Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8047,2,Mod(1,8047)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8047, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8047.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8047 = 13 \cdot 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8047.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: | \(64.2556185065\) |
Analytic rank: | \(0\) |
Dimension: | \(168\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 8047.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.38728 | −1.68806 | −0.844030 | − | 0.536295i | \(-0.819823\pi\) | ||||
−0.844030 | + | 0.536295i | \(0.819823\pi\) | |||||||
\(3\) | 1.74228 | 1.00591 | 0.502953 | − | 0.864314i | \(-0.332247\pi\) | ||||
0.502953 | + | 0.864314i | \(0.332247\pi\) | |||||||
\(4\) | 3.69910 | 1.84955 | ||||||||
\(5\) | −3.20056 | −1.43134 | −0.715668 | − | 0.698441i | \(-0.753877\pi\) | ||||
−0.715668 | + | 0.698441i | \(0.753877\pi\) | |||||||
\(6\) | −4.15931 | −1.69803 | ||||||||
\(7\) | −0.986874 | −0.373003 | −0.186502 | − | 0.982455i | \(-0.559715\pi\) | ||||
−0.186502 | + | 0.982455i | \(0.559715\pi\) | |||||||
\(8\) | −4.05622 | −1.43409 | ||||||||
\(9\) | 0.0355448 | 0.0118483 | ||||||||
\(10\) | 7.64064 | 2.41618 | ||||||||
\(11\) | −5.86061 | −1.76704 | −0.883520 | − | 0.468393i | \(-0.844833\pi\) | ||||
−0.883520 | + | 0.468393i | \(0.844833\pi\) | |||||||
\(12\) | 6.44487 | 1.86047 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 2.35594 | 0.629652 | ||||||||
\(15\) | −5.57628 | −1.43979 | ||||||||
\(16\) | 2.28513 | 0.571284 | ||||||||
\(17\) | 6.77979 | 1.64434 | 0.822170 | − | 0.569242i | \(-0.192763\pi\) | ||||
0.822170 | + | 0.569242i | \(0.192763\pi\) | |||||||
\(18\) | −0.0848553 | −0.0200006 | ||||||||
\(19\) | −7.90095 | −1.81260 | −0.906301 | − | 0.422633i | \(-0.861106\pi\) | ||||
−0.906301 | + | 0.422633i | \(0.861106\pi\) | |||||||
\(20\) | −11.8392 | −2.64733 | ||||||||
\(21\) | −1.71941 | −0.375207 | ||||||||
\(22\) | 13.9909 | 2.98287 | ||||||||
\(23\) | −5.15186 | −1.07424 | −0.537118 | − | 0.843507i | \(-0.680487\pi\) | ||||
−0.537118 | + | 0.843507i | \(0.680487\pi\) | |||||||
\(24\) | −7.06708 | −1.44256 | ||||||||
\(25\) | 5.24361 | 1.04872 | ||||||||
\(26\) | −2.38728 | −0.468184 | ||||||||
\(27\) | −5.16492 | −0.993988 | ||||||||
\(28\) | −3.65055 | −0.689888 | ||||||||
\(29\) | −2.57040 | −0.477312 | −0.238656 | − | 0.971104i | \(-0.576707\pi\) | ||||
−0.238656 | + | 0.971104i | \(0.576707\pi\) | |||||||
\(30\) | 13.3121 | 2.43045 | ||||||||
\(31\) | −10.3692 | −1.86236 | −0.931180 | − | 0.364560i | \(-0.881219\pi\) | ||||
−0.931180 | + | 0.364560i | \(0.881219\pi\) | |||||||
\(32\) | 2.65719 | 0.469730 | ||||||||
\(33\) | −10.2108 | −1.77748 | ||||||||
\(34\) | −16.1852 | −2.77575 | ||||||||
\(35\) | 3.15855 | 0.533893 | ||||||||
\(36\) | 0.131484 | 0.0219139 | ||||||||
\(37\) | −9.37540 | −1.54131 | −0.770653 | − | 0.637255i | \(-0.780070\pi\) | ||||
−0.770653 | + | 0.637255i | \(0.780070\pi\) | |||||||
\(38\) | 18.8618 | 3.05978 | ||||||||
\(39\) | 1.74228 | 0.278988 | ||||||||
\(40\) | 12.9822 | 2.05267 | ||||||||
\(41\) | 3.37936 | 0.527768 | 0.263884 | − | 0.964554i | \(-0.414996\pi\) | ||||
0.263884 | + | 0.964554i | \(0.414996\pi\) | |||||||
\(42\) | 4.10472 | 0.633372 | ||||||||
\(43\) | −9.97466 | −1.52112 | −0.760560 | − | 0.649267i | \(-0.775076\pi\) | ||||
−0.760560 | + | 0.649267i | \(0.775076\pi\) | |||||||
\(44\) | −21.6790 | −3.26823 | ||||||||
\(45\) | −0.113763 | −0.0169588 | ||||||||
\(46\) | 12.2989 | 1.81338 | ||||||||
\(47\) | −0.482556 | −0.0703880 | −0.0351940 | − | 0.999380i | \(-0.511205\pi\) | ||||
−0.0351940 | + | 0.999380i | \(0.511205\pi\) | |||||||
\(48\) | 3.98135 | 0.574658 | ||||||||
\(49\) | −6.02608 | −0.860868 | ||||||||
\(50\) | −12.5179 | −1.77031 | ||||||||
\(51\) | 11.8123 | 1.65405 | ||||||||
\(52\) | 3.69910 | 0.512973 | ||||||||
\(53\) | −6.80748 | −0.935079 | −0.467540 | − | 0.883972i | \(-0.654859\pi\) | ||||
−0.467540 | + | 0.883972i | \(0.654859\pi\) | |||||||
\(54\) | 12.3301 | 1.67791 | ||||||||
\(55\) | 18.7573 | 2.52923 | ||||||||
\(56\) | 4.00298 | 0.534921 | ||||||||
\(57\) | −13.7657 | −1.82331 | ||||||||
\(58\) | 6.13627 | 0.805731 | ||||||||
\(59\) | 9.59534 | 1.24921 | 0.624604 | − | 0.780942i | \(-0.285261\pi\) | ||||
0.624604 | + | 0.780942i | \(0.285261\pi\) | |||||||
\(60\) | −20.6272 | −2.66296 | ||||||||
\(61\) | 7.13348 | 0.913348 | 0.456674 | − | 0.889634i | \(-0.349041\pi\) | ||||
0.456674 | + | 0.889634i | \(0.349041\pi\) | |||||||
\(62\) | 24.7541 | 3.14378 | ||||||||
\(63\) | −0.0350782 | −0.00441944 | ||||||||
\(64\) | −10.9137 | −1.36422 | ||||||||
\(65\) | −3.20056 | −0.396981 | ||||||||
\(66\) | 24.3761 | 3.00049 | ||||||||
\(67\) | 0.362353 | 0.0442684 | 0.0221342 | − | 0.999755i | \(-0.492954\pi\) | ||||
0.0221342 | + | 0.999755i | \(0.492954\pi\) | |||||||
\(68\) | 25.0791 | 3.04129 | ||||||||
\(69\) | −8.97599 | −1.08058 | ||||||||
\(70\) | −7.54035 | −0.901244 | ||||||||
\(71\) | −10.2078 | −1.21144 | −0.605722 | − | 0.795676i | \(-0.707116\pi\) | ||||
−0.605722 | + | 0.795676i | \(0.707116\pi\) | |||||||
\(72\) | −0.144178 | −0.0169915 | ||||||||
\(73\) | 3.39206 | 0.397011 | 0.198505 | − | 0.980100i | \(-0.436391\pi\) | ||||
0.198505 | + | 0.980100i | \(0.436391\pi\) | |||||||
\(74\) | 22.3817 | 2.60182 | ||||||||
\(75\) | 9.13584 | 1.05492 | ||||||||
\(76\) | −29.2264 | −3.35250 | ||||||||
\(77\) | 5.78368 | 0.659112 | ||||||||
\(78\) | −4.15931 | −0.470949 | ||||||||
\(79\) | 1.78740 | 0.201098 | 0.100549 | − | 0.994932i | \(-0.467940\pi\) | ||||
0.100549 | + | 0.994932i | \(0.467940\pi\) | |||||||
\(80\) | −7.31372 | −0.817699 | ||||||||
\(81\) | −9.10537 | −1.01171 | ||||||||
\(82\) | −8.06748 | −0.890904 | ||||||||
\(83\) | −2.94940 | −0.323739 | −0.161870 | − | 0.986812i | \(-0.551752\pi\) | ||||
−0.161870 | + | 0.986812i | \(0.551752\pi\) | |||||||
\(84\) | −6.36028 | −0.693963 | ||||||||
\(85\) | −21.6991 | −2.35360 | ||||||||
\(86\) | 23.8123 | 2.56774 | ||||||||
\(87\) | −4.47836 | −0.480131 | ||||||||
\(88\) | 23.7719 | 2.53410 | ||||||||
\(89\) | 13.7505 | 1.45755 | 0.728774 | − | 0.684754i | \(-0.240090\pi\) | ||||
0.728774 | + | 0.684754i | \(0.240090\pi\) | |||||||
\(90\) | 0.271585 | 0.0286275 | ||||||||
\(91\) | −0.986874 | −0.103453 | ||||||||
\(92\) | −19.0572 | −1.98685 | ||||||||
\(93\) | −18.0660 | −1.87336 | ||||||||
\(94\) | 1.15200 | 0.118819 | ||||||||
\(95\) | 25.2875 | 2.59444 | ||||||||
\(96\) | 4.62958 | 0.472504 | ||||||||
\(97\) | −9.15631 | −0.929682 | −0.464841 | − | 0.885394i | \(-0.653889\pi\) | ||||
−0.464841 | + | 0.885394i | \(0.653889\pi\) | |||||||
\(98\) | 14.3859 | 1.45320 | ||||||||
\(99\) | −0.208314 | −0.0209364 | ||||||||
\(100\) | 19.3966 | 1.93966 | ||||||||
\(101\) | 6.91355 | 0.687923 | 0.343962 | − | 0.938984i | \(-0.388231\pi\) | ||||
0.343962 | + | 0.938984i | \(0.388231\pi\) | |||||||
\(102\) | −28.1992 | −2.79214 | ||||||||
\(103\) | −10.4093 | −1.02566 | −0.512830 | − | 0.858490i | \(-0.671403\pi\) | ||||
−0.512830 | + | 0.858490i | \(0.671403\pi\) | |||||||
\(104\) | −4.05622 | −0.397745 | ||||||||
\(105\) | 5.50309 | 0.537046 | ||||||||
