Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(1,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, 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("847.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.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: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.76156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.76156 | 1.95272 | 0.976358 | − | 0.216160i | \(-0.0693534\pi\) | ||||
0.976358 | + | 0.216160i | \(0.0693534\pi\) | |||||||
\(3\) | 1.76156 | 1.01704 | 0.508518 | − | 0.861052i | \(-0.330194\pi\) | ||||
0.508518 | + | 0.861052i | \(0.330194\pi\) | |||||||
\(4\) | 5.62620 | 2.81310 | ||||||||
\(5\) | −2.62620 | −1.17447 | −0.587236 | − | 0.809416i | \(-0.699784\pi\) | ||||
−0.587236 | + | 0.809416i | \(0.699784\pi\) | |||||||
\(6\) | 4.86464 | 1.98598 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 10.0140 | 3.54047 | ||||||||
\(9\) | 0.103084 | 0.0343612 | ||||||||
\(10\) | −7.25240 | −2.29341 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 9.91087 | 2.86102 | ||||||||
\(13\) | −2.38776 | −0.662244 | −0.331122 | − | 0.943588i | \(-0.607427\pi\) | ||||
−0.331122 | + | 0.943588i | \(0.607427\pi\) | |||||||
\(14\) | 2.76156 | 0.738057 | ||||||||
\(15\) | −4.62620 | −1.19448 | ||||||||
\(16\) | 16.4017 | 4.10043 | ||||||||
\(17\) | −2.38776 | −0.579116 | −0.289558 | − | 0.957161i | \(-0.593508\pi\) | ||||
−0.289558 | + | 0.957161i | \(0.593508\pi\) | |||||||
\(18\) | 0.284672 | 0.0670977 | ||||||||
\(19\) | −1.72928 | −0.396724 | −0.198362 | − | 0.980129i | \(-0.563562\pi\) | ||||
−0.198362 | + | 0.980129i | \(0.563562\pi\) | |||||||
\(20\) | −14.7755 | −3.30390 | ||||||||
\(21\) | 1.76156 | 0.384403 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.626198 | −0.130571 | −0.0652857 | − | 0.997867i | \(-0.520796\pi\) | ||||
−0.0652857 | + | 0.997867i | \(0.520796\pi\) | |||||||
\(24\) | 17.6402 | 3.60078 | ||||||||
\(25\) | 1.89692 | 0.379383 | ||||||||
\(26\) | −6.59392 | −1.29317 | ||||||||
\(27\) | −5.10308 | −0.982089 | ||||||||
\(28\) | 5.62620 | 1.06325 | ||||||||
\(29\) | 1.72928 | 0.321120 | 0.160560 | − | 0.987026i | \(-0.448670\pi\) | ||||
0.160560 | + | 0.987026i | \(0.448670\pi\) | |||||||
\(30\) | −12.7755 | −2.33248 | ||||||||
\(31\) | −2.23844 | −0.402036 | −0.201018 | − | 0.979588i | \(-0.564425\pi\) | ||||
−0.201018 | + | 0.979588i | \(0.564425\pi\) | |||||||
\(32\) | 25.2663 | 4.46650 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.59392 | −1.13085 | ||||||||
\(35\) | −2.62620 | −0.443908 | ||||||||
\(36\) | 0.579969 | 0.0966616 | ||||||||
\(37\) | −6.89692 | −1.13385 | −0.566923 | − | 0.823771i | \(-0.691866\pi\) | ||||
−0.566923 | + | 0.823771i | \(0.691866\pi\) | |||||||
\(38\) | −4.77551 | −0.774690 | ||||||||
\(39\) | −4.20617 | −0.673526 | ||||||||
\(40\) | −26.2986 | −4.15818 | ||||||||
\(41\) | 10.3878 | 1.62229 | 0.811147 | − | 0.584842i | \(-0.198843\pi\) | ||||
0.811147 | + | 0.584842i | \(0.198843\pi\) | |||||||
\(42\) | 4.86464 | 0.750630 | ||||||||
\(43\) | 7.25240 | 1.10598 | 0.552990 | − | 0.833188i | \(-0.313487\pi\) | ||||
0.552990 | + | 0.833188i | \(0.313487\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.270718 | −0.0403563 | ||||||||
\(46\) | −1.72928 | −0.254969 | ||||||||
\(47\) | 6.38776 | 0.931750 | 0.465875 | − | 0.884851i | \(-0.345740\pi\) | ||||
0.465875 | + | 0.884851i | \(0.345740\pi\) | |||||||
\(48\) | 28.8925 | 4.17028 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 5.23844 | 0.740828 | ||||||||
\(51\) | −4.20617 | −0.588981 | ||||||||
\(52\) | −13.4340 | −1.86296 | ||||||||
\(53\) | −9.25240 | −1.27091 | −0.635457 | − | 0.772136i | \(-0.719188\pi\) | ||||
−0.635457 | + | 0.772136i | \(0.719188\pi\) | |||||||
\(54\) | −14.0925 | −1.91774 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 10.0140 | 1.33817 | ||||||||
\(57\) | −3.04623 | −0.403483 | ||||||||
\(58\) | 4.77551 | 0.627055 | ||||||||
\(59\) | −1.76156 | −0.229335 | −0.114668 | − | 0.993404i | \(-0.536580\pi\) | ||||
−0.114668 | + | 0.993404i | \(0.536580\pi\) | |||||||
\(60\) | −26.0279 | −3.36019 | ||||||||
\(61\) | −10.3878 | −1.33002 | −0.665008 | − | 0.746836i | \(-0.731572\pi\) | ||||
−0.665008 | + | 0.746836i | \(0.731572\pi\) | |||||||
\(62\) | −6.18159 | −0.785062 | ||||||||
\(63\) | 0.103084 | 0.0129873 | ||||||||
\(64\) | 36.9711 | 4.62138 | ||||||||
\(65\) | 6.27072 | 0.777787 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.42003 | −0.784332 | −0.392166 | − | 0.919895i | \(-0.628274\pi\) | ||||
−0.392166 | + | 0.919895i | \(0.628274\pi\) | |||||||
\(68\) | −13.4340 | −1.62911 | ||||||||
\(69\) | −1.10308 | −0.132796 | ||||||||
\(70\) | −7.25240 | −0.866827 | ||||||||
\(71\) | 8.08476 | 0.959485 | 0.479742 | − | 0.877409i | \(-0.340730\pi\) | ||||
0.479742 | + | 0.877409i | \(0.340730\pi\) | |||||||
\(72\) | 1.03228 | 0.121655 | ||||||||
\(73\) | 10.3878 | 1.21579 | 0.607897 | − | 0.794016i | \(-0.292013\pi\) | ||||
0.607897 | + | 0.794016i | \(0.292013\pi\) | |||||||
\(74\) | −19.0462 | −2.21408 | ||||||||
\(75\) | 3.34153 | 0.385846 | ||||||||
\(76\) | −9.72928 | −1.11603 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −11.6156 | −1.31520 | ||||||||
\(79\) | 15.2524 | 1.71603 | 0.858014 | − | 0.513626i | \(-0.171698\pi\) | ||||
0.858014 | + | 0.513626i | \(0.171698\pi\) | |||||||
\(80\) | −43.0741 | −4.81583 | ||||||||
\(81\) | −9.29862 | −1.03318 | ||||||||
\(82\) | 28.6864 | 3.16788 | ||||||||
\(83\) | 12.7755 | 1.40229 | 0.701147 | − | 0.713017i | \(-0.252672\pi\) | ||||
0.701147 | + | 0.713017i | \(0.252672\pi\) | |||||||
\(84\) | 9.91087 | 1.08136 | ||||||||
\(85\) | 6.27072 | 0.680155 | ||||||||
\(86\) | 20.0279 | 2.15966 | ||||||||
\(87\) | 3.04623 | 0.326590 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.1493 | −1.49982 | −0.749912 | − | 0.661538i | \(-0.769904\pi\) | ||||
−0.749912 | + | 0.661538i | \(0.769904\pi\) | |||||||
\(90\) | −0.747604 | −0.0788044 | ||||||||
\(91\) | −2.38776 | −0.250305 | ||||||||
\(92\) | −3.52311 | −0.367310 | ||||||||
\(93\) | −3.94315 | −0.408885 | ||||||||
\(94\) | 17.6402 | 1.81944 | ||||||||
\(95\) | 4.54144 | 0.465942 | ||||||||
\(96\) | 44.5081 | 4.54259 | ||||||||
\(97\) | −8.35548 | −0.848370 | −0.424185 | − | 0.905575i | \(-0.639439\pi\) | ||||
−0.424185 | + | 0.905575i | \(0.639439\pi\) | |||||||
\(98\) | 2.76156 | 0.278959 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 10.6724 | 1.06724 | ||||||||
\(101\) | −13.8463 | −1.37776 | −0.688880 | − | 0.724875i | \(-0.741897\pi\) | ||||
−0.688880 | + | 0.724875i | \(0.741897\pi\) | |||||||
\(102\) | −11.6156 | −1.15011 | ||||||||
\(103\) | −2.92919 | −0.288622 | −0.144311 | − | 0.989532i | \(-0.546097\pi\) | ||||
−0.144311 | + | 0.989532i | \(0.546097\pi\) | |||||||
\(104\) | −23.9109 | −2.34465 | ||||||||
\(105\) | −4.62620 | −0.451471 | ||||||||
\(106\) | −25.5510 | −2.48173 | ||||||||
\(107\) | 3.45856 | 0.334352 | 0.167176 | − | 0.985927i | \(-0.446535\pi\) | ||||
0.167176 | + | 0.985927i | \(0.446535\pi\) | |||||||
\(108\) | −28.7110 | −2.76271 | ||||||||
\(109\) | −16.2341 | −1.55494 | −0.777471 | − | 0.628919i | \(-0.783498\pi\) | ||||
