Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4007,2,Mod(1,4007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4007, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4007 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4007.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: | \(31.9960560899\) |
Analytic rank: | \(1\) |
Dimension: | \(139\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 4007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.37198 | −1.67724 | −0.838621 | − | 0.544716i | \(-0.816637\pi\) | ||||
−0.838621 | + | 0.544716i | \(0.816637\pi\) | |||||||
\(3\) | 1.06086 | 0.612489 | 0.306245 | − | 0.951953i | \(-0.400927\pi\) | ||||
0.306245 | + | 0.951953i | \(0.400927\pi\) | |||||||
\(4\) | 3.62628 | 1.81314 | ||||||||
\(5\) | 2.75167 | 1.23058 | 0.615291 | − | 0.788300i | \(-0.289038\pi\) | ||||
0.615291 | + | 0.788300i | \(0.289038\pi\) | |||||||
\(6\) | −2.51634 | −1.02729 | ||||||||
\(7\) | 1.78055 | 0.672984 | 0.336492 | − | 0.941686i | \(-0.390759\pi\) | ||||
0.336492 | + | 0.941686i | \(0.390759\pi\) | |||||||
\(8\) | −3.85749 | −1.36383 | ||||||||
\(9\) | −1.87457 | −0.624857 | ||||||||
\(10\) | −6.52689 | −2.06398 | ||||||||
\(11\) | −0.928447 | −0.279937 | −0.139969 | − | 0.990156i | \(-0.544700\pi\) | ||||
−0.139969 | + | 0.990156i | \(0.544700\pi\) | |||||||
\(12\) | 3.84698 | 1.11053 | ||||||||
\(13\) | 0.274681 | 0.0761827 | 0.0380914 | − | 0.999274i | \(-0.487872\pi\) | ||||
0.0380914 | + | 0.999274i | \(0.487872\pi\) | |||||||
\(14\) | −4.22342 | −1.12876 | ||||||||
\(15\) | 2.91914 | 0.753719 | ||||||||
\(16\) | 1.89733 | 0.474332 | ||||||||
\(17\) | 1.61331 | 0.391286 | 0.195643 | − | 0.980675i | \(-0.437321\pi\) | ||||
0.195643 | + | 0.980675i | \(0.437321\pi\) | |||||||
\(18\) | 4.44644 | 1.04804 | ||||||||
\(19\) | −7.95141 | −1.82418 | −0.912090 | − | 0.409991i | \(-0.865532\pi\) | ||||
−0.912090 | + | 0.409991i | \(0.865532\pi\) | |||||||
\(20\) | 9.97830 | 2.23122 | ||||||||
\(21\) | 1.88892 | 0.412196 | ||||||||
\(22\) | 2.20225 | 0.469522 | ||||||||
\(23\) | −1.17201 | −0.244381 | −0.122190 | − | 0.992507i | \(-0.538992\pi\) | ||||
−0.122190 | + | 0.992507i | \(0.538992\pi\) | |||||||
\(24\) | −4.09227 | −0.835331 | ||||||||
\(25\) | 2.57167 | 0.514333 | ||||||||
\(26\) | −0.651536 | −0.127777 | ||||||||
\(27\) | −5.17125 | −0.995208 | ||||||||
\(28\) | 6.45676 | 1.22021 | ||||||||
\(29\) | −9.59192 | −1.78117 | −0.890587 | − | 0.454812i | \(-0.849706\pi\) | ||||
−0.890587 | + | 0.454812i | \(0.849706\pi\) | |||||||
\(30\) | −6.92413 | −1.26417 | ||||||||
\(31\) | 1.26834 | 0.227801 | 0.113900 | − | 0.993492i | \(-0.463666\pi\) | ||||
0.113900 | + | 0.993492i | \(0.463666\pi\) | |||||||
\(32\) | 3.21456 | 0.568260 | ||||||||
\(33\) | −0.984955 | −0.171459 | ||||||||
\(34\) | −3.82675 | −0.656282 | ||||||||
\(35\) | 4.89947 | 0.828162 | ||||||||
\(36\) | −6.79771 | −1.13295 | ||||||||
\(37\) | 0.0610377 | 0.0100345 | 0.00501727 | − | 0.999987i | \(-0.498403\pi\) | ||||
0.00501727 | + | 0.999987i | \(0.498403\pi\) | |||||||
\(38\) | 18.8606 | 3.05959 | ||||||||
\(39\) | 0.291399 | 0.0466611 | ||||||||
\(40\) | −10.6145 | −1.67830 | ||||||||
\(41\) | −1.20569 | −0.188298 | −0.0941489 | − | 0.995558i | \(-0.530013\pi\) | ||||
−0.0941489 | + | 0.995558i | \(0.530013\pi\) | |||||||
\(42\) | −4.48047 | −0.691351 | ||||||||
\(43\) | 10.7484 | 1.63911 | 0.819555 | − | 0.573000i | \(-0.194220\pi\) | ||||
0.819555 | + | 0.573000i | \(0.194220\pi\) | |||||||
\(44\) | −3.36680 | −0.507565 | ||||||||
\(45\) | −5.15819 | −0.768938 | ||||||||
\(46\) | 2.77998 | 0.409885 | ||||||||
\(47\) | −11.4740 | −1.67366 | −0.836830 | − | 0.547462i | \(-0.815594\pi\) | ||||
−0.836830 | + | 0.547462i | \(0.815594\pi\) | |||||||
\(48\) | 2.01280 | 0.290523 | ||||||||
\(49\) | −3.82965 | −0.547093 | ||||||||
\(50\) | −6.09993 | −0.862661 | ||||||||
\(51\) | 1.71151 | 0.239659 | ||||||||
\(52\) | 0.996068 | 0.138130 | ||||||||
\(53\) | 9.41522 | 1.29328 | 0.646640 | − | 0.762795i | \(-0.276174\pi\) | ||||
0.646640 | + | 0.762795i | \(0.276174\pi\) | |||||||
\(54\) | 12.2661 | 1.66920 | ||||||||
\(55\) | −2.55478 | −0.344486 | ||||||||
\(56\) | −6.86845 | −0.917835 | ||||||||
\(57\) | −8.43536 | −1.11729 | ||||||||
\(58\) | 22.7518 | 2.98746 | ||||||||
\(59\) | −5.31749 | −0.692278 | −0.346139 | − | 0.938183i | \(-0.612507\pi\) | ||||
−0.346139 | + | 0.938183i | \(0.612507\pi\) | |||||||
\(60\) | 10.5856 | 1.36660 | ||||||||
\(61\) | −7.47755 | −0.957402 | −0.478701 | − | 0.877978i | \(-0.658892\pi\) | ||||
−0.478701 | + | 0.877978i | \(0.658892\pi\) | |||||||
\(62\) | −3.00847 | −0.382077 | ||||||||
\(63\) | −3.33776 | −0.420519 | ||||||||
\(64\) | −11.4195 | −1.42744 | ||||||||
\(65\) | 0.755830 | 0.0937491 | ||||||||
\(66\) | 2.33629 | 0.287577 | ||||||||
\(67\) | −12.2619 | −1.49803 | −0.749015 | − | 0.662553i | \(-0.769473\pi\) | ||||
−0.749015 | + | 0.662553i | \(0.769473\pi\) | |||||||
\(68\) | 5.85033 | 0.709456 | ||||||||
\(69\) | −1.24334 | −0.149681 | ||||||||
\(70\) | −11.6214 | −1.38903 | ||||||||
\(71\) | 16.1915 | 1.92157 | 0.960787 | − | 0.277288i | \(-0.0894355\pi\) | ||||
0.960787 | + | 0.277288i | \(0.0894355\pi\) | |||||||
\(72\) | 7.23114 | 0.852198 | ||||||||
\(73\) | −2.66305 | −0.311687 | −0.155843 | − | 0.987782i | \(-0.549810\pi\) | ||||
−0.155843 | + | 0.987782i | \(0.549810\pi\) | |||||||
\(74\) | −0.144780 | −0.0168303 | ||||||||
\(75\) | 2.72818 | 0.315024 | ||||||||
\(76\) | −28.8340 | −3.30749 | ||||||||
\(77\) | −1.65314 | −0.188393 | ||||||||
\(78\) | −0.691191 | −0.0782619 | ||||||||
\(79\) | −2.58260 | −0.290566 | −0.145283 | − | 0.989390i | \(-0.546409\pi\) | ||||
−0.145283 | + | 0.989390i | \(0.546409\pi\) | |||||||
\(80\) | 5.22081 | 0.583704 | ||||||||
\(81\) | 0.137725 | 0.0153027 | ||||||||
\(82\) | 2.85988 | 0.315821 | ||||||||
\(83\) | 3.44977 | 0.378662 | 0.189331 | − | 0.981913i | \(-0.439368\pi\) | ||||
0.189331 | + | 0.981913i | \(0.439368\pi\) | |||||||
\(84\) | 6.84974 | 0.747367 | ||||||||
\(85\) | 4.43930 | 0.481510 | ||||||||
\(86\) | −25.4949 | −2.74918 | ||||||||
\(87\) | −10.1757 | −1.09095 | ||||||||
\(88\) | 3.58147 | 0.381786 | ||||||||
\(89\) | −11.2417 | −1.19162 | −0.595809 | − | 0.803126i | \(-0.703168\pi\) | ||||
−0.595809 | + | 0.803126i | \(0.703168\pi\) | |||||||
\(90\) | 12.2351 | 1.28969 | ||||||||
\(91\) | 0.489082 | 0.0512698 | ||||||||
\(92\) | −4.25003 | −0.443096 | ||||||||
\(93\) | 1.34553 | 0.139525 | ||||||||
\(94\) | 27.2162 | 2.80713 | ||||||||
\(95\) | −21.8796 | −2.24480 | ||||||||
\(96\) | 3.41021 | 0.348053 | ||||||||
\(97\) | 0.942699 | 0.0957165 | 0.0478583 | − | 0.998854i | \(-0.484760\pi\) | ||||
0.0478583 | + | 0.998854i | \(0.484760\pi\) | |||||||
\(98\) | 9.08384 | 0.917606 | ||||||||
\(99\) | 1.74044 | 0.174921 | ||||||||
\(100\) | 9.32557 | 0.932557 | ||||||||
\(101\) | −14.2768 | −1.42059 | −0.710297 | − | 0.703902i | \(-0.751439\pi\) | ||||
−0.710297 | + | 0.703902i | \(0.751439\pi\) | |||||||
\(102\) | −4.05965 | −0.401965 | ||||||||
\(103\) | 0.616639 | 0.0607593 | 0.0303796 | − | 0.999538i | \(-0.490328\pi\) | ||||
0.0303796 | + | 0.999538i | \(0.490328\pi\) | |||||||
\(104\) | −1.05958 | −0.103900 | ||||||||
