Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4011,2,Mod(1,4011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4011, 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("4011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4011 = 3 \cdot 7 \cdot 191 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4011.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0279962507\) |
Analytic rank: | \(0\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 4011.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.70789 | −1.20766 | −0.603831 | − | 0.797112i | \(-0.706360\pi\) | ||||
−0.603831 | + | 0.797112i | \(0.706360\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.916895 | 0.458447 | ||||||||
\(5\) | 2.36693 | 1.05852 | 0.529262 | − | 0.848459i | \(-0.322469\pi\) | ||||
0.529262 | + | 0.848459i | \(0.322469\pi\) | |||||||
\(6\) | −1.70789 | −0.697244 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.84983 | 0.654013 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −4.04246 | −1.27834 | ||||||||
\(11\) | −0.746546 | −0.225092 | −0.112546 | − | 0.993647i | \(-0.535901\pi\) | ||||
−0.112546 | + | 0.993647i | \(0.535901\pi\) | |||||||
\(12\) | 0.916895 | 0.264685 | ||||||||
\(13\) | 1.43337 | 0.397547 | 0.198773 | − | 0.980046i | \(-0.436304\pi\) | ||||
0.198773 | + | 0.980046i | \(0.436304\pi\) | |||||||
\(14\) | −1.70789 | −0.456453 | ||||||||
\(15\) | 2.36693 | 0.611139 | ||||||||
\(16\) | −4.99309 | −1.24827 | ||||||||
\(17\) | −0.954280 | −0.231447 | −0.115723 | − | 0.993281i | \(-0.536919\pi\) | ||||
−0.115723 | + | 0.993281i | \(0.536919\pi\) | |||||||
\(18\) | −1.70789 | −0.402554 | ||||||||
\(19\) | 0.503438 | 0.115497 | 0.0577483 | − | 0.998331i | \(-0.481608\pi\) | ||||
0.0577483 | + | 0.998331i | \(0.481608\pi\) | |||||||
\(20\) | 2.17023 | 0.485277 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 1.27502 | 0.271835 | ||||||||
\(23\) | 3.97252 | 0.828328 | 0.414164 | − | 0.910202i | \(-0.364074\pi\) | ||||
0.414164 | + | 0.910202i | \(0.364074\pi\) | |||||||
\(24\) | 1.84983 | 0.377594 | ||||||||
\(25\) | 0.602358 | 0.120472 | ||||||||
\(26\) | −2.44805 | −0.480102 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.916895 | 0.173277 | ||||||||
\(29\) | −7.00431 | −1.30067 | −0.650334 | − | 0.759649i | \(-0.725371\pi\) | ||||
−0.650334 | + | 0.759649i | \(0.725371\pi\) | |||||||
\(30\) | −4.04246 | −0.738049 | ||||||||
\(31\) | 3.89382 | 0.699350 | 0.349675 | − | 0.936871i | \(-0.386292\pi\) | ||||
0.349675 | + | 0.936871i | \(0.386292\pi\) | |||||||
\(32\) | 4.82801 | 0.853480 | ||||||||
\(33\) | −0.746546 | −0.129957 | ||||||||
\(34\) | 1.62981 | 0.279510 | ||||||||
\(35\) | 2.36693 | 0.400084 | ||||||||
\(36\) | 0.916895 | 0.152816 | ||||||||
\(37\) | 3.42569 | 0.563180 | 0.281590 | − | 0.959535i | \(-0.409138\pi\) | ||||
0.281590 | + | 0.959535i | \(0.409138\pi\) | |||||||
\(38\) | −0.859818 | −0.139481 | ||||||||
\(39\) | 1.43337 | 0.229524 | ||||||||
\(40\) | 4.37841 | 0.692288 | ||||||||
\(41\) | 2.77066 | 0.432704 | 0.216352 | − | 0.976315i | \(-0.430584\pi\) | ||||
0.216352 | + | 0.976315i | \(0.430584\pi\) | |||||||
\(42\) | −1.70789 | −0.263533 | ||||||||
\(43\) | 0.415126 | 0.0633062 | 0.0316531 | − | 0.999499i | \(-0.489923\pi\) | ||||
0.0316531 | + | 0.999499i | \(0.489923\pi\) | |||||||
\(44\) | −0.684504 | −0.103193 | ||||||||
\(45\) | 2.36693 | 0.352841 | ||||||||
\(46\) | −6.78463 | −1.00034 | ||||||||
\(47\) | −0.842645 | −0.122912 | −0.0614562 | − | 0.998110i | \(-0.519574\pi\) | ||||
−0.0614562 | + | 0.998110i | \(0.519574\pi\) | |||||||
\(48\) | −4.99309 | −0.720691 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.02876 | −0.145489 | ||||||||
\(51\) | −0.954280 | −0.133626 | ||||||||
\(52\) | 1.31425 | 0.182254 | ||||||||
\(53\) | 0.595852 | 0.0818465 | 0.0409233 | − | 0.999162i | \(-0.486970\pi\) | ||||
0.0409233 | + | 0.999162i | \(0.486970\pi\) | |||||||
\(54\) | −1.70789 | −0.232415 | ||||||||
\(55\) | −1.76702 | −0.238265 | ||||||||
\(56\) | 1.84983 | 0.247194 | ||||||||
\(57\) | 0.503438 | 0.0666820 | ||||||||
\(58\) | 11.9626 | 1.57077 | ||||||||
\(59\) | 14.5620 | 1.89581 | 0.947903 | − | 0.318560i | \(-0.103199\pi\) | ||||
0.947903 | + | 0.318560i | \(0.103199\pi\) | |||||||
\(60\) | 2.17023 | 0.280175 | ||||||||
\(61\) | −7.43261 | −0.951648 | −0.475824 | − | 0.879541i | \(-0.657850\pi\) | ||||
−0.475824 | + | 0.879541i | \(0.657850\pi\) | |||||||
\(62\) | −6.65022 | −0.844579 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.74047 | 0.217559 | ||||||||
\(65\) | 3.39270 | 0.420812 | ||||||||
\(66\) | 1.27502 | 0.156944 | ||||||||
\(67\) | 12.8339 | 1.56791 | 0.783955 | − | 0.620818i | \(-0.213199\pi\) | ||||
0.783955 | + | 0.620818i | \(0.213199\pi\) | |||||||
\(68\) | −0.874974 | −0.106106 | ||||||||
\(69\) | 3.97252 | 0.478235 | ||||||||
\(70\) | −4.04246 | −0.483166 | ||||||||
\(71\) | 11.9338 | 1.41628 | 0.708141 | − | 0.706071i | \(-0.249534\pi\) | ||||
0.708141 | + | 0.706071i | \(0.249534\pi\) | |||||||
\(72\) | 1.84983 | 0.218004 | ||||||||
\(73\) | 4.44314 | 0.520031 | 0.260015 | − | 0.965605i | \(-0.416272\pi\) | ||||
0.260015 | + | 0.965605i | \(0.416272\pi\) | |||||||
\(74\) | −5.85070 | −0.680131 | ||||||||
\(75\) | 0.602358 | 0.0695543 | ||||||||
\(76\) | 0.461600 | 0.0529491 | ||||||||
\(77\) | −0.746546 | −0.0850768 | ||||||||
\(78\) | −2.44805 | −0.277187 | ||||||||
\(79\) | −10.2846 | −1.15711 | −0.578557 | − | 0.815642i | \(-0.696384\pi\) | ||||
−0.578557 | + | 0.815642i | \(0.696384\pi\) | |||||||
\(80\) | −11.8183 | −1.32133 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.73199 | −0.522561 | ||||||||
\(83\) | −12.8515 | −1.41063 | −0.705316 | − | 0.708893i | \(-0.749195\pi\) | ||||
−0.705316 | + | 0.708893i | \(0.749195\pi\) | |||||||
\(84\) | 0.916895 | 0.100041 | ||||||||
\(85\) | −2.25871 | −0.244992 | ||||||||
\(86\) | −0.708991 | −0.0764524 | ||||||||
\(87\) | −7.00431 | −0.750940 | ||||||||
\(88\) | −1.38098 | −0.147213 | ||||||||
\(89\) | 2.33027 | 0.247008 | 0.123504 | − | 0.992344i | \(-0.460587\pi\) | ||||
0.123504 | + | 0.992344i | \(0.460587\pi\) | |||||||
\(90\) | −4.04246 | −0.426113 | ||||||||
\(91\) | 1.43337 | 0.150258 | ||||||||
\(92\) | 3.64238 | 0.379745 | ||||||||
\(93\) | 3.89382 | 0.403770 | ||||||||
\(94\) | 1.43915 | 0.148437 | ||||||||
\(95\) | 1.19160 | 0.122256 | ||||||||
\(96\) | 4.82801 | 0.492757 | ||||||||
\(97\) | −0.569211 | −0.0577946 | −0.0288973 | − | 0.999582i | \(-0.509200\pi\) | ||||
−0.0288973 | + | 0.999582i | \(0.509200\pi\) | |||||||
\(98\) | −1.70789 | −0.172523 | ||||||||
\(99\) | −0.746546 | −0.0750307 | ||||||||
\(100\) | 0.552298 | 0.0552298 | ||||||||
\(101\) | 10.1044 | 1.00542 | 0.502711 | − | 0.864454i | \(-0.332336\pi\) | ||||
0.502711 | + | 0.864454i | \(0.332336\pi\) | |||||||
\(102\) | 1.62981 | 0.161375 | ||||||||
\(103\) | 11.2842 | 1.11187 | 0.555933 | − | 0.831227i | \(-0.312361\pi\) | ||||
0.555933 | + | 0.831227i | \(0.312361\pi\) | |||||||
\(104\) | 2.65149 | 0.260000 | ||||||||
\(105\) | 2.36693 | 0.230989 | ||||||||
\(106\) | −1.01765 | −0.0988429 | ||||||||
\(107\) | 12.7716 | 1.23468 | 0.617340 | − | 0.786696i | \(-0.288210\pi\) | ||||
0.617340 | + | 0.786696i | \(0.288210\pi\) | |||||||
