Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.943890 | −0.667431 | −0.333715 | − | 0.942674i | \(-0.608302\pi\) | ||||
−0.333715 | + | 0.942674i | \(0.608302\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.10907 | −0.554536 | ||||||||
\(5\) | 3.50883 | 1.56920 | 0.784599 | − | 0.620004i | \(-0.212869\pi\) | ||||
0.784599 | + | 0.620004i | \(0.212869\pi\) | |||||||
\(6\) | −0.943890 | −0.385341 | ||||||||
\(7\) | −2.32814 | −0.879955 | −0.439978 | − | 0.898009i | \(-0.645014\pi\) | ||||
−0.439978 | + | 0.898009i | \(0.645014\pi\) | |||||||
\(8\) | 2.93462 | 1.03755 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.31195 | −1.04733 | ||||||||
\(11\) | −5.01861 | −1.51317 | −0.756583 | − | 0.653897i | \(-0.773133\pi\) | ||||
−0.756583 | + | 0.653897i | \(0.773133\pi\) | |||||||
\(12\) | −1.10907 | −0.320162 | ||||||||
\(13\) | 1.00539 | 0.278846 | 0.139423 | − | 0.990233i | \(-0.455475\pi\) | ||||
0.139423 | + | 0.990233i | \(0.455475\pi\) | |||||||
\(14\) | 2.19751 | 0.587309 | ||||||||
\(15\) | 3.50883 | 0.905977 | ||||||||
\(16\) | −0.551813 | −0.137953 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −0.943890 | −0.222477 | ||||||||
\(19\) | 3.26521 | 0.749091 | 0.374546 | − | 0.927209i | \(-0.377799\pi\) | ||||
0.374546 | + | 0.927209i | \(0.377799\pi\) | |||||||
\(20\) | −3.89155 | −0.870177 | ||||||||
\(21\) | −2.32814 | −0.508042 | ||||||||
\(22\) | 4.73701 | 1.00993 | ||||||||
\(23\) | −3.55015 | −0.740258 | −0.370129 | − | 0.928980i | \(-0.620686\pi\) | ||||
−0.370129 | + | 0.928980i | \(0.620686\pi\) | |||||||
\(24\) | 2.93462 | 0.599027 | ||||||||
\(25\) | 7.31191 | 1.46238 | ||||||||
\(26\) | −0.948979 | −0.186110 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.58208 | 0.487967 | ||||||||
\(29\) | −4.86661 | −0.903706 | −0.451853 | − | 0.892092i | \(-0.649237\pi\) | ||||
−0.451853 | + | 0.892092i | \(0.649237\pi\) | |||||||
\(30\) | −3.31195 | −0.604677 | ||||||||
\(31\) | 2.30575 | 0.414124 | 0.207062 | − | 0.978328i | \(-0.433610\pi\) | ||||
0.207062 | + | 0.978328i | \(0.433610\pi\) | |||||||
\(32\) | −5.34839 | −0.945471 | ||||||||
\(33\) | −5.01861 | −0.873627 | ||||||||
\(34\) | 0.943890 | 0.161876 | ||||||||
\(35\) | −8.16906 | −1.38082 | ||||||||
\(36\) | −1.10907 | −0.184845 | ||||||||
\(37\) | −1.16260 | −0.191129 | −0.0955647 | − | 0.995423i | \(-0.530466\pi\) | ||||
−0.0955647 | + | 0.995423i | \(0.530466\pi\) | |||||||
\(38\) | −3.08200 | −0.499966 | ||||||||
\(39\) | 1.00539 | 0.160992 | ||||||||
\(40\) | 10.2971 | 1.62811 | ||||||||
\(41\) | −10.1573 | −1.58631 | −0.793153 | − | 0.609022i | \(-0.791562\pi\) | ||||
−0.793153 | + | 0.609022i | \(0.791562\pi\) | |||||||
\(42\) | 2.19751 | 0.339083 | ||||||||
\(43\) | 10.0192 | 1.52791 | 0.763953 | − | 0.645272i | \(-0.223256\pi\) | ||||
0.763953 | + | 0.645272i | \(0.223256\pi\) | |||||||
\(44\) | 5.56600 | 0.839106 | ||||||||
\(45\) | 3.50883 | 0.523066 | ||||||||
\(46\) | 3.35095 | 0.494071 | ||||||||
\(47\) | 9.68937 | 1.41334 | 0.706670 | − | 0.707544i | \(-0.250197\pi\) | ||||
0.706670 | + | 0.707544i | \(0.250197\pi\) | |||||||
\(48\) | −0.551813 | −0.0796474 | ||||||||
\(49\) | −1.57975 | −0.225679 | ||||||||
\(50\) | −6.90163 | −0.976039 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −1.11505 | −0.154630 | ||||||||
\(53\) | 10.3774 | 1.42544 | 0.712719 | − | 0.701449i | \(-0.247463\pi\) | ||||
0.712719 | + | 0.701449i | \(0.247463\pi\) | |||||||
\(54\) | −0.943890 | −0.128447 | ||||||||
\(55\) | −17.6094 | −2.37446 | ||||||||
\(56\) | −6.83222 | −0.912993 | ||||||||
\(57\) | 3.26521 | 0.432488 | ||||||||
\(58\) | 4.59354 | 0.603161 | ||||||||
\(59\) | −5.16679 | −0.672659 | −0.336329 | − | 0.941744i | \(-0.609186\pi\) | ||||
−0.336329 | + | 0.941744i | \(0.609186\pi\) | |||||||
\(60\) | −3.89155 | −0.502397 | ||||||||
\(61\) | −1.49433 | −0.191329 | −0.0956646 | − | 0.995414i | \(-0.530498\pi\) | ||||
−0.0956646 | + | 0.995414i | \(0.530498\pi\) | |||||||
\(62\) | −2.17637 | −0.276399 | ||||||||
\(63\) | −2.32814 | −0.293318 | ||||||||
\(64\) | 6.15192 | 0.768990 | ||||||||
\(65\) | 3.52775 | 0.437564 | ||||||||
\(66\) | 4.73701 | 0.583086 | ||||||||
\(67\) | −3.48575 | −0.425853 | −0.212926 | − | 0.977068i | \(-0.568299\pi\) | ||||
−0.212926 | + | 0.977068i | \(0.568299\pi\) | |||||||
\(68\) | 1.10907 | 0.134495 | ||||||||
\(69\) | −3.55015 | −0.427388 | ||||||||
\(70\) | 7.71069 | 0.921604 | ||||||||
\(71\) | −6.84335 | −0.812156 | −0.406078 | − | 0.913838i | \(-0.633104\pi\) | ||||
−0.406078 | + | 0.913838i | \(0.633104\pi\) | |||||||
\(72\) | 2.93462 | 0.345848 | ||||||||
\(73\) | −1.60666 | −0.188045 | −0.0940226 | − | 0.995570i | \(-0.529973\pi\) | ||||
−0.0940226 | + | 0.995570i | \(0.529973\pi\) | |||||||
\(74\) | 1.09736 | 0.127566 | ||||||||
\(75\) | 7.31191 | 0.844307 | ||||||||
\(76\) | −3.62136 | −0.415398 | ||||||||
\(77\) | 11.6840 | 1.33152 | ||||||||
\(78\) | −0.948979 | −0.107451 | ||||||||
\(79\) | −11.4385 | −1.28693 | −0.643467 | − | 0.765474i | \(-0.722505\pi\) | ||||
−0.643467 | + | 0.765474i | \(0.722505\pi\) | |||||||
\(80\) | −1.93622 | −0.216476 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 9.58739 | 1.05875 | ||||||||
\(83\) | 8.66231 | 0.950812 | 0.475406 | − | 0.879767i | \(-0.342301\pi\) | ||||
0.475406 | + | 0.879767i | \(0.342301\pi\) | |||||||
\(84\) | 2.58208 | 0.281728 | ||||||||
\(85\) | −3.50883 | −0.380586 | ||||||||
\(86\) | −9.45697 | −1.01977 | ||||||||
\(87\) | −4.86661 | −0.521755 | ||||||||
\(88\) | −14.7277 | −1.56998 | ||||||||
\(89\) | −16.3560 | −1.73373 | −0.866865 | − | 0.498543i | \(-0.833869\pi\) | ||||
−0.866865 | + | 0.498543i | \(0.833869\pi\) | |||||||
\(90\) | −3.31195 | −0.349110 | ||||||||
\(91\) | −2.34070 | −0.245372 | ||||||||
\(92\) | 3.93738 | 0.410500 | ||||||||
\(93\) | 2.30575 | 0.239095 | ||||||||
\(94\) | −9.14569 | −0.943306 | ||||||||
\(95\) | 11.4571 | 1.17547 | ||||||||
\(96\) | −5.34839 | −0.545868 | ||||||||
\(97\) | −6.59296 | −0.669414 | −0.334707 | − | 0.942322i | \(-0.608637\pi\) | ||||
−0.334707 | + | 0.942322i | \(0.608637\pi\) | |||||||
\(98\) | 1.49111 | 0.150625 | ||||||||
\(99\) | −5.01861 | −0.504389 | ||||||||
\(100\) | −8.10944 | −0.810944 | ||||||||
\(101\) | 3.16781 | 0.315208 | 0.157604 | − | 0.987502i | \(-0.449623\pi\) | ||||
0.157604 | + | 0.987502i | \(0.449623\pi\) | |||||||
\(102\) | 0.943890 | 0.0934590 | ||||||||
\(103\) | 3.10167 | 0.305617 | 0.152808 | − | 0.988256i | \(-0.451168\pi\) | ||||
0.152808 | + | 0.988256i | \(0.451168\pi\) | |||||||
\(104\) | 2.95045 | 0.289315 | ||||||||
\(105\) | −8.16906 | −0.797219 | ||||||||
\(106\) | −9.79507 | −0.951382 | ||||||||
\(107\) | 8.91967 | 0.862297 | 0.431148 | − | 0.902281i | \(-0.358109\pi\) | ||||
0.431148 | + | 0.902281i | \(0.358109\pi\) | |||||||
\(108\) | −1.10907 | −0.106721 | ||||||||
\(109\) | −7.30757 | −0.699938 | −0.349969 | − | 0.936761i | \(-0.613808\pi\) | ||||
−0.349969 | + | 0.936761i | \(0.613808\pi\) | |||||||
\(110\) | 16.6214 | 1.58479 | ||||||||
\(111\) | −1.16260 | −0.110349 | ||||||||
\(112\) | 1.28470 | 0.121393 | ||||||||
\(113\) | −13.3017 | −1.25131 | −0.625657 | − | 0.780098i | \(-0.715169\pi\) | ||||
