Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8045,2,Mod(1,8045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8045.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8045 = 5 \cdot 1609 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8045.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2396484261\) |
Analytic rank: | \(1\) |
Dimension: | \(126\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 8045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.51572 | −1.77888 | −0.889441 | − | 0.457051i | \(-0.848906\pi\) | ||||
−0.889441 | + | 0.457051i | \(0.848906\pi\) | |||||||
\(3\) | −0.0214177 | −0.0123655 | −0.00618276 | − | 0.999981i | \(-0.501968\pi\) | ||||
−0.00618276 | + | 0.999981i | \(0.501968\pi\) | |||||||
\(4\) | 4.32884 | 2.16442 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.0538809 | 0.0219968 | ||||||||
\(7\) | 1.26771 | 0.479150 | 0.239575 | − | 0.970878i | \(-0.422992\pi\) | ||||
0.239575 | + | 0.970878i | \(0.422992\pi\) | |||||||
\(8\) | −5.85870 | −2.07136 | ||||||||
\(9\) | −2.99954 | −0.999847 | ||||||||
\(10\) | 2.51572 | 0.795540 | ||||||||
\(11\) | 3.93794 | 1.18733 | 0.593667 | − | 0.804711i | \(-0.297680\pi\) | ||||
0.593667 | + | 0.804711i | \(0.297680\pi\) | |||||||
\(12\) | −0.0927137 | −0.0267641 | ||||||||
\(13\) | 2.08307 | 0.577738 | 0.288869 | − | 0.957369i | \(-0.406721\pi\) | ||||
0.288869 | + | 0.957369i | \(0.406721\pi\) | |||||||
\(14\) | −3.18920 | −0.852351 | ||||||||
\(15\) | 0.0214177 | 0.00553002 | ||||||||
\(16\) | 6.08116 | 1.52029 | ||||||||
\(17\) | −3.08854 | −0.749082 | −0.374541 | − | 0.927210i | \(-0.622200\pi\) | ||||
−0.374541 | + | 0.927210i | \(0.622200\pi\) | |||||||
\(18\) | 7.54600 | 1.77861 | ||||||||
\(19\) | −6.53090 | −1.49829 | −0.749145 | − | 0.662406i | \(-0.769535\pi\) | ||||
−0.749145 | + | 0.662406i | \(0.769535\pi\) | |||||||
\(20\) | −4.32884 | −0.967957 | ||||||||
\(21\) | −0.0271515 | −0.00592493 | ||||||||
\(22\) | −9.90675 | −2.11213 | ||||||||
\(23\) | −1.53462 | −0.319991 | −0.159996 | − | 0.987118i | \(-0.551148\pi\) | ||||
−0.159996 | + | 0.987118i | \(0.551148\pi\) | |||||||
\(24\) | 0.125480 | 0.0256135 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −5.24041 | −1.02773 | ||||||||
\(27\) | 0.128496 | 0.0247291 | ||||||||
\(28\) | 5.48772 | 1.03708 | ||||||||
\(29\) | −0.108241 | −0.0200998 | −0.0100499 | − | 0.999949i | \(-0.503199\pi\) | ||||
−0.0100499 | + | 0.999949i | \(0.503199\pi\) | |||||||
\(30\) | −0.0538809 | −0.00983726 | ||||||||
\(31\) | 0.323055 | 0.0580225 | 0.0290112 | − | 0.999579i | \(-0.490764\pi\) | ||||
0.0290112 | + | 0.999579i | \(0.490764\pi\) | |||||||
\(32\) | −3.58108 | −0.633052 | ||||||||
\(33\) | −0.0843416 | −0.0146820 | ||||||||
\(34\) | 7.76990 | 1.33253 | ||||||||
\(35\) | −1.26771 | −0.214282 | ||||||||
\(36\) | −12.9845 | −2.16409 | ||||||||
\(37\) | 6.32518 | 1.03985 | 0.519927 | − | 0.854211i | \(-0.325959\pi\) | ||||
0.519927 | + | 0.854211i | \(0.325959\pi\) | |||||||
\(38\) | 16.4299 | 2.66528 | ||||||||
\(39\) | −0.0446145 | −0.00714403 | ||||||||
\(40\) | 5.85870 | 0.926341 | ||||||||
\(41\) | 9.10657 | 1.42221 | 0.711104 | − | 0.703087i | \(-0.248195\pi\) | ||||
0.711104 | + | 0.703087i | \(0.248195\pi\) | |||||||
\(42\) | 0.0683054 | 0.0105398 | ||||||||
\(43\) | −11.2121 | −1.70982 | −0.854911 | − | 0.518775i | \(-0.826388\pi\) | ||||
−0.854911 | + | 0.518775i | \(0.826388\pi\) | |||||||
\(44\) | 17.0467 | 2.56989 | ||||||||
\(45\) | 2.99954 | 0.447145 | ||||||||
\(46\) | 3.86068 | 0.569226 | ||||||||
\(47\) | 9.05621 | 1.32098 | 0.660492 | − | 0.750833i | \(-0.270348\pi\) | ||||
0.660492 | + | 0.750833i | \(0.270348\pi\) | |||||||
\(48\) | −0.130244 | −0.0187992 | ||||||||
\(49\) | −5.39291 | −0.770415 | ||||||||
\(50\) | −2.51572 | −0.355776 | ||||||||
\(51\) | 0.0661495 | 0.00926278 | ||||||||
\(52\) | 9.01725 | 1.25047 | ||||||||
\(53\) | 9.08799 | 1.24833 | 0.624166 | − | 0.781292i | \(-0.285439\pi\) | ||||
0.624166 | + | 0.781292i | \(0.285439\pi\) | |||||||
\(54\) | −0.323261 | −0.0439902 | ||||||||
\(55\) | −3.93794 | −0.530992 | ||||||||
\(56\) | −7.42714 | −0.992493 | ||||||||
\(57\) | 0.139877 | 0.0185271 | ||||||||
\(58\) | 0.272303 | 0.0357552 | ||||||||
\(59\) | −5.32710 | −0.693529 | −0.346765 | − | 0.937952i | \(-0.612720\pi\) | ||||
−0.346765 | + | 0.937952i | \(0.612720\pi\) | |||||||
\(60\) | 0.0927137 | 0.0119693 | ||||||||
\(61\) | 4.83182 | 0.618652 | 0.309326 | − | 0.950956i | \(-0.399897\pi\) | ||||
0.309326 | + | 0.950956i | \(0.399897\pi\) | |||||||
\(62\) | −0.812717 | −0.103215 | ||||||||
\(63\) | −3.80255 | −0.479077 | ||||||||
\(64\) | −3.15332 | −0.394165 | ||||||||
\(65\) | −2.08307 | −0.258372 | ||||||||
\(66\) | 0.212180 | 0.0261175 | ||||||||
\(67\) | −12.5127 | −1.52867 | −0.764335 | − | 0.644820i | \(-0.776933\pi\) | ||||
−0.764335 | + | 0.644820i | \(0.776933\pi\) | |||||||
\(68\) | −13.3698 | −1.62133 | ||||||||
\(69\) | 0.0328681 | 0.00395686 | ||||||||
\(70\) | 3.18920 | 0.381183 | ||||||||
\(71\) | 4.09103 | 0.485516 | 0.242758 | − | 0.970087i | \(-0.421948\pi\) | ||||
0.242758 | + | 0.970087i | \(0.421948\pi\) | |||||||
\(72\) | 17.5734 | 2.07105 | ||||||||
\(73\) | 14.6704 | 1.71704 | 0.858520 | − | 0.512781i | \(-0.171385\pi\) | ||||
0.858520 | + | 0.512781i | \(0.171385\pi\) | |||||||
\(74\) | −15.9124 | −1.84978 | ||||||||
\(75\) | −0.0214177 | −0.00247310 | ||||||||
\(76\) | −28.2712 | −3.24293 | ||||||||
\(77\) | 4.99217 | 0.568911 | ||||||||
\(78\) | 0.112237 | 0.0127084 | ||||||||
\(79\) | −8.24167 | −0.927261 | −0.463630 | − | 0.886029i | \(-0.653453\pi\) | ||||
−0.463630 | + | 0.886029i | \(0.653453\pi\) | |||||||
\(80\) | −6.08116 | −0.679894 | ||||||||
\(81\) | 8.99587 | 0.999541 | ||||||||
\(82\) | −22.9096 | −2.52994 | ||||||||
\(83\) | −12.1198 | −1.33032 | −0.665158 | − | 0.746703i | \(-0.731636\pi\) | ||||
−0.665158 | + | 0.746703i | \(0.731636\pi\) | |||||||
\(84\) | −0.117534 | −0.0128240 | ||||||||
\(85\) | 3.08854 | 0.335000 | ||||||||
\(86\) | 28.2064 | 3.04157 | ||||||||
\(87\) | 0.00231827 | 0.000248544 0 | ||||||||
\(88\) | −23.0712 | −2.45940 | ||||||||
\(89\) | 8.70002 | 0.922200 | 0.461100 | − | 0.887348i | \(-0.347455\pi\) | ||||
0.461100 | + | 0.887348i | \(0.347455\pi\) | |||||||
\(90\) | −7.54600 | −0.795418 | ||||||||
\(91\) | 2.64073 | 0.276823 | ||||||||
\(92\) | −6.64314 | −0.692595 | ||||||||
\(93\) | −0.00691910 | −0.000717478 0 | ||||||||
\(94\) | −22.7829 | −2.34987 | ||||||||
\(95\) | 6.53090 | 0.670056 | ||||||||
\(96\) | 0.0766985 | 0.00782801 | ||||||||
\(97\) | 8.03392 | 0.815721 | 0.407861 | − | 0.913044i | \(-0.366275\pi\) | ||||
0.407861 | + | 0.913044i | \(0.366275\pi\) | |||||||
\(98\) | 13.5670 | 1.37048 | ||||||||
\(99\) | −11.8120 | −1.18715 | ||||||||
\(100\) | 4.32884 | 0.432884 | ||||||||
\(101\) | −15.5135 | −1.54365 | −0.771825 | − | 0.635835i | \(-0.780656\pi\) | ||||
−0.771825 | + | 0.635835i | \(0.780656\pi\) | |||||||
\(102\) | −0.166413 | −0.0164774 | ||||||||
\(103\) | −6.50485 | −0.640942 | −0.320471 | − | 0.947258i | \(-0.603841\pi\) | ||||
−0.320471 | + | 0.947258i | \(0.603841\pi\) | |||||||
\(104\) | −12.2041 | −1.19671 | ||||||||
\(105\) | 0.0271515 | 0.00264971 | ||||||||
\(106\) | −22.8628 | −2.22063 | ||||||||