−0.777471 | + | 0.628919i | \(0.783498\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.1493 | −1.15316 | ||||||||
\(112\) | 16.4017 | 1.54982 | ||||||||
\(113\) | 7.10308 | 0.668202 | 0.334101 | − | 0.942537i | \(-0.391567\pi\) | ||||
0.334101 | + | 0.942537i | \(0.391567\pi\) | |||||||
\(114\) | −8.41233 | −0.787887 | ||||||||
\(115\) | 1.64452 | 0.153352 | ||||||||
\(116\) | 9.72928 | 0.903341 | ||||||||
\(117\) | −0.246139 | −0.0227555 | ||||||||
\(118\) | −4.86464 | −0.447826 | ||||||||
\(119\) | −2.38776 | −0.218885 | ||||||||
\(120\) | −46.3265 | −4.22901 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −28.6864 | −2.59714 | ||||||||
\(123\) | 18.2986 | 1.64993 | ||||||||
\(124\) | −12.5939 | −1.13097 | ||||||||
\(125\) | 8.14931 | 0.728897 | ||||||||
\(126\) | 0.284672 | 0.0253606 | ||||||||
\(127\) | −4.54144 | −0.402987 | −0.201494 | − | 0.979490i | \(-0.564580\pi\) | ||||
−0.201494 | + | 0.979490i | \(0.564580\pi\) | |||||||
\(128\) | 51.5650 | 4.55774 | ||||||||
\(129\) | 12.7755 | 1.12482 | ||||||||
\(130\) | 17.3169 | 1.51880 | ||||||||
\(131\) | −6.27072 | −0.547875 | −0.273938 | − | 0.961747i | \(-0.588326\pi\) | ||||
−0.273938 | + | 0.961747i | \(0.588326\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.72928 | −0.149948 | ||||||||
\(134\) | −17.7293 | −1.53158 | ||||||||
\(135\) | 13.4017 | 1.15344 | ||||||||
\(136\) | −23.9109 | −2.05034 | ||||||||
\(137\) | 9.40171 | 0.803242 | 0.401621 | − | 0.915806i | \(-0.368447\pi\) | ||||
0.401621 | + | 0.915806i | \(0.368447\pi\) | |||||||
\(138\) | −3.04623 | −0.259312 | ||||||||
\(139\) | 15.8217 | 1.34198 | 0.670991 | − | 0.741465i | \(-0.265869\pi\) | ||||
0.670991 | + | 0.741465i | \(0.265869\pi\) | |||||||
\(140\) | −14.7755 | −1.24876 | ||||||||
\(141\) | 11.2524 | 0.947623 | ||||||||
\(142\) | 22.3265 | 1.87360 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.69075 | 0.140896 | ||||||||
\(145\) | −4.54144 | −0.377146 | ||||||||
\(146\) | 28.6864 | 2.37410 | ||||||||
\(147\) | 1.76156 | 0.145291 | ||||||||
\(148\) | −38.8034 | −3.18962 | ||||||||
\(149\) | 3.45856 | 0.283337 | 0.141668 | − | 0.989914i | \(-0.454753\pi\) | ||||
0.141668 | + | 0.989914i | \(0.454753\pi\) | |||||||
\(150\) | 9.22782 | 0.753448 | ||||||||
\(151\) | −10.2986 | −0.838090 | −0.419045 | − | 0.907965i | \(-0.637635\pi\) | ||||
−0.419045 | + | 0.907965i | \(0.637635\pi\) | |||||||
\(152\) | −17.3169 | −1.40459 | ||||||||
\(153\) | −0.246139 | −0.0198991 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.87859 | 0.472180 | ||||||||
\(156\) | −23.6647 | −1.89469 | ||||||||
\(157\) | 11.3372 | 0.904804 | 0.452402 | − | 0.891814i | \(-0.350567\pi\) | ||||
0.452402 | + | 0.891814i | \(0.350567\pi\) | |||||||
\(158\) | 42.1204 | 3.35092 | ||||||||
\(159\) | −16.2986 | −1.29257 | ||||||||
\(160\) | −66.3544 | −5.24578 | ||||||||
\(161\) | −0.626198 | −0.0493513 | ||||||||
\(162\) | −25.6787 | −2.01751 | ||||||||
\(163\) | −9.72928 | −0.762056 | −0.381028 | − | 0.924563i | \(-0.624430\pi\) | ||||
−0.381028 | + | 0.924563i | \(0.624430\pi\) | |||||||
\(164\) | 58.4436 | 4.56368 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 35.2803 | 2.73828 | ||||||||
\(167\) | 22.5048 | 1.74147 | 0.870737 | − | 0.491750i | \(-0.163643\pi\) | ||||
0.870737 | + | 0.491750i | \(0.163643\pi\) | |||||||
\(168\) | 17.6402 | 1.36097 | ||||||||
\(169\) | −7.29862 | −0.561433 | ||||||||
\(170\) | 17.3169 | 1.32815 | ||||||||
\(171\) | −0.178261 | −0.0136319 | ||||||||
\(172\) | 40.8034 | 3.11123 | ||||||||
\(173\) | 6.92919 | 0.526817 | 0.263408 | − | 0.964684i | \(-0.415153\pi\) | ||||
0.263408 | + | 0.964684i | \(0.415153\pi\) | |||||||
\(174\) | 8.41233 | 0.637737 | ||||||||
\(175\) | 1.89692 | 0.143393 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.10308 | −0.233242 | ||||||||
\(178\) | −39.0741 | −2.92873 | ||||||||
\(179\) | 13.9431 | 1.04216 | 0.521080 | − | 0.853508i | \(-0.325529\pi\) | ||||
0.521080 | + | 0.853508i | \(0.325529\pi\) | |||||||
\(180\) | −1.52311 | −0.113526 | ||||||||
\(181\) | 3.16763 | 0.235448 | 0.117724 | − | 0.993046i | \(-0.462440\pi\) | ||||
0.117724 | + | 0.993046i | \(0.462440\pi\) | |||||||
\(182\) | −6.59392 | −0.488774 | ||||||||
\(183\) | −18.2986 | −1.35267 | ||||||||
\(184\) | −6.27072 | −0.462283 | ||||||||
\(185\) | 18.1127 | 1.33167 | ||||||||
\(186\) | −10.8892 | −0.798436 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 35.9388 | 2.62110 | ||||||||
\(189\) | −5.10308 | −0.371195 | ||||||||
\(190\) | 12.5414 | 0.909851 | ||||||||
\(191\) | 18.3555 | 1.32816 | 0.664078 | − | 0.747663i | \(-0.268824\pi\) | ||||
0.664078 | + | 0.747663i | \(0.268824\pi\) | |||||||
\(192\) | 65.1266 | 4.70011 | ||||||||
\(193\) | −3.04623 | −0.219272 | −0.109636 | − | 0.993972i | \(-0.534969\pi\) | ||||
−0.109636 | + | 0.993972i | \(0.534969\pi\) | |||||||
\(194\) | −23.0741 | −1.65663 | ||||||||
\(195\) | 11.0462 | 0.791037 | ||||||||
\(196\) | 5.62620 | 0.401871 | ||||||||
\(197\) | 4.95377 | 0.352942 | 0.176471 | − | 0.984306i | \(-0.443532\pi\) | ||||
0.176471 | + | 0.984306i | \(0.443532\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.7047 | 1.11328 | 0.556638 | − | 0.830755i | \(-0.312091\pi\) | ||||
0.556638 | + | 0.830755i | \(0.312091\pi\) | |||||||
\(200\) | 18.9956 | 1.34319 | ||||||||
\(201\) | −11.3093 | −0.797693 | ||||||||
\(202\) | −38.2374 | −2.69037 | ||||||||
\(203\) | 1.72928 | 0.121372 | ||||||||
\(204\) | −23.6647 | −1.65686 | ||||||||
\(205\) | −27.2803 | −1.90534 | ||||||||
\(206\) | −8.08913 | −0.563596 | ||||||||
\(207\) | −0.0645508 | −0.00448659 | ||||||||
\(208\) | −39.1633 | −2.71548 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −12.7755 | −0.881594 | ||||||||
\(211\) | 17.5510 | 1.20826 | 0.604131 | − | 0.796885i | \(-0.293520\pi\) | ||||
0.604131 | + | 0.796885i | \(0.293520\pi\) | |||||||
\(212\) | −52.0558 | −3.57521 | ||||||||
\(213\) | 14.2418 | 0.975830 | ||||||||
\(214\) | 9.55102 | 0.652894 | ||||||||
\(215\) | −19.0462 | −1.29894 | ||||||||
\(216\) | −51.1020 | −3.47705 | ||||||||
\(217\) | −2.23844 | −0.151955 | ||||||||
\(218\) | −44.8313 | −3.03636 | ||||||||
\(219\) | 18.2986 | 1.23651 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.70138 | 0.383516 | ||||||||
\(222\) | −33.5510 | −2.25180 | ||||||||
\(223\) | −22.2943 | −1.49293 | −0.746467 | − | 0.665423i | \(-0.768251\pi\) | ||||
−0.746467 | + | 0.665423i | \(0.768251\pi\) | |||||||
\(224\) | 25.2663 | 1.68818 | ||||||||
\(225\) | 0.195541 | 0.0130361 | ||||||||
\(226\) | 19.6156 | 1.30481 | ||||||||
\(227\) | 14.2707 | 0.947181 | 0.473590 | − | 0.880745i | \(-0.342958\pi\) | ||||
0.473590 | + | 0.880745i | \(0.342958\pi\) | |||||||
\(228\) | −17.1387 | −1.13504 | ||||||||
\(229\) | −3.87859 | −0.256305 | −0.128152 | − | 0.991754i | \(-0.540905\pi\) | ||||
−0.128152 | + | 0.991754i | \(0.540905\pi\) | |||||||
\(230\) | 4.54144 | 0.299453 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 17.3169 | 1.13691 | ||||||||
\(233\) | 6.68305 | 0.437821 | 0.218911 | − | 0.975745i | \(-0.429750\pi\) | ||||
0.218911 | + | 0.975745i | \(0.429750\pi\) | |||||||
\(234\) | −0.679726 | −0.0444351 | ||||||||
\(235\) | −16.7755 | −1.09431 | ||||||||
\(236\) | −9.91087 | −0.645143 | ||||||||