\(106\) | 16.2513 | 1.57847 | ||||||||
\(107\) | 7.13516 | 0.689782 | 0.344891 | − | 0.938643i | \(-0.387916\pi\) | ||||
0.344891 | + | 0.938643i | \(0.387916\pi\) | |||||||
\(108\) | −19.1055 | −1.83843 | ||||||||
\(109\) | −5.47913 | −0.524806 | −0.262403 | − | 0.964958i | \(-0.584515\pi\) | ||||
−0.262403 | + | 0.964958i | \(0.584515\pi\) | |||||||
\(110\) | −44.7788 | −4.26949 | ||||||||
\(111\) | −16.3346 | −1.55041 | ||||||||
\(112\) | −2.25514 | −0.213091 | ||||||||
\(113\) | −2.44436 | −0.229946 | −0.114973 | − | 0.993369i | \(-0.536678\pi\) | ||||
−0.114973 | + | 0.993369i | \(0.536678\pi\) | |||||||
\(114\) | 32.8625 | 3.07786 | ||||||||
\(115\) | 16.4888 | 1.53759 | ||||||||
\(116\) | −9.50817 | −0.882812 | ||||||||
\(117\) | 0.0355448 | 0.00328612 | ||||||||
\(118\) | −22.9068 | −2.10874 | ||||||||
\(119\) | −6.69080 | −0.613344 | ||||||||
\(120\) | 22.6186 | 2.06479 | ||||||||
\(121\) | 23.3467 | 2.12243 | ||||||||
\(122\) | −17.0296 | −1.54179 | ||||||||
\(123\) | 5.88780 | 0.530885 | ||||||||
\(124\) | −38.3566 | −3.44453 | ||||||||
\(125\) | −0.779675 | −0.0697363 | ||||||||
\(126\) | 0.0837415 | 0.00746028 | ||||||||
\(127\) | −9.36298 | −0.830830 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(128\) | 20.7397 | 1.83315 | ||||||||
\(129\) | −17.3787 | −1.53011 | ||||||||
\(130\) | 7.64064 | 0.670128 | ||||||||
\(131\) | 4.00214 | 0.349668 | 0.174834 | − | 0.984598i | \(-0.444061\pi\) | ||||
0.174834 | + | 0.984598i | \(0.444061\pi\) | |||||||
\(132\) | −37.7709 | −3.28753 | ||||||||
\(133\) | 7.79724 | 0.676107 | ||||||||
\(134\) | −0.865037 | −0.0747278 | ||||||||
\(135\) | 16.5306 | 1.42273 | ||||||||
\(136\) | −27.5003 | −2.35813 | ||||||||
\(137\) | −13.4295 | −1.14736 | −0.573682 | − | 0.819078i | \(-0.694485\pi\) | ||||
−0.573682 | + | 0.819078i | \(0.694485\pi\) | |||||||
\(138\) | 21.4282 | 1.82409 | ||||||||
\(139\) | −10.3722 | −0.879757 | −0.439879 | − | 0.898057i | \(-0.644979\pi\) | ||||
−0.439879 | + | 0.898057i | \(0.644979\pi\) | |||||||
\(140\) | 11.6838 | 0.987461 | ||||||||
\(141\) | −0.840748 | −0.0708038 | ||||||||
\(142\) | 24.3689 | 2.04499 | ||||||||
\(143\) | −5.86061 | −0.490089 | ||||||||
\(144\) | 0.0812246 | 0.00676872 | ||||||||
\(145\) | 8.22674 | 0.683193 | ||||||||
\(146\) | −8.09779 | −0.670178 | ||||||||
\(147\) | −10.4991 | −0.865953 | ||||||||
\(148\) | −34.6805 | −2.85072 | ||||||||
\(149\) | 1.33184 | 0.109108 | 0.0545542 | − | 0.998511i | \(-0.482626\pi\) | ||||
0.0545542 | + | 0.998511i | \(0.482626\pi\) | |||||||
\(150\) | −21.8098 | −1.78076 | ||||||||
\(151\) | −0.534036 | −0.0434592 | −0.0217296 | − | 0.999764i | \(-0.506917\pi\) | ||||
−0.0217296 | + | 0.999764i | \(0.506917\pi\) | |||||||
\(152\) | 32.0480 | 2.59944 | ||||||||
\(153\) | 0.240986 | 0.0194826 | ||||||||
\(154\) | −13.8073 | −1.11262 | ||||||||
\(155\) | 33.1872 | 2.66566 | ||||||||
\(156\) | 6.44487 | 0.516003 | ||||||||
\(157\) | −5.20413 | −0.415335 | −0.207667 | − | 0.978199i | \(-0.566587\pi\) | ||||
−0.207667 | + | 0.978199i | \(0.566587\pi\) | |||||||
\(158\) | −4.26702 | −0.339466 | ||||||||
\(159\) | −11.8605 | −0.940602 | ||||||||
\(160\) | −8.50451 | −0.672341 | ||||||||
\(161\) | 5.08424 | 0.400694 | ||||||||
\(162\) | 21.7371 | 1.70782 | ||||||||
\(163\) | −16.8511 | −1.31988 | −0.659942 | − | 0.751317i | \(-0.729419\pi\) | ||||
−0.659942 | + | 0.751317i | \(0.729419\pi\) | |||||||
\(164\) | 12.5006 | 0.976133 | ||||||||
\(165\) | 32.6804 | 2.54417 | ||||||||
\(166\) | 7.04105 | 0.546491 | ||||||||
\(167\) | 21.0844 | 1.63156 | 0.815782 | − | 0.578360i | \(-0.196307\pi\) | ||||
0.815782 | + | 0.578360i | \(0.196307\pi\) | |||||||
\(168\) | 6.97432 | 0.538080 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 51.8019 | 3.97302 | ||||||||
\(171\) | −0.280837 | −0.0214762 | ||||||||
\(172\) | −36.8972 | −2.81339 | ||||||||
\(173\) | −8.84818 | −0.672715 | −0.336357 | − | 0.941734i | \(-0.609195\pi\) | ||||
−0.336357 | + | 0.941734i | \(0.609195\pi\) | |||||||
\(174\) | 10.6911 | 0.810491 | ||||||||
\(175\) | −5.17478 | −0.391177 | ||||||||
\(176\) | −13.3923 | −1.00948 | ||||||||
\(177\) | 16.7178 | 1.25659 | ||||||||
\(178\) | −32.8262 | −2.46043 | ||||||||
\(179\) | −26.3370 | −1.96852 | −0.984261 | − | 0.176721i | \(-0.943451\pi\) | ||||
−0.984261 | + | 0.176721i | \(0.943451\pi\) | |||||||
\(180\) | −0.420822 | −0.0313662 | ||||||||
\(181\) | −20.7284 | −1.54073 | −0.770363 | − | 0.637605i | \(-0.779925\pi\) | ||||
−0.770363 | + | 0.637605i | \(0.779925\pi\) | |||||||
\(182\) | 2.35594 | 0.174634 | ||||||||
\(183\) | 12.4285 | 0.918743 | ||||||||
\(184\) | 20.8971 | 1.54055 | ||||||||
\(185\) | 30.0066 | 2.20613 | ||||||||
\(186\) | 43.1287 | 3.16235 | ||||||||
\(187\) | −39.7337 | −2.90561 | ||||||||
\(188\) | −1.78502 | −0.130186 | ||||||||
\(189\) | 5.09712 | 0.370761 | ||||||||
\(190\) | −60.3683 | −4.37958 | ||||||||
\(191\) | −13.1095 | −0.948573 | −0.474287 | − | 0.880370i | \(-0.657294\pi\) | ||||
−0.474287 | + | 0.880370i | \(0.657294\pi\) | |||||||
\(192\) | −19.0148 | −1.37227 | ||||||||
\(193\) | −1.47866 | −0.106436 | −0.0532182 | − | 0.998583i | \(-0.516948\pi\) | ||||
−0.0532182 | + | 0.998583i | \(0.516948\pi\) | |||||||
\(194\) | 21.8587 | 1.56936 | ||||||||
\(195\) | −5.57628 | −0.399326 | ||||||||
\(196\) | −22.2911 | −1.59222 | ||||||||
\(197\) | −5.75919 | −0.410325 | −0.205163 | − | 0.978728i | \(-0.565772\pi\) | ||||
−0.205163 | + | 0.978728i | \(0.565772\pi\) | |||||||
\(198\) | 0.497304 | 0.0353418 | ||||||||
\(199\) | −9.39868 | −0.666255 | −0.333127 | − | 0.942882i | \(-0.608104\pi\) | ||||
−0.333127 | + | 0.942882i | \(0.608104\pi\) | |||||||
\(200\) | −21.2692 | −1.50396 | ||||||||
\(201\) | 0.631320 | 0.0445299 | ||||||||
\(202\) | −16.5046 | −1.16126 | ||||||||
\(203\) | 2.53666 | 0.178039 | ||||||||
\(204\) | 43.6949 | 3.05925 | ||||||||
\(205\) | −10.8159 | −0.755413 | ||||||||
\(206\) | 24.8499 | 1.73138 | ||||||||
\(207\) | −0.183122 | −0.0127278 | ||||||||
\(208\) | 2.28513 | 0.158446 | ||||||||
\(209\) | 46.3044 | 3.20294 | ||||||||
\(210\) | −13.1374 | −0.906567 | ||||||||
\(211\) | 13.9639 | 0.961313 | 0.480657 | − | 0.876909i | \(-0.340398\pi\) | ||||
0.480657 | + | 0.876909i | \(0.340398\pi\) | |||||||
\(212\) | −25.1815 | −1.72947 | ||||||||
\(213\) | −17.7849 | −1.21860 | ||||||||
\(214\) | −17.0336 | −1.16439 | ||||||||
\(215\) | 31.9245 | 2.17723 | ||||||||
\(216\) | 20.9500 | 1.42547 | ||||||||
\(217\) | 10.2331 | 0.694667 | ||||||||
\(218\) | 13.0802 | 0.885904 | ||||||||
\(219\) | 5.90993 | 0.399356 | ||||||||
\(220\) | 69.3849 | 4.67793 | ||||||||
\(221\) | 6.77979 | 0.456058 | ||||||||
\(222\) | 38.9952 | 2.61719 | ||||||||
\(223\) | 11.1259 | 0.745048 | 0.372524 | − | 0.928022i | \(-0.378492\pi\) | ||||
0.372524 | + | 0.928022i | \(0.378492\pi\) | |||||||
\(224\) | −2.62231 | −0.175211 | ||||||||
\(225\) | 0.186383 | 0.0124255 | ||||||||
\(226\) | 5.83538 | 0.388164 | ||||||||
\(227\) | −15.1629 | −1.00640 | −0.503200 | − | 0.864170i | \(-0.667844\pi\) | ||||
−0.503200 | + | 0.864170i | \(0.667844\pi\) | |||||||
\(228\) | −50.9206 | −3.37230 | ||||||||
\(229\) | 9.39748 | 0.621003 | 0.310502 | − | 0.950573i | \(-0.399503\pi\) | ||||