−0.625657 | + | 0.780098i | \(0.715169\pi\) | |||||||
\(114\) | −3.08200 | −0.288656 | ||||||||
\(115\) | −12.4569 | −1.16161 | ||||||||
\(116\) | 5.39742 | 0.501138 | ||||||||
\(117\) | 1.00539 | 0.0929485 | ||||||||
\(118\) | 4.87688 | 0.448953 | ||||||||
\(119\) | 2.32814 | 0.213420 | ||||||||
\(120\) | 10.2971 | 0.939992 | ||||||||
\(121\) | 14.1864 | 1.28967 | ||||||||
\(122\) | 1.41048 | 0.127699 | ||||||||
\(123\) | −10.1573 | −0.915854 | ||||||||
\(124\) | −2.55724 | −0.229647 | ||||||||
\(125\) | 8.11210 | 0.725569 | ||||||||
\(126\) | 2.19751 | 0.195770 | ||||||||
\(127\) | 10.8779 | 0.965258 | 0.482629 | − | 0.875825i | \(-0.339682\pi\) | ||||
0.482629 | + | 0.875825i | \(0.339682\pi\) | |||||||
\(128\) | 4.89005 | 0.432224 | ||||||||
\(129\) | 10.0192 | 0.882137 | ||||||||
\(130\) | −3.32981 | −0.292044 | ||||||||
\(131\) | 8.73616 | 0.763282 | 0.381641 | − | 0.924311i | \(-0.375359\pi\) | ||||
0.381641 | + | 0.924311i | \(0.375359\pi\) | |||||||
\(132\) | 5.56600 | 0.484458 | ||||||||
\(133\) | −7.60188 | −0.659166 | ||||||||
\(134\) | 3.29017 | 0.284227 | ||||||||
\(135\) | 3.50883 | 0.301992 | ||||||||
\(136\) | −2.93462 | −0.251642 | ||||||||
\(137\) | −5.67042 | −0.484457 | −0.242229 | − | 0.970219i | \(-0.577878\pi\) | ||||
−0.242229 | + | 0.970219i | \(0.577878\pi\) | |||||||
\(138\) | 3.35095 | 0.285252 | ||||||||
\(139\) | −6.45656 | −0.547638 | −0.273819 | − | 0.961781i | \(-0.588287\pi\) | ||||
−0.273819 | + | 0.961781i | \(0.588287\pi\) | |||||||
\(140\) | 9.06008 | 0.765717 | ||||||||
\(141\) | 9.68937 | 0.815992 | ||||||||
\(142\) | 6.45936 | 0.542058 | ||||||||
\(143\) | −5.04567 | −0.421940 | ||||||||
\(144\) | −0.551813 | −0.0459844 | ||||||||
\(145\) | −17.0761 | −1.41809 | ||||||||
\(146\) | 1.51651 | 0.125507 | ||||||||
\(147\) | −1.57975 | −0.130296 | ||||||||
\(148\) | 1.28940 | 0.105988 | ||||||||
\(149\) | −21.6118 | −1.77051 | −0.885255 | − | 0.465106i | \(-0.846016\pi\) | ||||
−0.885255 | + | 0.465106i | \(0.846016\pi\) | |||||||
\(150\) | −6.90163 | −0.563516 | ||||||||
\(151\) | 2.51616 | 0.204762 | 0.102381 | − | 0.994745i | \(-0.467354\pi\) | ||||
0.102381 | + | 0.994745i | \(0.467354\pi\) | |||||||
\(152\) | 9.58216 | 0.777216 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −11.0284 | −0.888696 | ||||||||
\(155\) | 8.09048 | 0.649843 | ||||||||
\(156\) | −1.11505 | −0.0892757 | ||||||||
\(157\) | 1.00000 | 0.0798087 | ||||||||
\(158\) | 10.7967 | 0.858939 | ||||||||
\(159\) | 10.3774 | 0.822977 | ||||||||
\(160\) | −18.7666 | −1.48363 | ||||||||
\(161\) | 8.26526 | 0.651394 | ||||||||
\(162\) | −0.943890 | −0.0741590 | ||||||||
\(163\) | 17.4822 | 1.36931 | 0.684657 | − | 0.728865i | \(-0.259952\pi\) | ||||
0.684657 | + | 0.728865i | \(0.259952\pi\) | |||||||
\(164\) | 11.2652 | 0.879664 | ||||||||
\(165\) | −17.6094 | −1.37089 | ||||||||
\(166\) | −8.17626 | −0.634601 | ||||||||
\(167\) | −16.1605 | −1.25054 | −0.625268 | − | 0.780410i | \(-0.715010\pi\) | ||||
−0.625268 | + | 0.780410i | \(0.715010\pi\) | |||||||
\(168\) | −6.83222 | −0.527117 | ||||||||
\(169\) | −11.9892 | −0.922245 | ||||||||
\(170\) | 3.31195 | 0.254015 | ||||||||
\(171\) | 3.26521 | 0.249697 | ||||||||
\(172\) | −11.1120 | −0.847279 | ||||||||
\(173\) | 6.75760 | 0.513771 | 0.256885 | − | 0.966442i | \(-0.417304\pi\) | ||||
0.256885 | + | 0.966442i | \(0.417304\pi\) | |||||||
\(174\) | 4.59354 | 0.348235 | ||||||||
\(175\) | −17.0232 | −1.28683 | ||||||||
\(176\) | 2.76933 | 0.208746 | ||||||||
\(177\) | −5.16679 | −0.388360 | ||||||||
\(178\) | 15.4382 | 1.15714 | ||||||||
\(179\) | −18.5229 | −1.38447 | −0.692235 | − | 0.721672i | \(-0.743374\pi\) | ||||
−0.692235 | + | 0.721672i | \(0.743374\pi\) | |||||||
\(180\) | −3.89155 | −0.290059 | ||||||||
\(181\) | −20.7954 | −1.54571 | −0.772854 | − | 0.634584i | \(-0.781172\pi\) | ||||
−0.772854 | + | 0.634584i | \(0.781172\pi\) | |||||||
\(182\) | 2.20936 | 0.163769 | ||||||||
\(183\) | −1.49433 | −0.110464 | ||||||||
\(184\) | −10.4183 | −0.768051 | ||||||||
\(185\) | −4.07935 | −0.299920 | ||||||||
\(186\) | −2.17637 | −0.159579 | ||||||||
\(187\) | 5.01861 | 0.366997 | ||||||||
\(188\) | −10.7462 | −0.783748 | ||||||||
\(189\) | −2.32814 | −0.169347 | ||||||||
\(190\) | −10.8142 | −0.784546 | ||||||||
\(191\) | 13.5891 | 0.983271 | 0.491636 | − | 0.870801i | \(-0.336399\pi\) | ||||
0.491636 | + | 0.870801i | \(0.336399\pi\) | |||||||
\(192\) | 6.15192 | 0.443976 | ||||||||
\(193\) | −13.8923 | −0.999991 | −0.499996 | − | 0.866028i | \(-0.666665\pi\) | ||||
−0.499996 | + | 0.866028i | \(0.666665\pi\) | |||||||
\(194\) | 6.22303 | 0.446787 | ||||||||
\(195\) | 3.52775 | 0.252628 | ||||||||
\(196\) | 1.75206 | 0.125147 | ||||||||
\(197\) | 5.71584 | 0.407237 | 0.203618 | − | 0.979050i | \(-0.434730\pi\) | ||||
0.203618 | + | 0.979050i | \(0.434730\pi\) | |||||||
\(198\) | 4.73701 | 0.336645 | ||||||||
\(199\) | −24.5328 | −1.73908 | −0.869541 | − | 0.493861i | \(-0.835585\pi\) | ||||
−0.869541 | + | 0.493861i | \(0.835585\pi\) | |||||||
\(200\) | 21.4577 | 1.51729 | ||||||||
\(201\) | −3.48575 | −0.245866 | ||||||||
\(202\) | −2.99006 | −0.210380 | ||||||||
\(203\) | 11.3302 | 0.795221 | ||||||||
\(204\) | 1.10907 | 0.0776506 | ||||||||
\(205\) | −35.6403 | −2.48923 | ||||||||
\(206\) | −2.92764 | −0.203978 | ||||||||
\(207\) | −3.55015 | −0.246753 | ||||||||
\(208\) | −0.554789 | −0.0384677 | ||||||||
\(209\) | −16.3868 | −1.13350 | ||||||||
\(210\) | 7.71069 | 0.532088 | ||||||||
\(211\) | −2.65539 | −0.182805 | −0.0914023 | − | 0.995814i | \(-0.529135\pi\) | ||||
−0.0914023 | + | 0.995814i | \(0.529135\pi\) | |||||||
\(212\) | −11.5092 | −0.790457 | ||||||||
\(213\) | −6.84335 | −0.468898 | ||||||||
\(214\) | −8.41918 | −0.575523 | ||||||||
\(215\) | 35.1555 | 2.39759 | ||||||||
\(216\) | 2.93462 | 0.199676 | ||||||||
\(217\) | −5.36811 | −0.364411 | ||||||||
\(218\) | 6.89754 | 0.467160 | ||||||||
\(219\) | −1.60666 | −0.108568 | ||||||||
\(220\) | 19.5302 | 1.31672 | ||||||||
\(221\) | −1.00539 | −0.0676300 | ||||||||
\(222\) | 1.09736 | 0.0736501 | ||||||||
\(223\) | 8.14373 | 0.545345 | 0.272672 | − | 0.962107i | \(-0.412093\pi\) | ||||
0.272672 | + | 0.962107i | \(0.412093\pi\) | |||||||
\(224\) | 12.4518 | 0.831972 | ||||||||
\(225\) | 7.31191 | 0.487461 | ||||||||
\(226\) | 12.5553 | 0.835166 | ||||||||
\(227\) | −25.2961 | −1.67896 | −0.839479 | − | 0.543392i | \(-0.817140\pi\) | ||||
−0.839479 | + | 0.543392i | \(0.817140\pi\) | |||||||
\(228\) | −3.62136 | −0.239830 | ||||||||
\(229\) | −17.9428 | −1.18569 | −0.592847 | − | 0.805315i | \(-0.701996\pi\) | ||||
−0.592847 | + | 0.805315i | \(0.701996\pi\) | |||||||
\(230\) | 11.7579 | 0.775295 | ||||||||
\(231\) | 11.6840 | 0.768753 | ||||||||
\(232\) | −14.2816 | −0.937636 | ||||||||
\(233\) | 3.92422 | 0.257084 | 0.128542 | − | 0.991704i | \(-0.458970\pi\) | ||||
0.128542 | + | 0.991704i | \(0.458970\pi\) | |||||||
\(234\) | −0.948979 | −0.0620367 | ||||||||
\(235\) | 33.9984 | 2.21781 | ||||||||
\(236\) | 5.73034 | 0.373014 | ||||||||
\(237\) | −11.4385 | −0.743012 | ||||||||
