Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, 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("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.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: | \(48.1178522580\) |
Analytic rank: | \(1\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 5 x^{19} - 17 x^{18} + 115 x^{17} + 78 x^{16} - 1083 x^{15} + 248 x^{14} + 5359 x^{13} - 3723 x^{12} - 14776 x^{11} + 14837 x^{10} + 21886 x^{9} - 28084 x^{8} - 14682 x^{7} + \cdots - 18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(1.51806\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.51806 | −0.876452 | −0.438226 | − | 0.898865i | \(-0.644393\pi\) | ||||
−0.438226 | + | 0.898865i | \(0.644393\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.34509 | −1.49597 | −0.747985 | − | 0.663716i | \(-0.768979\pi\) | ||||
−0.747985 | + | 0.663716i | \(0.768979\pi\) | |||||||
\(6\) | −1.51806 | −0.619745 | ||||||||
\(7\) | 1.42565 | 0.538846 | 0.269423 | − | 0.963022i | \(-0.413167\pi\) | ||||
0.269423 | + | 0.963022i | \(0.413167\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.695496 | −0.231832 | ||||||||
\(10\) | −3.34509 | −1.05781 | ||||||||
\(11\) | −0.242144 | −0.0730092 | −0.0365046 | − | 0.999333i | \(-0.511622\pi\) | ||||
−0.0365046 | + | 0.999333i | \(0.511622\pi\) | |||||||
\(12\) | −1.51806 | −0.438226 | ||||||||
\(13\) | −0.284609 | −0.0789362 | −0.0394681 | − | 0.999221i | \(-0.512566\pi\) | ||||
−0.0394681 | + | 0.999221i | \(0.512566\pi\) | |||||||
\(14\) | 1.42565 | 0.381021 | ||||||||
\(15\) | 5.07805 | 1.31115 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.0256674 | −0.00622525 | −0.00311263 | − | 0.999995i | \(-0.500991\pi\) | ||||
−0.00311263 | + | 0.999995i | \(0.500991\pi\) | |||||||
\(18\) | −0.695496 | −0.163930 | ||||||||
\(19\) | −1.01981 | −0.233961 | −0.116981 | − | 0.993134i | \(-0.537322\pi\) | ||||
−0.116981 | + | 0.993134i | \(0.537322\pi\) | |||||||
\(20\) | −3.34509 | −0.747985 | ||||||||
\(21\) | −2.16422 | −0.472272 | ||||||||
\(22\) | −0.242144 | −0.0516253 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −1.51806 | −0.309873 | ||||||||
\(25\) | 6.18963 | 1.23793 | ||||||||
\(26\) | −0.284609 | −0.0558163 | ||||||||
\(27\) | 5.60998 | 1.07964 | ||||||||
\(28\) | 1.42565 | 0.269423 | ||||||||
\(29\) | 5.53979 | 1.02871 | 0.514357 | − | 0.857576i | \(-0.328031\pi\) | ||||
0.514357 | + | 0.857576i | \(0.328031\pi\) | |||||||
\(30\) | 5.07805 | 0.927120 | ||||||||
\(31\) | 4.70532 | 0.845101 | 0.422551 | − | 0.906339i | \(-0.361135\pi\) | ||||
0.422551 | + | 0.906339i | \(0.361135\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.367589 | 0.0639890 | ||||||||
\(34\) | −0.0256674 | −0.00440192 | ||||||||
\(35\) | −4.76893 | −0.806097 | ||||||||
\(36\) | −0.695496 | −0.115916 | ||||||||
\(37\) | −9.28988 | −1.52725 | −0.763624 | − | 0.645662i | \(-0.776582\pi\) | ||||
−0.763624 | + | 0.645662i | \(0.776582\pi\) | |||||||
\(38\) | −1.01981 | −0.165436 | ||||||||
\(39\) | 0.432053 | 0.0691838 | ||||||||
\(40\) | −3.34509 | −0.528905 | ||||||||
\(41\) | 2.00968 | 0.313859 | 0.156929 | − | 0.987610i | \(-0.449841\pi\) | ||||
0.156929 | + | 0.987610i | \(0.449841\pi\) | |||||||
\(42\) | −2.16422 | −0.333947 | ||||||||
\(43\) | −1.53875 | −0.234657 | −0.117328 | − | 0.993093i | \(-0.537433\pi\) | ||||
−0.117328 | + | 0.993093i | \(0.537433\pi\) | |||||||
\(44\) | −0.242144 | −0.0365046 | ||||||||
\(45\) | 2.32650 | 0.346814 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 4.25361 | 0.620453 | 0.310226 | − | 0.950663i | \(-0.399595\pi\) | ||||
0.310226 | + | 0.950663i | \(0.399595\pi\) | |||||||
\(48\) | −1.51806 | −0.219113 | ||||||||
\(49\) | −4.96752 | −0.709645 | ||||||||
\(50\) | 6.18963 | 0.875346 | ||||||||
\(51\) | 0.0389646 | 0.00545614 | ||||||||
\(52\) | −0.284609 | −0.0394681 | ||||||||
\(53\) | 11.3478 | 1.55874 | 0.779370 | − | 0.626564i | \(-0.215539\pi\) | ||||
0.779370 | + | 0.626564i | \(0.215539\pi\) | |||||||
\(54\) | 5.60998 | 0.763422 | ||||||||
\(55\) | 0.809994 | 0.109220 | ||||||||
\(56\) | 1.42565 | 0.190511 | ||||||||
\(57\) | 1.54814 | 0.205056 | ||||||||
\(58\) | 5.53979 | 0.727411 | ||||||||
\(59\) | −7.14634 | −0.930374 | −0.465187 | − | 0.885212i | \(-0.654013\pi\) | ||||
−0.465187 | + | 0.885212i | \(0.654013\pi\) | |||||||
\(60\) | 5.07805 | 0.655573 | ||||||||
\(61\) | 11.8713 | 1.51996 | 0.759980 | − | 0.649947i | \(-0.225209\pi\) | ||||
0.759980 | + | 0.649947i | \(0.225209\pi\) | |||||||
\(62\) | 4.70532 | 0.597577 | ||||||||
\(63\) | −0.991535 | −0.124922 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.952042 | 0.118086 | ||||||||
\(66\) | 0.367589 | 0.0452471 | ||||||||
\(67\) | 0.0480368 | 0.00586863 | 0.00293432 | − | 0.999996i | \(-0.499066\pi\) | ||||
0.00293432 | + | 0.999996i | \(0.499066\pi\) | |||||||
\(68\) | −0.0256674 | −0.00311263 | ||||||||
\(69\) | −1.51806 | −0.182753 | ||||||||
\(70\) | −4.76893 | −0.569997 | ||||||||
\(71\) | −11.2135 | −1.33080 | −0.665400 | − | 0.746487i | \(-0.731739\pi\) | ||||
−0.665400 | + | 0.746487i | \(0.731739\pi\) | |||||||
\(72\) | −0.695496 | −0.0819650 | ||||||||
\(73\) | −9.28856 | −1.08714 | −0.543572 | − | 0.839363i | \(-0.682928\pi\) | ||||
−0.543572 | + | 0.839363i | \(0.682928\pi\) | |||||||
\(74\) | −9.28988 | −1.07993 | ||||||||
\(75\) | −9.39623 | −1.08498 | ||||||||
\(76\) | −1.01981 | −0.116981 | ||||||||
\(77\) | −0.345213 | −0.0393407 | ||||||||
\(78\) | 0.432053 | 0.0489203 | ||||||||
\(79\) | −11.3638 | −1.27852 | −0.639262 | − | 0.768989i | \(-0.720760\pi\) | ||||
−0.639262 | + | 0.768989i | \(0.720760\pi\) | |||||||
\(80\) | −3.34509 | −0.373993 | ||||||||
\(81\) | −6.42980 | −0.714422 | ||||||||
\(82\) | 2.00968 | 0.221932 | ||||||||
\(83\) | −3.54124 | −0.388702 | −0.194351 | − | 0.980932i | \(-0.562260\pi\) | ||||
−0.194351 | + | 0.980932i | \(0.562260\pi\) | |||||||
\(84\) | −2.16422 | −0.236136 | ||||||||
\(85\) | 0.0858597 | 0.00931280 | ||||||||
\(86\) | −1.53875 | −0.165927 | ||||||||
\(87\) | −8.40974 | −0.901618 | ||||||||
\(88\) | −0.242144 | −0.0258126 | ||||||||
\(89\) | 5.04371 | 0.534632 | 0.267316 | − | 0.963609i | \(-0.413863\pi\) | ||||
0.267316 | + | 0.963609i | \(0.413863\pi\) | |||||||
\(90\) | 2.32650 | 0.245234 | ||||||||
\(91\) | −0.405753 | −0.0425344 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −7.14296 | −0.740691 | ||||||||
\(94\) | 4.25361 | 0.438726 | ||||||||
\(95\) | 3.41137 | 0.349999 | ||||||||
\(96\) | −1.51806 | −0.154936 | ||||||||
\(97\) | −8.28272 | −0.840983 | −0.420491 | − | 0.907297i | \(-0.638142\pi\) | ||||
−0.420491 | + | 0.907297i | \(0.638142\pi\) | |||||||
\(98\) | −4.96752 | −0.501795 | ||||||||
\(99\) | 0.168410 | 0.0169259 | ||||||||
\(100\) | 6.18963 | 0.618963 | ||||||||
\(101\) | −2.54819 | −0.253554 | −0.126777 | − | 0.991931i | \(-0.540463\pi\) | ||||
−0.126777 | + | 0.991931i | \(0.540463\pi\) | |||||||
\(102\) | 0.0389646 | 0.00385807 | ||||||||
\(103\) | 12.5761 | 1.23916 | 0.619581 | − | 0.784933i | \(-0.287303\pi\) | ||||
0.619581 | + | 0.784933i | \(0.287303\pi\) | |||||||
\(104\) | −0.284609 | −0.0279082 | ||||||||
\(105\) | 7.23952 | 0.706505 | ||||||||
\(106\) | 11.3478 | 1.10220 | ||||||||