0.310502 | + | 0.950573i | \(0.399503\pi\) | |||||||
\(230\) | −39.3635 | −2.59555 | ||||||||
\(231\) | 10.0768 | 0.663005 | ||||||||
\(232\) | 10.4261 | 0.684509 | ||||||||
\(233\) | −1.80719 | −0.118393 | −0.0591963 | − | 0.998246i | \(-0.518854\pi\) | ||||
−0.0591963 | + | 0.998246i | \(0.518854\pi\) | |||||||
\(234\) | −0.0848553 | −0.00554716 | ||||||||
\(235\) | 1.54445 | 0.100749 | ||||||||
\(236\) | 35.4941 | 2.31047 | ||||||||
\(237\) | 3.11415 | 0.202286 | ||||||||
\(238\) | 15.9728 | 1.03536 | ||||||||
\(239\) | −21.3107 | −1.37847 | −0.689237 | − | 0.724536i | \(-0.742054\pi\) | ||||
−0.689237 | + | 0.724536i | \(0.742054\pi\) | |||||||
\(240\) | −12.7426 | −0.822528 | ||||||||
\(241\) | −0.897215 | −0.0577947 | −0.0288973 | − | 0.999582i | \(-0.509200\pi\) | ||||
−0.0288973 | + | 0.999582i | \(0.509200\pi\) | |||||||
\(242\) | −55.7352 | −3.58279 | ||||||||
\(243\) | −0.369373 | −0.0236953 | ||||||||
\(244\) | 26.3874 | 1.68928 | ||||||||
\(245\) | 19.2868 | 1.23219 | ||||||||
\(246\) | −14.0558 | −0.896167 | ||||||||
\(247\) | −7.90095 | −0.502725 | ||||||||
\(248\) | 42.0597 | 2.67079 | ||||||||
\(249\) | −5.13869 | −0.325651 | ||||||||
\(250\) | 1.86130 | 0.117719 | ||||||||
\(251\) | 12.2572 | 0.773667 | 0.386833 | − | 0.922150i | \(-0.373569\pi\) | ||||
0.386833 | + | 0.922150i | \(0.373569\pi\) | |||||||
\(252\) | −0.129758 | −0.00817397 | ||||||||
\(253\) | 30.1930 | 1.89822 | ||||||||
\(254\) | 22.3520 | 1.40249 | ||||||||
\(255\) | −37.8060 | −2.36750 | ||||||||
\(256\) | −27.6840 | −1.73025 | ||||||||
\(257\) | −28.1192 | −1.75403 | −0.877015 | − | 0.480463i | \(-0.840469\pi\) | ||||
−0.877015 | + | 0.480463i | \(0.840469\pi\) | |||||||
\(258\) | 41.4877 | 2.58291 | ||||||||
\(259\) | 9.25234 | 0.574912 | ||||||||
\(260\) | −11.8392 | −0.734236 | ||||||||
\(261\) | −0.0913644 | −0.00565531 | ||||||||
\(262\) | −9.55421 | −0.590261 | ||||||||
\(263\) | −2.62590 | −0.161920 | −0.0809600 | − | 0.996717i | \(-0.525799\pi\) | ||||
−0.0809600 | + | 0.996717i | \(0.525799\pi\) | |||||||
\(264\) | 41.4174 | 2.54906 | ||||||||
\(265\) | 21.7878 | 1.33841 | ||||||||
\(266\) | −18.6142 | −1.14131 | ||||||||
\(267\) | 23.9572 | 1.46616 | ||||||||
\(268\) | 1.34038 | 0.0818766 | ||||||||
\(269\) | −28.2829 | −1.72444 | −0.862221 | − | 0.506533i | \(-0.830927\pi\) | ||||
−0.862221 | + | 0.506533i | \(0.830927\pi\) | |||||||
\(270\) | −39.4632 | −2.40166 | ||||||||
\(271\) | 28.1841 | 1.71206 | 0.856030 | − | 0.516926i | \(-0.172924\pi\) | ||||
0.856030 | + | 0.516926i | \(0.172924\pi\) | |||||||
\(272\) | 15.4927 | 0.939385 | ||||||||
\(273\) | −1.71941 | −0.104064 | ||||||||
\(274\) | 32.0601 | 1.93682 | ||||||||
\(275\) | −30.7307 | −1.85313 | ||||||||
\(276\) | −33.2031 | −1.99859 | ||||||||
\(277\) | 23.7606 | 1.42764 | 0.713818 | − | 0.700331i | \(-0.246964\pi\) | ||||
0.713818 | + | 0.700331i | \(0.246964\pi\) | |||||||
\(278\) | 24.7613 | 1.48508 | ||||||||
\(279\) | −0.368570 | −0.0220657 | ||||||||
\(280\) | −12.8118 | −0.765651 | ||||||||
\(281\) | 6.94305 | 0.414188 | 0.207094 | − | 0.978321i | \(-0.433599\pi\) | ||||
0.207094 | + | 0.978321i | \(0.433599\pi\) | |||||||
\(282\) | 2.00710 | 0.119521 | ||||||||
\(283\) | 2.70520 | 0.160807 | 0.0804036 | − | 0.996762i | \(-0.474379\pi\) | ||||
0.0804036 | + | 0.996762i | \(0.474379\pi\) | |||||||
\(284\) | −37.7597 | −2.24062 | ||||||||
\(285\) | 44.0579 | 2.60977 | ||||||||
\(286\) | 13.9909 | 0.827300 | ||||||||
\(287\) | −3.33501 | −0.196859 | ||||||||
\(288\) | 0.0944493 | 0.00556548 | ||||||||
\(289\) | 28.9655 | 1.70385 | ||||||||
\(290\) | −19.6395 | −1.15327 | ||||||||
\(291\) | −15.9529 | −0.935174 | ||||||||
\(292\) | 12.5476 | 0.734291 | ||||||||
\(293\) | 4.64742 | 0.271505 | 0.135753 | − | 0.990743i | \(-0.456655\pi\) | ||||
0.135753 | + | 0.990743i | \(0.456655\pi\) | |||||||
\(294\) | 25.0643 | 1.46178 | ||||||||
\(295\) | −30.7105 | −1.78803 | ||||||||
\(296\) | 38.0287 | 2.21037 | ||||||||
\(297\) | 30.2696 | 1.75642 | ||||||||
\(298\) | −3.17947 | −0.184182 | ||||||||
\(299\) | −5.15186 | −0.297940 | ||||||||
\(300\) | 33.7944 | 1.95112 | ||||||||
\(301\) | 9.84373 | 0.567383 | ||||||||
\(302\) | 1.27489 | 0.0733618 | ||||||||
\(303\) | 12.0453 | 0.691987 | ||||||||
\(304\) | −18.0547 | −1.03551 | ||||||||
\(305\) | −22.8312 | −1.30731 | ||||||||
\(306\) | −0.575301 | −0.0328878 | ||||||||
\(307\) | −7.43769 | −0.424492 | −0.212246 | − | 0.977216i | \(-0.568078\pi\) | ||||
−0.212246 | + | 0.977216i | \(0.568078\pi\) | |||||||
\(308\) | 21.3944 | 1.21906 | ||||||||
\(309\) | −18.1360 | −1.03172 | ||||||||
\(310\) | −79.2271 | −4.49980 | ||||||||
\(311\) | −29.2516 | −1.65871 | −0.829354 | − | 0.558724i | \(-0.811291\pi\) | ||||
−0.829354 | + | 0.558724i | \(0.811291\pi\) | |||||||
\(312\) | −7.06708 | −0.400095 | ||||||||
\(313\) | 22.0385 | 1.24569 | 0.622844 | − | 0.782346i | \(-0.285977\pi\) | ||||
0.622844 | + | 0.782346i | \(0.285977\pi\) | |||||||
\(314\) | 12.4237 | 0.701111 | ||||||||
\(315\) | 0.112270 | 0.00632570 | ||||||||
\(316\) | 6.61177 | 0.371941 | ||||||||
\(317\) | 19.2534 | 1.08138 | 0.540691 | − | 0.841222i | \(-0.318163\pi\) | ||||
0.540691 | + | 0.841222i | \(0.318163\pi\) | |||||||
\(318\) | 28.3144 | 1.58779 | ||||||||
\(319\) | 15.0641 | 0.843429 | ||||||||
\(320\) | 34.9301 | 1.95265 | ||||||||
\(321\) | 12.4315 | 0.693857 | ||||||||
\(322\) | −12.1375 | −0.676396 | ||||||||
\(323\) | −53.5668 | −2.98053 | ||||||||
\(324\) | −33.6817 | −1.87120 | ||||||||
\(325\) | 5.24361 | 0.290863 | ||||||||
\(326\) | 40.2284 | 2.22804 | ||||||||
\(327\) | −9.54619 | −0.527905 | ||||||||
\(328\) | −13.7075 | −0.756867 | ||||||||
\(329\) | 0.476222 | 0.0262550 | ||||||||
\(330\) | −78.0173 | −4.29471 | ||||||||
\(331\) | 1.78384 | 0.0980487 | 0.0490244 | − | 0.998798i | \(-0.484389\pi\) | ||||
0.0490244 | + | 0.998798i | \(0.484389\pi\) | |||||||
\(332\) | −10.9101 | −0.598771 | ||||||||
\(333\) | −0.333246 | −0.0182618 | ||||||||
\(334\) | −50.3345 | −2.75418 | ||||||||
\(335\) | −1.15973 | −0.0633630 | ||||||||
\(336\) | −3.92909 | −0.214349 | ||||||||
\(337\) | −12.8258 | −0.698665 | −0.349332 | − | 0.936999i | \(-0.613592\pi\) | ||||
−0.349332 | + | 0.936999i | \(0.613592\pi\) | |||||||
\(338\) | −2.38728 | −0.129851 | ||||||||
\(339\) | −4.25877 | −0.231305 | ||||||||
\(340\) | −80.2673 | −4.35310 | ||||||||
\(341\) | 60.7697 | 3.29086 | ||||||||
\(342\) | 0.670437 | 0.0362531 | ||||||||
\(343\) | 12.8551 | 0.694110 | ||||||||
\(344\) | 40.4594 | 2.18143 | ||||||||
\(345\) | 28.7282 | 1.54668 | ||||||||
\(346\) | 21.1231 | 1.13558 | ||||||||
\(347\) | −4.14197 | −0.222352 | −0.111176 | − | 0.993801i | \(-0.535462\pi\) | ||||
−0.111176 | + | 0.993801i | \(0.535462\pi\) | |||||||
\(348\) | −16.5659 | −0.888026 | ||||||||
\(349\) | −34.5192 | −1.84777 | −0.923887 | − | 0.382667i | \(-0.875006\pi\) | ||||
−0.923887 | + | 0.382667i | \(0.875006\pi\) | |||||||
\(350\) | 12.3536 | 0.660330 | ||||||||
\(351\) | −5.16492 | −0.275683 | ||||||||
\(352\) | −15.5728 | −0.830031 | ||||||||
\(353\) | 25.2462 | 1.34372 | 0.671861 | − | 0.740677i | \(-0.265495\pi\) | ||||
0.671861 | + | 0.740677i | \(0.265495\pi\) | |||||||