\(238\) | −2.19751 | −0.142443 | ||||||||
\(239\) | −3.38682 | −0.219075 | −0.109537 | − | 0.993983i | \(-0.534937\pi\) | ||||
−0.109537 | + | 0.993983i | \(0.534937\pi\) | |||||||
\(240\) | −1.93622 | −0.124983 | ||||||||
\(241\) | 26.9066 | 1.73321 | 0.866604 | − | 0.498996i | \(-0.166298\pi\) | ||||
0.866604 | + | 0.498996i | \(0.166298\pi\) | |||||||
\(242\) | −13.3904 | −0.860767 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 1.65732 | 0.106099 | ||||||||
\(245\) | −5.54309 | −0.354135 | ||||||||
\(246\) | 9.58739 | 0.611269 | ||||||||
\(247\) | 3.28282 | 0.208881 | ||||||||
\(248\) | 6.76649 | 0.429673 | ||||||||
\(249\) | 8.66231 | 0.548952 | ||||||||
\(250\) | −7.65693 | −0.484267 | ||||||||
\(251\) | −18.0513 | −1.13939 | −0.569693 | − | 0.821858i | \(-0.692938\pi\) | ||||
−0.569693 | + | 0.821858i | \(0.692938\pi\) | |||||||
\(252\) | 2.58208 | 0.162656 | ||||||||
\(253\) | 17.8168 | 1.12013 | ||||||||
\(254\) | −10.2675 | −0.644243 | ||||||||
\(255\) | −3.50883 | −0.219732 | ||||||||
\(256\) | −16.9195 | −1.05747 | ||||||||
\(257\) | 9.84097 | 0.613863 | 0.306931 | − | 0.951732i | \(-0.400698\pi\) | ||||
0.306931 | + | 0.951732i | \(0.400698\pi\) | |||||||
\(258\) | −9.45697 | −0.588765 | ||||||||
\(259\) | 2.70669 | 0.168185 | ||||||||
\(260\) | −3.91253 | −0.242645 | ||||||||
\(261\) | −4.86661 | −0.301235 | ||||||||
\(262\) | −8.24597 | −0.509438 | ||||||||
\(263\) | −26.3248 | −1.62326 | −0.811628 | − | 0.584175i | \(-0.801418\pi\) | ||||
−0.811628 | + | 0.584175i | \(0.801418\pi\) | |||||||
\(264\) | −14.7277 | −0.906428 | ||||||||
\(265\) | 36.4124 | 2.23680 | ||||||||
\(266\) | 7.17533 | 0.439948 | ||||||||
\(267\) | −16.3560 | −1.00097 | ||||||||
\(268\) | 3.86595 | 0.236151 | ||||||||
\(269\) | −26.8069 | −1.63444 | −0.817222 | − | 0.576323i | \(-0.804487\pi\) | ||||
−0.817222 | + | 0.576323i | \(0.804487\pi\) | |||||||
\(270\) | −3.31195 | −0.201559 | ||||||||
\(271\) | −14.8379 | −0.901339 | −0.450670 | − | 0.892691i | \(-0.648815\pi\) | ||||
−0.450670 | + | 0.892691i | \(0.648815\pi\) | |||||||
\(272\) | 0.551813 | 0.0334586 | ||||||||
\(273\) | −2.34070 | −0.141665 | ||||||||
\(274\) | 5.35225 | 0.323342 | ||||||||
\(275\) | −36.6956 | −2.21283 | ||||||||
\(276\) | 3.93738 | 0.237002 | ||||||||
\(277\) | −18.8597 | −1.13317 | −0.566584 | − | 0.824004i | \(-0.691735\pi\) | ||||
−0.566584 | + | 0.824004i | \(0.691735\pi\) | |||||||
\(278\) | 6.09428 | 0.365511 | ||||||||
\(279\) | 2.30575 | 0.138041 | ||||||||
\(280\) | −23.9731 | −1.43267 | ||||||||
\(281\) | 24.0689 | 1.43583 | 0.717916 | − | 0.696129i | \(-0.245096\pi\) | ||||
0.717916 | + | 0.696129i | \(0.245096\pi\) | |||||||
\(282\) | −9.14569 | −0.544618 | ||||||||
\(283\) | 15.7161 | 0.934228 | 0.467114 | − | 0.884197i | \(-0.345294\pi\) | ||||
0.467114 | + | 0.884197i | \(0.345294\pi\) | |||||||
\(284\) | 7.58977 | 0.450370 | ||||||||
\(285\) | 11.4571 | 0.678659 | ||||||||
\(286\) | 4.76255 | 0.281616 | ||||||||
\(287\) | 23.6477 | 1.39588 | ||||||||
\(288\) | −5.34839 | −0.315157 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 16.1180 | 0.946479 | ||||||||
\(291\) | −6.59296 | −0.386486 | ||||||||
\(292\) | 1.78190 | 0.104278 | ||||||||
\(293\) | −2.79213 | −0.163118 | −0.0815590 | − | 0.996669i | \(-0.525990\pi\) | ||||
−0.0815590 | + | 0.996669i | \(0.525990\pi\) | |||||||
\(294\) | 1.49111 | 0.0869635 | ||||||||
\(295\) | −18.1294 | −1.05553 | ||||||||
\(296\) | −3.41178 | −0.198305 | ||||||||
\(297\) | −5.01861 | −0.291209 | ||||||||
\(298\) | 20.3992 | 1.18169 | ||||||||
\(299\) | −3.56929 | −0.206418 | ||||||||
\(300\) | −8.10944 | −0.468199 | ||||||||
\(301\) | −23.3260 | −1.34449 | ||||||||
\(302\) | −2.37498 | −0.136665 | ||||||||
\(303\) | 3.16781 | 0.181986 | ||||||||
\(304\) | −1.80179 | −0.103340 | ||||||||
\(305\) | −5.24335 | −0.300233 | ||||||||
\(306\) | 0.943890 | 0.0539586 | ||||||||
\(307\) | 27.0903 | 1.54612 | 0.773062 | − | 0.634330i | \(-0.218724\pi\) | ||||
0.773062 | + | 0.634330i | \(0.218724\pi\) | |||||||
\(308\) | −12.9584 | −0.738375 | ||||||||
\(309\) | 3.10167 | 0.176448 | ||||||||
\(310\) | −7.63652 | −0.433725 | ||||||||
\(311\) | 24.4301 | 1.38530 | 0.692652 | − | 0.721272i | \(-0.256442\pi\) | ||||
0.692652 | + | 0.721272i | \(0.256442\pi\) | |||||||
\(312\) | 2.95045 | 0.167036 | ||||||||
\(313\) | 28.9536 | 1.63655 | 0.818276 | − | 0.574825i | \(-0.194930\pi\) | ||||
0.818276 | + | 0.574825i | \(0.194930\pi\) | |||||||
\(314\) | −0.943890 | −0.0532668 | ||||||||
\(315\) | −8.16906 | −0.460275 | ||||||||
\(316\) | 12.6861 | 0.713652 | ||||||||
\(317\) | −5.24581 | −0.294634 | −0.147317 | − | 0.989089i | \(-0.547064\pi\) | ||||
−0.147317 | + | 0.989089i | \(0.547064\pi\) | |||||||
\(318\) | −9.79507 | −0.549280 | ||||||||
\(319\) | 24.4236 | 1.36746 | ||||||||
\(320\) | 21.5861 | 1.20670 | ||||||||
\(321\) | 8.91967 | 0.497847 | ||||||||
\(322\) | −7.80149 | −0.434760 | ||||||||
\(323\) | −3.26521 | −0.181681 | ||||||||
\(324\) | −1.10907 | −0.0616151 | ||||||||
\(325\) | 7.35134 | 0.407779 | ||||||||
\(326\) | −16.5013 | −0.913923 | ||||||||
\(327\) | −7.30757 | −0.404109 | ||||||||
\(328\) | −29.8079 | −1.64586 | ||||||||
\(329\) | −22.5582 | −1.24367 | ||||||||
\(330\) | 16.6214 | 0.914977 | ||||||||
\(331\) | −17.9999 | −0.989364 | −0.494682 | − | 0.869074i | \(-0.664715\pi\) | ||||
−0.494682 | + | 0.869074i | \(0.664715\pi\) | |||||||
\(332\) | −9.60713 | −0.527260 | ||||||||
\(333\) | −1.16260 | −0.0637098 | ||||||||
\(334\) | 15.2537 | 0.834647 | ||||||||
\(335\) | −12.2309 | −0.668247 | ||||||||
\(336\) | 1.28470 | 0.0700861 | ||||||||
\(337\) | −33.1093 | −1.80358 | −0.901789 | − | 0.432177i | \(-0.857746\pi\) | ||||
−0.901789 | + | 0.432177i | \(0.857746\pi\) | |||||||
\(338\) | 11.3165 | 0.615535 | ||||||||
\(339\) | −13.3017 | −0.722447 | ||||||||
\(340\) | 3.89155 | 0.211049 | ||||||||
\(341\) | −11.5716 | −0.626639 | ||||||||
\(342\) | −3.08200 | −0.166655 | ||||||||
\(343\) | 19.9749 | 1.07854 | ||||||||
\(344\) | 29.4024 | 1.58527 | ||||||||
\(345\) | −12.4569 | −0.670656 | ||||||||
\(346\) | −6.37843 | −0.342906 | ||||||||
\(347\) | −4.18747 | −0.224795 | −0.112398 | − | 0.993663i | \(-0.535853\pi\) | ||||
−0.112398 | + | 0.993663i | \(0.535853\pi\) | |||||||
\(348\) | 5.39742 | 0.289332 | ||||||||
\(349\) | 23.6159 | 1.26413 | 0.632066 | − | 0.774915i | \(-0.282207\pi\) | ||||
0.632066 | + | 0.774915i | \(0.282207\pi\) | |||||||
\(350\) | 16.0680 | 0.858870 | ||||||||
\(351\) | 1.00539 | 0.0536639 | ||||||||
\(352\) | 26.8415 | 1.43066 | ||||||||
\(353\) | −4.53137 | −0.241181 | −0.120590 | − | 0.992702i | \(-0.538479\pi\) | ||||
−0.120590 | + | 0.992702i | \(0.538479\pi\) | |||||||
\(354\) | 4.87688 | 0.259203 | ||||||||
\(355\) | −24.0122 | −1.27443 | ||||||||
\(356\) | 18.1400 | 0.961416 | ||||||||
\(357\) | 2.32814 | 0.123218 | ||||||||
\(358\) | 17.4836 | 0.924037 | ||||||||
\(359\) | −3.37665 | −0.178213 | −0.0891065 | − | 0.996022i | \(-0.528401\pi\) | ||||
−0.0891065 | + | 0.996022i | \(0.528401\pi\) | |||||||
\(360\) | 10.2971 | 0.542705 | ||||||||
\(361\) | −8.33839 | −0.438863 | ||||||||
\(362\) | 19.6285 | 1.03165 | ||||||||