\(105\) | 5.19767 | 0.507241 | ||||||||
\(106\) | −22.3327 | −2.16914 | ||||||||
\(107\) | −18.4326 | −1.78194 | −0.890971 | − | 0.454059i | \(-0.849975\pi\) | ||||
−0.890971 | + | 0.454059i | \(0.849975\pi\) | |||||||
\(108\) | −18.7524 | −1.80445 | ||||||||
\(109\) | −12.1077 | −1.15971 | −0.579856 | − | 0.814719i | \(-0.696891\pi\) | ||||
−0.579856 | + | 0.814719i | \(0.696891\pi\) | |||||||
\(110\) | 6.05987 | 0.577786 | ||||||||
\(111\) | 0.0647527 | 0.00614605 | ||||||||
\(112\) | 3.37828 | 0.319218 | ||||||||
\(113\) | 1.48805 | 0.139984 | 0.0699920 | − | 0.997548i | \(-0.477703\pi\) | ||||
0.0699920 | + | 0.997548i | \(0.477703\pi\) | |||||||
\(114\) | 20.0085 | 1.87397 | ||||||||
\(115\) | −3.22498 | −0.300731 | ||||||||
\(116\) | −34.7829 | −3.22952 | ||||||||
\(117\) | −0.514908 | −0.0476033 | ||||||||
\(118\) | 12.6130 | 1.16112 | ||||||||
\(119\) | 2.87259 | 0.263329 | ||||||||
\(120\) | −11.2606 | −1.02794 | ||||||||
\(121\) | −10.1380 | −0.921635 | ||||||||
\(122\) | 17.7366 | 1.60579 | ||||||||
\(123\) | −1.27908 | −0.115330 | ||||||||
\(124\) | 4.59935 | 0.413034 | ||||||||
\(125\) | −6.68197 | −0.597653 | ||||||||
\(126\) | 7.91710 | 0.705311 | ||||||||
\(127\) | 4.82251 | 0.427929 | 0.213964 | − | 0.976841i | \(-0.431362\pi\) | ||||
0.213964 | + | 0.976841i | \(0.431362\pi\) | |||||||
\(128\) | 20.6577 | 1.82590 | ||||||||
\(129\) | 11.4025 | 1.00394 | ||||||||
\(130\) | −1.79281 | −0.157240 | ||||||||
\(131\) | −5.31053 | −0.463983 | −0.231992 | − | 0.972718i | \(-0.574524\pi\) | ||||
−0.231992 | + | 0.972718i | \(0.574524\pi\) | |||||||
\(132\) | −3.57172 | −0.310878 | ||||||||
\(133\) | −14.1579 | −1.22764 | ||||||||
\(134\) | 29.0849 | 2.51256 | ||||||||
\(135\) | −14.2296 | −1.22468 | ||||||||
\(136\) | −6.22335 | −0.533648 | ||||||||
\(137\) | 20.2409 | 1.72930 | 0.864650 | − | 0.502374i | \(-0.167540\pi\) | ||||
0.864650 | + | 0.502374i | \(0.167540\pi\) | |||||||
\(138\) | 2.94917 | 0.251050 | ||||||||
\(139\) | −15.4975 | −1.31448 | −0.657239 | − | 0.753682i | \(-0.728276\pi\) | ||||
−0.657239 | + | 0.753682i | \(0.728276\pi\) | |||||||
\(140\) | 17.7668 | 1.50157 | ||||||||
\(141\) | −12.1724 | −1.02510 | ||||||||
\(142\) | −38.4058 | −3.22294 | ||||||||
\(143\) | −0.255026 | −0.0213264 | ||||||||
\(144\) | −3.55667 | −0.296389 | ||||||||
\(145\) | −26.3938 | −2.19188 | ||||||||
\(146\) | 6.31670 | 0.522774 | ||||||||
\(147\) | −4.06273 | −0.335088 | ||||||||
\(148\) | 0.221340 | 0.0181940 | ||||||||
\(149\) | 10.2414 | 0.839005 | 0.419502 | − | 0.907754i | \(-0.362205\pi\) | ||||
0.419502 | + | 0.907754i | \(0.362205\pi\) | |||||||
\(150\) | −6.47119 | −0.528370 | ||||||||
\(151\) | −4.15410 | −0.338056 | −0.169028 | − | 0.985611i | \(-0.554063\pi\) | ||||
−0.169028 | + | 0.985611i | \(0.554063\pi\) | |||||||
\(152\) | 30.6725 | 2.48787 | ||||||||
\(153\) | −3.02427 | −0.244498 | ||||||||
\(154\) | 3.92122 | 0.315981 | ||||||||
\(155\) | 3.49005 | 0.280327 | ||||||||
\(156\) | 1.05669 | 0.0846030 | ||||||||
\(157\) | 12.3325 | 0.984240 | 0.492120 | − | 0.870527i | \(-0.336222\pi\) | ||||
0.492120 | + | 0.870527i | \(0.336222\pi\) | |||||||
\(158\) | 6.12588 | 0.487349 | ||||||||
\(159\) | 9.98825 | 0.792120 | ||||||||
\(160\) | 8.84541 | 0.699291 | ||||||||
\(161\) | −2.08682 | −0.164464 | ||||||||
\(162\) | −0.326679 | −0.0256664 | ||||||||
\(163\) | 12.5474 | 0.982791 | 0.491395 | − | 0.870937i | \(-0.336487\pi\) | ||||
0.491395 | + | 0.870937i | \(0.336487\pi\) | |||||||
\(164\) | −4.37218 | −0.341410 | ||||||||
\(165\) | −2.71027 | −0.210994 | ||||||||
\(166\) | −8.18279 | −0.635107 | ||||||||
\(167\) | −0.447377 | −0.0346191 | −0.0173095 | − | 0.999850i | \(-0.505510\pi\) | ||||
−0.0173095 | + | 0.999850i | \(0.505510\pi\) | |||||||
\(168\) | −7.28648 | −0.562164 | ||||||||
\(169\) | −12.9246 | −0.994196 | ||||||||
\(170\) | −10.5299 | −0.807609 | ||||||||
\(171\) | 14.9055 | 1.13985 | ||||||||
\(172\) | 38.9766 | 2.97193 | ||||||||
\(173\) | 16.6201 | 1.26360 | 0.631801 | − | 0.775131i | \(-0.282316\pi\) | ||||
0.631801 | + | 0.775131i | \(0.282316\pi\) | |||||||
\(174\) | 24.1366 | 1.82979 | ||||||||
\(175\) | 4.57897 | 0.346138 | ||||||||
\(176\) | −1.76157 | −0.132783 | ||||||||
\(177\) | −5.64113 | −0.424013 | ||||||||
\(178\) | 26.6651 | 1.99863 | ||||||||
\(179\) | 15.7084 | 1.17410 | 0.587050 | − | 0.809551i | \(-0.300289\pi\) | ||||
0.587050 | + | 0.809551i | \(0.300289\pi\) | |||||||
\(180\) | −18.7050 | −1.39419 | ||||||||
\(181\) | 14.7842 | 1.09890 | 0.549450 | − | 0.835527i | \(-0.314837\pi\) | ||||
0.549450 | + | 0.835527i | \(0.314837\pi\) | |||||||
\(182\) | −1.16009 | −0.0859918 | ||||||||
\(183\) | −7.93266 | −0.586399 | ||||||||
\(184\) | 4.52101 | 0.333293 | ||||||||
\(185\) | 0.167955 | 0.0123483 | ||||||||
\(186\) | −3.19158 | −0.234018 | ||||||||
\(187\) | −1.49788 | −0.109536 | ||||||||
\(188\) | −41.6080 | −3.03458 | ||||||||
\(189\) | −9.20766 | −0.669759 | ||||||||
\(190\) | 51.8980 | 3.76508 | ||||||||
\(191\) | −2.16281 | −0.156496 | −0.0782478 | − | 0.996934i | \(-0.524933\pi\) | ||||
−0.0782478 | + | 0.996934i | \(0.524933\pi\) | |||||||
\(192\) | −12.1146 | −0.874292 | ||||||||
\(193\) | 8.51585 | 0.612984 | 0.306492 | − | 0.951873i | \(-0.400845\pi\) | ||||
0.306492 | + | 0.951873i | \(0.400845\pi\) | |||||||
\(194\) | −2.23606 | −0.160540 | ||||||||
\(195\) | 0.801831 | 0.0574203 | ||||||||
\(196\) | −13.8874 | −0.991954 | ||||||||
\(197\) | 7.51834 | 0.535659 | 0.267830 | − | 0.963466i | \(-0.413694\pi\) | ||||
0.267830 | + | 0.963466i | \(0.413694\pi\) | |||||||
\(198\) | −4.12828 | −0.293384 | ||||||||
\(199\) | −2.78398 | −0.197351 | −0.0986755 | − | 0.995120i | \(-0.531461\pi\) | ||||
−0.0986755 | + | 0.995120i | \(0.531461\pi\) | |||||||
\(200\) | −9.92017 | −0.701462 | ||||||||
\(201\) | −13.0082 | −0.917527 | ||||||||
\(202\) | 33.8642 | 2.38268 | ||||||||
\(203\) | −17.0789 | −1.19870 | ||||||||
\(204\) | 6.20639 | 0.434534 | ||||||||
\(205\) | −3.31767 | −0.231716 | ||||||||
\(206\) | −1.46265 | −0.101908 | ||||||||
\(207\) | 2.19701 | 0.152703 | ||||||||
\(208\) | 0.521159 | 0.0361359 | ||||||||
\(209\) | 7.38246 | 0.510656 | ||||||||
\(210\) | −12.3288 | −0.850765 | ||||||||
\(211\) | 3.54400 | 0.243979 | 0.121990 | − | 0.992531i | \(-0.461073\pi\) | ||||
0.121990 | + | 0.992531i | \(0.461073\pi\) | |||||||
\(212\) | 34.1422 | 2.34489 | ||||||||
\(213\) | 17.1769 | 1.17694 | ||||||||
\(214\) | 43.7216 | 2.98875 | ||||||||
\(215\) | 29.5759 | 2.01706 | ||||||||
\(216\) | 19.9480 | 1.35729 | ||||||||
\(217\) | 2.25834 | 0.153306 | ||||||||
\(218\) | 28.7193 | 1.94512 | ||||||||
\(219\) | −2.82513 | −0.190905 | ||||||||
\(220\) | −9.26432 | −0.624600 | ||||||||
\(221\) | 0.443147 | 0.0298093 | ||||||||
\(222\) | −0.153592 | −0.0103084 | ||||||||
\(223\) | −29.1949 | −1.95504 | −0.977518 | − | 0.210854i | \(-0.932376\pi\) | ||||
−0.977518 | + | 0.210854i | \(0.932376\pi\) | |||||||
\(224\) | 5.72369 | 0.382430 | ||||||||
\(225\) | −4.82077 | −0.321384 | ||||||||
\(226\) | −3.52962 | −0.234787 | ||||||||
\(227\) | 23.2516 | 1.54326 | 0.771632 | − | 0.636069i | \(-0.219441\pi\) | ||||
0.771632 | + | 0.636069i | \(0.219441\pi\) | |||||||
\(228\) | −30.5889 | −2.02580 | ||||||||