\(354\) | −39.9100 | −2.12119 | ||||||||
\(355\) | 32.6707 | 1.73398 | ||||||||
\(356\) | 50.8644 | 2.69581 | ||||||||
\(357\) | −11.6573 | −0.616967 | ||||||||
\(358\) | 62.8738 | 3.32299 | ||||||||
\(359\) | 30.3795 | 1.60337 | 0.801684 | − | 0.597748i | \(-0.203938\pi\) | ||||
0.801684 | + | 0.597748i | \(0.203938\pi\) | |||||||
\(360\) | 0.461449 | 0.0243205 | ||||||||
\(361\) | 43.4250 | 2.28553 | ||||||||
\(362\) | 49.4844 | 2.60084 | ||||||||
\(363\) | 40.6766 | 2.13497 | ||||||||
\(364\) | −3.65055 | −0.191341 | ||||||||
\(365\) | −10.8565 | −0.568256 | ||||||||
\(366\) | −29.6704 | −1.55089 | ||||||||
\(367\) | −34.3821 | −1.79473 | −0.897365 | − | 0.441288i | \(-0.854522\pi\) | ||||
−0.897365 | + | 0.441288i | \(0.854522\pi\) | |||||||
\(368\) | −11.7727 | −0.613694 | ||||||||
\(369\) | 0.120119 | 0.00625313 | ||||||||
\(370\) | −71.6340 | −3.72407 | ||||||||
\(371\) | 6.71812 | 0.348788 | ||||||||
\(372\) | −66.8280 | −3.46487 | ||||||||
\(373\) | 36.4825 | 1.88899 | 0.944496 | − | 0.328524i | \(-0.106551\pi\) | ||||
0.944496 | + | 0.328524i | \(0.106551\pi\) | |||||||
\(374\) | 94.8554 | 4.90485 | ||||||||
\(375\) | −1.35841 | −0.0701482 | ||||||||
\(376\) | 1.95735 | 0.100943 | ||||||||
\(377\) | −2.57040 | −0.132382 | ||||||||
\(378\) | −12.1682 | −0.625867 | ||||||||
\(379\) | 13.5357 | 0.695281 | 0.347640 | − | 0.937628i | \(-0.386983\pi\) | ||||
0.347640 | + | 0.937628i | \(0.386983\pi\) | |||||||
\(380\) | 93.5409 | 4.79855 | ||||||||
\(381\) | −16.3129 | −0.835737 | ||||||||
\(382\) | 31.2961 | 1.60125 | ||||||||
\(383\) | 3.87031 | 0.197764 | 0.0988819 | − | 0.995099i | \(-0.468473\pi\) | ||||
0.0988819 | + | 0.995099i | \(0.468473\pi\) | |||||||
\(384\) | 36.1344 | 1.84398 | ||||||||
\(385\) | −18.5110 | −0.943410 | ||||||||
\(386\) | 3.52998 | 0.179671 | ||||||||
\(387\) | −0.354547 | −0.0180226 | ||||||||
\(388\) | −33.8701 | −1.71949 | ||||||||
\(389\) | 26.4002 | 1.33854 | 0.669272 | − | 0.743018i | \(-0.266606\pi\) | ||||
0.669272 | + | 0.743018i | \(0.266606\pi\) | |||||||
\(390\) | 13.3121 | 0.674086 | ||||||||
\(391\) | −34.9285 | −1.76641 | ||||||||
\(392\) | 24.4431 | 1.23456 | ||||||||
\(393\) | 6.97285 | 0.351734 | ||||||||
\(394\) | 13.7488 | 0.692654 | ||||||||
\(395\) | −5.72069 | −0.287839 | ||||||||
\(396\) | −0.770574 | −0.0387228 | ||||||||
\(397\) | −6.43157 | −0.322791 | −0.161396 | − | 0.986890i | \(-0.551599\pi\) | ||||
−0.161396 | + | 0.986890i | \(0.551599\pi\) | |||||||
\(398\) | 22.4373 | 1.12468 | ||||||||
\(399\) | 13.5850 | 0.680100 | ||||||||
\(400\) | 11.9823 | 0.599117 | ||||||||
\(401\) | 9.14685 | 0.456772 | 0.228386 | − | 0.973571i | \(-0.426655\pi\) | ||||
0.228386 | + | 0.973571i | \(0.426655\pi\) | |||||||
\(402\) | −1.50714 | −0.0751692 | ||||||||
\(403\) | −10.3692 | −0.516526 | ||||||||
\(404\) | 25.5739 | 1.27235 | ||||||||
\(405\) | 29.1423 | 1.44809 | ||||||||
\(406\) | −6.05572 | −0.300541 | ||||||||
\(407\) | 54.9455 | 2.72355 | ||||||||
\(408\) | −47.9133 | −2.37206 | ||||||||
\(409\) | 8.95387 | 0.442741 | 0.221370 | − | 0.975190i | \(-0.428947\pi\) | ||||
0.221370 | + | 0.975190i | \(0.428947\pi\) | |||||||
\(410\) | 25.8205 | 1.27518 | ||||||||
\(411\) | −23.3980 | −1.15414 | ||||||||
\(412\) | −38.5051 | −1.89701 | ||||||||
\(413\) | −9.46940 | −0.465958 | ||||||||
\(414\) | 0.437162 | 0.0214854 | ||||||||
\(415\) | 9.43975 | 0.463379 | ||||||||
\(416\) | 2.65719 | 0.130280 | ||||||||
\(417\) | −18.0713 | −0.884954 | ||||||||
\(418\) | −110.541 | −5.40676 | ||||||||
\(419\) | 32.0552 | 1.56600 | 0.782999 | − | 0.622023i | \(-0.213689\pi\) | ||||
0.782999 | + | 0.622023i | \(0.213689\pi\) | |||||||
\(420\) | 20.3565 | 0.993294 | ||||||||
\(421\) | −34.3602 | −1.67461 | −0.837306 | − | 0.546735i | \(-0.815871\pi\) | ||||
−0.837306 | + | 0.546735i | \(0.815871\pi\) | |||||||
\(422\) | −33.3357 | −1.62276 | ||||||||
\(423\) | −0.0171523 | −0.000833975 0 | ||||||||
\(424\) | 27.6126 | 1.34099 | ||||||||
\(425\) | 35.5505 | 1.72445 | ||||||||
\(426\) | 42.4574 | 2.05707 | ||||||||
\(427\) | −7.03985 | −0.340682 | ||||||||
\(428\) | 26.3937 | 1.27579 | ||||||||
\(429\) | −10.2108 | −0.492984 | ||||||||
\(430\) | −76.2127 | −3.67530 | ||||||||
\(431\) | −31.5625 | −1.52031 | −0.760155 | − | 0.649742i | \(-0.774877\pi\) | ||||
−0.760155 | + | 0.649742i | \(0.774877\pi\) | |||||||
\(432\) | −11.8025 | −0.567849 | ||||||||
\(433\) | −22.1376 | −1.06386 | −0.531932 | − | 0.846787i | \(-0.678534\pi\) | ||||
−0.531932 | + | 0.846787i | \(0.678534\pi\) | |||||||
\(434\) | −24.4292 | −1.17264 | ||||||||
\(435\) | 14.3333 | 0.687229 | ||||||||
\(436\) | −20.2678 | −0.970654 | ||||||||
\(437\) | 40.7046 | 1.94716 | ||||||||
\(438\) | −14.1086 | −0.674137 | ||||||||
\(439\) | 23.0860 | 1.10183 | 0.550917 | − | 0.834560i | \(-0.314278\pi\) | ||||
0.550917 | + | 0.834560i | \(0.314278\pi\) | |||||||
\(440\) | −76.0836 | −3.62714 | ||||||||
\(441\) | −0.214196 | −0.0101998 | ||||||||
\(442\) | −16.1852 | −0.769853 | ||||||||
\(443\) | −14.8704 | −0.706512 | −0.353256 | − | 0.935527i | \(-0.614925\pi\) | ||||
−0.353256 | + | 0.935527i | \(0.614925\pi\) | |||||||
\(444\) | −60.4232 | −2.86756 | ||||||||
\(445\) | −44.0093 | −2.08624 | ||||||||
\(446\) | −26.5607 | −1.25769 | ||||||||
\(447\) | 2.32044 | 0.109753 | ||||||||
\(448\) | 10.7705 | 0.508857 | ||||||||
\(449\) | 6.88856 | 0.325091 | 0.162546 | − | 0.986701i | \(-0.448030\pi\) | ||||
0.162546 | + | 0.986701i | \(0.448030\pi\) | |||||||
\(450\) | −0.444948 | −0.0209750 | ||||||||
\(451\) | −19.8051 | −0.932587 | ||||||||
\(452\) | −9.04194 | −0.425297 | ||||||||
\(453\) | −0.930440 | −0.0437159 | ||||||||
\(454\) | 36.1982 | 1.69886 | ||||||||
\(455\) | 3.15855 | 0.148075 | ||||||||
\(456\) | 55.8366 | 2.61479 | ||||||||
\(457\) | 9.74140 | 0.455683 | 0.227842 | − | 0.973698i | \(-0.426833\pi\) | ||||
0.227842 | + | 0.973698i | \(0.426833\pi\) | |||||||
\(458\) | −22.4344 | −1.04829 | ||||||||
\(459\) | −35.0170 | −1.63445 | ||||||||
\(460\) | 60.9939 | 2.84385 | ||||||||
\(461\) | 33.3934 | 1.55528 | 0.777642 | − | 0.628707i | \(-0.216416\pi\) | ||||
0.777642 | + | 0.628707i | \(0.216416\pi\) | |||||||
\(462\) | −24.0561 | −1.11919 | ||||||||
\(463\) | −10.3361 | −0.480358 | −0.240179 | − | 0.970729i | \(-0.577206\pi\) | ||||
−0.240179 | + | 0.970729i | \(0.577206\pi\) | |||||||
\(464\) | −5.87372 | −0.272680 | ||||||||
\(465\) | 57.8215 | 2.68141 | ||||||||
\(466\) | 4.31426 | 0.199854 | ||||||||
\(467\) | −1.56932 | −0.0726196 | −0.0363098 | − | 0.999341i | \(-0.511560\pi\) | ||||
−0.0363098 | + | 0.999341i | \(0.511560\pi\) | |||||||
\(468\) | 0.131484 | 0.00607783 | ||||||||
\(469\) | −0.357597 | −0.0165123 | ||||||||
\(470\) | −3.68703 | −0.170070 | ||||||||
\(471\) | −9.06706 | −0.417788 | ||||||||
\(472\) | −38.9208 | −1.79148 | ||||||||
\(473\) | 58.4576 | 2.68788 | ||||||||
\(474\) | −7.43435 | −0.341471 | ||||||||
\(475\) | −41.4295 | −1.90091 | ||||||||
\(476\) | −24.7499 | −1.13441 | ||||||||
\(477\) | −0.241970 | −0.0110791 | ||||||||
\(478\) | 50.8746 | 2.32695 | ||||||||
\(479\) | −28.7903 | −1.31546 | −0.657732 | − | 0.753252i | \(-0.728484\pi\) | ||||
−0.657732 | + | 0.753252i | \(0.728484\pi\) | |||||||
