Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.95065 | 1.37932 | 0.689659 | − | 0.724134i | \(-0.257760\pi\) | ||||
0.689659 | + | 0.724134i | \(0.257760\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.80504 | 0.902518 | ||||||||
\(5\) | −2.46699 | −1.10327 | −0.551635 | − | 0.834086i | \(-0.685996\pi\) | ||||
−0.551635 | + | 0.834086i | \(0.685996\pi\) | |||||||
\(6\) | −1.95065 | −0.796349 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.380308 | −0.134459 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −4.81223 | −1.52176 | ||||||||
\(11\) | 3.40967 | 1.02805 | 0.514027 | − | 0.857774i | \(-0.328153\pi\) | ||||
0.514027 | + | 0.857774i | \(0.328153\pi\) | |||||||
\(12\) | −1.80504 | −0.521069 | ||||||||
\(13\) | −3.78591 | −1.05002 | −0.525011 | − | 0.851096i | \(-0.675939\pi\) | ||||
−0.525011 | + | 0.851096i | \(0.675939\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.46699 | 0.636973 | ||||||||
\(16\) | −4.35192 | −1.08798 | ||||||||
\(17\) | 7.48620 | 1.81567 | 0.907835 | − | 0.419327i | \(-0.137734\pi\) | ||||
0.907835 | + | 0.419327i | \(0.137734\pi\) | |||||||
\(18\) | 1.95065 | 0.459773 | ||||||||
\(19\) | −1.93227 | −0.443293 | −0.221646 | − | 0.975127i | \(-0.571143\pi\) | ||||
−0.221646 | + | 0.975127i | \(0.571143\pi\) | |||||||
\(20\) | −4.45300 | −0.995720 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.65108 | 1.41801 | ||||||||
\(23\) | −1.38797 | −0.289412 | −0.144706 | − | 0.989475i | \(-0.546224\pi\) | ||||
−0.144706 | + | 0.989475i | \(0.546224\pi\) | |||||||
\(24\) | 0.380308 | 0.0776301 | ||||||||
\(25\) | 1.08602 | 0.217204 | ||||||||
\(26\) | −7.38498 | −1.44831 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.33428 | 0.804856 | 0.402428 | − | 0.915452i | \(-0.368166\pi\) | ||||
0.402428 | + | 0.915452i | \(0.368166\pi\) | |||||||
\(30\) | 4.81223 | 0.878588 | ||||||||
\(31\) | −10.1756 | −1.82759 | −0.913795 | − | 0.406175i | \(-0.866862\pi\) | ||||
−0.913795 | + | 0.406175i | \(0.866862\pi\) | |||||||
\(32\) | −7.72845 | −1.36621 | ||||||||
\(33\) | −3.40967 | −0.593548 | ||||||||
\(34\) | 14.6030 | 2.50439 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.80504 | 0.300839 | ||||||||
\(37\) | 8.77161 | 1.44204 | 0.721022 | − | 0.692913i | \(-0.243673\pi\) | ||||
0.721022 | + | 0.692913i | \(0.243673\pi\) | |||||||
\(38\) | −3.76918 | −0.611441 | ||||||||
\(39\) | 3.78591 | 0.606230 | ||||||||
\(40\) | 0.938215 | 0.148345 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.71076 | −0.870883 | −0.435442 | − | 0.900217i | \(-0.643408\pi\) | ||||
−0.435442 | + | 0.900217i | \(0.643408\pi\) | |||||||
\(44\) | 6.15458 | 0.927838 | ||||||||
\(45\) | −2.46699 | −0.367757 | ||||||||
\(46\) | −2.70744 | −0.399191 | ||||||||
\(47\) | −4.34350 | −0.633565 | −0.316782 | − | 0.948498i | \(-0.602602\pi\) | ||||
−0.316782 | + | 0.948498i | \(0.602602\pi\) | |||||||
\(48\) | 4.35192 | 0.628145 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.11845 | 0.299593 | ||||||||
\(51\) | −7.48620 | −1.04828 | ||||||||
\(52\) | −6.83369 | −0.947662 | ||||||||
\(53\) | 4.49496 | 0.617430 | 0.308715 | − | 0.951155i | \(-0.400101\pi\) | ||||
0.308715 | + | 0.951155i | \(0.400101\pi\) | |||||||
\(54\) | −1.95065 | −0.265450 | ||||||||
\(55\) | −8.41161 | −1.13422 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.93227 | 0.255935 | ||||||||
\(58\) | 8.45467 | 1.11015 | ||||||||
\(59\) | −9.48620 | −1.23500 | −0.617499 | − | 0.786571i | \(-0.711854\pi\) | ||||
−0.617499 | + | 0.786571i | \(0.711854\pi\) | |||||||
\(60\) | 4.45300 | 0.574879 | ||||||||
\(61\) | 12.7058 | 1.62681 | 0.813404 | − | 0.581699i | \(-0.197612\pi\) | ||||
0.813404 | + | 0.581699i | \(0.197612\pi\) | |||||||
\(62\) | −19.8490 | −2.52083 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.37167 | −0.796459 | ||||||||
\(65\) | 9.33978 | 1.15846 | ||||||||
\(66\) | −6.65108 | −0.818691 | ||||||||
\(67\) | 8.88133 | 1.08503 | 0.542514 | − | 0.840047i | \(-0.317473\pi\) | ||||
0.542514 | + | 0.840047i | \(0.317473\pi\) | |||||||
\(68\) | 13.5129 | 1.63867 | ||||||||
\(69\) | 1.38797 | 0.167092 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.4496 | 1.95221 | 0.976106 | − | 0.217294i | \(-0.0697230\pi\) | ||||
0.976106 | + | 0.217294i | \(0.0697230\pi\) | |||||||
\(72\) | −0.380308 | −0.0448198 | ||||||||
\(73\) | 0.523059 | 0.0612195 | 0.0306097 | − | 0.999531i | \(-0.490255\pi\) | ||||
0.0306097 | + | 0.999531i | \(0.490255\pi\) | |||||||
\(74\) | 17.1103 | 1.98904 | ||||||||
\(75\) | −1.08602 | −0.125403 | ||||||||
\(76\) | −3.48781 | −0.400079 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 7.38498 | 0.836184 | ||||||||
\(79\) | −11.0022 | −1.23784 | −0.618922 | − | 0.785452i | \(-0.712430\pi\) | ||||
−0.618922 | + | 0.785452i | \(0.712430\pi\) | |||||||
\(80\) | 10.7361 | 1.20033 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.95065 | 0.215413 | ||||||||
\(83\) | −14.1159 | −1.54942 | −0.774709 | − | 0.632318i | \(-0.782104\pi\) | ||||
−0.774709 | + | 0.632318i | \(0.782104\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −18.4684 | −2.00317 | ||||||||
\(86\) | −11.1397 | −1.20122 | ||||||||
\(87\) | −4.33428 | −0.464684 | ||||||||
\(88\) | −1.29673 | −0.138232 | ||||||||
\(89\) | 18.8161 | 1.99450 | 0.997251 | − | 0.0740962i | \(-0.0236072\pi\) | ||||
0.997251 | + | 0.0740962i | \(0.0236072\pi\) | |||||||
\(90\) | −4.81223 | −0.507253 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.50533 | −0.261199 | ||||||||
\(93\) | 10.1756 | 1.05516 | ||||||||
\(94\) | −8.47265 | −0.873887 | ||||||||
\(95\) | 4.76688 | 0.489071 | ||||||||
\(96\) | 7.72845 | 0.788782 | ||||||||
\(97\) | 8.05622 | 0.817985 | 0.408993 | − | 0.912538i | \(-0.365880\pi\) | ||||
0.408993 | + | 0.912538i | \(0.365880\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.40967 | 0.342685 | ||||||||
\(100\) | 1.96030 | 0.196030 | ||||||||
\(101\) | 19.1657 | 1.90706 | 0.953529 | − | 0.301302i | \(-0.0974212\pi\) | ||||
0.953529 | + | 0.301302i | \(0.0974212\pi\) | |||||||
\(102\) | −14.6030 | −1.44591 | ||||||||
\(103\) | 15.3244 | 1.50996 | 0.754979 | − | 0.655749i | \(-0.227647\pi\) | ||||
0.754979 | + | 0.655749i | \(0.227647\pi\) | |||||||
\(104\) | 1.43981 | 0.141185 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.76810 | 0.851633 | ||||||||
\(107\) | 8.53803 | 0.825403 | 0.412701 | − | 0.910866i | \(-0.364585\pi\) | ||||
0.412701 | + | 0.910866i | \(0.364585\pi\) | |||||||
\(108\) | −1.80504 | −0.173690 | ||||||||
\(109\) | 14.3317 | 1.37273 | 0.686366 | − | 0.727256i | \(-0.259205\pi\) | ||||
0.686366 | + | 0.727256i | \(0.259205\pi\) | |||||||
\(110\) | −16.4081 | −1.56445 | ||||||||
\(111\) | −8.77161 | −0.832564 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.0125194 | 0.00117773 | 0.000588865 | − | 1.00000i | \(-0.499813\pi\) | ||||
0.000588865 | 1.00000i | \(0.499813\pi\) | ||||||||
\(114\) | 3.76918 | 0.353016 | ||||||||