\(229\) | −12.0030 | −0.793182 | −0.396591 | − | 0.917995i | \(-0.629807\pi\) | ||||
−0.396591 | + | 0.917995i | \(0.629807\pi\) | |||||||
\(230\) | 7.64957 | 0.504398 | ||||||||
\(231\) | −1.75376 | −0.115389 | ||||||||
\(232\) | 37.0007 | 2.42922 | ||||||||
\(233\) | −20.3520 | −1.33331 | −0.666653 | − | 0.745368i | \(-0.732274\pi\) | ||||
−0.666653 | + | 0.745368i | \(0.732274\pi\) | |||||||
\(234\) | 1.22135 | 0.0798422 | ||||||||
\(235\) | −31.5727 | −2.05958 | ||||||||
\(236\) | −19.2827 | −1.25520 | ||||||||
\(237\) | −2.73979 | −0.177968 | ||||||||
\(238\) | −6.81371 | −0.441667 | ||||||||
\(239\) | 16.5870 | 1.07293 | 0.536463 | − | 0.843924i | \(-0.319760\pi\) | ||||
0.536463 | + | 0.843924i | \(0.319760\pi\) | |||||||
\(240\) | 5.53856 | 0.357513 | ||||||||
\(241\) | −4.36927 | −0.281449 | −0.140725 | − | 0.990049i | \(-0.544943\pi\) | ||||
−0.140725 | + | 0.990049i | \(0.544943\pi\) | |||||||
\(242\) | 24.0471 | 1.54580 | ||||||||
\(243\) | 15.6599 | 1.00458 | ||||||||
\(244\) | −27.1157 | −1.73590 | ||||||||
\(245\) | −10.5379 | −0.673242 | ||||||||
\(246\) | 3.03394 | 0.193437 | ||||||||
\(247\) | −2.18410 | −0.138971 | ||||||||
\(248\) | −4.89261 | −0.310681 | ||||||||
\(249\) | 3.65974 | 0.231926 | ||||||||
\(250\) | 15.8495 | 1.00241 | ||||||||
\(251\) | 22.1689 | 1.39929 | 0.699643 | − | 0.714492i | \(-0.253342\pi\) | ||||
0.699643 | + | 0.714492i | \(0.253342\pi\) | |||||||
\(252\) | −12.1037 | −0.762458 | ||||||||
\(253\) | 1.08815 | 0.0684113 | ||||||||
\(254\) | −11.4389 | −0.717740 | ||||||||
\(255\) | 4.70949 | 0.294920 | ||||||||
\(256\) | −26.1606 | −1.63504 | ||||||||
\(257\) | 11.1517 | 0.695627 | 0.347813 | − | 0.937564i | \(-0.386924\pi\) | ||||
0.347813 | + | 0.937564i | \(0.386924\pi\) | |||||||
\(258\) | −27.0466 | −1.68385 | ||||||||
\(259\) | 0.108681 | 0.00675309 | ||||||||
\(260\) | 2.74085 | 0.169980 | ||||||||
\(261\) | 17.9807 | 1.11298 | ||||||||
\(262\) | 12.5965 | 0.778212 | ||||||||
\(263\) | 25.6318 | 1.58052 | 0.790261 | − | 0.612770i | \(-0.209945\pi\) | ||||
0.790261 | + | 0.612770i | \(0.209945\pi\) | |||||||
\(264\) | 3.79945 | 0.233840 | ||||||||
\(265\) | 25.9075 | 1.59149 | ||||||||
\(266\) | 33.5822 | 2.05905 | ||||||||
\(267\) | −11.9259 | −0.729853 | ||||||||
\(268\) | −44.4650 | −2.71613 | ||||||||
\(269\) | −16.3535 | −0.997093 | −0.498546 | − | 0.866863i | \(-0.666133\pi\) | ||||
−0.498546 | + | 0.866863i | \(0.666133\pi\) | |||||||
\(270\) | 33.7522 | 2.05409 | ||||||||
\(271\) | 13.2467 | 0.804679 | 0.402339 | − | 0.915491i | \(-0.368197\pi\) | ||||
0.402339 | + | 0.915491i | \(0.368197\pi\) | |||||||
\(272\) | 3.06099 | 0.185599 | ||||||||
\(273\) | 0.518849 | 0.0314022 | ||||||||
\(274\) | −48.0111 | −2.90045 | ||||||||
\(275\) | −2.38765 | −0.143981 | ||||||||
\(276\) | −4.50870 | −0.271392 | ||||||||
\(277\) | −29.7751 | −1.78901 | −0.894506 | − | 0.447056i | \(-0.852473\pi\) | ||||
−0.894506 | + | 0.447056i | \(0.852473\pi\) | |||||||
\(278\) | 36.7597 | 2.20470 | ||||||||
\(279\) | −2.37759 | −0.142343 | ||||||||
\(280\) | −18.8997 | −1.12947 | ||||||||
\(281\) | −5.39714 | −0.321966 | −0.160983 | − | 0.986957i | \(-0.551466\pi\) | ||||
−0.160983 | + | 0.986957i | \(0.551466\pi\) | |||||||
\(282\) | 28.8726 | 1.71934 | ||||||||
\(283\) | 18.9195 | 1.12465 | 0.562324 | − | 0.826917i | \(-0.309907\pi\) | ||||
0.562324 | + | 0.826917i | \(0.309907\pi\) | |||||||
\(284\) | 58.7147 | 3.48408 | ||||||||
\(285\) | −23.2113 | −1.37492 | ||||||||
\(286\) | 0.604917 | 0.0357695 | ||||||||
\(287\) | −2.14680 | −0.126721 | ||||||||
\(288\) | −6.02593 | −0.355081 | ||||||||
\(289\) | −14.3972 | −0.846895 | ||||||||
\(290\) | 62.6054 | 3.67632 | ||||||||
\(291\) | 1.00007 | 0.0586254 | ||||||||
\(292\) | −9.65696 | −0.565131 | ||||||||
\(293\) | −9.55818 | −0.558395 | −0.279198 | − | 0.960234i | \(-0.590068\pi\) | ||||
−0.279198 | + | 0.960234i | \(0.590068\pi\) | |||||||
\(294\) | 9.63670 | 0.562024 | ||||||||
\(295\) | −14.6320 | −0.851906 | ||||||||
\(296\) | −0.235452 | −0.0136854 | ||||||||
\(297\) | 4.80123 | 0.278596 | ||||||||
\(298\) | −24.2923 | −1.40721 | ||||||||
\(299\) | −0.321928 | −0.0186176 | ||||||||
\(300\) | 9.89315 | 0.571181 | ||||||||
\(301\) | 19.1380 | 1.10310 | ||||||||
\(302\) | 9.85344 | 0.567002 | ||||||||
\(303\) | −15.1457 | −0.870099 | ||||||||
\(304\) | −15.0864 | −0.865266 | ||||||||
\(305\) | −20.5757 | −1.17816 | ||||||||
\(306\) | 7.17350 | 0.410082 | ||||||||
\(307\) | −22.1153 | −1.26218 | −0.631092 | − | 0.775708i | \(-0.717393\pi\) | ||||
−0.631092 | + | 0.775708i | \(0.717393\pi\) | |||||||
\(308\) | −5.99476 | −0.341583 | ||||||||
\(309\) | 0.654170 | 0.0372144 | ||||||||
\(310\) | −8.27832 | −0.470177 | ||||||||
\(311\) | 3.25543 | 0.184599 | 0.0922993 | − | 0.995731i | \(-0.470578\pi\) | ||||
0.0922993 | + | 0.995731i | \(0.470578\pi\) | |||||||
\(312\) | −1.12407 | −0.0636378 | ||||||||
\(313\) | −3.43022 | −0.193888 | −0.0969439 | − | 0.995290i | \(-0.530907\pi\) | ||||
−0.0969439 | + | 0.995290i | \(0.530907\pi\) | |||||||
\(314\) | −29.2524 | −1.65081 | ||||||||
\(315\) | −9.18441 | −0.517483 | ||||||||
\(316\) | −9.36524 | −0.526836 | ||||||||
\(317\) | 1.74273 | 0.0978814 | 0.0489407 | − | 0.998802i | \(-0.484415\pi\) | ||||
0.0489407 | + | 0.998802i | \(0.484415\pi\) | |||||||
\(318\) | −23.6919 | −1.32858 | ||||||||
\(319\) | 8.90559 | 0.498617 | ||||||||
\(320\) | −31.4227 | −1.75658 | ||||||||
\(321\) | −19.5544 | −1.09142 | ||||||||
\(322\) | 4.94989 | 0.275846 | ||||||||
\(323\) | −12.8281 | −0.713776 | ||||||||
\(324\) | 0.499427 | 0.0277460 | ||||||||
\(325\) | 0.706387 | 0.0391833 | ||||||||
\(326\) | −29.7622 | −1.64838 | ||||||||
\(327\) | −12.8447 | −0.710311 | ||||||||
\(328\) | 4.65096 | 0.256806 | ||||||||
\(329\) | −20.4301 | −1.12635 | ||||||||
\(330\) | 6.42869 | 0.353888 | ||||||||
\(331\) | −29.7765 | −1.63666 | −0.818332 | − | 0.574745i | \(-0.805101\pi\) | ||||
−0.818332 | + | 0.574745i | \(0.805101\pi\) | |||||||
\(332\) | 12.5098 | 0.686566 | ||||||||
\(333\) | −0.114420 | −0.00627015 | ||||||||
\(334\) | 1.06117 | 0.0580645 | ||||||||
\(335\) | −33.7406 | −1.84345 | ||||||||
\(336\) | 3.58389 | 0.195517 | ||||||||
\(337\) | −20.1527 | −1.09779 | −0.548893 | − | 0.835893i | \(-0.684951\pi\) | ||||
−0.548893 | + | 0.835893i | \(0.684951\pi\) | |||||||
\(338\) | 30.6567 | 1.66751 | ||||||||
\(339\) | 1.57862 | 0.0857387 | ||||||||
\(340\) | 16.0981 | 0.873044 | ||||||||
\(341\) | −1.17759 | −0.0637699 | ||||||||
\(342\) | −35.3555 | −1.91180 | ||||||||
\(343\) | −19.2827 | −1.04117 | ||||||||
\(344\) | −41.4617 | −2.23547 | ||||||||
\(345\) | −3.42126 | −0.184194 | ||||||||
\(346\) | −39.4224 | −2.11936 | ||||||||
\(347\) | 23.4396 | 1.25831 | 0.629153 | − | 0.777282i | \(-0.283402\pi\) | ||||
0.629153 | + | 0.777282i | \(0.283402\pi\) | |||||||
\(348\) | −36.8999 | −1.97804 | ||||||||
\(349\) | 2.11237 | 0.113073 | 0.0565363 | − | 0.998401i | \(-0.481994\pi\) | ||||
0.0565363 | + | 0.998401i | \(0.481994\pi\) | |||||||
\(350\) | −10.8612 | −0.580557 | ||||||||
\(351\) | −1.42044 | −0.0758176 | ||||||||
\(352\) | −2.98455 | −0.159077 | ||||||||
\(353\) | 24.1933 | 1.28768 | 0.643839 | − | 0.765161i | \(-0.277341\pi\) | ||||