\(108\) | 0.916895 | 0.0882282 | ||||||||
\(109\) | 4.78205 | 0.458037 | 0.229019 | − | 0.973422i | \(-0.426448\pi\) | ||||
0.229019 | + | 0.973422i | \(0.426448\pi\) | |||||||
\(110\) | 3.01788 | 0.287744 | ||||||||
\(111\) | 3.42569 | 0.325152 | ||||||||
\(112\) | −4.99309 | −0.471803 | ||||||||
\(113\) | 16.2874 | 1.53219 | 0.766095 | − | 0.642727i | \(-0.222197\pi\) | ||||
0.766095 | + | 0.642727i | \(0.222197\pi\) | |||||||
\(114\) | −0.859818 | −0.0805294 | ||||||||
\(115\) | 9.40268 | 0.876804 | ||||||||
\(116\) | −6.42221 | −0.596287 | ||||||||
\(117\) | 1.43337 | 0.132516 | ||||||||
\(118\) | −24.8702 | −2.28949 | ||||||||
\(119\) | −0.954280 | −0.0874787 | ||||||||
\(120\) | 4.37841 | 0.399692 | ||||||||
\(121\) | −10.4427 | −0.949334 | ||||||||
\(122\) | 12.6941 | 1.14927 | ||||||||
\(123\) | 2.77066 | 0.249822 | ||||||||
\(124\) | 3.57022 | 0.320615 | ||||||||
\(125\) | −10.4089 | −0.931001 | ||||||||
\(126\) | −1.70789 | −0.152151 | ||||||||
\(127\) | 15.7156 | 1.39454 | 0.697268 | − | 0.716811i | \(-0.254399\pi\) | ||||
0.697268 | + | 0.716811i | \(0.254399\pi\) | |||||||
\(128\) | −12.6286 | −1.11622 | ||||||||
\(129\) | 0.415126 | 0.0365498 | ||||||||
\(130\) | −5.79436 | −0.508199 | ||||||||
\(131\) | 4.13018 | 0.360856 | 0.180428 | − | 0.983588i | \(-0.442252\pi\) | ||||
0.180428 | + | 0.983588i | \(0.442252\pi\) | |||||||
\(132\) | −0.684504 | −0.0595784 | ||||||||
\(133\) | 0.503438 | 0.0436536 | ||||||||
\(134\) | −21.9189 | −1.89350 | ||||||||
\(135\) | 2.36693 | 0.203713 | ||||||||
\(136\) | −1.76525 | −0.151369 | ||||||||
\(137\) | −13.2408 | −1.13124 | −0.565618 | − | 0.824667i | \(-0.691362\pi\) | ||||
−0.565618 | + | 0.824667i | \(0.691362\pi\) | |||||||
\(138\) | −6.78463 | −0.577546 | ||||||||
\(139\) | −23.2299 | −1.97033 | −0.985167 | − | 0.171598i | \(-0.945107\pi\) | ||||
−0.985167 | + | 0.171598i | \(0.945107\pi\) | |||||||
\(140\) | 2.17023 | 0.183418 | ||||||||
\(141\) | −0.842645 | −0.0709635 | ||||||||
\(142\) | −20.3817 | −1.71039 | ||||||||
\(143\) | −1.07008 | −0.0894846 | ||||||||
\(144\) | −4.99309 | −0.416091 | ||||||||
\(145\) | −16.5787 | −1.37679 | ||||||||
\(146\) | −7.58841 | −0.628021 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 3.14099 | 0.258188 | ||||||||
\(149\) | −14.7076 | −1.20489 | −0.602445 | − | 0.798160i | \(-0.705807\pi\) | ||||
−0.602445 | + | 0.798160i | \(0.705807\pi\) | |||||||
\(150\) | −1.02876 | −0.0839980 | ||||||||
\(151\) | −9.96036 | −0.810562 | −0.405281 | − | 0.914192i | \(-0.632826\pi\) | ||||
−0.405281 | + | 0.914192i | \(0.632826\pi\) | |||||||
\(152\) | 0.931274 | 0.0755363 | ||||||||
\(153\) | −0.954280 | −0.0771490 | ||||||||
\(154\) | 1.27502 | 0.102744 | ||||||||
\(155\) | 9.21640 | 0.740279 | ||||||||
\(156\) | 1.31425 | 0.105224 | ||||||||
\(157\) | 9.69702 | 0.773906 | 0.386953 | − | 0.922099i | \(-0.373527\pi\) | ||||
0.386953 | + | 0.922099i | \(0.373527\pi\) | |||||||
\(158\) | 17.5651 | 1.39740 | ||||||||
\(159\) | 0.595852 | 0.0472541 | ||||||||
\(160\) | 11.4276 | 0.903428 | ||||||||
\(161\) | 3.97252 | 0.313078 | ||||||||
\(162\) | −1.70789 | −0.134185 | ||||||||
\(163\) | −20.3135 | −1.59108 | −0.795539 | − | 0.605902i | \(-0.792812\pi\) | ||||
−0.795539 | + | 0.605902i | \(0.792812\pi\) | |||||||
\(164\) | 2.54040 | 0.198372 | ||||||||
\(165\) | −1.76702 | −0.137562 | ||||||||
\(166\) | 21.9489 | 1.70357 | ||||||||
\(167\) | 1.08305 | 0.0838091 | 0.0419045 | − | 0.999122i | \(-0.486657\pi\) | ||||
0.0419045 | + | 0.999122i | \(0.486657\pi\) | |||||||
\(168\) | 1.84983 | 0.142717 | ||||||||
\(169\) | −10.9454 | −0.841957 | ||||||||
\(170\) | 3.85764 | 0.295867 | ||||||||
\(171\) | 0.503438 | 0.0384989 | ||||||||
\(172\) | 0.380627 | 0.0290225 | ||||||||
\(173\) | 20.2032 | 1.53602 | 0.768010 | − | 0.640437i | \(-0.221247\pi\) | ||||
0.768010 | + | 0.640437i | \(0.221247\pi\) | |||||||
\(174\) | 11.9626 | 0.906882 | ||||||||
\(175\) | 0.602358 | 0.0455340 | ||||||||
\(176\) | 3.72757 | 0.280976 | ||||||||
\(177\) | 14.5620 | 1.09454 | ||||||||
\(178\) | −3.97984 | −0.298302 | ||||||||
\(179\) | 4.86978 | 0.363985 | 0.181992 | − | 0.983300i | \(-0.441745\pi\) | ||||
0.181992 | + | 0.983300i | \(0.441745\pi\) | |||||||
\(180\) | 2.17023 | 0.161759 | ||||||||
\(181\) | 9.52144 | 0.707723 | 0.353861 | − | 0.935298i | \(-0.384868\pi\) | ||||
0.353861 | + | 0.935298i | \(0.384868\pi\) | |||||||
\(182\) | −2.44805 | −0.181461 | ||||||||
\(183\) | −7.43261 | −0.549434 | ||||||||
\(184\) | 7.34847 | 0.541737 | ||||||||
\(185\) | 8.10836 | 0.596139 | ||||||||
\(186\) | −6.65022 | −0.487618 | ||||||||
\(187\) | 0.712414 | 0.0520969 | ||||||||
\(188\) | −0.772617 | −0.0563489 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −2.03513 | −0.147644 | ||||||||
\(191\) | 1.00000 | 0.0723575 | ||||||||
\(192\) | 1.74047 | 0.125607 | ||||||||
\(193\) | −4.40259 | −0.316905 | −0.158453 | − | 0.987367i | \(-0.550651\pi\) | ||||
−0.158453 | + | 0.987367i | \(0.550651\pi\) | |||||||
\(194\) | 0.972150 | 0.0697963 | ||||||||
\(195\) | 3.39270 | 0.242956 | ||||||||
\(196\) | 0.916895 | 0.0654925 | ||||||||
\(197\) | 24.3950 | 1.73807 | 0.869036 | − | 0.494748i | \(-0.164740\pi\) | ||||
0.869036 | + | 0.494748i | \(0.164740\pi\) | |||||||
\(198\) | 1.27502 | 0.0906117 | ||||||||
\(199\) | −0.175370 | −0.0124316 | −0.00621582 | − | 0.999981i | \(-0.501979\pi\) | ||||
−0.00621582 | + | 0.999981i | \(0.501979\pi\) | |||||||
\(200\) | 1.11426 | 0.0787899 | ||||||||
\(201\) | 12.8339 | 0.905233 | ||||||||
\(202\) | −17.2572 | −1.21421 | ||||||||
\(203\) | −7.00431 | −0.491606 | ||||||||
\(204\) | −0.874974 | −0.0612604 | ||||||||
\(205\) | 6.55796 | 0.458028 | ||||||||
\(206\) | −19.2722 | −1.34276 | ||||||||
\(207\) | 3.97252 | 0.276109 | ||||||||
\(208\) | −7.15697 | −0.496247 | ||||||||
\(209\) | −0.375840 | −0.0259974 | ||||||||
\(210\) | −4.04246 | −0.278956 | ||||||||
\(211\) | −14.1014 | −0.970783 | −0.485391 | − | 0.874297i | \(-0.661323\pi\) | ||||
−0.485391 | + | 0.874297i | \(0.661323\pi\) | |||||||
\(212\) | 0.546333 | 0.0375223 | ||||||||
\(213\) | 11.9338 | 0.817691 | ||||||||
\(214\) | −21.8126 | −1.49108 | ||||||||
\(215\) | 0.982575 | 0.0670110 | ||||||||
\(216\) | 1.84983 | 0.125865 | ||||||||
\(217\) | 3.89382 | 0.264330 | ||||||||
\(218\) | −8.16722 | −0.553154 | ||||||||
\(219\) | 4.44314 | 0.300240 | ||||||||
\(220\) | −1.62017 | −0.109232 | ||||||||
\(221\) | −1.36784 | −0.0920109 | ||||||||
\(222\) | −5.85070 | −0.392674 | ||||||||
\(223\) | −3.29267 | −0.220493 | −0.110247 | − | 0.993904i | \(-0.535164\pi\) | ||||
−0.110247 | + | 0.993904i | \(0.535164\pi\) | |||||||
\(224\) | 4.82801 | 0.322585 | ||||||||
\(225\) | 0.602358 | 0.0401572 | ||||||||
\(226\) | −27.8171 | −1.85037 | ||||||||
\(227\) | 1.78164 | 0.118252 | 0.0591259 | − | 0.998251i | \(-0.481169\pi\) | ||||
0.0591259 | + | 0.998251i | \(0.481169\pi\) | |||||||
\(228\) | 0.461600 | 0.0305702 | ||||||||
\(229\) | −22.0061 | −1.45420 | −0.727102 | − | 0.686529i | \(-0.759133\pi\) | ||||
−0.727102 | + | 0.686529i | \(0.759133\pi\) | |||||||
\(230\) | −16.0588 | −1.05888 | ||||||||
\(231\) | −0.746546 | −0.0491191 | ||||||||
\(232\) | −12.9568 | −0.850653 | ||||||||