\(107\) | −13.2032 | −1.27640 | −0.638200 | − | 0.769871i | \(-0.720321\pi\) | ||||
−0.638200 | + | 0.769871i | \(0.720321\pi\) | |||||||
\(108\) | 0.556240 | 0.0535242 | ||||||||
\(109\) | 8.83368 | 0.846113 | 0.423057 | − | 0.906103i | \(-0.360957\pi\) | ||||
0.423057 | + | 0.906103i | \(0.360957\pi\) | |||||||
\(110\) | 9.90675 | 0.944571 | ||||||||
\(111\) | −0.135471 | −0.0128583 | ||||||||
\(112\) | 7.70915 | 0.728447 | ||||||||
\(113\) | 14.1582 | 1.33189 | 0.665946 | − | 0.746000i | \(-0.268028\pi\) | ||||
0.665946 | + | 0.746000i | \(0.268028\pi\) | |||||||
\(114\) | −0.351890 | −0.0329576 | ||||||||
\(115\) | 1.53462 | 0.143104 | ||||||||
\(116\) | −0.468557 | −0.0435044 | ||||||||
\(117\) | −6.24824 | −0.577650 | ||||||||
\(118\) | 13.4015 | 1.23371 | ||||||||
\(119\) | −3.91538 | −0.358923 | ||||||||
\(120\) | −0.125480 | −0.0114547 | ||||||||
\(121\) | 4.50737 | 0.409761 | ||||||||
\(122\) | −12.1555 | −1.10051 | ||||||||
\(123\) | −0.195042 | −0.0175863 | ||||||||
\(124\) | 1.39845 | 0.125585 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 9.56615 | 0.852220 | ||||||||
\(127\) | −17.7093 | −1.57145 | −0.785724 | − | 0.618577i | \(-0.787709\pi\) | ||||
−0.785724 | + | 0.618577i | \(0.787709\pi\) | |||||||
\(128\) | 15.0950 | 1.33423 | ||||||||
\(129\) | 0.240136 | 0.0211428 | ||||||||
\(130\) | 5.24041 | 0.459614 | ||||||||
\(131\) | −2.35056 | −0.205370 | −0.102685 | − | 0.994714i | \(-0.532743\pi\) | ||||
−0.102685 | + | 0.994714i | \(0.532743\pi\) | |||||||
\(132\) | −0.365101 | −0.0317780 | ||||||||
\(133\) | −8.27929 | −0.717906 | ||||||||
\(134\) | 31.4784 | 2.71932 | ||||||||
\(135\) | −0.128496 | −0.0110592 | ||||||||
\(136\) | 18.0948 | 1.55162 | ||||||||
\(137\) | 18.2047 | 1.55533 | 0.777664 | − | 0.628680i | \(-0.216404\pi\) | ||||
0.777664 | + | 0.628680i | \(0.216404\pi\) | |||||||
\(138\) | −0.0826869 | −0.00703878 | ||||||||
\(139\) | −7.19896 | −0.610608 | −0.305304 | − | 0.952255i | \(-0.598758\pi\) | ||||
−0.305304 | + | 0.952255i | \(0.598758\pi\) | |||||||
\(140\) | −5.48772 | −0.463797 | ||||||||
\(141\) | −0.193963 | −0.0163346 | ||||||||
\(142\) | −10.2919 | −0.863675 | ||||||||
\(143\) | 8.20299 | 0.685968 | ||||||||
\(144\) | −18.2407 | −1.52006 | ||||||||
\(145\) | 0.108241 | 0.00898891 | ||||||||
\(146\) | −36.9066 | −3.05441 | ||||||||
\(147\) | 0.115504 | 0.00952658 | ||||||||
\(148\) | 27.3807 | 2.25068 | ||||||||
\(149\) | −19.0213 | −1.55828 | −0.779142 | − | 0.626848i | \(-0.784345\pi\) | ||||
−0.779142 | + | 0.626848i | \(0.784345\pi\) | |||||||
\(150\) | 0.0538809 | 0.00439936 | ||||||||
\(151\) | 0.316605 | 0.0257649 | 0.0128825 | − | 0.999917i | \(-0.495899\pi\) | ||||
0.0128825 | + | 0.999917i | \(0.495899\pi\) | |||||||
\(152\) | 38.2625 | 3.10350 | ||||||||
\(153\) | 9.26421 | 0.748967 | ||||||||
\(154\) | −12.5589 | −1.01202 | ||||||||
\(155\) | −0.323055 | −0.0259484 | ||||||||
\(156\) | −0.193129 | −0.0154627 | ||||||||
\(157\) | 12.9229 | 1.03136 | 0.515680 | − | 0.856782i | \(-0.327540\pi\) | ||||
0.515680 | + | 0.856782i | \(0.327540\pi\) | |||||||
\(158\) | 20.7337 | 1.64949 | ||||||||
\(159\) | −0.194644 | −0.0154363 | ||||||||
\(160\) | 3.58108 | 0.283109 | ||||||||
\(161\) | −1.94546 | −0.153324 | ||||||||
\(162\) | −22.6311 | −1.77807 | ||||||||
\(163\) | 14.1740 | 1.11020 | 0.555098 | − | 0.831785i | \(-0.312681\pi\) | ||||
0.555098 | + | 0.831785i | \(0.312681\pi\) | |||||||
\(164\) | 39.4209 | 3.07825 | ||||||||
\(165\) | 0.0843416 | 0.00656598 | ||||||||
\(166\) | 30.4899 | 2.36647 | ||||||||
\(167\) | 16.5749 | 1.28261 | 0.641304 | − | 0.767287i | \(-0.278394\pi\) | ||||
0.641304 | + | 0.767287i | \(0.278394\pi\) | |||||||
\(168\) | 0.159072 | 0.0122727 | ||||||||
\(169\) | −8.66084 | −0.666218 | ||||||||
\(170\) | −7.76990 | −0.595925 | ||||||||
\(171\) | 19.5897 | 1.49806 | ||||||||
\(172\) | −48.5351 | −3.70077 | ||||||||
\(173\) | −19.0261 | −1.44653 | −0.723265 | − | 0.690570i | \(-0.757360\pi\) | ||||
−0.723265 | + | 0.690570i | \(0.757360\pi\) | |||||||
\(174\) | −0.00583211 | −0.000442131 0 | ||||||||
\(175\) | 1.26771 | 0.0958300 | ||||||||
\(176\) | 23.9472 | 1.80509 | ||||||||
\(177\) | 0.114094 | 0.00857584 | ||||||||
\(178\) | −21.8868 | −1.64048 | ||||||||
\(179\) | −8.46273 | −0.632534 | −0.316267 | − | 0.948670i | \(-0.602430\pi\) | ||||
−0.316267 | + | 0.948670i | \(0.602430\pi\) | |||||||
\(180\) | 12.9845 | 0.967809 | ||||||||
\(181\) | −18.9450 | −1.40817 | −0.704087 | − | 0.710114i | \(-0.748643\pi\) | ||||
−0.704087 | + | 0.710114i | \(0.748643\pi\) | |||||||
\(182\) | −6.64332 | −0.492436 | ||||||||
\(183\) | −0.103487 | −0.00764995 | ||||||||
\(184\) | 8.99090 | 0.662818 | ||||||||
\(185\) | −6.32518 | −0.465036 | ||||||||
\(186\) | 0.0174065 | 0.00127631 | ||||||||
\(187\) | −12.1625 | −0.889410 | ||||||||
\(188\) | 39.2029 | 2.85916 | ||||||||
\(189\) | 0.162896 | 0.0118490 | ||||||||
\(190\) | −16.4299 | −1.19195 | ||||||||
\(191\) | 7.70723 | 0.557675 | 0.278838 | − | 0.960338i | \(-0.410051\pi\) | ||||
0.278838 | + | 0.960338i | \(0.410051\pi\) | |||||||
\(192\) | 0.0675369 | 0.00487406 | ||||||||
\(193\) | 22.0565 | 1.58766 | 0.793832 | − | 0.608138i | \(-0.208083\pi\) | ||||
0.793832 | + | 0.608138i | \(0.208083\pi\) | |||||||
\(194\) | −20.2111 | −1.45107 | ||||||||
\(195\) | 0.0446145 | 0.00319491 | ||||||||
\(196\) | −23.3450 | −1.66750 | ||||||||
\(197\) | 8.97138 | 0.639184 | 0.319592 | − | 0.947555i | \(-0.396454\pi\) | ||||
0.319592 | + | 0.947555i | \(0.396454\pi\) | |||||||
\(198\) | 29.7157 | 2.11180 | ||||||||
\(199\) | −3.41567 | −0.242130 | −0.121065 | − | 0.992645i | \(-0.538631\pi\) | ||||
−0.121065 | + | 0.992645i | \(0.538631\pi\) | |||||||
\(200\) | −5.85870 | −0.414273 | ||||||||
\(201\) | 0.267993 | 0.0189028 | ||||||||
\(202\) | 39.0276 | 2.74597 | ||||||||
\(203\) | −0.137218 | −0.00963082 | ||||||||
\(204\) | 0.286350 | 0.0200485 | ||||||||
\(205\) | −9.10657 | −0.636031 | ||||||||
\(206\) | 16.3644 | 1.14016 | ||||||||
\(207\) | 4.60317 | 0.319942 | ||||||||
\(208\) | 12.6675 | 0.878330 | ||||||||
\(209\) | −25.7183 | −1.77897 | ||||||||
\(210\) | −0.0683054 | −0.00471352 | ||||||||
\(211\) | −21.9784 | −1.51305 | −0.756526 | − | 0.653963i | \(-0.773105\pi\) | ||||
−0.756526 | + | 0.653963i | \(0.773105\pi\) | |||||||
\(212\) | 39.3404 | 2.70191 | ||||||||
\(213\) | −0.0876204 | −0.00600365 | ||||||||
\(214\) | 33.2155 | 2.27056 | ||||||||
\(215\) | 11.2121 | 0.764656 | ||||||||
\(216\) | −0.752821 | −0.0512230 | ||||||||
\(217\) | 0.409541 | 0.0278015 | ||||||||
\(218\) | −22.2231 | −1.50513 | ||||||||
\(219\) | −0.314206 | −0.0212321 | ||||||||
\(220\) | −17.0467 | −1.14929 | ||||||||
\(221\) | −6.43364 | −0.432773 | ||||||||
\(222\) | 0.340806 | 0.0228734 | ||||||||
\(223\) | −23.4337 | −1.56924 | −0.784619 | − | 0.619978i | \(-0.787141\pi\) | ||||
−0.784619 | + | 0.619978i | \(0.787141\pi\) | |||||||
\(224\) | −4.53978 | −0.303327 | ||||||||
\(225\) | −2.99954 | −0.199969 | ||||||||
\(226\) | −35.6180 | −2.36928 | ||||||||
\(227\) | 9.70141 | 0.643905 | 0.321952 | − | 0.946756i | \(-0.395661\pi\) | ||||
0.321952 | + | 0.946756i | \(0.395661\pi\) | |||||||
\(228\) | 0.605504 | 0.0401005 | ||||||||
\(229\) | −15.4174 | −1.01881 | −0.509405 | − | 0.860527i | \(-0.670134\pi\) | ||||
−0.509405 | + | 0.860527i | \(0.670134\pi\) | |||||||