\(363\) | 14.1864 | 0.744593 | ||||||||
\(364\) | 2.59600 | 0.136067 | ||||||||
\(365\) | −5.63750 | −0.295080 | ||||||||
\(366\) | 1.41048 | 0.0737270 | ||||||||
\(367\) | −30.0202 | −1.56704 | −0.783521 | − | 0.621365i | \(-0.786578\pi\) | ||||
−0.783521 | + | 0.621365i | \(0.786578\pi\) | |||||||
\(368\) | 1.95902 | 0.102121 | ||||||||
\(369\) | −10.1573 | −0.528769 | ||||||||
\(370\) | 3.85046 | 0.200176 | ||||||||
\(371\) | −24.1599 | −1.25432 | ||||||||
\(372\) | −2.55724 | −0.132587 | ||||||||
\(373\) | −4.41263 | −0.228477 | −0.114239 | − | 0.993453i | \(-0.536443\pi\) | ||||
−0.114239 | + | 0.993453i | \(0.536443\pi\) | |||||||
\(374\) | −4.73701 | −0.244945 | ||||||||
\(375\) | 8.11210 | 0.418907 | ||||||||
\(376\) | 28.4346 | 1.46640 | ||||||||
\(377\) | −4.89285 | −0.251995 | ||||||||
\(378\) | 2.19751 | 0.113028 | ||||||||
\(379\) | −20.0683 | −1.03084 | −0.515419 | − | 0.856938i | \(-0.672364\pi\) | ||||
−0.515419 | + | 0.856938i | \(0.672364\pi\) | |||||||
\(380\) | −12.7067 | −0.651842 | ||||||||
\(381\) | 10.8779 | 0.557292 | ||||||||
\(382\) | −12.8266 | −0.656265 | ||||||||
\(383\) | 22.4140 | 1.14530 | 0.572651 | − | 0.819799i | \(-0.305915\pi\) | ||||
0.572651 | + | 0.819799i | \(0.305915\pi\) | |||||||
\(384\) | 4.89005 | 0.249544 | ||||||||
\(385\) | 40.9973 | 2.08942 | ||||||||
\(386\) | 13.1128 | 0.667425 | ||||||||
\(387\) | 10.0192 | 0.509302 | ||||||||
\(388\) | 7.31207 | 0.371214 | ||||||||
\(389\) | 3.95429 | 0.200490 | 0.100245 | − | 0.994963i | \(-0.468037\pi\) | ||||
0.100245 | + | 0.994963i | \(0.468037\pi\) | |||||||
\(390\) | −3.32981 | −0.168611 | ||||||||
\(391\) | 3.55015 | 0.179539 | ||||||||
\(392\) | −4.63598 | −0.234152 | ||||||||
\(393\) | 8.73616 | 0.440681 | ||||||||
\(394\) | −5.39513 | −0.271802 | ||||||||
\(395\) | −40.1359 | −2.01945 | ||||||||
\(396\) | 5.56600 | 0.279702 | ||||||||
\(397\) | 21.5545 | 1.08179 | 0.540894 | − | 0.841091i | \(-0.318086\pi\) | ||||
0.540894 | + | 0.841091i | \(0.318086\pi\) | |||||||
\(398\) | 23.1562 | 1.16072 | ||||||||
\(399\) | −7.60188 | −0.380570 | ||||||||
\(400\) | −4.03481 | −0.201740 | ||||||||
\(401\) | 16.5882 | 0.828375 | 0.414187 | − | 0.910192i | \(-0.364066\pi\) | ||||
0.414187 | + | 0.910192i | \(0.364066\pi\) | |||||||
\(402\) | 3.29017 | 0.164099 | ||||||||
\(403\) | 2.31818 | 0.115477 | ||||||||
\(404\) | −3.51333 | −0.174795 | ||||||||
\(405\) | 3.50883 | 0.174355 | ||||||||
\(406\) | −10.6944 | −0.530755 | ||||||||
\(407\) | 5.83461 | 0.289211 | ||||||||
\(408\) | −2.93462 | −0.145285 | ||||||||
\(409\) | 37.6527 | 1.86181 | 0.930903 | − | 0.365267i | \(-0.119022\pi\) | ||||
0.930903 | + | 0.365267i | \(0.119022\pi\) | |||||||
\(410\) | 33.6405 | 1.66139 | ||||||||
\(411\) | −5.67042 | −0.279701 | ||||||||
\(412\) | −3.43998 | −0.169476 | ||||||||
\(413\) | 12.0290 | 0.591909 | ||||||||
\(414\) | 3.35095 | 0.164690 | ||||||||
\(415\) | 30.3946 | 1.49201 | ||||||||
\(416\) | −5.37723 | −0.263640 | ||||||||
\(417\) | −6.45656 | −0.316179 | ||||||||
\(418\) | 15.4673 | 0.756532 | ||||||||
\(419\) | −17.8056 | −0.869859 | −0.434930 | − | 0.900464i | \(-0.643227\pi\) | ||||
−0.434930 | + | 0.900464i | \(0.643227\pi\) | |||||||
\(420\) | 9.06008 | 0.442087 | ||||||||
\(421\) | 19.0402 | 0.927961 | 0.463981 | − | 0.885845i | \(-0.346421\pi\) | ||||
0.463981 | + | 0.885845i | \(0.346421\pi\) | |||||||
\(422\) | 2.50640 | 0.122009 | ||||||||
\(423\) | 9.68937 | 0.471113 | ||||||||
\(424\) | 30.4536 | 1.47896 | ||||||||
\(425\) | −7.31191 | −0.354680 | ||||||||
\(426\) | 6.45936 | 0.312957 | ||||||||
\(427\) | 3.47901 | 0.168361 | ||||||||
\(428\) | −9.89256 | −0.478175 | ||||||||
\(429\) | −5.04567 | −0.243607 | ||||||||
\(430\) | −33.1829 | −1.60022 | ||||||||
\(431\) | 30.5449 | 1.47130 | 0.735648 | − | 0.677364i | \(-0.236878\pi\) | ||||
0.735648 | + | 0.677364i | \(0.236878\pi\) | |||||||
\(432\) | −0.551813 | −0.0265491 | ||||||||
\(433\) | 4.19960 | 0.201820 | 0.100910 | − | 0.994896i | \(-0.467825\pi\) | ||||
0.100910 | + | 0.994896i | \(0.467825\pi\) | |||||||
\(434\) | 5.06690 | 0.243219 | ||||||||
\(435\) | −17.0761 | −0.818737 | ||||||||
\(436\) | 8.10462 | 0.388141 | ||||||||
\(437\) | −11.5920 | −0.554520 | ||||||||
\(438\) | 1.51651 | 0.0724616 | ||||||||
\(439\) | 29.3668 | 1.40160 | 0.700801 | − | 0.713357i | \(-0.252826\pi\) | ||||
0.700801 | + | 0.713357i | \(0.252826\pi\) | |||||||
\(440\) | −51.6771 | −2.46361 | ||||||||
\(441\) | −1.57975 | −0.0752264 | ||||||||
\(442\) | 0.948979 | 0.0451383 | ||||||||
\(443\) | 24.7954 | 1.17807 | 0.589033 | − | 0.808109i | \(-0.299509\pi\) | ||||
0.589033 | + | 0.808109i | \(0.299509\pi\) | |||||||
\(444\) | 1.28940 | 0.0611923 | ||||||||
\(445\) | −57.3904 | −2.72057 | ||||||||
\(446\) | −7.68678 | −0.363980 | ||||||||
\(447\) | −21.6118 | −1.02220 | ||||||||
\(448\) | −14.3225 | −0.676676 | ||||||||
\(449\) | −4.65991 | −0.219915 | −0.109957 | − | 0.993936i | \(-0.535071\pi\) | ||||
−0.109957 | + | 0.993936i | \(0.535071\pi\) | |||||||
\(450\) | −6.90163 | −0.325346 | ||||||||
\(451\) | 50.9756 | 2.40035 | ||||||||
\(452\) | 14.7525 | 0.693899 | ||||||||
\(453\) | 2.51616 | 0.118220 | ||||||||
\(454\) | 23.8767 | 1.12059 | ||||||||
\(455\) | −8.21311 | −0.385037 | ||||||||
\(456\) | 9.58216 | 0.448726 | ||||||||
\(457\) | −4.81819 | −0.225385 | −0.112693 | − | 0.993630i | \(-0.535948\pi\) | ||||
−0.112693 | + | 0.993630i | \(0.535948\pi\) | |||||||
\(458\) | 16.9360 | 0.791368 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 13.8156 | 0.644155 | ||||||||
\(461\) | −7.87020 | −0.366552 | −0.183276 | − | 0.983062i | \(-0.558670\pi\) | ||||
−0.183276 | + | 0.983062i | \(0.558670\pi\) | |||||||
\(462\) | −11.0284 | −0.513089 | ||||||||
\(463\) | 4.08451 | 0.189823 | 0.0949116 | − | 0.995486i | \(-0.469743\pi\) | ||||
0.0949116 | + | 0.995486i | \(0.469743\pi\) | |||||||
\(464\) | 2.68546 | 0.124669 | ||||||||
\(465\) | 8.09048 | 0.375187 | ||||||||
\(466\) | −3.70403 | −0.171586 | ||||||||
\(467\) | −16.2716 | −0.752961 | −0.376481 | − | 0.926424i | \(-0.622866\pi\) | ||||
−0.376481 | + | 0.926424i | \(0.622866\pi\) | |||||||
\(468\) | −1.11505 | −0.0515433 | ||||||||
\(469\) | 8.11533 | 0.374731 | ||||||||
\(470\) | −32.0907 | −1.48023 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | −15.1626 | −0.697914 | ||||||||
\(473\) | −50.2822 | −2.31198 | ||||||||
\(474\) | 10.7967 | 0.495909 | ||||||||
\(475\) | 23.8749 | 1.09546 | ||||||||
\(476\) | −2.58208 | −0.118349 | ||||||||
\(477\) | 10.3774 | 0.475146 | ||||||||
\(478\) | 3.19678 | 0.146217 | ||||||||
\(479\) | −31.3862 | −1.43407 | −0.717037 | − | 0.697035i | \(-0.754502\pi\) | ||||
−0.717037 | + | 0.697035i | \(0.754502\pi\) | |||||||
\(480\) | −18.7666 | −0.856575 | ||||||||
\(481\) | −1.16886 | −0.0532956 | ||||||||
\(482\) | −25.3969 | −1.15680 | ||||||||
\(483\) | 8.26526 | 0.376082 | ||||||||
\(484\) | −15.7337 | −0.715170 | ||||||||
\(485\) | −23.1336 | −1.05044 | ||||||||
\(486\) | −0.943890 | −0.0428157 | ||||||||
\(487\) | −14.7583 | −0.668762 | −0.334381 | − | 0.942438i | \(-0.608527\pi\) | ||||