\(115\) | 3.42410 | 0.319299 | ||||||||
\(116\) | 7.82353 | 0.726397 | ||||||||
\(117\) | −3.78591 | −0.350007 | ||||||||
\(118\) | −18.5043 | −1.70346 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.938215 | −0.0856469 | ||||||||
\(121\) | 0.625868 | 0.0568971 | ||||||||
\(122\) | 24.7845 | 2.24389 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | −18.3673 | −1.64943 | ||||||||
\(125\) | 9.65573 | 0.863635 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.83107 | −0.251217 | −0.125608 | − | 0.992080i | \(-0.540088\pi\) | ||||
−0.125608 | + | 0.992080i | \(0.540088\pi\) | |||||||
\(128\) | 3.02801 | 0.267641 | ||||||||
\(129\) | 5.71076 | 0.502805 | ||||||||
\(130\) | 18.2186 | 1.59788 | ||||||||
\(131\) | 8.54530 | 0.746607 | 0.373303 | − | 0.927709i | \(-0.378225\pi\) | ||||
0.373303 | + | 0.927709i | \(0.378225\pi\) | |||||||
\(132\) | −6.15458 | −0.535687 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 17.3244 | 1.49660 | ||||||||
\(135\) | 2.46699 | 0.212324 | ||||||||
\(136\) | −2.84706 | −0.244134 | ||||||||
\(137\) | −3.47348 | −0.296760 | −0.148380 | − | 0.988930i | \(-0.547406\pi\) | ||||
−0.148380 | + | 0.988930i | \(0.547406\pi\) | |||||||
\(138\) | 2.70744 | 0.230473 | ||||||||
\(139\) | −2.23775 | −0.189804 | −0.0949018 | − | 0.995487i | \(-0.530254\pi\) | ||||
−0.0949018 | + | 0.995487i | \(0.530254\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.34350 | 0.365789 | ||||||||
\(142\) | 32.0875 | 2.69272 | ||||||||
\(143\) | −12.9087 | −1.07948 | ||||||||
\(144\) | −4.35192 | −0.362660 | ||||||||
\(145\) | −10.6926 | −0.887973 | ||||||||
\(146\) | 1.02031 | 0.0844411 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 15.8331 | 1.30147 | ||||||||
\(149\) | 8.91994 | 0.730750 | 0.365375 | − | 0.930860i | \(-0.380941\pi\) | ||||
0.365375 | + | 0.930860i | \(0.380941\pi\) | |||||||
\(150\) | −2.11845 | −0.172970 | ||||||||
\(151\) | −11.9438 | −0.971974 | −0.485987 | − | 0.873966i | \(-0.661540\pi\) | ||||
−0.485987 | + | 0.873966i | \(0.661540\pi\) | |||||||
\(152\) | 0.734858 | 0.0596048 | ||||||||
\(153\) | 7.48620 | 0.605223 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 25.1031 | 2.01633 | ||||||||
\(156\) | 6.83369 | 0.547133 | ||||||||
\(157\) | 17.3359 | 1.38356 | 0.691778 | − | 0.722110i | \(-0.256828\pi\) | ||||
0.691778 | + | 0.722110i | \(0.256828\pi\) | |||||||
\(158\) | −21.4614 | −1.70738 | ||||||||
\(159\) | −4.49496 | −0.356474 | ||||||||
\(160\) | 19.0660 | 1.50730 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.95065 | 0.153258 | ||||||||
\(163\) | −1.43399 | −0.112319 | −0.0561593 | − | 0.998422i | \(-0.517885\pi\) | ||||
−0.0561593 | + | 0.998422i | \(0.517885\pi\) | |||||||
\(164\) | 1.80504 | 0.140950 | ||||||||
\(165\) | 8.41161 | 0.654843 | ||||||||
\(166\) | −27.5351 | −2.13714 | ||||||||
\(167\) | 16.8506 | 1.30394 | 0.651971 | − | 0.758244i | \(-0.273942\pi\) | ||||
0.651971 | + | 0.758244i | \(0.273942\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.33308 | 0.102544 | ||||||||
\(170\) | −36.0253 | −2.76301 | ||||||||
\(171\) | −1.93227 | −0.147764 | ||||||||
\(172\) | −10.3081 | −0.785987 | ||||||||
\(173\) | 2.36949 | 0.180149 | 0.0900744 | − | 0.995935i | \(-0.471290\pi\) | ||||
0.0900744 | + | 0.995935i | \(0.471290\pi\) | |||||||
\(174\) | −8.45467 | −0.640947 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −14.8386 | −1.11850 | ||||||||
\(177\) | 9.48620 | 0.713027 | ||||||||
\(178\) | 36.7036 | 2.75105 | ||||||||
\(179\) | −12.3125 | −0.920279 | −0.460139 | − | 0.887847i | \(-0.652201\pi\) | ||||
−0.460139 | + | 0.887847i | \(0.652201\pi\) | |||||||
\(180\) | −4.45300 | −0.331907 | ||||||||
\(181\) | −24.0143 | −1.78497 | −0.892483 | − | 0.451080i | \(-0.851039\pi\) | ||||
−0.892483 | + | 0.451080i | \(0.851039\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.7058 | −0.939238 | ||||||||
\(184\) | 0.527856 | 0.0389141 | ||||||||
\(185\) | −21.6394 | −1.59096 | ||||||||
\(186\) | 19.8490 | 1.45540 | ||||||||
\(187\) | 25.5255 | 1.86661 | ||||||||
\(188\) | −7.84017 | −0.571803 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.29851 | 0.674585 | ||||||||
\(191\) | 10.0853 | 0.729747 | 0.364873 | − | 0.931057i | \(-0.381112\pi\) | ||||
0.364873 | + | 0.931057i | \(0.381112\pi\) | |||||||
\(192\) | 6.37167 | 0.459836 | ||||||||
\(193\) | 4.38437 | 0.315594 | 0.157797 | − | 0.987472i | \(-0.449561\pi\) | ||||
0.157797 | + | 0.987472i | \(0.449561\pi\) | |||||||
\(194\) | 15.7149 | 1.12826 | ||||||||
\(195\) | −9.33978 | −0.668835 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.57135 | −0.396942 | −0.198471 | − | 0.980107i | \(-0.563598\pi\) | ||||
−0.198471 | + | 0.980107i | \(0.563598\pi\) | |||||||
\(198\) | 6.65108 | 0.472672 | ||||||||
\(199\) | 19.2500 | 1.36460 | 0.682300 | − | 0.731072i | \(-0.260980\pi\) | ||||
0.682300 | + | 0.731072i | \(0.260980\pi\) | |||||||
\(200\) | −0.413023 | −0.0292051 | ||||||||
\(201\) | −8.88133 | −0.626441 | ||||||||
\(202\) | 37.3856 | 2.63044 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −13.5129 | −0.946089 | ||||||||
\(205\) | −2.46699 | −0.172302 | ||||||||
\(206\) | 29.8925 | 2.08271 | ||||||||
\(207\) | −1.38797 | −0.0964705 | ||||||||
\(208\) | 16.4760 | 1.14240 | ||||||||
\(209\) | −6.58840 | −0.455729 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.16241 | −0.355395 | −0.177698 | − | 0.984085i | \(-0.556865\pi\) | ||||
−0.177698 | + | 0.984085i | \(0.556865\pi\) | |||||||
\(212\) | 8.11356 | 0.557242 | ||||||||
\(213\) | −16.4496 | −1.12711 | ||||||||
\(214\) | 16.6547 | 1.13849 | ||||||||
\(215\) | 14.0884 | 0.960819 | ||||||||
\(216\) | 0.380308 | 0.0258767 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 27.9562 | 1.89343 | ||||||||
\(219\) | −0.523059 | −0.0353451 | ||||||||
\(220\) | −15.1833 | −1.02366 | ||||||||
\(221\) | −28.3420 | −1.90649 | ||||||||
\(222\) | −17.1103 | −1.14837 | ||||||||
\(223\) | −5.91934 | −0.396388 | −0.198194 | − | 0.980163i | \(-0.563508\pi\) | ||||
−0.198194 | + | 0.980163i | \(0.563508\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.08602 | 0.0724014 | ||||||||
\(226\) | 0.0244210 | 0.00162446 | ||||||||
\(227\) | 24.0214 | 1.59435 | 0.797177 | − | 0.603746i | \(-0.206326\pi\) | ||||
0.797177 | + | 0.603746i | \(0.206326\pi\) | |||||||
\(228\) | 3.48781 | 0.230986 | ||||||||
\(229\) | 5.99435 | 0.396118 | 0.198059 | − | 0.980190i | \(-0.436536\pi\) | ||||
0.198059 | + | 0.980190i | \(0.436536\pi\) | |||||||
\(230\) | 6.67922 | 0.440415 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.64836 | −0.108220 | ||||||||
\(233\) | 16.8529 | 1.10407 | 0.552035 | − | 0.833821i | \(-0.313851\pi\) | ||||
0.552035 | + | 0.833821i | \(0.313851\pi\) | |||||||
\(234\) | −7.38498 | −0.482771 | ||||||||
\(235\) | 10.7154 | 0.698993 | ||||||||
\(236\) | −17.1229 | −1.11461 | ||||||||
\(237\) | 11.0022 | 0.714670 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.05568 | 0.0682864 | 0.0341432 | − | 0.999417i | \(-0.489130\pi\) | ||||
