45537 | −0.398148 | ||||||||
\(452\) | −11.9270 | −0.560998 | ||||||||
\(453\) | 4.97235 | 0.233622 | ||||||||
\(454\) | 38.9805 | 1.82945 | ||||||||
\(455\) | −3.26846 | −0.153228 | ||||||||
\(456\) | 7.26544 | 0.340236 | ||||||||
\(457\) | 13.5275 | 0.632789 | 0.316394 | − | 0.948628i | \(-0.397528\pi\) | ||||
0.316394 | + | 0.948628i | \(0.397528\pi\) | |||||||
\(458\) | 1.94503 | 0.0908852 | ||||||||
\(459\) | 15.2697 | 0.712730 | ||||||||
\(460\) | −6.18247 | −0.288259 | ||||||||
\(461\) | 27.8589 | 1.29752 | 0.648760 | − | 0.760993i | \(-0.275288\pi\) | ||||
0.648760 | + | 0.760993i | \(0.275288\pi\) | |||||||
\(462\) | 25.8755 | 1.20384 | ||||||||
\(463\) | −5.80127 | −0.269608 | −0.134804 | − | 0.990872i | \(-0.543040\pi\) | ||||
−0.134804 | + | 0.990872i | \(0.543040\pi\) | |||||||
\(464\) | −27.8737 | −1.29400 | ||||||||
\(465\) | −9.58101 | −0.444308 | ||||||||
\(466\) | −46.9651 | −2.17562 | ||||||||
\(467\) | −27.0355 | −1.25106 | −0.625528 | − | 0.780202i | \(-0.715116\pi\) | ||||
−0.625528 | + | 0.780202i | \(0.715116\pi\) | |||||||
\(468\) | 10.2856 | 0.475453 | ||||||||
\(469\) | −8.63416 | −0.398689 | ||||||||
\(470\) | 10.6830 | 0.492772 | ||||||||
\(471\) | −49.9897 | −2.30340 | ||||||||
\(472\) | 5.04090 | 0.232026 | ||||||||
\(473\) | 36.9922 | 1.70090 | ||||||||
\(474\) | −21.0816 | −0.968311 | ||||||||
\(475\) | 7.89079 | 0.362054 | ||||||||
\(476\) | 10.0987 | 0.462874 | ||||||||
\(477\) | −20.7784 | −0.951377 | ||||||||
\(478\) | −17.0747 | −0.780976 | ||||||||
\(479\) | −11.8206 | −0.540097 | −0.270048 | − | 0.962847i | \(-0.587040\pi\) | ||||
−0.270048 | + | 0.962847i | \(0.587040\pi\) | |||||||
\(480\) | 16.7831 | 0.766042 | ||||||||
\(481\) | −17.3082 | −0.789185 | ||||||||
\(482\) | −10.3039 | −0.469330 | ||||||||
\(483\) | 7.56836 | 0.344372 | ||||||||
\(484\) | 46.6165 | 2.11893 | ||||||||
\(485\) | −7.08866 | −0.321879 | ||||||||
\(486\) | 31.7340 | 1.43948 | ||||||||
\(487\) | −39.4987 | −1.78986 | −0.894929 | − | 0.446208i | \(-0.852774\pi\) | ||||
−0.894929 | + | 0.446208i | \(0.852774\pi\) | |||||||
\(488\) | 2.95430 | 0.133735 | ||||||||
\(489\) | −8.37728 | −0.378833 | ||||||||
\(490\) | −1.94503 | −0.0878674 | ||||||||
\(491\) | −17.4209 | −0.786192 | −0.393096 | − | 0.919497i | \(-0.628596\pi\) | ||||
−0.393096 | + | 0.919497i | \(0.628596\pi\) | |||||||
\(492\) | −5.40010 | −0.243455 | ||||||||
\(493\) | −35.9864 | −1.62075 | ||||||||
\(494\) | −50.1636 | −2.25697 | ||||||||
\(495\) | 10.7558 | 0.483438 | ||||||||
\(496\) | 19.2542 | 0.864539 | ||||||||
\(497\) | −14.7022 | −0.659483 | ||||||||
\(498\) | −3.01361 | −0.135043 | ||||||||
\(499\) | 32.2937 | 1.44567 | 0.722833 | − | 0.691022i | \(-0.242839\pi\) | ||||
0.722833 | + | 0.691022i | \(0.242839\pi\) | |||||||
\(500\) | 1.78313 | 0.0797442 | ||||||||
\(501\) | −11.4083 | −0.509684 | ||||||||
\(502\) | 16.9283 | 0.755546 | ||||||||
\(503\) | −9.08506 | −0.405083 | −0.202541 | − | 0.979274i | \(-0.564920\pi\) | ||||
−0.202541 | + | 0.979274i | \(0.564920\pi\) | |||||||
\(504\) | −0.744427 | −0.0331594 | ||||||||
\(505\) | −5.16388 | −0.229790 | ||||||||
\(506\) | 41.1001 | 1.82712 | ||||||||
\(507\) | −5.05808 | −0.224637 | ||||||||
\(508\) | 28.0402 | 1.24408 | ||||||||
\(509\) | −36.6965 | −1.62654 | −0.813272 | − | 0.581884i | \(-0.802316\pi\) | ||||
−0.813272 | + | 0.581884i | \(0.802316\pi\) | |||||||
\(510\) | 24.0454 | 1.06475 | ||||||||
\(511\) | −4.02309 | −0.177971 | ||||||||
\(512\) | −30.0270 | −1.32702 | ||||||||
\(513\) | −21.2750 | −0.939313 | ||||||||
\(514\) | −57.1314 | −2.51996 | ||||||||
\(515\) | 6.94975 | 0.306243 | ||||||||
\(516\) | 23.6254 | 1.04005 | ||||||||
\(517\) | −33.4740 | −1.47219 | ||||||||
\(518\) | −10.2999 | −0.452553 | ||||||||
\(519\) | 10.5595 | 0.463511 | ||||||||