\(230\) | −3.86068 | −0.254566 | ||||||||
\(231\) | −0.106921 | −0.00703487 | ||||||||
\(232\) | 0.634150 | 0.0416340 | ||||||||
\(233\) | 18.6783 | 1.22366 | 0.611828 | − | 0.790991i | \(-0.290435\pi\) | ||||
0.611828 | + | 0.790991i | \(0.290435\pi\) | |||||||
\(234\) | 15.7188 | 1.02757 | ||||||||
\(235\) | −9.05621 | −0.590762 | ||||||||
\(236\) | −23.0601 | −1.50109 | ||||||||
\(237\) | 0.176518 | 0.0114661 | ||||||||
\(238\) | 9.85000 | 0.638481 | ||||||||
\(239\) | 4.87905 | 0.315600 | 0.157800 | − | 0.987471i | \(-0.449560\pi\) | ||||
0.157800 | + | 0.987471i | \(0.449560\pi\) | |||||||
\(240\) | 0.130244 | 0.00840724 | ||||||||
\(241\) | −9.37107 | −0.603644 | −0.301822 | − | 0.953364i | \(-0.597595\pi\) | ||||
−0.301822 | + | 0.953364i | \(0.597595\pi\) | |||||||
\(242\) | −11.3393 | −0.728916 | ||||||||
\(243\) | −0.578160 | −0.0370890 | ||||||||
\(244\) | 20.9162 | 1.33902 | ||||||||
\(245\) | 5.39291 | 0.344540 | ||||||||
\(246\) | 0.490670 | 0.0312840 | ||||||||
\(247\) | −13.6043 | −0.865620 | ||||||||
\(248\) | −1.89268 | −0.120186 | ||||||||
\(249\) | 0.259577 | 0.0164500 | ||||||||
\(250\) | 2.51572 | 0.159108 | ||||||||
\(251\) | 11.9094 | 0.751714 | 0.375857 | − | 0.926678i | \(-0.377348\pi\) | ||||
0.375857 | + | 0.926678i | \(0.377348\pi\) | |||||||
\(252\) | −16.4606 | −1.03692 | ||||||||
\(253\) | −6.04326 | −0.379936 | ||||||||
\(254\) | 44.5517 | 2.79542 | ||||||||
\(255\) | −0.0661495 | −0.00414244 | ||||||||
\(256\) | −31.6682 | −1.97926 | ||||||||
\(257\) | −2.71330 | −0.169251 | −0.0846255 | − | 0.996413i | \(-0.526969\pi\) | ||||
−0.0846255 | + | 0.996413i | \(0.526969\pi\) | |||||||
\(258\) | −0.604115 | −0.0376106 | ||||||||
\(259\) | 8.01850 | 0.498246 | ||||||||
\(260\) | −9.01725 | −0.559226 | ||||||||
\(261\) | 0.324673 | 0.0200967 | ||||||||
\(262\) | 5.91335 | 0.365328 | ||||||||
\(263\) | 22.3399 | 1.37754 | 0.688770 | − | 0.724980i | \(-0.258151\pi\) | ||||
0.688770 | + | 0.724980i | \(0.258151\pi\) | |||||||
\(264\) | 0.494132 | 0.0304117 | ||||||||
\(265\) | −9.08799 | −0.558271 | ||||||||
\(266\) | 20.8284 | 1.27707 | ||||||||
\(267\) | −0.186334 | −0.0114035 | ||||||||
\(268\) | −54.1654 | −3.30868 | ||||||||
\(269\) | −9.80238 | −0.597662 | −0.298831 | − | 0.954306i | \(-0.596597\pi\) | ||||
−0.298831 | + | 0.954306i | \(0.596597\pi\) | |||||||
\(270\) | 0.323261 | 0.0196730 | ||||||||
\(271\) | −4.43509 | −0.269413 | −0.134706 | − | 0.990886i | \(-0.543009\pi\) | ||||
−0.134706 | + | 0.990886i | \(0.543009\pi\) | |||||||
\(272\) | −18.7819 | −1.13882 | ||||||||
\(273\) | −0.0565583 | −0.00342306 | ||||||||
\(274\) | −45.7978 | −2.76674 | ||||||||
\(275\) | 3.93794 | 0.237467 | ||||||||
\(276\) | 0.142281 | 0.00856429 | ||||||||
\(277\) | −12.9549 | −0.778385 | −0.389192 | − | 0.921157i | \(-0.627246\pi\) | ||||
−0.389192 | + | 0.921157i | \(0.627246\pi\) | |||||||
\(278\) | 18.1105 | 1.08620 | ||||||||
\(279\) | −0.969018 | −0.0580136 | ||||||||
\(280\) | 7.42714 | 0.443856 | ||||||||
\(281\) | −30.3181 | −1.80863 | −0.904314 | − | 0.426869i | \(-0.859617\pi\) | ||||
−0.904314 | + | 0.426869i | \(0.859617\pi\) | |||||||
\(282\) | 0.487957 | 0.0290574 | ||||||||
\(283\) | −13.1938 | −0.784290 | −0.392145 | − | 0.919903i | \(-0.628267\pi\) | ||||
−0.392145 | + | 0.919903i | \(0.628267\pi\) | |||||||
\(284\) | 17.7094 | 1.05086 | ||||||||
\(285\) | −0.139877 | −0.00828558 | ||||||||
\(286\) | −20.6364 | −1.22026 | ||||||||
\(287\) | 11.5445 | 0.681451 | ||||||||
\(288\) | 10.7416 | 0.632955 | ||||||||
\(289\) | −7.46090 | −0.438876 | ||||||||
\(290\) | −0.272303 | −0.0159902 | ||||||||
\(291\) | −0.172068 | −0.0100868 | ||||||||
\(292\) | 63.5057 | 3.71639 | ||||||||
\(293\) | −19.5195 | −1.14034 | −0.570170 | − | 0.821527i | \(-0.693123\pi\) | ||||
−0.570170 | + | 0.821527i | \(0.693123\pi\) | |||||||
\(294\) | −0.290575 | −0.0169467 | ||||||||
\(295\) | 5.32710 | 0.310156 | ||||||||
\(296\) | −37.0573 | −2.15391 | ||||||||
\(297\) | 0.506011 | 0.0293617 | ||||||||
\(298\) | 47.8522 | 2.77200 | ||||||||
\(299\) | −3.19672 | −0.184871 | ||||||||
\(300\) | −0.0927137 | −0.00535283 | ||||||||
\(301\) | −14.2136 | −0.819261 | ||||||||
\(302\) | −0.796488 | −0.0458327 | ||||||||
\(303\) | 0.332263 | 0.0190880 | ||||||||
\(304\) | −39.7154 | −2.27783 | ||||||||
\(305\) | −4.83182 | −0.276669 | ||||||||
\(306\) | −23.3062 | −1.33232 | ||||||||
\(307\) | 10.3006 | 0.587884 | 0.293942 | − | 0.955823i | \(-0.405033\pi\) | ||||
0.293942 | + | 0.955823i | \(0.405033\pi\) | |||||||
\(308\) | 21.6103 | 1.23136 | ||||||||
\(309\) | 0.139319 | 0.00792558 | ||||||||
\(310\) | 0.812717 | 0.0461592 | ||||||||
\(311\) | 20.1218 | 1.14101 | 0.570503 | − | 0.821296i | \(-0.306748\pi\) | ||||
0.570503 | + | 0.821296i | \(0.306748\pi\) | |||||||
\(312\) | 0.261383 | 0.0147979 | ||||||||
\(313\) | −30.9648 | −1.75024 | −0.875118 | − | 0.483910i | \(-0.839216\pi\) | ||||
−0.875118 | + | 0.483910i | \(0.839216\pi\) | |||||||
\(314\) | −32.5104 | −1.83467 | ||||||||
\(315\) | 3.80255 | 0.214250 | ||||||||
\(316\) | −35.6769 | −2.00698 | ||||||||
\(317\) | 3.82181 | 0.214655 | 0.107327 | − | 0.994224i | \(-0.465771\pi\) | ||||
0.107327 | + | 0.994224i | \(0.465771\pi\) | |||||||
\(318\) | 0.489669 | 0.0274593 | ||||||||
\(319\) | −0.426246 | −0.0238652 | ||||||||
\(320\) | 3.15332 | 0.176276 | ||||||||
\(321\) | 0.282782 | 0.0157833 | ||||||||
\(322\) | 4.89423 | 0.272745 | ||||||||
\(323\) | 20.1710 | 1.12234 | ||||||||
\(324\) | 38.9417 | 2.16343 | ||||||||
\(325\) | 2.08307 | 0.115548 | ||||||||
\(326\) | −35.6578 | −1.97491 | ||||||||
\(327\) | −0.189197 | −0.0104626 | ||||||||
\(328\) | −53.3527 | −2.94591 | ||||||||
\(329\) | 11.4807 | 0.632949 | ||||||||
\(330\) | −0.212180 | −0.0116801 | ||||||||
\(331\) | 7.37932 | 0.405604 | 0.202802 | − | 0.979220i | \(-0.434995\pi\) | ||||
0.202802 | + | 0.979220i | \(0.434995\pi\) | |||||||
\(332\) | −52.4644 | −2.87936 | ||||||||
\(333\) | −18.9726 | −1.03969 | ||||||||
\(334\) | −41.6979 | −2.28161 | ||||||||
\(335\) | 12.5127 | 0.683642 | ||||||||
\(336\) | −0.165112 | −0.00900761 | ||||||||
\(337\) | −8.65898 | −0.471685 | −0.235842 | − | 0.971791i | \(-0.575785\pi\) | ||||
−0.235842 | + | 0.971791i | \(0.575785\pi\) | |||||||
\(338\) | 21.7882 | 1.18512 | ||||||||
\(339\) | −0.303236 | −0.0164695 | ||||||||
\(340\) | 13.3698 | 0.725079 | ||||||||
\(341\) | 1.27217 | 0.0688920 | ||||||||
\(342\) | −49.2821 | −2.66487 | ||||||||
\(343\) | −15.7106 | −0.848294 | ||||||||
\(344\) | 65.6880 | 3.54166 | ||||||||
\(345\) | −0.0328681 | −0.00176956 | ||||||||
\(346\) | 47.8644 | 2.57321 | ||||||||
\(347\) | 13.8217 | 0.741987 | 0.370993 | − | 0.928635i | \(-0.379017\pi\) | ||||
0.370993 | + | 0.928635i | \(0.379017\pi\) | |||||||
\(348\) | 0.0100354 | 0.000537954 0 | ||||||||
\(349\) | 7.84849 | 0.420120 | 0.210060 | − | 0.977688i | \(-0.432634\pi\) | ||||
0.210060 | + | 0.977688i | \(0.432634\pi\) | |||||||
\(350\) | −3.18920 | −0.170470 | ||||||||
\(351\) | 0.267666 | 0.0142870 | ||||||||
\(352\) | −14.1021 | −0.751644 | ||||||||
\(353\) | 23.3237 | 1.24140 | 0.620699 | − | 0.784049i | \(-0.286849\pi\) | ||||
0.620699 | + | 0.784049i | \(0.286849\pi\) | |||||||
\(354\) | −0.287029 | −0.0152554 | ||||||||
\(355\) | −4.09103 | −0.217129 | ||||||||