0.0341432 | + | 0.999417i | \(0.489130\pi\) | |||||||
\(240\) | −10.7361 | −0.693014 | ||||||||
\(241\) | −29.7927 | −1.91911 | −0.959557 | − | 0.281515i | \(-0.909163\pi\) | ||||
−0.959557 | + | 0.281515i | \(0.909163\pi\) | |||||||
\(242\) | 1.22085 | 0.0784791 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 22.9344 | 1.46822 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.95065 | −0.124369 | ||||||||
\(247\) | 7.31538 | 0.465467 | ||||||||
\(248\) | 3.86986 | 0.245737 | ||||||||
\(249\) | 14.1159 | 0.894557 | ||||||||
\(250\) | 18.8350 | 1.19123 | ||||||||
\(251\) | −16.0282 | −1.01169 | −0.505845 | − | 0.862624i | \(-0.668819\pi\) | ||||
−0.505845 | + | 0.862624i | \(0.668819\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.73252 | −0.297531 | ||||||||
\(254\) | −5.52243 | −0.346508 | ||||||||
\(255\) | 18.4684 | 1.15653 | ||||||||
\(256\) | 18.6499 | 1.16562 | ||||||||
\(257\) | 3.41486 | 0.213013 | 0.106507 | − | 0.994312i | \(-0.466033\pi\) | ||||
0.106507 | + | 0.994312i | \(0.466033\pi\) | |||||||
\(258\) | 11.1397 | 0.693527 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 16.8586 | 1.04553 | ||||||||
\(261\) | 4.33428 | 0.268285 | ||||||||
\(262\) | 16.6689 | 1.02981 | ||||||||
\(263\) | −6.96532 | −0.429500 | −0.214750 | − | 0.976669i | \(-0.568894\pi\) | ||||
−0.214750 | + | 0.976669i | \(0.568894\pi\) | |||||||
\(264\) | 1.29673 | 0.0798080 | ||||||||
\(265\) | −11.0890 | −0.681192 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.8161 | −1.15153 | ||||||||
\(268\) | 16.0311 | 0.979256 | ||||||||
\(269\) | −7.67353 | −0.467863 | −0.233932 | − | 0.972253i | \(-0.575159\pi\) | ||||
−0.233932 | + | 0.972253i | \(0.575159\pi\) | |||||||
\(270\) | 4.81223 | 0.292863 | ||||||||
\(271\) | 28.1522 | 1.71013 | 0.855063 | − | 0.518525i | \(-0.173519\pi\) | ||||
0.855063 | + | 0.518525i | \(0.173519\pi\) | |||||||
\(272\) | −32.5793 | −1.97541 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.77555 | −0.409326 | ||||||||
\(275\) | 3.70297 | 0.223298 | ||||||||
\(276\) | 2.50533 | 0.150803 | ||||||||
\(277\) | 4.85108 | 0.291473 | 0.145737 | − | 0.989323i | \(-0.453445\pi\) | ||||
0.145737 | + | 0.989323i | \(0.453445\pi\) | |||||||
\(278\) | −4.36507 | −0.261800 | ||||||||
\(279\) | −10.1756 | −0.609197 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.4939 | −0.804977 | −0.402489 | − | 0.915425i | \(-0.631855\pi\) | ||||
−0.402489 | + | 0.915425i | \(0.631855\pi\) | |||||||
\(282\) | 8.47265 | 0.504539 | ||||||||
\(283\) | 3.39249 | 0.201662 | 0.100831 | − | 0.994904i | \(-0.467850\pi\) | ||||
0.100831 | + | 0.994904i | \(0.467850\pi\) | |||||||
\(284\) | 29.6922 | 1.76191 | ||||||||
\(285\) | −4.76688 | −0.282365 | ||||||||
\(286\) | −25.1803 | −1.48895 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −7.72845 | −0.455403 | ||||||||
\(289\) | 39.0432 | 2.29666 | ||||||||
\(290\) | −20.8576 | −1.22480 | ||||||||
\(291\) | −8.05622 | −0.472264 | ||||||||
\(292\) | 0.944140 | 0.0552516 | ||||||||
\(293\) | −19.8814 | −1.16148 | −0.580742 | − | 0.814088i | \(-0.697237\pi\) | ||||
−0.580742 | + | 0.814088i | \(0.697237\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 23.4023 | 1.36254 | ||||||||
\(296\) | −3.33592 | −0.193896 | ||||||||
\(297\) | −3.40967 | −0.197849 | ||||||||
\(298\) | 17.3997 | 1.00794 | ||||||||
\(299\) | 5.25472 | 0.303888 | ||||||||
\(300\) | −1.96030 | −0.113178 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −23.2982 | −1.34066 | ||||||||
\(303\) | −19.1657 | −1.10104 | ||||||||
\(304\) | 8.40907 | 0.482293 | ||||||||
\(305\) | −31.3450 | −1.79481 | ||||||||
\(306\) | 14.6030 | 0.834795 | ||||||||
\(307\) | −20.5502 | −1.17286 | −0.586431 | − | 0.809999i | \(-0.699467\pi\) | ||||
−0.586431 | + | 0.809999i | \(0.699467\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.3244 | −0.871774 | ||||||||
\(310\) | 48.9673 | 2.78115 | ||||||||
\(311\) | 7.09527 | 0.402336 | 0.201168 | − | 0.979557i | \(-0.435526\pi\) | ||||
0.201168 | + | 0.979557i | \(0.435526\pi\) | |||||||
\(312\) | −1.43981 | −0.0815133 | ||||||||
\(313\) | 10.8328 | 0.612308 | 0.306154 | − | 0.951982i | \(-0.400958\pi\) | ||||
0.306154 | + | 0.951982i | \(0.400958\pi\) | |||||||
\(314\) | 33.8163 | 1.90836 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −19.8594 | −1.11718 | ||||||||
\(317\) | 15.8780 | 0.891799 | 0.445900 | − | 0.895083i | \(-0.352884\pi\) | ||||
0.445900 | + | 0.895083i | \(0.352884\pi\) | |||||||
\(318\) | −8.76810 | −0.491690 | ||||||||
\(319\) | 14.7785 | 0.827436 | ||||||||
\(320\) | 15.7188 | 0.878709 | ||||||||
\(321\) | −8.53803 | −0.476547 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.4653 | −0.804873 | ||||||||
\(324\) | 1.80504 | 0.100280 | ||||||||
\(325\) | −4.11157 | −0.228069 | ||||||||
\(326\) | −2.79721 | −0.154923 | ||||||||
\(327\) | −14.3317 | −0.792548 | ||||||||
\(328\) | −0.380308 | −0.0209990 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 16.4081 | 0.903237 | ||||||||
\(331\) | 8.57678 | 0.471423 | 0.235711 | − | 0.971823i | \(-0.424258\pi\) | ||||
0.235711 | + | 0.971823i | \(0.424258\pi\) | |||||||
\(332\) | −25.4796 | −1.39838 | ||||||||
\(333\) | 8.77161 | 0.480681 | ||||||||
\(334\) | 32.8697 | 1.79855 | ||||||||
\(335\) | −21.9101 | −1.19708 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.6799 | −0.636247 | −0.318123 | − | 0.948049i | \(-0.603053\pi\) | ||||
−0.318123 | + | 0.948049i | \(0.603053\pi\) | |||||||
\(338\) | 2.60037 | 0.141441 | ||||||||
\(339\) | −0.0125194 | −0.000679963 0 | ||||||||
\(340\) | −33.3360 | −1.80790 | ||||||||
\(341\) | −34.6954 | −1.87886 | ||||||||
\(342\) | −3.76918 | −0.203814 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.17185 | 0.117098 | ||||||||
\(345\) | −3.42410 | −0.184347 | ||||||||
\(346\) | 4.62204 | 0.248483 | ||||||||
\(347\) | −8.68399 | −0.466181 | −0.233091 | − | 0.972455i | \(-0.574884\pi\) | ||||
−0.233091 | + | 0.972455i | \(0.574884\pi\) | |||||||
\(348\) | −7.82353 | −0.419385 | ||||||||
\(349\) | 18.9911 | 1.01657 | 0.508284 | − | 0.861189i | \(-0.330280\pi\) | ||||
0.508284 | + | 0.861189i | \(0.330280\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.78591 | 0.202077 | ||||||||
\(352\) | −26.3515 | −1.40454 | ||||||||
\(353\) | −11.8748 | −0.632030 | −0.316015 | − | 0.948754i | \(-0.602345\pi\) | ||||
−0.316015 | + | 0.948754i | \(0.602345\pi\) | |||||||
\(354\) | 18.5043 | 0.983490 | ||||||||
\(355\) | −40.5810 | −2.15382 | ||||||||
\(356\) | 33.9637 | 1.80007 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −24.0174 | −1.26936 | ||||||||
\(359\) | −30.1157 | −1.58944 | −0.794722 | − | 0.606973i | \(-0.792384\pi\) | ||||
−0.794722 | + | 0.606973i | \(0.792384\pi\) | |||||||
\(360\) | 0.938215 | 0.0494483 | ||||||||
\(361\) | −15.2663 | −0.803492 | ||||||||
\(362\) | −46.8434 | −2.46204 | ||||||||