\(107\) | −0.240696 | −0.0232690 | −0.0116345 | − | 0.999932i | \(-0.503703\pi\) | ||||
−0.0116345 | + | 0.999932i | \(0.503703\pi\) | |||||||
\(108\) | 5.60998 | 0.539821 | ||||||||
\(109\) | 8.40992 | 0.805524 | 0.402762 | − | 0.915305i | \(-0.368050\pi\) | ||||
0.402762 | + | 0.915305i | \(0.368050\pi\) | |||||||
\(110\) | 0.809994 | 0.0772299 | ||||||||
\(111\) | 14.1026 | 1.33856 | ||||||||
\(112\) | 1.42565 | 0.134711 | ||||||||
\(113\) | −4.52840 | −0.425996 | −0.212998 | − | 0.977053i | \(-0.568323\pi\) | ||||
−0.212998 | + | 0.977053i | \(0.568323\pi\) | |||||||
\(114\) | 1.54814 | 0.144996 | ||||||||
\(115\) | −3.34509 | −0.311931 | ||||||||
\(116\) | 5.53979 | 0.514357 | ||||||||
\(117\) | 0.197944 | 0.0182999 | ||||||||
\(118\) | −7.14634 | −0.657874 | ||||||||
\(119\) | −0.0365927 | −0.00335445 | ||||||||
\(120\) | 5.07805 | 0.463560 | ||||||||
\(121\) | −10.9414 | −0.994670 | ||||||||
\(122\) | 11.8713 | 1.07477 | ||||||||
\(123\) | −3.05081 | −0.275082 | ||||||||
\(124\) | 4.70532 | 0.422551 | ||||||||
\(125\) | −3.97943 | −0.355931 | ||||||||
\(126\) | −0.991535 | −0.0883329 | ||||||||
\(127\) | 3.57380 | 0.317124 | 0.158562 | − | 0.987349i | \(-0.449314\pi\) | ||||
0.158562 | + | 0.987349i | \(0.449314\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.33591 | 0.205665 | ||||||||
\(130\) | 0.952042 | 0.0834996 | ||||||||
\(131\) | −1.00000 | −0.0873704 | ||||||||
\(132\) | 0.367589 | 0.0319945 | ||||||||
\(133\) | −1.45390 | −0.126069 | ||||||||
\(134\) | 0.0480368 | 0.00414975 | ||||||||
\(135\) | −18.7659 | −1.61511 | ||||||||
\(136\) | −0.0256674 | −0.00220096 | ||||||||
\(137\) | −14.4973 | −1.23859 | −0.619293 | − | 0.785160i | \(-0.712581\pi\) | ||||
−0.619293 | + | 0.785160i | \(0.712581\pi\) | |||||||
\(138\) | −1.51806 | −0.129226 | ||||||||
\(139\) | 3.57168 | 0.302946 | 0.151473 | − | 0.988461i | \(-0.451598\pi\) | ||||
0.151473 | + | 0.988461i | \(0.451598\pi\) | |||||||
\(140\) | −4.76893 | −0.403048 | ||||||||
\(141\) | −6.45723 | −0.543797 | ||||||||
\(142\) | −11.2135 | −0.941018 | ||||||||
\(143\) | 0.0689163 | 0.00576307 | ||||||||
\(144\) | −0.695496 | −0.0579580 | ||||||||
\(145\) | −18.5311 | −1.53893 | ||||||||
\(146\) | −9.28856 | −0.768726 | ||||||||
\(147\) | 7.54099 | 0.621970 | ||||||||
\(148\) | −9.28988 | −0.763624 | ||||||||
\(149\) | 3.68598 | 0.301967 | 0.150984 | − | 0.988536i | \(-0.451756\pi\) | ||||
0.150984 | + | 0.988536i | \(0.451756\pi\) | |||||||
\(150\) | −9.39623 | −0.767199 | ||||||||
\(151\) | −17.0736 | −1.38943 | −0.694716 | − | 0.719284i | \(-0.744470\pi\) | ||||
−0.694716 | + | 0.719284i | \(0.744470\pi\) | |||||||
\(152\) | −1.01981 | −0.0827178 | ||||||||
\(153\) | 0.0178516 | 0.00144321 | ||||||||
\(154\) | −0.345213 | −0.0278181 | ||||||||
\(155\) | −15.7397 | −1.26425 | ||||||||
\(156\) | 0.432053 | 0.0345919 | ||||||||
\(157\) | 1.73823 | 0.138726 | 0.0693631 | − | 0.997591i | \(-0.477903\pi\) | ||||
0.0693631 | + | 0.997591i | \(0.477903\pi\) | |||||||
\(158\) | −11.3638 | −0.904053 | ||||||||
\(159\) | −17.2266 | −1.36616 | ||||||||
\(160\) | −3.34509 | −0.264453 | ||||||||
\(161\) | 1.42565 | 0.112357 | ||||||||
\(162\) | −6.42980 | −0.505173 | ||||||||
\(163\) | 1.72531 | 0.135137 | 0.0675685 | − | 0.997715i | \(-0.478476\pi\) | ||||
0.0675685 | + | 0.997715i | \(0.478476\pi\) | |||||||
\(164\) | 2.00968 | 0.156929 | ||||||||
\(165\) | −1.22962 | −0.0957257 | ||||||||
\(166\) | −3.54124 | −0.274854 | ||||||||
\(167\) | −23.3349 | −1.80571 | −0.902853 | − | 0.429950i | \(-0.858531\pi\) | ||||
−0.902853 | + | 0.429950i | \(0.858531\pi\) | |||||||
\(168\) | −2.16422 | −0.166973 | ||||||||
\(169\) | −12.9190 | −0.993769 | ||||||||
\(170\) | 0.0858597 | 0.00658514 | ||||||||
\(171\) | 0.709276 | 0.0542397 | ||||||||
\(172\) | −1.53875 | −0.117328 | ||||||||
\(173\) | −2.53110 | −0.192436 | −0.0962178 | − | 0.995360i | \(-0.530675\pi\) | ||||
−0.0962178 | + | 0.995360i | \(0.530675\pi\) | |||||||
\(174\) | −8.40974 | −0.637540 | ||||||||
\(175\) | 8.82426 | 0.667051 | ||||||||
\(176\) | −0.242144 | −0.0182523 | ||||||||
\(177\) | 10.8486 | 0.815428 | ||||||||
\(178\) | 5.04371 | 0.378042 | ||||||||
\(179\) | −13.9783 | −1.04479 | −0.522394 | − | 0.852704i | \(-0.674961\pi\) | ||||
−0.522394 | + | 0.852704i | \(0.674961\pi\) | |||||||
\(180\) | 2.32650 | 0.173407 | ||||||||
\(181\) | 0.262286 | 0.0194956 | 0.00974778 | − | 0.999952i | \(-0.496897\pi\) | ||||
0.00974778 | + | 0.999952i | \(0.496897\pi\) | |||||||
\(182\) | −0.405753 | −0.0300764 | ||||||||
\(183\) | −18.0213 | −1.33217 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 31.0755 | 2.28472 | ||||||||
\(186\) | −7.14296 | −0.523747 | ||||||||
\(187\) | 0.00621520 | 0.000454501 0 | ||||||||
\(188\) | 4.25361 | 0.310226 | ||||||||
\(189\) | 7.99788 | 0.581760 | ||||||||
\(190\) | 3.41137 | 0.247487 | ||||||||
\(191\) | −0.485117 | −0.0351019 | −0.0175509 | − | 0.999846i | \(-0.505587\pi\) | ||||
−0.0175509 | + | 0.999846i | \(0.505587\pi\) | |||||||
\(192\) | −1.51806 | −0.109556 | ||||||||
\(193\) | −10.6447 | −0.766223 | −0.383111 | − | 0.923702i | \(-0.625147\pi\) | ||||
−0.383111 | + | 0.923702i | \(0.625147\pi\) | |||||||
\(194\) | −8.28272 | −0.594665 | ||||||||
\(195\) | −1.44526 | −0.103497 | ||||||||
\(196\) | −4.96752 | −0.354823 | ||||||||
\(197\) | 23.5902 | 1.68073 | 0.840366 | − | 0.542019i | \(-0.182340\pi\) | ||||
0.840366 | + | 0.542019i | \(0.182340\pi\) | |||||||
\(198\) | 0.168410 | 0.0119684 | ||||||||
\(199\) | 3.73124 | 0.264501 | 0.132250 | − | 0.991216i | \(-0.457780\pi\) | ||||
0.132250 | + | 0.991216i | \(0.457780\pi\) | |||||||
\(200\) | 6.18963 | 0.437673 | ||||||||
\(201\) | −0.0729227 | −0.00514357 | ||||||||
\(202\) | −2.54819 | −0.179290 | ||||||||
\(203\) | 7.89782 | 0.554318 | ||||||||
\(204\) | 0.0389646 | 0.00272807 | ||||||||
\(205\) | −6.72255 | −0.469523 | ||||||||
\(206\) | 12.5761 | 0.876220 | ||||||||
\(207\) | −0.695496 | −0.0483403 | ||||||||
\(208\) | −0.284609 | −0.0197341 | ||||||||
\(209\) | 0.246942 | 0.0170813 | ||||||||
\(210\) | 7.23952 | 0.499575 | ||||||||
\(211\) | −10.4901 | −0.722170 | −0.361085 | − | 0.932533i | \(-0.617594\pi\) | ||||
−0.361085 | + | 0.932533i | \(0.617594\pi\) | |||||||
\(212\) | 11.3478 | 0.779370 | ||||||||
\(213\) | 17.0228 | 1.16638 | ||||||||
\(214\) | −0.240696 | −0.0164537 | ||||||||
\(215\) | 5.14725 | 0.351039 | ||||||||
\(216\) | 5.60998 | 0.381711 | ||||||||
\(217\) | 6.70815 | 0.455379 | ||||||||
\(218\) | 8.40992 | 0.569592 | ||||||||
\(219\) | 14.1006 | 0.952829 | ||||||||
\(220\) | 0.809994 | 0.0546098 | ||||||||
\(221\) | 0.00730516 | 0.000491398 0 | ||||||||
\(222\) | 14.1026 | 0.946504 | ||||||||
\(223\) | −11.4435 | −0.766313 | −0.383156 | − | 0.923684i | \(-0.625163\pi\) | ||||
−0.383156 | + | 0.923684i | \(0.625163\pi\) | |||||||
\(224\) | 1.42565 | 0.0952553 | ||||||||
\(225\) | −4.30486 | −0.286991 | ||||||||
\(226\) | −4.52840 | −0.301225 | ||||||||
\(227\) | −11.2876 | −0.749186 | −0.374593 | − | 0.927189i | \(-0.622218\pi\) | ||||
−0.374593 | + | 0.927189i | \(0.622218\pi\) | |||||||
\(228\) | 1.54814 | 0.102528 | ||||||||
\(229\) | −2.10543 | −0.139131 | −0.0695655 | − | 0.997577i | \(-0.522161\pi\) | ||||
−0.0695655 | + | 0.997577i | \(0.522161\pi\) | |||||||