−0.334381 | + | 0.942438i | \(0.608527\pi\) | |||||||
\(488\) | −4.38529 | −0.198513 | ||||||||
\(489\) | 17.4822 | 0.790574 | ||||||||
\(490\) | 5.23207 | 0.236361 | ||||||||
\(491\) | −17.0491 | −0.769417 | −0.384708 | − | 0.923038i | \(-0.625698\pi\) | ||||
−0.384708 | + | 0.923038i | \(0.625698\pi\) | |||||||
\(492\) | 11.2652 | 0.507874 | ||||||||
\(493\) | 4.86661 | 0.219181 | ||||||||
\(494\) | −3.09862 | −0.139413 | ||||||||
\(495\) | −17.6094 | −0.791486 | ||||||||
\(496\) | −1.27234 | −0.0571298 | ||||||||
\(497\) | 15.9323 | 0.714660 | ||||||||
\(498\) | −8.17626 | −0.366387 | ||||||||
\(499\) | −6.81219 | −0.304955 | −0.152478 | − | 0.988307i | \(-0.548725\pi\) | ||||
−0.152478 | + | 0.988307i | \(0.548725\pi\) | |||||||
\(500\) | −8.99691 | −0.402354 | ||||||||
\(501\) | −16.1605 | −0.721998 | ||||||||
\(502\) | 17.0384 | 0.760461 | ||||||||
\(503\) | −25.1211 | −1.12009 | −0.560047 | − | 0.828461i | \(-0.689217\pi\) | ||||
−0.560047 | + | 0.828461i | \(0.689217\pi\) | |||||||
\(504\) | −6.83222 | −0.304331 | ||||||||
\(505\) | 11.1153 | 0.494624 | ||||||||
\(506\) | −16.8171 | −0.747611 | ||||||||
\(507\) | −11.9892 | −0.532458 | ||||||||
\(508\) | −12.0644 | −0.535271 | ||||||||
\(509\) | −14.8097 | −0.656427 | −0.328214 | − | 0.944604i | \(-0.606447\pi\) | ||||
−0.328214 | + | 0.944604i | \(0.606447\pi\) | |||||||
\(510\) | 3.31195 | 0.146656 | ||||||||
\(511\) | 3.74053 | 0.165471 | ||||||||
\(512\) | 6.19004 | 0.273564 | ||||||||
\(513\) | 3.26521 | 0.144163 | ||||||||
\(514\) | −9.28879 | −0.409711 | ||||||||
\(515\) | 10.8832 | 0.479573 | ||||||||
\(516\) | −11.1120 | −0.489177 | ||||||||
\(517\) | −48.6271 | −2.13862 | ||||||||
\(518\) | −2.55481 | −0.112252 | ||||||||
\(519\) | 6.75760 | 0.296626 | ||||||||
\(520\) | 10.3526 | 0.453992 | ||||||||
\(521\) | −18.6113 | −0.815374 | −0.407687 | − | 0.913122i | \(-0.633665\pi\) | ||||
−0.407687 | + | 0.913122i | \(0.633665\pi\) | |||||||
\(522\) | 4.59354 | 0.201054 | ||||||||
\(523\) | 12.2074 | 0.533790 | 0.266895 | − | 0.963726i | \(-0.414002\pi\) | ||||
0.266895 | + | 0.963726i | \(0.414002\pi\) | |||||||
\(524\) | −9.68903 | −0.423267 | ||||||||
\(525\) | −17.0232 | −0.742952 | ||||||||
\(526\) | 24.8477 | 1.08341 | ||||||||
\(527\) | −2.30575 | −0.100440 | ||||||||
\(528\) | 2.76933 | 0.120520 | ||||||||
\(529\) | −10.3964 | −0.452018 | ||||||||
\(530\) | −34.3693 | −1.49291 | ||||||||
\(531\) | −5.16679 | −0.224220 | ||||||||
\(532\) | 8.43103 | 0.365532 | ||||||||
\(533\) | −10.2121 | −0.442335 | ||||||||
\(534\) | 15.4382 | 0.668078 | ||||||||
\(535\) | 31.2976 | 1.35311 | ||||||||
\(536\) | −10.2294 | −0.441841 | ||||||||
\(537\) | −18.5229 | −0.799324 | ||||||||
\(538\) | 25.3027 | 1.09088 | ||||||||
\(539\) | 7.92816 | 0.341490 | ||||||||
\(540\) | −3.89155 | −0.167466 | ||||||||
\(541\) | 2.27708 | 0.0978993 | 0.0489497 | − | 0.998801i | \(-0.484413\pi\) | ||||
0.0489497 | + | 0.998801i | \(0.484413\pi\) | |||||||
\(542\) | 14.0054 | 0.601582 | ||||||||
\(543\) | −20.7954 | −0.892415 | ||||||||
\(544\) | 5.34839 | 0.229310 | ||||||||
\(545\) | −25.6410 | −1.09834 | ||||||||
\(546\) | 2.20936 | 0.0945518 | ||||||||
\(547\) | −19.5696 | −0.836736 | −0.418368 | − | 0.908278i | \(-0.637398\pi\) | ||||
−0.418368 | + | 0.908278i | \(0.637398\pi\) | |||||||
\(548\) | 6.28891 | 0.268649 | ||||||||
\(549\) | −1.49433 | −0.0637764 | ||||||||
\(550\) | 34.6366 | 1.47691 | ||||||||
\(551\) | −15.8905 | −0.676958 | ||||||||
\(552\) | −10.4183 | −0.443434 | ||||||||
\(553\) | 26.6305 | 1.13244 | ||||||||
\(554\) | 17.8014 | 0.756310 | ||||||||
\(555\) | −4.07935 | −0.173159 | ||||||||
\(556\) | 7.16079 | 0.303685 | ||||||||
\(557\) | 4.77606 | 0.202368 | 0.101184 | − | 0.994868i | \(-0.467737\pi\) | ||||
0.101184 | + | 0.994868i | \(0.467737\pi\) | |||||||
\(558\) | −2.17637 | −0.0921331 | ||||||||
\(559\) | 10.0732 | 0.426050 | ||||||||
\(560\) | 4.50780 | 0.190489 | ||||||||
\(561\) | 5.01861 | 0.211886 | ||||||||
\(562\) | −22.7184 | −0.958319 | ||||||||
\(563\) | 12.6274 | 0.532181 | 0.266091 | − | 0.963948i | \(-0.414268\pi\) | ||||
0.266091 | + | 0.963948i | \(0.414268\pi\) | |||||||
\(564\) | −10.7462 | −0.452497 | ||||||||
\(565\) | −46.6733 | −1.96356 | ||||||||
\(566\) | −14.8343 | −0.623532 | ||||||||
\(567\) | −2.32814 | −0.0977728 | ||||||||
\(568\) | −20.0826 | −0.842648 | ||||||||
\(569\) | −15.3620 | −0.644007 | −0.322003 | − | 0.946739i | \(-0.604356\pi\) | ||||
−0.322003 | + | 0.946739i | \(0.604356\pi\) | |||||||
\(570\) | −10.8142 | −0.452958 | ||||||||
\(571\) | −11.6263 | −0.486544 | −0.243272 | − | 0.969958i | \(-0.578221\pi\) | ||||
−0.243272 | + | 0.969958i | \(0.578221\pi\) | |||||||
\(572\) | 5.59601 | 0.233981 | ||||||||
\(573\) | 13.5891 | 0.567692 | ||||||||
\(574\) | −22.3208 | −0.931652 | ||||||||
\(575\) | −25.9584 | −1.08254 | ||||||||
\(576\) | 6.15192 | 0.256330 | ||||||||
\(577\) | 0.662416 | 0.0275768 | 0.0137884 | − | 0.999905i | \(-0.495611\pi\) | ||||
0.0137884 | + | 0.999905i | \(0.495611\pi\) | |||||||
\(578\) | −0.943890 | −0.0392606 | ||||||||
\(579\) | −13.8923 | −0.577345 | ||||||||
\(580\) | 18.9386 | 0.786384 | ||||||||
\(581\) | −20.1671 | −0.836672 | ||||||||
\(582\) | 6.22303 | 0.257953 | ||||||||
\(583\) | −52.0798 | −2.15693 | ||||||||
\(584\) | −4.71494 | −0.195106 | ||||||||
\(585\) | 3.52775 | 0.145855 | ||||||||
\(586\) | 2.63546 | 0.108870 | ||||||||
\(587\) | 19.5779 | 0.808067 | 0.404034 | − | 0.914744i | \(-0.367608\pi\) | ||||
0.404034 | + | 0.914744i | \(0.367608\pi\) | |||||||
\(588\) | 1.75206 | 0.0722538 | ||||||||
\(589\) | 7.52875 | 0.310217 | ||||||||
\(590\) | 17.1121 | 0.704496 | ||||||||
\(591\) | 5.71584 | 0.235118 | ||||||||
\(592\) | 0.641535 | 0.0263669 | ||||||||
\(593\) | −5.06598 | −0.208035 | −0.104018 | − | 0.994575i | \(-0.533170\pi\) | ||||
−0.104018 | + | 0.994575i | \(0.533170\pi\) | |||||||
\(594\) | 4.73701 | 0.194362 | ||||||||
\(595\) | 8.16906 | 0.334899 | ||||||||
\(596\) | 23.9691 | 0.981812 | ||||||||
\(597\) | −24.5328 | −1.00406 | ||||||||
\(598\) | 3.36902 | 0.137769 | ||||||||
\(599\) | −3.15884 | −0.129067 | −0.0645333 | − | 0.997916i | \(-0.520556\pi\) | ||||
−0.0645333 | + | 0.997916i | \(0.520556\pi\) | |||||||
\(600\) | 21.4577 | 0.876006 | ||||||||
\(601\) | −28.8749 | −1.17783 | −0.588916 | − | 0.808194i | \(-0.700445\pi\) | ||||
−0.588916 | + | 0.808194i | \(0.700445\pi\) | |||||||
\(602\) | 22.0172 | 0.897353 | ||||||||
\(603\) | −3.48575 | −0.141951 | ||||||||
\(604\) | −2.79060 | −0.113548 | ||||||||
\(605\) | 49.7777 | 2.02375 | ||||||||
\(606\) | −2.99006 | −0.121463 | ||||||||
\(607\) | −17.2862 | −0.701626 | −0.350813 | − | 0.936446i | \(-0.614095\pi\) | ||||
−0.350813 | + | 0.936446i | \(0.614095\pi\) | |||||||
\(608\) | −17.4636 | −0.708244 | ||||||||
\(609\) | 11.3302 | 0.459121 | ||||||||
\(610\) | 4.94914 | 0.200385 | ||||||||
\(611\) | 9.74161 | 0.394103 | ||||||||
\(612\) | 1.10907 | 0.0448316 | ||||||||
\(613\) | −8.17573 | −0.330214 | −0.165107 | − | 0.986276i | \(-0.552797\pi\) | ||||
−0.165107 | + | 0.986276i | \(0.552797\pi\) | |||||||
\(614\) | −25.5702 | −1.03193 | ||||||||