0.643839 | + | 0.765161i | \(0.277341\pi\) | |||||||
\(354\) | 13.3806 | 0.711172 | ||||||||
\(355\) | 44.5535 | 2.36466 | ||||||||
\(356\) | −40.7655 | −2.16057 | ||||||||
\(357\) | 3.04742 | 0.161286 | ||||||||
\(358\) | −37.2599 | −1.96925 | ||||||||
\(359\) | −4.37065 | −0.230674 | −0.115337 | − | 0.993326i | \(-0.536795\pi\) | ||||
−0.115337 | + | 0.993326i | \(0.536795\pi\) | |||||||
\(360\) | 19.8977 | 1.04870 | ||||||||
\(361\) | 44.2250 | 2.32763 | ||||||||
\(362\) | −35.0678 | −1.84312 | ||||||||
\(363\) | −10.7550 | −0.564492 | ||||||||
\(364\) | 1.77355 | 0.0929592 | ||||||||
\(365\) | −7.32783 | −0.383556 | ||||||||
\(366\) | 18.8161 | 0.983532 | ||||||||
\(367\) | 16.2536 | 0.848431 | 0.424216 | − | 0.905561i | \(-0.360550\pi\) | ||||
0.424216 | + | 0.905561i | \(0.360550\pi\) | |||||||
\(368\) | −2.22368 | −0.115917 | ||||||||
\(369\) | 2.26016 | 0.117659 | ||||||||
\(370\) | −0.398387 | −0.0207111 | ||||||||
\(371\) | 16.7643 | 0.870357 | ||||||||
\(372\) | 4.87928 | 0.252979 | ||||||||
\(373\) | 10.8715 | 0.562905 | 0.281452 | − | 0.959575i | \(-0.409184\pi\) | ||||
0.281452 | + | 0.959575i | \(0.409184\pi\) | |||||||
\(374\) | 3.55293 | 0.183718 | ||||||||
\(375\) | −7.08865 | −0.366056 | ||||||||
\(376\) | 44.2610 | 2.28259 | ||||||||
\(377\) | −2.63472 | −0.135695 | ||||||||
\(378\) | 21.8404 | 1.12335 | ||||||||
\(379\) | 35.2353 | 1.80992 | 0.904959 | − | 0.425499i | \(-0.139901\pi\) | ||||
0.904959 | + | 0.425499i | \(0.139901\pi\) | |||||||
\(380\) | −79.3416 | −4.07014 | ||||||||
\(381\) | 5.11602 | 0.262102 | ||||||||
\(382\) | 5.13014 | 0.262481 | ||||||||
\(383\) | 4.38853 | 0.224244 | 0.112122 | − | 0.993694i | \(-0.464235\pi\) | ||||
0.112122 | + | 0.993694i | \(0.464235\pi\) | |||||||
\(384\) | 21.9150 | 1.11835 | ||||||||
\(385\) | −4.54890 | −0.231833 | ||||||||
\(386\) | −20.1994 | −1.02812 | ||||||||
\(387\) | −20.1486 | −1.02421 | ||||||||
\(388\) | 3.41849 | 0.173547 | ||||||||
\(389\) | −26.7997 | −1.35880 | −0.679399 | − | 0.733769i | \(-0.737760\pi\) | ||||
−0.679399 | + | 0.733769i | \(0.737760\pi\) | |||||||
\(390\) | −1.90193 | −0.0963078 | ||||||||
\(391\) | −1.89082 | −0.0956228 | ||||||||
\(392\) | 14.7728 | 0.746140 | ||||||||
\(393\) | −5.63374 | −0.284185 | ||||||||
\(394\) | −17.8333 | −0.898430 | ||||||||
\(395\) | −7.10646 | −0.357565 | ||||||||
\(396\) | 6.31131 | 0.317155 | ||||||||
\(397\) | 8.27675 | 0.415398 | 0.207699 | − | 0.978193i | \(-0.433403\pi\) | ||||
0.207699 | + | 0.978193i | \(0.433403\pi\) | |||||||
\(398\) | 6.60353 | 0.331005 | ||||||||
\(399\) | −15.0196 | −0.751919 | ||||||||
\(400\) | 4.87929 | 0.243964 | ||||||||
\(401\) | −19.3558 | −0.966584 | −0.483292 | − | 0.875459i | \(-0.660559\pi\) | ||||
−0.483292 | + | 0.875459i | \(0.660559\pi\) | |||||||
\(402\) | 30.8551 | 1.53891 | ||||||||
\(403\) | 0.348389 | 0.0173545 | ||||||||
\(404\) | −51.7716 | −2.57573 | ||||||||
\(405\) | 0.378972 | 0.0188313 | ||||||||
\(406\) | 40.5107 | 2.01051 | ||||||||
\(407\) | −0.0566703 | −0.00280904 | ||||||||
\(408\) | −6.60212 | −0.326853 | ||||||||
\(409\) | −7.85318 | −0.388315 | −0.194157 | − | 0.980970i | \(-0.562197\pi\) | ||||
−0.194157 | + | 0.980970i | \(0.562197\pi\) | |||||||
\(410\) | 7.86944 | 0.388644 | ||||||||
\(411\) | 21.4729 | 1.05918 | ||||||||
\(412\) | 2.23610 | 0.110165 | ||||||||
\(413\) | −9.46805 | −0.465892 | ||||||||
\(414\) | −5.21126 | −0.256120 | ||||||||
\(415\) | 9.49263 | 0.465975 | ||||||||
\(416\) | 0.882979 | 0.0432916 | ||||||||
\(417\) | −16.4407 | −0.805104 | ||||||||
\(418\) | −17.5110 | −0.856493 | ||||||||
\(419\) | 33.6026 | 1.64159 | 0.820797 | − | 0.571220i | \(-0.193530\pi\) | ||||
0.820797 | + | 0.571220i | \(0.193530\pi\) | |||||||
\(420\) | 18.8482 | 0.919697 | ||||||||
\(421\) | 18.9360 | 0.922882 | 0.461441 | − | 0.887171i | \(-0.347333\pi\) | ||||
0.461441 | + | 0.887171i | \(0.347333\pi\) | |||||||
\(422\) | −8.40629 | −0.409212 | ||||||||
\(423\) | 21.5089 | 1.04580 | ||||||||
\(424\) | −36.3191 | −1.76381 | ||||||||
\(425\) | 4.14891 | 0.201251 | ||||||||
\(426\) | −40.7433 | −1.97402 | ||||||||
\(427\) | −13.3141 | −0.644316 | ||||||||
\(428\) | −66.8416 | −3.23091 | ||||||||
\(429\) | −0.270548 | −0.0130622 | ||||||||
\(430\) | −70.1534 | −3.38310 | ||||||||
\(431\) | −14.1153 | −0.679911 | −0.339956 | − | 0.940441i | \(-0.610412\pi\) | ||||
−0.339956 | + | 0.940441i | \(0.610412\pi\) | |||||||
\(432\) | −9.81155 | −0.472058 | ||||||||
\(433\) | 15.7197 | 0.755439 | 0.377720 | − | 0.925920i | \(-0.376708\pi\) | ||||
0.377720 | + | 0.925920i | \(0.376708\pi\) | |||||||
\(434\) | −5.35673 | −0.257131 | ||||||||
\(435\) | −28.0002 | −1.34250 | ||||||||
\(436\) | −43.9060 | −2.10272 | ||||||||
\(437\) | 9.31913 | 0.445794 | ||||||||
\(438\) | 6.70115 | 0.320193 | ||||||||
\(439\) | 16.4489 | 0.785064 | 0.392532 | − | 0.919738i | \(-0.371599\pi\) | ||||
0.392532 | + | 0.919738i | \(0.371599\pi\) | |||||||
\(440\) | 9.85502 | 0.469820 | ||||||||
\(441\) | 7.17894 | 0.341854 | ||||||||
\(442\) | −1.05113 | −0.0499973 | ||||||||
\(443\) | −21.2134 | −1.00788 | −0.503940 | − | 0.863738i | \(-0.668117\pi\) | ||||
−0.503940 | + | 0.863738i | \(0.668117\pi\) | |||||||
\(444\) | 0.234811 | 0.0111436 | ||||||||
\(445\) | −30.9334 | −1.46638 | ||||||||
\(446\) | 69.2496 | 3.27907 | ||||||||
\(447\) | 10.8647 | 0.513882 | ||||||||
\(448\) | −20.3330 | −0.960645 | ||||||||
\(449\) | 15.9824 | 0.754255 | 0.377127 | − | 0.926161i | \(-0.376912\pi\) | ||||
0.377127 | + | 0.926161i | \(0.376912\pi\) | |||||||
\(450\) | 11.4347 | 0.539039 | ||||||||
\(451\) | 1.11942 | 0.0527116 | ||||||||
\(452\) | 5.39608 | 0.253810 | ||||||||
\(453\) | −4.40693 | −0.207056 | ||||||||
\(454\) | −55.1523 | −2.58843 | ||||||||
\(455\) | 1.34579 | 0.0630917 | ||||||||
\(456\) | 32.5393 | 1.52379 | ||||||||
\(457\) | −17.3437 | −0.811304 | −0.405652 | − | 0.914028i | \(-0.632956\pi\) | ||||
−0.405652 | + | 0.914028i | \(0.632956\pi\) | |||||||
\(458\) | 28.4709 | 1.33036 | ||||||||
\(459\) | −8.34285 | −0.389411 | ||||||||
\(460\) | −11.6947 | −0.545266 | ||||||||
\(461\) | 20.3795 | 0.949167 | 0.474584 | − | 0.880210i | \(-0.342599\pi\) | ||||
0.474584 | + | 0.880210i | \(0.342599\pi\) | |||||||
\(462\) | 4.15988 | 0.193535 | ||||||||
\(463\) | −17.3638 | −0.806966 | −0.403483 | − | 0.914987i | \(-0.632201\pi\) | ||||
−0.403483 | + | 0.914987i | \(0.632201\pi\) | |||||||
\(464\) | −18.1990 | −0.844867 | ||||||||
\(465\) | 3.70246 | 0.171698 | ||||||||
\(466\) | 48.2745 | 2.23627 | ||||||||
\(467\) | −10.4241 | −0.482371 | −0.241185 | − | 0.970479i | \(-0.577536\pi\) | ||||
−0.241185 | + | 0.970479i | \(0.577536\pi\) | |||||||
\(468\) | −1.86720 | −0.0863113 | ||||||||
\(469\) | −21.8329 | −1.00815 | ||||||||
\(470\) | 74.8898 | 3.45441 | ||||||||
\(471\) | 13.0831 | 0.602837 | ||||||||
\(472\) | 20.5122 | 0.944149 | ||||||||
\(473\) | −9.97929 | −0.458848 | ||||||||
\(474\) | 6.49872 | 0.298496 | ||||||||
\(475\) | −20.4484 | −0.938236 | ||||||||
\(476\) | 10.4168 | 0.477453 | ||||||||
\(477\) | −17.6495 | −0.808115 | ||||||||
\(478\) | −39.3440 | −1.79955 | ||||||||
\(479\) | −33.9845 | −1.55279 | −0.776395 | − | 0.630247i | \(-0.782954\pi\) | ||||
−0.776395 | + | 0.630247i | \(0.782954\pi\) | |||||||