\(230\) | −3.34509 | −0.220569 | ||||||||
\(231\) | 0.524054 | 0.0344802 | ||||||||
\(232\) | 5.53979 | 0.363705 | ||||||||
\(233\) | −20.9416 | −1.37193 | −0.685966 | − | 0.727634i | \(-0.740620\pi\) | ||||
−0.685966 | + | 0.727634i | \(0.740620\pi\) | |||||||
\(234\) | 0.197944 | 0.0129400 | ||||||||
\(235\) | −14.2287 | −0.928179 | ||||||||
\(236\) | −7.14634 | −0.465187 | ||||||||
\(237\) | 17.2509 | 1.12056 | ||||||||
\(238\) | −0.0365927 | −0.00237196 | ||||||||
\(239\) | 1.88750 | 0.122093 | 0.0610463 | − | 0.998135i | \(-0.480556\pi\) | ||||
0.0610463 | + | 0.998135i | \(0.480556\pi\) | |||||||
\(240\) | 5.07805 | 0.327787 | ||||||||
\(241\) | 10.5965 | 0.682578 | 0.341289 | − | 0.939958i | \(-0.389136\pi\) | ||||
0.341289 | + | 0.939958i | \(0.389136\pi\) | |||||||
\(242\) | −10.9414 | −0.703338 | ||||||||
\(243\) | −7.06913 | −0.453485 | ||||||||
\(244\) | 11.8713 | 0.759980 | ||||||||
\(245\) | 16.6168 | 1.06161 | ||||||||
\(246\) | −3.05081 | −0.194512 | ||||||||
\(247\) | 0.290248 | 0.0184680 | ||||||||
\(248\) | 4.70532 | 0.298788 | ||||||||
\(249\) | 5.37582 | 0.340678 | ||||||||
\(250\) | −3.97943 | −0.251682 | ||||||||
\(251\) | −4.15487 | −0.262253 | −0.131126 | − | 0.991366i | \(-0.541859\pi\) | ||||
−0.131126 | + | 0.991366i | \(0.541859\pi\) | |||||||
\(252\) | −0.991535 | −0.0624608 | ||||||||
\(253\) | −0.242144 | −0.0152235 | ||||||||
\(254\) | 3.57380 | 0.224240 | ||||||||
\(255\) | −0.130340 | −0.00816222 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.4462 | 0.963506 | 0.481753 | − | 0.876307i | \(-0.340000\pi\) | ||||
0.481753 | + | 0.876307i | \(0.340000\pi\) | |||||||
\(258\) | 2.33591 | 0.145427 | ||||||||
\(259\) | −13.2441 | −0.822951 | ||||||||
\(260\) | 0.952042 | 0.0590431 | ||||||||
\(261\) | −3.85290 | −0.238489 | ||||||||
\(262\) | −1.00000 | −0.0617802 | ||||||||
\(263\) | −14.0059 | −0.863640 | −0.431820 | − | 0.901960i | \(-0.642129\pi\) | ||||
−0.431820 | + | 0.901960i | \(0.642129\pi\) | |||||||
\(264\) | 0.367589 | 0.0226235 | ||||||||
\(265\) | −37.9594 | −2.33183 | ||||||||
\(266\) | −1.45390 | −0.0891443 | ||||||||
\(267\) | −7.65664 | −0.468579 | ||||||||
\(268\) | 0.0480368 | 0.00293432 | ||||||||
\(269\) | 15.9454 | 0.972207 | 0.486104 | − | 0.873901i | \(-0.338418\pi\) | ||||
0.486104 | + | 0.873901i | \(0.338418\pi\) | |||||||
\(270\) | −18.7659 | −1.14206 | ||||||||
\(271\) | −29.9498 | −1.81932 | −0.909661 | − | 0.415353i | \(-0.863658\pi\) | ||||
−0.909661 | + | 0.415353i | \(0.863658\pi\) | |||||||
\(272\) | −0.0256674 | −0.00155631 | ||||||||
\(273\) | 0.615957 | 0.0372794 | ||||||||
\(274\) | −14.4973 | −0.875813 | ||||||||
\(275\) | −1.49878 | −0.0903800 | ||||||||
\(276\) | −1.51806 | −0.0913764 | ||||||||
\(277\) | −11.4541 | −0.688208 | −0.344104 | − | 0.938931i | \(-0.611817\pi\) | ||||
−0.344104 | + | 0.938931i | \(0.611817\pi\) | |||||||
\(278\) | 3.57168 | 0.214215 | ||||||||
\(279\) | −3.27253 | −0.195921 | ||||||||
\(280\) | −4.76893 | −0.284998 | ||||||||
\(281\) | 13.5857 | 0.810452 | 0.405226 | − | 0.914216i | \(-0.367193\pi\) | ||||
0.405226 | + | 0.914216i | \(0.367193\pi\) | |||||||
\(282\) | −6.45723 | −0.384523 | ||||||||
\(283\) | 23.4573 | 1.39439 | 0.697197 | − | 0.716879i | \(-0.254430\pi\) | ||||
0.697197 | + | 0.716879i | \(0.254430\pi\) | |||||||
\(284\) | −11.2135 | −0.665400 | ||||||||
\(285\) | −5.17866 | −0.306758 | ||||||||
\(286\) | 0.0689163 | 0.00407510 | ||||||||
\(287\) | 2.86510 | 0.169121 | ||||||||
\(288\) | −0.695496 | −0.0409825 | ||||||||
\(289\) | −16.9993 | −0.999961 | ||||||||
\(290\) | −18.5311 | −1.08818 | ||||||||
\(291\) | 12.5737 | 0.737081 | ||||||||
\(292\) | −9.28856 | −0.543572 | ||||||||
\(293\) | −20.7920 | −1.21468 | −0.607341 | − | 0.794441i | \(-0.707764\pi\) | ||||
−0.607341 | + | 0.794441i | \(0.707764\pi\) | |||||||
\(294\) | 7.54099 | 0.439799 | ||||||||
\(295\) | 23.9051 | 1.39181 | ||||||||
\(296\) | −9.28988 | −0.539964 | ||||||||
\(297\) | −1.35842 | −0.0788237 | ||||||||
\(298\) | 3.68598 | 0.213523 | ||||||||
\(299\) | −0.284609 | −0.0164593 | ||||||||
\(300\) | −9.39623 | −0.542492 | ||||||||
\(301\) | −2.19372 | −0.126444 | ||||||||
\(302\) | −17.0736 | −0.982477 | ||||||||
\(303\) | 3.86830 | 0.222228 | ||||||||
\(304\) | −1.01981 | −0.0584904 | ||||||||
\(305\) | −39.7105 | −2.27381 | ||||||||
\(306\) | 0.0178516 | 0.00102051 | ||||||||
\(307\) | −14.5758 | −0.831886 | −0.415943 | − | 0.909391i | \(-0.636548\pi\) | ||||
−0.415943 | + | 0.909391i | \(0.636548\pi\) | |||||||
\(308\) | −0.345213 | −0.0196703 | ||||||||
\(309\) | −19.0913 | −1.08607 | ||||||||
\(310\) | −15.7397 | −0.893957 | ||||||||
\(311\) | 21.0112 | 1.19144 | 0.595718 | − | 0.803194i | \(-0.296868\pi\) | ||||
0.595718 | + | 0.803194i | \(0.296868\pi\) | |||||||
\(312\) | 0.432053 | 0.0244602 | ||||||||
\(313\) | 5.22613 | 0.295398 | 0.147699 | − | 0.989032i | \(-0.452813\pi\) | ||||
0.147699 | + | 0.989032i | \(0.452813\pi\) | |||||||
\(314\) | 1.73823 | 0.0980942 | ||||||||
\(315\) | 3.31677 | 0.186879 | ||||||||
\(316\) | −11.3638 | −0.639262 | ||||||||
\(317\) | −15.7787 | −0.886222 | −0.443111 | − | 0.896467i | \(-0.646125\pi\) | ||||
−0.443111 | + | 0.896467i | \(0.646125\pi\) | |||||||
\(318\) | −17.2266 | −0.966021 | ||||||||
\(319\) | −1.34143 | −0.0751056 | ||||||||
\(320\) | −3.34509 | −0.186996 | ||||||||
\(321\) | 0.365391 | 0.0203941 | ||||||||
\(322\) | 1.42565 | 0.0794484 | ||||||||
\(323\) | 0.0261760 | 0.00145647 | ||||||||
\(324\) | −6.42980 | −0.357211 | ||||||||
\(325\) | −1.76162 | −0.0977173 | ||||||||
\(326\) | 1.72531 | 0.0955562 | ||||||||
\(327\) | −12.7668 | −0.706003 | ||||||||
\(328\) | 2.00968 | 0.110966 | ||||||||
\(329\) | 6.06416 | 0.334328 | ||||||||
\(330\) | −1.22962 | −0.0676883 | ||||||||
\(331\) | 15.0855 | 0.829173 | 0.414586 | − | 0.910010i | \(-0.363926\pi\) | ||||
0.414586 | + | 0.910010i | \(0.363926\pi\) | |||||||
\(332\) | −3.54124 | −0.194351 | ||||||||
\(333\) | 6.46107 | 0.354065 | ||||||||
\(334\) | −23.3349 | −1.27683 | ||||||||
\(335\) | −0.160688 | −0.00877930 | ||||||||
\(336\) | −2.16422 | −0.118068 | ||||||||
\(337\) | −25.5476 | −1.39167 | −0.695833 | − | 0.718203i | \(-0.744965\pi\) | ||||
−0.695833 | + | 0.718203i | \(0.744965\pi\) | |||||||
\(338\) | −12.9190 | −0.702701 | ||||||||
\(339\) | 6.87438 | 0.373365 | ||||||||
\(340\) | 0.0858597 | 0.00465640 | ||||||||
\(341\) | −1.13937 | −0.0617001 | ||||||||
\(342\) | 0.709276 | 0.0383533 | ||||||||
\(343\) | −17.0615 | −0.921235 | ||||||||
\(344\) | −1.53875 | −0.0829637 | ||||||||
\(345\) | 5.07805 | 0.273393 | ||||||||
\(346\) | −2.53110 | −0.136073 | ||||||||
\(347\) | 0.898187 | 0.0482172 | 0.0241086 | − | 0.999709i | \(-0.492325\pi\) | ||||
0.0241086 | + | 0.999709i | \(0.492325\pi\) | |||||||
\(348\) | −8.40974 | −0.450809 | ||||||||
\(349\) | −11.0097 | −0.589337 | −0.294669 | − | 0.955599i | \(-0.595209\pi\) | ||||
−0.294669 | + | 0.955599i | \(0.595209\pi\) | |||||||
\(350\) | 8.82426 | 0.471677 | ||||||||
\(351\) | −1.59665 | −0.0852228 | ||||||||
\(352\) | −0.242144 | −0.0129063 | ||||||||
\(353\) | 9.77410 | 0.520223 | 0.260111 | − | 0.965579i | \(-0.416241\pi\) | ||||
0.260111 | + | 0.965579i | \(0.416241\pi\) | |||||||
\(354\) | 10.8486 | 0.576595 | ||||||||