\(615\) | −35.6403 | −1.43716 | ||||||||
\(616\) | 34.2882 | 1.38151 | ||||||||
\(617\) | −7.63160 | −0.307237 | −0.153618 | − | 0.988130i | \(-0.549093\pi\) | ||||
−0.153618 | + | 0.988130i | \(0.549093\pi\) | |||||||
\(618\) | −2.92764 | −0.117767 | ||||||||
\(619\) | 19.6432 | 0.789525 | 0.394763 | − | 0.918783i | \(-0.370827\pi\) | ||||
0.394763 | + | 0.918783i | \(0.370827\pi\) | |||||||
\(620\) | −8.97293 | −0.360362 | ||||||||
\(621\) | −3.55015 | −0.142463 | ||||||||
\(622\) | −23.0593 | −0.924594 | ||||||||
\(623\) | 38.0790 | 1.52560 | ||||||||
\(624\) | −0.554789 | −0.0222093 | ||||||||
\(625\) | −8.09553 | −0.323821 | ||||||||
\(626\) | −27.3290 | −1.09229 | ||||||||
\(627\) | −16.3868 | −0.654426 | ||||||||
\(628\) | −1.10907 | −0.0442568 | ||||||||
\(629\) | 1.16260 | 0.0463557 | ||||||||
\(630\) | 7.71069 | 0.307201 | ||||||||
\(631\) | 43.5189 | 1.73246 | 0.866229 | − | 0.499647i | \(-0.166537\pi\) | ||||
0.866229 | + | 0.499647i | \(0.166537\pi\) | |||||||
\(632\) | −33.5677 | −1.33525 | ||||||||
\(633\) | −2.65539 | −0.105542 | ||||||||
\(634\) | 4.95147 | 0.196648 | ||||||||
\(635\) | 38.1688 | 1.51468 | ||||||||
\(636\) | −11.5092 | −0.456371 | ||||||||
\(637\) | −1.58827 | −0.0629296 | ||||||||
\(638\) | −23.0532 | −0.912683 | ||||||||
\(639\) | −6.84335 | −0.270719 | ||||||||
\(640\) | 17.1584 | 0.678244 | ||||||||
\(641\) | −35.6057 | −1.40634 | −0.703170 | − | 0.711022i | \(-0.748233\pi\) | ||||
−0.703170 | + | 0.711022i | \(0.748233\pi\) | |||||||
\(642\) | −8.41918 | −0.332279 | ||||||||
\(643\) | −38.1629 | −1.50500 | −0.752500 | − | 0.658593i | \(-0.771152\pi\) | ||||
−0.752500 | + | 0.658593i | \(0.771152\pi\) | |||||||
\(644\) | −9.16677 | −0.361221 | ||||||||
\(645\) | 35.1555 | 1.38425 | ||||||||
\(646\) | 3.08200 | 0.121260 | ||||||||
\(647\) | 29.6505 | 1.16568 | 0.582840 | − | 0.812587i | \(-0.301942\pi\) | ||||
0.582840 | + | 0.812587i | \(0.301942\pi\) | |||||||
\(648\) | 2.93462 | 0.115283 | ||||||||
\(649\) | 25.9301 | 1.01784 | ||||||||
\(650\) | −6.93885 | −0.272164 | ||||||||
\(651\) | −5.36811 | −0.210393 | ||||||||
\(652\) | −19.3891 | −0.759334 | ||||||||
\(653\) | −20.4813 | −0.801496 | −0.400748 | − | 0.916188i | \(-0.631250\pi\) | ||||
−0.400748 | + | 0.916188i | \(0.631250\pi\) | |||||||
\(654\) | 6.89754 | 0.269715 | ||||||||
\(655\) | 30.6537 | 1.19774 | ||||||||
\(656\) | 5.60494 | 0.218836 | ||||||||
\(657\) | −1.60666 | −0.0626818 | ||||||||
\(658\) | 21.2925 | 0.830067 | ||||||||
\(659\) | 11.2831 | 0.439528 | 0.219764 | − | 0.975553i | \(-0.429471\pi\) | ||||
0.219764 | + | 0.975553i | \(0.429471\pi\) | |||||||
\(660\) | 19.5302 | 0.760210 | ||||||||
\(661\) | −30.2059 | −1.17487 | −0.587436 | − | 0.809271i | \(-0.699863\pi\) | ||||
−0.587436 | + | 0.809271i | \(0.699863\pi\) | |||||||
\(662\) | 16.9899 | 0.660332 | ||||||||
\(663\) | −1.00539 | −0.0390462 | ||||||||
\(664\) | 25.4206 | 0.986510 | ||||||||
\(665\) | −26.6737 | −1.03436 | ||||||||
\(666\) | 1.09736 | 0.0425219 | ||||||||
\(667\) | 17.2772 | 0.668975 | ||||||||
\(668\) | 17.9232 | 0.693468 | ||||||||
\(669\) | 8.14373 | 0.314855 | ||||||||
\(670\) | 11.5446 | 0.446009 | ||||||||
\(671\) | 7.49945 | 0.289513 | ||||||||
\(672\) | 12.4518 | 0.480339 | ||||||||
\(673\) | 21.1764 | 0.816291 | 0.408145 | − | 0.912917i | \(-0.366176\pi\) | ||||
0.408145 | + | 0.912917i | \(0.366176\pi\) | |||||||
\(674\) | 31.2515 | 1.20376 | ||||||||
\(675\) | 7.31191 | 0.281436 | ||||||||
\(676\) | 13.2969 | 0.511418 | ||||||||
\(677\) | −2.85289 | −0.109645 | −0.0548227 | − | 0.998496i | \(-0.517459\pi\) | ||||
−0.0548227 | + | 0.998496i | \(0.517459\pi\) | |||||||
\(678\) | 12.5553 | 0.482183 | ||||||||
\(679\) | 15.3494 | 0.589054 | ||||||||
\(680\) | −10.2971 | −0.394876 | ||||||||
\(681\) | −25.2961 | −0.969347 | ||||||||
\(682\) | 10.9223 | 0.418238 | ||||||||
\(683\) | 25.1103 | 0.960821 | 0.480410 | − | 0.877044i | \(-0.340488\pi\) | ||||
0.480410 | + | 0.877044i | \(0.340488\pi\) | |||||||
\(684\) | −3.62136 | −0.138466 | ||||||||
\(685\) | −19.8966 | −0.760209 | ||||||||
\(686\) | −18.8541 | −0.719852 | ||||||||
\(687\) | −17.9428 | −0.684560 | ||||||||
\(688\) | −5.52870 | −0.210780 | ||||||||
\(689\) | 10.4333 | 0.397477 | ||||||||
\(690\) | 11.7579 | 0.447617 | ||||||||
\(691\) | 32.2779 | 1.22791 | 0.613955 | − | 0.789341i | \(-0.289578\pi\) | ||||
0.613955 | + | 0.789341i | \(0.289578\pi\) | |||||||
\(692\) | −7.49467 | −0.284905 | ||||||||
\(693\) | 11.6840 | 0.443840 | ||||||||
\(694\) | 3.95251 | 0.150035 | ||||||||
\(695\) | −22.6550 | −0.859353 | ||||||||
\(696\) | −14.2816 | −0.541344 | ||||||||
\(697\) | 10.1573 | 0.384736 | ||||||||
\(698\) | −22.2908 | −0.843720 | ||||||||
\(699\) | 3.92422 | 0.148427 | ||||||||
\(700\) | 18.8799 | 0.713594 | ||||||||
\(701\) | −4.68951 | −0.177120 | −0.0885601 | − | 0.996071i | \(-0.528227\pi\) | ||||
−0.0885601 | + | 0.996071i | \(0.528227\pi\) | |||||||
\(702\) | −0.948979 | −0.0358169 | ||||||||
\(703\) | −3.79612 | −0.143173 | ||||||||
\(704\) | −30.8740 | −1.16361 | ||||||||
\(705\) | 33.9984 | 1.28045 | ||||||||
\(706\) | 4.27711 | 0.160971 | ||||||||
\(707\) | −7.37510 | −0.277369 | ||||||||
\(708\) | 5.73034 | 0.215359 | ||||||||
\(709\) | −25.6853 | −0.964631 | −0.482315 | − | 0.875998i | \(-0.660204\pi\) | ||||
−0.482315 | + | 0.875998i | \(0.660204\pi\) | |||||||
\(710\) | 22.6648 | 0.850596 | ||||||||
\(711\) | −11.4385 | −0.428978 | ||||||||
\(712\) | −47.9986 | −1.79882 | ||||||||
\(713\) | −8.18575 | −0.306559 | ||||||||
\(714\) | −2.19751 | −0.0822397 | ||||||||
\(715\) | −17.7044 | −0.662107 | ||||||||
\(716\) | 20.5433 | 0.767738 | ||||||||
\(717\) | −3.38682 | −0.126483 | ||||||||
\(718\) | 3.18719 | 0.118945 | ||||||||
\(719\) | 23.9735 | 0.894062 | 0.447031 | − | 0.894518i | \(-0.352481\pi\) | ||||
0.447031 | + | 0.894518i | \(0.352481\pi\) | |||||||
\(720\) | −1.93622 | −0.0721587 | ||||||||
\(721\) | −7.22113 | −0.268929 | ||||||||
\(722\) | 7.87052 | 0.292910 | ||||||||
\(723\) | 26.9066 | 1.00067 | ||||||||
\(724\) | 23.0636 | 0.857151 | ||||||||
\(725\) | −35.5842 | −1.32156 | ||||||||
\(726\) | −13.3904 | −0.496964 | ||||||||
\(727\) | 11.4994 | 0.426489 | 0.213245 | − | 0.976999i | \(-0.431597\pi\) | ||||
0.213245 | + | 0.976999i | \(0.431597\pi\) | |||||||
\(728\) | −6.86906 | −0.254584 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 5.32118 | 0.196946 | ||||||||
\(731\) | −10.0192 | −0.370572 | ||||||||
\(732\) | 1.65732 | 0.0612563 | ||||||||
\(733\) | 2.16985 | 0.0801453 | 0.0400726 | − | 0.999197i | \(-0.487241\pi\) | ||||
0.0400726 | + | 0.999197i | \(0.487241\pi\) | |||||||
\(734\) | 28.3358 | 1.04589 | ||||||||
\(735\) | −5.54309 | −0.204460 | ||||||||
\(736\) | 18.9876 | 0.699892 | ||||||||
\(737\) | 17.4936 | 0.644386 | ||||||||
\(738\) | 9.58739 | 0.352917 | ||||||||
\(739\) | 30.3377 | 1.11599 | 0.557995 | − | 0.829844i | \(-0.311571\pi\) | ||||
0.557995 | + | 0.829844i | \(0.311571\pi\) | |||||||
\(740\) | 4.52430 | 0.166316 | ||||||||
\(741\) | 3.28282 | 0.120597 | ||||||||
\(742\) | 22.8043 | 0.837173 | ||||||||
\(743\) | 12.0601 | 0.442444 | 0.221222 | − | 0.975224i | \(-0.428996\pi\) | ||||