\(363\) | −0.625868 | −0.0328495 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.29038 | −0.0675416 | ||||||||
\(366\) | −24.7845 | −1.29551 | ||||||||
\(367\) | −4.88812 | −0.255158 | −0.127579 | − | 0.991828i | \(-0.540721\pi\) | ||||
−0.127579 | + | 0.991828i | \(0.540721\pi\) | |||||||
\(368\) | 6.04033 | 0.314874 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | −42.2110 | −2.19444 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 18.3673 | 0.952300 | ||||||||
\(373\) | −15.8244 | −0.819358 | −0.409679 | − | 0.912230i | \(-0.634359\pi\) | ||||
−0.409679 | + | 0.912230i | \(0.634359\pi\) | |||||||
\(374\) | 49.7913 | 2.57465 | ||||||||
\(375\) | −9.65573 | −0.498620 | ||||||||
\(376\) | 1.65187 | 0.0851886 | ||||||||
\(377\) | −16.4092 | −0.845116 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.5020 | 0.693549 | 0.346774 | − | 0.937949i | \(-0.387277\pi\) | ||||
0.346774 | + | 0.937949i | \(0.387277\pi\) | |||||||
\(380\) | 8.60438 | 0.441395 | ||||||||
\(381\) | 2.83107 | 0.145040 | ||||||||
\(382\) | 19.6729 | 1.00655 | ||||||||
\(383\) | −25.0776 | −1.28140 | −0.640702 | − | 0.767790i | \(-0.721357\pi\) | ||||
−0.640702 | + | 0.767790i | \(0.721357\pi\) | |||||||
\(384\) | −3.02801 | −0.154523 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.55238 | 0.435305 | ||||||||
\(387\) | −5.71076 | −0.290294 | ||||||||
\(388\) | 14.5418 | 0.738246 | ||||||||
\(389\) | −34.0257 | −1.72517 | −0.862585 | − | 0.505912i | \(-0.831156\pi\) | ||||
−0.862585 | + | 0.505912i | \(0.831156\pi\) | |||||||
\(390\) | −18.2186 | −0.922536 | ||||||||
\(391\) | −10.3906 | −0.525476 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.54530 | −0.431054 | ||||||||
\(394\) | −10.8677 | −0.547509 | ||||||||
\(395\) | 27.1423 | 1.36568 | ||||||||
\(396\) | 6.15458 | 0.309279 | ||||||||
\(397\) | −2.33249 | −0.117064 | −0.0585321 | − | 0.998286i | \(-0.518642\pi\) | ||||
−0.0585321 | + | 0.998286i | \(0.518642\pi\) | |||||||
\(398\) | 37.5501 | 1.88222 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.72627 | −0.236314 | ||||||||
\(401\) | −1.65085 | −0.0824396 | −0.0412198 | − | 0.999150i | \(-0.513124\pi\) | ||||
−0.0412198 | + | 0.999150i | \(0.513124\pi\) | |||||||
\(402\) | −17.3244 | −0.864061 | ||||||||
\(403\) | 38.5238 | 1.91901 | ||||||||
\(404\) | 34.5947 | 1.72115 | ||||||||
\(405\) | −2.46699 | −0.122586 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 29.9083 | 1.48250 | ||||||||
\(408\) | 2.84706 | 0.140951 | ||||||||
\(409\) | 9.18226 | 0.454033 | 0.227017 | − | 0.973891i | \(-0.427103\pi\) | ||||
0.227017 | + | 0.973891i | \(0.427103\pi\) | |||||||
\(410\) | −4.81223 | −0.237659 | ||||||||
\(411\) | 3.47348 | 0.171334 | ||||||||
\(412\) | 27.6611 | 1.36276 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.70744 | −0.133064 | ||||||||
\(415\) | 34.8236 | 1.70943 | ||||||||
\(416\) | 29.2592 | 1.43455 | ||||||||
\(417\) | 2.23775 | 0.109583 | ||||||||
\(418\) | −12.8517 | −0.628595 | ||||||||
\(419\) | −3.34417 | −0.163374 | −0.0816868 | − | 0.996658i | \(-0.526031\pi\) | ||||
−0.0816868 | + | 0.996658i | \(0.526031\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.9541 | 1.06998 | 0.534988 | − | 0.844860i | \(-0.320316\pi\) | ||||
0.534988 | + | 0.844860i | \(0.320316\pi\) | |||||||
\(422\) | −10.0701 | −0.490203 | ||||||||
\(423\) | −4.34350 | −0.211188 | ||||||||
\(424\) | −1.70947 | −0.0830193 | ||||||||
\(425\) | 8.13016 | 0.394371 | ||||||||
\(426\) | −32.0875 | −1.55464 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 15.4115 | 0.744941 | ||||||||
\(429\) | 12.9087 | 0.623238 | ||||||||
\(430\) | 27.4815 | 1.32527 | ||||||||
\(431\) | 9.23239 | 0.444709 | 0.222354 | − | 0.974966i | \(-0.428626\pi\) | ||||
0.222354 | + | 0.974966i | \(0.428626\pi\) | |||||||
\(432\) | 4.35192 | 0.209382 | ||||||||
\(433\) | 17.2047 | 0.826807 | 0.413403 | − | 0.910548i | \(-0.364340\pi\) | ||||
0.413403 | + | 0.910548i | \(0.364340\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.6926 | 0.512672 | ||||||||
\(436\) | 25.8693 | 1.23892 | ||||||||
\(437\) | 2.68193 | 0.128294 | ||||||||
\(438\) | −1.02031 | −0.0487521 | ||||||||
\(439\) | 40.7622 | 1.94548 | 0.972738 | − | 0.231907i | \(-0.0744966\pi\) | ||||
0.972738 | + | 0.231907i | \(0.0744966\pi\) | |||||||
\(440\) | 3.19901 | 0.152507 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −55.2854 | −2.62966 | ||||||||
\(443\) | 15.9825 | 0.759350 | 0.379675 | − | 0.925120i | \(-0.376036\pi\) | ||||
0.379675 | + | 0.925120i | \(0.376036\pi\) | |||||||
\(444\) | −15.8331 | −0.751404 | ||||||||
\(445\) | −46.4190 | −2.20047 | ||||||||
\(446\) | −11.5466 | −0.546745 | ||||||||
\(447\) | −8.91994 | −0.421899 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.3328 | 1.28991 | 0.644957 | − | 0.764218i | \(-0.276875\pi\) | ||||
0.644957 | + | 0.764218i | \(0.276875\pi\) | |||||||
\(450\) | 2.11845 | 0.0998645 | ||||||||
\(451\) | 3.40967 | 0.160555 | ||||||||
\(452\) | 0.0225980 | 0.00106292 | ||||||||
\(453\) | 11.9438 | 0.561169 | ||||||||
\(454\) | 46.8572 | 2.19912 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.734858 | −0.0344129 | ||||||||
\(457\) | 30.3192 | 1.41827 | 0.709136 | − | 0.705072i | \(-0.249085\pi\) | ||||
0.709136 | + | 0.705072i | \(0.249085\pi\) | |||||||
\(458\) | 11.6929 | 0.546373 | ||||||||
\(459\) | −7.48620 | −0.349426 | ||||||||
\(460\) | 6.18062 | 0.288173 | ||||||||
\(461\) | 14.9967 | 0.698465 | 0.349232 | − | 0.937036i | \(-0.386442\pi\) | ||||
0.349232 | + | 0.937036i | \(0.386442\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.4478 | −0.857343 | −0.428671 | − | 0.903461i | \(-0.641018\pi\) | ||||
−0.428671 | + | 0.903461i | \(0.641018\pi\) | |||||||
\(464\) | −18.8624 | −0.875667 | ||||||||
\(465\) | −25.1031 | −1.16413 | ||||||||
\(466\) | 32.8741 | 1.52286 | ||||||||
\(467\) | −14.8885 | −0.688957 | −0.344478 | − | 0.938794i | \(-0.611944\pi\) | ||||
−0.344478 | + | 0.938794i | \(0.611944\pi\) | |||||||
\(468\) | −6.83369 | −0.315887 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 20.9019 | 0.964133 | ||||||||
\(471\) | −17.3359 | −0.798797 | ||||||||
\(472\) | 3.60768 | 0.166057 | ||||||||
\(473\) | −19.4718 | −0.895316 | ||||||||
\(474\) | 21.4614 | 0.985757 | ||||||||
\(475\) | −2.09848 | −0.0962850 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.49496 | 0.205810 | ||||||||
\(478\) | 2.05927 | 0.0941886 | ||||||||
\(479\) | −20.8298 | −0.951736 | −0.475868 | − | 0.879517i | \(-0.657866\pi\) | ||||
−0.475868 | + | 0.879517i | \(0.657866\pi\) | |||||||
\(480\) | −19.0660 | −0.870239 | ||||||||
\(481\) | −33.2085 | −1.51418 | ||||||||
\(482\) | −58.1150 | −2.64707 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.12971 | 0.0513506 | ||||||||
\(485\) | −19.8746 | −0.902459 | ||||||||
\(486\) | −1.95065 | −0.0884833 | ||||||||
\(487\) | −34.9111 | −1.58197 | −0.790986 | − | 0.611834i | \(-0.790432\pi\) | ||||
−0.790986 | + | 0.611834i | \(0.790432\pi\) | |||||||