\(356\) | 37.6610 | 1.99603 | ||||||||
\(357\) | 0.0838585 | 0.00443826 | ||||||||
\(358\) | 21.2899 | 1.12520 | ||||||||
\(359\) | −4.09597 | −0.216177 | −0.108088 | − | 0.994141i | \(-0.534473\pi\) | ||||
−0.108088 | + | 0.994141i | \(0.534473\pi\) | |||||||
\(360\) | −17.5734 | −0.926200 | ||||||||
\(361\) | 23.6526 | 1.24487 | ||||||||
\(362\) | 47.6604 | 2.50497 | ||||||||
\(363\) | −0.0965374 | −0.00506690 | ||||||||
\(364\) | 11.4313 | 0.599162 | ||||||||
\(365\) | −14.6704 | −0.767883 | ||||||||
\(366\) | 0.260343 | 0.0136083 | ||||||||
\(367\) | 23.3001 | 1.21626 | 0.608129 | − | 0.793838i | \(-0.291920\pi\) | ||||
0.608129 | + | 0.793838i | \(0.291920\pi\) | |||||||
\(368\) | −9.33229 | −0.486479 | ||||||||
\(369\) | −27.3155 | −1.42199 | ||||||||
\(370\) | 15.9124 | 0.827245 | ||||||||
\(371\) | 11.5209 | 0.598138 | ||||||||
\(372\) | −0.0299517 | −0.00155292 | ||||||||
\(373\) | −3.07530 | −0.159233 | −0.0796166 | − | 0.996826i | \(-0.525370\pi\) | ||||
−0.0796166 | + | 0.996826i | \(0.525370\pi\) | |||||||
\(374\) | 30.5974 | 1.58215 | ||||||||
\(375\) | 0.0214177 | 0.00110600 | ||||||||
\(376\) | −53.0576 | −2.73624 | ||||||||
\(377\) | −0.225473 | −0.0116124 | ||||||||
\(378\) | −0.409801 | −0.0210779 | ||||||||
\(379\) | −14.9385 | −0.767340 | −0.383670 | − | 0.923470i | \(-0.625340\pi\) | ||||
−0.383670 | + | 0.923470i | \(0.625340\pi\) | |||||||
\(380\) | 28.2712 | 1.45028 | ||||||||
\(381\) | 0.379293 | 0.0194318 | ||||||||
\(382\) | −19.3892 | −0.992038 | ||||||||
\(383\) | −37.6380 | −1.92321 | −0.961606 | − | 0.274435i | \(-0.911509\pi\) | ||||
−0.961606 | + | 0.274435i | \(0.911509\pi\) | |||||||
\(384\) | −0.323301 | −0.0164984 | ||||||||
\(385\) | −4.99217 | −0.254425 | ||||||||
\(386\) | −55.4880 | −2.82426 | ||||||||
\(387\) | 33.6310 | 1.70956 | ||||||||
\(388\) | 34.7776 | 1.76556 | ||||||||
\(389\) | 9.88125 | 0.500999 | 0.250500 | − | 0.968117i | \(-0.419405\pi\) | ||||
0.250500 | + | 0.968117i | \(0.419405\pi\) | |||||||
\(390\) | −0.112237 | −0.00568336 | ||||||||
\(391\) | 4.73975 | 0.239700 | ||||||||
\(392\) | 31.5954 | 1.59581 | ||||||||
\(393\) | 0.0503436 | 0.00253950 | ||||||||
\(394\) | −22.5695 | −1.13703 | ||||||||
\(395\) | 8.24167 | 0.414684 | ||||||||
\(396\) | −51.1323 | −2.56949 | ||||||||
\(397\) | 13.3821 | 0.671629 | 0.335815 | − | 0.941928i | \(-0.390988\pi\) | ||||
0.335815 | + | 0.941928i | \(0.390988\pi\) | |||||||
\(398\) | 8.59286 | 0.430721 | ||||||||
\(399\) | 0.177323 | 0.00887727 | ||||||||
\(400\) | 6.08116 | 0.304058 | ||||||||
\(401\) | 1.69938 | 0.0848631 | 0.0424316 | − | 0.999099i | \(-0.486490\pi\) | ||||
0.0424316 | + | 0.999099i | \(0.486490\pi\) | |||||||
\(402\) | −0.674195 | −0.0336258 | ||||||||
\(403\) | 0.672946 | 0.0335218 | ||||||||
\(404\) | −67.1554 | −3.34110 | ||||||||
\(405\) | −8.99587 | −0.447008 | ||||||||
\(406\) | 0.345202 | 0.0171321 | ||||||||
\(407\) | 24.9082 | 1.23465 | ||||||||
\(408\) | −0.387550 | −0.0191866 | ||||||||
\(409\) | 36.0371 | 1.78192 | 0.890959 | − | 0.454084i | \(-0.150033\pi\) | ||||
0.890959 | + | 0.454084i | \(0.150033\pi\) | |||||||
\(410\) | 22.9096 | 1.13142 | ||||||||
\(411\) | −0.389902 | −0.0192324 | ||||||||
\(412\) | −28.1584 | −1.38727 | ||||||||
\(413\) | −6.75323 | −0.332304 | ||||||||
\(414\) | −11.5803 | −0.569139 | ||||||||
\(415\) | 12.1198 | 0.594935 | ||||||||
\(416\) | −7.45963 | −0.365738 | ||||||||
\(417\) | 0.154185 | 0.00755047 | ||||||||
\(418\) | 64.6999 | 3.16458 | ||||||||
\(419\) | 25.8445 | 1.26259 | 0.631294 | − | 0.775543i | \(-0.282524\pi\) | ||||
0.631294 | + | 0.775543i | \(0.282524\pi\) | |||||||
\(420\) | 0.117534 | 0.00573508 | ||||||||
\(421\) | −16.9095 | −0.824118 | −0.412059 | − | 0.911157i | \(-0.635190\pi\) | ||||
−0.412059 | + | 0.911157i | \(0.635190\pi\) | |||||||
\(422\) | 55.2914 | 2.69154 | ||||||||
\(423\) | −27.1645 | −1.32078 | ||||||||
\(424\) | −53.2438 | −2.58575 | ||||||||
\(425\) | −3.08854 | −0.149816 | ||||||||
\(426\) | 0.220428 | 0.0106798 | ||||||||
\(427\) | 6.12536 | 0.296427 | ||||||||
\(428\) | −57.1544 | −2.76266 | ||||||||
\(429\) | −0.175689 | −0.00848235 | ||||||||
\(430\) | −28.2064 | −1.36023 | ||||||||
\(431\) | 0.684825 | 0.0329869 | 0.0164934 | − | 0.999864i | \(-0.494750\pi\) | ||||
0.0164934 | + | 0.999864i | \(0.494750\pi\) | |||||||
\(432\) | 0.781406 | 0.0375954 | ||||||||
\(433\) | 17.2171 | 0.827403 | 0.413702 | − | 0.910413i | \(-0.364236\pi\) | ||||
0.413702 | + | 0.910413i | \(0.364236\pi\) | |||||||
\(434\) | −1.03029 | −0.0494555 | ||||||||
\(435\) | −0.00231827 | −0.000111152 0 | ||||||||
\(436\) | 38.2396 | 1.83134 | ||||||||
\(437\) | 10.0225 | 0.479440 | ||||||||
\(438\) | 0.790454 | 0.0377693 | ||||||||
\(439\) | 16.7665 | 0.800222 | 0.400111 | − | 0.916467i | \(-0.368972\pi\) | ||||
0.400111 | + | 0.916467i | \(0.368972\pi\) | |||||||
\(440\) | 23.0712 | 1.09988 | ||||||||
\(441\) | 16.1762 | 0.770298 | ||||||||
\(442\) | 16.1852 | 0.769852 | ||||||||
\(443\) | 13.2202 | 0.628111 | 0.314056 | − | 0.949405i | \(-0.398312\pi\) | ||||
0.314056 | + | 0.949405i | \(0.398312\pi\) | |||||||
\(444\) | −0.586431 | −0.0278308 | ||||||||
\(445\) | −8.70002 | −0.412421 | ||||||||
\(446\) | 58.9526 | 2.79149 | ||||||||
\(447\) | 0.407392 | 0.0192690 | ||||||||
\(448\) | −3.99750 | −0.188864 | ||||||||
\(449\) | −8.15974 | −0.385082 | −0.192541 | − | 0.981289i | \(-0.561673\pi\) | ||||
−0.192541 | + | 0.981289i | \(0.561673\pi\) | |||||||
\(450\) | 7.54600 | 0.355722 | ||||||||
\(451\) | 35.8611 | 1.68864 | ||||||||
\(452\) | 61.2886 | 2.88277 | ||||||||
\(453\) | −0.00678094 | −0.000318596 0 | ||||||||
\(454\) | −24.4060 | −1.14543 | ||||||||
\(455\) | −2.64073 | −0.123799 | ||||||||
\(456\) | −0.819495 | −0.0383764 | ||||||||
\(457\) | 35.4853 | 1.65993 | 0.829966 | − | 0.557814i | \(-0.188360\pi\) | ||||
0.829966 | + | 0.557814i | \(0.188360\pi\) | |||||||
\(458\) | 38.7858 | 1.81234 | ||||||||
\(459\) | −0.396867 | −0.0185241 | ||||||||
\(460\) | 6.64314 | 0.309738 | ||||||||
\(461\) | 19.6134 | 0.913485 | 0.456743 | − | 0.889599i | \(-0.349016\pi\) | ||||
0.456743 | + | 0.889599i | \(0.349016\pi\) | |||||||
\(462\) | 0.268983 | 0.0125142 | ||||||||
\(463\) | −0.538993 | −0.0250491 | −0.0125246 | − | 0.999922i | \(-0.503987\pi\) | ||||
−0.0125246 | + | 0.999922i | \(0.503987\pi\) | |||||||
\(464\) | −0.658229 | −0.0305575 | ||||||||
\(465\) | 0.00691910 | 0.000320866 0 | ||||||||
\(466\) | −46.9893 | −2.17674 | ||||||||
\(467\) | −37.2477 | −1.72362 | −0.861810 | − | 0.507232i | \(-0.830669\pi\) | ||||
−0.861810 | + | 0.507232i | \(0.830669\pi\) | |||||||
\(468\) | −27.0476 | −1.25028 | ||||||||
\(469\) | −15.8625 | −0.732462 | ||||||||
\(470\) | 22.7829 | 1.05090 | ||||||||
\(471\) | −0.276779 | −0.0127533 | ||||||||
\(472\) | 31.2099 | 1.43655 | ||||||||
\(473\) | −44.1524 | −2.03013 | ||||||||
\(474\) | −0.444069 | −0.0203967 | ||||||||
\(475\) | −6.53090 | −0.299658 | ||||||||
\(476\) | −16.9491 | −0.776859 | ||||||||
\(477\) | −27.2598 | −1.24814 | ||||||||
\(478\) | −12.2743 | −0.561414 | ||||||||
\(479\) | −10.1785 | −0.465070 | −0.232535 | − | 0.972588i | \(-0.574702\pi\) | ||||
−0.232535 | + | 0.972588i | \(0.574702\pi\) | |||||||
\(480\) | −0.0766985 | −0.00350079 | ||||||||
\(481\) | 13.1758 | 0.600763 | ||||||||