\(237\) | 26.8680 | 1.74526 | ||||||||
\(238\) | −6.59392 | −0.427421 | ||||||||
\(239\) | −4.54144 | −0.293761 | −0.146881 | − | 0.989154i | \(-0.546923\pi\) | ||||
−0.146881 | + | 0.989154i | \(0.546923\pi\) | |||||||
\(240\) | −75.8776 | −4.89787 | ||||||||
\(241\) | −3.70470 | −0.238641 | −0.119320 | − | 0.992856i | \(-0.538072\pi\) | ||||
−0.119320 | + | 0.992856i | \(0.538072\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.07081 | −0.0686924 | ||||||||
\(244\) | −58.4436 | −3.74147 | ||||||||
\(245\) | −2.62620 | −0.167782 | ||||||||
\(246\) | 50.5327 | 3.22185 | ||||||||
\(247\) | 4.12910 | 0.262728 | ||||||||
\(248\) | −22.4157 | −1.42340 | ||||||||
\(249\) | 22.5048 | 1.42618 | ||||||||
\(250\) | 22.5048 | 1.42333 | ||||||||
\(251\) | 8.50916 | 0.537093 | 0.268547 | − | 0.963267i | \(-0.413457\pi\) | ||||
0.268547 | + | 0.963267i | \(0.413457\pi\) | |||||||
\(252\) | 0.579969 | 0.0365346 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −12.5414 | −0.786920 | ||||||||
\(255\) | 11.0462 | 0.691742 | ||||||||
\(256\) | 68.4575 | 4.27860 | ||||||||
\(257\) | −2.95377 | −0.184251 | −0.0921256 | − | 0.995747i | \(-0.529366\pi\) | ||||
−0.0921256 | + | 0.995747i | \(0.529366\pi\) | |||||||
\(258\) | 35.2803 | 2.19646 | ||||||||
\(259\) | −6.89692 | −0.428554 | ||||||||
\(260\) | 35.2803 | 2.18799 | ||||||||
\(261\) | 0.178261 | 0.0110341 | ||||||||
\(262\) | −17.3169 | −1.06984 | ||||||||
\(263\) | −16.0000 | −0.986602 | −0.493301 | − | 0.869859i | \(-0.664210\pi\) | ||||
−0.493301 | + | 0.869859i | \(0.664210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.2986 | 1.49265 | ||||||||
\(266\) | −4.77551 | −0.292805 | ||||||||
\(267\) | −24.9248 | −1.52537 | ||||||||
\(268\) | −36.1204 | −2.20640 | ||||||||
\(269\) | −6.77551 | −0.413110 | −0.206555 | − | 0.978435i | \(-0.566225\pi\) | ||||
−0.206555 | + | 0.978435i | \(0.566225\pi\) | |||||||
\(270\) | 37.0096 | 2.25233 | ||||||||
\(271\) | 3.45856 | 0.210093 | 0.105046 | − | 0.994467i | \(-0.466501\pi\) | ||||
0.105046 | + | 0.994467i | \(0.466501\pi\) | |||||||
\(272\) | −39.1633 | −2.37462 | ||||||||
\(273\) | −4.20617 | −0.254569 | ||||||||
\(274\) | 25.9634 | 1.56850 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.20617 | −0.373567 | ||||||||
\(277\) | −11.4586 | −0.688478 | −0.344239 | − | 0.938882i | \(-0.611863\pi\) | ||||
−0.344239 | + | 0.938882i | \(0.611863\pi\) | |||||||
\(278\) | 43.6926 | 2.62051 | ||||||||
\(279\) | −0.230747 | −0.0138145 | ||||||||
\(280\) | −26.2986 | −1.57164 | ||||||||
\(281\) | −22.3265 | −1.33189 | −0.665945 | − | 0.746001i | \(-0.731971\pi\) | ||||
−0.665945 | + | 0.746001i | \(0.731971\pi\) | |||||||
\(282\) | 31.0741 | 1.85044 | ||||||||
\(283\) | −12.3632 | −0.734915 | −0.367457 | − | 0.930040i | \(-0.619772\pi\) | ||||
−0.367457 | + | 0.930040i | \(0.619772\pi\) | |||||||
\(284\) | 45.4865 | 2.69913 | ||||||||
\(285\) | 8.00000 | 0.473879 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.3878 | 0.613170 | ||||||||
\(288\) | 2.60455 | 0.153475 | ||||||||
\(289\) | −11.2986 | −0.664625 | ||||||||
\(290\) | −12.5414 | −0.736459 | ||||||||
\(291\) | −14.7187 | −0.862823 | ||||||||
\(292\) | 58.4436 | 3.42015 | ||||||||
\(293\) | 2.15368 | 0.125819 | 0.0629097 | − | 0.998019i | \(-0.479962\pi\) | ||||
0.0629097 | + | 0.998019i | \(0.479962\pi\) | |||||||
\(294\) | 4.86464 | 0.283712 | ||||||||
\(295\) | 4.62620 | 0.269348 | ||||||||
\(296\) | −69.0654 | −4.01434 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.55102 | 0.553276 | ||||||||
\(299\) | 1.49521 | 0.0864701 | ||||||||
\(300\) | 18.8001 | 1.08542 | ||||||||
\(301\) | 7.25240 | 0.418021 | ||||||||
\(302\) | −28.4402 | −1.63655 | ||||||||
\(303\) | −24.3911 | −1.40123 | ||||||||
\(304\) | −28.3632 | −1.62674 | ||||||||
\(305\) | 27.2803 | 1.56207 | ||||||||
\(306\) | −0.679726 | −0.0388573 | ||||||||
\(307\) | −31.8217 | −1.81616 | −0.908081 | − | 0.418794i | \(-0.862453\pi\) | ||||
−0.908081 | + | 0.418794i | \(0.862453\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.15994 | −0.293539 | ||||||||
\(310\) | 16.2341 | 0.922033 | ||||||||
\(311\) | −10.9292 | −0.619738 | −0.309869 | − | 0.950779i | \(-0.600285\pi\) | ||||
−0.309869 | + | 0.950779i | \(0.600285\pi\) | |||||||
\(312\) | −42.1204 | −2.38460 | ||||||||
\(313\) | 7.40171 | 0.418369 | 0.209185 | − | 0.977876i | \(-0.432919\pi\) | ||||
0.209185 | + | 0.977876i | \(0.432919\pi\) | |||||||
\(314\) | 31.3082 | 1.76682 | ||||||||
\(315\) | −0.270718 | −0.0152532 | ||||||||
\(316\) | 85.8130 | 4.82736 | ||||||||
\(317\) | −8.89692 | −0.499701 | −0.249850 | − | 0.968284i | \(-0.580381\pi\) | ||||
−0.249850 | + | 0.968284i | \(0.580381\pi\) | |||||||
\(318\) | −45.0096 | −2.52401 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −97.0933 | −5.42768 | ||||||||
\(321\) | 6.09246 | 0.340048 | ||||||||
\(322\) | −1.72928 | −0.0963691 | ||||||||
\(323\) | 4.12910 | 0.229749 | ||||||||
\(324\) | −52.3159 | −2.90644 | ||||||||
\(325\) | −4.52937 | −0.251244 | ||||||||
\(326\) | −26.8680 | −1.48808 | ||||||||
\(327\) | −28.5972 | −1.58143 | ||||||||
\(328\) | 104.022 | 5.74368 | ||||||||
\(329\) | 6.38776 | 0.352168 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.56165 | 0.470591 | 0.235295 | − | 0.971924i | \(-0.424394\pi\) | ||||
0.235295 | + | 0.971924i | \(0.424394\pi\) | |||||||
\(332\) | 71.8776 | 3.94479 | ||||||||
\(333\) | −0.710960 | −0.0389604 | ||||||||
\(334\) | 62.1483 | 3.40060 | ||||||||
\(335\) | 16.8603 | 0.921175 | ||||||||
\(336\) | 28.8925 | 1.57622 | ||||||||
\(337\) | −9.72928 | −0.529988 | −0.264994 | − | 0.964250i | \(-0.585370\pi\) | ||||
−0.264994 | + | 0.964250i | \(0.585370\pi\) | |||||||
\(338\) | −20.1556 | −1.09632 | ||||||||
\(339\) | 12.5125 | 0.679585 | ||||||||
\(340\) | 35.2803 | 1.91334 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −0.492277 | −0.0266193 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 72.6252 | 3.91569 | ||||||||
\(345\) | 2.89692 | 0.155965 | ||||||||
\(346\) | 19.1354 | 1.02872 | ||||||||
\(347\) | 14.8401 | 0.796656 | 0.398328 | − | 0.917243i | \(-0.369591\pi\) | ||||
0.398328 | + | 0.917243i | \(0.369591\pi\) | |||||||
\(348\) | 17.1387 | 0.918730 | ||||||||
\(349\) | 16.2461 | 0.869636 | 0.434818 | − | 0.900518i | \(-0.356813\pi\) | ||||
0.434818 | + | 0.900518i | \(0.356813\pi\) | |||||||
\(350\) | 5.23844 | 0.280007 | ||||||||
\(351\) | 12.1849 | 0.650383 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.8603 | 1.64253 | 0.821263 | − | 0.570549i | \(-0.193270\pi\) | ||||
0.821263 | + | 0.570549i | \(0.193270\pi\) | |||||||
\(354\) | −8.56934 | −0.455455 | ||||||||
\(355\) | −21.2322 | −1.12689 | ||||||||
\(356\) | −79.6068 | −4.21915 | ||||||||
\(357\) | −4.20617 | −0.222614 | ||||||||
\(358\) | 38.5048 | 2.03504 | ||||||||
\(359\) | −11.7938 | −0.622455 | −0.311227 | − | 0.950335i | \(-0.600740\pi\) | ||||
−0.311227 | + | 0.950335i | \(0.600740\pi\) | |||||||
\(360\) | −2.71096 | −0.142880 | ||||||||
\(361\) | −16.0096 | −0.842610 | ||||||||
\(362\) | 8.74760 | 0.459764 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −13.4340 | −0.704132 | ||||||||
\(365\) | −27.2803 | −1.42792 | ||||||||