\(488\) | −4.83211 | −0.218740 | ||||||||
\(489\) | 1.43399 | 0.0648472 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.0789 | −1.31231 | −0.656156 | − | 0.754625i | \(-0.727819\pi\) | ||||
−0.656156 | + | 0.754625i | \(0.727819\pi\) | |||||||
\(492\) | −1.80504 | −0.0813773 | ||||||||
\(493\) | 32.4473 | 1.46135 | ||||||||
\(494\) | 14.2698 | 0.642026 | ||||||||
\(495\) | −8.41161 | −0.378074 | ||||||||
\(496\) | 44.2834 | 1.98838 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 27.5351 | 1.23388 | ||||||||
\(499\) | 6.60144 | 0.295521 | 0.147760 | − | 0.989023i | \(-0.452794\pi\) | ||||
0.147760 | + | 0.989023i | \(0.452794\pi\) | |||||||
\(500\) | 17.4289 | 0.779446 | ||||||||
\(501\) | −16.8506 | −0.752831 | ||||||||
\(502\) | −31.2654 | −1.39544 | ||||||||
\(503\) | 32.6788 | 1.45708 | 0.728539 | − | 0.685005i | \(-0.240200\pi\) | ||||
0.728539 | + | 0.685005i | \(0.240200\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −47.2815 | −2.10400 | ||||||||
\(506\) | −9.23149 | −0.410390 | ||||||||
\(507\) | −1.33308 | −0.0592040 | ||||||||
\(508\) | −5.11018 | −0.226728 | ||||||||
\(509\) | 30.5152 | 1.35256 | 0.676281 | − | 0.736644i | \(-0.263591\pi\) | ||||
0.676281 | + | 0.736644i | \(0.263591\pi\) | |||||||
\(510\) | 36.0253 | 1.59523 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 30.3235 | 1.34012 | ||||||||
\(513\) | 1.93227 | 0.0853117 | ||||||||
\(514\) | 6.66120 | 0.293813 | ||||||||
\(515\) | −37.8051 | −1.66589 | ||||||||
\(516\) | 10.3081 | 0.453790 | ||||||||
\(517\) | −14.8099 | −0.651339 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.36949 | −0.104009 | ||||||||
\(520\) | −3.55199 | −0.155765 | ||||||||
\(521\) | 18.8954 | 0.827820 | 0.413910 | − | 0.910318i | \(-0.364163\pi\) | ||||
0.413910 | + | 0.910318i | \(0.364163\pi\) | |||||||
\(522\) | 8.45467 | 0.370051 | ||||||||
\(523\) | 9.39131 | 0.410653 | 0.205327 | − | 0.978694i | \(-0.434174\pi\) | ||||
0.205327 | + | 0.978694i | \(0.434174\pi\) | |||||||
\(524\) | 15.4246 | 0.673826 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.5869 | −0.592417 | ||||||||
\(527\) | −76.1765 | −3.31830 | ||||||||
\(528\) | 14.8386 | 0.645768 | ||||||||
\(529\) | −21.0735 | −0.916241 | ||||||||
\(530\) | −21.6308 | −0.939581 | ||||||||
\(531\) | −9.48620 | −0.411666 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.78591 | −0.163986 | ||||||||
\(534\) | −36.7036 | −1.58832 | ||||||||
\(535\) | −21.0632 | −0.910642 | ||||||||
\(536\) | −3.37764 | −0.145892 | ||||||||
\(537\) | 12.3125 | 0.531323 | ||||||||
\(538\) | −14.9684 | −0.645332 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.45300 | 0.191626 | ||||||||
\(541\) | 7.79461 | 0.335116 | 0.167558 | − | 0.985862i | \(-0.446412\pi\) | ||||
0.167558 | + | 0.985862i | \(0.446412\pi\) | |||||||
\(542\) | 54.9151 | 2.35881 | ||||||||
\(543\) | 24.0143 | 1.03055 | ||||||||
\(544\) | −57.8567 | −2.48059 | ||||||||
\(545\) | −35.3562 | −1.51449 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.8239 | 1.40345 | 0.701725 | − | 0.712448i | \(-0.252414\pi\) | ||||
0.701725 | + | 0.712448i | \(0.252414\pi\) | |||||||
\(548\) | −6.26976 | −0.267831 | ||||||||
\(549\) | 12.7058 | 0.542270 | ||||||||
\(550\) | 7.22321 | 0.307999 | ||||||||
\(551\) | −8.37500 | −0.356787 | ||||||||
\(552\) | −0.527856 | −0.0224671 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 9.46276 | 0.402034 | ||||||||
\(555\) | 21.6394 | 0.918543 | ||||||||
\(556\) | −4.03922 | −0.171301 | ||||||||
\(557\) | −8.23895 | −0.349096 | −0.174548 | − | 0.984649i | \(-0.555846\pi\) | ||||
−0.174548 | + | 0.984649i | \(0.555846\pi\) | |||||||
\(558\) | −19.8490 | −0.840276 | ||||||||
\(559\) | 21.6204 | 0.914446 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −25.5255 | −1.07769 | ||||||||
\(562\) | −26.3218 | −1.11032 | ||||||||
\(563\) | 2.24259 | 0.0945137 | 0.0472569 | − | 0.998883i | \(-0.484952\pi\) | ||||
0.0472569 | + | 0.998883i | \(0.484952\pi\) | |||||||
\(564\) | 7.84017 | 0.330131 | ||||||||
\(565\) | −0.0308853 | −0.00129935 | ||||||||
\(566\) | 6.61756 | 0.278157 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.25593 | −0.262493 | ||||||||
\(569\) | −22.0558 | −0.924625 | −0.462313 | − | 0.886717i | \(-0.652980\pi\) | ||||
−0.462313 | + | 0.886717i | \(0.652980\pi\) | |||||||
\(570\) | −9.29851 | −0.389472 | ||||||||
\(571\) | −22.8597 | −0.956650 | −0.478325 | − | 0.878183i | \(-0.658756\pi\) | ||||
−0.478325 | + | 0.878183i | \(0.658756\pi\) | |||||||
\(572\) | −23.3007 | −0.974249 | ||||||||
\(573\) | −10.0853 | −0.421319 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.50736 | −0.0628614 | ||||||||
\(576\) | −6.37167 | −0.265486 | ||||||||
\(577\) | 6.08498 | 0.253321 | 0.126660 | − | 0.991946i | \(-0.459574\pi\) | ||||
0.126660 | + | 0.991946i | \(0.459574\pi\) | |||||||
\(578\) | 76.1596 | 3.16782 | ||||||||
\(579\) | −4.38437 | −0.182208 | ||||||||
\(580\) | −19.3005 | −0.801412 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −15.7149 | −0.651402 | ||||||||
\(583\) | 15.3263 | 0.634752 | ||||||||
\(584\) | −0.198924 | −0.00823152 | ||||||||
\(585\) | 9.33978 | 0.386152 | ||||||||
\(586\) | −38.7816 | −1.60205 | ||||||||
\(587\) | −9.48311 | −0.391410 | −0.195705 | − | 0.980663i | \(-0.562699\pi\) | ||||
−0.195705 | + | 0.980663i | \(0.562699\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.6620 | 0.810158 | ||||||||
\(590\) | 45.6498 | 1.87937 | ||||||||
\(591\) | 5.57135 | 0.229175 | ||||||||
\(592\) | −38.1733 | −1.56891 | ||||||||
\(593\) | −26.7188 | −1.09721 | −0.548604 | − | 0.836082i | \(-0.684840\pi\) | ||||
−0.548604 | + | 0.836082i | \(0.684840\pi\) | |||||||
\(594\) | −6.65108 | −0.272897 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.1008 | 0.659514 | ||||||||
\(597\) | −19.2500 | −0.787852 | ||||||||
\(598\) | 10.2501 | 0.419159 | ||||||||
\(599\) | −10.9319 | −0.446667 | −0.223333 | − | 0.974742i | \(-0.571694\pi\) | ||||
−0.223333 | + | 0.974742i | \(0.571694\pi\) | |||||||
\(600\) | 0.413023 | 0.0168616 | ||||||||
\(601\) | −31.5604 | −1.28738 | −0.643688 | − | 0.765288i | \(-0.722597\pi\) | ||||
−0.643688 | + | 0.765288i | \(0.722597\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.88133 | 0.361676 | ||||||||
\(604\) | −21.5590 | −0.877224 | ||||||||
\(605\) | −1.54401 | −0.0627728 | ||||||||
\(606\) | −37.3856 | −1.51868 | ||||||||
\(607\) | 24.8257 | 1.00765 | 0.503823 | − | 0.863807i | \(-0.331926\pi\) | ||||
0.503823 | + | 0.863807i | \(0.331926\pi\) | |||||||
\(608\) | 14.9334 | 0.605631 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −61.1431 | −2.47561 | ||||||||
\(611\) | 16.4441 | 0.665256 | ||||||||
\(612\) | 13.5129 | 0.546225 | ||||||||
\(613\) | −17.3856 | −0.702198 | −0.351099 | − | 0.936338i | \(-0.614192\pi\) | ||||
−0.351099 | + | 0.936338i | \(0.614192\pi\) | |||||||
\(614\) | −40.0862 | −1.61775 | ||||||||
\(615\) | 2.46699 | 0.0994785 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.7106 | 1.51817 | 0.759085 | − | 0.650992i | \(-0.225647\pi\) | ||||