\(233\) | 21.8651 | 1.43243 | 0.716216 | − | 0.697879i | \(-0.245873\pi\) | ||||
0.716216 | + | 0.697879i | \(0.245873\pi\) | |||||||
\(234\) | −2.44805 | −0.160034 | ||||||||
\(235\) | −1.99448 | −0.130106 | ||||||||
\(236\) | 13.3518 | 0.869127 | ||||||||
\(237\) | −10.2846 | −0.668060 | ||||||||
\(238\) | 1.62981 | 0.105645 | ||||||||
\(239\) | 19.9407 | 1.28986 | 0.644930 | − | 0.764242i | \(-0.276887\pi\) | ||||
0.644930 | + | 0.764242i | \(0.276887\pi\) | |||||||
\(240\) | −11.8183 | −0.762868 | ||||||||
\(241\) | 12.3395 | 0.794854 | 0.397427 | − | 0.917634i | \(-0.369903\pi\) | ||||
0.397427 | + | 0.917634i | \(0.369903\pi\) | |||||||
\(242\) | 17.8349 | 1.14647 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −6.81492 | −0.436280 | ||||||||
\(245\) | 2.36693 | 0.151218 | ||||||||
\(246\) | −4.73199 | −0.301701 | ||||||||
\(247\) | 0.721616 | 0.0459153 | ||||||||
\(248\) | 7.20289 | 0.457384 | ||||||||
\(249\) | −12.8515 | −0.814428 | ||||||||
\(250\) | 17.7773 | 1.12433 | ||||||||
\(251\) | 22.6131 | 1.42733 | 0.713664 | − | 0.700488i | \(-0.247034\pi\) | ||||
0.713664 | + | 0.700488i | \(0.247034\pi\) | |||||||
\(252\) | 0.916895 | 0.0577589 | ||||||||
\(253\) | −2.96567 | −0.186450 | ||||||||
\(254\) | −26.8406 | −1.68413 | ||||||||
\(255\) | −2.25871 | −0.141446 | ||||||||
\(256\) | 18.0873 | 1.13045 | ||||||||
\(257\) | −15.4648 | −0.964669 | −0.482335 | − | 0.875987i | \(-0.660211\pi\) | ||||
−0.482335 | + | 0.875987i | \(0.660211\pi\) | |||||||
\(258\) | −0.708991 | −0.0441398 | ||||||||
\(259\) | 3.42569 | 0.212862 | ||||||||
\(260\) | 3.11075 | 0.192920 | ||||||||
\(261\) | −7.00431 | −0.433556 | ||||||||
\(262\) | −7.05390 | −0.435792 | ||||||||
\(263\) | −18.9232 | −1.16686 | −0.583428 | − | 0.812165i | \(-0.698289\pi\) | ||||
−0.583428 | + | 0.812165i | \(0.698289\pi\) | |||||||
\(264\) | −1.38098 | −0.0849935 | ||||||||
\(265\) | 1.41034 | 0.0866364 | ||||||||
\(266\) | −0.859818 | −0.0527188 | ||||||||
\(267\) | 2.33027 | 0.142610 | ||||||||
\(268\) | 11.7673 | 0.718804 | ||||||||
\(269\) | 13.1886 | 0.804124 | 0.402062 | − | 0.915613i | \(-0.368294\pi\) | ||||
0.402062 | + | 0.915613i | \(0.368294\pi\) | |||||||
\(270\) | −4.04246 | −0.246016 | ||||||||
\(271\) | −24.8772 | −1.51118 | −0.755590 | − | 0.655044i | \(-0.772650\pi\) | ||||
−0.755590 | + | 0.655044i | \(0.772650\pi\) | |||||||
\(272\) | 4.76481 | 0.288909 | ||||||||
\(273\) | 1.43337 | 0.0867518 | ||||||||
\(274\) | 22.6138 | 1.36615 | ||||||||
\(275\) | −0.449688 | −0.0271172 | ||||||||
\(276\) | 3.64238 | 0.219246 | ||||||||
\(277\) | 5.52870 | 0.332187 | 0.166094 | − | 0.986110i | \(-0.446885\pi\) | ||||
0.166094 | + | 0.986110i | \(0.446885\pi\) | |||||||
\(278\) | 39.6741 | 2.37950 | ||||||||
\(279\) | 3.89382 | 0.233117 | ||||||||
\(280\) | 4.37841 | 0.261660 | ||||||||
\(281\) | 10.0736 | 0.600940 | 0.300470 | − | 0.953791i | \(-0.402856\pi\) | ||||
0.300470 | + | 0.953791i | \(0.402856\pi\) | |||||||
\(282\) | 1.43915 | 0.0856999 | ||||||||
\(283\) | −30.4246 | −1.80855 | −0.904276 | − | 0.426947i | \(-0.859589\pi\) | ||||
−0.904276 | + | 0.426947i | \(0.859589\pi\) | |||||||
\(284\) | 10.9420 | 0.649291 | ||||||||
\(285\) | 1.19160 | 0.0705845 | ||||||||
\(286\) | 1.82758 | 0.108067 | ||||||||
\(287\) | 2.77066 | 0.163547 | ||||||||
\(288\) | 4.82801 | 0.284493 | ||||||||
\(289\) | −16.0893 | −0.946432 | ||||||||
\(290\) | 28.3146 | 1.66269 | ||||||||
\(291\) | −0.569211 | −0.0333677 | ||||||||
\(292\) | 4.07389 | 0.238407 | ||||||||
\(293\) | −14.6843 | −0.857867 | −0.428934 | − | 0.903336i | \(-0.641111\pi\) | ||||
−0.428934 | + | 0.903336i | \(0.641111\pi\) | |||||||
\(294\) | −1.70789 | −0.0996063 | ||||||||
\(295\) | 34.4671 | 2.00675 | ||||||||
\(296\) | 6.33693 | 0.368327 | ||||||||
\(297\) | −0.746546 | −0.0433190 | ||||||||
\(298\) | 25.1189 | 1.45510 | ||||||||
\(299\) | 5.69411 | 0.329299 | ||||||||
\(300\) | 0.552298 | 0.0318870 | ||||||||
\(301\) | 0.415126 | 0.0239275 | ||||||||
\(302\) | 17.0112 | 0.978885 | ||||||||
\(303\) | 10.1044 | 0.580481 | ||||||||
\(304\) | −2.51372 | −0.144171 | ||||||||
\(305\) | −17.5925 | −1.00734 | ||||||||
\(306\) | 1.62981 | 0.0931699 | ||||||||
\(307\) | 15.3466 | 0.875875 | 0.437938 | − | 0.899005i | \(-0.355709\pi\) | ||||
0.437938 | + | 0.899005i | \(0.355709\pi\) | |||||||
\(308\) | −0.684504 | −0.0390032 | ||||||||
\(309\) | 11.2842 | 0.641936 | ||||||||
\(310\) | −15.7406 | −0.894006 | ||||||||
\(311\) | −3.49075 | −0.197942 | −0.0989712 | − | 0.995090i | \(-0.531555\pi\) | ||||
−0.0989712 | + | 0.995090i | \(0.531555\pi\) | |||||||
\(312\) | 2.65149 | 0.150111 | ||||||||
\(313\) | 7.15230 | 0.404272 | 0.202136 | − | 0.979357i | \(-0.435212\pi\) | ||||
0.202136 | + | 0.979357i | \(0.435212\pi\) | |||||||
\(314\) | −16.5615 | −0.934617 | ||||||||
\(315\) | 2.36693 | 0.133361 | ||||||||
\(316\) | −9.42994 | −0.530475 | ||||||||
\(317\) | −13.5085 | −0.758713 | −0.379357 | − | 0.925251i | \(-0.623855\pi\) | ||||
−0.379357 | + | 0.925251i | \(0.623855\pi\) | |||||||
\(318\) | −1.01765 | −0.0570670 | ||||||||
\(319\) | 5.22904 | 0.292770 | ||||||||
\(320\) | 4.11957 | 0.230291 | ||||||||
\(321\) | 12.7716 | 0.712843 | ||||||||
\(322\) | −6.78463 | −0.378093 | ||||||||
\(323\) | −0.480421 | −0.0267313 | ||||||||
\(324\) | 0.916895 | 0.0509386 | ||||||||
\(325\) | 0.863404 | 0.0478930 | ||||||||
\(326\) | 34.6933 | 1.92148 | ||||||||
\(327\) | 4.78205 | 0.264448 | ||||||||
\(328\) | 5.12524 | 0.282994 | ||||||||
\(329\) | −0.842645 | −0.0464565 | ||||||||
\(330\) | 3.01788 | 0.166129 | ||||||||
\(331\) | −21.5798 | −1.18614 | −0.593068 | − | 0.805153i | \(-0.702083\pi\) | ||||
−0.593068 | + | 0.805153i | \(0.702083\pi\) | |||||||
\(332\) | −11.7834 | −0.646700 | ||||||||
\(333\) | 3.42569 | 0.187727 | ||||||||
\(334\) | −1.84974 | −0.101213 | ||||||||
\(335\) | 30.3769 | 1.65967 | ||||||||
\(336\) | −4.99309 | −0.272396 | ||||||||
\(337\) | 22.3815 | 1.21920 | 0.609600 | − | 0.792709i | \(-0.291330\pi\) | ||||
0.609600 | + | 0.792709i | \(0.291330\pi\) | |||||||
\(338\) | 18.6936 | 1.01680 | ||||||||
\(339\) | 16.2874 | 0.884610 | ||||||||
\(340\) | −2.07100 | −0.112316 | ||||||||
\(341\) | −2.90691 | −0.157418 | ||||||||
\(342\) | −0.859818 | −0.0464937 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0.767912 | 0.0414030 | ||||||||
\(345\) | 9.40268 | 0.506223 | ||||||||
\(346\) | −34.5049 | −1.85499 | ||||||||
\(347\) | 23.8265 | 1.27907 | 0.639536 | − | 0.768761i | \(-0.279127\pi\) | ||||
0.639536 | + | 0.768761i | \(0.279127\pi\) | |||||||
\(348\) | −6.42221 | −0.344267 | ||||||||
\(349\) | −2.98546 | −0.159808 | −0.0799039 | − | 0.996803i | \(-0.525461\pi\) | ||||
−0.0799039 | + | 0.996803i | \(0.525461\pi\) | |||||||
\(350\) | −1.02876 | −0.0549896 | ||||||||
\(351\) | 1.43337 | 0.0765079 | ||||||||
\(352\) | −3.60433 | −0.192112 | ||||||||
\(353\) | −13.4246 | −0.714520 | −0.357260 | − | 0.934005i | \(-0.616289\pi\) | ||||
−0.357260 | + | 0.934005i | \(0.616289\pi\) | |||||||
\(354\) | −24.8702 | −1.32184 | ||||||||
\(355\) | 28.2465 | 1.49917 | ||||||||
\(356\) | 2.13661 | 0.113240 | ||||||||
\(357\) | −0.954280 | −0.0505058 | ||||||||
\(358\) | −8.31706 | −0.439570 | ||||||||