\(520\) | 1.37867 | 0.0604587 | ||||||||
\(521\) | −9.09670 | −0.398534 | −0.199267 | − | 0.979945i | \(-0.563856\pi\) | ||||
−0.199267 | + | 0.979945i | \(0.563856\pi\) | |||||||
\(522\) | −21.8115 | −0.954664 | ||||||||
\(523\) | −9.79116 | −0.428138 | −0.214069 | − | 0.976819i | \(-0.568672\pi\) | ||||
−0.214069 | + | 0.976819i | \(0.568672\pi\) | |||||||
\(524\) | 16.4887 | 0.720311 | ||||||||
\(525\) | −2.18285 | −0.0952674 | ||||||||
\(526\) | −27.5885 | −1.20292 | ||||||||
\(527\) | 24.8582 | 1.08284 | ||||||||
\(528\) | −58.3580 | −2.53971 | ||||||||
\(529\) | −10.9786 | −0.477329 | ||||||||
\(530\) | 22.8999 | 0.994707 | ||||||||
\(531\) | 21.0909 | 0.915266 | ||||||||
\(532\) | −14.0703 | −0.610026 | ||||||||
\(533\) | −4.53458 | −0.196414 | ||||||||
\(534\) | −62.8162 | −2.71832 | ||||||||
\(535\) | 18.0290 | 0.779461 | ||||||||
\(536\) | 3.64198 | 0.157310 | ||||||||
\(537\) | −13.4388 | −0.579926 | ||||||||
\(538\) | −26.0540 | −1.12327 | ||||||||
\(539\) | 6.09451 | 0.262509 | ||||||||
\(540\) | −4.80765 | −0.206888 | ||||||||
\(541\) | 24.4772 | 1.05236 | 0.526178 | − | 0.850375i | \(-0.323625\pi\) | ||||
0.526178 | + | 0.850375i | \(0.323625\pi\) | |||||||
\(542\) | −11.6268 | −0.499415 | ||||||||
\(543\) | −30.5964 | −1.31302 | ||||||||
\(544\) | −43.5444 | −1.86695 | ||||||||
\(545\) | −13.0278 | −0.558049 | ||||||||
\(546\) | 13.8769 | 0.593877 | ||||||||
\(547\) | 2.77529 | 0.118663 | 0.0593315 | − | 0.998238i | \(-0.481103\pi\) | ||||
0.0593315 | + | 0.998238i | \(0.481103\pi\) | |||||||
\(548\) | −12.0645 | −0.515371 | ||||||||
\(549\) | 12.3606 | 0.527539 | ||||||||
\(550\) | −11.8540 | −0.505456 | ||||||||
\(551\) | 50.1390 | 2.13600 | ||||||||
\(552\) | −3.19242 | −0.135878 | ||||||||
\(553\) | −4.96540 | −0.211150 | ||||||||
\(554\) | −17.2635 | −0.733456 | ||||||||
\(555\) | −11.5593 | −0.490666 | ||||||||
\(556\) | 5.50104 | 0.233296 | ||||||||
\(557\) | −20.8517 | −0.883517 | −0.441758 | − | 0.897134i | \(-0.645645\pi\) | ||||
−0.441758 | + | 0.897134i | \(0.645645\pi\) | |||||||
\(558\) | 15.0667 | 0.637823 | ||||||||
\(559\) | 19.8387 | 0.839089 | ||||||||
\(560\) | 4.38670 | 0.185372 | ||||||||
\(561\) | −75.3434 | −3.18100 | ||||||||
\(562\) | 43.0060 | 1.81410 | ||||||||
\(563\) | 20.5705 | 0.866943 | 0.433472 | − | 0.901167i | \(-0.357288\pi\) | ||||
0.433472 | + | 0.901167i | \(0.357288\pi\) | |||||||
\(564\) | −21.3785 | −0.900197 | ||||||||
\(565\) | −6.68878 | −0.281399 | ||||||||
\(566\) | −4.58064 | −0.192539 | ||||||||
\(567\) | 11.1799 | 0.469510 | ||||||||
\(568\) | 6.20154 | 0.260211 | ||||||||
\(569\) | −25.6461 | −1.07514 | −0.537571 | − | 0.843219i | \(-0.680658\pi\) | ||||
−0.537571 | + | 0.843219i | \(0.680658\pi\) | |||||||
\(570\) | −33.5020 | −1.40324 | ||||||||
\(571\) | 11.2058 | 0.468949 | 0.234474 | − | 0.972122i | \(-0.424663\pi\) | ||||
0.234474 | + | 0.972122i | \(0.424663\pi\) | |||||||
\(572\) | 35.5194 | 1.48514 | ||||||||
\(573\) | 0.176150 | 0.00735877 | ||||||||
\(574\) | −2.69848 | −0.112633 | ||||||||
\(575\) | −3.46719 | −0.144592 | ||||||||
\(576\) | −10.9088 | −0.454534 | ||||||||
\(577\) | 43.5874 | 1.81457 | 0.907283 | − | 0.420521i | \(-0.138153\pi\) | ||||
0.907283 | + | 0.420521i | \(0.138153\pi\) | |||||||
\(578\) | −29.3211 | −1.21960 | ||||||||
\(579\) | −4.40196 | −0.182939 | ||||||||
\(580\) | 11.3303 | 0.470463 | ||||||||
\(581\) | −0.709802 | −0.0294475 | ||||||||
\(582\) | 30.0963 | 1.24753 | ||||||||
\(583\) | −71.7540 | −2.97175 | ||||||||
\(584\) | 1.69698 | 0.0702217 | ||||||||
\(585\) | 5.76829 | 0.238489 | ||||||||
\(586\) | 6.55167 | 0.270647 | ||||||||
\(587\) | 5.94833 | 0.245514 | 0.122757 | − | 0.992437i | \(-0.460826\pi\) | ||||
0.122757 | + | 0.992437i | \(0.460826\pi\) | |||||||
\(588\) | 3.89231 | 0.160516 | ||||||||
\(589\) | −34.6344 | −1.42708 | ||||||||