\(366\) | −50.5327 | −2.64139 | ||||||||
\(367\) | −3.55539 | −0.185590 | −0.0927949 | − | 0.995685i | \(-0.529580\pi\) | ||||
−0.0927949 | + | 0.995685i | \(0.529580\pi\) | |||||||
\(368\) | −10.2707 | −0.535398 | ||||||||
\(369\) | 1.07081 | 0.0557441 | ||||||||
\(370\) | 50.0192 | 2.60037 | ||||||||
\(371\) | −9.25240 | −0.480360 | ||||||||
\(372\) | −22.1849 | −1.15023 | ||||||||
\(373\) | 22.5048 | 1.16525 | 0.582627 | − | 0.812740i | \(-0.302025\pi\) | ||||
0.582627 | + | 0.812740i | \(0.302025\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.3555 | 0.741314 | ||||||||
\(376\) | 63.9667 | 3.29883 | ||||||||
\(377\) | −4.12910 | −0.212660 | ||||||||
\(378\) | −14.0925 | −0.724838 | ||||||||
\(379\) | 23.4296 | 1.20350 | 0.601749 | − | 0.798685i | \(-0.294471\pi\) | ||||
0.601749 | + | 0.798685i | \(0.294471\pi\) | |||||||
\(380\) | 25.5510 | 1.31074 | ||||||||
\(381\) | −8.00000 | −0.409852 | ||||||||
\(382\) | 50.6897 | 2.59351 | ||||||||
\(383\) | −3.42629 | −0.175075 | −0.0875376 | − | 0.996161i | \(-0.527900\pi\) | ||||
−0.0875376 | + | 0.996161i | \(0.527900\pi\) | |||||||
\(384\) | 90.8347 | 4.63539 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.41233 | −0.428177 | ||||||||
\(387\) | 0.747604 | 0.0380028 | ||||||||
\(388\) | −47.0096 | −2.38655 | ||||||||
\(389\) | 8.05685 | 0.408499 | 0.204249 | − | 0.978919i | \(-0.434525\pi\) | ||||
0.204249 | + | 0.978919i | \(0.434525\pi\) | |||||||
\(390\) | 30.5048 | 1.54467 | ||||||||
\(391\) | 1.49521 | 0.0756159 | ||||||||
\(392\) | 10.0140 | 0.505781 | ||||||||
\(393\) | −11.0462 | −0.557209 | ||||||||
\(394\) | 13.6801 | 0.689195 | ||||||||
\(395\) | −40.0558 | −2.01543 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.3632 | −1.32313 | −0.661565 | − | 0.749888i | \(-0.730107\pi\) | ||||
−0.661565 | + | 0.749888i | \(0.730107\pi\) | |||||||
\(398\) | 43.3694 | 2.17391 | ||||||||
\(399\) | −3.04623 | −0.152502 | ||||||||
\(400\) | 31.1127 | 1.55563 | ||||||||
\(401\) | −22.5972 | −1.12845 | −0.564226 | − | 0.825620i | \(-0.690825\pi\) | ||||
−0.564226 | + | 0.825620i | \(0.690825\pi\) | |||||||
\(402\) | −31.2311 | −1.55767 | ||||||||
\(403\) | 5.34485 | 0.266246 | ||||||||
\(404\) | −77.9021 | −3.87578 | ||||||||
\(405\) | 24.4200 | 1.21344 | ||||||||
\(406\) | 4.77551 | 0.237005 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −42.1204 | −2.08527 | ||||||||
\(409\) | 9.30488 | 0.460097 | 0.230048 | − | 0.973179i | \(-0.426112\pi\) | ||||
0.230048 | + | 0.973179i | \(0.426112\pi\) | |||||||
\(410\) | −75.3361 | −3.72059 | ||||||||
\(411\) | 16.5616 | 0.816926 | ||||||||
\(412\) | −16.4802 | −0.811922 | ||||||||
\(413\) | −1.76156 | −0.0866806 | ||||||||
\(414\) | −0.178261 | −0.00876104 | ||||||||
\(415\) | −33.5510 | −1.64695 | ||||||||
\(416\) | −60.3299 | −2.95791 | ||||||||
\(417\) | 27.8709 | 1.36484 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.8463 | −0.676437 | −0.338218 | − | 0.941068i | \(-0.609824\pi\) | ||||
−0.338218 | + | 0.941068i | \(0.609824\pi\) | |||||||
\(420\) | −26.0279 | −1.27003 | ||||||||
\(421\) | −35.7572 | −1.74270 | −0.871349 | − | 0.490663i | \(-0.836755\pi\) | ||||
−0.871349 | + | 0.490663i | \(0.836755\pi\) | |||||||
\(422\) | 48.4681 | 2.35939 | ||||||||
\(423\) | 0.658473 | 0.0320161 | ||||||||
\(424\) | −92.6531 | −4.49963 | ||||||||
\(425\) | −4.52937 | −0.219707 | ||||||||
\(426\) | 39.3295 | 1.90552 | ||||||||
\(427\) | −10.3878 | −0.502699 | ||||||||
\(428\) | 19.4586 | 0.940565 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −52.5972 | −2.53646 | ||||||||
\(431\) | −31.3082 | −1.50806 | −0.754032 | − | 0.656838i | \(-0.771894\pi\) | ||||
−0.754032 | + | 0.656838i | \(0.771894\pi\) | |||||||
\(432\) | −83.6993 | −4.02698 | ||||||||
\(433\) | 21.6079 | 1.03841 | 0.519204 | − | 0.854650i | \(-0.326228\pi\) | ||||
0.519204 | + | 0.854650i | \(0.326228\pi\) | |||||||
\(434\) | −6.18159 | −0.296726 | ||||||||
\(435\) | −8.00000 | −0.383571 | ||||||||
\(436\) | −91.3361 | −4.37421 | ||||||||
\(437\) | 1.08287 | 0.0518008 | ||||||||
\(438\) | 50.5327 | 2.41455 | ||||||||
\(439\) | 15.5877 | 0.743959 | 0.371979 | − | 0.928241i | \(-0.378679\pi\) | ||||
0.371979 | + | 0.928241i | \(0.378679\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.103084 | 0.00490875 | ||||||||
\(442\) | 15.7447 | 0.748898 | ||||||||
\(443\) | 23.4942 | 1.11624 | 0.558121 | − | 0.829760i | \(-0.311523\pi\) | ||||
0.558121 | + | 0.829760i | \(0.311523\pi\) | |||||||
\(444\) | −68.3544 | −3.24396 | ||||||||
\(445\) | 37.1589 | 1.76150 | ||||||||
\(446\) | −61.5669 | −2.91528 | ||||||||
\(447\) | 6.09246 | 0.288163 | ||||||||
\(448\) | 36.9711 | 1.74672 | ||||||||
\(449\) | 22.7832 | 1.07521 | 0.537603 | − | 0.843198i | \(-0.319330\pi\) | ||||
0.537603 | + | 0.843198i | \(0.319330\pi\) | |||||||
\(450\) | 0.539998 | 0.0254558 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 39.9634 | 1.87972 | ||||||||
\(453\) | −18.1416 | −0.852368 | ||||||||
\(454\) | 39.4094 | 1.84957 | ||||||||
\(455\) | 6.27072 | 0.293976 | ||||||||
\(456\) | −30.5048 | −1.42852 | ||||||||
\(457\) | −14.5048 | −0.678506 | −0.339253 | − | 0.940695i | \(-0.610174\pi\) | ||||
−0.339253 | + | 0.940695i | \(0.610174\pi\) | |||||||
\(458\) | −10.7110 | −0.500490 | ||||||||
\(459\) | 12.1849 | 0.568743 | ||||||||
\(460\) | 9.25240 | 0.431395 | ||||||||
\(461\) | −31.1633 | −1.45142 | −0.725709 | − | 0.688002i | \(-0.758488\pi\) | ||||
−0.725709 | + | 0.688002i | \(0.758488\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.87859 | −0.273201 | −0.136601 | − | 0.990626i | \(-0.543618\pi\) | ||||
−0.136601 | + | 0.990626i | \(0.543618\pi\) | |||||||
\(464\) | 28.3632 | 1.31673 | ||||||||
\(465\) | 10.3555 | 0.480224 | ||||||||
\(466\) | 18.4556 | 0.854941 | ||||||||
\(467\) | −23.7249 | −1.09786 | −0.548929 | − | 0.835869i | \(-0.684964\pi\) | ||||
−0.548929 | + | 0.835869i | \(0.684964\pi\) | |||||||
\(468\) | −1.38482 | −0.0640136 | ||||||||
\(469\) | −6.42003 | −0.296449 | ||||||||
\(470\) | −46.3265 | −2.13688 | ||||||||
\(471\) | 19.9711 | 0.920217 | ||||||||
\(472\) | −17.6402 | −0.811954 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 74.1974 | 3.40800 | ||||||||
\(475\) | −3.28030 | −0.150511 | ||||||||
\(476\) | −13.4340 | −0.615746 | ||||||||
\(477\) | −0.953771 | −0.0436702 | ||||||||
\(478\) | −12.5414 | −0.573632 | ||||||||
\(479\) | 8.41233 | 0.384369 | 0.192185 | − | 0.981359i | \(-0.438443\pi\) | ||||
0.192185 | + | 0.981359i | \(0.438443\pi\) | |||||||
\(480\) | −116.887 | −5.33514 | ||||||||
\(481\) | 16.4681 | 0.750883 | ||||||||
\(482\) | −10.2307 | −0.465998 | ||||||||
\(483\) | −1.10308 | −0.0501920 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.9431 | 0.996387 | ||||||||
\(486\) | −2.95710 | −0.134137 | ||||||||
\(487\) | 24.7957 | 1.12360 | 0.561801 | − | 0.827273i | \(-0.310109\pi\) | ||||
0.561801 | + | 0.827273i | \(0.310109\pi\) | |||||||
\(488\) | −104.022 | −4.70888 | ||||||||
\(489\) | −17.1387 | −0.775038 | ||||||||
\(490\) | −7.25240 | −0.327630 | ||||||||
\(491\) | 12.2062 | 0.550857 | 0.275428 | − | 0.961322i | \(-0.411180\pi\) | ||||
0.275428 | + | 0.961322i | \(0.411180\pi\) | |||||||
\(492\) | 102.952 | 4.64142 | ||||||||