\(355\) | 37.5102 | 1.99084 | ||||||||
\(356\) | 5.04371 | 0.267316 | ||||||||
\(357\) | 0.0555500 | 0.00294002 | ||||||||
\(358\) | −13.9783 | −0.738776 | ||||||||
\(359\) | −5.52789 | −0.291751 | −0.145875 | − | 0.989303i | \(-0.546600\pi\) | ||||
−0.145875 | + | 0.989303i | \(0.546600\pi\) | |||||||
\(360\) | 2.32650 | 0.122617 | ||||||||
\(361\) | −17.9600 | −0.945262 | ||||||||
\(362\) | 0.262286 | 0.0137854 | ||||||||
\(363\) | 16.6096 | 0.871780 | ||||||||
\(364\) | −0.405753 | −0.0212672 | ||||||||
\(365\) | 31.0711 | 1.62633 | ||||||||
\(366\) | −18.0213 | −0.941988 | ||||||||
\(367\) | −20.1212 | −1.05032 | −0.525160 | − | 0.851004i | \(-0.675994\pi\) | ||||
−0.525160 | + | 0.851004i | \(0.675994\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | −1.39772 | −0.0727624 | ||||||||
\(370\) | 31.0755 | 1.61554 | ||||||||
\(371\) | 16.1780 | 0.839920 | ||||||||
\(372\) | −7.14296 | −0.370345 | ||||||||
\(373\) | 8.89645 | 0.460640 | 0.230320 | − | 0.973115i | \(-0.426023\pi\) | ||||
0.230320 | + | 0.973115i | \(0.426023\pi\) | |||||||
\(374\) | 0.00621520 | 0.000321381 0 | ||||||||
\(375\) | 6.04102 | 0.311957 | ||||||||
\(376\) | 4.25361 | 0.219363 | ||||||||
\(377\) | −1.57667 | −0.0812028 | ||||||||
\(378\) | 7.99788 | 0.411367 | ||||||||
\(379\) | −24.6742 | −1.26743 | −0.633714 | − | 0.773567i | \(-0.718470\pi\) | ||||
−0.633714 | + | 0.773567i | \(0.718470\pi\) | |||||||
\(380\) | 3.41137 | 0.175000 | ||||||||
\(381\) | −5.42525 | −0.277944 | ||||||||
\(382\) | −0.485117 | −0.0248208 | ||||||||
\(383\) | −1.03057 | −0.0526598 | −0.0263299 | − | 0.999653i | \(-0.508382\pi\) | ||||
−0.0263299 | + | 0.999653i | \(0.508382\pi\) | |||||||
\(384\) | −1.51806 | −0.0774681 | ||||||||
\(385\) | 1.15477 | 0.0588525 | ||||||||
\(386\) | −10.6447 | −0.541801 | ||||||||
\(387\) | 1.07019 | 0.0544009 | ||||||||
\(388\) | −8.28272 | −0.420491 | ||||||||
\(389\) | −10.7550 | −0.545298 | −0.272649 | − | 0.962114i | \(-0.587900\pi\) | ||||
−0.272649 | + | 0.962114i | \(0.587900\pi\) | |||||||
\(390\) | −1.44526 | −0.0731834 | ||||||||
\(391\) | −0.0256674 | −0.00129806 | ||||||||
\(392\) | −4.96752 | −0.250898 | ||||||||
\(393\) | 1.51806 | 0.0765760 | ||||||||
\(394\) | 23.5902 | 1.18846 | ||||||||
\(395\) | 38.0128 | 1.91263 | ||||||||
\(396\) | 0.168410 | 0.00846293 | ||||||||
\(397\) | −8.17805 | −0.410445 | −0.205222 | − | 0.978715i | \(-0.565792\pi\) | ||||
−0.205222 | + | 0.978715i | \(0.565792\pi\) | |||||||
\(398\) | 3.73124 | 0.187030 | ||||||||
\(399\) | 2.20711 | 0.110493 | ||||||||
\(400\) | 6.18963 | 0.309482 | ||||||||
\(401\) | −28.2132 | −1.40890 | −0.704451 | − | 0.709752i | \(-0.748807\pi\) | ||||
−0.704451 | + | 0.709752i | \(0.748807\pi\) | |||||||
\(402\) | −0.0729227 | −0.00363706 | ||||||||
\(403\) | −1.33918 | −0.0667091 | ||||||||
\(404\) | −2.54819 | −0.126777 | ||||||||
\(405\) | 21.5083 | 1.06875 | ||||||||
\(406\) | 7.89782 | 0.391962 | ||||||||
\(407\) | 2.24949 | 0.111503 | ||||||||
\(408\) | 0.0389646 | 0.00192904 | ||||||||
\(409\) | 15.0756 | 0.745441 | 0.372721 | − | 0.927944i | \(-0.378425\pi\) | ||||
0.372721 | + | 0.927944i | \(0.378425\pi\) | |||||||
\(410\) | −6.72255 | −0.332003 | ||||||||
\(411\) | 22.0077 | 1.08556 | ||||||||
\(412\) | 12.5761 | 0.619581 | ||||||||
\(413\) | −10.1882 | −0.501328 | ||||||||
\(414\) | −0.695496 | −0.0341818 | ||||||||
\(415\) | 11.8458 | 0.581486 | ||||||||
\(416\) | −0.284609 | −0.0139541 | ||||||||
\(417\) | −5.42202 | −0.265517 | ||||||||
\(418\) | 0.246942 | 0.0120783 | ||||||||
\(419\) | −15.9757 | −0.780463 | −0.390232 | − | 0.920717i | \(-0.627605\pi\) | ||||
−0.390232 | + | 0.920717i | \(0.627605\pi\) | |||||||
\(420\) | 7.23952 | 0.353253 | ||||||||
\(421\) | 20.6924 | 1.00849 | 0.504243 | − | 0.863562i | \(-0.331772\pi\) | ||||
0.504243 | + | 0.863562i | \(0.331772\pi\) | |||||||
\(422\) | −10.4901 | −0.510652 | ||||||||
\(423\) | −2.95837 | −0.143841 | ||||||||
\(424\) | 11.3478 | 0.551098 | ||||||||
\(425\) | −0.158872 | −0.00770641 | ||||||||
\(426\) | 17.0228 | 0.824757 | ||||||||
\(427\) | 16.9243 | 0.819024 | ||||||||
\(428\) | −0.240696 | −0.0116345 | ||||||||
\(429\) | −0.104619 | −0.00505105 | ||||||||
\(430\) | 5.14725 | 0.248222 | ||||||||
\(431\) | 33.2990 | 1.60395 | 0.801977 | − | 0.597355i | \(-0.203781\pi\) | ||||
0.801977 | + | 0.597355i | \(0.203781\pi\) | |||||||
\(432\) | 5.60998 | 0.269910 | ||||||||
\(433\) | 3.63773 | 0.174818 | 0.0874091 | − | 0.996173i | \(-0.472141\pi\) | ||||
0.0874091 | + | 0.996173i | \(0.472141\pi\) | |||||||
\(434\) | 6.70815 | 0.322002 | ||||||||
\(435\) | 28.1313 | 1.34879 | ||||||||
\(436\) | 8.40992 | 0.402762 | ||||||||
\(437\) | −1.01981 | −0.0487843 | ||||||||
\(438\) | 14.1006 | 0.673752 | ||||||||
\(439\) | −30.7511 | −1.46767 | −0.733835 | − | 0.679328i | \(-0.762271\pi\) | ||||
−0.733835 | + | 0.679328i | \(0.762271\pi\) | |||||||
\(440\) | 0.809994 | 0.0386149 | ||||||||
\(441\) | 3.45489 | 0.164518 | ||||||||
\(442\) | 0.00730516 | 0.000347471 0 | ||||||||
\(443\) | 15.9167 | 0.756226 | 0.378113 | − | 0.925759i | \(-0.376573\pi\) | ||||
0.378113 | + | 0.925759i | \(0.376573\pi\) | |||||||
\(444\) | 14.1026 | 0.669280 | ||||||||
\(445\) | −16.8717 | −0.799793 | ||||||||
\(446\) | −11.4435 | −0.541865 | ||||||||
\(447\) | −5.59554 | −0.264660 | ||||||||
\(448\) | 1.42565 | 0.0673557 | ||||||||
\(449\) | 1.59335 | 0.0751949 | 0.0375975 | − | 0.999293i | \(-0.488030\pi\) | ||||
0.0375975 | + | 0.999293i | \(0.488030\pi\) | |||||||
\(450\) | −4.30486 | −0.202933 | ||||||||
\(451\) | −0.486631 | −0.0229146 | ||||||||
\(452\) | −4.52840 | −0.212998 | ||||||||
\(453\) | 25.9188 | 1.21777 | ||||||||
\(454\) | −11.2876 | −0.529754 | ||||||||
\(455\) | 1.35728 | 0.0636302 | ||||||||
\(456\) | 1.54814 | 0.0724982 | ||||||||
\(457\) | −20.2064 | −0.945215 | −0.472607 | − | 0.881273i | \(-0.656687\pi\) | ||||
−0.472607 | + | 0.881273i | \(0.656687\pi\) | |||||||
\(458\) | −2.10543 | −0.0983805 | ||||||||
\(459\) | −0.143994 | −0.00672104 | ||||||||
\(460\) | −3.34509 | −0.155966 | ||||||||
\(461\) | −35.4263 | −1.64997 | −0.824983 | − | 0.565157i | \(-0.808816\pi\) | ||||
−0.824983 | + | 0.565157i | \(0.808816\pi\) | |||||||
\(462\) | 0.524054 | 0.0243812 | ||||||||
\(463\) | −12.8218 | −0.595880 | −0.297940 | − | 0.954585i | \(-0.596300\pi\) | ||||
−0.297940 | + | 0.954585i | \(0.596300\pi\) | |||||||
\(464\) | 5.53979 | 0.257178 | ||||||||
\(465\) | 23.8939 | 1.10805 | ||||||||
\(466\) | −20.9416 | −0.970102 | ||||||||
\(467\) | 0.0775715 | 0.00358958 | 0.00179479 | − | 0.999998i | \(-0.499429\pi\) | ||||
0.00179479 | + | 0.999998i | \(0.499429\pi\) | |||||||
\(468\) | 0.197944 | 0.00914997 | ||||||||
\(469\) | 0.0684838 | 0.00316229 | ||||||||
\(470\) | −14.2287 | −0.656321 | ||||||||
\(471\) | −2.63874 | −0.121587 | ||||||||
\(472\) | −7.14634 | −0.328937 | ||||||||
\(473\) | 0.372598 | 0.0171321 | ||||||||
\(474\) | 17.2509 | 0.792359 | ||||||||
\(475\) | −6.31228 | −0.289627 | ||||||||
\(476\) | −0.0365927 | −0.00167723 | ||||||||
\(477\) | −7.89234 | −0.361366 | ||||||||
\(478\) | 1.88750 | 0.0863325 | ||||||||
\(479\) | 34.8965 | 1.59446 | 0.797230 | − | 0.603676i | \(-0.206298\pi\) | ||||
0.797230 | + | 0.603676i | \(0.206298\pi\) | |||||||