\(480\) | −14.8173 | −0.676312 | ||||||||
\(481\) | −9.37540 | −0.427481 | ||||||||
\(482\) | 2.14190 | 0.0975609 | ||||||||
\(483\) | 8.85817 | 0.403061 | ||||||||
\(484\) | 86.3619 | 3.92554 | ||||||||
\(485\) | 29.3054 | 1.33069 | ||||||||
\(486\) | 0.881796 | 0.0399991 | ||||||||
\(487\) | −24.5738 | −1.11355 | −0.556774 | − | 0.830664i | \(-0.687961\pi\) | ||||
−0.556774 | + | 0.830664i | \(0.687961\pi\) | |||||||
\(488\) | −28.9350 | −1.30982 | ||||||||
\(489\) | −29.3594 | −1.32768 | ||||||||
\(490\) | −46.0431 | −2.08001 | ||||||||
\(491\) | 26.4205 | 1.19234 | 0.596171 | − | 0.802857i | \(-0.296688\pi\) | ||||
0.596171 | + | 0.802857i | \(0.296688\pi\) | |||||||
\(492\) | 21.7796 | 0.981899 | ||||||||
\(493\) | −17.4268 | −0.784863 | ||||||||
\(494\) | 18.8618 | 0.848631 | ||||||||
\(495\) | 0.666722 | 0.0299669 | ||||||||
\(496\) | −23.6950 | −1.06394 | ||||||||
\(497\) | 10.0738 | 0.451873 | ||||||||
\(498\) | 12.2675 | 0.549719 | ||||||||
\(499\) | 4.27998 | 0.191598 | 0.0957991 | − | 0.995401i | \(-0.469459\pi\) | ||||
0.0957991 | + | 0.995401i | \(0.469459\pi\) | |||||||
\(500\) | −2.88410 | −0.128981 | ||||||||
\(501\) | 36.7350 | 1.64120 | ||||||||
\(502\) | −29.2613 | −1.30600 | ||||||||
\(503\) | −35.6571 | −1.58987 | −0.794935 | − | 0.606694i | \(-0.792495\pi\) | ||||
−0.794935 | + | 0.606694i | \(0.792495\pi\) | |||||||
\(504\) | 0.142285 | 0.00633788 | ||||||||
\(505\) | −22.1272 | −0.984649 | ||||||||
\(506\) | −72.0792 | −3.20431 | ||||||||
\(507\) | 1.74228 | 0.0773774 | ||||||||
\(508\) | −34.6346 | −1.53666 | ||||||||
\(509\) | −15.6121 | −0.691995 | −0.345998 | − | 0.938235i | \(-0.612459\pi\) | ||||
−0.345998 | + | 0.938235i | \(0.612459\pi\) | |||||||
\(510\) | 90.2535 | 3.99649 | ||||||||
\(511\) | −3.34754 | −0.148086 | ||||||||
\(512\) | 24.6101 | 1.08762 | ||||||||
\(513\) | 40.8077 | 1.80171 | ||||||||
\(514\) | 67.1285 | 2.96091 | ||||||||
\(515\) | 33.3157 | 1.46806 | ||||||||
\(516\) | −64.2854 | −2.83001 | ||||||||
\(517\) | 2.82807 | 0.124378 | ||||||||
\(518\) | −22.0879 | −0.970487 | ||||||||
\(519\) | −15.4160 | −0.676688 | ||||||||
\(520\) | 12.9822 | 0.569307 | ||||||||
\(521\) | −4.12333 | −0.180647 | −0.0903233 | − | 0.995913i | \(-0.528790\pi\) | ||||
−0.0903233 | + | 0.995913i | \(0.528790\pi\) | |||||||
\(522\) | 0.218112 | 0.00954651 | ||||||||
\(523\) | −37.7161 | −1.64921 | −0.824604 | − | 0.565710i | \(-0.808602\pi\) | ||||
−0.824604 | + | 0.565710i | \(0.808602\pi\) | |||||||
\(524\) | 14.8043 | 0.646729 | ||||||||
\(525\) | −9.01592 | −0.393487 | ||||||||
\(526\) | 6.26876 | 0.273331 | ||||||||
\(527\) | −70.3008 | −3.06235 | ||||||||
\(528\) | −23.3331 | −1.01544 | ||||||||
\(529\) | 3.54164 | 0.153984 | ||||||||
\(530\) | −52.0135 | −2.25932 | ||||||||
\(531\) | 0.341064 | 0.0148009 | ||||||||
\(532\) | 28.8428 | 1.25049 | ||||||||
\(533\) | 3.37936 | 0.146377 | ||||||||
\(534\) | −57.1926 | −2.47496 | ||||||||
\(535\) | −22.8365 | −0.987310 | ||||||||
\(536\) | −1.46978 | −0.0634850 | ||||||||
\(537\) | −45.8865 | −1.98015 | ||||||||
\(538\) | 67.5193 | 2.91096 | ||||||||
\(539\) | 35.3165 | 1.52119 | ||||||||
\(540\) | 61.1485 | 2.63141 | ||||||||
\(541\) | 5.49342 | 0.236181 | 0.118090 | − | 0.993003i | \(-0.462323\pi\) | ||||
0.118090 | + | 0.993003i | \(0.462323\pi\) | |||||||
\(542\) | −67.2832 | −2.89006 | ||||||||
\(543\) | −36.1146 | −1.54983 | ||||||||
\(544\) | 18.0152 | 0.772395 | ||||||||
\(545\) | 17.5363 | 0.751173 | ||||||||
\(546\) | 4.10472 | 0.175666 | ||||||||
\(547\) | 7.34043 | 0.313854 | 0.156927 | − | 0.987610i | \(-0.449841\pi\) | ||||
0.156927 | + | 0.987610i | \(0.449841\pi\) | |||||||
\(548\) | −49.6772 | −2.12211 | ||||||||
\(549\) | 0.253558 | 0.0108216 | ||||||||
\(550\) | 73.3628 | 3.12820 | ||||||||
\(551\) | 20.3086 | 0.865176 | ||||||||
\(552\) | 36.4086 | 1.54965 | ||||||||
\(553\) | −1.76394 | −0.0750103 | ||||||||
\(554\) | −56.7232 | −2.40994 | ||||||||
\(555\) | 52.2799 | 2.21916 | ||||||||
\(556\) | −38.3677 | −1.62715 | ||||||||
\(557\) | 29.5059 | 1.25021 | 0.625103 | − | 0.780543i | \(-0.285057\pi\) | ||||
0.625103 | + | 0.780543i | \(0.285057\pi\) | |||||||
\(558\) | 0.879880 | 0.0372483 | ||||||||
\(559\) | −9.97466 | −0.421883 | ||||||||
\(560\) | 7.21772 | 0.305004 | ||||||||
\(561\) | −69.2273 | −2.92278 | ||||||||
\(562\) | −16.5750 | −0.699174 | ||||||||
\(563\) | 0.0881931 | 0.00371690 | 0.00185845 | − | 0.999998i | \(-0.499408\pi\) | ||||
0.00185845 | + | 0.999998i | \(0.499408\pi\) | |||||||
\(564\) | −3.11001 | −0.130955 | ||||||||
\(565\) | 7.82334 | 0.329130 | ||||||||
\(566\) | −6.45806 | −0.271452 | ||||||||
\(567\) | 8.98586 | 0.377370 | ||||||||
\(568\) | 41.4051 | 1.73732 | ||||||||
\(569\) | 23.1666 | 0.971193 | 0.485597 | − | 0.874183i | \(-0.338602\pi\) | ||||
0.485597 | + | 0.874183i | \(0.338602\pi\) | |||||||
\(570\) | −105.179 | −4.40544 | ||||||||
\(571\) | 18.3964 | 0.769867 | 0.384934 | − | 0.922944i | \(-0.374224\pi\) | ||||
0.384934 | + | 0.922944i | \(0.374224\pi\) | |||||||
\(572\) | −21.6790 | −0.906443 | ||||||||
\(573\) | −22.8405 | −0.954176 | ||||||||
\(574\) | 7.96159 | 0.332310 | ||||||||
\(575\) | −27.0143 | −1.12657 | ||||||||
\(576\) | −0.387926 | −0.0161636 | ||||||||
\(577\) | −19.6062 | −0.816215 | −0.408108 | − | 0.912934i | \(-0.633811\pi\) | ||||
−0.408108 | + | 0.912934i | \(0.633811\pi\) | |||||||
\(578\) | −69.1488 | −2.87621 | ||||||||
\(579\) | −2.57625 | −0.107065 | ||||||||
\(580\) | 30.4315 | 1.26360 | ||||||||
\(581\) | 2.91069 | 0.120756 | ||||||||
\(582\) | 38.0839 | 1.57863 | ||||||||
\(583\) | 39.8960 | 1.65232 | ||||||||
\(584\) | −13.7590 | −0.569350 | ||||||||
\(585\) | −0.113763 | −0.00470353 | ||||||||
\(586\) | −11.0947 | −0.458317 | ||||||||
\(587\) | −26.6217 | −1.09879 | −0.549397 | − | 0.835561i | \(-0.685143\pi\) | ||||
−0.549397 | + | 0.835561i | \(0.685143\pi\) | |||||||
\(588\) | −38.8373 | −1.60162 | ||||||||
\(589\) | 81.9264 | 3.37572 | ||||||||
\(590\) | 73.3145 | 3.01831 | ||||||||
\(591\) | −10.0341 | −0.412749 | ||||||||
\(592\) | −21.4240 | −0.880523 | ||||||||
\(593\) | −16.7625 | −0.688353 | −0.344176 | − | 0.938905i | \(-0.611842\pi\) | ||||
−0.344176 | + | 0.938905i | \(0.611842\pi\) | |||||||
\(594\) | −72.2619 | −2.96494 | ||||||||
\(595\) | 21.4143 | 0.877901 | ||||||||
\(596\) | 4.92660 | 0.201801 | ||||||||
\(597\) | −16.3752 | −0.670190 | ||||||||
\(598\) | 12.2989 | 0.502940 | ||||||||
\(599\) | 15.3183 | 0.625889 | 0.312945 | − | 0.949771i | \(-0.398685\pi\) | ||||
0.312945 | + | 0.949771i | \(0.398685\pi\) | |||||||
\(600\) | −37.0570 | −1.51285 | ||||||||
\(601\) | −40.1710 | −1.63861 | −0.819304 | − | 0.573360i | \(-0.805640\pi\) | ||||
−0.819304 | + | 0.573360i | \(0.805640\pi\) | |||||||
\(602\) | −23.4997 | −0.957777 | ||||||||
\(603\) | 0.0128797 | 0.000524504 0 | ||||||||
\(604\) | −1.97545 | −0.0803799 | ||||||||
\(605\) | −74.7227 | −3.03791 | ||||||||
\(606\) | −28.7556 | −1.16812 | ||||||||
\(607\) | −36.4367 | −1.47892 | −0.739461 | − | 0.673199i | \(-0.764920\pi\) | ||||
−0.739461 | + | 0.673199i | \(0.764920\pi\) | |||||||
\(608\) | −20.9943 | −0.851433 | ||||||||
\(609\) | 4.41958 | 0.179091 | ||||||||