0.759085 | + | 0.650992i | \(0.225647\pi\) | |||||||
\(618\) | −29.8925 | −1.20245 | ||||||||
\(619\) | 30.7411 | 1.23559 | 0.617794 | − | 0.786340i | \(-0.288026\pi\) | ||||
0.617794 | + | 0.786340i | \(0.288026\pi\) | |||||||
\(620\) | 45.3119 | 1.81977 | ||||||||
\(621\) | 1.38797 | 0.0556973 | ||||||||
\(622\) | 13.8404 | 0.554949 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −16.4760 | −0.659566 | ||||||||
\(625\) | −29.2507 | −1.17003 | ||||||||
\(626\) | 21.1311 | 0.844567 | ||||||||
\(627\) | 6.58840 | 0.263115 | ||||||||
\(628\) | 31.2919 | 1.24868 | ||||||||
\(629\) | 65.6660 | 2.61827 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.48516 | 0.0989325 | 0.0494663 | − | 0.998776i | \(-0.484248\pi\) | ||||
0.0494663 | + | 0.998776i | \(0.484248\pi\) | |||||||
\(632\) | 4.18423 | 0.166440 | ||||||||
\(633\) | 5.16241 | 0.205188 | ||||||||
\(634\) | 30.9725 | 1.23007 | ||||||||
\(635\) | 6.98421 | 0.277160 | ||||||||
\(636\) | −8.11356 | −0.321724 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 28.8277 | 1.14130 | ||||||||
\(639\) | 16.4496 | 0.650737 | ||||||||
\(640\) | −7.47006 | −0.295280 | ||||||||
\(641\) | −3.47852 | −0.137393 | −0.0686967 | − | 0.997638i | \(-0.521884\pi\) | ||||
−0.0686967 | + | 0.997638i | \(0.521884\pi\) | |||||||
\(642\) | −16.6547 | −0.657309 | ||||||||
\(643\) | −6.66666 | −0.262907 | −0.131454 | − | 0.991322i | \(-0.541964\pi\) | ||||
−0.131454 | + | 0.991322i | \(0.541964\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14.0884 | −0.554729 | ||||||||
\(646\) | −28.2168 | −1.11018 | ||||||||
\(647\) | 12.7615 | 0.501707 | 0.250853 | − | 0.968025i | \(-0.419289\pi\) | ||||
0.250853 | + | 0.968025i | \(0.419289\pi\) | |||||||
\(648\) | −0.380308 | −0.0149399 | ||||||||
\(649\) | −32.3448 | −1.26965 | ||||||||
\(650\) | −8.02023 | −0.314579 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.58840 | −0.101369 | ||||||||
\(653\) | −48.3605 | −1.89249 | −0.946247 | − | 0.323445i | \(-0.895159\pi\) | ||||
−0.946247 | + | 0.323445i | \(0.895159\pi\) | |||||||
\(654\) | −27.9562 | −1.09317 | ||||||||
\(655\) | −21.0811 | −0.823708 | ||||||||
\(656\) | −4.35192 | −0.169914 | ||||||||
\(657\) | 0.523059 | 0.0204065 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.3864 | −1.22264 | −0.611320 | − | 0.791383i | \(-0.709361\pi\) | ||||
−0.611320 | + | 0.791383i | \(0.709361\pi\) | |||||||
\(660\) | 15.1833 | 0.591008 | ||||||||
\(661\) | 27.8855 | 1.08462 | 0.542310 | − | 0.840178i | \(-0.317550\pi\) | ||||
0.542310 | + | 0.840178i | \(0.317550\pi\) | |||||||
\(662\) | 16.7303 | 0.650242 | ||||||||
\(663\) | 28.3420 | 1.10071 | ||||||||
\(664\) | 5.36838 | 0.208334 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 17.1103 | 0.663012 | ||||||||
\(667\) | −6.01585 | −0.232935 | ||||||||
\(668\) | 30.4160 | 1.17683 | ||||||||
\(669\) | 5.91934 | 0.228855 | ||||||||
\(670\) | −42.7390 | −1.65115 | ||||||||
\(671\) | 43.3226 | 1.67245 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.8350 | −0.764583 | −0.382291 | − | 0.924042i | \(-0.624865\pi\) | ||||
−0.382291 | + | 0.924042i | \(0.624865\pi\) | |||||||
\(674\) | −22.7835 | −0.877586 | ||||||||
\(675\) | −1.08602 | −0.0418009 | ||||||||
\(676\) | 2.40625 | 0.0925481 | ||||||||
\(677\) | −3.64538 | −0.140103 | −0.0700517 | − | 0.997543i | \(-0.522316\pi\) | ||||
−0.0700517 | + | 0.997543i | \(0.522316\pi\) | |||||||
\(678\) | −0.0244210 | −0.000937885 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 7.02367 | 0.269345 | ||||||||
\(681\) | −24.0214 | −0.920500 | ||||||||
\(682\) | −67.6787 | −2.59155 | ||||||||
\(683\) | 39.2949 | 1.50358 | 0.751790 | − | 0.659403i | \(-0.229191\pi\) | ||||
0.751790 | + | 0.659403i | \(0.229191\pi\) | |||||||
\(684\) | −3.48781 | −0.133360 | ||||||||
\(685\) | 8.56903 | 0.327406 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.99435 | −0.228699 | ||||||||
\(688\) | 24.8528 | 0.947503 | ||||||||
\(689\) | −17.0175 | −0.648315 | ||||||||
\(690\) | −6.67922 | −0.254274 | ||||||||
\(691\) | 0.957556 | 0.0364272 | 0.0182136 | − | 0.999834i | \(-0.494202\pi\) | ||||
0.0182136 | + | 0.999834i | \(0.494202\pi\) | |||||||
\(692\) | 4.27701 | 0.162588 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16.9394 | −0.643012 | ||||||||
\(695\) | 5.52050 | 0.209405 | ||||||||
\(696\) | 1.64836 | 0.0624811 | ||||||||
\(697\) | 7.48620 | 0.283560 | ||||||||
\(698\) | 37.0449 | 1.40217 | ||||||||
\(699\) | −16.8529 | −0.637435 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.4024 | 1.14828 | 0.574141 | − | 0.818757i | \(-0.305336\pi\) | ||||
0.574141 | + | 0.818757i | \(0.305336\pi\) | |||||||
\(702\) | 7.38498 | 0.278728 | ||||||||
\(703\) | −16.9491 | −0.639247 | ||||||||
\(704\) | −21.7253 | −0.818803 | ||||||||
\(705\) | −10.7154 | −0.403564 | ||||||||
\(706\) | −23.1635 | −0.871770 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 17.1229 | 0.643519 | ||||||||
\(709\) | 48.6578 | 1.82738 | 0.913691 | − | 0.406410i | \(-0.133220\pi\) | ||||
0.913691 | + | 0.406410i | \(0.133220\pi\) | |||||||
\(710\) | −79.1594 | −2.97080 | ||||||||
\(711\) | −11.0022 | −0.412615 | ||||||||
\(712\) | −7.15592 | −0.268179 | ||||||||
\(713\) | 14.1234 | 0.528926 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 31.8456 | 1.19096 | ||||||||
\(716\) | −22.2245 | −0.830568 | ||||||||
\(717\) | −1.05568 | −0.0394252 | ||||||||
\(718\) | −58.7451 | −2.19235 | ||||||||
\(719\) | −1.65328 | −0.0616570 | −0.0308285 | − | 0.999525i | \(-0.509815\pi\) | ||||
−0.0308285 | + | 0.999525i | \(0.509815\pi\) | |||||||
\(720\) | 10.7361 | 0.400112 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −29.7793 | −1.10827 | ||||||||
\(723\) | 29.7927 | 1.10800 | ||||||||
\(724\) | −43.3466 | −1.61096 | ||||||||
\(725\) | 4.70712 | 0.174818 | ||||||||
\(726\) | −1.22085 | −0.0453099 | ||||||||
\(727\) | −32.4853 | −1.20481 | −0.602407 | − | 0.798189i | \(-0.705792\pi\) | ||||
−0.602407 | + | 0.798189i | \(0.705792\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −2.51708 | −0.0931613 | ||||||||
\(731\) | −42.7519 | −1.58124 | ||||||||
\(732\) | −22.9344 | −0.847679 | ||||||||
\(733\) | −18.1869 | −0.671750 | −0.335875 | − | 0.941907i | \(-0.609032\pi\) | ||||
−0.335875 | + | 0.941907i | \(0.609032\pi\) | |||||||
\(734\) | −9.53501 | −0.351944 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.7269 | 0.395397 | ||||||||
\(737\) | 30.2824 | 1.11547 | ||||||||
\(738\) | 1.95065 | 0.0718044 | ||||||||
\(739\) | −12.5060 | −0.460042 | −0.230021 | − | 0.973186i | \(-0.573880\pi\) | ||||
−0.230021 | + | 0.973186i | \(0.573880\pi\) | |||||||
\(740\) | −39.0599 | −1.43587 | ||||||||
\(741\) | −7.31538 | −0.268737 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.6638 | 0.501277 | 0.250639 | − | 0.968081i | \(-0.419359\pi\) | ||||
0.250639 | + | 0.968081i | \(0.419359\pi\) | |||||||