\(480\) | 5.07805 | 0.231780 | ||||||||
\(481\) | 2.64398 | 0.120555 | ||||||||
\(482\) | 10.5965 | 0.482656 | ||||||||
\(483\) | −2.16422 | −0.0984756 | ||||||||
\(484\) | −10.9414 | −0.497335 | ||||||||
\(485\) | 27.7064 | 1.25808 | ||||||||
\(486\) | −7.06913 | −0.320662 | ||||||||
\(487\) | 10.5321 | 0.477257 | 0.238629 | − | 0.971111i | \(-0.423302\pi\) | ||||
0.238629 | + | 0.971111i | \(0.423302\pi\) | |||||||
\(488\) | 11.8713 | 0.537387 | ||||||||
\(489\) | −2.61913 | −0.118441 | ||||||||
\(490\) | 16.6168 | 0.750670 | ||||||||
\(491\) | −5.87798 | −0.265269 | −0.132635 | − | 0.991165i | \(-0.542344\pi\) | ||||
−0.132635 | + | 0.991165i | \(0.542344\pi\) | |||||||
\(492\) | −3.05081 | −0.137541 | ||||||||
\(493\) | −0.142192 | −0.00640401 | ||||||||
\(494\) | 0.290248 | 0.0130589 | ||||||||
\(495\) | −0.563347 | −0.0253206 | ||||||||
\(496\) | 4.70532 | 0.211275 | ||||||||
\(497\) | −15.9866 | −0.717096 | ||||||||
\(498\) | 5.37582 | 0.240896 | ||||||||
\(499\) | −36.7786 | −1.64644 | −0.823219 | − | 0.567724i | \(-0.807824\pi\) | ||||
−0.823219 | + | 0.567724i | \(0.807824\pi\) | |||||||
\(500\) | −3.97943 | −0.177966 | ||||||||
\(501\) | 35.4237 | 1.58261 | ||||||||
\(502\) | −4.15487 | −0.185441 | ||||||||
\(503\) | 8.00730 | 0.357028 | 0.178514 | − | 0.983937i | \(-0.442871\pi\) | ||||
0.178514 | + | 0.983937i | \(0.442871\pi\) | |||||||
\(504\) | −0.991535 | −0.0441665 | ||||||||
\(505\) | 8.52392 | 0.379309 | ||||||||
\(506\) | −0.242144 | −0.0107646 | ||||||||
\(507\) | 19.6118 | 0.870991 | ||||||||
\(508\) | 3.57380 | 0.158562 | ||||||||
\(509\) | 17.3759 | 0.770173 | 0.385086 | − | 0.922881i | \(-0.374172\pi\) | ||||
0.385086 | + | 0.922881i | \(0.374172\pi\) | |||||||
\(510\) | −0.130340 | −0.00577156 | ||||||||
\(511\) | −13.2422 | −0.585802 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −5.72114 | −0.252594 | ||||||||
\(514\) | 15.4462 | 0.681302 | ||||||||
\(515\) | −42.0683 | −1.85375 | ||||||||
\(516\) | 2.33591 | 0.102833 | ||||||||
\(517\) | −1.02999 | −0.0452987 | ||||||||
\(518\) | −13.2441 | −0.581914 | ||||||||
\(519\) | 3.84235 | 0.168661 | ||||||||
\(520\) | 0.952042 | 0.0417498 | ||||||||
\(521\) | 1.68675 | 0.0738978 | 0.0369489 | − | 0.999317i | \(-0.488236\pi\) | ||||
0.0369489 | + | 0.999317i | \(0.488236\pi\) | |||||||
\(522\) | −3.85290 | −0.168637 | ||||||||
\(523\) | 40.9102 | 1.78888 | 0.894438 | − | 0.447191i | \(-0.147576\pi\) | ||||
0.894438 | + | 0.447191i | \(0.147576\pi\) | |||||||
\(524\) | −1.00000 | −0.0436852 | ||||||||
\(525\) | −13.3958 | −0.584639 | ||||||||
\(526\) | −14.0059 | −0.610686 | ||||||||
\(527\) | −0.120773 | −0.00526097 | ||||||||
\(528\) | 0.367589 | 0.0159973 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −37.9594 | −1.64885 | ||||||||
\(531\) | 4.97025 | 0.215690 | ||||||||
\(532\) | −1.45390 | −0.0630345 | ||||||||
\(533\) | −0.571971 | −0.0247748 | ||||||||
\(534\) | −7.65664 | −0.331335 | ||||||||
\(535\) | 0.805151 | 0.0348097 | ||||||||
\(536\) | 0.0480368 | 0.00207487 | ||||||||
\(537\) | 21.2199 | 0.915706 | ||||||||
\(538\) | 15.9454 | 0.687454 | ||||||||
\(539\) | 1.20285 | 0.0518106 | ||||||||
\(540\) | −18.7659 | −0.807556 | ||||||||
\(541\) | −0.421542 | −0.0181235 | −0.00906175 | − | 0.999959i | \(-0.502884\pi\) | ||||
−0.00906175 | + | 0.999959i | \(0.502884\pi\) | |||||||
\(542\) | −29.9498 | −1.28645 | ||||||||
\(543\) | −0.398166 | −0.0170869 | ||||||||
\(544\) | −0.0256674 | −0.00110048 | ||||||||
\(545\) | −28.1319 | −1.20504 | ||||||||
\(546\) | 0.615957 | 0.0263605 | ||||||||
\(547\) | −12.8562 | −0.549693 | −0.274847 | − | 0.961488i | \(-0.588627\pi\) | ||||
−0.274847 | + | 0.961488i | \(0.588627\pi\) | |||||||
\(548\) | −14.4973 | −0.619293 | ||||||||
\(549\) | −8.25641 | −0.352375 | ||||||||
\(550\) | −1.49878 | −0.0639083 | ||||||||
\(551\) | −5.64956 | −0.240679 | ||||||||
\(552\) | −1.51806 | −0.0646129 | ||||||||
\(553\) | −16.2008 | −0.688927 | ||||||||
\(554\) | −11.4541 | −0.486637 | ||||||||
\(555\) | −47.1745 | −2.00244 | ||||||||
\(556\) | 3.57168 | 0.151473 | ||||||||
\(557\) | 15.5151 | 0.657397 | 0.328699 | − | 0.944435i | \(-0.393390\pi\) | ||||
0.328699 | + | 0.944435i | \(0.393390\pi\) | |||||||
\(558\) | −3.27253 | −0.138537 | ||||||||
\(559\) | 0.437941 | 0.0185229 | ||||||||
\(560\) | −4.76893 | −0.201524 | ||||||||
\(561\) | −0.00943505 | −0.000398348 0 | ||||||||
\(562\) | 13.5857 | 0.573076 | ||||||||
\(563\) | 43.3884 | 1.82860 | 0.914301 | − | 0.405036i | \(-0.132741\pi\) | ||||
0.914301 | + | 0.405036i | \(0.132741\pi\) | |||||||
\(564\) | −6.45723 | −0.271898 | ||||||||
\(565\) | 15.1479 | 0.637278 | ||||||||
\(566\) | 23.4573 | 0.985986 | ||||||||
\(567\) | −9.16665 | −0.384963 | ||||||||
\(568\) | −11.2135 | −0.470509 | ||||||||
\(569\) | 18.6647 | 0.782465 | 0.391232 | − | 0.920292i | \(-0.372049\pi\) | ||||
0.391232 | + | 0.920292i | \(0.372049\pi\) | |||||||
\(570\) | −5.17866 | −0.216910 | ||||||||
\(571\) | 1.17536 | 0.0491871 | 0.0245936 | − | 0.999698i | \(-0.492171\pi\) | ||||
0.0245936 | + | 0.999698i | \(0.492171\pi\) | |||||||
\(572\) | 0.0689163 | 0.00288153 | ||||||||
\(573\) | 0.736437 | 0.0307651 | ||||||||
\(574\) | 2.86510 | 0.119587 | ||||||||
\(575\) | 6.18963 | 0.258126 | ||||||||
\(576\) | −0.695496 | −0.0289790 | ||||||||
\(577\) | −14.7055 | −0.612197 | −0.306098 | − | 0.952000i | \(-0.599024\pi\) | ||||
−0.306098 | + | 0.952000i | \(0.599024\pi\) | |||||||
\(578\) | −16.9993 | −0.707079 | ||||||||
\(579\) | 16.1593 | 0.671557 | ||||||||
\(580\) | −18.5311 | −0.769463 | ||||||||
\(581\) | −5.04858 | −0.209450 | ||||||||
\(582\) | 12.5737 | 0.521195 | ||||||||
\(583\) | −2.74780 | −0.113802 | ||||||||
\(584\) | −9.28856 | −0.384363 | ||||||||
\(585\) | −0.662141 | −0.0273762 | ||||||||
\(586\) | −20.7920 | −0.858910 | ||||||||
\(587\) | 33.4349 | 1.38001 | 0.690004 | − | 0.723806i | \(-0.257609\pi\) | ||||
0.690004 | + | 0.723806i | \(0.257609\pi\) | |||||||
\(588\) | 7.54099 | 0.310985 | ||||||||
\(589\) | −4.79856 | −0.197721 | ||||||||
\(590\) | 23.9051 | 0.984159 | ||||||||
\(591\) | −35.8113 | −1.47308 | ||||||||
\(592\) | −9.28988 | −0.381812 | ||||||||
\(593\) | 8.92318 | 0.366431 | 0.183216 | − | 0.983073i | \(-0.441349\pi\) | ||||
0.183216 | + | 0.983073i | \(0.441349\pi\) | |||||||
\(594\) | −1.35842 | −0.0557368 | ||||||||
\(595\) | 0.122406 | 0.00501816 | ||||||||
\(596\) | 3.68598 | 0.150984 | ||||||||
\(597\) | −5.66425 | −0.231822 | ||||||||
\(598\) | −0.284609 | −0.0116385 | ||||||||
\(599\) | −13.5307 | −0.552847 | −0.276424 | − | 0.961036i | \(-0.589149\pi\) | ||||
−0.276424 | + | 0.961036i | \(0.589149\pi\) | |||||||
\(600\) | −9.39623 | −0.383600 | ||||||||
\(601\) | 41.4625 | 1.69129 | 0.845644 | − | 0.533747i | \(-0.179216\pi\) | ||||
0.845644 | + | 0.533747i | \(0.179216\pi\) | |||||||
\(602\) | −2.19372 | −0.0894092 | ||||||||
\(603\) | −0.0334094 | −0.00136054 | ||||||||
\(604\) | −17.0736 | −0.694716 | ||||||||
\(605\) | 36.5999 | 1.48800 | ||||||||
\(606\) | 3.86830 | 0.157139 | ||||||||
\(607\) | 11.9826 | 0.486361 | 0.243180 | − | 0.969981i | \(-0.421809\pi\) | ||||
0.243180 | + | 0.969981i | \(0.421809\pi\) | |||||||
\(608\) | −1.01981 | −0.0413589 | ||||||||
\(609\) | −11.9894 | −0.485833 | ||||||||