0.221222 | + | 0.975224i | \(0.428996\pi\) | |||||||
\(744\) | 6.76649 | 0.248072 | ||||||||
\(745\) | −75.8323 | −2.77828 | ||||||||
\(746\) | 4.16503 | 0.152493 | ||||||||
\(747\) | 8.66231 | 0.316937 | ||||||||
\(748\) | −5.56600 | −0.203513 | ||||||||
\(749\) | −20.7663 | −0.758782 | ||||||||
\(750\) | −7.65693 | −0.279592 | ||||||||
\(751\) | −43.1501 | −1.57457 | −0.787285 | − | 0.616589i | \(-0.788514\pi\) | ||||
−0.787285 | + | 0.616589i | \(0.788514\pi\) | |||||||
\(752\) | −5.34672 | −0.194975 | ||||||||
\(753\) | −18.0513 | −0.657825 | ||||||||
\(754\) | 4.61831 | 0.168189 | ||||||||
\(755\) | 8.82878 | 0.321312 | ||||||||
\(756\) | 2.58208 | 0.0939093 | ||||||||
\(757\) | −12.5373 | −0.455675 | −0.227838 | − | 0.973699i | \(-0.573166\pi\) | ||||
−0.227838 | + | 0.973699i | \(0.573166\pi\) | |||||||
\(758\) | 18.9422 | 0.688013 | ||||||||
\(759\) | 17.8168 | 0.646709 | ||||||||
\(760\) | 33.6222 | 1.21961 | ||||||||
\(761\) | 16.7430 | 0.606935 | 0.303467 | − | 0.952842i | \(-0.401856\pi\) | ||||
0.303467 | + | 0.952842i | \(0.401856\pi\) | |||||||
\(762\) | −10.2675 | −0.371954 | ||||||||
\(763\) | 17.0131 | 0.615914 | ||||||||
\(764\) | −15.0713 | −0.545259 | ||||||||
\(765\) | −3.50883 | −0.126862 | ||||||||
\(766\) | −21.1563 | −0.764409 | ||||||||
\(767\) | −5.19465 | −0.187568 | ||||||||
\(768\) | −16.9195 | −0.610530 | ||||||||
\(769\) | −41.8387 | −1.50874 | −0.754372 | − | 0.656447i | \(-0.772058\pi\) | ||||
−0.754372 | + | 0.656447i | \(0.772058\pi\) | |||||||
\(770\) | −38.6969 | −1.39454 | ||||||||
\(771\) | 9.84097 | 0.354414 | ||||||||
\(772\) | 15.4076 | 0.554531 | ||||||||
\(773\) | −42.0271 | −1.51161 | −0.755804 | − | 0.654798i | \(-0.772754\pi\) | ||||
−0.755804 | + | 0.654798i | \(0.772754\pi\) | |||||||
\(774\) | −9.45697 | −0.339924 | ||||||||
\(775\) | 16.8594 | 0.605608 | ||||||||
\(776\) | −19.3478 | −0.694547 | ||||||||
\(777\) | 2.70669 | 0.0971019 | ||||||||
\(778\) | −3.73241 | −0.133813 | ||||||||
\(779\) | −33.1658 | −1.18829 | ||||||||
\(780\) | −3.91253 | −0.140091 | ||||||||
\(781\) | 34.3441 | 1.22893 | ||||||||
\(782\) | −3.35095 | −0.119830 | ||||||||
\(783\) | −4.86661 | −0.173918 | ||||||||
\(784\) | 0.871729 | 0.0311332 | ||||||||
\(785\) | 3.50883 | 0.125236 | ||||||||
\(786\) | −8.24597 | −0.294124 | ||||||||
\(787\) | 2.07376 | 0.0739214 | 0.0369607 | − | 0.999317i | \(-0.488232\pi\) | ||||
0.0369607 | + | 0.999317i | \(0.488232\pi\) | |||||||
\(788\) | −6.33928 | −0.225828 | ||||||||
\(789\) | −26.3248 | −0.937187 | ||||||||
\(790\) | 37.8838 | 1.34785 | ||||||||
\(791\) | 30.9681 | 1.10110 | ||||||||
\(792\) | −14.7277 | −0.523326 | ||||||||
\(793\) | −1.50239 | −0.0533513 | ||||||||
\(794\) | −20.3450 | −0.722018 | ||||||||
\(795\) | 36.4124 | 1.29141 | ||||||||
\(796\) | 27.2086 | 0.964384 | ||||||||
\(797\) | 27.2290 | 0.964501 | 0.482250 | − | 0.876033i | \(-0.339820\pi\) | ||||
0.482250 | + | 0.876033i | \(0.339820\pi\) | |||||||
\(798\) | 7.17533 | 0.254004 | ||||||||
\(799\) | −9.68937 | −0.342785 | ||||||||
\(800\) | −39.1070 | −1.38264 | ||||||||
\(801\) | −16.3560 | −0.577910 | ||||||||
\(802\) | −15.6574 | −0.552883 | ||||||||
\(803\) | 8.06319 | 0.284544 | ||||||||
\(804\) | 3.86595 | 0.136342 | ||||||||
\(805\) | 29.0014 | 1.02217 | ||||||||
\(806\) | −2.18811 | −0.0770728 | ||||||||
\(807\) | −26.8069 | −0.943647 | ||||||||
\(808\) | 9.29631 | 0.327043 | ||||||||
\(809\) | −41.9532 | −1.47500 | −0.737498 | − | 0.675350i | \(-0.763993\pi\) | ||||
−0.737498 | + | 0.675350i | \(0.763993\pi\) | |||||||
\(810\) | −3.31195 | −0.116370 | ||||||||
\(811\) | −6.55463 | −0.230164 | −0.115082 | − | 0.993356i | \(-0.536713\pi\) | ||||
−0.115082 | + | 0.993356i | \(0.536713\pi\) | |||||||
\(812\) | −12.5660 | −0.440979 | ||||||||
\(813\) | −14.8379 | −0.520389 | ||||||||
\(814\) | −5.50722 | −0.193028 | ||||||||
\(815\) | 61.3422 | 2.14873 | ||||||||
\(816\) | 0.551813 | 0.0193173 | ||||||||
\(817\) | 32.7147 | 1.14454 | ||||||||
\(818\) | −35.5400 | −1.24263 | ||||||||
\(819\) | −2.34070 | −0.0817905 | ||||||||
\(820\) | 39.5277 | 1.38037 | ||||||||
\(821\) | 23.4737 | 0.819237 | 0.409618 | − | 0.912257i | \(-0.365662\pi\) | ||||
0.409618 | + | 0.912257i | \(0.365662\pi\) | |||||||
\(822\) | 5.35225 | 0.186681 | ||||||||
\(823\) | −16.1427 | −0.562700 | −0.281350 | − | 0.959605i | \(-0.590782\pi\) | ||||
−0.281350 | + | 0.959605i | \(0.590782\pi\) | |||||||
\(824\) | 9.10223 | 0.317091 | ||||||||
\(825\) | −36.6956 | −1.27758 | ||||||||
\(826\) | −11.3541 | −0.395058 | ||||||||
\(827\) | 6.01408 | 0.209130 | 0.104565 | − | 0.994518i | \(-0.466655\pi\) | ||||
0.104565 | + | 0.994518i | \(0.466655\pi\) | |||||||
\(828\) | 3.93738 | 0.136833 | ||||||||
\(829\) | 23.0125 | 0.799258 | 0.399629 | − | 0.916677i | \(-0.369139\pi\) | ||||
0.399629 | + | 0.916677i | \(0.369139\pi\) | |||||||
\(830\) | −28.6891 | −0.995815 | ||||||||
\(831\) | −18.8597 | −0.654234 | ||||||||
\(832\) | 6.18509 | 0.214429 | ||||||||
\(833\) | 1.57975 | 0.0547352 | ||||||||
\(834\) | 6.09428 | 0.211028 | ||||||||
\(835\) | −56.7045 | −1.96234 | ||||||||
\(836\) | 18.1742 | 0.628567 | ||||||||
\(837\) | 2.30575 | 0.0796983 | ||||||||
\(838\) | 16.8065 | 0.580571 | ||||||||
\(839\) | −23.0000 | −0.794048 | −0.397024 | − | 0.917808i | \(-0.629957\pi\) | ||||
−0.397024 | + | 0.917808i | \(0.629957\pi\) | |||||||
\(840\) | −23.9731 | −0.827151 | ||||||||
\(841\) | −5.31614 | −0.183315 | ||||||||
\(842\) | −17.9718 | −0.619350 | ||||||||
\(843\) | 24.0689 | 0.828978 | ||||||||
\(844\) | 2.94502 | 0.101372 | ||||||||
\(845\) | −42.0681 | −1.44719 | ||||||||
\(846\) | −9.14569 | −0.314435 | ||||||||
\(847\) | −33.0280 | −1.13485 | ||||||||
\(848\) | −5.72636 | −0.196644 | ||||||||
\(849\) | 15.7161 | 0.539377 | ||||||||
\(850\) | 6.90163 | 0.236724 | ||||||||
\(851\) | 4.12739 | 0.141485 | ||||||||
\(852\) | 7.58977 | 0.260021 | ||||||||
\(853\) | −56.0393 | −1.91875 | −0.959374 | − | 0.282136i | \(-0.908957\pi\) | ||||
−0.959374 | + | 0.282136i | \(0.908957\pi\) | |||||||
\(854\) | −3.28380 | −0.112369 | ||||||||
\(855\) | 11.4571 | 0.391824 | ||||||||
\(856\) | 26.1758 | 0.894672 | ||||||||
\(857\) | −24.5248 | −0.837750 | −0.418875 | − | 0.908044i | \(-0.637575\pi\) | ||||
−0.418875 | + | 0.908044i | \(0.637575\pi\) | |||||||
\(858\) | 4.76255 | 0.162591 | ||||||||
\(859\) | −43.5237 | −1.48501 | −0.742506 | − | 0.669840i | \(-0.766363\pi\) | ||||
−0.742506 | + | 0.669840i | \(0.766363\pi\) | |||||||
\(860\) | −38.9900 | −1.32955 | ||||||||
\(861\) | 23.6477 | 0.805911 | ||||||||
\(862\) | −28.8310 | −0.981988 | ||||||||
\(863\) | −26.1440 | −0.889952 | −0.444976 | − | 0.895543i | \(-0.646788\pi\) | ||||
−0.444976 | + | 0.895543i | \(0.646788\pi\) | |||||||
\(864\) | −5.34839 | −0.181956 | ||||||||
\(865\) | 23.7113 | 0.806208 | ||||||||
\(866\) | −3.96396 | −0.134701 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 5.95362 | 0.202079 | ||||||||
\(869\) | 57.4054 | 1.94735 | ||||||||
\(870\) | 16.1180 | 0.546450 | ||||||||
\(871\) | −3.50455 | −0.118747 | ||||||||
\(872\) | −21.4449 | −0.726217 | ||||||||