\(744\) | −3.86986 | −0.141876 | ||||||||
\(745\) | −22.0054 | −0.806214 | ||||||||
\(746\) | −30.8679 | −1.13015 | ||||||||
\(747\) | −14.1159 | −0.516473 | ||||||||
\(748\) | 46.0744 | 1.68465 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −18.8350 | −0.687755 | ||||||||
\(751\) | −25.4172 | −0.927487 | −0.463743 | − | 0.885970i | \(-0.653494\pi\) | ||||
−0.463743 | + | 0.885970i | \(0.653494\pi\) | |||||||
\(752\) | 18.9026 | 0.689305 | ||||||||
\(753\) | 16.0282 | 0.584100 | ||||||||
\(754\) | −32.0086 | −1.16568 | ||||||||
\(755\) | 29.4652 | 1.07235 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.3522 | 1.39393 | 0.696967 | − | 0.717103i | \(-0.254532\pi\) | ||||
0.696967 | + | 0.717103i | \(0.254532\pi\) | |||||||
\(758\) | 26.3376 | 0.956624 | ||||||||
\(759\) | 4.73252 | 0.171780 | ||||||||
\(760\) | −1.81288 | −0.0657602 | ||||||||
\(761\) | −3.94762 | −0.143101 | −0.0715506 | − | 0.997437i | \(-0.522795\pi\) | ||||
−0.0715506 | + | 0.997437i | \(0.522795\pi\) | |||||||
\(762\) | 5.52243 | 0.200056 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 18.2043 | 0.658609 | ||||||||
\(765\) | −18.4684 | −0.667725 | ||||||||
\(766\) | −48.9176 | −1.76746 | ||||||||
\(767\) | 35.9139 | 1.29677 | ||||||||
\(768\) | −18.6499 | −0.672971 | ||||||||
\(769\) | −39.2114 | −1.41400 | −0.707000 | − | 0.707214i | \(-0.749952\pi\) | ||||
−0.707000 | + | 0.707214i | \(0.749952\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.41486 | −0.122983 | ||||||||
\(772\) | 7.91395 | 0.284829 | ||||||||
\(773\) | −12.5429 | −0.451137 | −0.225569 | − | 0.974227i | \(-0.572424\pi\) | ||||
−0.225569 | + | 0.974227i | \(0.572424\pi\) | |||||||
\(774\) | −11.1397 | −0.400408 | ||||||||
\(775\) | −11.0509 | −0.396960 | ||||||||
\(776\) | −3.06385 | −0.109986 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −66.3722 | −2.37956 | ||||||||
\(779\) | −1.93227 | −0.0692307 | ||||||||
\(780\) | −16.8586 | −0.603635 | ||||||||
\(781\) | 56.0879 | 2.00698 | ||||||||
\(782\) | −20.2685 | −0.724798 | ||||||||
\(783\) | −4.33428 | −0.154895 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −42.7675 | −1.52644 | ||||||||
\(786\) | −16.6689 | −0.594560 | ||||||||
\(787\) | 40.8000 | 1.45436 | 0.727182 | − | 0.686445i | \(-0.240830\pi\) | ||||
0.727182 | + | 0.686445i | \(0.240830\pi\) | |||||||
\(788\) | −10.0565 | −0.358247 | ||||||||
\(789\) | 6.96532 | 0.247972 | ||||||||
\(790\) | 52.9451 | 1.88370 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.29673 | −0.0460772 | ||||||||
\(793\) | −48.1029 | −1.70818 | ||||||||
\(794\) | −4.54987 | −0.161469 | ||||||||
\(795\) | 11.0890 | 0.393287 | ||||||||
\(796\) | 34.7470 | 1.23158 | ||||||||
\(797\) | −22.4983 | −0.796930 | −0.398465 | − | 0.917184i | \(-0.630457\pi\) | ||||
−0.398465 | + | 0.917184i | \(0.630457\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.5163 | −1.15034 | ||||||||
\(800\) | −8.39326 | −0.296746 | ||||||||
\(801\) | 18.8161 | 0.664834 | ||||||||
\(802\) | −3.22023 | −0.113710 | ||||||||
\(803\) | 1.78346 | 0.0629370 | ||||||||
\(804\) | −16.0311 | −0.565374 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 75.1465 | 2.64692 | ||||||||
\(807\) | 7.67353 | 0.270121 | ||||||||
\(808\) | −7.28887 | −0.256422 | ||||||||
\(809\) | 32.3502 | 1.13737 | 0.568686 | − | 0.822555i | \(-0.307452\pi\) | ||||
0.568686 | + | 0.822555i | \(0.307452\pi\) | |||||||
\(810\) | −4.81223 | −0.169084 | ||||||||
\(811\) | 41.8941 | 1.47110 | 0.735551 | − | 0.677469i | \(-0.236923\pi\) | ||||
0.735551 | + | 0.677469i | \(0.236923\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −28.1522 | −0.987341 | ||||||||
\(814\) | 58.3406 | 2.04484 | ||||||||
\(815\) | 3.53763 | 0.123918 | ||||||||
\(816\) | 32.5793 | 1.14050 | ||||||||
\(817\) | 11.0347 | 0.386056 | ||||||||
\(818\) | 17.9114 | 0.626256 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.45300 | −0.155505 | ||||||||
\(821\) | −38.7515 | −1.35244 | −0.676219 | − | 0.736701i | \(-0.736383\pi\) | ||||
−0.676219 | + | 0.736701i | \(0.736383\pi\) | |||||||
\(822\) | 6.77555 | 0.236324 | ||||||||
\(823\) | 38.8323 | 1.35361 | 0.676804 | − | 0.736163i | \(-0.263364\pi\) | ||||
0.676804 | + | 0.736163i | \(0.263364\pi\) | |||||||
\(824\) | −5.82799 | −0.203028 | ||||||||
\(825\) | −3.70297 | −0.128921 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.4060 | 0.431397 | 0.215699 | − | 0.976460i | \(-0.430797\pi\) | ||||
0.215699 | + | 0.976460i | \(0.430797\pi\) | |||||||
\(828\) | −2.50533 | −0.0870664 | ||||||||
\(829\) | 21.5753 | 0.749341 | 0.374670 | − | 0.927158i | \(-0.377756\pi\) | ||||
0.374670 | + | 0.927158i | \(0.377756\pi\) | |||||||
\(830\) | 67.9287 | 2.35784 | ||||||||
\(831\) | −4.85108 | −0.168282 | ||||||||
\(832\) | 24.1225 | 0.836298 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4.36507 | 0.151150 | ||||||||
\(835\) | −41.5703 | −1.43860 | ||||||||
\(836\) | −11.8923 | −0.411304 | ||||||||
\(837\) | 10.1756 | 0.351720 | ||||||||
\(838\) | −6.52331 | −0.225344 | ||||||||
\(839\) | −9.21299 | −0.318068 | −0.159034 | − | 0.987273i | \(-0.550838\pi\) | ||||
−0.159034 | + | 0.987273i | \(0.550838\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.2140 | −0.352207 | ||||||||
\(842\) | 42.8247 | 1.47584 | ||||||||
\(843\) | 13.4939 | 0.464754 | ||||||||
\(844\) | −9.31834 | −0.320750 | ||||||||
\(845\) | −3.28868 | −0.113134 | ||||||||
\(846\) | −8.47265 | −0.291296 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −19.5617 | −0.671752 | ||||||||
\(849\) | −3.39249 | −0.116430 | ||||||||
\(850\) | 15.8591 | 0.543963 | ||||||||
\(851\) | −12.1747 | −0.417344 | ||||||||
\(852\) | −29.6922 | −1.01724 | ||||||||
\(853\) | −12.8696 | −0.440646 | −0.220323 | − | 0.975427i | \(-0.570711\pi\) | ||||
−0.220323 | + | 0.975427i | \(0.570711\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.76688 | 0.163024 | ||||||||
\(856\) | −3.24709 | −0.110983 | ||||||||
\(857\) | 0.400158 | 0.0136691 | 0.00683457 | − | 0.999977i | \(-0.497824\pi\) | ||||
0.00683457 | + | 0.999977i | \(0.497824\pi\) | |||||||
\(858\) | 25.1803 | 0.859643 | ||||||||
\(859\) | 28.9248 | 0.986902 | 0.493451 | − | 0.869774i | \(-0.335735\pi\) | ||||
0.493451 | + | 0.869774i | \(0.335735\pi\) | |||||||
\(860\) | 25.4300 | 0.867156 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.0092 | 0.613394 | ||||||||
\(863\) | −10.5621 | −0.359540 | −0.179770 | − | 0.983709i | \(-0.557535\pi\) | ||||
−0.179770 | + | 0.983709i | \(0.557535\pi\) | |||||||
\(864\) | 7.72845 | 0.262927 | ||||||||
\(865\) | −5.84550 | −0.198753 | ||||||||
\(866\) | 33.5604 | 1.14043 | ||||||||
\(867\) | −39.0432 | −1.32598 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −37.5139 | −1.27257 | ||||||||
\(870\) | 20.8576 | 0.707137 | ||||||||
\(871\) | −33.6239 | −1.13930 | ||||||||
\(872\) | −5.45048 | −0.184577 | ||||||||
\(873\) | 8.05622 | 0.272662 | ||||||||