\(610\) | 54.5043 | 2.20682 | ||||||||
\(611\) | −0.482556 | −0.0195221 | ||||||||
\(612\) | 0.891431 | 0.0360340 | ||||||||
\(613\) | 23.1716 | 0.935894 | 0.467947 | − | 0.883757i | \(-0.344994\pi\) | ||||
0.467947 | + | 0.883757i | \(0.344994\pi\) | |||||||
\(614\) | 17.7558 | 0.716568 | ||||||||
\(615\) | −18.8443 | −0.759875 | ||||||||
\(616\) | −23.4599 | −0.945227 | ||||||||
\(617\) | 21.0966 | 0.849317 | 0.424659 | − | 0.905354i | \(-0.360394\pi\) | ||||
0.424659 | + | 0.905354i | \(0.360394\pi\) | |||||||
\(618\) | 43.2956 | 1.74160 | ||||||||
\(619\) | −1.00000 | −0.0401934 | ||||||||
\(620\) | 122.763 | 4.93027 | ||||||||
\(621\) | 26.6089 | 1.06778 | ||||||||
\(622\) | 69.8318 | 2.80000 | ||||||||
\(623\) | −13.5700 | −0.543671 | ||||||||
\(624\) | 3.98135 | 0.159381 | ||||||||
\(625\) | −23.7226 | −0.948905 | ||||||||
\(626\) | −52.6120 | −2.10280 | ||||||||
\(627\) | 80.6753 | 3.22186 | ||||||||
\(628\) | −19.2506 | −0.768182 | ||||||||
\(629\) | −63.5632 | −2.53443 | ||||||||
\(630\) | −0.268020 | −0.0106782 | ||||||||
\(631\) | 8.58974 | 0.341952 | 0.170976 | − | 0.985275i | \(-0.445308\pi\) | ||||
0.170976 | + | 0.985275i | \(0.445308\pi\) | |||||||
\(632\) | −7.25009 | −0.288393 | ||||||||
\(633\) | 24.3290 | 0.966991 | ||||||||
\(634\) | −45.9633 | −1.82544 | ||||||||
\(635\) | 29.9668 | 1.18920 | ||||||||
\(636\) | −43.8733 | −1.73969 | ||||||||
\(637\) | −6.02608 | −0.238762 | ||||||||
\(638\) | −35.9623 | −1.42376 | ||||||||
\(639\) | −0.362834 | −0.0143535 | ||||||||
\(640\) | −66.3788 | −2.62385 | ||||||||
\(641\) | 21.6920 | 0.856782 | 0.428391 | − | 0.903593i | \(-0.359081\pi\) | ||||
0.428391 | + | 0.903593i | \(0.359081\pi\) | |||||||
\(642\) | −29.6774 | −1.17127 | ||||||||
\(643\) | 17.5591 | 0.692462 | 0.346231 | − | 0.938149i | \(-0.387461\pi\) | ||||
0.346231 | + | 0.938149i | \(0.387461\pi\) | |||||||
\(644\) | 18.8071 | 0.741103 | ||||||||
\(645\) | 55.6215 | 2.19009 | ||||||||
\(646\) | 127.879 | 5.03132 | ||||||||
\(647\) | −3.92753 | −0.154407 | −0.0772036 | − | 0.997015i | \(-0.524599\pi\) | ||||
−0.0772036 | + | 0.997015i | \(0.524599\pi\) | |||||||
\(648\) | 36.9334 | 1.45088 | ||||||||
\(649\) | −56.2346 | −2.20740 | ||||||||
\(650\) | −12.5179 | −0.490994 | ||||||||
\(651\) | 17.8289 | 0.698770 | ||||||||
\(652\) | −62.3340 | −2.44119 | ||||||||
\(653\) | 40.3900 | 1.58058 | 0.790291 | − | 0.612732i | \(-0.209929\pi\) | ||||
0.790291 | + | 0.612732i | \(0.209929\pi\) | |||||||
\(654\) | 22.7894 | 0.891137 | ||||||||
\(655\) | −12.8091 | −0.500493 | ||||||||
\(656\) | 7.72230 | 0.301505 | ||||||||
\(657\) | 0.120570 | 0.00470389 | ||||||||
\(658\) | −1.13687 | −0.0443200 | ||||||||
\(659\) | −49.9401 | −1.94539 | −0.972695 | − | 0.232087i | \(-0.925444\pi\) | ||||
−0.972695 | + | 0.232087i | \(0.925444\pi\) | |||||||
\(660\) | 120.888 | 4.70556 | ||||||||
\(661\) | −50.8176 | −1.97658 | −0.988288 | − | 0.152599i | \(-0.951236\pi\) | ||||
−0.988288 | + | 0.152599i | \(0.951236\pi\) | |||||||
\(662\) | −4.25852 | −0.165512 | ||||||||
\(663\) | 11.8123 | 0.458752 | ||||||||
\(664\) | 11.9634 | 0.464271 | ||||||||
\(665\) | −24.9556 | −0.967735 | ||||||||
\(666\) | 0.795552 | 0.0308270 | ||||||||
\(667\) | 13.2424 | 0.512746 | ||||||||
\(668\) | 77.9935 | 3.01766 | ||||||||
\(669\) | 19.3845 | 0.749449 | ||||||||
\(670\) | 2.76861 | 0.106961 | ||||||||
\(671\) | −41.8065 | −1.61392 | ||||||||
\(672\) | −4.56881 | −0.176246 | ||||||||
\(673\) | 31.9860 | 1.23297 | 0.616485 | − | 0.787367i | \(-0.288556\pi\) | ||||
0.616485 | + | 0.787367i | \(0.288556\pi\) | |||||||
\(674\) | 30.6187 | 1.17939 | ||||||||
\(675\) | −27.0828 | −1.04242 | ||||||||
\(676\) | 3.69910 | 0.142273 | ||||||||
\(677\) | 2.49332 | 0.0958262 | 0.0479131 | − | 0.998852i | \(-0.484743\pi\) | ||||
0.0479131 | + | 0.998852i | \(0.484743\pi\) | |||||||
\(678\) | 10.1669 | 0.390456 | ||||||||
\(679\) | 9.03613 | 0.346775 | ||||||||
\(680\) | 88.0165 | 3.37528 | ||||||||
\(681\) | −26.4181 | −1.01234 | ||||||||
\(682\) | −145.074 | −5.55518 | ||||||||
\(683\) | 7.23096 | 0.276685 | 0.138342 | − | 0.990384i | \(-0.455823\pi\) | ||||
0.138342 | + | 0.990384i | \(0.455823\pi\) | |||||||
\(684\) | −1.03885 | −0.0397213 | ||||||||
\(685\) | 42.9821 | 1.64226 | ||||||||
\(686\) | −30.6887 | −1.17170 | ||||||||
\(687\) | 16.3731 | 0.624671 | ||||||||
\(688\) | −22.7934 | −0.868991 | ||||||||
\(689\) | −6.80748 | −0.259344 | ||||||||
\(690\) | −68.5823 | −2.61088 | ||||||||
\(691\) | −18.3608 | −0.698477 | −0.349238 | − | 0.937034i | \(-0.613560\pi\) | ||||
−0.349238 | + | 0.937034i | \(0.613560\pi\) | |||||||
\(692\) | −32.7303 | −1.24422 | ||||||||
\(693\) | 0.205580 | 0.00780933 | ||||||||
\(694\) | 9.88803 | 0.375344 | ||||||||
\(695\) | 33.1968 | 1.25923 | ||||||||
\(696\) | 18.1652 | 0.688552 | ||||||||
\(697\) | 22.9114 | 0.867830 | ||||||||
\(698\) | 82.4071 | 3.11915 | ||||||||
\(699\) | −3.14863 | −0.119092 | ||||||||
\(700\) | −19.1420 | −0.723500 | ||||||||
\(701\) | −42.7262 | −1.61375 | −0.806873 | − | 0.590725i | \(-0.798842\pi\) | ||||
−0.806873 | + | 0.590725i | \(0.798842\pi\) | |||||||
\(702\) | 12.3301 | 0.465369 | ||||||||
\(703\) | 74.0745 | 2.79377 | ||||||||
\(704\) | 63.9611 | 2.41062 | ||||||||
\(705\) | 2.69087 | 0.101344 | ||||||||
\(706\) | −60.2698 | −2.26828 | ||||||||
\(707\) | −6.82280 | −0.256598 | ||||||||
\(708\) | 61.8407 | 2.32412 | ||||||||
\(709\) | −15.8188 | −0.594087 | −0.297044 | − | 0.954864i | \(-0.596001\pi\) | ||||
−0.297044 | + | 0.954864i | \(0.596001\pi\) | |||||||
\(710\) | −77.9941 | −2.92707 | ||||||||
\(711\) | 0.0635327 | 0.00238266 | ||||||||
\(712\) | −55.7750 | −2.09026 | ||||||||
\(713\) | 53.4206 | 2.00062 | ||||||||
\(714\) | 27.8291 | 1.04148 | ||||||||
\(715\) | 18.7573 | 0.701481 | ||||||||
\(716\) | −97.4233 | −3.64088 | ||||||||
\(717\) | −37.1292 | −1.38662 | ||||||||
\(718\) | −72.5243 | −2.70658 | ||||||||
\(719\) | 20.6869 | 0.771490 | 0.385745 | − | 0.922605i | \(-0.373944\pi\) | ||||
0.385745 | + | 0.922605i | \(0.373944\pi\) | |||||||
\(720\) | −0.259964 | −0.00968830 | ||||||||
\(721\) | 10.2727 | 0.382575 | ||||||||
\(722\) | −103.668 | −3.85811 | ||||||||
\(723\) | −1.56320 | −0.0581360 | ||||||||
\(724\) | −76.6762 | −2.84965 | ||||||||
\(725\) | −13.4782 | −0.500567 | ||||||||
\(726\) | −97.1064 | −3.60396 | ||||||||
\(727\) | 25.0977 | 0.930822 | 0.465411 | − | 0.885095i | \(-0.345906\pi\) | ||||
0.465411 | + | 0.885095i | \(0.345906\pi\) | |||||||
\(728\) | 4.00298 | 0.148360 | ||||||||
\(729\) | 26.6726 | 0.987873 | ||||||||
\(730\) | 25.9175 | 0.959250 | ||||||||
\(731\) | −67.6260 | −2.50124 | ||||||||
\(732\) | 45.9744 | 1.69926 | ||||||||
\(733\) | 19.4550 | 0.718587 | 0.359293 | − | 0.933225i | \(-0.383018\pi\) | ||||
0.359293 | + | 0.933225i | \(0.383018\pi\) | |||||||
\(734\) | 82.0796 | 3.02962 | ||||||||
\(735\) | 33.6031 | 1.23947 | ||||||||
\(736\) | −13.6895 | −0.504601 | ||||||||
\(737\) | −2.12361 | −0.0782241 | ||||||||
\(738\) | −0.286757 | −0.0105557 | ||||||||
\(739\) | −13.9101 | −0.511692 | −0.255846 | − | 0.966717i | \(-0.582354\pi\) | ||||
−0.255846 | + | 0.966717i | \(0.582354\pi\) | |||||||