\(873\) | −6.59296 | −0.223138 | ||||||||
\(874\) | 10.9416 | 0.370104 | ||||||||
\(875\) | −18.8861 | −0.638468 | ||||||||
\(876\) | 1.78190 | 0.0602049 | ||||||||
\(877\) | −13.6800 | −0.461941 | −0.230970 | − | 0.972961i | \(-0.574190\pi\) | ||||
−0.230970 | + | 0.972961i | \(0.574190\pi\) | |||||||
\(878\) | −27.7190 | −0.935472 | ||||||||
\(879\) | −2.79213 | −0.0941762 | ||||||||
\(880\) | 9.71713 | 0.327564 | ||||||||
\(881\) | −19.4123 | −0.654018 | −0.327009 | − | 0.945021i | \(-0.606041\pi\) | ||||
−0.327009 | + | 0.945021i | \(0.606041\pi\) | |||||||
\(882\) | 1.49111 | 0.0502084 | ||||||||
\(883\) | −23.0824 | −0.776785 | −0.388392 | − | 0.921494i | \(-0.626969\pi\) | ||||
−0.388392 | + | 0.921494i | \(0.626969\pi\) | |||||||
\(884\) | 1.11505 | 0.0375033 | ||||||||
\(885\) | −18.1294 | −0.609413 | ||||||||
\(886\) | −23.4042 | −0.786278 | ||||||||
\(887\) | −12.6679 | −0.425347 | −0.212674 | − | 0.977123i | \(-0.568217\pi\) | ||||
−0.212674 | + | 0.977123i | \(0.568217\pi\) | |||||||
\(888\) | −3.41178 | −0.114492 | ||||||||
\(889\) | −25.3253 | −0.849384 | ||||||||
\(890\) | 54.1702 | 1.81579 | ||||||||
\(891\) | −5.01861 | −0.168130 | ||||||||
\(892\) | −9.03199 | −0.302413 | ||||||||
\(893\) | 31.6378 | 1.05872 | ||||||||
\(894\) | 20.3992 | 0.682251 | ||||||||
\(895\) | −64.9939 | −2.17251 | ||||||||
\(896\) | −11.3847 | −0.380337 | ||||||||
\(897\) | −3.56929 | −0.119175 | ||||||||
\(898\) | 4.39844 | 0.146778 | ||||||||
\(899\) | −11.2212 | −0.374247 | ||||||||
\(900\) | −8.10944 | −0.270315 | ||||||||
\(901\) | −10.3774 | −0.345720 | ||||||||
\(902\) | −48.1153 | −1.60206 | ||||||||
\(903\) | −23.3260 | −0.776241 | ||||||||
\(904\) | −39.0353 | −1.29830 | ||||||||
\(905\) | −72.9675 | −2.42552 | ||||||||
\(906\) | −2.37498 | −0.0789033 | ||||||||
\(907\) | 31.7150 | 1.05308 | 0.526540 | − | 0.850150i | \(-0.323489\pi\) | ||||
0.526540 | + | 0.850150i | \(0.323489\pi\) | |||||||
\(908\) | 28.0552 | 0.931043 | ||||||||
\(909\) | 3.16781 | 0.105069 | ||||||||
\(910\) | 7.75227 | 0.256985 | ||||||||
\(911\) | 9.15482 | 0.303313 | 0.151656 | − | 0.988433i | \(-0.451539\pi\) | ||||
0.151656 | + | 0.988433i | \(0.451539\pi\) | |||||||
\(912\) | −1.80179 | −0.0596631 | ||||||||
\(913\) | −43.4727 | −1.43874 | ||||||||
\(914\) | 4.54784 | 0.150429 | ||||||||
\(915\) | −5.24335 | −0.173340 | ||||||||
\(916\) | 19.8999 | 0.657510 | ||||||||
\(917\) | −20.3390 | −0.671653 | ||||||||
\(918\) | 0.943890 | 0.0311530 | ||||||||
\(919\) | −33.2804 | −1.09782 | −0.548909 | − | 0.835882i | \(-0.684957\pi\) | ||||
−0.548909 | + | 0.835882i | \(0.684957\pi\) | |||||||
\(920\) | −36.5562 | −1.20522 | ||||||||
\(921\) | 27.0903 | 0.892655 | ||||||||
\(922\) | 7.42860 | 0.244648 | ||||||||
\(923\) | −6.88025 | −0.226466 | ||||||||
\(924\) | −12.9584 | −0.426301 | ||||||||
\(925\) | −8.50079 | −0.279504 | ||||||||
\(926\) | −3.85533 | −0.126694 | ||||||||
\(927\) | 3.10167 | 0.101872 | ||||||||
\(928\) | 26.0285 | 0.854428 | ||||||||
\(929\) | −24.3960 | −0.800407 | −0.400204 | − | 0.916426i | \(-0.631061\pi\) | ||||
−0.400204 | + | 0.916426i | \(0.631061\pi\) | |||||||
\(930\) | −7.63652 | −0.250411 | ||||||||
\(931\) | −5.15823 | −0.169054 | ||||||||
\(932\) | −4.35224 | −0.142562 | ||||||||
\(933\) | 24.4301 | 0.799805 | ||||||||
\(934\) | 15.3586 | 0.502550 | ||||||||
\(935\) | 17.6094 | 0.575891 | ||||||||
\(936\) | 2.95045 | 0.0964383 | ||||||||
\(937\) | 46.8690 | 1.53114 | 0.765571 | − | 0.643351i | \(-0.222456\pi\) | ||||
0.765571 | + | 0.643351i | \(0.222456\pi\) | |||||||
\(938\) | −7.65998 | −0.250107 | ||||||||
\(939\) | 28.9536 | 0.944864 | ||||||||
\(940\) | −37.7067 | −1.22986 | ||||||||
\(941\) | −57.9973 | −1.89066 | −0.945328 | − | 0.326120i | \(-0.894259\pi\) | ||||
−0.945328 | + | 0.326120i | \(0.894259\pi\) | |||||||
\(942\) | −0.943890 | −0.0307536 | ||||||||
\(943\) | 36.0600 | 1.17428 | ||||||||
\(944\) | 2.85110 | 0.0927955 | ||||||||
\(945\) | −8.16906 | −0.265740 | ||||||||
\(946\) | 47.4608 | 1.54308 | ||||||||
\(947\) | 26.2220 | 0.852101 | 0.426050 | − | 0.904699i | \(-0.359905\pi\) | ||||
0.426050 | + | 0.904699i | \(0.359905\pi\) | |||||||
\(948\) | 12.6861 | 0.412027 | ||||||||
\(949\) | −1.61532 | −0.0524356 | ||||||||
\(950\) | −22.5353 | −0.731142 | ||||||||
\(951\) | −5.24581 | −0.170107 | ||||||||
\(952\) | 6.83222 | 0.221433 | ||||||||
\(953\) | 33.6122 | 1.08881 | 0.544404 | − | 0.838823i | \(-0.316756\pi\) | ||||
0.544404 | + | 0.838823i | \(0.316756\pi\) | |||||||
\(954\) | −9.79507 | −0.317127 | ||||||||
\(955\) | 47.6818 | 1.54295 | ||||||||
\(956\) | 3.75622 | 0.121485 | ||||||||
\(957\) | 24.4236 | 0.789502 | ||||||||
\(958\) | 29.6251 | 0.957145 | ||||||||
\(959\) | 13.2016 | 0.426300 | ||||||||
\(960\) | 21.5861 | 0.696687 | ||||||||
\(961\) | −25.6835 | −0.828501 | ||||||||
\(962\) | 1.10328 | 0.0355711 | ||||||||
\(963\) | 8.91967 | 0.287432 | ||||||||
\(964\) | −29.8414 | −0.961127 | ||||||||
\(965\) | −48.7458 | −1.56918 | ||||||||
\(966\) | −7.80149 | −0.251009 | ||||||||
\(967\) | −41.2020 | −1.32497 | −0.662484 | − | 0.749076i | \(-0.730498\pi\) | ||||
−0.662484 | + | 0.749076i | \(0.730498\pi\) | |||||||
\(968\) | 41.6317 | 1.33809 | ||||||||
\(969\) | −3.26521 | −0.104894 | ||||||||
\(970\) | 21.8356 | 0.701098 | ||||||||
\(971\) | −4.14084 | −0.132886 | −0.0664429 | − | 0.997790i | \(-0.521165\pi\) | ||||
−0.0664429 | + | 0.997790i | \(0.521165\pi\) | |||||||
\(972\) | −1.10907 | −0.0355735 | ||||||||
\(973\) | 15.0318 | 0.481897 | ||||||||
\(974\) | 13.9302 | 0.446353 | ||||||||
\(975\) | 7.35134 | 0.235431 | ||||||||
\(976\) | 0.824590 | 0.0263945 | ||||||||
\(977\) | −6.84908 | −0.219122 | −0.109561 | − | 0.993980i | \(-0.534944\pi\) | ||||
−0.109561 | + | 0.993980i | \(0.534944\pi\) | |||||||
\(978\) | −16.5013 | −0.527653 | ||||||||
\(979\) | 82.0842 | 2.62342 | ||||||||
\(980\) | 6.14769 | 0.196381 | ||||||||
\(981\) | −7.30757 | −0.233313 | ||||||||
\(982\) | 16.0925 | 0.513532 | ||||||||
\(983\) | 13.9052 | 0.443508 | 0.221754 | − | 0.975103i | \(-0.428822\pi\) | ||||
0.221754 | + | 0.975103i | \(0.428822\pi\) | |||||||
\(984\) | −29.8079 | −0.950240 | ||||||||
\(985\) | 20.0559 | 0.639035 | ||||||||
\(986\) | −4.59354 | −0.146288 | ||||||||
\(987\) | −22.5582 | −0.718036 | ||||||||
\(988\) | −3.64088 | −0.115832 | ||||||||
\(989\) | −35.5695 | −1.13104 | ||||||||
\(990\) | 16.6214 | 0.528262 | ||||||||
\(991\) | 56.9848 | 1.81018 | 0.905091 | − | 0.425218i | \(-0.139802\pi\) | ||||
0.905091 | + | 0.425218i | \(0.139802\pi\) | |||||||
\(992\) | −12.3320 | −0.391543 | ||||||||
\(993\) | −17.9999 | −0.571209 | ||||||||
\(994\) | −15.0383 | −0.476986 | ||||||||
\(995\) | −86.0814 | −2.72896 | ||||||||
\(996\) | −9.60713 | −0.304414 | ||||||||
\(997\) | 45.0997 | 1.42832 | 0.714161 | − | 0.699982i | \(-0.246808\pi\) | ||||
0.714161 | + | 0.699982i | \(0.246808\pi\) | |||||||
\(998\) | 6.42995 | 0.203537 | ||||||||
\(999\) | −1.16260 | −0.0367829 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8007.2.a.e.1.17 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.e.1.17 | ✓ | 46 | 1.1 | even | 1 | trivial |