\(874\) | 5.23150 | 0.176958 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.944140 | −0.0318995 | ||||||||
\(877\) | 1.53055 | 0.0516830 | 0.0258415 | − | 0.999666i | \(-0.491773\pi\) | ||||
0.0258415 | + | 0.999666i | \(0.491773\pi\) | |||||||
\(878\) | 79.5129 | 2.68343 | ||||||||
\(879\) | 19.8814 | 0.670583 | ||||||||
\(880\) | 36.6067 | 1.23401 | ||||||||
\(881\) | −8.25921 | −0.278260 | −0.139130 | − | 0.990274i | \(-0.544431\pi\) | ||||
−0.139130 | + | 0.990274i | \(0.544431\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.5389 | 0.556578 | 0.278289 | − | 0.960497i | \(-0.410233\pi\) | ||||
0.278289 | + | 0.960497i | \(0.410233\pi\) | |||||||
\(884\) | −51.1584 | −1.72064 | ||||||||
\(885\) | −23.4023 | −0.786661 | ||||||||
\(886\) | 31.1762 | 1.04738 | ||||||||
\(887\) | −28.9877 | −0.973310 | −0.486655 | − | 0.873594i | \(-0.661783\pi\) | ||||
−0.486655 | + | 0.873594i | \(0.661783\pi\) | |||||||
\(888\) | 3.33592 | 0.111946 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −90.5473 | −3.03515 | ||||||||
\(891\) | 3.40967 | 0.114228 | ||||||||
\(892\) | −10.6846 | −0.357747 | ||||||||
\(893\) | 8.39281 | 0.280855 | ||||||||
\(894\) | −17.3997 | −0.581932 | ||||||||
\(895\) | 30.3747 | 1.01532 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.25472 | −0.175450 | ||||||||
\(898\) | 53.3167 | 1.77920 | ||||||||
\(899\) | −44.1039 | −1.47095 | ||||||||
\(900\) | 1.96030 | 0.0653435 | ||||||||
\(901\) | 33.6502 | 1.12105 | ||||||||
\(902\) | 6.65108 | 0.221457 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.00476125 | −0.000158357 0 | ||||||||
\(905\) | 59.2429 | 1.96930 | ||||||||
\(906\) | 23.2982 | 0.774031 | ||||||||
\(907\) | −4.20847 | −0.139740 | −0.0698700 | − | 0.997556i | \(-0.522258\pi\) | ||||
−0.0698700 | + | 0.997556i | \(0.522258\pi\) | |||||||
\(908\) | 43.3594 | 1.43893 | ||||||||
\(909\) | 19.1657 | 0.635686 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45.2126 | −1.49796 | −0.748980 | − | 0.662593i | \(-0.769456\pi\) | ||||
−0.748980 | + | 0.662593i | \(0.769456\pi\) | |||||||
\(912\) | −8.40907 | −0.278452 | ||||||||
\(913\) | −48.1305 | −1.59289 | ||||||||
\(914\) | 59.1421 | 1.95625 | ||||||||
\(915\) | 31.3450 | 1.03623 | ||||||||
\(916\) | 10.8200 | 0.357504 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −14.6030 | −0.481969 | ||||||||
\(919\) | −39.1541 | −1.29158 | −0.645788 | − | 0.763517i | \(-0.723471\pi\) | ||||
−0.645788 | + | 0.763517i | \(0.723471\pi\) | |||||||
\(920\) | −1.30221 | −0.0429327 | ||||||||
\(921\) | 20.5502 | 0.677152 | ||||||||
\(922\) | 29.2533 | 0.963405 | ||||||||
\(923\) | −62.2768 | −2.04986 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.52614 | 0.313218 | ||||||||
\(926\) | −35.9852 | −1.18255 | ||||||||
\(927\) | 15.3244 | 0.503319 | ||||||||
\(928\) | −33.4973 | −1.09960 | ||||||||
\(929\) | −13.0337 | −0.427621 | −0.213811 | − | 0.976875i | \(-0.568588\pi\) | ||||
−0.213811 | + | 0.976875i | \(0.568588\pi\) | |||||||
\(930\) | −48.9673 | −1.60570 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 30.4201 | 0.996442 | ||||||||
\(933\) | −7.09527 | −0.232289 | ||||||||
\(934\) | −29.0422 | −0.950290 | ||||||||
\(935\) | −62.9710 | −2.05937 | ||||||||
\(936\) | 1.43981 | 0.0470617 | ||||||||
\(937\) | 27.4537 | 0.896874 | 0.448437 | − | 0.893815i | \(-0.351981\pi\) | ||||
0.448437 | + | 0.893815i | \(0.351981\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.8328 | −0.353516 | ||||||||
\(940\) | 19.3416 | 0.630853 | ||||||||
\(941\) | −52.6685 | −1.71694 | −0.858472 | − | 0.512861i | \(-0.828586\pi\) | ||||
−0.858472 | + | 0.512861i | \(0.828586\pi\) | |||||||
\(942\) | −33.8163 | −1.10179 | ||||||||
\(943\) | −1.38797 | −0.0451985 | ||||||||
\(944\) | 41.2832 | 1.34365 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −37.9827 | −1.23492 | ||||||||
\(947\) | −35.1078 | −1.14085 | −0.570425 | − | 0.821350i | \(-0.693221\pi\) | ||||
−0.570425 | + | 0.821350i | \(0.693221\pi\) | |||||||
\(948\) | 19.8594 | 0.645002 | ||||||||
\(949\) | −1.98025 | −0.0642817 | ||||||||
\(950\) | −4.09340 | −0.132808 | ||||||||
\(951\) | −15.8780 | −0.514880 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.7506 | 0.639784 | 0.319892 | − | 0.947454i | \(-0.396353\pi\) | ||||
0.319892 | + | 0.947454i | \(0.396353\pi\) | |||||||
\(954\) | 8.76810 | 0.283878 | ||||||||
\(955\) | −24.8803 | −0.805107 | ||||||||
\(956\) | 1.90554 | 0.0616297 | ||||||||
\(957\) | −14.7785 | −0.477721 | ||||||||
\(958\) | −40.6316 | −1.31275 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −15.7188 | −0.507323 | ||||||||
\(961\) | 72.5427 | 2.34009 | ||||||||
\(962\) | −64.7781 | −2.08853 | ||||||||
\(963\) | 8.53803 | 0.275134 | ||||||||
\(964\) | −53.7768 | −1.73203 | ||||||||
\(965\) | −10.8162 | −0.348186 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.7402 | 0.506171 | 0.253085 | − | 0.967444i | \(-0.418555\pi\) | ||||
0.253085 | + | 0.967444i | \(0.418555\pi\) | |||||||
\(968\) | −0.238023 | −0.00765034 | ||||||||
\(969\) | 14.4653 | 0.464694 | ||||||||
\(970\) | −38.7684 | −1.24478 | ||||||||
\(971\) | 16.8101 | 0.539462 | 0.269731 | − | 0.962936i | \(-0.413065\pi\) | ||||
0.269731 | + | 0.962936i | \(0.413065\pi\) | |||||||
\(972\) | −1.80504 | −0.0578965 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −68.0993 | −2.18204 | ||||||||
\(975\) | 4.11157 | 0.131676 | ||||||||
\(976\) | −55.2945 | −1.76993 | ||||||||
\(977\) | 4.71491 | 0.150843 | 0.0754217 | − | 0.997152i | \(-0.475970\pi\) | ||||
0.0754217 | + | 0.997152i | \(0.475970\pi\) | |||||||
\(978\) | 2.79721 | 0.0894448 | ||||||||
\(979\) | 64.1567 | 2.05046 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.3317 | 0.457578 | ||||||||
\(982\) | −56.7228 | −1.81010 | ||||||||
\(983\) | −24.6443 | −0.786032 | −0.393016 | − | 0.919532i | \(-0.628568\pi\) | ||||
−0.393016 | + | 0.919532i | \(0.628568\pi\) | |||||||
\(984\) | 0.380308 | 0.0121238 | ||||||||
\(985\) | 13.7444 | 0.437934 | ||||||||
\(986\) | 63.2933 | 2.01567 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 13.2045 | 0.420092 | ||||||||
\(989\) | 7.92636 | 0.252044 | ||||||||
\(990\) | −16.4081 | −0.521484 | ||||||||
\(991\) | 0.939287 | 0.0298374 | 0.0149187 | − | 0.999889i | \(-0.495251\pi\) | ||||
0.0149187 | + | 0.999889i | \(0.495251\pi\) | |||||||
\(992\) | 78.6416 | 2.49687 | ||||||||
\(993\) | −8.57678 | −0.272176 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −47.4896 | −1.50552 | ||||||||
\(996\) | 25.4796 | 0.807353 | ||||||||
\(997\) | 20.4352 | 0.647188 | 0.323594 | − | 0.946196i | \(-0.395109\pi\) | ||||
0.323594 | + | 0.946196i | \(0.395109\pi\) | |||||||
\(998\) | 12.8771 | 0.407617 | ||||||||
\(999\) | −8.77161 | −0.277521 |
(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 | 6027.2.a.bn.1.18 | ✓ | 24 | |
7.6 | odd | 2 | 6027.2.a.bo.1.18 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bn.1.18 | ✓ | 24 | 1.1 | even | 1 | trivial | |
6027.2.a.bo.1.18 | yes | 24 | 7.6 | odd | 2 |