\(359\) | −23.1991 | −1.22440 | −0.612200 | − | 0.790703i | \(-0.709715\pi\) | ||||
−0.612200 | + | 0.790703i | \(0.709715\pi\) | |||||||
\(360\) | 4.37841 | 0.230763 | ||||||||
\(361\) | −18.7465 | −0.986661 | ||||||||
\(362\) | −16.2616 | −0.854690 | ||||||||
\(363\) | −10.4427 | −0.548098 | ||||||||
\(364\) | 1.31425 | 0.0688856 | ||||||||
\(365\) | 10.5166 | 0.550464 | ||||||||
\(366\) | 12.6941 | 0.663531 | ||||||||
\(367\) | 10.3364 | 0.539553 | 0.269777 | − | 0.962923i | \(-0.413050\pi\) | ||||
0.269777 | + | 0.962923i | \(0.413050\pi\) | |||||||
\(368\) | −19.8352 | −1.03398 | ||||||||
\(369\) | 2.77066 | 0.144235 | ||||||||
\(370\) | −13.8482 | −0.719934 | ||||||||
\(371\) | 0.595852 | 0.0309351 | ||||||||
\(372\) | 3.57022 | 0.185107 | ||||||||
\(373\) | 19.7210 | 1.02112 | 0.510558 | − | 0.859843i | \(-0.329439\pi\) | ||||
0.510558 | + | 0.859843i | \(0.329439\pi\) | |||||||
\(374\) | −1.21673 | −0.0629154 | ||||||||
\(375\) | −10.4089 | −0.537514 | ||||||||
\(376\) | −1.55875 | −0.0803863 | ||||||||
\(377\) | −10.0398 | −0.517076 | ||||||||
\(378\) | −1.70789 | −0.0878445 | ||||||||
\(379\) | 19.7899 | 1.01654 | 0.508270 | − | 0.861198i | \(-0.330285\pi\) | ||||
0.508270 | + | 0.861198i | \(0.330285\pi\) | |||||||
\(380\) | 1.09257 | 0.0560479 | ||||||||
\(381\) | 15.7156 | 0.805136 | ||||||||
\(382\) | −1.70789 | −0.0873833 | ||||||||
\(383\) | −17.7405 | −0.906498 | −0.453249 | − | 0.891384i | \(-0.649735\pi\) | ||||
−0.453249 | + | 0.891384i | \(0.649735\pi\) | |||||||
\(384\) | −12.6286 | −0.644448 | ||||||||
\(385\) | −1.76702 | −0.0900558 | ||||||||
\(386\) | 7.51915 | 0.382715 | ||||||||
\(387\) | 0.415126 | 0.0211021 | ||||||||
\(388\) | −0.521906 | −0.0264958 | ||||||||
\(389\) | 21.7958 | 1.10509 | 0.552547 | − | 0.833482i | \(-0.313656\pi\) | ||||
0.552547 | + | 0.833482i | \(0.313656\pi\) | |||||||
\(390\) | −5.79436 | −0.293409 | ||||||||
\(391\) | −3.79090 | −0.191714 | ||||||||
\(392\) | 1.84983 | 0.0934304 | ||||||||
\(393\) | 4.13018 | 0.208340 | ||||||||
\(394\) | −41.6641 | −2.09900 | ||||||||
\(395\) | −24.3430 | −1.22483 | ||||||||
\(396\) | −0.684504 | −0.0343976 | ||||||||
\(397\) | 33.3843 | 1.67551 | 0.837755 | − | 0.546046i | \(-0.183868\pi\) | ||||
0.837755 | + | 0.546046i | \(0.183868\pi\) | |||||||
\(398\) | 0.299513 | 0.0150132 | ||||||||
\(399\) | 0.503438 | 0.0252034 | ||||||||
\(400\) | −3.00763 | −0.150381 | ||||||||
\(401\) | 24.7226 | 1.23459 | 0.617294 | − | 0.786733i | \(-0.288229\pi\) | ||||
0.617294 | + | 0.786733i | \(0.288229\pi\) | |||||||
\(402\) | −21.9189 | −1.09322 | ||||||||
\(403\) | 5.58130 | 0.278024 | ||||||||
\(404\) | 9.26464 | 0.460933 | ||||||||
\(405\) | 2.36693 | 0.117614 | ||||||||
\(406\) | 11.9626 | 0.593694 | ||||||||
\(407\) | −2.55743 | −0.126767 | ||||||||
\(408\) | −1.76525 | −0.0873930 | ||||||||
\(409\) | 2.23356 | 0.110443 | 0.0552213 | − | 0.998474i | \(-0.482414\pi\) | ||||
0.0552213 | + | 0.998474i | \(0.482414\pi\) | |||||||
\(410\) | −11.2003 | −0.553143 | ||||||||
\(411\) | −13.2408 | −0.653120 | ||||||||
\(412\) | 10.3464 | 0.509732 | ||||||||
\(413\) | 14.5620 | 0.716547 | ||||||||
\(414\) | −6.78463 | −0.333447 | ||||||||
\(415\) | −30.4185 | −1.49319 | ||||||||
\(416\) | 6.92035 | 0.339298 | ||||||||
\(417\) | −23.2299 | −1.13757 | ||||||||
\(418\) | 0.641894 | 0.0313961 | ||||||||
\(419\) | 5.99881 | 0.293061 | 0.146530 | − | 0.989206i | \(-0.453189\pi\) | ||||
0.146530 | + | 0.989206i | \(0.453189\pi\) | |||||||
\(420\) | 2.17023 | 0.105896 | ||||||||
\(421\) | −20.0574 | −0.977539 | −0.488769 | − | 0.872413i | \(-0.662554\pi\) | ||||
−0.488769 | + | 0.872413i | \(0.662554\pi\) | |||||||
\(422\) | 24.0837 | 1.17238 | ||||||||
\(423\) | −0.842645 | −0.0409708 | ||||||||
\(424\) | 1.10222 | 0.0535287 | ||||||||
\(425\) | −0.574818 | −0.0278828 | ||||||||
\(426\) | −20.3817 | −0.987494 | ||||||||
\(427\) | −7.43261 | −0.359689 | ||||||||
\(428\) | 11.7102 | 0.566036 | ||||||||
\(429\) | −1.07008 | −0.0516639 | ||||||||
\(430\) | −1.67813 | −0.0809267 | ||||||||
\(431\) | 30.8562 | 1.48629 | 0.743145 | − | 0.669130i | \(-0.233333\pi\) | ||||
0.743145 | + | 0.669130i | \(0.233333\pi\) | |||||||
\(432\) | −4.99309 | −0.240230 | ||||||||
\(433\) | 35.7742 | 1.71920 | 0.859600 | − | 0.510968i | \(-0.170713\pi\) | ||||
0.859600 | + | 0.510968i | \(0.170713\pi\) | |||||||
\(434\) | −6.65022 | −0.319221 | ||||||||
\(435\) | −16.5787 | −0.794888 | ||||||||
\(436\) | 4.38464 | 0.209986 | ||||||||
\(437\) | 1.99992 | 0.0956691 | ||||||||
\(438\) | −7.58841 | −0.362588 | ||||||||
\(439\) | −19.9489 | −0.952107 | −0.476053 | − | 0.879416i | \(-0.657933\pi\) | ||||
−0.476053 | + | 0.879416i | \(0.657933\pi\) | |||||||
\(440\) | −3.26869 | −0.155828 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 2.33612 | 0.111118 | ||||||||
\(443\) | 11.6104 | 0.551627 | 0.275814 | − | 0.961211i | \(-0.411053\pi\) | ||||
0.275814 | + | 0.961211i | \(0.411053\pi\) | |||||||
\(444\) | 3.14099 | 0.149065 | ||||||||
\(445\) | 5.51558 | 0.261463 | ||||||||
\(446\) | 5.62352 | 0.266281 | ||||||||
\(447\) | −14.7076 | −0.695644 | ||||||||
\(448\) | 1.74047 | 0.0822294 | ||||||||
\(449\) | 38.5350 | 1.81858 | 0.909290 | − | 0.416162i | \(-0.136625\pi\) | ||||
0.909290 | + | 0.416162i | \(0.136625\pi\) | |||||||
\(450\) | −1.02876 | −0.0484963 | ||||||||
\(451\) | −2.06843 | −0.0973984 | ||||||||
\(452\) | 14.9338 | 0.702428 | ||||||||
\(453\) | −9.96036 | −0.467978 | ||||||||
\(454\) | −3.04285 | −0.142808 | ||||||||
\(455\) | 3.39270 | 0.159052 | ||||||||
\(456\) | 0.931274 | 0.0436109 | ||||||||
\(457\) | 25.1155 | 1.17486 | 0.587428 | − | 0.809277i | \(-0.300141\pi\) | ||||
0.587428 | + | 0.809277i | \(0.300141\pi\) | |||||||
\(458\) | 37.5841 | 1.75619 | ||||||||
\(459\) | −0.954280 | −0.0445420 | ||||||||
\(460\) | 8.62126 | 0.401968 | ||||||||
\(461\) | 26.6182 | 1.23973 | 0.619867 | − | 0.784707i | \(-0.287186\pi\) | ||||
0.619867 | + | 0.784707i | \(0.287186\pi\) | |||||||
\(462\) | 1.27502 | 0.0593193 | ||||||||
\(463\) | 11.1856 | 0.519838 | 0.259919 | − | 0.965630i | \(-0.416304\pi\) | ||||
0.259919 | + | 0.965630i | \(0.416304\pi\) | |||||||
\(464\) | 34.9732 | 1.62359 | ||||||||
\(465\) | 9.21640 | 0.427400 | ||||||||
\(466\) | −37.3433 | −1.72989 | ||||||||
\(467\) | −14.3359 | −0.663387 | −0.331694 | − | 0.943387i | \(-0.607620\pi\) | ||||
−0.331694 | + | 0.943387i | \(0.607620\pi\) | |||||||
\(468\) | 1.31425 | 0.0607514 | ||||||||
\(469\) | 12.8339 | 0.592614 | ||||||||
\(470\) | 3.40636 | 0.157124 | ||||||||
\(471\) | 9.69702 | 0.446815 | ||||||||
\(472\) | 26.9371 | 1.23988 | ||||||||
\(473\) | −0.309911 | −0.0142497 | ||||||||
\(474\) | 17.5651 | 0.806790 | ||||||||
\(475\) | 0.303250 | 0.0139141 | ||||||||
\(476\) | −0.874974 | −0.0401044 | ||||||||
\(477\) | 0.595852 | 0.0272822 | ||||||||
\(478\) | −34.0566 | −1.55771 | ||||||||
\(479\) | −26.0704 | −1.19119 | −0.595593 | − | 0.803286i | \(-0.703083\pi\) | ||||
−0.595593 | + | 0.803286i | \(0.703083\pi\) | |||||||
\(480\) | 11.4276 | 0.521594 | ||||||||
\(481\) | 4.91029 | 0.223890 | ||||||||
\(482\) | −21.0745 | −0.959915 | ||||||||
\(483\) | 3.97252 | 0.180756 | ||||||||
\(484\) | −9.57483 | −0.435219 | ||||||||