\(482\) | 23.5750 | 1.07381 | ||||||||
\(483\) | 0.0416673 | 0.00189593 | ||||||||
\(484\) | 19.5117 | 0.886894 | ||||||||
\(485\) | −8.03392 | −0.364802 | ||||||||
\(486\) | 1.45449 | 0.0659769 | ||||||||
\(487\) | 4.21503 | 0.191001 | 0.0955006 | − | 0.995429i | \(-0.469555\pi\) | ||||
0.0955006 | + | 0.995429i | \(0.469555\pi\) | |||||||
\(488\) | −28.3082 | −1.28145 | ||||||||
\(489\) | −0.303575 | −0.0137281 | ||||||||
\(490\) | −13.5670 | −0.612896 | ||||||||
\(491\) | 15.5155 | 0.700204 | 0.350102 | − | 0.936712i | \(-0.386147\pi\) | ||||
0.350102 | + | 0.936712i | \(0.386147\pi\) | |||||||
\(492\) | −0.844304 | −0.0380642 | ||||||||
\(493\) | 0.334306 | 0.0150564 | ||||||||
\(494\) | 34.2245 | 1.53984 | ||||||||
\(495\) | 11.8120 | 0.530910 | ||||||||
\(496\) | 1.96455 | 0.0882110 | ||||||||
\(497\) | 5.18624 | 0.232635 | ||||||||
\(498\) | −0.653023 | −0.0292627 | ||||||||
\(499\) | −9.02280 | −0.403916 | −0.201958 | − | 0.979394i | \(-0.564730\pi\) | ||||
−0.201958 | + | 0.979394i | \(0.564730\pi\) | |||||||
\(500\) | −4.32884 | −0.193591 | ||||||||
\(501\) | −0.354997 | −0.0158601 | ||||||||
\(502\) | −29.9607 | −1.33721 | ||||||||
\(503\) | −36.0803 | −1.60874 | −0.804370 | − | 0.594128i | \(-0.797497\pi\) | ||||
−0.804370 | + | 0.594128i | \(0.797497\pi\) | |||||||
\(504\) | 22.2780 | 0.992341 | ||||||||
\(505\) | 15.5135 | 0.690341 | ||||||||
\(506\) | 15.2031 | 0.675862 | ||||||||
\(507\) | 0.185495 | 0.00823813 | ||||||||
\(508\) | −76.6608 | −3.40127 | ||||||||
\(509\) | −23.0572 | −1.02199 | −0.510995 | − | 0.859584i | \(-0.670723\pi\) | ||||
−0.510995 | + | 0.859584i | \(0.670723\pi\) | |||||||
\(510\) | 0.166413 | 0.00736891 | ||||||||
\(511\) | 18.5978 | 0.822719 | ||||||||
\(512\) | 49.4782 | 2.18665 | ||||||||
\(513\) | −0.839196 | −0.0370514 | ||||||||
\(514\) | 6.82590 | 0.301077 | ||||||||
\(515\) | 6.50485 | 0.286638 | ||||||||
\(516\) | 1.03951 | 0.0457619 | ||||||||
\(517\) | 35.6628 | 1.56845 | ||||||||
\(518\) | −20.1723 | −0.886320 | ||||||||
\(519\) | 0.407496 | 0.0178871 | ||||||||
\(520\) | 12.2041 | 0.535183 | ||||||||
\(521\) | −18.6325 | −0.816306 | −0.408153 | − | 0.912914i | \(-0.633827\pi\) | ||||
−0.408153 | + | 0.912914i | \(0.633827\pi\) | |||||||
\(522\) | −0.816785 | −0.0357497 | ||||||||
\(523\) | −8.50789 | −0.372024 | −0.186012 | − | 0.982547i | \(-0.559556\pi\) | ||||
−0.186012 | + | 0.982547i | \(0.559556\pi\) | |||||||
\(524\) | −10.1752 | −0.444506 | ||||||||
\(525\) | −0.0271515 | −0.00118499 | ||||||||
\(526\) | −56.2010 | −2.45048 | ||||||||
\(527\) | −0.997771 | −0.0434636 | ||||||||
\(528\) | −0.512894 | −0.0223209 | ||||||||
\(529\) | −20.6449 | −0.897606 | ||||||||
\(530\) | 22.8628 | 0.993097 | ||||||||
\(531\) | 15.9789 | 0.693423 | ||||||||
\(532\) | −35.8397 | −1.55385 | ||||||||
\(533\) | 18.9696 | 0.821664 | ||||||||
\(534\) | 0.468765 | 0.0202854 | ||||||||
\(535\) | 13.2032 | 0.570823 | ||||||||
\(536\) | 73.3081 | 3.16643 | ||||||||
\(537\) | 0.181252 | 0.00782161 | ||||||||
\(538\) | 24.6600 | 1.06317 | ||||||||
\(539\) | −21.2369 | −0.914740 | ||||||||
\(540\) | −0.556240 | −0.0239367 | ||||||||
\(541\) | 7.38012 | 0.317296 | 0.158648 | − | 0.987335i | \(-0.449287\pi\) | ||||
0.158648 | + | 0.987335i | \(0.449287\pi\) | |||||||
\(542\) | 11.1574 | 0.479253 | ||||||||
\(543\) | 0.405759 | 0.0174128 | ||||||||
\(544\) | 11.0603 | 0.474208 | ||||||||
\(545\) | −8.83368 | −0.378393 | ||||||||
\(546\) | 0.142285 | 0.00608922 | ||||||||
\(547\) | 6.81094 | 0.291215 | 0.145607 | − | 0.989342i | \(-0.453486\pi\) | ||||
0.145607 | + | 0.989342i | \(0.453486\pi\) | |||||||
\(548\) | 78.8050 | 3.36638 | ||||||||
\(549\) | −14.4933 | −0.618557 | ||||||||
\(550\) | −9.90675 | −0.422425 | ||||||||
\(551\) | 0.706909 | 0.0301153 | ||||||||
\(552\) | −0.192564 | −0.00819608 | ||||||||
\(553\) | −10.4481 | −0.444297 | ||||||||
\(554\) | 32.5909 | 1.38465 | ||||||||
\(555\) | 0.135471 | 0.00575041 | ||||||||
\(556\) | −31.1631 | −1.32161 | ||||||||
\(557\) | −39.4581 | −1.67189 | −0.835946 | − | 0.548811i | \(-0.815081\pi\) | ||||
−0.835946 | + | 0.548811i | \(0.815081\pi\) | |||||||
\(558\) | 2.43778 | 0.103199 | ||||||||
\(559\) | −23.3554 | −0.987830 | ||||||||
\(560\) | −7.70915 | −0.325771 | ||||||||
\(561\) | 0.260493 | 0.0109980 | ||||||||
\(562\) | 76.2718 | 3.21733 | ||||||||
\(563\) | −36.9578 | −1.55758 | −0.778792 | − | 0.627282i | \(-0.784167\pi\) | ||||
−0.778792 | + | 0.627282i | \(0.784167\pi\) | |||||||
\(564\) | −0.839635 | −0.0353550 | ||||||||
\(565\) | −14.1582 | −0.595640 | ||||||||
\(566\) | 33.1919 | 1.39516 | ||||||||
\(567\) | 11.4042 | 0.478930 | ||||||||
\(568\) | −23.9681 | −1.00568 | ||||||||
\(569\) | −1.88975 | −0.0792224 | −0.0396112 | − | 0.999215i | \(-0.512612\pi\) | ||||
−0.0396112 | + | 0.999215i | \(0.512612\pi\) | |||||||
\(570\) | 0.351890 | 0.0147391 | ||||||||
\(571\) | −21.9563 | −0.918842 | −0.459421 | − | 0.888219i | \(-0.651943\pi\) | ||||
−0.459421 | + | 0.888219i | \(0.651943\pi\) | |||||||
\(572\) | 35.5094 | 1.48472 | ||||||||
\(573\) | −0.165071 | −0.00689594 | ||||||||
\(574\) | −29.0427 | −1.21222 | ||||||||
\(575\) | −1.53462 | −0.0639983 | ||||||||
\(576\) | 9.45852 | 0.394105 | ||||||||
\(577\) | −8.33988 | −0.347194 | −0.173597 | − | 0.984817i | \(-0.555539\pi\) | ||||
−0.173597 | + | 0.984817i | \(0.555539\pi\) | |||||||
\(578\) | 18.7695 | 0.780709 | ||||||||
\(579\) | −0.472400 | −0.0196323 | ||||||||
\(580\) | 0.468557 | 0.0194558 | ||||||||
\(581\) | −15.3643 | −0.637421 | ||||||||
\(582\) | 0.432875 | 0.0179432 | ||||||||
\(583\) | 35.7879 | 1.48219 | ||||||||
\(584\) | −85.9494 | −3.55661 | ||||||||
\(585\) | 6.24824 | 0.258333 | ||||||||
\(586\) | 49.1055 | 2.02853 | ||||||||
\(587\) | 1.84695 | 0.0762316 | 0.0381158 | − | 0.999273i | \(-0.487864\pi\) | ||||
0.0381158 | + | 0.999273i | \(0.487864\pi\) | |||||||
\(588\) | 0.499996 | 0.0206195 | ||||||||
\(589\) | −2.10984 | −0.0869345 | ||||||||
\(590\) | −13.4015 | −0.551730 | ||||||||
\(591\) | −0.192146 | −0.00790384 | ||||||||
\(592\) | 38.4644 | 1.58088 | ||||||||
\(593\) | −39.3393 | −1.61547 | −0.807736 | − | 0.589545i | \(-0.799307\pi\) | ||||
−0.807736 | + | 0.589545i | \(0.799307\pi\) | |||||||
\(594\) | −1.27298 | −0.0522310 | ||||||||
\(595\) | 3.91538 | 0.160515 | ||||||||
\(596\) | −82.3400 | −3.37278 | ||||||||
\(597\) | 0.0731557 | 0.00299406 | ||||||||
\(598\) | 8.04205 | 0.328864 | ||||||||
\(599\) | −39.8306 | −1.62744 | −0.813718 | − | 0.581260i | \(-0.802560\pi\) | ||||
−0.813718 | + | 0.581260i | \(0.802560\pi\) | |||||||
\(600\) | 0.125480 | 0.00512269 | ||||||||
\(601\) | 29.9928 | 1.22343 | 0.611716 | − | 0.791077i | \(-0.290479\pi\) | ||||
0.611716 | + | 0.791077i | \(0.290479\pi\) | |||||||
\(602\) | 35.7575 | 1.45737 | ||||||||
\(603\) | 37.5324 | 1.52844 | ||||||||
\(604\) | 1.37053 | 0.0557661 | ||||||||
\(605\) | −4.50737 | −0.183251 | ||||||||
\(606\) | −0.835880 | −0.0339553 | ||||||||
\(607\) | −6.62954 | −0.269085 | −0.134542 | − | 0.990908i | \(-0.542956\pi\) | ||||
−0.134542 | + | 0.990908i | \(0.542956\pi\) | |||||||
\(608\) | 23.3877 | 0.948495 | ||||||||
\(609\) | 0.00293889 | 0.000119090 0 | ||||||||
\(610\) | 12.1555 | 0.492162 | ||||||||
\(611\) | 18.8647 | 0.763183 | ||||||||
\(612\) | 40.1033 | 1.62108 | ||||||||