\(590\) | −23.2443 | −0.956952 | ||||||||
\(591\) | −2.39062 | −0.0983370 | ||||||||
\(592\) | 23.2299 | 0.954742 | ||||||||
\(593\) | 4.79044 | 0.196720 | 0.0983600 | − | 0.995151i | \(-0.468640\pi\) | ||||
0.0983600 | + | 0.995151i | \(0.468640\pi\) | |||||||
\(594\) | 31.9605 | 1.31135 | ||||||||
\(595\) | 5.66347 | 0.232180 | ||||||||
\(596\) | −14.8589 | −0.608646 | ||||||||
\(597\) | −23.0133 | −0.941872 | ||||||||
\(598\) | 22.0418 | 0.901355 | ||||||||
\(599\) | 26.2777 | 1.07368 | 0.536840 | − | 0.843684i | \(-0.319618\pi\) | ||||
0.536840 | + | 0.843684i | \(0.319618\pi\) | |||||||
\(600\) | 0.920750 | 0.0375895 | ||||||||
\(601\) | 46.1625 | 1.88301 | 0.941505 | − | 0.337000i | \(-0.109412\pi\) | ||||
0.941505 | + | 0.337000i | \(0.109412\pi\) | |||||||
\(602\) | 11.8058 | 0.481170 | ||||||||
\(603\) | 15.2379 | 0.620535 | ||||||||
\(604\) | 4.06183 | 0.165274 | ||||||||
\(605\) | 26.1430 | 1.06287 | ||||||||
\(606\) | 21.9243 | 0.890615 | ||||||||
\(607\) | −21.0505 | −0.854415 | −0.427207 | − | 0.904154i | \(-0.640503\pi\) | ||||
−0.427207 | + | 0.904154i | \(0.640503\pi\) | |||||||
\(608\) | 60.6694 | 2.46047 | ||||||||
\(609\) | −13.8701 | −0.562045 | ||||||||
\(610\) | −13.6227 | −0.551566 | ||||||||
\(611\) | −17.9520 | −0.726259 | ||||||||
\(612\) | −17.8226 | −0.720435 | ||||||||
\(613\) | −44.7882 | −1.80898 | −0.904489 | − | 0.426496i | \(-0.859748\pi\) | ||||
−0.904489 | + | 0.426496i | \(0.859748\pi\) | |||||||
\(614\) | −34.1618 | −1.37866 | ||||||||
\(615\) | −3.02843 | −0.122118 | ||||||||
\(616\) | −2.57073 | −0.103578 | ||||||||
\(617\) | 18.4952 | 0.744589 | 0.372294 | − | 0.928115i | \(-0.378571\pi\) | ||||
0.372294 | + | 0.928115i | \(0.378571\pi\) | |||||||
\(618\) | −29.5066 | −1.18693 | ||||||||
\(619\) | 17.7844 | 0.714814 | 0.357407 | − | 0.933949i | \(-0.383661\pi\) | ||||
0.357407 | + | 0.933949i | \(0.383661\pi\) | |||||||
\(620\) | −7.82656 | −0.314322 | ||||||||
\(621\) | 9.34817 | 0.375129 | ||||||||
\(622\) | −3.62753 | −0.145451 | ||||||||
\(623\) | −14.7952 | −0.592758 | ||||||||
\(624\) | −31.2971 | −1.25289 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −50.1781 | −2.00552 | ||||||||
\(627\) | 104.974 | 4.19227 | ||||||||
\(628\) | −40.8357 | −1.62952 | ||||||||
\(629\) | 29.9910 | 1.19582 | ||||||||
\(630\) | 3.43266 | 0.136760 | ||||||||
\(631\) | 40.9276 | 1.62930 | 0.814651 | − | 0.579952i | \(-0.196929\pi\) | ||||
0.814651 | + | 0.579952i | \(0.196929\pi\) | |||||||
\(632\) | 2.09446 | 0.0833132 | ||||||||
\(633\) | −28.5128 | −1.13328 | ||||||||
\(634\) | −14.2728 | −0.566846 | ||||||||
\(635\) | 15.7252 | 0.624037 | ||||||||
\(636\) | −45.8263 | −1.81713 | ||||||||
\(637\) | 3.26846 | 0.129501 | ||||||||
\(638\) | −75.3217 | −2.98202 | ||||||||
\(639\) | 25.9470 | 1.02645 | ||||||||
\(640\) | −3.35465 | −0.132604 | ||||||||
\(641\) | −47.7144 | −1.88460 | −0.942302 | − | 0.334763i | \(-0.891344\pi\) | ||||
−0.942302 | + | 0.334763i | \(0.891344\pi\) | |||||||
\(642\) | −76.5457 | −3.02102 | ||||||||
\(643\) | 31.0126 | 1.22302 | 0.611508 | − | 0.791238i | \(-0.290563\pi\) | ||||
0.611508 | + | 0.791238i | \(0.290563\pi\) | |||||||
\(644\) | 6.18247 | 0.243623 | ||||||||
\(645\) | 13.2494 | 0.521693 | ||||||||
\(646\) | 86.9218 | 3.41989 | ||||||||
\(647\) | −2.51737 | −0.0989681 | −0.0494840 | − | 0.998775i | \(-0.515758\pi\) | ||||
−0.0494840 | + | 0.998775i | \(0.515758\pi\) | |||||||
\(648\) | −4.71579 | −0.185254 | ||||||||
\(649\) | 72.8331 | 2.85895 | ||||||||
\(650\) | −6.35724 | −0.249351 | ||||||||
\(651\) | 9.58101 | 0.375509 | ||||||||
\(652\) | −6.84326 | −0.268003 | ||||||||
\(653\) | −5.10081 | −0.199610 | −0.0998050 | − | 0.995007i | \(-0.531822\pi\) | ||||
−0.0998050 | + | 0.995007i | \(0.531822\pi\) | |||||||
\(654\) | 55.3122 | 2.16288 | ||||||||