\(480\) | 9.38376 | 0.428308 | ||||||||
\(481\) | 0.0167659 | 0.000764459 0 | ||||||||
\(482\) | 10.3638 | 0.472059 | ||||||||
\(483\) | −2.21383 | −0.100733 | ||||||||
\(484\) | −36.7631 | −1.67105 | ||||||||
\(485\) | 2.59399 | 0.117787 | ||||||||
\(486\) | −37.1448 | −1.68492 | ||||||||
\(487\) | −26.6363 | −1.20701 | −0.603504 | − | 0.797360i | \(-0.706229\pi\) | ||||
−0.603504 | + | 0.797360i | \(0.706229\pi\) | |||||||
\(488\) | 28.8446 | 1.30573 | ||||||||
\(489\) | 13.3111 | 0.601949 | ||||||||
\(490\) | 24.9957 | 1.12919 | ||||||||
\(491\) | 35.4972 | 1.60197 | 0.800984 | − | 0.598686i | \(-0.204310\pi\) | ||||
0.800984 | + | 0.598686i | \(0.204310\pi\) | |||||||
\(492\) | −4.63828 | −0.209110 | ||||||||
\(493\) | −15.4748 | −0.696949 | ||||||||
\(494\) | 5.18064 | 0.233088 | ||||||||
\(495\) | 4.78911 | 0.215254 | ||||||||
\(496\) | 2.40646 | 0.108053 | ||||||||
\(497\) | 28.8297 | 1.29319 | ||||||||
\(498\) | −8.68081 | −0.388997 | ||||||||
\(499\) | −5.59753 | −0.250580 | −0.125290 | − | 0.992120i | \(-0.539986\pi\) | ||||
−0.125290 | + | 0.992120i | \(0.539986\pi\) | |||||||
\(500\) | −24.2307 | −1.08363 | ||||||||
\(501\) | −0.474605 | −0.0212038 | ||||||||
\(502\) | −52.5841 | −2.34694 | ||||||||
\(503\) | −5.00451 | −0.223140 | −0.111570 | − | 0.993757i | \(-0.535588\pi\) | ||||
−0.111570 | + | 0.993757i | \(0.535588\pi\) | |||||||
\(504\) | 12.8754 | 0.573515 | ||||||||
\(505\) | −39.2850 | −1.74816 | ||||||||
\(506\) | −2.58106 | −0.114742 | ||||||||
\(507\) | −13.7112 | −0.608935 | ||||||||
\(508\) | 17.4878 | 0.775894 | ||||||||
\(509\) | 23.9450 | 1.06134 | 0.530671 | − | 0.847578i | \(-0.321940\pi\) | ||||
0.530671 | + | 0.847578i | \(0.321940\pi\) | |||||||
\(510\) | −11.1708 | −0.494652 | ||||||||
\(511\) | −4.74169 | −0.209760 | ||||||||
\(512\) | 20.7369 | 0.916451 | ||||||||
\(513\) | 41.1187 | 1.81544 | ||||||||
\(514\) | −26.4517 | −1.16673 | ||||||||
\(515\) | 1.69679 | 0.0747693 | ||||||||
\(516\) | 41.3488 | 1.82028 | ||||||||
\(517\) | 10.6530 | 0.468520 | ||||||||
\(518\) | −0.257788 | −0.0113266 | ||||||||
\(519\) | 17.6316 | 0.773942 | ||||||||
\(520\) | −2.91561 | −0.127858 | ||||||||
\(521\) | −21.0755 | −0.923336 | −0.461668 | − | 0.887053i | \(-0.652749\pi\) | ||||
−0.461668 | + | 0.887053i | \(0.652749\pi\) | |||||||
\(522\) | −42.6499 | −1.86673 | ||||||||
\(523\) | −34.8043 | −1.52188 | −0.760942 | − | 0.648820i | \(-0.775263\pi\) | ||||
−0.760942 | + | 0.648820i | \(0.775263\pi\) | |||||||
\(524\) | −19.2574 | −0.841266 | ||||||||
\(525\) | 4.85766 | 0.212006 | ||||||||
\(526\) | −60.7980 | −2.65092 | ||||||||
\(527\) | 2.04623 | 0.0891353 | ||||||||
\(528\) | −1.86878 | −0.0813282 | ||||||||
\(529\) | −21.6264 | −0.940278 | ||||||||
\(530\) | −61.4521 | −2.66931 | ||||||||
\(531\) | 9.96801 | 0.432575 | ||||||||
\(532\) | −51.3404 | −2.22589 | ||||||||
\(533\) | −0.331181 | −0.0143450 | ||||||||
\(534\) | 28.2880 | 1.22414 | ||||||||
\(535\) | −50.7202 | −2.19283 | ||||||||
\(536\) | 47.3002 | 2.04306 | ||||||||
\(537\) | 16.6644 | 0.719124 | ||||||||
\(538\) | 38.7902 | 1.67236 | ||||||||
\(539\) | 3.55562 | 0.153152 | ||||||||
\(540\) | −51.6003 | −2.22052 | ||||||||
\(541\) | −41.9037 | −1.80158 | −0.900791 | − | 0.434254i | \(-0.857012\pi\) | ||||
−0.900791 | + | 0.434254i | \(0.857012\pi\) | |||||||
\(542\) | −31.4208 | −1.34964 | ||||||||
\(543\) | 15.6840 | 0.673065 | ||||||||
\(544\) | 5.18611 | 0.222352 | ||||||||
\(545\) | −33.3165 | −1.42712 | ||||||||
\(546\) | −1.23070 | −0.0526690 | ||||||||
\(547\) | 11.5202 | 0.492569 | 0.246285 | − | 0.969198i | \(-0.420790\pi\) | ||||
0.246285 | + | 0.969198i | \(0.420790\pi\) | |||||||
\(548\) | 73.3992 | 3.13546 | ||||||||
\(549\) | 14.0172 | 0.598239 | ||||||||
\(550\) | 5.66346 | 0.241491 | ||||||||
\(551\) | 76.2693 | 3.24918 | ||||||||
\(552\) | 4.79617 | 0.204139 | ||||||||
\(553\) | −4.59845 | −0.195546 | ||||||||
\(554\) | 70.6259 | 3.00060 | ||||||||
\(555\) | 0.178178 | 0.00756322 | ||||||||
\(556\) | −56.1981 | −2.38333 | ||||||||
\(557\) | −4.63438 | −0.196365 | −0.0981826 | − | 0.995168i | \(-0.531303\pi\) | ||||
−0.0981826 | + | 0.995168i | \(0.531303\pi\) | |||||||
\(558\) | 5.63960 | 0.238743 | ||||||||
\(559\) | 2.95237 | 0.124872 | ||||||||
\(560\) | 9.29590 | 0.392824 | ||||||||
\(561\) | −1.58904 | −0.0670894 | ||||||||
\(562\) | 12.8019 | 0.540015 | ||||||||
\(563\) | −40.8567 | −1.72191 | −0.860953 | − | 0.508685i | \(-0.830132\pi\) | ||||
−0.860953 | + | 0.508685i | \(0.830132\pi\) | |||||||
\(564\) | −44.1404 | −1.85865 | ||||||||
\(565\) | 4.09462 | 0.172262 | ||||||||
\(566\) | −44.8766 | −1.88631 | ||||||||
\(567\) | 0.245225 | 0.0102985 | ||||||||
\(568\) | −62.4584 | −2.62070 | ||||||||
\(569\) | −31.8050 | −1.33334 | −0.666668 | − | 0.745355i | \(-0.732280\pi\) | ||||
−0.666668 | + | 0.745355i | \(0.732280\pi\) | |||||||
\(570\) | 55.0566 | 2.30607 | ||||||||
\(571\) | −35.2861 | −1.47668 | −0.738338 | − | 0.674431i | \(-0.764389\pi\) | ||||
−0.738338 | + | 0.674431i | \(0.764389\pi\) | |||||||
\(572\) | −0.924796 | −0.0386677 | ||||||||
\(573\) | −2.29445 | −0.0958518 | ||||||||
\(574\) | 5.09216 | 0.212542 | ||||||||
\(575\) | −3.01401 | −0.125693 | ||||||||
\(576\) | 21.4067 | 0.891946 | ||||||||
\(577\) | 38.8359 | 1.61676 | 0.808379 | − | 0.588663i | \(-0.200345\pi\) | ||||
0.808379 | + | 0.588663i | \(0.200345\pi\) | |||||||
\(578\) | 34.1499 | 1.42045 | ||||||||
\(579\) | 9.03415 | 0.375446 | ||||||||
\(580\) | −95.7111 | −3.97419 | ||||||||
\(581\) | 6.14249 | 0.254833 | ||||||||
\(582\) | −2.37215 | −0.0983289 | ||||||||
\(583\) | −8.74153 | −0.362037 | ||||||||
\(584\) | 10.2727 | 0.425087 | ||||||||
\(585\) | −1.41686 | −0.0585798 | ||||||||
\(586\) | 22.6718 | 0.936563 | ||||||||
\(587\) | −13.1307 | −0.541963 | −0.270982 | − | 0.962585i | \(-0.587348\pi\) | ||||
−0.270982 | + | 0.962585i | \(0.587348\pi\) | |||||||
\(588\) | −14.7326 | −0.607561 | ||||||||
\(589\) | −10.0851 | −0.415549 | ||||||||
\(590\) | 34.7067 | 1.42885 | ||||||||
\(591\) | 7.97592 | 0.328086 | ||||||||
\(592\) | 0.115809 | 0.00475970 | ||||||||
\(593\) | −29.0930 | −1.19471 | −0.597353 | − | 0.801978i | \(-0.703781\pi\) | ||||
−0.597353 | + | 0.801978i | \(0.703781\pi\) | |||||||
\(594\) | −11.3884 | −0.467272 | ||||||||
\(595\) | 7.90439 | 0.324049 | ||||||||
\(596\) | 37.1380 | 1.52123 | ||||||||
\(597\) | −2.95342 | −0.120875 | ||||||||
\(598\) | 0.763606 | 0.0312262 | ||||||||
\(599\) | −6.13200 | −0.250547 | −0.125273 | − | 0.992122i | \(-0.539981\pi\) | ||||
−0.125273 | + | 0.992122i | \(0.539981\pi\) | |||||||
\(600\) | −10.5239 | −0.429638 | ||||||||
\(601\) | 34.3762 | 1.40224 | 0.701118 | − | 0.713046i | \(-0.252685\pi\) | ||||
0.701118 | + | 0.713046i | \(0.252685\pi\) | |||||||
\(602\) | −45.3949 | −1.85016 | ||||||||
\(603\) | 22.9858 | 0.936054 | ||||||||
\(604\) | −15.0639 | −0.612942 | ||||||||
\(605\) | −27.8964 | −1.13415 | ||||||||
\(606\) | 35.9253 | 1.45937 | ||||||||
\(607\) | −38.6864 | −1.57023 | −0.785116 | − | 0.619349i | \(-0.787397\pi\) | ||||
−0.785116 | + | 0.619349i | \(0.787397\pi\) | |||||||
\(608\) | −25.5603 | −1.03661 | ||||||||
\(609\) | −18.1183 | −0.734192 | ||||||||
\(610\) | 48.8051 | 1.97606 | ||||||||