\(613\) | −15.5642 | −0.628632 | −0.314316 | − | 0.949318i | \(-0.601775\pi\) | ||||
−0.314316 | + | 0.949318i | \(0.601775\pi\) | |||||||
\(614\) | −25.9133 | −1.04578 | ||||||||
\(615\) | 0.195042 | 0.00786485 | ||||||||
\(616\) | −29.2476 | −1.17842 | ||||||||
\(617\) | 44.4051 | 1.78768 | 0.893841 | − | 0.448383i | \(-0.148000\pi\) | ||||
0.893841 | + | 0.448383i | \(0.148000\pi\) | |||||||
\(618\) | −0.350487 | −0.0140987 | ||||||||
\(619\) | −14.7452 | −0.592660 | −0.296330 | − | 0.955086i | \(-0.595763\pi\) | ||||
−0.296330 | + | 0.955086i | \(0.595763\pi\) | |||||||
\(620\) | −1.39845 | −0.0561633 | ||||||||
\(621\) | −0.197194 | −0.00791311 | ||||||||
\(622\) | −50.6209 | −2.02971 | ||||||||
\(623\) | 11.0291 | 0.441872 | ||||||||
\(624\) | −0.271308 | −0.0108610 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 77.8988 | 3.11346 | ||||||||
\(627\) | 0.550826 | 0.0219979 | ||||||||
\(628\) | 55.9411 | 2.23229 | ||||||||
\(629\) | −19.5356 | −0.778935 | ||||||||
\(630\) | −9.56615 | −0.381125 | ||||||||
\(631\) | −42.3246 | −1.68492 | −0.842459 | − | 0.538761i | \(-0.818893\pi\) | ||||
−0.842459 | + | 0.538761i | \(0.818893\pi\) | |||||||
\(632\) | 48.2855 | 1.92069 | ||||||||
\(633\) | 0.470726 | 0.0187097 | ||||||||
\(634\) | −9.61461 | −0.381845 | ||||||||
\(635\) | 17.7093 | 0.702773 | ||||||||
\(636\) | −0.842581 | −0.0334105 | ||||||||
\(637\) | −11.2338 | −0.445099 | ||||||||
\(638\) | 1.07231 | 0.0424533 | ||||||||
\(639\) | −12.2712 | −0.485442 | ||||||||
\(640\) | −15.0950 | −0.596684 | ||||||||
\(641\) | −13.7514 | −0.543147 | −0.271574 | − | 0.962418i | \(-0.587544\pi\) | ||||
−0.271574 | + | 0.962418i | \(0.587544\pi\) | |||||||
\(642\) | −0.711399 | −0.0280767 | ||||||||
\(643\) | 42.9626 | 1.69428 | 0.847139 | − | 0.531372i | \(-0.178323\pi\) | ||||
0.847139 | + | 0.531372i | \(0.178323\pi\) | |||||||
\(644\) | −8.42158 | −0.331857 | ||||||||
\(645\) | −0.240136 | −0.00945536 | ||||||||
\(646\) | −50.7444 | −1.99651 | ||||||||
\(647\) | −32.6448 | −1.28340 | −0.641699 | − | 0.766957i | \(-0.721770\pi\) | ||||
−0.641699 | + | 0.766957i | \(0.721770\pi\) | |||||||
\(648\) | −52.7041 | −2.07041 | ||||||||
\(649\) | −20.9778 | −0.823451 | ||||||||
\(650\) | −5.24041 | −0.205546 | ||||||||
\(651\) | −0.00877143 | −0.000343779 0 | ||||||||
\(652\) | 61.3570 | 2.40293 | ||||||||
\(653\) | −12.5443 | −0.490895 | −0.245448 | − | 0.969410i | \(-0.578935\pi\) | ||||
−0.245448 | + | 0.969410i | \(0.578935\pi\) | |||||||
\(654\) | 0.475966 | 0.0186118 | ||||||||
\(655\) | 2.35056 | 0.0918440 | ||||||||
\(656\) | 55.3785 | 2.16217 | ||||||||
\(657\) | −44.0044 | −1.71678 | ||||||||
\(658\) | −28.8821 | −1.12594 | ||||||||
\(659\) | −11.2640 | −0.438783 | −0.219391 | − | 0.975637i | \(-0.570407\pi\) | ||||
−0.219391 | + | 0.975637i | \(0.570407\pi\) | |||||||
\(660\) | 0.365101 | 0.0142115 | ||||||||
\(661\) | −8.20495 | −0.319136 | −0.159568 | − | 0.987187i | \(-0.551010\pi\) | ||||
−0.159568 | + | 0.987187i | \(0.551010\pi\) | |||||||
\(662\) | −18.5643 | −0.721522 | ||||||||
\(663\) | 0.137794 | 0.00535146 | ||||||||
\(664\) | 71.0060 | 2.75557 | ||||||||
\(665\) | 8.27929 | 0.321057 | ||||||||
\(666\) | 47.7298 | 1.84949 | ||||||||
\(667\) | 0.166109 | 0.00643176 | ||||||||
\(668\) | 71.7502 | 2.77610 | ||||||||
\(669\) | 0.501896 | 0.0194044 | ||||||||
\(670\) | −31.4784 | −1.21612 | ||||||||
\(671\) | 19.0274 | 0.734546 | ||||||||
\(672\) | 0.0972316 | 0.00375079 | ||||||||
\(673\) | −23.3084 | −0.898473 | −0.449237 | − | 0.893413i | \(-0.648304\pi\) | ||||
−0.449237 | + | 0.893413i | \(0.648304\pi\) | |||||||
\(674\) | 21.7836 | 0.839071 | ||||||||
\(675\) | 0.128496 | 0.00494583 | ||||||||
\(676\) | −37.4914 | −1.44198 | ||||||||
\(677\) | 22.2055 | 0.853428 | 0.426714 | − | 0.904387i | \(-0.359671\pi\) | ||||
0.426714 | + | 0.904387i | \(0.359671\pi\) | |||||||
\(678\) | 0.762856 | 0.0292973 | ||||||||
\(679\) | 10.1847 | 0.390853 | ||||||||
\(680\) | −18.0948 | −0.693906 | ||||||||
\(681\) | −0.207782 | −0.00796221 | ||||||||
\(682\) | −3.20043 | −0.122551 | ||||||||
\(683\) | 26.6312 | 1.01902 | 0.509508 | − | 0.860466i | \(-0.329828\pi\) | ||||
0.509508 | + | 0.860466i | \(0.329828\pi\) | |||||||
\(684\) | 84.8006 | 3.24243 | ||||||||
\(685\) | −18.2047 | −0.695564 | ||||||||
\(686\) | 39.5235 | 1.50901 | ||||||||
\(687\) | 0.330205 | 0.0125981 | ||||||||
\(688\) | −68.1823 | −2.59942 | ||||||||
\(689\) | 18.9309 | 0.721209 | ||||||||
\(690\) | 0.0826869 | 0.00314784 | ||||||||
\(691\) | −10.9495 | −0.416539 | −0.208270 | − | 0.978071i | \(-0.566783\pi\) | ||||
−0.208270 | + | 0.978071i | \(0.566783\pi\) | |||||||
\(692\) | −82.3611 | −3.13090 | ||||||||
\(693\) | −14.9742 | −0.568824 | ||||||||
\(694\) | −34.7715 | −1.31991 | ||||||||
\(695\) | 7.19896 | 0.273072 | ||||||||
\(696\) | −0.0135820 | −0.000514826 0 | ||||||||
\(697\) | −28.1261 | −1.06535 | ||||||||
\(698\) | −19.7446 | −0.747344 | ||||||||
\(699\) | −0.400046 | −0.0151311 | ||||||||
\(700\) | 5.48772 | 0.207416 | ||||||||
\(701\) | −28.5516 | −1.07838 | −0.539189 | − | 0.842184i | \(-0.681269\pi\) | ||||
−0.539189 | + | 0.842184i | \(0.681269\pi\) | |||||||
\(702\) | −0.673373 | −0.0254148 | ||||||||
\(703\) | −41.3091 | −1.55800 | ||||||||
\(704\) | −12.4176 | −0.468006 | ||||||||
\(705\) | 0.193963 | 0.00730508 | ||||||||
\(706\) | −58.6760 | −2.20830 | ||||||||
\(707\) | −19.6666 | −0.739640 | ||||||||
\(708\) | 0.493895 | 0.0185617 | ||||||||
\(709\) | 36.8908 | 1.38546 | 0.692732 | − | 0.721195i | \(-0.256407\pi\) | ||||
0.692732 | + | 0.721195i | \(0.256407\pi\) | |||||||
\(710\) | 10.2919 | 0.386247 | ||||||||
\(711\) | 24.7212 | 0.927119 | ||||||||
\(712\) | −50.9708 | −1.91021 | ||||||||
\(713\) | −0.495769 | −0.0185667 | ||||||||
\(714\) | −0.210964 | −0.00789514 | ||||||||
\(715\) | −8.20299 | −0.306774 | ||||||||
\(716\) | −36.6338 | −1.36907 | ||||||||
\(717\) | −0.104498 | −0.00390255 | ||||||||
\(718\) | 10.3043 | 0.384553 | ||||||||
\(719\) | −31.0765 | −1.15896 | −0.579478 | − | 0.814988i | \(-0.696744\pi\) | ||||
−0.579478 | + | 0.814988i | \(0.696744\pi\) | |||||||
\(720\) | 18.2407 | 0.679790 | ||||||||
\(721\) | −8.24628 | −0.307107 | ||||||||
\(722\) | −59.5033 | −2.21448 | ||||||||
\(723\) | 0.200707 | 0.00746436 | ||||||||
\(724\) | −82.0100 | −3.04788 | ||||||||
\(725\) | −0.108241 | −0.00401996 | ||||||||
\(726\) | 0.242861 | 0.00901342 | ||||||||
\(727\) | −29.8411 | −1.10674 | −0.553372 | − | 0.832934i | \(-0.686659\pi\) | ||||
−0.553372 | + | 0.832934i | \(0.686659\pi\) | |||||||
\(728\) | −15.4712 | −0.573401 | ||||||||
\(729\) | −26.9752 | −0.999083 | ||||||||
\(730\) | 36.9066 | 1.36597 | ||||||||
\(731\) | 34.6289 | 1.28080 | ||||||||
\(732\) | −0.447976 | −0.0165577 | ||||||||
\(733\) | 51.3143 | 1.89534 | 0.947668 | − | 0.319257i | \(-0.103433\pi\) | ||||
0.947668 | + | 0.319257i | \(0.103433\pi\) | |||||||
\(734\) | −58.6166 | −2.16358 | ||||||||
\(735\) | −0.115504 | −0.00426042 | ||||||||
\(736\) | 5.49561 | 0.202571 | ||||||||
\(737\) | −49.2743 | −1.81504 | ||||||||
\(738\) | 68.7182 | 2.52955 | ||||||||
\(739\) | −2.51638 | −0.0925665 | −0.0462833 | − | 0.998928i | \(-0.514738\pi\) | ||||
−0.0462833 | + | 0.998928i | \(0.514738\pi\) | |||||||
\(740\) | −27.3807 | −1.00653 | ||||||||