\(655\) | 9.24702 | 0.361311 | ||||||||
\(656\) | 6.08600 | 0.237619 | ||||||||
\(657\) | 7.10010 | 0.277001 | ||||||||
\(658\) | −10.6830 | −0.416469 | ||||||||
\(659\) | 23.5714 | 0.918213 | 0.459106 | − | 0.888381i | \(-0.348170\pi\) | ||||
0.459106 | + | 0.888381i | \(0.348170\pi\) | |||||||
\(660\) | 23.7217 | 0.923367 | ||||||||
\(661\) | −23.1544 | −0.900601 | −0.450301 | − | 0.892877i | \(-0.648683\pi\) | ||||
−0.450301 | + | 0.892877i | \(0.648683\pi\) | |||||||
\(662\) | −22.1288 | −0.860061 | ||||||||
\(663\) | −40.4063 | −1.56925 | ||||||||
\(664\) | 0.299402 | 0.0116191 | ||||||||
\(665\) | −7.89079 | −0.305992 | ||||||||
\(666\) | 18.1777 | 0.704372 | ||||||||
\(667\) | −22.0310 | −0.853043 | ||||||||
\(668\) | −9.31922 | −0.360571 | ||||||||
\(669\) | −5.89736 | −0.228005 | ||||||||
\(670\) | −16.7937 | −0.648797 | ||||||||
\(671\) | 42.6850 | 1.64784 | ||||||||
\(672\) | −16.7831 | −0.647424 | ||||||||
\(673\) | −21.3514 | −0.823035 | −0.411517 | − | 0.911402i | \(-0.635001\pi\) | ||||
−0.411517 | + | 0.911402i | \(0.635001\pi\) | |||||||
\(674\) | 60.3928 | 2.32624 | ||||||||
\(675\) | −2.69618 | −0.103776 | ||||||||
\(676\) | −4.13186 | −0.158918 | ||||||||
\(677\) | 4.28442 | 0.164664 | 0.0823318 | − | 0.996605i | \(-0.473763\pi\) | ||||
0.0823318 | + | 0.996605i | \(0.473763\pi\) | |||||||
\(678\) | 28.3986 | 1.09064 | ||||||||
\(679\) | 7.08866 | 0.272038 | ||||||||
\(680\) | −2.38891 | −0.0916107 | ||||||||
\(681\) | −43.7468 | −1.67638 | ||||||||
\(682\) | 52.0297 | 1.99232 | ||||||||
\(683\) | 14.4763 | 0.553921 | 0.276960 | − | 0.960881i | \(-0.410673\pi\) | ||||
0.276960 | + | 0.960881i | \(0.410673\pi\) | |||||||
\(684\) | 24.8318 | 0.949468 | ||||||||
\(685\) | −6.76591 | −0.258512 | ||||||||
\(686\) | 1.94503 | 0.0742615 | ||||||||
\(687\) | −2.18285 | −0.0832809 | ||||||||
\(688\) | −26.6262 | −1.01511 | ||||||||
\(689\) | −38.4813 | −1.46602 | ||||||||
\(690\) | 14.7207 | 0.560407 | ||||||||
\(691\) | −17.0017 | −0.646775 | −0.323387 | − | 0.946267i | \(-0.604822\pi\) | ||||
−0.323387 | + | 0.946267i | \(0.604822\pi\) | |||||||
\(692\) | 8.62589 | 0.327907 | ||||||||
\(693\) | −10.7558 | −0.408579 | ||||||||
\(694\) | −19.2183 | −0.729518 | ||||||||
\(695\) | 3.08504 | 0.117022 | ||||||||
\(696\) | 5.85056 | 0.221765 | ||||||||
\(697\) | 7.85736 | 0.297619 | ||||||||
\(698\) | 34.2913 | 1.29795 | ||||||||
\(699\) | 52.7076 | 1.99359 | ||||||||
\(700\) | −1.78313 | −0.0673961 | ||||||||
\(701\) | −15.8705 | −0.599421 | −0.299710 | − | 0.954030i | \(-0.596890\pi\) | ||||
−0.299710 | + | 0.954030i | \(0.596890\pi\) | |||||||
\(702\) | 17.1403 | 0.646917 | ||||||||
\(703\) | −41.7858 | −1.57598 | ||||||||
\(704\) | −37.6714 | −1.41979 | ||||||||
\(705\) | −11.9893 | −0.451543 | ||||||||
\(706\) | 41.1161 | 1.54743 | ||||||||
\(707\) | 5.16388 | 0.194208 | ||||||||
\(708\) | 46.5155 | 1.74816 | ||||||||
\(709\) | −4.60502 | −0.172945 | −0.0864726 | − | 0.996254i | \(-0.527559\pi\) | ||||
−0.0864726 | + | 0.996254i | \(0.527559\pi\) | |||||||
\(710\) | −28.5962 | −1.07320 | ||||||||
\(711\) | 8.76312 | 0.328643 | ||||||||
\(712\) | 6.24079 | 0.233883 | ||||||||
\(713\) | 15.2183 | 0.569928 | ||||||||
\(714\) | −24.0454 | −0.899877 | ||||||||
\(715\) | 19.9196 | 0.744952 | ||||||||
\(716\) | −10.9779 | −0.410264 | ||||||||
\(717\) | 19.1624 | 0.715633 | ||||||||
\(718\) | 54.3332 | 2.02770 | ||||||||
\(719\) | 43.7672 | 1.63224 | 0.816121 | − | 0.577881i | \(-0.196120\pi\) | ||||
0.816121 | + | 0.577881i | \(0.196120\pi\) | |||||||
\(720\) | −7.74181 | −0.288520 | ||||||||
\(721\) | −6.94975 | −0.258822 | ||||||||
\(722\) | −84.1507 | −3.13176 | ||||||||
\(723\) | 11.5638 | 0.430062 | ||||||||
\(724\) | −24.9936 | −0.928881 | ||||||||
\(725\) | 6.35413 | 0.235986 | ||||||||