\(611\) | −3.15170 | −0.127504 | ||||||||
\(612\) | −10.9668 | −0.443308 | ||||||||
\(613\) | −12.4308 | −0.502077 | −0.251039 | − | 0.967977i | \(-0.580772\pi\) | ||||
−0.251039 | + | 0.967977i | \(0.580772\pi\) | |||||||
\(614\) | 52.4569 | 2.11699 | ||||||||
\(615\) | −3.51959 | −0.141924 | ||||||||
\(616\) | 6.37699 | 0.256936 | ||||||||
\(617\) | 22.4610 | 0.904244 | 0.452122 | − | 0.891956i | \(-0.350667\pi\) | ||||
0.452122 | + | 0.891956i | \(0.350667\pi\) | |||||||
\(618\) | −1.55168 | −0.0624176 | ||||||||
\(619\) | 14.6684 | 0.589575 | 0.294787 | − | 0.955563i | \(-0.404751\pi\) | ||||
0.294787 | + | 0.955563i | \(0.404751\pi\) | |||||||
\(620\) | 12.6559 | 0.508272 | ||||||||
\(621\) | 6.06075 | 0.243210 | ||||||||
\(622\) | −7.72181 | −0.309616 | ||||||||
\(623\) | −20.0164 | −0.801940 | ||||||||
\(624\) | 0.552878 | 0.0221328 | ||||||||
\(625\) | −31.2449 | −1.24979 | ||||||||
\(626\) | 8.13641 | 0.325197 | ||||||||
\(627\) | 7.83178 | 0.312771 | ||||||||
\(628\) | 44.7210 | 1.78456 | ||||||||
\(629\) | 0.0984731 | 0.00392638 | ||||||||
\(630\) | 21.7852 | 0.867943 | ||||||||
\(631\) | −42.5097 | −1.69228 | −0.846142 | − | 0.532958i | \(-0.821081\pi\) | ||||
−0.846142 | + | 0.532958i | \(0.821081\pi\) | |||||||
\(632\) | 9.96237 | 0.396282 | ||||||||
\(633\) | 3.75970 | 0.149435 | ||||||||
\(634\) | −4.13371 | −0.164171 | ||||||||
\(635\) | 13.2699 | 0.526602 | ||||||||
\(636\) | 36.2202 | 1.43622 | ||||||||
\(637\) | −1.05193 | −0.0416790 | ||||||||
\(638\) | −21.1238 | −0.836301 | ||||||||
\(639\) | −30.3520 | −1.20071 | ||||||||
\(640\) | 56.8432 | 2.24692 | ||||||||
\(641\) | 40.6171 | 1.60428 | 0.802140 | − | 0.597136i | \(-0.203695\pi\) | ||||
0.802140 | + | 0.597136i | \(0.203695\pi\) | |||||||
\(642\) | 46.3826 | 1.83058 | ||||||||
\(643\) | 12.1274 | 0.478260 | 0.239130 | − | 0.970988i | \(-0.423138\pi\) | ||||
0.239130 | + | 0.970988i | \(0.423138\pi\) | |||||||
\(644\) | −7.56738 | −0.298196 | ||||||||
\(645\) | 31.3760 | 1.23543 | ||||||||
\(646\) | 30.4280 | 1.19718 | ||||||||
\(647\) | −12.4708 | −0.490278 | −0.245139 | − | 0.969488i | \(-0.578834\pi\) | ||||
−0.245139 | + | 0.969488i | \(0.578834\pi\) | |||||||
\(648\) | −0.531271 | −0.0208703 | ||||||||
\(649\) | 4.93701 | 0.193794 | ||||||||
\(650\) | −1.67553 | −0.0657198 | ||||||||
\(651\) | 2.39579 | 0.0938984 | ||||||||
\(652\) | 45.5004 | 1.78194 | ||||||||
\(653\) | −10.2829 | −0.402402 | −0.201201 | − | 0.979550i | \(-0.564484\pi\) | ||||
−0.201201 | + | 0.979550i | \(0.564484\pi\) | |||||||
\(654\) | 30.4672 | 1.19136 | ||||||||
\(655\) | −14.6128 | −0.570970 | ||||||||
\(656\) | −2.28760 | −0.0893156 | ||||||||
\(657\) | 4.99208 | 0.194760 | ||||||||
\(658\) | 48.4597 | 1.88916 | ||||||||
\(659\) | 37.1571 | 1.44743 | 0.723717 | − | 0.690097i | \(-0.242432\pi\) | ||||
0.723717 | + | 0.690097i | \(0.242432\pi\) | |||||||
\(660\) | −9.82817 | −0.382561 | ||||||||
\(661\) | −42.0846 | −1.63690 | −0.818450 | − | 0.574578i | \(-0.805166\pi\) | ||||
−0.818450 | + | 0.574578i | \(0.805166\pi\) | |||||||
\(662\) | 70.6292 | 2.74508 | ||||||||
\(663\) | 0.470118 | 0.0182579 | ||||||||
\(664\) | −13.3075 | −0.516430 | ||||||||
\(665\) | −38.9577 | −1.51072 | ||||||||
\(666\) | 0.271401 | 0.0105166 | ||||||||
\(667\) | 11.2418 | 0.435285 | ||||||||
\(668\) | −1.62231 | −0.0627691 | ||||||||
\(669\) | −30.9718 | −1.19744 | ||||||||
\(670\) | 80.0320 | 3.09191 | ||||||||
\(671\) | 6.94251 | 0.268013 | ||||||||
\(672\) | 6.07205 | 0.234234 | ||||||||
\(673\) | −40.7528 | −1.57090 | −0.785452 | − | 0.618922i | \(-0.787570\pi\) | ||||
−0.785452 | + | 0.618922i | \(0.787570\pi\) | |||||||
\(674\) | 47.8017 | 1.84125 | ||||||||
\(675\) | −13.2987 | −0.511868 | ||||||||
\(676\) | −46.8680 | −1.80261 | ||||||||
\(677\) | 4.94661 | 0.190114 | 0.0950568 | − | 0.995472i | \(-0.469697\pi\) | ||||
0.0950568 | + | 0.995472i | \(0.469697\pi\) | |||||||
\(678\) | −3.74444 | −0.143805 | ||||||||
\(679\) | 1.67852 | 0.0644157 | ||||||||
\(680\) | −17.1246 | −0.656697 | ||||||||
\(681\) | 24.6668 | 0.945233 | ||||||||
\(682\) | 2.79321 | 0.106957 | ||||||||
\(683\) | −26.9424 | −1.03092 | −0.515462 | − | 0.856913i | \(-0.672380\pi\) | ||||
−0.515462 | + | 0.856913i | \(0.672380\pi\) | |||||||
\(684\) | 54.0514 | 2.06671 | ||||||||
\(685\) | 55.6963 | 2.12805 | ||||||||
\(686\) | 45.7382 | 1.74629 | ||||||||
\(687\) | −12.7336 | −0.485816 | ||||||||
\(688\) | 20.3932 | 0.777482 | ||||||||
\(689\) | 2.58618 | 0.0985256 | ||||||||
\(690\) | 8.11514 | 0.308938 | ||||||||
\(691\) | 45.1013 | 1.71573 | 0.857867 | − | 0.513873i | \(-0.171790\pi\) | ||||
0.857867 | + | 0.513873i | \(0.171790\pi\) | |||||||
\(692\) | 60.2690 | 2.29108 | ||||||||
\(693\) | 3.09894 | 0.117719 | ||||||||
\(694\) | −55.5983 | −2.11048 | ||||||||
\(695\) | −42.6439 | −1.61757 | ||||||||
\(696\) | 39.2527 | 1.48787 | ||||||||
\(697\) | −1.94517 | −0.0736784 | ||||||||
\(698\) | −5.01050 | −0.189650 | ||||||||
\(699\) | −21.5907 | −0.816635 | ||||||||
\(700\) | 16.6046 | 0.627596 | ||||||||
\(701\) | 49.3381 | 1.86348 | 0.931738 | − | 0.363133i | \(-0.118293\pi\) | ||||
0.931738 | + | 0.363133i | \(0.118293\pi\) | |||||||
\(702\) | 3.36926 | 0.127164 | ||||||||
\(703\) | −0.485336 | −0.0183048 | ||||||||
\(704\) | 10.6024 | 0.399594 | ||||||||
\(705\) | −33.4943 | −1.26147 | ||||||||
\(706\) | −57.3859 | −2.15975 | ||||||||
\(707\) | −25.4205 | −0.956037 | ||||||||
\(708\) | −20.4563 | −0.768794 | ||||||||
\(709\) | −10.6945 | −0.401640 | −0.200820 | − | 0.979628i | \(-0.564361\pi\) | ||||
−0.200820 | + | 0.979628i | \(0.564361\pi\) | |||||||
\(710\) | −105.680 | −3.96610 | ||||||||
\(711\) | 4.84127 | 0.181562 | ||||||||
\(712\) | 43.3647 | 1.62516 | ||||||||
\(713\) | −1.48651 | −0.0556701 | ||||||||
\(714\) | −7.22841 | −0.270516 | ||||||||
\(715\) | −0.701748 | −0.0262439 | ||||||||
\(716\) | 56.9630 | 2.12881 | ||||||||
\(717\) | 17.5966 | 0.657155 | ||||||||
\(718\) | 10.3671 | 0.386896 | ||||||||
\(719\) | −11.0211 | −0.411019 | −0.205510 | − | 0.978655i | \(-0.565885\pi\) | ||||
−0.205510 | + | 0.978655i | \(0.565885\pi\) | |||||||
\(720\) | −9.78677 | −0.364731 | ||||||||
\(721\) | 1.09796 | 0.0408900 | ||||||||
\(722\) | −104.901 | −3.90400 | ||||||||
\(723\) | −4.63520 | −0.172385 | ||||||||
\(724\) | 53.6116 | 1.99246 | ||||||||
\(725\) | −24.6672 | −0.916117 | ||||||||
\(726\) | 25.5106 | 0.946789 | ||||||||
\(727\) | 6.00254 | 0.222622 | 0.111311 | − | 0.993786i | \(-0.464495\pi\) | ||||
0.111311 | + | 0.993786i | \(0.464495\pi\) | |||||||
\(728\) | −1.88663 | −0.0699232 | ||||||||
\(729\) | 16.1998 | 0.599992 | ||||||||
\(730\) | 17.3814 | 0.643316 | ||||||||
\(731\) | 17.3405 | 0.641362 | ||||||||
\(732\) | −28.7660 | −1.06322 | ||||||||
\(733\) | −28.3259 | −1.04624 | −0.523120 | − | 0.852259i | \(-0.675232\pi\) | ||||
−0.523120 | + | 0.852259i | \(0.675232\pi\) | |||||||
\(734\) | −38.5532 | −1.42302 | ||||||||
\(735\) | −11.1793 | −0.412354 | ||||||||
\(736\) | −3.76750 | −0.138872 | ||||||||
\(737\) | 11.3845 | 0.419354 | ||||||||
\(738\) | −5.36105 | −0.197343 | ||||||||
\(739\) | 36.8596 | 1.35590 | 0.677951 | − | 0.735107i | \(-0.262868\pi\) | ||||
0.677951 | + | 0.735107i | \(0.262868\pi\) | |||||||