\(740\) | 110.997 | 4.08034 | ||||||||
\(741\) | −13.7657 | −0.505695 | ||||||||
\(742\) | −16.0380 | −0.588775 | ||||||||
\(743\) | −24.2200 | −0.888545 | −0.444272 | − | 0.895892i | \(-0.646538\pi\) | ||||
−0.444272 | + | 0.895892i | \(0.646538\pi\) | |||||||
\(744\) | 73.2798 | 2.68657 | ||||||||
\(745\) | −4.26263 | −0.156171 | ||||||||
\(746\) | −87.0939 | −3.18873 | ||||||||
\(747\) | −0.104836 | −0.00383574 | ||||||||
\(748\) | −146.979 | −5.37408 | ||||||||
\(749\) | −7.04151 | −0.257291 | ||||||||
\(750\) | 3.24291 | 0.118414 | ||||||||
\(751\) | 26.2924 | 0.959422 | 0.479711 | − | 0.877427i | \(-0.340742\pi\) | ||||
0.479711 | + | 0.877427i | \(0.340742\pi\) | |||||||
\(752\) | −1.10271 | −0.0402115 | ||||||||
\(753\) | 21.3555 | 0.778237 | ||||||||
\(754\) | 6.13627 | 0.223470 | ||||||||
\(755\) | 1.70921 | 0.0622047 | ||||||||
\(756\) | 18.8548 | 0.685741 | ||||||||
\(757\) | −16.2700 | −0.591342 | −0.295671 | − | 0.955290i | \(-0.595543\pi\) | ||||
−0.295671 | + | 0.955290i | \(0.595543\pi\) | |||||||
\(758\) | −32.3134 | −1.17368 | ||||||||
\(759\) | 52.6048 | 1.90943 | ||||||||
\(760\) | −102.572 | −3.72067 | ||||||||
\(761\) | −8.05102 | −0.291849 | −0.145925 | − | 0.989296i | \(-0.546616\pi\) | ||||
−0.145925 | + | 0.989296i | \(0.546616\pi\) | |||||||
\(762\) | 38.9435 | 1.41078 | ||||||||
\(763\) | 5.40721 | 0.195754 | ||||||||
\(764\) | −48.4935 | −1.75443 | ||||||||
\(765\) | −0.771291 | −0.0278861 | ||||||||
\(766\) | −9.23952 | −0.333837 | ||||||||
\(767\) | 9.59534 | 0.346468 | ||||||||
\(768\) | −48.2334 | −1.74047 | ||||||||
\(769\) | 23.9975 | 0.865371 | 0.432686 | − | 0.901545i | \(-0.357566\pi\) | ||||
0.432686 | + | 0.901545i | \(0.357566\pi\) | |||||||
\(770\) | 44.1910 | 1.59253 | ||||||||
\(771\) | −48.9916 | −1.76439 | ||||||||
\(772\) | −5.46972 | −0.196860 | ||||||||
\(773\) | −11.9882 | −0.431184 | −0.215592 | − | 0.976483i | \(-0.569168\pi\) | ||||
−0.215592 | + | 0.976483i | \(0.569168\pi\) | |||||||
\(774\) | 0.846402 | 0.0304233 | ||||||||
\(775\) | −54.3719 | −1.95310 | ||||||||
\(776\) | 37.1400 | 1.33325 | ||||||||
\(777\) | 16.1202 | 0.578308 | ||||||||
\(778\) | −63.0246 | −2.25954 | ||||||||
\(779\) | −26.7002 | −0.956633 | ||||||||
\(780\) | −20.6272 | −0.738573 | ||||||||
\(781\) | 59.8240 | 2.14067 | ||||||||
\(782\) | 83.3841 | 2.98181 | ||||||||
\(783\) | 13.2759 | 0.474442 | ||||||||
\(784\) | −13.7704 | −0.491800 | ||||||||
\(785\) | 16.6562 | 0.594484 | ||||||||
\(786\) | −16.6461 | −0.593748 | ||||||||
\(787\) | 15.5633 | 0.554773 | 0.277387 | − | 0.960758i | \(-0.410532\pi\) | ||||
0.277387 | + | 0.960758i | \(0.410532\pi\) | |||||||
\(788\) | −21.3038 | −0.758917 | ||||||||
\(789\) | −4.57506 | −0.162876 | ||||||||
\(790\) | 13.6569 | 0.485890 | ||||||||
\(791\) | 2.41228 | 0.0857708 | ||||||||
\(792\) | 0.844968 | 0.0300246 | ||||||||
\(793\) | 7.13348 | 0.253317 | ||||||||
\(794\) | 15.3539 | 0.544891 | ||||||||
\(795\) | 37.9604 | 1.34632 | ||||||||
\(796\) | −34.7667 | −1.23227 | ||||||||
\(797\) | −47.2689 | −1.67435 | −0.837174 | − | 0.546936i | \(-0.815794\pi\) | ||||
−0.837174 | + | 0.546936i | \(0.815794\pi\) | |||||||
\(798\) | −32.4312 | −1.14805 | ||||||||
\(799\) | −3.27163 | −0.115742 | ||||||||
\(800\) | 13.9333 | 0.492615 | ||||||||
\(801\) | 0.488758 | 0.0172694 | ||||||||
\(802\) | −21.8361 | −0.771058 | ||||||||
\(803\) | −19.8795 | −0.701534 | ||||||||
\(804\) | 2.33532 | 0.0823603 | ||||||||
\(805\) | −16.2724 | −0.573527 | ||||||||
\(806\) | 24.7541 | 0.871927 | ||||||||
\(807\) | −49.2768 | −1.73463 | ||||||||
\(808\) | −28.0429 | −0.986545 | ||||||||
\(809\) | 47.1752 | 1.65859 | 0.829296 | − | 0.558810i | \(-0.188742\pi\) | ||||
0.829296 | + | 0.558810i | \(0.188742\pi\) | |||||||
\(810\) | −69.5708 | −2.44447 | ||||||||
\(811\) | 37.9727 | 1.33340 | 0.666700 | − | 0.745326i | \(-0.267706\pi\) | ||||
0.666700 | + | 0.745326i | \(0.267706\pi\) | |||||||
\(812\) | 9.38337 | 0.329292 | ||||||||
\(813\) | 49.1046 | 1.72217 | ||||||||
\(814\) | −131.170 | −4.59752 | ||||||||
\(815\) | 53.9331 | 1.88920 | ||||||||
\(816\) | 26.9927 | 0.944933 | ||||||||
\(817\) | 78.8092 | 2.75719 | ||||||||
\(818\) | −21.3754 | −0.747373 | ||||||||
\(819\) | −0.0350782 | −0.00122573 | ||||||||
\(820\) | −40.0090 | −1.39717 | ||||||||
\(821\) | −5.77991 | −0.201720 | −0.100860 | − | 0.994901i | \(-0.532159\pi\) | ||||
−0.100860 | + | 0.994901i | \(0.532159\pi\) | |||||||
\(822\) | 55.8577 | 1.94826 | ||||||||
\(823\) | 43.6664 | 1.52212 | 0.761058 | − | 0.648684i | \(-0.224680\pi\) | ||||
0.761058 | + | 0.648684i | \(0.224680\pi\) | |||||||
\(824\) | 42.2225 | 1.47089 | ||||||||
\(825\) | −53.5416 | −1.86408 | ||||||||
\(826\) | 22.6061 | 0.786566 | ||||||||
\(827\) | −44.4992 | −1.54739 | −0.773695 | − | 0.633559i | \(-0.781594\pi\) | ||||
−0.773695 | + | 0.633559i | \(0.781594\pi\) | |||||||
\(828\) | −0.677385 | −0.0235408 | ||||||||
\(829\) | 43.0497 | 1.49518 | 0.747588 | − | 0.664163i | \(-0.231212\pi\) | ||||
0.747588 | + | 0.664163i | \(0.231212\pi\) | |||||||
\(830\) | −22.5353 | −0.782212 | ||||||||
\(831\) | 41.3977 | 1.43607 | ||||||||
\(832\) | −10.9137 | −0.378365 | ||||||||
\(833\) | −40.8555 | −1.41556 | ||||||||
\(834\) | 43.1411 | 1.49386 | ||||||||
\(835\) | −67.4821 | −2.33531 | ||||||||
\(836\) | 171.284 | 5.92400 | ||||||||
\(837\) | 53.5559 | 1.85116 | ||||||||
\(838\) | −76.5246 | −2.64350 | ||||||||
\(839\) | −40.6136 | −1.40214 | −0.701069 | − | 0.713093i | \(-0.747294\pi\) | ||||
−0.701069 | + | 0.713093i | \(0.747294\pi\) | |||||||
\(840\) | −22.3218 | −0.770174 | ||||||||
\(841\) | −22.3930 | −0.772173 | ||||||||
\(842\) | 82.0273 | 2.82685 | ||||||||
\(843\) | 12.0968 | 0.416634 | ||||||||
\(844\) | 51.6538 | 1.77800 | ||||||||
\(845\) | −3.20056 | −0.110103 | ||||||||
\(846\) | 0.0409474 | 0.00140780 | ||||||||
\(847\) | −23.0403 | −0.791674 | ||||||||
\(848\) | −15.5560 | −0.534195 | ||||||||
\(849\) | 4.71321 | 0.161757 | ||||||||
\(850\) | −84.8690 | −2.91098 | ||||||||
\(851\) | 48.3007 | 1.65573 | ||||||||
\(852\) | −65.7880 | −2.25386 | ||||||||
\(853\) | −3.80426 | −0.130255 | −0.0651277 | − | 0.997877i | \(-0.520745\pi\) | ||||
−0.0651277 | + | 0.997877i | \(0.520745\pi\) | |||||||
\(854\) | 16.8061 | 0.575092 | ||||||||
\(855\) | 0.898838 | 0.0307396 | ||||||||
\(856\) | −28.9418 | −0.989211 | ||||||||
\(857\) | 33.3951 | 1.14075 | 0.570377 | − | 0.821383i | \(-0.306797\pi\) | ||||
0.570377 | + | 0.821383i | \(0.306797\pi\) | |||||||
\(858\) | 24.3761 | 0.832186 | ||||||||
\(859\) | 18.1438 | 0.619057 | 0.309529 | − | 0.950890i | \(-0.399829\pi\) | ||||
0.309529 | + | 0.950890i | \(0.399829\pi\) | |||||||
\(860\) | 118.092 | 4.02690 | ||||||||
\(861\) | −5.81052 | −0.198022 | ||||||||
\(862\) | 75.3484 | 2.56638 | ||||||||
\(863\) | −10.9303 | −0.372072 | −0.186036 | − | 0.982543i | \(-0.559564\pi\) | ||||
−0.186036 | + | 0.982543i | \(0.559564\pi\) | |||||||
\(864\) | −13.7242 | −0.466906 | ||||||||
\(865\) | 28.3192 | 0.962880 | ||||||||
\(866\) | 52.8485 | 1.79587 | ||||||||
\(867\) | 50.4661 | 1.71392 | ||||||||
\(868\) | 37.8532 | 1.28482 | ||||||||
\(869\) | −10.4753 | −0.355349 | ||||||||
\(870\) | −34.2176 | −1.16008 | ||||||||