\(726\) | −110.996 | −4.11943 | ||||||||
\(727\) | 37.0322 | 1.37345 | 0.686725 | − | 0.726918i | \(-0.259048\pi\) | ||||
0.686725 | + | 0.726918i | \(0.259048\pi\) | |||||||
\(728\) | −1.37867 | −0.0510969 | ||||||||
\(729\) | −2.07456 | −0.0768355 | ||||||||
\(730\) | −7.82503 | −0.289617 | ||||||||
\(731\) | −34.3759 | −1.27144 | ||||||||
\(732\) | 27.2612 | 1.00760 | ||||||||
\(733\) | −11.5213 | −0.425548 | −0.212774 | − | 0.977101i | \(-0.568250\pi\) | ||||
−0.212774 | + | 0.977101i | \(0.568250\pi\) | |||||||
\(734\) | −4.78764 | −0.176715 | ||||||||
\(735\) | 2.18285 | 0.0805157 | ||||||||
\(736\) | −26.6580 | −0.982626 | ||||||||
\(737\) | 52.6210 | 1.93832 | ||||||||
\(738\) | 4.76238 | 0.175306 | ||||||||
\(739\) | −3.09239 | −0.113755 | −0.0568777 | − | 0.998381i | \(-0.518115\pi\) | ||||
−0.0568777 | + | 0.998381i | \(0.518115\pi\) | |||||||
\(740\) | −9.44263 | −0.347118 | ||||||||
\(741\) | 56.2972 | 2.06813 | ||||||||
\(742\) | −22.8999 | −0.840681 | ||||||||
\(743\) | −40.5707 | −1.48839 | −0.744197 | − | 0.667960i | \(-0.767168\pi\) | ||||
−0.744197 | + | 0.667960i | \(0.767168\pi\) | |||||||
\(744\) | −4.04137 | −0.148164 | ||||||||
\(745\) | −8.33305 | −0.305299 | ||||||||
\(746\) | −61.0084 | −2.23368 | ||||||||
\(747\) | 1.25268 | 0.0458333 | ||||||||
\(748\) | −61.5468 | −2.25037 | ||||||||
\(749\) | −18.0290 | −0.658765 | ||||||||
\(750\) | −4.24571 | −0.155031 | ||||||||
\(751\) | 19.8437 | 0.724106 | 0.362053 | − | 0.932157i | \(-0.382076\pi\) | ||||
0.362053 | + | 0.932157i | \(0.382076\pi\) | |||||||
\(752\) | 24.0939 | 0.878615 | ||||||||
\(753\) | −18.9981 | −0.692330 | ||||||||
\(754\) | −40.3947 | −1.47109 | ||||||||
\(755\) | 2.27792 | 0.0829019 | ||||||||
\(756\) | 4.80765 | 0.174852 | ||||||||
\(757\) | 5.05572 | 0.183753 | 0.0918766 | − | 0.995770i | \(-0.470713\pi\) | ||||
0.0918766 | + | 0.995770i | \(0.470713\pi\) | |||||||
\(758\) | −67.2408 | −2.44230 | ||||||||
\(759\) | −46.1254 | −1.67425 | ||||||||
\(760\) | 3.32842 | 0.120734 | ||||||||
\(761\) | 3.88152 | 0.140705 | 0.0703525 | − | 0.997522i | \(-0.477588\pi\) | ||||
0.0703525 | + | 0.997522i | \(0.477588\pi\) | |||||||
\(762\) | −66.7648 | −2.41863 | ||||||||
\(763\) | 13.0278 | 0.471638 | ||||||||
\(764\) | 0.143894 | 0.00520590 | ||||||||
\(765\) | −9.99509 | −0.361373 | ||||||||
\(766\) | −38.3893 | −1.38706 | ||||||||
\(767\) | 39.0601 | 1.41038 | ||||||||
\(768\) | 41.2282 | 1.48769 | ||||||||
\(769\) | −23.3927 | −0.843562 | −0.421781 | − | 0.906698i | \(-0.638595\pi\) | ||||
−0.421781 | + | 0.906698i | \(0.638595\pi\) | |||||||
\(770\) | 11.8540 | 0.427188 | ||||||||
\(771\) | 64.1169 | 2.30912 | ||||||||
\(772\) | −3.59589 | −0.129419 | ||||||||
\(773\) | −24.6255 | −0.885719 | −0.442859 | − | 0.896591i | \(-0.646036\pi\) | ||||
−0.442859 | + | 0.896591i | \(0.646036\pi\) | |||||||
\(774\) | −20.8354 | −0.748912 | ||||||||
\(775\) | −4.38922 | −0.157665 | ||||||||
\(776\) | −2.99007 | −0.107337 | ||||||||
\(777\) | 11.5593 | 0.414689 | ||||||||
\(778\) | 56.3456 | 2.02009 | ||||||||
\(779\) | −10.9475 | −0.392234 | ||||||||
\(780\) | 12.7219 | 0.455516 | ||||||||
\(781\) | 89.6026 | 3.20623 | ||||||||
\(782\) | −38.1932 | −1.36579 | ||||||||
\(783\) | −17.1319 | −0.612243 | ||||||||
\(784\) | −4.38670 | −0.156668 | ||||||||
\(785\) | −22.9011 | −0.817375 | ||||||||
\(786\) | −39.2601 | −1.40036 | ||||||||
\(787\) | 35.5427 | 1.26696 | 0.633481 | − | 0.773759i | \(-0.281626\pi\) | ||||
0.633481 | + | 0.773759i | \(0.281626\pi\) | |||||||
\(788\) | −1.95286 | −0.0695677 | ||||||||
\(789\) | 30.9618 | 1.10227 | ||||||||
\(790\) | −9.65785 | −0.343611 | ||||||||
\(791\) | 6.68878 | 0.237826 | ||||||||
\(792\) | 4.53692 | 0.161212 | ||||||||
\(793\) | 22.8918 | 0.812911 | ||||||||
\(794\) | −50.7463 | −1.80092 | ||||||||