\(740\) | 0.609053 | 0.0223892 | ||||||||
\(741\) | −2.31703 | −0.0851182 | ||||||||
\(742\) | −39.7644 | −1.45980 | ||||||||
\(743\) | 6.63581 | 0.243444 | 0.121722 | − | 0.992564i | \(-0.461158\pi\) | ||||
0.121722 | + | 0.992564i | \(0.461158\pi\) | |||||||
\(744\) | −5.19039 | −0.190289 | ||||||||
\(745\) | 28.1808 | 1.03246 | ||||||||
\(746\) | −25.7869 | −0.944127 | ||||||||
\(747\) | −6.46685 | −0.236609 | ||||||||
\(748\) | −5.43172 | −0.198603 | ||||||||
\(749\) | −32.8201 | −1.19922 | ||||||||
\(750\) | 16.8141 | 0.613965 | ||||||||
\(751\) | −10.4902 | −0.382795 | −0.191397 | − | 0.981513i | \(-0.561302\pi\) | ||||
−0.191397 | + | 0.981513i | \(0.561302\pi\) | |||||||
\(752\) | −21.7700 | −0.793870 | ||||||||
\(753\) | 23.5181 | 0.857048 | ||||||||
\(754\) | 6.24949 | 0.227593 | ||||||||
\(755\) | −11.4307 | −0.416006 | ||||||||
\(756\) | −33.3895 | −1.21437 | ||||||||
\(757\) | 35.0830 | 1.27511 | 0.637557 | − | 0.770403i | \(-0.279945\pi\) | ||||
0.637557 | + | 0.770403i | \(0.279945\pi\) | |||||||
\(758\) | −83.5774 | −3.03567 | ||||||||
\(759\) | 1.15438 | 0.0419012 | ||||||||
\(760\) | 84.4005 | 3.06153 | ||||||||
\(761\) | 43.0733 | 1.56141 | 0.780704 | − | 0.624901i | \(-0.214861\pi\) | ||||
0.780704 | + | 0.624901i | \(0.214861\pi\) | |||||||
\(762\) | −12.1351 | −0.439608 | ||||||||
\(763\) | −21.5584 | −0.780468 | ||||||||
\(764\) | −7.84295 | −0.283748 | ||||||||
\(765\) | −8.32179 | −0.300875 | ||||||||
\(766\) | −10.4095 | −0.376111 | ||||||||
\(767\) | −1.46061 | −0.0527397 | ||||||||
\(768\) | −27.7528 | −1.00144 | ||||||||
\(769\) | 38.3731 | 1.38377 | 0.691884 | − | 0.722009i | \(-0.256781\pi\) | ||||
0.691884 | + | 0.722009i | \(0.256781\pi\) | |||||||
\(770\) | 10.7899 | 0.388841 | ||||||||
\(771\) | 11.8305 | 0.426064 | ||||||||
\(772\) | 30.8808 | 1.11143 | ||||||||
\(773\) | −12.4723 | −0.448598 | −0.224299 | − | 0.974520i | \(-0.572009\pi\) | ||||
−0.224299 | + | 0.974520i | \(0.572009\pi\) | |||||||
\(774\) | 47.7920 | 1.71785 | ||||||||
\(775\) | 3.26175 | 0.117165 | ||||||||
\(776\) | −3.63645 | −0.130541 | ||||||||
\(777\) | 0.115295 | 0.00413619 | ||||||||
\(778\) | 63.5683 | 2.27903 | ||||||||
\(779\) | 9.58698 | 0.343489 | ||||||||
\(780\) | 2.90766 | 0.104111 | ||||||||
\(781\) | −15.0329 | −0.537920 | ||||||||
\(782\) | 4.48498 | 0.160383 | ||||||||
\(783\) | 49.6022 | 1.77264 | ||||||||
\(784\) | −7.26609 | −0.259503 | ||||||||
\(785\) | 33.9349 | 1.21119 | ||||||||
\(786\) | 13.3631 | 0.476646 | ||||||||
\(787\) | 36.9367 | 1.31665 | 0.658326 | − | 0.752733i | \(-0.271265\pi\) | ||||
0.658326 | + | 0.752733i | \(0.271265\pi\) | |||||||
\(788\) | 27.2636 | 0.971224 | ||||||||
\(789\) | 27.1918 | 0.968053 | ||||||||
\(790\) | 16.8564 | 0.599723 | ||||||||
\(791\) | 2.64955 | 0.0942070 | ||||||||
\(792\) | −6.71373 | −0.238562 | ||||||||
\(793\) | −2.05394 | −0.0729375 | ||||||||
\(794\) | −19.6323 | −0.696723 | ||||||||
\(795\) | 27.4843 | 0.974769 | ||||||||
\(796\) | −10.0955 | −0.357825 | ||||||||
\(797\) | 50.8525 | 1.80129 | 0.900644 | − | 0.434557i | \(-0.143095\pi\) | ||||
0.900644 | + | 0.434557i | \(0.143095\pi\) | |||||||
\(798\) | 35.6261 | 1.26115 | ||||||||
\(799\) | −18.5112 | −0.654881 | ||||||||
\(800\) | 8.26678 | 0.292275 | ||||||||
\(801\) | 21.0734 | 0.744590 | ||||||||
\(802\) | 45.9116 | 1.62119 | ||||||||
\(803\) | 2.47250 | 0.0872527 | ||||||||
\(804\) | −47.1713 | −1.66360 | ||||||||
\(805\) | −5.74223 | −0.202387 | ||||||||
\(806\) | −0.826370 | −0.0291076 | ||||||||
\(807\) | −17.3489 | −0.610709 | ||||||||
\(808\) | 55.0726 | 1.93745 | ||||||||
\(809\) | 39.8269 | 1.40024 | 0.700120 | − | 0.714026i | \(-0.253130\pi\) | ||||
0.700120 | + | 0.714026i | \(0.253130\pi\) | |||||||
\(810\) | −0.898913 | −0.0315846 | ||||||||
\(811\) | −20.6010 | −0.723401 | −0.361700 | − | 0.932294i | \(-0.617804\pi\) | ||||
−0.361700 | + | 0.932294i | \(0.617804\pi\) | |||||||
\(812\) | −61.9327 | −2.17341 | ||||||||
\(813\) | 14.0529 | 0.492857 | ||||||||
\(814\) | 0.134421 | 0.00471144 | ||||||||
\(815\) | 34.5263 | 1.20940 | ||||||||
\(816\) | 3.24729 | 0.113678 | ||||||||
\(817\) | −85.4647 | −2.99003 | ||||||||
\(818\) | 18.6276 | 0.651298 | ||||||||
\(819\) | −0.916819 | −0.0320363 | ||||||||
\(820\) | −12.0308 | −0.420133 | ||||||||
\(821\) | −22.0460 | −0.769409 | −0.384705 | − | 0.923040i | \(-0.625697\pi\) | ||||
−0.384705 | + | 0.923040i | \(0.625697\pi\) | |||||||
\(822\) | −50.9331 | −1.77650 | ||||||||
\(823\) | 30.0411 | 1.04717 | 0.523583 | − | 0.851975i | \(-0.324595\pi\) | ||||
0.523583 | + | 0.851975i | \(0.324595\pi\) | |||||||
\(824\) | −2.37868 | −0.0828653 | ||||||||
\(825\) | −2.53297 | −0.0881868 | ||||||||
\(826\) | 22.4580 | 0.781414 | ||||||||
\(827\) | −2.00976 | −0.0698862 | −0.0349431 | − | 0.999389i | \(-0.511125\pi\) | ||||
−0.0349431 | + | 0.999389i | \(0.511125\pi\) | |||||||
\(828\) | 7.96697 | 0.276872 | ||||||||
\(829\) | −30.3566 | −1.05433 | −0.527163 | − | 0.849764i | \(-0.676744\pi\) | ||||
−0.527163 | + | 0.849764i | \(0.676744\pi\) | |||||||
\(830\) | −22.5163 | −0.781552 | ||||||||
\(831\) | −31.5873 | −1.09575 | ||||||||
\(832\) | −3.13672 | −0.108746 | ||||||||
\(833\) | −6.17843 | −0.214070 | ||||||||
\(834\) | 38.9970 | 1.35035 | ||||||||
\(835\) | −1.23103 | −0.0426016 | ||||||||
\(836\) | 26.7709 | 0.925889 | ||||||||
\(837\) | −6.55890 | −0.226709 | ||||||||
\(838\) | −79.7046 | −2.75335 | ||||||||
\(839\) | −37.7547 | −1.30344 | −0.651719 | − | 0.758460i | \(-0.725952\pi\) | ||||
−0.651719 | + | 0.758460i | \(0.725952\pi\) | |||||||
\(840\) | −20.0500 | −0.691789 | ||||||||
\(841\) | 63.0049 | 2.17258 | ||||||||
\(842\) | −44.9157 | −1.54790 | ||||||||
\(843\) | −5.72562 | −0.197201 | ||||||||
\(844\) | 12.8515 | 0.442368 | ||||||||
\(845\) | −35.5640 | −1.22344 | ||||||||
\(846\) | −51.0186 | −1.75406 | ||||||||
\(847\) | −18.0512 | −0.620246 | ||||||||
\(848\) | 17.8637 | 0.613443 | ||||||||
\(849\) | 20.0710 | 0.688835 | ||||||||
\(850\) | −9.84111 | −0.337547 | ||||||||
\(851\) | −0.0715368 | −0.00245225 | ||||||||
\(852\) | 62.2883 | 2.13396 | ||||||||
\(853\) | −11.7867 | −0.403569 | −0.201785 | − | 0.979430i | \(-0.564674\pi\) | ||||
−0.201785 | + | 0.979430i | \(0.564674\pi\) | |||||||
\(854\) | 31.5808 | 1.08067 | ||||||||
\(855\) | 41.0149 | 1.40268 | ||||||||
\(856\) | 71.1034 | 2.43026 | ||||||||
\(857\) | −43.7306 | −1.49381 | −0.746904 | − | 0.664932i | \(-0.768460\pi\) | ||||
−0.746904 | + | 0.664932i | \(0.768460\pi\) | |||||||
\(858\) | 0.641734 | 0.0219084 | ||||||||
\(859\) | 34.1861 | 1.16641 | 0.583207 | − | 0.812323i | \(-0.301798\pi\) | ||||
0.583207 | + | 0.812323i | \(0.301798\pi\) | |||||||
\(860\) | 107.250 | 3.65721 | ||||||||
\(861\) | −2.27746 | −0.0776155 | ||||||||
\(862\) | 33.4812 | 1.14038 | ||||||||
\(863\) | −24.4079 | −0.830855 | −0.415427 | − | 0.909626i | \(-0.636368\pi\) | ||||
−0.415427 | + | 0.909626i | \(0.636368\pi\) | |||||||
\(864\) | −16.6233 | −0.565537 | ||||||||
\(865\) | 45.7329 | 1.55497 | ||||||||
\(866\) | −37.2867 | −1.26705 | ||||||||
\(867\) | −15.2735 | −0.518714 | ||||||||
\(868\) | 8.18937 | 0.277965 | ||||||||
\(869\) | 2.39781 | 0.0813401 | ||||||||
\(870\) | 66.4157 | 2.25170 | ||||||||