\(493\) | −4.12910 | −0.185965 | ||||||||
\(494\) | 11.4028 | 0.513034 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −36.7143 | −1.64852 | ||||||||
\(497\) | 8.08476 | 0.362651 | ||||||||
\(498\) | 62.1483 | 2.78493 | ||||||||
\(499\) | 22.3265 | 0.999473 | 0.499736 | − | 0.866178i | \(-0.333430\pi\) | ||||
0.499736 | + | 0.866178i | \(0.333430\pi\) | |||||||
\(500\) | 45.8496 | 2.05046 | ||||||||
\(501\) | 39.6435 | 1.77114 | ||||||||
\(502\) | 23.4985 | 1.04879 | ||||||||
\(503\) | −4.54144 | −0.202493 | −0.101246 | − | 0.994861i | \(-0.532283\pi\) | ||||
−0.101246 | + | 0.994861i | \(0.532283\pi\) | |||||||
\(504\) | 1.03228 | 0.0459812 | ||||||||
\(505\) | 36.3632 | 1.61814 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.8569 | −0.570997 | ||||||||
\(508\) | −25.5510 | −1.13364 | ||||||||
\(509\) | 4.12141 | 0.182678 | 0.0913391 | − | 0.995820i | \(-0.470885\pi\) | ||||
0.0913391 | + | 0.995820i | \(0.470885\pi\) | |||||||
\(510\) | 30.5048 | 1.35077 | ||||||||
\(511\) | 10.3878 | 0.459527 | ||||||||
\(512\) | 85.9194 | 3.79714 | ||||||||
\(513\) | 8.82467 | 0.389619 | ||||||||
\(514\) | −8.15701 | −0.359790 | ||||||||
\(515\) | 7.69264 | 0.338978 | ||||||||
\(516\) | 71.8776 | 3.16423 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −19.0462 | −0.836843 | ||||||||
\(519\) | 12.2062 | 0.535791 | ||||||||
\(520\) | 62.7947 | 2.75373 | ||||||||
\(521\) | 39.2880 | 1.72124 | 0.860619 | − | 0.509249i | \(-0.170077\pi\) | ||||
0.860619 | + | 0.509249i | \(0.170077\pi\) | |||||||
\(522\) | 0.492277 | 0.0215464 | ||||||||
\(523\) | −2.14162 | −0.0936464 | −0.0468232 | − | 0.998903i | \(-0.514910\pi\) | ||||
−0.0468232 | + | 0.998903i | \(0.514910\pi\) | |||||||
\(524\) | −35.2803 | −1.54123 | ||||||||
\(525\) | 3.34153 | 0.145836 | ||||||||
\(526\) | −44.1849 | −1.92655 | ||||||||
\(527\) | 5.34485 | 0.232825 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6079 | −0.982951 | ||||||||
\(530\) | 67.1020 | 2.91473 | ||||||||
\(531\) | −0.181588 | −0.00788024 | ||||||||
\(532\) | −9.72928 | −0.421818 | ||||||||
\(533\) | −24.8034 | −1.07436 | ||||||||
\(534\) | −68.8313 | −2.97862 | ||||||||
\(535\) | −9.08287 | −0.392687 | ||||||||
\(536\) | −64.2899 | −2.77690 | ||||||||
\(537\) | 24.5616 | 1.05991 | ||||||||
\(538\) | −18.7110 | −0.806687 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 75.4007 | 3.24473 | ||||||||
\(541\) | −43.0462 | −1.85070 | −0.925351 | − | 0.379112i | \(-0.876230\pi\) | ||||
−0.925351 | + | 0.379112i | \(0.876230\pi\) | |||||||
\(542\) | 9.55102 | 0.410251 | ||||||||
\(543\) | 5.57997 | 0.239459 | ||||||||
\(544\) | −60.3299 | −2.58662 | ||||||||
\(545\) | 42.6339 | 1.82624 | ||||||||
\(546\) | −11.6156 | −0.497101 | ||||||||
\(547\) | −29.0096 | −1.24036 | −0.620180 | − | 0.784459i | \(-0.712940\pi\) | ||||
−0.620180 | + | 0.784459i | \(0.712940\pi\) | |||||||
\(548\) | 52.8959 | 2.25960 | ||||||||
\(549\) | −1.07081 | −0.0457010 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.99042 | −0.127396 | ||||||||
\(552\) | −11.0462 | −0.470159 | ||||||||
\(553\) | 15.2524 | 0.648598 | ||||||||
\(554\) | −31.6435 | −1.34440 | ||||||||
\(555\) | 31.9065 | 1.35436 | ||||||||
\(556\) | 89.0162 | 3.77513 | ||||||||
\(557\) | −1.49521 | −0.0633540 | −0.0316770 | − | 0.999498i | \(-0.510085\pi\) | ||||
−0.0316770 | + | 0.999498i | \(0.510085\pi\) | |||||||
\(558\) | −0.637221 | −0.0269757 | ||||||||
\(559\) | −17.3169 | −0.732429 | ||||||||
\(560\) | −43.0741 | −1.82021 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −61.6560 | −2.60080 | ||||||||
\(563\) | 6.27072 | 0.264279 | 0.132140 | − | 0.991231i | \(-0.457815\pi\) | ||||
0.132140 | + | 0.991231i | \(0.457815\pi\) | |||||||
\(564\) | 63.3082 | 2.66576 | ||||||||
\(565\) | −18.6541 | −0.784784 | ||||||||
\(566\) | −34.1416 | −1.43508 | ||||||||
\(567\) | −9.29862 | −0.390506 | ||||||||
\(568\) | 80.9604 | 3.39702 | ||||||||
\(569\) | 7.82174 | 0.327904 | 0.163952 | − | 0.986468i | \(-0.447576\pi\) | ||||
0.163952 | + | 0.986468i | \(0.447576\pi\) | |||||||
\(570\) | 22.0925 | 0.925351 | ||||||||
\(571\) | −15.1753 | −0.635068 | −0.317534 | − | 0.948247i | \(-0.602855\pi\) | ||||
−0.317534 | + | 0.948247i | \(0.602855\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 32.3342 | 1.35078 | ||||||||
\(574\) | 28.6864 | 1.19735 | ||||||||
\(575\) | −1.18785 | −0.0495366 | ||||||||
\(576\) | 3.81111 | 0.158796 | ||||||||
\(577\) | 23.6445 | 0.984334 | 0.492167 | − | 0.870501i | \(-0.336205\pi\) | ||||
0.492167 | + | 0.870501i | \(0.336205\pi\) | |||||||
\(578\) | −31.2018 | −1.29782 | ||||||||
\(579\) | −5.36611 | −0.223008 | ||||||||
\(580\) | −25.5510 | −1.06095 | ||||||||
\(581\) | 12.7755 | 0.530017 | ||||||||
\(582\) | −40.6464 | −1.68485 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 104.022 | 4.30448 | ||||||||
\(585\) | 0.646409 | 0.0267257 | ||||||||
\(586\) | 5.94751 | 0.245690 | ||||||||
\(587\) | −10.1537 | −0.419087 | −0.209544 | − | 0.977799i | \(-0.567198\pi\) | ||||
−0.209544 | + | 0.977799i | \(0.567198\pi\) | |||||||
\(588\) | 9.91087 | 0.408717 | ||||||||
\(589\) | 3.87090 | 0.159498 | ||||||||
\(590\) | 12.7755 | 0.525959 | ||||||||
\(591\) | 8.72635 | 0.358954 | ||||||||
\(592\) | −113.121 | −4.64925 | ||||||||
\(593\) | 33.7972 | 1.38788 | 0.693942 | − | 0.720031i | \(-0.255873\pi\) | ||||
0.693942 | + | 0.720031i | \(0.255873\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.27072 | 0.257074 | ||||||||
\(596\) | 19.4586 | 0.797054 | ||||||||
\(597\) | 27.6647 | 1.13224 | ||||||||
\(598\) | 4.12910 | 0.168852 | ||||||||
\(599\) | −18.3265 | −0.748802 | −0.374401 | − | 0.927267i | \(-0.622152\pi\) | ||||
−0.374401 | + | 0.927267i | \(0.622152\pi\) | |||||||
\(600\) | 33.4619 | 1.36608 | ||||||||
\(601\) | 48.4802 | 1.97755 | 0.988775 | − | 0.149415i | \(-0.0477391\pi\) | ||||
0.988775 | + | 0.149415i | \(0.0477391\pi\) | |||||||
\(602\) | 20.0279 | 0.816277 | ||||||||
\(603\) | −0.661801 | −0.0269506 | ||||||||
\(604\) | −57.9421 | −2.35763 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −67.3574 | −2.73621 | ||||||||
\(607\) | −20.5972 | −0.836017 | −0.418008 | − | 0.908443i | \(-0.637272\pi\) | ||||
−0.418008 | + | 0.908443i | \(0.637272\pi\) | |||||||
\(608\) | −43.6926 | −1.77197 | ||||||||
\(609\) | 3.04623 | 0.123439 | ||||||||
\(610\) | 75.3361 | 3.05027 | ||||||||
\(611\) | −15.2524 | −0.617046 | ||||||||
\(612\) | −1.38482 | −0.0559782 | ||||||||
\(613\) | 18.8122 | 0.759816 | 0.379908 | − | 0.925024i | \(-0.375956\pi\) | ||||
0.379908 | + | 0.925024i | \(0.375956\pi\) | |||||||
\(614\) | −87.8776 | −3.54645 | ||||||||
\(615\) | −48.0558 | −1.93780 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.2062 | −0.571919 | −0.285959 | − | 0.958242i | \(-0.592312\pi\) | ||||
−0.285959 | + | 0.958242i | \(0.592312\pi\) | |||||||
\(618\) | −14.2495 | −0.573198 | ||||||||
\(619\) | −16.0235 | −0.644040 | −0.322020 | − | 0.946733i | \(-0.604362\pi\) | ||||
−0.322020 | + | 0.946733i | \(0.604362\pi\) | |||||||
\(620\) | 33.0741 | 1.32829 | ||||||||
\(621\) | 3.19554 | 0.128233 | ||||||||
\(622\) | −30.1816 | −1.21017 | ||||||||
\(623\) | −14.1493 | −0.566880 | ||||||||
\(624\) | −68.9883 | −2.76174 | ||||||||