\(795\) | −25.6999 | −0.911481 | ||||||||
\(796\) | −18.7992 | −0.666319 | ||||||||
\(797\) | −7.86184 | −0.278481 | −0.139240 | − | 0.990259i | \(-0.544466\pi\) | ||||
−0.139240 | + | 0.990259i | \(0.544466\pi\) | |||||||
\(798\) | 33.5020 | 1.18596 | ||||||||
\(799\) | 31.1066 | 1.10047 | ||||||||
\(800\) | 7.68864 | 0.271834 | ||||||||
\(801\) | 26.1111 | 0.922592 | ||||||||
\(802\) | 42.2488 | 1.49186 | ||||||||
\(803\) | 24.5188 | 0.865248 | ||||||||
\(804\) | 33.6069 | 1.18522 | ||||||||
\(805\) | 3.46719 | 0.122202 | ||||||||
\(806\) | 27.9033 | 0.982852 | ||||||||
\(807\) | 29.2397 | 1.02929 | ||||||||
\(808\) | −2.17818 | −0.0766282 | ||||||||
\(809\) | 4.72254 | 0.166036 | 0.0830178 | − | 0.996548i | \(-0.473544\pi\) | ||||
0.0830178 | + | 0.996548i | \(0.473544\pi\) | |||||||
\(810\) | 21.7451 | 0.764046 | ||||||||
\(811\) | 11.1467 | 0.391412 | 0.195706 | − | 0.980663i | \(-0.437300\pi\) | ||||
0.195706 | + | 0.980663i | \(0.437300\pi\) | |||||||
\(812\) | −11.3303 | −0.397614 | ||||||||
\(813\) | 13.0485 | 0.457629 | ||||||||
\(814\) | 62.7731 | 2.20019 | ||||||||
\(815\) | −3.83777 | −0.134431 | ||||||||
\(816\) | 54.2306 | 1.89845 | ||||||||
\(817\) | 47.8951 | 1.67564 | ||||||||
\(818\) | −34.6238 | −1.21059 | ||||||||
\(819\) | −5.76829 | −0.201560 | ||||||||
\(820\) | −2.47388 | −0.0863915 | ||||||||
\(821\) | 15.6043 | 0.544593 | 0.272297 | − | 0.962213i | \(-0.412217\pi\) | ||||
0.272297 | + | 0.962213i | \(0.412217\pi\) | |||||||
\(822\) | 28.7261 | 1.00194 | ||||||||
\(823\) | −25.9271 | −0.903763 | −0.451881 | − | 0.892078i | \(-0.649247\pi\) | ||||
−0.451881 | + | 0.892078i | \(0.649247\pi\) | |||||||
\(824\) | 2.93148 | 0.102123 | ||||||||
\(825\) | 13.3034 | 0.463165 | ||||||||
\(826\) | 23.2443 | 0.808772 | ||||||||
\(827\) | −4.83166 | −0.168013 | −0.0840066 | − | 0.996465i | \(-0.526772\pi\) | ||||
−0.0840066 | + | 0.996465i | \(0.526772\pi\) | |||||||
\(828\) | −10.9110 | −0.379185 | ||||||||
\(829\) | 28.6631 | 0.995509 | 0.497754 | − | 0.867318i | \(-0.334158\pi\) | ||||
0.497754 | + | 0.867318i | \(0.334158\pi\) | |||||||
\(830\) | −1.38058 | −0.0479208 | ||||||||
\(831\) | 19.3743 | 0.672088 | ||||||||
\(832\) | −20.2030 | −0.700413 | ||||||||
\(833\) | −5.66347 | −0.196228 | ||||||||
\(834\) | −13.0982 | −0.453553 | ||||||||
\(835\) | −5.22631 | −0.180864 | ||||||||
\(836\) | 85.7517 | 2.96579 | ||||||||
\(837\) | 11.8341 | 0.409047 | ||||||||
\(838\) | −16.9668 | −0.586107 | ||||||||
\(839\) | 19.8815 | 0.686385 | 0.343193 | − | 0.939265i | \(-0.388492\pi\) | ||||
0.343193 | + | 0.939265i | \(0.388492\pi\) | |||||||
\(840\) | −0.920750 | −0.0317689 | ||||||||
\(841\) | 11.3749 | 0.392238 | ||||||||
\(842\) | −9.19321 | −0.316819 | ||||||||
\(843\) | −48.2644 | −1.66232 | ||||||||
\(844\) | −23.2916 | −0.801730 | ||||||||
\(845\) | −2.31719 | −0.0797138 | ||||||||
\(846\) | 18.8538 | 0.648208 | ||||||||
\(847\) | −26.1430 | −0.898285 | ||||||||
\(848\) | 51.6470 | 1.77357 | ||||||||
\(849\) | 5.14072 | 0.176429 | ||||||||
\(850\) | 11.0156 | 0.377832 | ||||||||
\(851\) | 18.3606 | 0.629393 | ||||||||
\(852\) | 57.2255 | 1.96051 | ||||||||
\(853\) | 3.69666 | 0.126571 | 0.0632856 | − | 0.997995i | \(-0.479842\pi\) | ||||
0.0632856 | + | 0.997995i | \(0.479842\pi\) | |||||||
\(854\) | 13.6227 | 0.466158 | ||||||||
\(855\) | 13.9259 | 0.476257 | ||||||||
\(856\) | 7.60482 | 0.259927 | ||||||||
\(857\) | −12.2556 | −0.418642 | −0.209321 | − | 0.977847i | \(-0.567125\pi\) | ||||
−0.209321 | + | 0.977847i | \(0.567125\pi\) | |||||||
\(858\) | −84.5729 | −2.88727 | ||||||||
\(859\) | −28.2914 | −0.965291 | −0.482645 | − | 0.875816i | \(-0.660324\pi\) | ||||
−0.482645 | + | 0.875816i | \(0.660324\pi\) | |||||||
\(860\) | 10.8232 | 0.369067 | ||||||||
\(861\) | 3.02843 | 0.103209 | ||||||||