\(871\) | −3.36811 | −0.114124 | ||||||||
\(872\) | 46.7055 | 1.58165 | ||||||||
\(873\) | −1.76715 | −0.0598091 | ||||||||
\(874\) | −22.1048 | −0.747704 | ||||||||
\(875\) | −11.8976 | −0.402211 | ||||||||
\(876\) | −10.2447 | −0.346137 | ||||||||
\(877\) | 22.0781 | 0.745524 | 0.372762 | − | 0.927927i | \(-0.378411\pi\) | ||||
0.372762 | + | 0.927927i | \(0.378411\pi\) | |||||||
\(878\) | −39.0165 | −1.31674 | ||||||||
\(879\) | −10.1399 | −0.342011 | ||||||||
\(880\) | −4.84724 | −0.163401 | ||||||||
\(881\) | −32.0825 | −1.08089 | −0.540444 | − | 0.841380i | \(-0.681744\pi\) | ||||
−0.540444 | + | 0.841380i | \(0.681744\pi\) | |||||||
\(882\) | −17.0283 | −0.573372 | ||||||||
\(883\) | 45.4919 | 1.53093 | 0.765463 | − | 0.643480i | \(-0.222510\pi\) | ||||
0.765463 | + | 0.643480i | \(0.222510\pi\) | |||||||
\(884\) | 1.60697 | 0.0540483 | ||||||||
\(885\) | −15.5225 | −0.521783 | ||||||||
\(886\) | 50.3178 | 1.69046 | ||||||||
\(887\) | −17.9109 | −0.601390 | −0.300695 | − | 0.953720i | \(-0.597219\pi\) | ||||
−0.300695 | + | 0.953720i | \(0.597219\pi\) | |||||||
\(888\) | −0.249783 | −0.00838216 | ||||||||
\(889\) | 8.58672 | 0.287989 | ||||||||
\(890\) | 73.3733 | 2.45948 | ||||||||
\(891\) | −0.127870 | −0.00428380 | ||||||||
\(892\) | −105.869 | −3.54475 | ||||||||
\(893\) | 91.2348 | 3.05306 | ||||||||
\(894\) | −25.7708 | −0.861903 | ||||||||
\(895\) | 43.2242 | 1.44483 | ||||||||
\(896\) | 36.7821 | 1.22880 | ||||||||
\(897\) | −0.341522 | −0.0114031 | ||||||||
\(898\) | −37.9098 | −1.26507 | ||||||||
\(899\) | −12.1658 | −0.405753 | ||||||||
\(900\) | −17.4814 | −0.582714 | ||||||||
\(901\) | 15.1897 | 0.506043 | ||||||||
\(902\) | −2.65525 | −0.0884100 | ||||||||
\(903\) | 20.3028 | 0.675634 | ||||||||
\(904\) | −5.74014 | −0.190914 | ||||||||
\(905\) | 40.6812 | 1.35229 | ||||||||
\(906\) | 10.4531 | 0.347282 | ||||||||
\(907\) | 25.4200 | 0.844057 | 0.422028 | − | 0.906583i | \(-0.361318\pi\) | ||||
0.422028 | + | 0.906583i | \(0.361318\pi\) | |||||||
\(908\) | 84.3168 | 2.79815 | ||||||||
\(909\) | 26.7629 | 0.887668 | ||||||||
\(910\) | −3.19219 | −0.105820 | ||||||||
\(911\) | 16.1759 | 0.535931 | 0.267966 | − | 0.963428i | \(-0.413649\pi\) | ||||
0.267966 | + | 0.963428i | \(0.413649\pi\) | |||||||
\(912\) | −16.0046 | −0.529966 | ||||||||
\(913\) | −3.20293 | −0.106002 | ||||||||
\(914\) | 41.1389 | 1.36075 | ||||||||
\(915\) | −21.8280 | −0.721612 | ||||||||
\(916\) | −43.5263 | −1.43815 | ||||||||
\(917\) | −9.45566 | −0.312253 | ||||||||
\(918\) | 19.7891 | 0.653136 | ||||||||
\(919\) | 3.26868 | 0.107824 | 0.0539118 | − | 0.998546i | \(-0.482831\pi\) | ||||
0.0539118 | + | 0.998546i | \(0.482831\pi\) | |||||||
\(920\) | 12.4403 | 0.410145 | ||||||||
\(921\) | −23.4612 | −0.773074 | ||||||||
\(922\) | −48.3397 | −1.59198 | ||||||||
\(923\) | 4.44749 | 0.146391 | ||||||||
\(924\) | −6.35962 | −0.209216 | ||||||||
\(925\) | 0.156969 | 0.00516110 | ||||||||
\(926\) | 41.1866 | 1.35348 | ||||||||
\(927\) | −1.15593 | −0.0379659 | ||||||||
\(928\) | −30.8338 | −1.01217 | ||||||||
\(929\) | −23.9458 | −0.785636 | −0.392818 | − | 0.919616i | \(-0.628500\pi\) | ||||
−0.392818 | + | 0.919616i | \(0.628500\pi\) | |||||||
\(930\) | −8.78216 | −0.287978 | ||||||||
\(931\) | 30.4511 | 0.997995 | ||||||||
\(932\) | −73.8021 | −2.41747 | ||||||||
\(933\) | 3.45356 | 0.113065 | ||||||||
\(934\) | 24.7258 | 0.809052 | ||||||||
\(935\) | −4.12166 | −0.134793 | ||||||||
\(936\) | 1.98625 | 0.0649227 | ||||||||
\(937\) | 9.97607 | 0.325904 | 0.162952 | − | 0.986634i | \(-0.447898\pi\) | ||||
0.162952 | + | 0.986634i | \(0.447898\pi\) | |||||||
\(938\) | 51.7871 | 1.69091 | ||||||||
\(939\) | −3.63900 | −0.118754 | ||||||||
\(940\) | −114.491 | −3.73430 | ||||||||
\(941\) | 9.65315 | 0.314684 | 0.157342 | − | 0.987544i | \(-0.449708\pi\) | ||||
0.157342 | + | 0.987544i | \(0.449708\pi\) | |||||||
\(942\) | −31.0328 | −1.01110 | ||||||||
\(943\) | 1.41308 | 0.0460164 | ||||||||
\(944\) | −10.0890 | −0.328370 | ||||||||
\(945\) | −25.3364 | −0.824193 | ||||||||
\(946\) | 23.6706 | 0.769599 | ||||||||
\(947\) | 53.3362 | 1.73319 | 0.866597 | − | 0.499009i | \(-0.166303\pi\) | ||||
0.866597 | + | 0.499009i | \(0.166303\pi\) | |||||||
\(948\) | −9.93523 | −0.322681 | ||||||||
\(949\) | −0.731489 | −0.0237451 | ||||||||
\(950\) | 48.5031 | 1.57365 | ||||||||
\(951\) | 1.84880 | 0.0599513 | ||||||||
\(952\) | −11.0810 | −0.359136 | ||||||||
\(953\) | −20.7581 | −0.672421 | −0.336210 | − | 0.941787i | \(-0.609145\pi\) | ||||
−0.336210 | + | 0.941787i | \(0.609145\pi\) | |||||||
\(954\) | 41.8642 | 1.35540 | ||||||||
\(955\) | −5.95133 | −0.192581 | ||||||||
\(956\) | 60.1491 | 1.94536 | ||||||||
\(957\) | 9.44760 | 0.305398 | ||||||||
\(958\) | 80.6104 | 2.60440 | ||||||||
\(959\) | 36.0400 | 1.16379 | ||||||||
\(960\) | −33.3352 | −1.07589 | ||||||||
\(961\) | −29.3913 | −0.948107 | ||||||||
\(962\) | −0.0397683 | −0.00128218 | ||||||||
\(963\) | 34.5531 | 1.11346 | ||||||||
\(964\) | −15.8442 | −0.510307 | ||||||||
\(965\) | 23.4328 | 0.754328 | ||||||||
\(966\) | 5.25115 | 0.168953 | ||||||||
\(967\) | 27.4841 | 0.883829 | 0.441914 | − | 0.897057i | \(-0.354299\pi\) | ||||
0.441914 | + | 0.897057i | \(0.354299\pi\) | |||||||
\(968\) | 39.1072 | 1.25695 | ||||||||
\(969\) | −13.6089 | −0.437180 | ||||||||
\(970\) | −6.15289 | −0.197557 | ||||||||
\(971\) | −0.823985 | −0.0264430 | −0.0132215 | − | 0.999913i | \(-0.504209\pi\) | ||||
−0.0132215 | + | 0.999913i | \(0.504209\pi\) | |||||||
\(972\) | 56.7870 | 1.82144 | ||||||||
\(973\) | −27.5940 | −0.884623 | ||||||||
\(974\) | 63.1808 | 2.02444 | ||||||||
\(975\) | 0.749380 | 0.0239994 | ||||||||
\(976\) | −14.1874 | −0.454126 | ||||||||
\(977\) | −42.7702 | −1.36834 | −0.684170 | − | 0.729323i | \(-0.739835\pi\) | ||||
−0.684170 | + | 0.729323i | \(0.739835\pi\) | |||||||
\(978\) | −31.5736 | −1.00961 | ||||||||
\(979\) | 10.4373 | 0.333578 | ||||||||
\(980\) | −38.2134 | −1.22068 | ||||||||
\(981\) | 22.6968 | 0.724654 | ||||||||
\(982\) | −84.1987 | −2.68689 | ||||||||
\(983\) | 55.9328 | 1.78398 | 0.891989 | − | 0.452057i | \(-0.149310\pi\) | ||||
0.891989 | + | 0.452057i | \(0.149310\pi\) | |||||||
\(984\) | 4.93402 | 0.157291 | ||||||||
\(985\) | 20.6880 | 0.659173 | ||||||||
\(986\) | 36.7058 | 1.16895 | ||||||||
\(987\) | −21.6735 | −0.689876 | ||||||||
\(988\) | −7.92015 | −0.251974 | ||||||||
\(989\) | −12.5972 | −0.400567 | ||||||||
\(990\) | −11.3597 | −0.361033 | ||||||||
\(991\) | −25.7381 | −0.817599 | −0.408799 | − | 0.912624i | \(-0.634052\pi\) | ||||
−0.408799 | + | 0.912624i | \(0.634052\pi\) | |||||||
\(992\) | 4.07716 | 0.129450 | ||||||||
\(993\) | −31.5888 | −1.00244 | ||||||||
\(994\) | −68.3834 | −2.16899 | ||||||||
\(995\) | −7.66058 | −0.242857 | ||||||||
\(996\) | 13.2712 | 0.420515 | ||||||||
\(997\) | −48.0077 | −1.52042 | −0.760210 | − | 0.649678i | \(-0.774904\pi\) | ||||
−0.760210 | + | 0.649678i | \(0.774904\pi\) | |||||||
\(998\) | 13.2772 | 0.420283 | ||||||||
\(999\) | −0.315641 | −0.00998645 |
(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 | 4007.2.a.a.1.16 | ✓ | 139 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4007.2.a.a.1.16 | ✓ | 139 | 1.1 | even | 1 | trivial |