\(625\) | −30.8863 | −1.23545 | ||||||||
\(626\) | 20.4402 | 0.816956 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 63.7851 | 2.54530 | ||||||||
\(629\) | 16.4681 | 0.656628 | ||||||||
\(630\) | −0.747604 | −0.0297853 | ||||||||
\(631\) | 15.1955 | 0.604925 | 0.302462 | − | 0.953161i | \(-0.402191\pi\) | ||||
0.302462 | + | 0.953161i | \(0.402191\pi\) | |||||||
\(632\) | 152.737 | 6.07554 | ||||||||
\(633\) | 30.9171 | 1.22885 | ||||||||
\(634\) | −24.5693 | −0.975773 | ||||||||
\(635\) | 11.9267 | 0.473297 | ||||||||
\(636\) | −91.6993 | −3.63611 | ||||||||
\(637\) | −2.38776 | −0.0946063 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.833407 | 0.0329691 | ||||||||
\(640\) | −135.420 | −5.35294 | ||||||||
\(641\) | −10.2264 | −0.403918 | −0.201959 | − | 0.979394i | \(-0.564731\pi\) | ||||
−0.201959 | + | 0.979394i | \(0.564731\pi\) | |||||||
\(642\) | 16.8247 | 0.664017 | ||||||||
\(643\) | 20.5650 | 0.811003 | 0.405502 | − | 0.914094i | \(-0.367097\pi\) | ||||
0.405502 | + | 0.914094i | \(0.367097\pi\) | |||||||
\(644\) | −3.52311 | −0.138830 | ||||||||
\(645\) | −33.5510 | −1.32107 | ||||||||
\(646\) | 11.4028 | 0.448635 | ||||||||
\(647\) | −25.4542 | −1.00071 | −0.500354 | − | 0.865821i | \(-0.666797\pi\) | ||||
−0.500354 | + | 0.865821i | \(0.666797\pi\) | |||||||
\(648\) | −93.1160 | −3.65794 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −12.5081 | −0.490609 | ||||||||
\(651\) | −3.94315 | −0.154544 | ||||||||
\(652\) | −54.7389 | −2.14374 | ||||||||
\(653\) | −45.2514 | −1.77082 | −0.885411 | − | 0.464809i | \(-0.846123\pi\) | ||||
−0.885411 | + | 0.464809i | \(0.846123\pi\) | |||||||
\(654\) | −78.9729 | −3.08809 | ||||||||
\(655\) | 16.4681 | 0.643464 | ||||||||
\(656\) | 170.377 | 6.65210 | ||||||||
\(657\) | 1.07081 | 0.0417762 | ||||||||
\(658\) | 17.6402 | 0.687685 | ||||||||
\(659\) | −50.3544 | −1.96153 | −0.980765 | − | 0.195191i | \(-0.937467\pi\) | ||||
−0.980765 | + | 0.195191i | \(0.937467\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.2234 | −0.903287 | −0.451644 | − | 0.892198i | \(-0.649162\pi\) | ||||
−0.451644 | + | 0.892198i | \(0.649162\pi\) | |||||||
\(662\) | 23.6435 | 0.918930 | ||||||||
\(663\) | 10.0433 | 0.390049 | ||||||||
\(664\) | 127.933 | 4.96478 | ||||||||
\(665\) | 4.54144 | 0.176109 | ||||||||
\(666\) | −1.96336 | −0.0760785 | ||||||||
\(667\) | −1.08287 | −0.0419290 | ||||||||
\(668\) | 126.616 | 4.89894 | ||||||||
\(669\) | −39.2726 | −1.51837 | ||||||||
\(670\) | 46.5606 | 1.79879 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 44.5081 | 1.71694 | ||||||||
\(673\) | −3.22449 | −0.124295 | −0.0621475 | − | 0.998067i | \(-0.519795\pi\) | ||||
−0.0621475 | + | 0.998067i | \(0.519795\pi\) | |||||||
\(674\) | −26.8680 | −1.03492 | ||||||||
\(675\) | −9.68012 | −0.372588 | ||||||||
\(676\) | −41.0635 | −1.57937 | ||||||||
\(677\) | 42.6218 | 1.63809 | 0.819045 | − | 0.573729i | \(-0.194504\pi\) | ||||
0.819045 | + | 0.573729i | \(0.194504\pi\) | |||||||
\(678\) | 34.5540 | 1.32704 | ||||||||
\(679\) | −8.35548 | −0.320654 | ||||||||
\(680\) | 62.7947 | 2.40807 | ||||||||
\(681\) | 25.1387 | 0.963317 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.5877 | 0.596445 | 0.298223 | − | 0.954496i | \(-0.403606\pi\) | ||||
0.298223 | + | 0.954496i | \(0.403606\pi\) | |||||||
\(684\) | −1.00293 | −0.0383480 | ||||||||
\(685\) | −24.6907 | −0.943385 | ||||||||
\(686\) | 2.76156 | 0.105437 | ||||||||
\(687\) | −6.83237 | −0.260671 | ||||||||
\(688\) | 118.952 | 4.53499 | ||||||||
\(689\) | 22.0925 | 0.841656 | ||||||||
\(690\) | 8.00000 | 0.304555 | ||||||||
\(691\) | 41.9311 | 1.59513 | 0.797567 | − | 0.603231i | \(-0.206120\pi\) | ||||
0.797567 | + | 0.603231i | \(0.206120\pi\) | |||||||
\(692\) | 38.9850 | 1.48199 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 40.9817 | 1.55564 | ||||||||
\(695\) | −41.5510 | −1.57612 | ||||||||
\(696\) | 30.5048 | 1.15628 | ||||||||
\(697\) | −24.8034 | −0.939496 | ||||||||
\(698\) | 44.8646 | 1.69815 | ||||||||
\(699\) | 11.7726 | 0.445280 | ||||||||
\(700\) | 10.6724 | 0.403380 | ||||||||
\(701\) | −15.4094 | −0.582005 | −0.291003 | − | 0.956722i | \(-0.593989\pi\) | ||||
−0.291003 | + | 0.956722i | \(0.593989\pi\) | |||||||
\(702\) | 33.6493 | 1.27001 | ||||||||
\(703\) | 11.9267 | 0.449824 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −29.5510 | −1.11296 | ||||||||
\(706\) | 85.2224 | 3.20739 | ||||||||
\(707\) | −13.8463 | −0.520744 | ||||||||
\(708\) | −17.4586 | −0.656133 | ||||||||
\(709\) | 2.86027 | 0.107420 | 0.0537099 | − | 0.998557i | \(-0.482895\pi\) | ||||
0.0537099 | + | 0.998557i | \(0.482895\pi\) | |||||||
\(710\) | −58.6339 | −2.20049 | ||||||||
\(711\) | 1.57227 | 0.0589649 | ||||||||
\(712\) | −141.691 | −5.31008 | ||||||||
\(713\) | 1.40171 | 0.0524944 | ||||||||
\(714\) | −11.6156 | −0.434702 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 78.4469 | 2.93170 | ||||||||
\(717\) | −8.00000 | −0.298765 | ||||||||
\(718\) | −32.5693 | −1.21548 | ||||||||
\(719\) | −34.4725 | −1.28561 | −0.642804 | − | 0.766031i | \(-0.722229\pi\) | ||||
−0.642804 | + | 0.766031i | \(0.722229\pi\) | |||||||
\(720\) | −4.44024 | −0.165478 | ||||||||
\(721\) | −2.92919 | −0.109089 | ||||||||
\(722\) | −44.2114 | −1.64538 | ||||||||
\(723\) | −6.52604 | −0.242706 | ||||||||
\(724\) | 17.8217 | 0.662340 | ||||||||
\(725\) | 3.28030 | 0.121827 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.3309 | −1.49579 | −0.747895 | − | 0.663817i | \(-0.768935\pi\) | ||||
−0.747895 | + | 0.663817i | \(0.768935\pi\) | |||||||
\(728\) | −23.9109 | −0.886196 | ||||||||
\(729\) | 26.0096 | 0.963318 | ||||||||
\(730\) | −75.3361 | −2.78831 | ||||||||
\(731\) | −17.3169 | −0.640490 | ||||||||
\(732\) | −102.952 | −3.80520 | ||||||||
\(733\) | −28.7634 | −1.06240 | −0.531201 | − | 0.847246i | \(-0.678259\pi\) | ||||
−0.531201 | + | 0.847246i | \(0.678259\pi\) | |||||||
\(734\) | −9.81841 | −0.362404 | ||||||||
\(735\) | −4.62620 | −0.170640 | ||||||||
\(736\) | −15.8217 | −0.583197 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 2.95710 | 0.108852 | ||||||||
\(739\) | 35.1020 | 1.29125 | 0.645625 | − | 0.763655i | \(-0.276597\pi\) | ||||
0.645625 | + | 0.763655i | \(0.276597\pi\) | |||||||
\(740\) | 101.905 | 3.74612 | ||||||||
\(741\) | 7.27365 | 0.267204 | ||||||||
\(742\) | −25.5510 | −0.938007 | ||||||||
\(743\) | −32.4681 | −1.19114 | −0.595570 | − | 0.803303i | \(-0.703074\pi\) | ||||
−0.595570 | + | 0.803303i | \(0.703074\pi\) | |||||||
\(744\) | −39.4865 | −1.44764 | ||||||||
\(745\) | −9.08287 | −0.332771 | ||||||||
\(746\) | 62.1483 | 2.27541 | ||||||||
\(747\) | 1.31695 | 0.0481846 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.45856 | 0.126373 | ||||||||
\(750\) | 39.6435 | 1.44758 | ||||||||
\(751\) | −28.3834 | −1.03572 | −0.517862 | − | 0.855464i | \(-0.673272\pi\) | ||||
−0.517862 | + | 0.855464i | \(0.673272\pi\) | |||||||
\(752\) | 104.770 | 3.82057 | ||||||||
\(753\) | 14.9894 | 0.546243 | ||||||||
\(754\) | −11.4028 | −0.415264 | ||||||||
\(755\) | 27.0462 | 0.984313 | ||||||||
\(756\) | −28.7110 | −1.04421 | ||||||||
\(757\) | −17.0462 | −0.619556 | −0.309778 | − | 0.950809i | \(-0.600255\pi\) | ||||