\(862\) | 47.0923 | 1.60397 | ||||||||
\(863\) | 20.0807 | 0.683555 | 0.341777 | − | 0.939781i | \(-0.388971\pi\) | ||||
0.341777 | + | 0.939781i | \(0.388971\pi\) | |||||||
\(864\) | −20.7299 | −0.705247 | ||||||||
\(865\) | 4.83749 | 0.164480 | ||||||||
\(866\) | 34.7271 | 1.18007 | ||||||||
\(867\) | 32.9062 | 1.11755 | ||||||||
\(868\) | 7.82656 | 0.265651 | ||||||||
\(869\) | 30.2617 | 1.02656 | ||||||||
\(870\) | −26.9777 | −0.914631 | ||||||||
\(871\) | 28.2204 | 0.956211 | ||||||||
\(872\) | −5.49527 | −0.186093 | ||||||||
\(873\) | −12.5103 | −0.423410 | ||||||||
\(874\) | 53.2138 | 1.79998 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 15.6591 | 0.529073 | ||||||||
\(877\) | 39.5867 | 1.33675 | 0.668374 | − | 0.743825i | \(-0.266991\pi\) | ||||
0.668374 | + | 0.743825i | \(0.266991\pi\) | |||||||
\(878\) | −53.1470 | −1.79363 | ||||||||
\(879\) | −7.35276 | −0.248002 | ||||||||
\(880\) | −26.7348 | −0.901230 | ||||||||
\(881\) | 18.1508 | 0.611516 | 0.305758 | − | 0.952109i | \(-0.401090\pi\) | ||||
0.305758 | + | 0.952109i | \(0.401090\pi\) | |||||||
\(882\) | −3.43266 | −0.115584 | ||||||||
\(883\) | −34.6179 | −1.16499 | −0.582493 | − | 0.812836i | \(-0.697923\pi\) | ||||
−0.582493 | + | 0.812836i | \(0.697923\pi\) | |||||||
\(884\) | −33.0072 | −1.11015 | ||||||||
\(885\) | 26.0864 | 0.876885 | ||||||||
\(886\) | −42.9661 | −1.44347 | ||||||||
\(887\) | 39.6897 | 1.33265 | 0.666325 | − | 0.745662i | \(-0.267866\pi\) | ||||
0.666325 | + | 0.745662i | \(0.267866\pi\) | |||||||
\(888\) | −4.87585 | −0.163623 | ||||||||
\(889\) | −15.7252 | −0.527408 | ||||||||
\(890\) | −28.7771 | −0.964612 | ||||||||
\(891\) | −68.1358 | −2.28263 | ||||||||
\(892\) | −4.81746 | −0.161300 | ||||||||
\(893\) | −43.3401 | −1.45032 | ||||||||
\(894\) | 35.3797 | 1.18327 | ||||||||
\(895\) | −6.15653 | −0.205790 | ||||||||
\(896\) | 3.35465 | 0.112071 | ||||||||
\(897\) | −24.7369 | −0.825940 | ||||||||
\(898\) | 64.2870 | 2.14528 | ||||||||
\(899\) | −27.8896 | −0.930172 | ||||||||
\(900\) | 3.14694 | 0.104898 | ||||||||
\(901\) | 66.6791 | 2.22140 | ||||||||
\(902\) | 16.4459 | 0.547590 | ||||||||
\(903\) | −13.2494 | −0.440911 | ||||||||
\(904\) | −2.82140 | −0.0938384 | ||||||||
\(905\) | −14.0167 | −0.465931 | ||||||||
\(906\) | −9.67137 | −0.321310 | ||||||||
\(907\) | −50.2224 | −1.66761 | −0.833804 | − | 0.552060i | \(-0.813842\pi\) | ||||
−0.833804 | + | 0.552060i | \(0.813842\pi\) | |||||||
\(908\) | −35.7360 | −1.18594 | ||||||||
\(909\) | −9.11341 | −0.302273 | ||||||||
\(910\) | 6.35724 | 0.210740 | ||||||||
\(911\) | −45.3281 | −1.50179 | −0.750894 | − | 0.660423i | \(-0.770377\pi\) | ||||
−0.750894 | + | 0.660423i | \(0.770377\pi\) | |||||||
\(912\) | −75.5583 | −2.50199 | ||||||||
\(913\) | 4.32589 | 0.143166 | ||||||||
\(914\) | −26.3113 | −0.870301 | ||||||||
\(915\) | 15.2884 | 0.505417 | ||||||||
\(916\) | −1.78313 | −0.0589164 | ||||||||
\(917\) | −9.24702 | −0.305364 | ||||||||
\(918\) | −29.7000 | −0.980247 | ||||||||
\(919\) | −41.1704 | −1.35809 | −0.679043 | − | 0.734099i | \(-0.737605\pi\) | ||||
−0.679043 | + | 0.734099i | \(0.737605\pi\) | |||||||
\(920\) | −1.46250 | −0.0482172 | ||||||||
\(921\) | 38.3389 | 1.26331 | ||||||||
\(922\) | −54.1864 | −1.78454 | ||||||||
\(923\) | 48.0535 | 1.58170 | ||||||||
\(924\) | −23.7217 | −0.780388 | ||||||||
\(925\) | −5.29552 | −0.174116 | ||||||||
\(926\) | 11.2836 | 0.370803 | ||||||||
\(927\) | 12.2652 | 0.402841 | ||||||||
\(928\) | 48.8546 | 1.60373 | ||||||||
\(929\) | −58.9729 | −1.93484 | −0.967419 | − | 0.253179i | \(-0.918524\pi\) | ||||
−0.967419 | + | 0.253179i | \(0.918524\pi\) | |||||||
\(930\) | 18.6353 | 0.611076 | ||||||||
\(931\) | 7.89079 | 0.258610 | ||||||||
\(932\) | 43.0560 | 1.41035 | ||||||||
\(933\) | 4.07107 | 0.133281 | ||||||||