\(741\) | 0.291372 | 0.0107038 | ||||||||
\(742\) | −28.9835 | −1.06402 | ||||||||
\(743\) | −23.9465 | −0.878511 | −0.439255 | − | 0.898362i | \(-0.644758\pi\) | ||||
−0.439255 | + | 0.898362i | \(0.644758\pi\) | |||||||
\(744\) | 0.0405369 | 0.00148616 | ||||||||
\(745\) | 19.0213 | 0.696886 | ||||||||
\(746\) | 7.73659 | 0.283257 | ||||||||
\(747\) | 36.3537 | 1.33011 | ||||||||
\(748\) | −52.6495 | −1.92506 | ||||||||
\(749\) | −16.7378 | −0.611587 | ||||||||
\(750\) | −0.0538809 | −0.00196745 | ||||||||
\(751\) | −0.514508 | −0.0187747 | −0.00938733 | − | 0.999956i | \(-0.502988\pi\) | ||||
−0.00938733 | + | 0.999956i | \(0.502988\pi\) | |||||||
\(752\) | 55.0723 | 2.00828 | ||||||||
\(753\) | −0.255072 | −0.00929533 | ||||||||
\(754\) | 0.567226 | 0.0206571 | ||||||||
\(755\) | −0.316605 | −0.0115224 | ||||||||
\(756\) | 0.705151 | 0.0256461 | ||||||||
\(757\) | 27.1889 | 0.988198 | 0.494099 | − | 0.869406i | \(-0.335498\pi\) | ||||
0.494099 | + | 0.869406i | \(0.335498\pi\) | |||||||
\(758\) | 37.5811 | 1.36501 | ||||||||
\(759\) | 0.129433 | 0.00469811 | ||||||||
\(760\) | −38.2625 | −1.38793 | ||||||||
\(761\) | 28.3709 | 1.02845 | 0.514223 | − | 0.857657i | \(-0.328080\pi\) | ||||
0.514223 | + | 0.857657i | \(0.328080\pi\) | |||||||
\(762\) | −0.954194 | −0.0345668 | ||||||||
\(763\) | 11.1986 | 0.405415 | ||||||||
\(764\) | 33.3633 | 1.20704 | ||||||||
\(765\) | −9.26421 | −0.334948 | ||||||||
\(766\) | 94.6866 | 3.42116 | ||||||||
\(767\) | −11.0967 | −0.400679 | ||||||||
\(768\) | 0.678260 | 0.0244746 | ||||||||
\(769\) | 5.38533 | 0.194200 | 0.0970999 | − | 0.995275i | \(-0.469043\pi\) | ||||
0.0970999 | + | 0.995275i | \(0.469043\pi\) | |||||||
\(770\) | 12.5589 | 0.452591 | ||||||||
\(771\) | 0.0581126 | 0.00209287 | ||||||||
\(772\) | 95.4791 | 3.43637 | ||||||||
\(773\) | 21.4638 | 0.772000 | 0.386000 | − | 0.922499i | \(-0.373856\pi\) | ||||
0.386000 | + | 0.922499i | \(0.373856\pi\) | |||||||
\(774\) | −84.6061 | −3.04110 | ||||||||
\(775\) | 0.323055 | 0.0116045 | ||||||||
\(776\) | −47.0683 | −1.68965 | ||||||||
\(777\) | −0.171738 | −0.00616106 | ||||||||
\(778\) | −24.8584 | −0.891219 | ||||||||
\(779\) | −59.4741 | −2.13088 | ||||||||
\(780\) | 0.193129 | 0.00691512 | ||||||||
\(781\) | 16.1102 | 0.576469 | ||||||||
\(782\) | −11.9239 | −0.426397 | ||||||||
\(783\) | −0.0139085 | −0.000497051 0 | ||||||||
\(784\) | −32.7951 | −1.17125 | ||||||||
\(785\) | −12.9229 | −0.461238 | ||||||||
\(786\) | −0.126650 | −0.00451747 | ||||||||
\(787\) | −40.8320 | −1.45550 | −0.727751 | − | 0.685841i | \(-0.759435\pi\) | ||||
−0.727751 | + | 0.685841i | \(0.759435\pi\) | |||||||
\(788\) | 38.8356 | 1.38346 | ||||||||
\(789\) | −0.478470 | −0.0170340 | ||||||||
\(790\) | −20.7337 | −0.737673 | ||||||||
\(791\) | 17.9485 | 0.638176 | ||||||||
\(792\) | 69.2030 | 2.45902 | ||||||||
\(793\) | 10.0650 | 0.357419 | ||||||||
\(794\) | −33.6656 | −1.19475 | ||||||||
\(795\) | 0.194644 | 0.00690330 | ||||||||
\(796\) | −14.7859 | −0.524071 | ||||||||
\(797\) | 6.37040 | 0.225651 | 0.112826 | − | 0.993615i | \(-0.464010\pi\) | ||||
0.112826 | + | 0.993615i | \(0.464010\pi\) | |||||||
\(798\) | −0.446096 | −0.0157916 | ||||||||
\(799\) | −27.9705 | −0.989525 | ||||||||
\(800\) | −3.58108 | −0.126610 | ||||||||
\(801\) | −26.0961 | −0.922059 | ||||||||
\(802\) | −4.27517 | −0.150961 | ||||||||
\(803\) | 57.7711 | 2.03870 | ||||||||
\(804\) | 1.16010 | 0.0409135 | ||||||||
\(805\) | 1.94546 | 0.0685685 | ||||||||
\(806\) | −1.69294 | −0.0596313 | ||||||||
\(807\) | 0.209944 | 0.00739039 | ||||||||
\(808\) | 90.8888 | 3.19746 | ||||||||
\(809\) | 48.8112 | 1.71611 | 0.858056 | − | 0.513557i | \(-0.171672\pi\) | ||||
0.858056 | + | 0.513557i | \(0.171672\pi\) | |||||||
\(810\) | 22.6311 | 0.795175 | ||||||||
\(811\) | −37.5599 | −1.31890 | −0.659452 | − | 0.751746i | \(-0.729212\pi\) | ||||
−0.659452 | + | 0.751746i | \(0.729212\pi\) | |||||||
\(812\) | −0.593995 | −0.0208451 | ||||||||
\(813\) | 0.0949894 | 0.00333142 | ||||||||
\(814\) | −62.6619 | −2.19630 | ||||||||
\(815\) | −14.1740 | −0.496494 | ||||||||
\(816\) | 0.402265 | 0.0140821 | ||||||||
\(817\) | 73.2247 | 2.56181 | ||||||||
\(818\) | −90.6591 | −3.16982 | ||||||||
\(819\) | −7.92097 | −0.276781 | ||||||||
\(820\) | −39.4209 | −1.37664 | ||||||||
\(821\) | 12.7298 | 0.444273 | 0.222136 | − | 0.975016i | \(-0.428697\pi\) | ||||
0.222136 | + | 0.975016i | \(0.428697\pi\) | |||||||
\(822\) | 0.980883 | 0.0342122 | ||||||||
\(823\) | −49.3245 | −1.71934 | −0.859671 | − | 0.510848i | \(-0.829332\pi\) | ||||
−0.859671 | + | 0.510848i | \(0.829332\pi\) | |||||||
\(824\) | 38.1100 | 1.32762 | ||||||||
\(825\) | −0.0843416 | −0.00293640 | ||||||||
\(826\) | 16.9892 | 0.591130 | ||||||||
\(827\) | 23.4532 | 0.815546 | 0.407773 | − | 0.913083i | \(-0.366305\pi\) | ||||
0.407773 | + | 0.913083i | \(0.366305\pi\) | |||||||
\(828\) | 19.9264 | 0.692489 | ||||||||
\(829\) | −20.6405 | −0.716873 | −0.358437 | − | 0.933554i | \(-0.616690\pi\) | ||||
−0.358437 | + | 0.933554i | \(0.616690\pi\) | |||||||
\(830\) | −30.4899 | −1.05832 | ||||||||
\(831\) | 0.277464 | 0.00962512 | ||||||||
\(832\) | −6.56858 | −0.227724 | ||||||||
\(833\) | 16.6562 | 0.577104 | ||||||||
\(834\) | −0.387886 | −0.0134314 | ||||||||
\(835\) | −16.5749 | −0.573600 | ||||||||
\(836\) | −111.330 | −3.85044 | ||||||||
\(837\) | 0.0415114 | 0.00143485 | ||||||||
\(838\) | −65.0176 | −2.24599 | ||||||||
\(839\) | 33.7685 | 1.16582 | 0.582910 | − | 0.812537i | \(-0.301914\pi\) | ||||
0.582910 | + | 0.812537i | \(0.301914\pi\) | |||||||
\(840\) | −0.159072 | −0.00548851 | ||||||||
\(841\) | −28.9883 | −0.999596 | ||||||||
\(842\) | 42.5395 | 1.46601 | ||||||||
\(843\) | 0.649344 | 0.0223646 | ||||||||
\(844\) | −95.1407 | −3.27488 | ||||||||
\(845\) | 8.66084 | 0.297942 | ||||||||
\(846\) | 68.3382 | 2.34951 | ||||||||
\(847\) | 5.71404 | 0.196337 | ||||||||
\(848\) | 55.2655 | 1.89782 | ||||||||
\(849\) | 0.282581 | 0.00969815 | ||||||||
\(850\) | 7.76990 | 0.266506 | ||||||||
\(851\) | −9.70677 | −0.332744 | ||||||||
\(852\) | −0.379294 | −0.0129944 | ||||||||
\(853\) | −45.2096 | −1.54795 | −0.773974 | − | 0.633218i | \(-0.781734\pi\) | ||||
−0.773974 | + | 0.633218i | \(0.781734\pi\) | |||||||
\(854\) | −15.4097 | −0.527308 | ||||||||
\(855\) | −19.5897 | −0.669953 | ||||||||
\(856\) | 77.3534 | 2.64389 | ||||||||
\(857\) | −12.3968 | −0.423467 | −0.211734 | − | 0.977327i | \(-0.567911\pi\) | ||||
−0.211734 | + | 0.977327i | \(0.567911\pi\) | |||||||
\(858\) | 0.441984 | 0.0150891 | ||||||||
\(859\) | −36.2245 | −1.23597 | −0.617983 | − | 0.786192i | \(-0.712050\pi\) | ||||
−0.617983 | + | 0.786192i | \(0.712050\pi\) | |||||||
\(860\) | 48.5351 | 1.65503 | ||||||||
\(861\) | −0.247257 | −0.00842649 | ||||||||
\(862\) | −1.72283 | −0.0586797 | ||||||||
\(863\) | −9.86760 | −0.335897 | −0.167948 | − | 0.985796i | \(-0.553714\pi\) | ||||
−0.167948 | + | 0.985796i | \(0.553714\pi\) | |||||||
\(864\) | −0.460156 | −0.0156548 | ||||||||
\(865\) | 19.0261 | 0.646908 | ||||||||
\(866\) | −43.3135 | −1.47185 | ||||||||
\(867\) | 0.159795 | 0.00542693 | ||||||||
\(868\) | 1.77284 | 0.0601740 | ||||||||
\(869\) | −32.4552 | −1.10097 | ||||||||
\(870\) | 0.00583211 | 0.000197727 0 | ||||||||
\(871\) | −26.0648 | −0.883171 | ||||||||