−0.309778 | + | 0.950809i | \(0.600255\pi\) | |||||||
\(758\) | 64.7022 | 2.35009 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 45.4777 | 1.64965 | ||||||||
\(761\) | 27.9388 | 1.01278 | 0.506390 | − | 0.862305i | \(-0.330980\pi\) | ||||
0.506390 | + | 0.862305i | \(0.330980\pi\) | |||||||
\(762\) | −22.0925 | −0.800325 | ||||||||
\(763\) | −16.2341 | −0.587713 | ||||||||
\(764\) | 103.272 | 3.73623 | ||||||||
\(765\) | 0.646409 | 0.0233710 | ||||||||
\(766\) | −9.46189 | −0.341872 | ||||||||
\(767\) | 4.20617 | 0.151876 | ||||||||
\(768\) | 120.592 | 4.35148 | ||||||||
\(769\) | 6.69512 | 0.241432 | 0.120716 | − | 0.992687i | \(-0.461481\pi\) | ||||
0.120716 | + | 0.992687i | \(0.461481\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.20324 | −0.187390 | ||||||||
\(772\) | −17.1387 | −0.616835 | ||||||||
\(773\) | 27.9142 | 1.00400 | 0.502002 | − | 0.864866i | \(-0.332597\pi\) | ||||
0.502002 | + | 0.864866i | \(0.332597\pi\) | |||||||
\(774\) | 2.06455 | 0.0742087 | ||||||||
\(775\) | −4.24614 | −0.152526 | ||||||||
\(776\) | −83.6714 | −3.00363 | ||||||||
\(777\) | −12.1493 | −0.435854 | ||||||||
\(778\) | 22.2495 | 0.797682 | ||||||||
\(779\) | −17.9634 | −0.643604 | ||||||||
\(780\) | 62.1483 | 2.22527 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 4.12910 | 0.147656 | ||||||||
\(783\) | −8.82467 | −0.315368 | ||||||||
\(784\) | 16.4017 | 0.585775 | ||||||||
\(785\) | −29.7736 | −1.06267 | ||||||||
\(786\) | −30.5048 | −1.08807 | ||||||||
\(787\) | 21.8584 | 0.779167 | 0.389584 | − | 0.920991i | \(-0.372619\pi\) | ||||
0.389584 | + | 0.920991i | \(0.372619\pi\) | |||||||
\(788\) | 27.8709 | 0.992860 | ||||||||
\(789\) | −28.1849 | −1.00341 | ||||||||
\(790\) | −110.616 | −3.93556 | ||||||||
\(791\) | 7.10308 | 0.252557 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.8034 | 0.880795 | ||||||||
\(794\) | −72.8034 | −2.58370 | ||||||||
\(795\) | 42.8034 | 1.51808 | ||||||||
\(796\) | 88.3578 | 3.13176 | ||||||||
\(797\) | −34.6262 | −1.22652 | −0.613261 | − | 0.789880i | \(-0.710143\pi\) | ||||
−0.613261 | + | 0.789880i | \(0.710143\pi\) | |||||||
\(798\) | −8.41233 | −0.297793 | ||||||||
\(799\) | −15.2524 | −0.539591 | ||||||||
\(800\) | 47.9282 | 1.69452 | ||||||||
\(801\) | −1.45856 | −0.0515358 | ||||||||
\(802\) | −62.4036 | −2.20355 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −63.6281 | −2.24399 | ||||||||
\(805\) | 1.64452 | 0.0579617 | ||||||||
\(806\) | 14.7601 | 0.519903 | ||||||||
\(807\) | −11.9354 | −0.420148 | ||||||||
\(808\) | −138.656 | −4.87791 | ||||||||
\(809\) | 35.0462 | 1.23216 | 0.616080 | − | 0.787684i | \(-0.288720\pi\) | ||||
0.616080 | + | 0.787684i | \(0.288720\pi\) | |||||||
\(810\) | 67.4373 | 2.36951 | ||||||||
\(811\) | −18.1416 | −0.637038 | −0.318519 | − | 0.947916i | \(-0.603186\pi\) | ||||
−0.318519 | + | 0.947916i | \(0.603186\pi\) | |||||||
\(812\) | 9.72928 | 0.341431 | ||||||||
\(813\) | 6.09246 | 0.213672 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 25.5510 | 0.895013 | ||||||||
\(816\) | −68.9883 | −2.41507 | ||||||||
\(817\) | −12.5414 | −0.438769 | ||||||||
\(818\) | 25.6960 | 0.898438 | ||||||||
\(819\) | −0.246139 | −0.00860078 | ||||||||
\(820\) | −153.484 | −5.35991 | ||||||||
\(821\) | −3.45856 | −0.120705 | −0.0603524 | − | 0.998177i | \(-0.519222\pi\) | ||||
−0.0603524 | + | 0.998177i | \(0.519222\pi\) | |||||||
\(822\) | 45.7359 | 1.59522 | ||||||||
\(823\) | −33.5308 | −1.16881 | −0.584405 | − | 0.811462i | \(-0.698672\pi\) | ||||
−0.584405 | + | 0.811462i | \(0.698672\pi\) | |||||||
\(824\) | −29.3328 | −1.02186 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.86464 | −0.169263 | ||||||||
\(827\) | −26.2986 | −0.914493 | −0.457246 | − | 0.889340i | \(-0.651164\pi\) | ||||
−0.457246 | + | 0.889340i | \(0.651164\pi\) | |||||||
\(828\) | −0.363176 | −0.0126212 | ||||||||
\(829\) | −29.0019 | −1.00728 | −0.503639 | − | 0.863914i | \(-0.668006\pi\) | ||||
−0.503639 | + | 0.863914i | \(0.668006\pi\) | |||||||
\(830\) | −92.6531 | −3.21603 | ||||||||
\(831\) | −20.1849 | −0.700207 | ||||||||
\(832\) | −88.2778 | −3.06048 | ||||||||
\(833\) | −2.38776 | −0.0827308 | ||||||||
\(834\) | 76.9671 | 2.66515 | ||||||||
\(835\) | −59.1020 | −2.04531 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.4230 | 0.394835 | ||||||||
\(838\) | −38.2374 | −1.32089 | ||||||||
\(839\) | 29.1710 | 1.00709 | 0.503547 | − | 0.863968i | \(-0.332028\pi\) | ||||
0.503547 | + | 0.863968i | \(0.332028\pi\) | |||||||
\(840\) | −46.3265 | −1.59842 | ||||||||
\(841\) | −26.0096 | −0.896882 | ||||||||
\(842\) | −98.7455 | −3.40300 | ||||||||
\(843\) | −39.3295 | −1.35458 | ||||||||
\(844\) | 98.7455 | 3.39896 | ||||||||
\(845\) | 19.1676 | 0.659387 | ||||||||
\(846\) | 1.81841 | 0.0625183 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −151.755 | −5.21129 | ||||||||
\(849\) | −21.7784 | −0.747434 | ||||||||
\(850\) | −12.5081 | −0.429025 | ||||||||
\(851\) | 4.31884 | 0.148048 | ||||||||
\(852\) | 80.1270 | 2.74511 | ||||||||
\(853\) | 10.6218 | 0.363685 | 0.181842 | − | 0.983328i | \(-0.441794\pi\) | ||||
0.181842 | + | 0.983328i | \(0.441794\pi\) | |||||||
\(854\) | −28.6864 | −0.981628 | ||||||||
\(855\) | 0.468148 | 0.0160103 | ||||||||
\(856\) | 34.6339 | 1.18376 | ||||||||
\(857\) | 37.8463 | 1.29281 | 0.646403 | − | 0.762996i | \(-0.276273\pi\) | ||||
0.646403 | + | 0.762996i | \(0.276273\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.0785 | −0.650950 | −0.325475 | − | 0.945551i | \(-0.605524\pi\) | ||||
−0.325475 | + | 0.945551i | \(0.605524\pi\) | |||||||
\(860\) | −107.158 | −3.65405 | ||||||||
\(861\) | 18.2986 | 0.623615 | ||||||||
\(862\) | −86.4594 | −2.94482 | ||||||||
\(863\) | 11.1753 | 0.380413 | 0.190206 | − | 0.981744i | \(-0.439084\pi\) | ||||
0.190206 | + | 0.981744i | \(0.439084\pi\) | |||||||
\(864\) | −128.936 | −4.38650 | ||||||||
\(865\) | −18.1974 | −0.618731 | ||||||||
\(866\) | 59.6714 | 2.02772 | ||||||||
\(867\) | −19.9032 | −0.675947 | ||||||||
\(868\) | −12.5939 | −0.427466 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −22.0925 | −0.749004 | ||||||||
\(871\) | 15.3295 | 0.519419 | ||||||||
\(872\) | −162.567 | −5.50522 | ||||||||
\(873\) | −0.861314 | −0.0291511 | ||||||||
\(874\) | 2.99042 | 0.101152 | ||||||||
\(875\) | 8.14931 | 0.275497 | ||||||||
\(876\) | 102.952 | 3.47842 | ||||||||
\(877\) | −5.85838 | −0.197824 | −0.0989118 | − | 0.995096i | \(-0.531536\pi\) | ||||
−0.0989118 | + | 0.995096i | \(0.531536\pi\) | |||||||
\(878\) | 43.0462 | 1.45274 | ||||||||
\(879\) | 3.79383 | 0.127963 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.9065 | −0.872812 | −0.436406 | − | 0.899750i | \(-0.643749\pi\) | ||||
−0.436406 | + | 0.899750i | \(0.643749\pi\) | |||||||
\(882\) | 0.284672 | 0.00958539 | ||||||||
\(883\) | 13.4219 | 0.451684 | 0.225842 | − | 0.974164i | \(-0.427487\pi\) | ||||
0.225842 | + | 0.974164i | \(0.427487\pi\) | |||||||
\(884\) | 32.0771 | 1.07887 | ||||||||
\(885\) | 8.14931 | 0.273936 | ||||||||
\(886\) | 64.8805 | 2.17970 | ||||||||
\(887\) | −49.6068 | −1.66563 | −0.832817 | − | 0.553548i | \(-0.813274\pi\) | ||||