\(610\) | −39.7105 | −1.60783 | ||||||||
\(611\) | −1.21061 | −0.0489762 | ||||||||
\(612\) | 0.0178516 | 0.000721606 0 | ||||||||
\(613\) | 32.5549 | 1.31488 | 0.657439 | − | 0.753508i | \(-0.271640\pi\) | ||||
0.657439 | + | 0.753508i | \(0.271640\pi\) | |||||||
\(614\) | −14.5758 | −0.588232 | ||||||||
\(615\) | 10.2052 | 0.411514 | ||||||||
\(616\) | −0.345213 | −0.0139090 | ||||||||
\(617\) | −12.9067 | −0.519604 | −0.259802 | − | 0.965662i | \(-0.583657\pi\) | ||||
−0.259802 | + | 0.965662i | \(0.583657\pi\) | |||||||
\(618\) | −19.0913 | −0.767965 | ||||||||
\(619\) | 19.5392 | 0.785345 | 0.392673 | − | 0.919678i | \(-0.371551\pi\) | ||||
0.392673 | + | 0.919678i | \(0.371551\pi\) | |||||||
\(620\) | −15.7397 | −0.632123 | ||||||||
\(621\) | 5.60998 | 0.225121 | ||||||||
\(622\) | 21.0112 | 0.842472 | ||||||||
\(623\) | 7.19057 | 0.288084 | ||||||||
\(624\) | 0.432053 | 0.0172960 | ||||||||
\(625\) | −17.6366 | −0.705464 | ||||||||
\(626\) | 5.22613 | 0.208878 | ||||||||
\(627\) | −0.374873 | −0.0149710 | ||||||||
\(628\) | 1.73823 | 0.0693631 | ||||||||
\(629\) | 0.238447 | 0.00950750 | ||||||||
\(630\) | 3.31677 | 0.132143 | ||||||||
\(631\) | −22.0761 | −0.878834 | −0.439417 | − | 0.898283i | \(-0.644815\pi\) | ||||
−0.439417 | + | 0.898283i | \(0.644815\pi\) | |||||||
\(632\) | −11.3638 | −0.452026 | ||||||||
\(633\) | 15.9246 | 0.632948 | ||||||||
\(634\) | −15.7787 | −0.626654 | ||||||||
\(635\) | −11.9547 | −0.474408 | ||||||||
\(636\) | −17.2266 | −0.683080 | ||||||||
\(637\) | 1.41380 | 0.0560167 | ||||||||
\(638\) | −1.34143 | −0.0531077 | ||||||||
\(639\) | 7.79895 | 0.308522 | ||||||||
\(640\) | −3.34509 | −0.132226 | ||||||||
\(641\) | −25.7924 | −1.01874 | −0.509370 | − | 0.860548i | \(-0.670122\pi\) | ||||
−0.509370 | + | 0.860548i | \(0.670122\pi\) | |||||||
\(642\) | 0.365391 | 0.0144208 | ||||||||
\(643\) | −5.32432 | −0.209971 | −0.104985 | − | 0.994474i | \(-0.533480\pi\) | ||||
−0.104985 | + | 0.994474i | \(0.533480\pi\) | |||||||
\(644\) | 1.42565 | 0.0561785 | ||||||||
\(645\) | −7.81383 | −0.307669 | ||||||||
\(646\) | 0.0261760 | 0.00102988 | ||||||||
\(647\) | 20.7785 | 0.816886 | 0.408443 | − | 0.912784i | \(-0.366072\pi\) | ||||
0.408443 | + | 0.912784i | \(0.366072\pi\) | |||||||
\(648\) | −6.42980 | −0.252586 | ||||||||
\(649\) | 1.73044 | 0.0679258 | ||||||||
\(650\) | −1.76162 | −0.0690965 | ||||||||
\(651\) | −10.1834 | −0.399118 | ||||||||
\(652\) | 1.72531 | 0.0675685 | ||||||||
\(653\) | −2.71806 | −0.106366 | −0.0531829 | − | 0.998585i | \(-0.516937\pi\) | ||||
−0.0531829 | + | 0.998585i | \(0.516937\pi\) | |||||||
\(654\) | −12.7668 | −0.499220 | ||||||||
\(655\) | 3.34509 | 0.130704 | ||||||||
\(656\) | 2.00968 | 0.0784647 | ||||||||
\(657\) | 6.46015 | 0.252035 | ||||||||
\(658\) | 6.06416 | 0.236406 | ||||||||
\(659\) | 8.40079 | 0.327248 | 0.163624 | − | 0.986523i | \(-0.447682\pi\) | ||||
0.163624 | + | 0.986523i | \(0.447682\pi\) | |||||||
\(660\) | −1.22962 | −0.0478628 | ||||||||
\(661\) | −31.2897 | −1.21703 | −0.608514 | − | 0.793543i | \(-0.708234\pi\) | ||||
−0.608514 | + | 0.793543i | \(0.708234\pi\) | |||||||
\(662\) | 15.0855 | 0.586314 | ||||||||
\(663\) | −0.0110897 | −0.000430687 0 | ||||||||
\(664\) | −3.54124 | −0.137427 | ||||||||
\(665\) | 4.86343 | 0.188596 | ||||||||
\(666\) | 6.46107 | 0.250362 | ||||||||
\(667\) | 5.53979 | 0.214502 | ||||||||
\(668\) | −23.3349 | −0.902853 | ||||||||
\(669\) | 17.3719 | 0.671636 | ||||||||
\(670\) | −0.160688 | −0.00620790 | ||||||||
\(671\) | −2.87456 | −0.110971 | ||||||||
\(672\) | −2.16422 | −0.0834867 | ||||||||
\(673\) | −9.16447 | −0.353264 | −0.176632 | − | 0.984277i | \(-0.556520\pi\) | ||||
−0.176632 | + | 0.984277i | \(0.556520\pi\) | |||||||
\(674\) | −25.5476 | −0.984057 | ||||||||
\(675\) | 34.7237 | 1.33652 | ||||||||
\(676\) | −12.9190 | −0.496885 | ||||||||
\(677\) | −42.6490 | −1.63913 | −0.819567 | − | 0.572984i | \(-0.805786\pi\) | ||||
−0.819567 | + | 0.572984i | \(0.805786\pi\) | |||||||
\(678\) | 6.87438 | 0.264009 | ||||||||
\(679\) | −11.8083 | −0.453160 | ||||||||
\(680\) | 0.0858597 | 0.00329257 | ||||||||
\(681\) | 17.1353 | 0.656625 | ||||||||
\(682\) | −1.13937 | −0.0436286 | ||||||||
\(683\) | 48.6322 | 1.86086 | 0.930430 | − | 0.366469i | \(-0.119434\pi\) | ||||
0.930430 | + | 0.366469i | \(0.119434\pi\) | |||||||
\(684\) | 0.709276 | 0.0271199 | ||||||||
\(685\) | 48.4947 | 1.85289 | ||||||||
\(686\) | −17.0615 | −0.651411 | ||||||||
\(687\) | 3.19617 | 0.121942 | ||||||||
\(688\) | −1.53875 | −0.0586642 | ||||||||
\(689\) | −3.22968 | −0.123041 | ||||||||
\(690\) | 5.07805 | 0.193318 | ||||||||
\(691\) | 11.8745 | 0.451727 | 0.225864 | − | 0.974159i | \(-0.427480\pi\) | ||||
0.225864 | + | 0.974159i | \(0.427480\pi\) | |||||||
\(692\) | −2.53110 | −0.0962178 | ||||||||
\(693\) | 0.240094 | 0.00912042 | ||||||||
\(694\) | 0.898187 | 0.0340947 | ||||||||
\(695\) | −11.9476 | −0.453198 | ||||||||
\(696\) | −8.40974 | −0.318770 | ||||||||
\(697\) | −0.0515831 | −0.00195385 | ||||||||
\(698\) | −11.0097 | −0.416724 | ||||||||
\(699\) | 31.7906 | 1.20243 | ||||||||
\(700\) | 8.82426 | 0.333526 | ||||||||
\(701\) | 13.6797 | 0.516674 | 0.258337 | − | 0.966055i | \(-0.416825\pi\) | ||||
0.258337 | + | 0.966055i | \(0.416825\pi\) | |||||||
\(702\) | −1.59665 | −0.0602616 | ||||||||
\(703\) | 9.47395 | 0.357317 | ||||||||
\(704\) | −0.242144 | −0.00912615 | ||||||||
\(705\) | 21.6000 | 0.813504 | ||||||||
\(706\) | 9.77410 | 0.367853 | ||||||||
\(707\) | −3.63283 | −0.136627 | ||||||||
\(708\) | 10.8486 | 0.407714 | ||||||||
\(709\) | −34.5404 | −1.29719 | −0.648596 | − | 0.761133i | \(-0.724644\pi\) | ||||
−0.648596 | + | 0.761133i | \(0.724644\pi\) | |||||||
\(710\) | 37.5102 | 1.40773 | ||||||||
\(711\) | 7.90345 | 0.296403 | ||||||||
\(712\) | 5.04371 | 0.189021 | ||||||||
\(713\) | 4.70532 | 0.176216 | ||||||||
\(714\) | 0.0555500 | 0.00207890 | ||||||||
\(715\) | −0.230531 | −0.00862138 | ||||||||
\(716\) | −13.9783 | −0.522394 | ||||||||
\(717\) | −2.86534 | −0.107008 | ||||||||
\(718\) | −5.52789 | −0.206299 | ||||||||
\(719\) | −28.5673 | −1.06538 | −0.532690 | − | 0.846311i | \(-0.678819\pi\) | ||||
−0.532690 | + | 0.846311i | \(0.678819\pi\) | |||||||
\(720\) | 2.32650 | 0.0867034 | ||||||||
\(721\) | 17.9292 | 0.667717 | ||||||||
\(722\) | −17.9600 | −0.668401 | ||||||||
\(723\) | −16.0861 | −0.598247 | ||||||||
\(724\) | 0.262286 | 0.00974778 | ||||||||
\(725\) | 34.2893 | 1.27347 | ||||||||
\(726\) | 16.6096 | 0.616442 | ||||||||
\(727\) | −34.1512 | −1.26660 | −0.633299 | − | 0.773907i | \(-0.718300\pi\) | ||||
−0.633299 | + | 0.773907i | \(0.718300\pi\) | |||||||
\(728\) | −0.405753 | −0.0150382 | ||||||||
\(729\) | 30.0208 | 1.11188 | ||||||||
\(730\) | 31.0711 | 1.14999 | ||||||||
\(731\) | 0.0394956 | 0.00146080 | ||||||||
\(732\) | −18.0213 | −0.666086 | ||||||||
\(733\) | −28.0442 | −1.03584 | −0.517918 | − | 0.855430i | \(-0.673293\pi\) | ||||
−0.517918 | + | 0.855430i | \(0.673293\pi\) | |||||||
\(734\) | −20.1212 | −0.742688 | ||||||||
\(735\) | −25.2253 | −0.930449 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −0.0116318 | −0.000428464 0 | ||||||||
\(738\) | −1.39772 | −0.0514508 | ||||||||