\(934\) | 52.5849 | 1.72063 | ||||||||
\(935\) | −34.5161 | −1.12880 | ||||||||
\(936\) | 2.43313 | 0.0795293 | ||||||||
\(937\) | −46.3749 | −1.51500 | −0.757501 | − | 0.652834i | \(-0.773580\pi\) | ||||
−0.757501 | + | 0.652834i | \(0.773580\pi\) | |||||||
\(938\) | 16.7937 | 0.548333 | ||||||||
\(939\) | 56.3135 | 1.83772 | ||||||||
\(940\) | −9.79385 | −0.319440 | ||||||||
\(941\) | −35.2353 | −1.14864 | −0.574319 | − | 0.818632i | \(-0.694733\pi\) | ||||
−0.574319 | + | 0.818632i | \(0.694733\pi\) | |||||||
\(942\) | 97.2313 | 3.16797 | ||||||||
\(943\) | 4.81030 | 0.156645 | ||||||||
\(944\) | −52.4238 | −1.70625 | ||||||||
\(945\) | 2.69618 | 0.0877067 | ||||||||
\(946\) | −71.9508 | −2.33932 | ||||||||
\(947\) | 31.5509 | 1.02527 | 0.512633 | − | 0.858608i | \(-0.328670\pi\) | ||||
0.512633 | + | 0.858608i | \(0.328670\pi\) | |||||||
\(948\) | 19.3269 | 0.627709 | ||||||||
\(949\) | 13.1493 | 0.426844 | ||||||||
\(950\) | −15.3478 | −0.497948 | ||||||||
\(951\) | 16.0180 | 0.519419 | ||||||||
\(952\) | 2.38891 | 0.0774251 | ||||||||
\(953\) | 22.4196 | 0.726242 | 0.363121 | − | 0.931742i | \(-0.381711\pi\) | ||||
0.363121 | + | 0.931742i | \(0.381711\pi\) | |||||||
\(954\) | 40.4145 | 1.30847 | ||||||||
\(955\) | 0.0806972 | 0.00261130 | ||||||||
\(956\) | 15.6534 | 0.506269 | ||||||||
\(957\) | 84.5315 | 2.73251 | ||||||||
\(958\) | 22.9914 | 0.742818 | ||||||||
\(959\) | 6.76591 | 0.218483 | ||||||||
\(960\) | −13.4927 | −0.435473 | ||||||||
\(961\) | −11.7348 | −0.378541 | ||||||||
\(962\) | 33.6649 | 1.08540 | ||||||||
\(963\) | 31.8182 | 1.02533 | ||||||||
\(964\) | 9.44627 | 0.304244 | ||||||||
\(965\) | −2.01661 | −0.0649170 | ||||||||
\(966\) | −14.7207 | −0.473630 | ||||||||
\(967\) | −25.0441 | −0.805365 | −0.402683 | − | 0.915340i | \(-0.631922\pi\) | ||||
−0.402683 | + | 0.915340i | \(0.631922\pi\) | |||||||
\(968\) | 11.0274 | 0.354435 | ||||||||
\(969\) | −97.5499 | −3.13375 | ||||||||
\(970\) | 13.7876 | 0.442694 | ||||||||
\(971\) | 46.5107 | 1.49260 | 0.746299 | − | 0.665610i | \(-0.231829\pi\) | ||||
0.746299 | + | 0.665610i | \(0.231829\pi\) | |||||||
\(972\) | −29.0926 | −0.933145 | ||||||||
\(973\) | −3.08504 | −0.0989019 | ||||||||
\(974\) | 76.8261 | 2.46167 | ||||||||
\(975\) | 7.13455 | 0.228489 | ||||||||
\(976\) | −30.7238 | −0.983444 | ||||||||
\(977\) | −37.4191 | −1.19714 | −0.598572 | − | 0.801069i | \(-0.704265\pi\) | ||||
−0.598572 | + | 0.801069i | \(0.704265\pi\) | |||||||
\(978\) | 16.2940 | 0.521026 | ||||||||
\(979\) | 90.1696 | 2.88183 | ||||||||
\(980\) | 1.78313 | 0.0569601 | ||||||||
\(981\) | −22.9919 | −0.734075 | ||||||||
\(982\) | 33.8840 | 1.08128 | ||||||||
\(983\) | −32.5613 | −1.03854 | −0.519272 | − | 0.854609i | \(-0.673797\pi\) | ||||
−0.519272 | + | 0.854609i | \(0.673797\pi\) | |||||||
\(984\) | −1.27743 | −0.0407229 | ||||||||
\(985\) | −1.09518 | −0.0348954 | ||||||||
\(986\) | 69.9945 | 2.22908 | ||||||||
\(987\) | 11.9893 | 0.381623 | ||||||||
\(988\) | 45.9883 | 1.46308 | ||||||||
\(989\) | −21.0450 | −0.669192 | ||||||||
\(990\) | −20.9203 | −0.664892 | ||||||||
\(991\) | 0.547631 | 0.0173961 | 0.00869804 | − | 0.999962i | \(-0.497231\pi\) | ||||
0.00869804 | + | 0.999962i | \(0.497231\pi\) | |||||||
\(992\) | −33.7471 | −1.07147 | ||||||||
\(993\) | 24.8345 | 0.788101 | ||||||||
\(994\) | 28.5962 | 0.907015 | ||||||||
\(995\) | −10.5428 | −0.334229 | ||||||||
\(996\) | 2.76277 | 0.0875418 | ||||||||
\(997\) | 44.2506 | 1.40143 | 0.700716 | − | 0.713441i | \(-0.252864\pi\) | ||||
0.700716 | + | 0.713441i | \(0.252864\pi\) | |||||||
\(998\) | −62.8122 | −1.98829 | ||||||||
\(999\) | 14.2777 | 0.451726 |
(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.m.1.11 | ✓ | 67 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.m.1.11 | ✓ | 67 | 1.1 | even | 1 | trivial |