−0.832817 | + | 0.553548i | \(0.813274\pi\) | |||||||
\(888\) | −121.663 | −4.08273 | ||||||||
\(889\) | −4.54144 | −0.152315 | ||||||||
\(890\) | 102.616 | 3.43971 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −125.432 | −4.19977 | ||||||||
\(893\) | −11.0462 | −0.369648 | ||||||||
\(894\) | 16.8247 | 0.562701 | ||||||||
\(895\) | −36.6175 | −1.22399 | ||||||||
\(896\) | 51.5650 | 1.72266 | ||||||||
\(897\) | 2.63389 | 0.0879432 | ||||||||
\(898\) | 62.9171 | 2.09957 | ||||||||
\(899\) | −3.87090 | −0.129102 | ||||||||
\(900\) | 1.10015 | 0.0366718 | ||||||||
\(901\) | 22.0925 | 0.736006 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.7755 | 0.425142 | ||||||||
\(904\) | 71.1299 | 2.36575 | ||||||||
\(905\) | −8.31884 | −0.276527 | ||||||||
\(906\) | −50.0991 | −1.66443 | ||||||||
\(907\) | −47.8776 | −1.58975 | −0.794874 | − | 0.606775i | \(-0.792463\pi\) | ||||
−0.794874 | + | 0.606775i | \(0.792463\pi\) | |||||||
\(908\) | 80.2899 | 2.66451 | ||||||||
\(909\) | −1.42733 | −0.0473415 | ||||||||
\(910\) | 17.3169 | 0.574051 | ||||||||
\(911\) | 22.8122 | 0.755800 | 0.377900 | − | 0.925846i | \(-0.376646\pi\) | ||||
0.377900 | + | 0.925846i | \(0.376646\pi\) | |||||||
\(912\) | −49.9634 | −1.65445 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −40.0558 | −1.32493 | ||||||||
\(915\) | 48.0558 | 1.58868 | ||||||||
\(916\) | −21.8217 | −0.721011 | ||||||||
\(917\) | −6.27072 | −0.207077 | ||||||||
\(918\) | 33.6493 | 1.11059 | ||||||||
\(919\) | −40.0000 | −1.31948 | −0.659739 | − | 0.751495i | \(-0.729333\pi\) | ||||
−0.659739 | + | 0.751495i | \(0.729333\pi\) | |||||||
\(920\) | 16.4681 | 0.542939 | ||||||||
\(921\) | −56.0558 | −1.84710 | ||||||||
\(922\) | −86.0591 | −2.83421 | ||||||||
\(923\) | −19.3044 | −0.635413 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.0829 | −0.430162 | ||||||||
\(926\) | −16.2341 | −0.533485 | ||||||||
\(927\) | −0.301952 | −0.00991740 | ||||||||
\(928\) | 43.6926 | 1.43428 | ||||||||
\(929\) | −16.0366 | −0.526145 | −0.263073 | − | 0.964776i | \(-0.584736\pi\) | ||||
−0.263073 | + | 0.964776i | \(0.584736\pi\) | |||||||
\(930\) | 28.5972 | 0.937741 | ||||||||
\(931\) | −1.72928 | −0.0566749 | ||||||||
\(932\) | 37.6002 | 1.23163 | ||||||||
\(933\) | −19.2524 | −0.630295 | ||||||||
\(934\) | −65.5177 | −2.14380 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.46482 | −0.0805652 | ||||||||
\(937\) | −25.3049 | −0.826674 | −0.413337 | − | 0.910578i | \(-0.635637\pi\) | ||||
−0.413337 | + | 0.910578i | \(0.635637\pi\) | |||||||
\(938\) | −17.7293 | −0.578882 | ||||||||
\(939\) | 13.0385 | 0.425496 | ||||||||
\(940\) | −94.3823 | −3.07841 | ||||||||
\(941\) | 20.5294 | 0.669238 | 0.334619 | − | 0.942353i | \(-0.391392\pi\) | ||||
0.334619 | + | 0.942353i | \(0.391392\pi\) | |||||||
\(942\) | 55.1512 | 1.79692 | ||||||||
\(943\) | −6.50479 | −0.211825 | ||||||||
\(944\) | −28.8925 | −0.940372 | ||||||||
\(945\) | 13.4017 | 0.435958 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.6907 | −0.542376 | −0.271188 | − | 0.962526i | \(-0.587417\pi\) | ||||
−0.271188 | + | 0.962526i | \(0.587417\pi\) | |||||||
\(948\) | 151.165 | 4.90960 | ||||||||
\(949\) | −24.8034 | −0.805153 | ||||||||
\(950\) | −9.05874 | −0.293904 | ||||||||
\(951\) | −15.6724 | −0.508213 | ||||||||
\(952\) | −23.9109 | −0.774956 | ||||||||
\(953\) | 56.4681 | 1.82918 | 0.914591 | − | 0.404379i | \(-0.132512\pi\) | ||||
0.914591 | + | 0.404379i | \(0.132512\pi\) | |||||||
\(954\) | −2.63389 | −0.0852755 | ||||||||
\(955\) | −48.2051 | −1.55988 | ||||||||
\(956\) | −25.5510 | −0.826379 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 23.2311 | 0.750564 | ||||||||
\(959\) | 9.40171 | 0.303597 | ||||||||
\(960\) | −171.035 | −5.52014 | ||||||||
\(961\) | −25.9894 | −0.838367 | ||||||||
\(962\) | 45.4777 | 1.46626 | ||||||||
\(963\) | 0.356522 | 0.0114887 | ||||||||
\(964\) | −20.8434 | −0.671320 | ||||||||
\(965\) | 8.00000 | 0.257529 | ||||||||
\(966\) | −3.04623 | −0.0980108 | ||||||||
\(967\) | 47.3082 | 1.52133 | 0.760665 | − | 0.649145i | \(-0.224873\pi\) | ||||
0.760665 | + | 0.649145i | \(0.224873\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.27365 | 0.233663 | ||||||||
\(970\) | 60.5972 | 1.94566 | ||||||||
\(971\) | −25.2355 | −0.809846 | −0.404923 | − | 0.914351i | \(-0.632702\pi\) | ||||
−0.404923 | + | 0.914351i | \(0.632702\pi\) | |||||||
\(972\) | −6.02458 | −0.193238 | ||||||||
\(973\) | 15.8217 | 0.507222 | ||||||||
\(974\) | 68.4748 | 2.19407 | ||||||||
\(975\) | −7.97875 | −0.255524 | ||||||||
\(976\) | −170.377 | −5.45363 | ||||||||
\(977\) | 7.10308 | 0.227248 | 0.113624 | − | 0.993524i | \(-0.463754\pi\) | ||||
0.113624 | + | 0.993524i | \(0.463754\pi\) | |||||||
\(978\) | −47.3295 | −1.51343 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −14.7755 | −0.471986 | ||||||||
\(981\) | −1.67347 | −0.0534297 | ||||||||
\(982\) | 33.7080 | 1.07567 | ||||||||
\(983\) | −14.1893 | −0.452568 | −0.226284 | − | 0.974061i | \(-0.572658\pi\) | ||||
−0.226284 | + | 0.974061i | \(0.572658\pi\) | |||||||
\(984\) | 183.242 | 5.84153 | ||||||||
\(985\) | −13.0096 | −0.414520 | ||||||||
\(986\) | −11.4028 | −0.363138 | ||||||||
\(987\) | 11.2524 | 0.358168 | ||||||||
\(988\) | 23.2311 | 0.739081 | ||||||||
\(989\) | −4.54144 | −0.144409 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.23407 | 0.134500 | 0.0672499 | − | 0.997736i | \(-0.478578\pi\) | ||||
0.0672499 | + | 0.997736i | \(0.478578\pi\) | |||||||
\(992\) | −56.5573 | −1.79570 | ||||||||
\(993\) | 15.0818 | 0.478607 | ||||||||
\(994\) | 22.3265 | 0.708155 | ||||||||
\(995\) | −41.2437 | −1.30751 | ||||||||
\(996\) | 126.616 | 4.01199 | ||||||||
\(997\) | −27.7047 | −0.877417 | −0.438708 | − | 0.898629i | \(-0.644564\pi\) | ||||
−0.438708 | + | 0.898629i | \(0.644564\pi\) | |||||||
\(998\) | 61.6560 | 1.95169 | ||||||||
\(999\) | 35.1955 | 1.11354 |
(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 | 847.2.a.j.1.3 | yes | 3 | |
3.2 | odd | 2 | 7623.2.a.bz.1.1 | 3 | |||
7.6 | odd | 2 | 5929.2.a.y.1.3 | 3 | |||
11.2 | odd | 10 | 847.2.f.u.323.3 | 12 | |||
11.3 | even | 5 | 847.2.f.t.372.3 | 12 | |||
11.4 | even | 5 | 847.2.f.t.148.3 | 12 | |||
11.5 | even | 5 | 847.2.f.t.729.1 | 12 | |||
11.6 | odd | 10 | 847.2.f.u.729.3 | 12 | |||
11.7 | odd | 10 | 847.2.f.u.148.1 | 12 | |||
11.8 | odd | 10 | 847.2.f.u.372.1 | 12 | |||
11.9 | even | 5 | 847.2.f.t.323.1 | 12 | |||
11.10 | odd | 2 | 847.2.a.i.1.1 | ✓ | 3 | ||
33.32 | even | 2 | 7623.2.a.ce.1.3 | 3 | |||
77.76 | even | 2 | 5929.2.a.t.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.i.1.1 | ✓ | 3 | 11.10 | odd | 2 | ||
847.2.a.j.1.3 | yes | 3 | 1.1 | even | 1 | trivial | |
847.2.f.t.148.3 | 12 | 11.4 | even | 5 | |||
847.2.f.t.323.1 | 12 | 11.9 | even | 5 | |||
847.2.f.t.372.3 | 12 | 11.3 | even | 5 | |||
847.2.f.t.729.1 | 12 | 11.5 | even | 5 | |||
847.2.f.u.148.1 | 12 | 11.7 | odd | 10 | |||
847.2.f.u.323.3 | 12 | 11.2 | odd | 10 | |||
847.2.f.u.372.1 | 12 | 11.8 | odd | 10 | |||
847.2.f.u.729.3 | 12 | 11.6 | odd | 10 | |||
5929.2.a.t.1.1 | 3 | 77.76 | even | 2 | |||
5929.2.a.y.1.3 | 3 | 7.6 | odd | 2 | |||
7623.2.a.bz.1.1 | 3 | 3.2 | odd | 2 | |||
7623.2.a.ce.1.3 | 3 | 33.32 | even | 2 |