\(485\) | −1.34728 | −0.0611769 | ||||||||
\(486\) | −1.70789 | −0.0774715 | ||||||||
\(487\) | −31.3411 | −1.42020 | −0.710100 | − | 0.704100i | \(-0.751351\pi\) | ||||
−0.710100 | + | 0.704100i | \(0.751351\pi\) | |||||||
\(488\) | −13.7490 | −0.622390 | ||||||||
\(489\) | −20.3135 | −0.918609 | ||||||||
\(490\) | −4.04246 | −0.182620 | ||||||||
\(491\) | −31.5245 | −1.42268 | −0.711339 | − | 0.702849i | \(-0.751911\pi\) | ||||
−0.711339 | + | 0.702849i | \(0.751911\pi\) | |||||||
\(492\) | 2.54040 | 0.114530 | ||||||||
\(493\) | 6.68407 | 0.301035 | ||||||||
\(494\) | −1.23244 | −0.0554502 | ||||||||
\(495\) | −1.76702 | −0.0794217 | ||||||||
\(496\) | −19.4422 | −0.872981 | ||||||||
\(497\) | 11.9338 | 0.535304 | ||||||||
\(498\) | 21.9489 | 0.983554 | ||||||||
\(499\) | −5.94417 | −0.266098 | −0.133049 | − | 0.991109i | \(-0.542477\pi\) | ||||
−0.133049 | + | 0.991109i | \(0.542477\pi\) | |||||||
\(500\) | −9.54387 | −0.426815 | ||||||||
\(501\) | 1.08305 | 0.0483872 | ||||||||
\(502\) | −38.6208 | −1.72373 | ||||||||
\(503\) | 3.59264 | 0.160188 | 0.0800941 | − | 0.996787i | \(-0.474478\pi\) | ||||
0.0800941 | + | 0.996787i | \(0.474478\pi\) | |||||||
\(504\) | 1.84983 | 0.0823978 | ||||||||
\(505\) | 23.9163 | 1.06426 | ||||||||
\(506\) | 5.06504 | 0.225169 | ||||||||
\(507\) | −10.9454 | −0.486104 | ||||||||
\(508\) | 14.4096 | 0.639321 | ||||||||
\(509\) | −15.2981 | −0.678076 | −0.339038 | − | 0.940773i | \(-0.610101\pi\) | ||||
−0.339038 | + | 0.940773i | \(0.610101\pi\) | |||||||
\(510\) | 3.85764 | 0.170819 | ||||||||
\(511\) | 4.44314 | 0.196553 | ||||||||
\(512\) | −5.63399 | −0.248989 | ||||||||
\(513\) | 0.503438 | 0.0222273 | ||||||||
\(514\) | 26.4123 | 1.16499 | ||||||||
\(515\) | 26.7089 | 1.17694 | ||||||||
\(516\) | 0.380627 | 0.0167562 | ||||||||
\(517\) | 0.629073 | 0.0276666 | ||||||||
\(518\) | −5.85070 | −0.257065 | ||||||||
\(519\) | 20.2032 | 0.886822 | ||||||||
\(520\) | 6.27590 | 0.275216 | ||||||||
\(521\) | 16.0166 | 0.701702 | 0.350851 | − | 0.936431i | \(-0.385892\pi\) | ||||
0.350851 | + | 0.936431i | \(0.385892\pi\) | |||||||
\(522\) | 11.9626 | 0.523589 | ||||||||
\(523\) | −28.2136 | −1.23369 | −0.616847 | − | 0.787083i | \(-0.711590\pi\) | ||||
−0.616847 | + | 0.787083i | \(0.711590\pi\) | |||||||
\(524\) | 3.78694 | 0.165433 | ||||||||
\(525\) | 0.602358 | 0.0262890 | ||||||||
\(526\) | 32.3188 | 1.40917 | ||||||||
\(527\) | −3.71579 | −0.161862 | ||||||||
\(528\) | 3.72757 | 0.162222 | ||||||||
\(529\) | −7.21909 | −0.313873 | ||||||||
\(530\) | −2.40871 | −0.104628 | ||||||||
\(531\) | 14.5620 | 0.631935 | ||||||||
\(532\) | 0.461600 | 0.0200129 | ||||||||
\(533\) | 3.97139 | 0.172020 | ||||||||
\(534\) | −3.97984 | −0.172225 | ||||||||
\(535\) | 30.2296 | 1.30694 | ||||||||
\(536\) | 23.7405 | 1.02543 | ||||||||
\(537\) | 4.86978 | 0.210147 | ||||||||
\(538\) | −22.5247 | −0.971110 | ||||||||
\(539\) | −0.746546 | −0.0321560 | ||||||||
\(540\) | 2.17023 | 0.0933916 | ||||||||
\(541\) | 7.82222 | 0.336303 | 0.168152 | − | 0.985761i | \(-0.446220\pi\) | ||||
0.168152 | + | 0.985761i | \(0.446220\pi\) | |||||||
\(542\) | 42.4875 | 1.82500 | ||||||||
\(543\) | 9.52144 | 0.408604 | ||||||||
\(544\) | −4.60727 | −0.197535 | ||||||||
\(545\) | 11.3188 | 0.484843 | ||||||||
\(546\) | −2.44805 | −0.104767 | ||||||||
\(547\) | 32.3132 | 1.38161 | 0.690806 | − | 0.723040i | \(-0.257256\pi\) | ||||
0.690806 | + | 0.723040i | \(0.257256\pi\) | |||||||
\(548\) | −12.1404 | −0.518612 | ||||||||
\(549\) | −7.43261 | −0.317216 | ||||||||
\(550\) | 0.768018 | 0.0327484 | ||||||||
\(551\) | −3.52624 | −0.150223 | ||||||||
\(552\) | 7.34847 | 0.312772 | ||||||||
\(553\) | −10.2846 | −0.437348 | ||||||||
\(554\) | −9.44241 | −0.401170 | ||||||||
\(555\) | 8.10836 | 0.344181 | ||||||||
\(556\) | −21.2994 | −0.903294 | ||||||||
\(557\) | 17.0617 | 0.722929 | 0.361464 | − | 0.932386i | \(-0.382277\pi\) | ||||
0.361464 | + | 0.932386i | \(0.382277\pi\) | |||||||
\(558\) | −6.65022 | −0.281526 | ||||||||
\(559\) | 0.595031 | 0.0251671 | ||||||||
\(560\) | −11.8183 | −0.499414 | ||||||||
\(561\) | 0.712414 | 0.0300781 | ||||||||
\(562\) | −17.2046 | −0.725733 | ||||||||
\(563\) | −7.44612 | −0.313817 | −0.156908 | − | 0.987613i | \(-0.550153\pi\) | ||||
−0.156908 | + | 0.987613i | \(0.550153\pi\) | |||||||
\(564\) | −0.772617 | −0.0325330 | ||||||||
\(565\) | 38.5511 | 1.62186 | ||||||||
\(566\) | 51.9619 | 2.18412 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 22.0755 | 0.926266 | ||||||||
\(569\) | −27.4004 | −1.14868 | −0.574341 | − | 0.818616i | \(-0.694742\pi\) | ||||
−0.574341 | + | 0.818616i | \(0.694742\pi\) | |||||||
\(570\) | −2.03513 | −0.0852422 | ||||||||
\(571\) | 0.577266 | 0.0241578 | 0.0120789 | − | 0.999927i | \(-0.496155\pi\) | ||||
0.0120789 | + | 0.999927i | \(0.496155\pi\) | |||||||
\(572\) | −0.981151 | −0.0410240 | ||||||||
\(573\) | 1.00000 | 0.0417756 | ||||||||
\(574\) | −4.73199 | −0.197509 | ||||||||
\(575\) | 2.39288 | 0.0997899 | ||||||||
\(576\) | 1.74047 | 0.0725195 | ||||||||
\(577\) | −22.4514 | −0.934663 | −0.467331 | − | 0.884082i | \(-0.654785\pi\) | ||||
−0.467331 | + | 0.884082i | \(0.654785\pi\) | |||||||
\(578\) | 27.4789 | 1.14297 | ||||||||
\(579\) | −4.40259 | −0.182965 | ||||||||
\(580\) | −15.2009 | −0.631184 | ||||||||
\(581\) | −12.8515 | −0.533168 | ||||||||
\(582\) | 0.972150 | 0.0402969 | ||||||||
\(583\) | −0.444831 | −0.0184230 | ||||||||
\(584\) | 8.21904 | 0.340106 | ||||||||
\(585\) | 3.39270 | 0.140271 | ||||||||
\(586\) | 25.0792 | 1.03601 | ||||||||
\(587\) | 22.8094 | 0.941445 | 0.470722 | − | 0.882281i | \(-0.343993\pi\) | ||||
0.470722 | + | 0.882281i | \(0.343993\pi\) | |||||||
\(588\) | 0.916895 | 0.0378121 | ||||||||
\(589\) | 1.96030 | 0.0807727 | ||||||||
\(590\) | −58.8661 | −2.42348 | ||||||||
\(591\) | 24.3950 | 1.00348 | ||||||||
\(592\) | −17.1048 | −0.703002 | ||||||||
\(593\) | −11.4661 | −0.470856 | −0.235428 | − | 0.971892i | \(-0.575649\pi\) | ||||
−0.235428 | + | 0.971892i | \(0.575649\pi\) | |||||||
\(594\) | 1.27502 | 0.0523147 | ||||||||
\(595\) | −2.25871 | −0.0925982 | ||||||||
\(596\) | −13.4853 | −0.552379 | ||||||||
\(597\) | −0.175370 | −0.00717741 | ||||||||
\(598\) | −9.72492 | −0.397682 | ||||||||
\(599\) | 16.6536 | 0.680447 | 0.340224 | − | 0.940345i | \(-0.389497\pi\) | ||||
0.340224 | + | 0.940345i | \(0.389497\pi\) | |||||||
\(600\) | 1.11426 | 0.0454894 | ||||||||
\(601\) | 37.9878 | 1.54956 | 0.774778 | − | 0.632234i | \(-0.217862\pi\) | ||||
0.774778 | + | 0.632234i | \(0.217862\pi\) | |||||||
\(602\) | −0.708991 | −0.0288963 | ||||||||
\(603\) | 12.8339 | 0.522636 | ||||||||
\(604\) | −9.13260 | −0.371600 | ||||||||
\(605\) | −24.7171 | −1.00489 | ||||||||
\(606\) | −17.2572 | −0.701025 | ||||||||
\(607\) | −37.2374 | −1.51142 | −0.755711 | − | 0.654906i | \(-0.772708\pi\) | ||||
−0.755711 | + | 0.654906i | \(0.772708\pi\) | |||||||
\(608\) | 2.43061 | 0.0985741 | ||||||||
\(609\) | −7.00431 | −0.283829 | ||||||||
\(610\) | 30.0460 | 1.21653 | ||||||||
\(611\) | −1.20783 | −0.0488634 | ||||||||
\(612\) | −0.874974 | −0.0353687 | ||||||||
\(613\) | −38.2344 | −1.54427 | −0.772137 | − | 0.635456i | \(-0.780812\pi\) | ||||