\(872\) | −51.7539 | −1.75261 | ||||||||
\(873\) | −24.0981 | −0.815597 | ||||||||
\(874\) | −25.2137 | −0.852866 | ||||||||
\(875\) | −1.26771 | −0.0428565 | ||||||||
\(876\) | −1.36015 | −0.0459551 | ||||||||
\(877\) | −28.3506 | −0.957330 | −0.478665 | − | 0.877998i | \(-0.658879\pi\) | ||||
−0.478665 | + | 0.877998i | \(0.658879\pi\) | |||||||
\(878\) | −42.1798 | −1.42350 | ||||||||
\(879\) | 0.418062 | 0.0141009 | ||||||||
\(880\) | −23.9472 | −0.807261 | ||||||||
\(881\) | −13.4698 | −0.453810 | −0.226905 | − | 0.973917i | \(-0.572861\pi\) | ||||
−0.226905 | + | 0.973917i | \(0.572861\pi\) | |||||||
\(882\) | −40.6949 | −1.37027 | ||||||||
\(883\) | 6.75618 | 0.227364 | 0.113682 | − | 0.993517i | \(-0.463736\pi\) | ||||
0.113682 | + | 0.993517i | \(0.463736\pi\) | |||||||
\(884\) | −27.8502 | −0.936703 | ||||||||
\(885\) | −0.114094 | −0.00383523 | ||||||||
\(886\) | −33.2583 | −1.11734 | ||||||||
\(887\) | −14.7753 | −0.496106 | −0.248053 | − | 0.968746i | \(-0.579791\pi\) | ||||
−0.248053 | + | 0.968746i | \(0.579791\pi\) | |||||||
\(888\) | 0.793682 | 0.0266342 | ||||||||
\(889\) | −22.4503 | −0.752959 | ||||||||
\(890\) | 21.8868 | 0.733647 | ||||||||
\(891\) | 35.4252 | 1.18679 | ||||||||
\(892\) | −101.441 | −3.39649 | ||||||||
\(893\) | −59.1452 | −1.97922 | ||||||||
\(894\) | −1.02488 | −0.0342772 | ||||||||
\(895\) | 8.46273 | 0.282878 | ||||||||
\(896\) | 19.1361 | 0.639294 | ||||||||
\(897\) | 0.0684664 | 0.00228603 | ||||||||
\(898\) | 20.5276 | 0.685015 | ||||||||
\(899\) | −0.0349678 | −0.00116624 | ||||||||
\(900\) | −12.9845 | −0.432818 | ||||||||
\(901\) | −28.0686 | −0.935102 | ||||||||
\(902\) | −90.2165 | −3.00388 | ||||||||
\(903\) | 0.304424 | 0.0101306 | ||||||||
\(904\) | −82.9486 | −2.75883 | ||||||||
\(905\) | 18.9450 | 0.629754 | ||||||||
\(906\) | 0.0170589 | 0.000566745 0 | ||||||||
\(907\) | −47.8168 | −1.58773 | −0.793865 | − | 0.608094i | \(-0.791934\pi\) | ||||
−0.793865 | + | 0.608094i | \(0.791934\pi\) | |||||||
\(908\) | 41.9958 | 1.39368 | ||||||||
\(909\) | 46.5333 | 1.54341 | ||||||||
\(910\) | 6.64332 | 0.220224 | ||||||||
\(911\) | −54.4120 | −1.80275 | −0.901374 | − | 0.433041i | \(-0.857441\pi\) | ||||
−0.901374 | + | 0.433041i | \(0.857441\pi\) | |||||||
\(912\) | 0.850612 | 0.0281666 | ||||||||
\(913\) | −47.7268 | −1.57953 | ||||||||
\(914\) | −89.2710 | −2.95282 | ||||||||
\(915\) | 0.103487 | 0.00342116 | ||||||||
\(916\) | −66.7393 | −2.20513 | ||||||||
\(917\) | −2.97983 | −0.0984028 | ||||||||
\(918\) | 0.998404 | 0.0329523 | ||||||||
\(919\) | −44.0111 | −1.45179 | −0.725895 | − | 0.687805i | \(-0.758574\pi\) | ||||
−0.725895 | + | 0.687805i | \(0.758574\pi\) | |||||||
\(920\) | −8.99090 | −0.296421 | ||||||||
\(921\) | −0.220614 | −0.00726949 | ||||||||
\(922\) | −49.3417 | −1.62498 | ||||||||
\(923\) | 8.52188 | 0.280501 | ||||||||
\(924\) | −0.462843 | −0.0152264 | ||||||||
\(925\) | 6.32518 | 0.207971 | ||||||||
\(926\) | 1.35595 | 0.0445594 | ||||||||
\(927\) | 19.5116 | 0.640844 | ||||||||
\(928\) | 0.387619 | 0.0127242 | ||||||||
\(929\) | 60.5207 | 1.98562 | 0.992809 | − | 0.119706i | \(-0.0381952\pi\) | ||||
0.992809 | + | 0.119706i | \(0.0381952\pi\) | |||||||
\(930\) | −0.0174065 | −0.000570782 0 | ||||||||
\(931\) | 35.2205 | 1.15431 | ||||||||
\(932\) | 80.8553 | 2.64850 | ||||||||
\(933\) | −0.430964 | −0.0141091 | ||||||||
\(934\) | 93.7048 | 3.06611 | ||||||||
\(935\) | 12.1625 | 0.397756 | ||||||||
\(936\) | 36.6066 | 1.19652 | ||||||||
\(937\) | −3.40446 | −0.111219 | −0.0556095 | − | 0.998453i | \(-0.517710\pi\) | ||||
−0.0556095 | + | 0.998453i | \(0.517710\pi\) | |||||||
\(938\) | 39.9056 | 1.30296 | ||||||||
\(939\) | 0.663195 | 0.0216426 | ||||||||
\(940\) | −39.2029 | −1.27866 | ||||||||
\(941\) | −43.9118 | −1.43148 | −0.715742 | − | 0.698364i | \(-0.753912\pi\) | ||||
−0.715742 | + | 0.698364i | \(0.753912\pi\) | |||||||
\(942\) | 0.696297 | 0.0226866 | ||||||||
\(943\) | −13.9752 | −0.455094 | ||||||||
\(944\) | −32.3949 | −1.05437 | ||||||||
\(945\) | −0.162896 | −0.00529902 | ||||||||
\(946\) | 111.075 | 3.61136 | ||||||||
\(947\) | −56.8336 | −1.84684 | −0.923422 | − | 0.383786i | \(-0.874620\pi\) | ||||
−0.923422 | + | 0.383786i | \(0.874620\pi\) | |||||||
\(948\) | 0.764116 | 0.0248173 | ||||||||
\(949\) | 30.5594 | 0.992000 | ||||||||
\(950\) | 16.4299 | 0.533056 | ||||||||
\(951\) | −0.0818545 | −0.00265431 | ||||||||
\(952\) | 22.9390 | 0.743459 | ||||||||
\(953\) | −7.08751 | −0.229587 | −0.114793 | − | 0.993389i | \(-0.536621\pi\) | ||||
−0.114793 | + | 0.993389i | \(0.536621\pi\) | |||||||
\(954\) | 68.5780 | 2.22029 | ||||||||
\(955\) | −7.70723 | −0.249400 | ||||||||
\(956\) | 21.1206 | 0.683090 | ||||||||
\(957\) | 0.00912920 | 0.000295105 0 | ||||||||
\(958\) | 25.6063 | 0.827304 | ||||||||
\(959\) | 23.0782 | 0.745235 | ||||||||
\(960\) | −0.0675369 | −0.00217974 | ||||||||
\(961\) | −30.8956 | −0.996633 | ||||||||
\(962\) | −33.1465 | −1.06869 | ||||||||
\(963\) | 39.6035 | 1.27620 | ||||||||
\(964\) | −40.5658 | −1.30654 | ||||||||
\(965\) | −22.0565 | −0.710025 | ||||||||
\(966\) | −0.104823 | −0.00337263 | ||||||||
\(967\) | −21.1696 | −0.680768 | −0.340384 | − | 0.940287i | \(-0.610557\pi\) | ||||
−0.340384 | + | 0.940287i | \(0.610557\pi\) | |||||||
\(968\) | −26.4073 | −0.848763 | ||||||||
\(969\) | −0.432015 | −0.0138783 | ||||||||
\(970\) | 20.2111 | 0.648939 | ||||||||
\(971\) | 48.4383 | 1.55446 | 0.777230 | − | 0.629217i | \(-0.216624\pi\) | ||||
0.777230 | + | 0.629217i | \(0.216624\pi\) | |||||||
\(972\) | −2.50276 | −0.0802761 | ||||||||
\(973\) | −9.12620 | −0.292573 | ||||||||
\(974\) | −10.6038 | −0.339769 | ||||||||
\(975\) | −0.0446145 | −0.00142881 | ||||||||
\(976\) | 29.3831 | 0.940530 | ||||||||
\(977\) | −21.9998 | −0.703836 | −0.351918 | − | 0.936031i | \(-0.614470\pi\) | ||||
−0.351918 | + | 0.936031i | \(0.614470\pi\) | |||||||
\(978\) | 0.763709 | 0.0244207 | ||||||||
\(979\) | 34.2602 | 1.09496 | ||||||||
\(980\) | 23.3450 | 0.745729 | ||||||||
\(981\) | −26.4970 | −0.845984 | ||||||||
\(982\) | −39.0326 | −1.24558 | ||||||||
\(983\) | 5.81550 | 0.185486 | 0.0927428 | − | 0.995690i | \(-0.470437\pi\) | ||||
0.0927428 | + | 0.995690i | \(0.470437\pi\) | |||||||
\(984\) | 1.14269 | 0.0364277 | ||||||||
\(985\) | −8.97138 | −0.285852 | ||||||||
\(986\) | −0.841021 | −0.0267836 | ||||||||
\(987\) | −0.245889 | −0.00782674 | ||||||||
\(988\) | −58.8907 | −1.87356 | ||||||||
\(989\) | 17.2063 | 0.547128 | ||||||||
\(990\) | −29.7157 | −0.944427 | ||||||||
\(991\) | 12.3809 | 0.393293 | 0.196647 | − | 0.980474i | \(-0.436995\pi\) | ||||
0.196647 | + | 0.980474i | \(0.436995\pi\) | |||||||
\(992\) | −1.15689 | −0.0367312 | ||||||||
\(993\) | −0.158048 | −0.00501550 | ||||||||
\(994\) | −13.0471 | −0.413830 | ||||||||
\(995\) | 3.41567 | 0.108284 | ||||||||
\(996\) | 1.12367 | 0.0356048 | ||||||||
\(997\) | 40.4347 | 1.28058 | 0.640290 | − | 0.768133i | \(-0.278814\pi\) | ||||
0.640290 | + | 0.768133i | \(0.278814\pi\) | |||||||
\(998\) | 22.6988 | 0.718518 | ||||||||
\(999\) | 0.812762 | 0.0257147 |
(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 | 8045.2.a.b.1.8 | ✓ | 126 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8045.2.a.b.1.8 | ✓ | 126 | 1.1 | even | 1 | trivial |