\(739\) | 10.2899 | 0.378519 | 0.189260 | − | 0.981927i | \(-0.439391\pi\) | ||||
0.189260 | + | 0.981927i | \(0.439391\pi\) | |||||||
\(740\) | 31.0755 | 1.14236 | ||||||||
\(741\) | −0.440613 | −0.0161863 | ||||||||
\(742\) | 16.1780 | 0.593913 | ||||||||
\(743\) | −21.7983 | −0.799704 | −0.399852 | − | 0.916580i | \(-0.630938\pi\) | ||||
−0.399852 | + | 0.916580i | \(0.630938\pi\) | |||||||
\(744\) | −7.14296 | −0.261874 | ||||||||
\(745\) | −12.3299 | −0.451734 | ||||||||
\(746\) | 8.89645 | 0.325722 | ||||||||
\(747\) | 2.46292 | 0.0901135 | ||||||||
\(748\) | 0.00621520 | 0.000227250 0 | ||||||||
\(749\) | −0.343149 | −0.0125384 | ||||||||
\(750\) | 6.04102 | 0.220587 | ||||||||
\(751\) | 30.2844 | 1.10509 | 0.552547 | − | 0.833482i | \(-0.313656\pi\) | ||||
0.552547 | + | 0.833482i | \(0.313656\pi\) | |||||||
\(752\) | 4.25361 | 0.155113 | ||||||||
\(753\) | 6.30734 | 0.229852 | ||||||||
\(754\) | −1.57667 | −0.0574190 | ||||||||
\(755\) | 57.1128 | 2.07855 | ||||||||
\(756\) | 7.99788 | 0.290880 | ||||||||
\(757\) | 35.9962 | 1.30830 | 0.654152 | − | 0.756363i | \(-0.273026\pi\) | ||||
0.654152 | + | 0.756363i | \(0.273026\pi\) | |||||||
\(758\) | −24.6742 | −0.896207 | ||||||||
\(759\) | 0.367589 | 0.0133426 | ||||||||
\(760\) | 3.41137 | 0.123743 | ||||||||
\(761\) | 34.1259 | 1.23706 | 0.618532 | − | 0.785760i | \(-0.287728\pi\) | ||||
0.618532 | + | 0.785760i | \(0.287728\pi\) | |||||||
\(762\) | −5.42525 | −0.196536 | ||||||||
\(763\) | 11.9896 | 0.434053 | ||||||||
\(764\) | −0.485117 | −0.0175509 | ||||||||
\(765\) | −0.0597151 | −0.00215900 | ||||||||
\(766\) | −1.03057 | −0.0372361 | ||||||||
\(767\) | 2.03391 | 0.0734402 | ||||||||
\(768\) | −1.51806 | −0.0547782 | ||||||||
\(769\) | −19.9982 | −0.721154 | −0.360577 | − | 0.932729i | \(-0.617420\pi\) | ||||
−0.360577 | + | 0.932729i | \(0.617420\pi\) | |||||||
\(770\) | 1.15477 | 0.0416150 | ||||||||
\(771\) | −23.4482 | −0.844467 | ||||||||
\(772\) | −10.6447 | −0.383111 | ||||||||
\(773\) | −20.7467 | −0.746207 | −0.373104 | − | 0.927790i | \(-0.621706\pi\) | ||||
−0.373104 | + | 0.927790i | \(0.621706\pi\) | |||||||
\(774\) | 1.07019 | 0.0384673 | ||||||||
\(775\) | 29.1242 | 1.04617 | ||||||||
\(776\) | −8.28272 | −0.297332 | ||||||||
\(777\) | 20.1054 | 0.721277 | ||||||||
\(778\) | −10.7550 | −0.385584 | ||||||||
\(779\) | −2.04950 | −0.0734308 | ||||||||
\(780\) | −1.44526 | −0.0517485 | ||||||||
\(781\) | 2.71529 | 0.0971606 | ||||||||
\(782\) | −0.0256674 | −0.000917864 0 | ||||||||
\(783\) | 31.0781 | 1.11064 | ||||||||
\(784\) | −4.96752 | −0.177411 | ||||||||
\(785\) | −5.81455 | −0.207530 | ||||||||
\(786\) | 1.51806 | 0.0541474 | ||||||||
\(787\) | −4.87434 | −0.173751 | −0.0868757 | − | 0.996219i | \(-0.527688\pi\) | ||||
−0.0868757 | + | 0.996219i | \(0.527688\pi\) | |||||||
\(788\) | 23.5902 | 0.840366 | ||||||||
\(789\) | 21.2618 | 0.756939 | ||||||||
\(790\) | 38.0128 | 1.35244 | ||||||||
\(791\) | −6.45592 | −0.229546 | ||||||||
\(792\) | 0.168410 | 0.00598419 | ||||||||
\(793\) | −3.37866 | −0.119980 | ||||||||
\(794\) | −8.17805 | −0.290228 | ||||||||
\(795\) | 57.6246 | 2.04373 | ||||||||
\(796\) | 3.73124 | 0.132250 | ||||||||
\(797\) | −3.49650 | −0.123852 | −0.0619261 | − | 0.998081i | \(-0.519724\pi\) | ||||
−0.0619261 | + | 0.998081i | \(0.519724\pi\) | |||||||
\(798\) | 2.20711 | 0.0781307 | ||||||||
\(799\) | −0.109179 | −0.00386248 | ||||||||
\(800\) | 6.18963 | 0.218837 | ||||||||
\(801\) | −3.50788 | −0.123945 | ||||||||
\(802\) | −28.2132 | −0.996244 | ||||||||
\(803\) | 2.24917 | 0.0793714 | ||||||||
\(804\) | −0.0729227 | −0.00257179 | ||||||||
\(805\) | −4.76893 | −0.168083 | ||||||||
\(806\) | −1.33918 | −0.0471704 | ||||||||
\(807\) | −24.2060 | −0.852093 | ||||||||
\(808\) | −2.54819 | −0.0896449 | ||||||||
\(809\) | 54.0935 | 1.90183 | 0.950914 | − | 0.309456i | \(-0.100147\pi\) | ||||
0.950914 | + | 0.309456i | \(0.100147\pi\) | |||||||
\(810\) | 21.5083 | 0.755723 | ||||||||
\(811\) | −51.5933 | −1.81169 | −0.905844 | − | 0.423612i | \(-0.860762\pi\) | ||||
−0.905844 | + | 0.423612i | \(0.860762\pi\) | |||||||
\(812\) | 7.89782 | 0.277159 | ||||||||
\(813\) | 45.4656 | 1.59455 | ||||||||
\(814\) | 2.24949 | 0.0788446 | ||||||||
\(815\) | −5.77133 | −0.202161 | ||||||||
\(816\) | 0.0389646 | 0.00136403 | ||||||||
\(817\) | 1.56924 | 0.0549006 | ||||||||
\(818\) | 15.0756 | 0.527107 | ||||||||
\(819\) | 0.282199 | 0.00986084 | ||||||||
\(820\) | −6.72255 | −0.234762 | ||||||||
\(821\) | 3.60087 | 0.125671 | 0.0628356 | − | 0.998024i | \(-0.479986\pi\) | ||||
0.0628356 | + | 0.998024i | \(0.479986\pi\) | |||||||
\(822\) | 22.0077 | 0.767608 | ||||||||
\(823\) | 37.5669 | 1.30950 | 0.654750 | − | 0.755845i | \(-0.272774\pi\) | ||||
0.654750 | + | 0.755845i | \(0.272774\pi\) | |||||||
\(824\) | 12.5761 | 0.438110 | ||||||||
\(825\) | 2.27524 | 0.0792137 | ||||||||
\(826\) | −10.1882 | −0.354492 | ||||||||
\(827\) | 9.55413 | 0.332230 | 0.166115 | − | 0.986106i | \(-0.446878\pi\) | ||||
0.166115 | + | 0.986106i | \(0.446878\pi\) | |||||||
\(828\) | −0.695496 | −0.0241701 | ||||||||
\(829\) | −5.87724 | −0.204125 | −0.102063 | − | 0.994778i | \(-0.532544\pi\) | ||||
−0.102063 | + | 0.994778i | \(0.532544\pi\) | |||||||
\(830\) | 11.8458 | 0.411173 | ||||||||
\(831\) | 17.3880 | 0.603182 | ||||||||
\(832\) | −0.284609 | −0.00986703 | ||||||||
\(833\) | 0.127503 | 0.00441772 | ||||||||
\(834\) | −5.42202 | −0.187749 | ||||||||
\(835\) | 78.0572 | 2.70128 | ||||||||
\(836\) | 0.246942 | 0.00854067 | ||||||||
\(837\) | 26.3968 | 0.912406 | ||||||||
\(838\) | −15.9757 | −0.551871 | ||||||||
\(839\) | 14.2876 | 0.493263 | 0.246631 | − | 0.969109i | \(-0.420676\pi\) | ||||
0.246631 | + | 0.969109i | \(0.420676\pi\) | |||||||
\(840\) | 7.23952 | 0.249787 | ||||||||
\(841\) | 1.68932 | 0.0582524 | ||||||||
\(842\) | 20.6924 | 0.713107 | ||||||||
\(843\) | −20.6238 | −0.710323 | ||||||||
\(844\) | −10.4901 | −0.361085 | ||||||||
\(845\) | 43.2152 | 1.48665 | ||||||||
\(846\) | −2.95837 | −0.101711 | ||||||||
\(847\) | −15.5986 | −0.535973 | ||||||||
\(848\) | 11.3478 | 0.389685 | ||||||||
\(849\) | −35.6096 | −1.22212 | ||||||||
\(850\) | −0.158872 | −0.00544925 | ||||||||
\(851\) | −9.28988 | −0.318453 | ||||||||
\(852\) | 17.0228 | 0.583191 | ||||||||
\(853\) | −9.43993 | −0.323217 | −0.161609 | − | 0.986855i | \(-0.551668\pi\) | ||||
−0.161609 | + | 0.986855i | \(0.551668\pi\) | |||||||
\(854\) | 16.9243 | 0.579137 | ||||||||
\(855\) | −2.37259 | −0.0811410 | ||||||||
\(856\) | −0.240696 | −0.00822683 | ||||||||
\(857\) | −35.2303 | −1.20344 | −0.601722 | − | 0.798706i | \(-0.705519\pi\) | ||||
−0.601722 | + | 0.798706i | \(0.705519\pi\) | |||||||
\(858\) | −0.104619 | −0.00357163 | ||||||||
\(859\) | 17.7354 | 0.605123 | 0.302561 | − | 0.953130i | \(-0.402158\pi\) | ||||
0.302561 | + | 0.953130i | \(0.402158\pi\) | |||||||
\(860\) | 5.14725 | 0.175520 | ||||||||
\(861\) | −4.34939 | −0.148227 | ||||||||
\(862\) | 33.2990 | 1.13417 | ||||||||
\(863\) | 56.5877 | 1.92627 | 0.963134 | − | 0.269023i | \(-0.0867009\pi\) | ||||
0.963134 | + | 0.269023i | \(0.0867009\pi\) | |||||||
\(864\) | 5.60998 | 0.190855 | ||||||||
\(865\) | 8.46674 | 0.287878 | ||||||||
\(866\) | 3.63773 | 0.123615 | ||||||||