−0.772137 | + | 0.635456i | \(0.780812\pi\) | |||||||
\(614\) | −26.2103 | −1.05776 | ||||||||
\(615\) | 6.55796 | 0.264442 | ||||||||
\(616\) | −1.38098 | −0.0556413 | ||||||||
\(617\) | 6.80928 | 0.274131 | 0.137066 | − | 0.990562i | \(-0.456233\pi\) | ||||
0.137066 | + | 0.990562i | \(0.456233\pi\) | |||||||
\(618\) | −19.2722 | −0.775242 | ||||||||
\(619\) | 23.9525 | 0.962734 | 0.481367 | − | 0.876519i | \(-0.340140\pi\) | ||||
0.481367 | + | 0.876519i | \(0.340140\pi\) | |||||||
\(620\) | 8.45046 | 0.339379 | ||||||||
\(621\) | 3.97252 | 0.159412 | ||||||||
\(622\) | 5.96183 | 0.239048 | ||||||||
\(623\) | 2.33027 | 0.0933602 | ||||||||
\(624\) | −7.15697 | −0.286508 | ||||||||
\(625\) | −27.6490 | −1.10596 | ||||||||
\(626\) | −12.2154 | −0.488224 | ||||||||
\(627\) | −0.375840 | −0.0150096 | ||||||||
\(628\) | 8.89114 | 0.354795 | ||||||||
\(629\) | −3.26907 | −0.130346 | ||||||||
\(630\) | −4.04246 | −0.161055 | ||||||||
\(631\) | −28.9444 | −1.15226 | −0.576129 | − | 0.817359i | \(-0.695437\pi\) | ||||
−0.576129 | + | 0.817359i | \(0.695437\pi\) | |||||||
\(632\) | −19.0248 | −0.756766 | ||||||||
\(633\) | −14.1014 | −0.560482 | ||||||||
\(634\) | 23.0711 | 0.916269 | ||||||||
\(635\) | 37.1978 | 1.47615 | ||||||||
\(636\) | 0.546333 | 0.0216635 | ||||||||
\(637\) | 1.43337 | 0.0567924 | ||||||||
\(638\) | −8.93063 | −0.353567 | ||||||||
\(639\) | 11.9338 | 0.472094 | ||||||||
\(640\) | −29.8909 | −1.18154 | ||||||||
\(641\) | 6.98089 | 0.275729 | 0.137864 | − | 0.990451i | \(-0.455976\pi\) | ||||
0.137864 | + | 0.990451i | \(0.455976\pi\) | |||||||
\(642\) | −21.8126 | −0.860873 | ||||||||
\(643\) | −41.2065 | −1.62503 | −0.812513 | − | 0.582943i | \(-0.801901\pi\) | ||||
−0.812513 | + | 0.582943i | \(0.801901\pi\) | |||||||
\(644\) | 3.64238 | 0.143530 | ||||||||
\(645\) | 0.982575 | 0.0386888 | ||||||||
\(646\) | 0.820507 | 0.0322824 | ||||||||
\(647\) | −23.8577 | −0.937944 | −0.468972 | − | 0.883213i | \(-0.655376\pi\) | ||||
−0.468972 | + | 0.883213i | \(0.655376\pi\) | |||||||
\(648\) | 1.84983 | 0.0726681 | ||||||||
\(649\) | −10.8712 | −0.426731 | ||||||||
\(650\) | −1.47460 | −0.0578386 | ||||||||
\(651\) | 3.89382 | 0.152611 | ||||||||
\(652\) | −18.6254 | −0.729426 | ||||||||
\(653\) | 39.5460 | 1.54755 | 0.773777 | − | 0.633459i | \(-0.218365\pi\) | ||||
0.773777 | + | 0.633459i | \(0.218365\pi\) | |||||||
\(654\) | −8.16722 | −0.319364 | ||||||||
\(655\) | 9.77585 | 0.381974 | ||||||||
\(656\) | −13.8342 | −0.540133 | ||||||||
\(657\) | 4.44314 | 0.173344 | ||||||||
\(658\) | 1.43915 | 0.0561038 | ||||||||
\(659\) | 0.428389 | 0.0166876 | 0.00834382 | − | 0.999965i | \(-0.497344\pi\) | ||||
0.00834382 | + | 0.999965i | \(0.497344\pi\) | |||||||
\(660\) | −1.62017 | −0.0630652 | ||||||||
\(661\) | 37.8857 | 1.47358 | 0.736791 | − | 0.676121i | \(-0.236340\pi\) | ||||
0.736791 | + | 0.676121i | \(0.236340\pi\) | |||||||
\(662\) | 36.8560 | 1.43245 | ||||||||
\(663\) | −1.36784 | −0.0531225 | ||||||||
\(664\) | −23.7730 | −0.922571 | ||||||||
\(665\) | 1.19160 | 0.0462084 | ||||||||
\(666\) | −5.85070 | −0.226710 | ||||||||
\(667\) | −27.8247 | −1.07738 | ||||||||
\(668\) | 0.993044 | 0.0384220 | ||||||||
\(669\) | −3.29267 | −0.127302 | ||||||||
\(670\) | −51.8805 | −2.00432 | ||||||||
\(671\) | 5.54878 | 0.214208 | ||||||||
\(672\) | 4.82801 | 0.186245 | ||||||||
\(673\) | 29.6589 | 1.14327 | 0.571633 | − | 0.820509i | \(-0.306310\pi\) | ||||
0.571633 | + | 0.820509i | \(0.306310\pi\) | |||||||
\(674\) | −38.2252 | −1.47238 | ||||||||
\(675\) | 0.602358 | 0.0231848 | ||||||||
\(676\) | −10.0358 | −0.385993 | ||||||||
\(677\) | −11.6409 | −0.447396 | −0.223698 | − | 0.974659i | \(-0.571813\pi\) | ||||
−0.223698 | + | 0.974659i | \(0.571813\pi\) | |||||||
\(678\) | −27.8171 | −1.06831 | ||||||||
\(679\) | −0.569211 | −0.0218443 | ||||||||
\(680\) | −4.17823 | −0.160228 | ||||||||
\(681\) | 1.78164 | 0.0682727 | ||||||||
\(682\) | 4.96470 | 0.190108 | ||||||||
\(683\) | −7.68360 | −0.294005 | −0.147002 | − | 0.989136i | \(-0.546962\pi\) | ||||
−0.147002 | + | 0.989136i | \(0.546962\pi\) | |||||||
\(684\) | 0.461600 | 0.0176497 | ||||||||
\(685\) | −31.3400 | −1.19744 | ||||||||
\(686\) | −1.70789 | −0.0652076 | ||||||||
\(687\) | −22.0061 | −0.839586 | ||||||||
\(688\) | −2.07276 | −0.0790234 | ||||||||
\(689\) | 0.854078 | 0.0325378 | ||||||||
\(690\) | −16.0588 | −0.611346 | ||||||||
\(691\) | 34.3930 | 1.30837 | 0.654185 | − | 0.756335i | \(-0.273012\pi\) | ||||
0.654185 | + | 0.756335i | \(0.273012\pi\) | |||||||
\(692\) | 18.5242 | 0.704185 | ||||||||
\(693\) | −0.746546 | −0.0283589 | ||||||||
\(694\) | −40.6930 | −1.54469 | ||||||||
\(695\) | −54.9835 | −2.08564 | ||||||||
\(696\) | −12.9568 | −0.491125 | ||||||||
\(697\) | −2.64399 | −0.100148 | ||||||||
\(698\) | 5.09884 | 0.192994 | ||||||||
\(699\) | 21.8651 | 0.827015 | ||||||||
\(700\) | 0.552298 | 0.0208749 | ||||||||
\(701\) | 25.5989 | 0.966857 | 0.483428 | − | 0.875384i | \(-0.339391\pi\) | ||||
0.483428 | + | 0.875384i | \(0.339391\pi\) | |||||||
\(702\) | −2.44805 | −0.0923956 | ||||||||
\(703\) | 1.72462 | 0.0650454 | ||||||||
\(704\) | −1.29934 | −0.0489707 | ||||||||
\(705\) | −1.99448 | −0.0751165 | ||||||||
\(706\) | 22.9278 | 0.862899 | ||||||||
\(707\) | 10.1044 | 0.380014 | ||||||||
\(708\) | 13.3518 | 0.501791 | ||||||||
\(709\) | −45.9736 | −1.72658 | −0.863288 | − | 0.504712i | \(-0.831599\pi\) | ||||
−0.863288 | + | 0.504712i | \(0.831599\pi\) | |||||||
\(710\) | −48.2419 | −1.81049 | ||||||||
\(711\) | −10.2846 | −0.385704 | ||||||||
\(712\) | 4.31059 | 0.161546 | ||||||||
\(713\) | 15.4683 | 0.579291 | ||||||||
\(714\) | 1.62981 | 0.0609940 | ||||||||
\(715\) | −2.53280 | −0.0947215 | ||||||||
\(716\) | 4.46508 | 0.166868 | ||||||||
\(717\) | 19.9407 | 0.744701 | ||||||||
\(718\) | 39.6215 | 1.47866 | ||||||||
\(719\) | 8.85492 | 0.330233 | 0.165116 | − | 0.986274i | \(-0.447200\pi\) | ||||
0.165116 | + | 0.986274i | \(0.447200\pi\) | |||||||
\(720\) | −11.8183 | −0.440442 | ||||||||
\(721\) | 11.2842 | 0.420246 | ||||||||
\(722\) | 32.0171 | 1.19155 | ||||||||
\(723\) | 12.3395 | 0.458909 | ||||||||
\(724\) | 8.73015 | 0.324454 | ||||||||
\(725\) | −4.21910 | −0.156693 | ||||||||
\(726\) | 17.8349 | 0.661917 | ||||||||
\(727\) | −17.0445 | −0.632147 | −0.316073 | − | 0.948735i | \(-0.602365\pi\) | ||||
−0.316073 | + | 0.948735i | \(0.602365\pi\) | |||||||
\(728\) | 2.65149 | 0.0982709 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −17.9612 | −0.664775 | ||||||||
\(731\) | −0.396147 | −0.0146520 | ||||||||
\(732\) | −6.81492 | −0.251887 | ||||||||
\(733\) | −18.3332 | −0.677153 | −0.338576 | − | 0.940939i | \(-0.609945\pi\) | ||||
−0.338576 | + | 0.940939i | \(0.609945\pi\) | |||||||
\(734\) | −17.6534 | −0.651598 | ||||||||
\(735\) | 2.36693 | 0.0873055 | ||||||||
\(736\) | 19.1794 | 0.706961 | ||||||||
\(737\) | −9.58109 | −0.352924 | ||||||||
\(738\) | −4.73199 | −0.174187 | ||||||||
\(739\) | 24.4925 | 0.900971 | 0.450486 | − | 0.892784i | \(-0.351251\pi\) | ||||
0.450486 | + | 0.892784i | \(0.351251\pi\) | |||||||
\(740\) | 7.43451 | 0.273298 | ||||||||
\(741\) | 0.721616 | 0.0265092 | ||||||||