\(871\) | 0.362353 | 0.0122779 | ||||||||
\(872\) | 22.2246 | 0.752619 | ||||||||
\(873\) | −0.325459 | −0.0110151 | ||||||||
\(874\) | −97.1731 | −3.28693 | ||||||||
\(875\) | 0.769442 | 0.0260119 | ||||||||
\(876\) | 21.8614 | 0.738628 | ||||||||
\(877\) | 5.12585 | 0.173088 | 0.0865439 | − | 0.996248i | \(-0.472418\pi\) | ||||
0.0865439 | + | 0.996248i | \(0.472418\pi\) | |||||||
\(878\) | −55.1127 | −1.85996 | ||||||||
\(879\) | 8.09711 | 0.273109 | ||||||||
\(880\) | 42.8628 | 1.44491 | ||||||||
\(881\) | 12.9170 | 0.435185 | 0.217592 | − | 0.976040i | \(-0.430180\pi\) | ||||
0.217592 | + | 0.976040i | \(0.430180\pi\) | |||||||
\(882\) | 0.511345 | 0.0172179 | ||||||||
\(883\) | −48.7337 | −1.64002 | −0.820009 | − | 0.572350i | \(-0.806032\pi\) | ||||
−0.820009 | + | 0.572350i | \(0.806032\pi\) | |||||||
\(884\) | 25.0791 | 0.843502 | ||||||||
\(885\) | −53.5063 | −1.79860 | ||||||||
\(886\) | 35.4997 | 1.19263 | ||||||||
\(887\) | 47.3372 | 1.58943 | 0.794714 | − | 0.606983i | \(-0.207621\pi\) | ||||
0.794714 | + | 0.606983i | \(0.207621\pi\) | |||||||
\(888\) | 66.2567 | 2.22343 | ||||||||
\(889\) | 9.24008 | 0.309902 | ||||||||
\(890\) | 105.062 | 3.52170 | ||||||||
\(891\) | 53.3630 | 1.78773 | ||||||||
\(892\) | 41.1560 | 1.37800 | ||||||||
\(893\) | 3.81265 | 0.127585 | ||||||||
\(894\) | −5.53953 | −0.185269 | ||||||||
\(895\) | 84.2933 | 2.81762 | ||||||||
\(896\) | −20.4675 | −0.683771 | ||||||||
\(897\) | −8.97599 | −0.299699 | ||||||||
\(898\) | −16.4449 | −0.548774 | ||||||||
\(899\) | 26.6530 | 0.888926 | ||||||||
\(900\) | 0.689448 | 0.0229816 | ||||||||
\(901\) | −46.1533 | −1.53759 | ||||||||
\(902\) | 47.2804 | 1.57426 | ||||||||
\(903\) | 17.1505 | 0.570734 | ||||||||
\(904\) | 9.91488 | 0.329764 | ||||||||
\(905\) | 66.3424 | 2.20530 | ||||||||
\(906\) | 2.22122 | 0.0737951 | ||||||||
\(907\) | 34.3721 | 1.14131 | 0.570653 | − | 0.821191i | \(-0.306690\pi\) | ||||
0.570653 | + | 0.821191i | \(0.306690\pi\) | |||||||
\(908\) | −56.0892 | −1.86139 | ||||||||
\(909\) | 0.245740 | 0.00815070 | ||||||||
\(910\) | −7.54035 | −0.249960 | ||||||||
\(911\) | −9.54372 | −0.316198 | −0.158099 | − | 0.987423i | \(-0.550536\pi\) | ||||
−0.158099 | + | 0.987423i | \(0.550536\pi\) | |||||||
\(912\) | −31.4564 | −1.04163 | ||||||||
\(913\) | 17.2853 | 0.572060 | ||||||||
\(914\) | −23.2554 | −0.769221 | ||||||||
\(915\) | −39.7783 | −1.31503 | ||||||||
\(916\) | 34.7622 | 1.14858 | ||||||||
\(917\) | −3.94960 | −0.130427 | ||||||||
\(918\) | 83.5954 | 2.75906 | ||||||||
\(919\) | 15.2581 | 0.503319 | 0.251660 | − | 0.967816i | \(-0.419024\pi\) | ||||
0.251660 | + | 0.967816i | \(0.419024\pi\) | |||||||
\(920\) | −66.8824 | −2.20505 | ||||||||
\(921\) | −12.9586 | −0.426999 | ||||||||
\(922\) | −79.7193 | −2.62541 | ||||||||
\(923\) | −10.2078 | −0.335994 | ||||||||
\(924\) | 37.2751 | 1.22626 | ||||||||
\(925\) | −49.1609 | −1.61640 | ||||||||
\(926\) | 24.6751 | 0.810873 | ||||||||
\(927\) | −0.369997 | −0.0121523 | ||||||||
\(928\) | −6.83005 | −0.224207 | ||||||||
\(929\) | −35.2448 | −1.15635 | −0.578173 | − | 0.815914i | \(-0.696234\pi\) | ||||
−0.578173 | + | 0.815914i | \(0.696234\pi\) | |||||||
\(930\) | −138.036 | −4.52638 | ||||||||
\(931\) | 47.6117 | 1.56041 | ||||||||
\(932\) | −6.68496 | −0.218973 | ||||||||
\(933\) | −50.9646 | −1.66850 | ||||||||
\(934\) | 3.74641 | 0.122586 | ||||||||
\(935\) | 127.170 | 4.15891 | ||||||||
\(936\) | −0.144178 | −0.00471259 | ||||||||
\(937\) | −15.2078 | −0.496817 | −0.248408 | − | 0.968655i | \(-0.579907\pi\) | ||||
−0.248408 | + | 0.968655i | \(0.579907\pi\) | |||||||
\(938\) | 0.853683 | 0.0278737 | ||||||||
\(939\) | 38.3972 | 1.25305 | ||||||||
\(940\) | 5.71308 | 0.186340 | ||||||||
\(941\) | −36.1377 | −1.17806 | −0.589028 | − | 0.808113i | \(-0.700489\pi\) | ||||
−0.589028 | + | 0.808113i | \(0.700489\pi\) | |||||||
\(942\) | 21.6456 | 0.705252 | ||||||||
\(943\) | −17.4100 | −0.566948 | ||||||||
\(944\) | 21.9266 | 0.713652 | ||||||||
\(945\) | −16.3137 | −0.530683 | ||||||||
\(946\) | −139.554 | −4.53731 | ||||||||
\(947\) | 25.6507 | 0.833535 | 0.416767 | − | 0.909013i | \(-0.363163\pi\) | ||||
0.416767 | + | 0.909013i | \(0.363163\pi\) | |||||||
\(948\) | 11.5196 | 0.374138 | ||||||||
\(949\) | 3.39206 | 0.110111 | ||||||||
\(950\) | 98.9037 | 3.20886 | ||||||||
\(951\) | 33.5449 | 1.08777 | ||||||||
\(952\) | 27.1394 | 0.879592 | ||||||||
\(953\) | −28.7245 | −0.930477 | −0.465238 | − | 0.885185i | \(-0.654031\pi\) | ||||
−0.465238 | + | 0.885185i | \(0.654031\pi\) | |||||||
\(954\) | 0.577651 | 0.0187021 | ||||||||
\(955\) | 41.9579 | 1.35773 | ||||||||
\(956\) | −78.8304 | −2.54956 | ||||||||
\(957\) | 26.2459 | 0.848411 | ||||||||
\(958\) | 68.7306 | 2.22058 | ||||||||
\(959\) | 13.2533 | 0.427970 | ||||||||
\(960\) | 60.8580 | 1.96418 | ||||||||
\(961\) | 76.5199 | 2.46838 | ||||||||
\(962\) | 22.3817 | 0.721615 | ||||||||
\(963\) | 0.253618 | 0.00817272 | ||||||||
\(964\) | −3.31889 | −0.106894 | ||||||||
\(965\) | 4.73255 | 0.152346 | ||||||||
\(966\) | −21.1469 | −0.680391 | ||||||||
\(967\) | 35.4224 | 1.13911 | 0.569554 | − | 0.821954i | \(-0.307116\pi\) | ||||
0.569554 | + | 0.821954i | \(0.307116\pi\) | |||||||
\(968\) | −94.6996 | −3.04376 | ||||||||
\(969\) | −93.3284 | −2.99814 | ||||||||
\(970\) | −69.9600 | −2.24628 | ||||||||
\(971\) | −49.1404 | −1.57699 | −0.788495 | − | 0.615041i | \(-0.789140\pi\) | ||||
−0.788495 | + | 0.615041i | \(0.789140\pi\) | |||||||
\(972\) | −1.36635 | −0.0438256 | ||||||||
\(973\) | 10.2360 | 0.328152 | ||||||||
\(974\) | 58.6646 | 1.87974 | ||||||||
\(975\) | 9.13584 | 0.292581 | ||||||||
\(976\) | 16.3010 | 0.521781 | ||||||||
\(977\) | −55.0668 | −1.76174 | −0.880872 | − | 0.473355i | \(-0.843043\pi\) | ||||
−0.880872 | + | 0.473355i | \(0.843043\pi\) | |||||||
\(978\) | 70.0891 | 2.24120 | ||||||||
\(979\) | −80.5862 | −2.57555 | ||||||||
\(980\) | 71.3440 | 2.27900 | ||||||||
\(981\) | −0.194755 | −0.00621803 | ||||||||
\(982\) | −63.0732 | −2.01275 | ||||||||
\(983\) | 14.4430 | 0.460661 | 0.230331 | − | 0.973112i | \(-0.426019\pi\) | ||||
0.230331 | + | 0.973112i | \(0.426019\pi\) | |||||||
\(984\) | −23.8822 | −0.761338 | ||||||||
\(985\) | 18.4326 | 0.587313 | ||||||||
\(986\) | 41.6026 | 1.32490 | ||||||||
\(987\) | 0.829713 | 0.0264100 | ||||||||
\(988\) | −29.2264 | −0.929815 | ||||||||
\(989\) | 51.3880 | 1.63404 | ||||||||
\(990\) | −1.59165 | −0.0505860 | ||||||||
\(991\) | 24.9464 | 0.792449 | 0.396224 | − | 0.918154i | \(-0.370320\pi\) | ||||
0.396224 | + | 0.918154i | \(0.370320\pi\) | |||||||
\(992\) | −27.5529 | −0.874805 | ||||||||
\(993\) | 3.10795 | 0.0986279 | ||||||||
\(994\) | −24.0490 | −0.762788 | ||||||||
\(995\) | 30.0811 | 0.953634 | ||||||||
\(996\) | −19.0085 | −0.602308 | ||||||||
\(997\) | 33.9696 | 1.07583 | 0.537914 | − | 0.843000i | \(-0.319213\pi\) | ||||
0.537914 | + | 0.843000i | \(0.319213\pi\) | |||||||
\(998\) | −10.2175 | −0.323429 | ||||||||
\(999\) | 48.4231 | 1.53204 |
(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 | 8047.2.a.e.1.18 | ✓ | 168 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8047.2.a.e.1.18 | ✓ | 168 | 1.1 | even | 1 | trivial |