\(742\) | −1.01765 | −0.0373591 | ||||||||
\(743\) | −38.3160 | −1.40568 | −0.702839 | − | 0.711349i | \(-0.748085\pi\) | ||||
−0.702839 | + | 0.711349i | \(0.748085\pi\) | |||||||
\(744\) | 7.20289 | 0.264071 | ||||||||
\(745\) | −34.8118 | −1.27540 | ||||||||
\(746\) | −33.6814 | −1.23316 | ||||||||
\(747\) | −12.8515 | −0.470210 | ||||||||
\(748\) | 0.653208 | 0.0238837 | ||||||||
\(749\) | 12.7716 | 0.466665 | ||||||||
\(750\) | 17.7773 | 0.649135 | ||||||||
\(751\) | 19.2324 | 0.701799 | 0.350899 | − | 0.936413i | \(-0.385876\pi\) | ||||
0.350899 | + | 0.936413i | \(0.385876\pi\) | |||||||
\(752\) | 4.20741 | 0.153428 | ||||||||
\(753\) | 22.6131 | 0.824068 | ||||||||
\(754\) | 17.1469 | 0.624453 | ||||||||
\(755\) | −23.5755 | −0.857999 | ||||||||
\(756\) | 0.916895 | 0.0333471 | ||||||||
\(757\) | −27.0104 | −0.981711 | −0.490856 | − | 0.871241i | \(-0.663316\pi\) | ||||
−0.490856 | + | 0.871241i | \(0.663316\pi\) | |||||||
\(758\) | −33.7990 | −1.22764 | ||||||||
\(759\) | −2.96567 | −0.107647 | ||||||||
\(760\) | 2.20426 | 0.0799569 | ||||||||
\(761\) | −15.8137 | −0.573248 | −0.286624 | − | 0.958043i | \(-0.592533\pi\) | ||||
−0.286624 | + | 0.958043i | \(0.592533\pi\) | |||||||
\(762\) | −26.8406 | −0.972332 | ||||||||
\(763\) | 4.78205 | 0.173122 | ||||||||
\(764\) | 0.916895 | 0.0331721 | ||||||||
\(765\) | −2.25871 | −0.0816640 | ||||||||
\(766\) | 30.2989 | 1.09474 | ||||||||
\(767\) | 20.8727 | 0.753671 | ||||||||
\(768\) | 18.0873 | 0.652668 | ||||||||
\(769\) | 17.4587 | 0.629576 | 0.314788 | − | 0.949162i | \(-0.398067\pi\) | ||||
0.314788 | + | 0.949162i | \(0.398067\pi\) | |||||||
\(770\) | 3.01788 | 0.108757 | ||||||||
\(771\) | −15.4648 | −0.556952 | ||||||||
\(772\) | −4.03671 | −0.145284 | ||||||||
\(773\) | −35.2203 | −1.26679 | −0.633394 | − | 0.773830i | \(-0.718339\pi\) | ||||
−0.633394 | + | 0.773830i | \(0.718339\pi\) | |||||||
\(774\) | −0.708991 | −0.0254841 | ||||||||
\(775\) | 2.34547 | 0.0842518 | ||||||||
\(776\) | −1.05294 | −0.0377984 | ||||||||
\(777\) | 3.42569 | 0.122896 | ||||||||
\(778\) | −37.2249 | −1.33458 | ||||||||
\(779\) | 1.39486 | 0.0499759 | ||||||||
\(780\) | 3.11075 | 0.111383 | ||||||||
\(781\) | −8.90914 | −0.318794 | ||||||||
\(782\) | 6.47444 | 0.231525 | ||||||||
\(783\) | −7.00431 | −0.250313 | ||||||||
\(784\) | −4.99309 | −0.178325 | ||||||||
\(785\) | 22.9522 | 0.819198 | ||||||||
\(786\) | −7.05390 | −0.251604 | ||||||||
\(787\) | 42.1517 | 1.50255 | 0.751273 | − | 0.659992i | \(-0.229440\pi\) | ||||
0.751273 | + | 0.659992i | \(0.229440\pi\) | |||||||
\(788\) | 22.3677 | 0.796815 | ||||||||
\(789\) | −18.9232 | −0.673685 | ||||||||
\(790\) | 41.5753 | 1.47918 | ||||||||
\(791\) | 16.2874 | 0.579113 | ||||||||
\(792\) | −1.38098 | −0.0490710 | ||||||||
\(793\) | −10.6537 | −0.378324 | ||||||||
\(794\) | −57.0168 | −2.02345 | ||||||||
\(795\) | 1.41034 | 0.0500196 | ||||||||
\(796\) | −0.160796 | −0.00569925 | ||||||||
\(797\) | −31.0489 | −1.09981 | −0.549904 | − | 0.835228i | \(-0.685336\pi\) | ||||
−0.549904 | + | 0.835228i | \(0.685336\pi\) | |||||||
\(798\) | −0.859818 | −0.0304372 | ||||||||
\(799\) | 0.804119 | 0.0284477 | ||||||||
\(800\) | 2.90819 | 0.102820 | ||||||||
\(801\) | 2.33027 | 0.0823359 | ||||||||
\(802\) | −42.2235 | −1.49096 | ||||||||
\(803\) | −3.31701 | −0.117055 | ||||||||
\(804\) | 11.7673 | 0.415002 | ||||||||
\(805\) | 9.40268 | 0.331401 | ||||||||
\(806\) | −9.53226 | −0.335759 | ||||||||
\(807\) | 13.1886 | 0.464261 | ||||||||
\(808\) | 18.6913 | 0.657559 | ||||||||
\(809\) | 16.4521 | 0.578425 | 0.289213 | − | 0.957265i | \(-0.406607\pi\) | ||||
0.289213 | + | 0.957265i | \(0.406607\pi\) | |||||||
\(810\) | −4.04246 | −0.142038 | ||||||||
\(811\) | −7.60557 | −0.267068 | −0.133534 | − | 0.991044i | \(-0.542633\pi\) | ||||
−0.133534 | + | 0.991044i | \(0.542633\pi\) | |||||||
\(812\) | −6.42221 | −0.225375 | ||||||||
\(813\) | −24.8772 | −0.872481 | ||||||||
\(814\) | 4.36782 | 0.153092 | ||||||||
\(815\) | −48.0807 | −1.68419 | ||||||||
\(816\) | 4.76481 | 0.166802 | ||||||||
\(817\) | 0.208990 | 0.00731165 | ||||||||
\(818\) | −3.81468 | −0.133377 | ||||||||
\(819\) | 1.43337 | 0.0500862 | ||||||||
\(820\) | 6.01296 | 0.209982 | ||||||||
\(821\) | 26.2294 | 0.915412 | 0.457706 | − | 0.889104i | \(-0.348671\pi\) | ||||
0.457706 | + | 0.889104i | \(0.348671\pi\) | |||||||
\(822\) | 22.6138 | 0.788748 | ||||||||
\(823\) | 18.7004 | 0.651856 | 0.325928 | − | 0.945395i | \(-0.394323\pi\) | ||||
0.325928 | + | 0.945395i | \(0.394323\pi\) | |||||||
\(824\) | 20.8738 | 0.727175 | ||||||||
\(825\) | −0.449688 | −0.0156561 | ||||||||
\(826\) | −24.8702 | −0.865346 | ||||||||
\(827\) | 7.57979 | 0.263575 | 0.131787 | − | 0.991278i | \(-0.457928\pi\) | ||||
0.131787 | + | 0.991278i | \(0.457928\pi\) | |||||||
\(828\) | 3.64238 | 0.126582 | ||||||||
\(829\) | 30.0250 | 1.04281 | 0.521406 | − | 0.853309i | \(-0.325408\pi\) | ||||
0.521406 | + | 0.853309i | \(0.325408\pi\) | |||||||
\(830\) | 51.9515 | 1.80326 | ||||||||
\(831\) | 5.52870 | 0.191788 | ||||||||
\(832\) | 2.49474 | 0.0864896 | ||||||||
\(833\) | −0.954280 | −0.0330638 | ||||||||
\(834\) | 39.6741 | 1.37380 | ||||||||
\(835\) | 2.56351 | 0.0887139 | ||||||||
\(836\) | −0.344606 | −0.0119184 | ||||||||
\(837\) | 3.89382 | 0.134590 | ||||||||
\(838\) | −10.2453 | −0.353918 | ||||||||
\(839\) | −50.6858 | −1.74987 | −0.874934 | − | 0.484241i | \(-0.839096\pi\) | ||||
−0.874934 | + | 0.484241i | \(0.839096\pi\) | |||||||
\(840\) | 4.37841 | 0.151070 | ||||||||
\(841\) | 20.0603 | 0.691735 | ||||||||
\(842\) | 34.2559 | 1.18054 | ||||||||
\(843\) | 10.0736 | 0.346953 | ||||||||
\(844\) | −12.9295 | −0.445053 | ||||||||
\(845\) | −25.9071 | −0.891231 | ||||||||
\(846\) | 1.43915 | 0.0494789 | ||||||||
\(847\) | −10.4427 | −0.358814 | ||||||||
\(848\) | −2.97514 | −0.102167 | ||||||||
\(849\) | −30.4246 | −1.04417 | ||||||||
\(850\) | 0.981727 | 0.0336729 | ||||||||
\(851\) | 13.6086 | 0.466497 | ||||||||
\(852\) | 10.9420 | 0.374868 | ||||||||
\(853\) | −56.1334 | −1.92197 | −0.960986 | − | 0.276598i | \(-0.910793\pi\) | ||||
−0.960986 | + | 0.276598i | \(0.910793\pi\) | |||||||
\(854\) | 12.6941 | 0.434383 | ||||||||
\(855\) | 1.19160 | 0.0407520 | ||||||||
\(856\) | 23.6253 | 0.807496 | ||||||||
\(857\) | −41.2925 | −1.41053 | −0.705263 | − | 0.708946i | \(-0.749171\pi\) | ||||
−0.705263 | + | 0.708946i | \(0.749171\pi\) | |||||||
\(858\) | 1.82758 | 0.0623926 | ||||||||
\(859\) | −26.9755 | −0.920392 | −0.460196 | − | 0.887817i | \(-0.652221\pi\) | ||||
−0.460196 | + | 0.887817i | \(0.652221\pi\) | |||||||
\(860\) | 0.900917 | 0.0307210 | ||||||||
\(861\) | 2.77066 | 0.0944239 | ||||||||
\(862\) | −52.6991 | −1.79494 | ||||||||
\(863\) | −11.9250 | −0.405933 | −0.202966 | − | 0.979186i | \(-0.565058\pi\) | ||||
−0.202966 | + | 0.979186i | \(0.565058\pi\) | |||||||
\(864\) | 4.82801 | 0.164252 | ||||||||
\(865\) | 47.8196 | 1.62591 | ||||||||
\(866\) | −61.0985 | −2.07621 | ||||||||
\(867\) | −16.0893 | −0.546423 | ||||||||
\(868\) | 3.57022 | 0.121181 | ||||||||
\(869\) | 7.67796 | 0.260457 | ||||||||
\(870\) | 28.3146 | 0.959956 | ||||||||
\(871\) | 18.3958 | 0.623317 | ||||||||
\(872\) | 8.84596 | 0.299562 | ||||||||
\(873\) | −0.569211 | −0.0192649 | ||||||||
\(874\) | −3.41565 | −0.115536 | ||||||||
\(875\) | −10.4089 | −0.351885 | ||||||||
\(876\) | 4.07389 | 0.137644 | ||||||||
\(877\) | −24.2848 | −0.820038 | −0.410019 | − | 0.912077i | \(-0.634478\pi\) | ||||
−0.410019 | + | 0.912077i | \(0.634478\pi\) | |||||||
\(878\) | 34.0705 | 1.14982 | ||||||||
\(879\) | −14.6843 | −0.495290 | ||||||||
\(880\) | 8.82291 | 0.297420 | ||||||||
\(881\) | −20.8148 | −0.701267 | −0.350633 | − | 0.936513i | \(-0.614034\pi\) | ||||
−0.350633 | + | 0.936513i | \(0.614034\pi\) | |||||||
\(882\) | −1.70789 | −0.0575077 | ||||||||
\(883\) | −5.60631 | −0.188667 | −0.0943337 | − | 0.995541i | \(-0.530072\pi\) | ||||
−0.0943337 | + | 0.995541i | \(0.530072\pi\) | |||||||
\(884\) | −1.25417 | −0.0421821 | ||||||||
\(885\) | 34.4671 | 1.15860 | ||||||||
\(886\) | −19.8293 | −0.666179 | ||||||||
\(887\) | −22.1866 | −0.744953 | −0.372476 | − | 0.928042i | \(-0.621491\pi\) | ||||
−0.372476 | + | 0.928042i | \(0.621491\pi\) | |||||||
\(888\) | 6.33693 | 0.212653 | ||||||||
\(889\) | 15.7156 | 0.527085 | ||||||||
\(890\) | −9.42001 | −0.315759 | ||||||||
\(891\) | −0.746546 | −0.0250102 | ||||||||
\(892\) | −3.01903 | −0.101084 | ||||||||
\(893\) | −0.424220 | −0.0141960 | ||||||||
\(894\) | 25.1189 | 0.840103 | ||||||||
\(895\) | 11.5264 | 0.385286 | ||||||||
\(896\) | −12.6286 | −0.421890 | ||||||||
\(897\) | 5.69411 | 0.190121 | ||||||||
\(898\) | −65.8137 | −2.19623 | ||||||||
\(899\) | −27.2735 | −0.909622 | ||||||||
\(900\) | 0.552298 | 0.0184099 | ||||||||
\(901\) | −0.568609 | −0.0189431 | ||||||||
\(902\) | 3.53265 | 0.117624 | ||||||||
\(903\) | 0.415126 | 0.0138145 | ||||||||
\(904\) | 30.1289 | 1.00207 | ||||||||
\(905\) | 22.5366 | 0.749141 | ||||||||
\(906\) | 17.0112 | 0.565160 | ||||||||
\(907\) | −0.353016 | −0.0117217 | −0.00586086 | − | 0.999983i | \(-0.501866\pi\) | ||||
−0.00586086 | + | 0.999983i | \(0.501866\pi\) | |||||||
\(908\) | 1.63358 | 0.0542122 | ||||||||
\(909\) | 10.1044 | 0.335141 | ||||||||
\(910\) | −5.79436 | −0.192081 | ||||||||
\(911\) | 2.60705 | 0.0863755 | 0.0431877 | − | 0.999067i | \(-0.486249\pi\) | ||||
0.0431877 | + | 0.999067i | \(0.486249\pi\) | |||||||
\(912\) | −2.51372 | −0.0832374 | ||||||||
\(913\) | 9.59421 | 0.317522 | ||||||||
\(914\) | −42.8946 | −1.41883 | ||||||||
\(915\) | −17.5925 | −0.581589 | ||||||||
\(916\) | −20.1773 | −0.666676 | ||||||||
\(917\) | 4.13018 | 0.136391 | ||||||||
\(918\) | 1.62981 | 0.0537916 | ||||||||
\(919\) | −9.64557 | −0.318178 | −0.159089 | − | 0.987264i | \(-0.550856\pi\) | ||||
−0.159089 | + | 0.987264i | \(0.550856\pi\) | |||||||
\(920\) | 17.3933 | 0.573441 | ||||||||
\(921\) | 15.3466 | 0.505687 | ||||||||
\(922\) | −45.4611 | −1.49718 | ||||||||
\(923\) | 17.1056 | 0.563038 | ||||||||
\(924\) | −0.684504 | −0.0225185 | ||||||||
\(925\) | 2.06349 | 0.0678471 | ||||||||
\(926\) | −19.1038 | −0.627789 | ||||||||
\(927\) | 11.2842 | 0.370622 | ||||||||
\(928\) | −33.8169 | −1.11009 | ||||||||
\(929\) | −38.1951 | −1.25314 | −0.626570 | − | 0.779365i | \(-0.715542\pi\) | ||||
−0.626570 | + | 0.779365i | \(0.715542\pi\) | |||||||
\(930\) | −15.7406 | −0.516155 | ||||||||
\(931\) | 0.503438 | 0.0164995 | ||||||||
\(932\) | 20.0480 | 0.656695 | ||||||||
\(933\) | −3.49075 | −0.114282 | ||||||||
\(934\) | 24.4842 | 0.801148 | ||||||||
\(935\) | 1.68623 | 0.0551457 | ||||||||
\(936\) | 2.65149 | 0.0866668 | ||||||||
\(937\) | −1.80104 | −0.0588373 | −0.0294186 | − | 0.999567i | \(-0.509366\pi\) | ||||
−0.0294186 | + | 0.999567i | \(0.509366\pi\) | |||||||
\(938\) | −21.9189 | −0.715677 | ||||||||
\(939\) | 7.15230 | 0.233407 | ||||||||
\(940\) | −1.82873 | −0.0596466 | ||||||||
\(941\) | −15.8526 | −0.516781 | −0.258390 | − | 0.966041i | \(-0.583192\pi\) | ||||
−0.258390 | + | 0.966041i | \(0.583192\pi\) | |||||||
\(942\) | −16.5615 | −0.539602 | ||||||||
\(943\) | 11.0065 | 0.358421 | ||||||||
\(944\) | −72.7092 | −2.36648 | ||||||||
\(945\) | 2.36693 | 0.0769962 | ||||||||
\(946\) | 0.529294 | 0.0172088 | ||||||||
\(947\) | −3.13169 | −0.101766 | −0.0508832 | − | 0.998705i | \(-0.516204\pi\) | ||||
−0.0508832 | + | 0.998705i | \(0.516204\pi\) | |||||||
\(948\) | −9.42994 | −0.306270 | ||||||||
\(949\) | 6.36869 | 0.206736 | ||||||||
\(950\) | −0.517918 | −0.0168035 | ||||||||
\(951\) | −13.5085 | −0.438043 | ||||||||
\(952\) | −1.76525 | −0.0572122 | ||||||||
\(953\) | −58.3557 | −1.89033 | −0.945163 | − | 0.326599i | \(-0.894097\pi\) | ||||
−0.945163 | + | 0.326599i | \(0.894097\pi\) | |||||||
\(954\) | −1.01765 | −0.0329476 | ||||||||
\(955\) | 2.36693 | 0.0765921 | ||||||||
\(956\) | 18.2836 | 0.591333 | ||||||||
\(957\) | 5.22904 | 0.169031 | ||||||||
\(958\) | 44.5254 | 1.43855 | ||||||||
\(959\) | −13.2408 | −0.427567 | ||||||||
\(960\) | 4.11957 | 0.132958 | ||||||||
\(961\) | −15.8382 | −0.510909 | ||||||||
\(962\) | −8.38625 | −0.270384 | ||||||||
\(963\) | 12.7716 | 0.411560 | ||||||||
\(964\) | 11.3140 | 0.364399 | ||||||||
\(965\) | −10.4206 | −0.335452 | ||||||||
\(966\) | −6.78463 | −0.218292 | ||||||||
\(967\) | −51.0738 | −1.64242 | −0.821211 | − | 0.570625i | \(-0.806701\pi\) | ||||
−0.821211 | + | 0.570625i | \(0.806701\pi\) | |||||||
\(968\) | −19.3171 | −0.620876 | ||||||||
\(969\) | −0.480421 | −0.0154334 | ||||||||
\(970\) | 2.30101 | 0.0738810 | ||||||||
\(971\) | −14.8890 | −0.477811 | −0.238905 | − | 0.971043i | \(-0.576789\pi\) | ||||
−0.238905 | + | 0.971043i | \(0.576789\pi\) | |||||||
\(972\) | 0.916895 | 0.0294094 | ||||||||
\(973\) | −23.2299 | −0.744716 | ||||||||
\(974\) | 53.5272 | 1.71512 | ||||||||
\(975\) | 0.863404 | 0.0276511 | ||||||||
\(976\) | 37.1117 | 1.18792 | ||||||||
\(977\) | 15.5786 | 0.498402 | 0.249201 | − | 0.968452i | \(-0.419832\pi\) | ||||
0.249201 | + | 0.968452i | \(0.419832\pi\) | |||||||
\(978\) | 34.6933 | 1.10937 | ||||||||
\(979\) | −1.73965 | −0.0555995 | ||||||||
\(980\) | 2.17023 | 0.0693253 | ||||||||
\(981\) | 4.78205 | 0.152679 | ||||||||
\(982\) | 53.8404 | 1.71811 | ||||||||
\(983\) | −0.245331 | −0.00782483 | −0.00391242 | − | 0.999992i | \(-0.501245\pi\) | ||||
−0.00391242 | + | 0.999992i | \(0.501245\pi\) | |||||||
\(984\) | 5.12524 | 0.163387 | ||||||||
\(985\) | 57.7413 | 1.83979 | ||||||||
\(986\) | −11.4157 | −0.363549 | ||||||||
\(987\) | −0.842645 | −0.0268217 | ||||||||
\(988\) | 0.661646 | 0.0210497 | ||||||||
\(989\) | 1.64910 | 0.0524382 | ||||||||
\(990\) | 3.01788 | 0.0959146 | ||||||||
\(991\) | 5.33448 | 0.169455 | 0.0847276 | − | 0.996404i | \(-0.472998\pi\) | ||||
0.0847276 | + | 0.996404i | \(0.472998\pi\) | |||||||
\(992\) | 18.7994 | 0.596881 | ||||||||
\(993\) | −21.5798 | −0.684816 | ||||||||
\(994\) | −20.3817 | −0.646467 | ||||||||
\(995\) | −0.415088 | −0.0131592 | ||||||||
\(996\) | −11.7834 | −0.373372 | ||||||||
\(997\) | 10.2018 | 0.323096 | 0.161548 | − | 0.986865i | \(-0.448351\pi\) | ||||
0.161548 | + | 0.986865i | \(0.448351\pi\) | |||||||
\(998\) | 10.1520 | 0.321356 | ||||||||
\(999\) | 3.42569 | 0.108384 |
(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 | 4011.2.a.k.1.4 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4011.2.a.k.1.4 | ✓ | 27 | 1.1 | even | 1 | trivial |