\(867\) | 25.8060 | 0.876418 | ||||||||
\(868\) | 6.70815 | 0.227690 | ||||||||
\(869\) | 2.75167 | 0.0933440 | ||||||||
\(870\) | 28.1313 | 0.953742 | ||||||||
\(871\) | −0.0136717 | −0.000463248 0 | ||||||||
\(872\) | 8.40992 | 0.284796 | ||||||||
\(873\) | 5.76060 | 0.194967 | ||||||||
\(874\) | −1.01981 | −0.0344957 | ||||||||
\(875\) | −5.67329 | −0.191792 | ||||||||
\(876\) | 14.1006 | 0.476414 | ||||||||
\(877\) | −28.1482 | −0.950499 | −0.475249 | − | 0.879851i | \(-0.657642\pi\) | ||||
−0.475249 | + | 0.879851i | \(0.657642\pi\) | |||||||
\(878\) | −30.7511 | −1.03780 | ||||||||
\(879\) | 31.5635 | 1.06461 | ||||||||
\(880\) | 0.809994 | 0.0273049 | ||||||||
\(881\) | 54.8871 | 1.84919 | 0.924597 | − | 0.380946i | \(-0.124401\pi\) | ||||
0.924597 | + | 0.380946i | \(0.124401\pi\) | |||||||
\(882\) | 3.45489 | 0.116332 | ||||||||
\(883\) | 28.5953 | 0.962309 | 0.481155 | − | 0.876636i | \(-0.340218\pi\) | ||||
0.481155 | + | 0.876636i | \(0.340218\pi\) | |||||||
\(884\) | 0.00730516 | 0.000245699 0 | ||||||||
\(885\) | −36.2894 | −1.21986 | ||||||||
\(886\) | 15.9167 | 0.534733 | ||||||||
\(887\) | 41.7374 | 1.40141 | 0.700703 | − | 0.713453i | \(-0.252870\pi\) | ||||
0.700703 | + | 0.713453i | \(0.252870\pi\) | |||||||
\(888\) | 14.1026 | 0.473252 | ||||||||
\(889\) | 5.09500 | 0.170881 | ||||||||
\(890\) | −16.8717 | −0.565539 | ||||||||
\(891\) | 1.55694 | 0.0521594 | ||||||||
\(892\) | −11.4435 | −0.383156 | ||||||||
\(893\) | −4.33789 | −0.145162 | ||||||||
\(894\) | −5.59554 | −0.187143 | ||||||||
\(895\) | 46.7587 | 1.56297 | ||||||||
\(896\) | 1.42565 | 0.0476277 | ||||||||
\(897\) | 0.432053 | 0.0144258 | ||||||||
\(898\) | 1.59335 | 0.0531708 | ||||||||
\(899\) | 26.0665 | 0.869367 | ||||||||
\(900\) | −4.30486 | −0.143495 | ||||||||
\(901\) | −0.291268 | −0.00970355 | ||||||||
\(902\) | −0.486631 | −0.0162030 | ||||||||
\(903\) | 3.33019 | 0.110822 | ||||||||
\(904\) | −4.52840 | −0.150612 | ||||||||
\(905\) | −0.877370 | −0.0291648 | ||||||||
\(906\) | 25.9188 | 0.861094 | ||||||||
\(907\) | −11.6471 | −0.386735 | −0.193368 | − | 0.981126i | \(-0.561941\pi\) | ||||
−0.193368 | + | 0.981126i | \(0.561941\pi\) | |||||||
\(908\) | −11.2876 | −0.374593 | ||||||||
\(909\) | 1.77225 | 0.0587820 | ||||||||
\(910\) | 1.35728 | 0.0449934 | ||||||||
\(911\) | −6.13556 | −0.203280 | −0.101640 | − | 0.994821i | \(-0.532409\pi\) | ||||
−0.101640 | + | 0.994821i | \(0.532409\pi\) | |||||||
\(912\) | 1.54814 | 0.0512640 | ||||||||
\(913\) | 0.857491 | 0.0283788 | ||||||||
\(914\) | −20.2064 | −0.668368 | ||||||||
\(915\) | 60.2828 | 1.99289 | ||||||||
\(916\) | −2.10543 | −0.0695655 | ||||||||
\(917\) | −1.42565 | −0.0470792 | ||||||||
\(918\) | −0.143994 | −0.00475250 | ||||||||
\(919\) | −12.3695 | −0.408034 | −0.204017 | − | 0.978967i | \(-0.565400\pi\) | ||||
−0.204017 | + | 0.978967i | \(0.565400\pi\) | |||||||
\(920\) | −3.34509 | −0.110284 | ||||||||
\(921\) | 22.1270 | 0.729108 | ||||||||
\(922\) | −35.4263 | −1.16670 | ||||||||
\(923\) | 3.19146 | 0.105048 | ||||||||
\(924\) | 0.524054 | 0.0172401 | ||||||||
\(925\) | −57.5010 | −1.89062 | ||||||||
\(926\) | −12.8218 | −0.421351 | ||||||||
\(927\) | −8.74664 | −0.287277 | ||||||||
\(928\) | 5.53979 | 0.181853 | ||||||||
\(929\) | −9.44974 | −0.310036 | −0.155018 | − | 0.987912i | \(-0.549544\pi\) | ||||
−0.155018 | + | 0.987912i | \(0.549544\pi\) | |||||||
\(930\) | 23.8939 | 0.783510 | ||||||||
\(931\) | 5.06594 | 0.166030 | ||||||||
\(932\) | −20.9416 | −0.685966 | ||||||||
\(933\) | −31.8962 | −1.04424 | ||||||||
\(934\) | 0.0775715 | 0.00253822 | ||||||||
\(935\) | −0.0207904 | −0.000679920 0 | ||||||||
\(936\) | 0.197944 | 0.00647000 | ||||||||
\(937\) | −11.3421 | −0.370531 | −0.185266 | − | 0.982688i | \(-0.559315\pi\) | ||||
−0.185266 | + | 0.982688i | \(0.559315\pi\) | |||||||
\(938\) | 0.0684838 | 0.00223607 | ||||||||
\(939\) | −7.93357 | −0.258902 | ||||||||
\(940\) | −14.2287 | −0.464089 | ||||||||
\(941\) | −21.6547 | −0.705922 | −0.352961 | − | 0.935638i | \(-0.614825\pi\) | ||||
−0.352961 | + | 0.935638i | \(0.614825\pi\) | |||||||
\(942\) | −2.63874 | −0.0859749 | ||||||||
\(943\) | 2.00968 | 0.0654440 | ||||||||
\(944\) | −7.14634 | −0.232593 | ||||||||
\(945\) | −26.7536 | −0.870296 | ||||||||
\(946\) | 0.372598 | 0.0121142 | ||||||||
\(947\) | −41.1382 | −1.33681 | −0.668406 | − | 0.743796i | \(-0.733023\pi\) | ||||
−0.668406 | + | 0.743796i | \(0.733023\pi\) | |||||||
\(948\) | 17.2509 | 0.560282 | ||||||||
\(949\) | 2.64360 | 0.0858150 | ||||||||
\(950\) | −6.31228 | −0.204797 | ||||||||
\(951\) | 23.9531 | 0.776731 | ||||||||
\(952\) | −0.0365927 | −0.00118598 | ||||||||
\(953\) | −1.92653 | −0.0624065 | −0.0312033 | − | 0.999513i | \(-0.509934\pi\) | ||||
−0.0312033 | + | 0.999513i | \(0.509934\pi\) | |||||||
\(954\) | −7.89234 | −0.255524 | ||||||||
\(955\) | 1.62276 | 0.0525113 | ||||||||
\(956\) | 1.88750 | 0.0610463 | ||||||||
\(957\) | 2.03637 | 0.0658264 | ||||||||
\(958\) | 34.8965 | 1.12745 | ||||||||
\(959\) | −20.6681 | −0.667407 | ||||||||
\(960\) | 5.07805 | 0.163893 | ||||||||
\(961\) | −8.85993 | −0.285804 | ||||||||
\(962\) | 2.64398 | 0.0852454 | ||||||||
\(963\) | 0.167403 | 0.00539449 | ||||||||
\(964\) | 10.5965 | 0.341289 | ||||||||
\(965\) | 35.6075 | 1.14625 | ||||||||
\(966\) | −2.16422 | −0.0696328 | ||||||||
\(967\) | −41.1207 | −1.32235 | −0.661176 | − | 0.750231i | \(-0.729942\pi\) | ||||
−0.661176 | + | 0.750231i | \(0.729942\pi\) | |||||||
\(968\) | −10.9414 | −0.351669 | ||||||||
\(969\) | −0.0397367 | −0.00127653 | ||||||||
\(970\) | 27.7064 | 0.889600 | ||||||||
\(971\) | 51.0303 | 1.63764 | 0.818820 | − | 0.574050i | \(-0.194628\pi\) | ||||
0.818820 | + | 0.574050i | \(0.194628\pi\) | |||||||
\(972\) | −7.06913 | −0.226742 | ||||||||
\(973\) | 5.09197 | 0.163241 | ||||||||
\(974\) | 10.5321 | 0.337472 | ||||||||
\(975\) | 2.67425 | 0.0856445 | ||||||||
\(976\) | 11.8713 | 0.379990 | ||||||||
\(977\) | −7.47761 | −0.239230 | −0.119615 | − | 0.992820i | \(-0.538166\pi\) | ||||
−0.119615 | + | 0.992820i | \(0.538166\pi\) | |||||||
\(978\) | −2.61913 | −0.0837505 | ||||||||
\(979\) | −1.22130 | −0.0390330 | ||||||||
\(980\) | 16.6168 | 0.530804 | ||||||||
\(981\) | −5.84906 | −0.186746 | ||||||||
\(982\) | −5.87798 | −0.187574 | ||||||||
\(983\) | 33.2459 | 1.06038 | 0.530191 | − | 0.847879i | \(-0.322120\pi\) | ||||
0.530191 | + | 0.847879i | \(0.322120\pi\) | |||||||
\(984\) | −3.05081 | −0.0972562 | ||||||||
\(985\) | −78.9114 | −2.51433 | ||||||||
\(986\) | −0.142192 | −0.00452832 | ||||||||
\(987\) | −9.20576 | −0.293023 | ||||||||
\(988\) | 0.290248 | 0.00923401 | ||||||||
\(989\) | −1.53875 | −0.0489293 | ||||||||
\(990\) | −0.563347 | −0.0179044 | ||||||||
\(991\) | −61.0702 | −1.93996 | −0.969979 | − | 0.243188i | \(-0.921807\pi\) | ||||
−0.969979 | + | 0.243188i | \(0.921807\pi\) | |||||||
\(992\) | 4.70532 | 0.149394 | ||||||||
\(993\) | −22.9007 | −0.726730 | ||||||||
\(994\) | −15.9866 | −0.507063 | ||||||||
\(995\) | −12.4813 | −0.395685 | ||||||||
\(996\) | 5.37582 | 0.170339 | ||||||||
\(997\) | 41.4885 | 1.31395 | 0.656976 | − | 0.753911i | \(-0.271835\pi\) | ||||
0.656976 | + | 0.753911i | \(0.271835\pi\) | |||||||
\(998\) | −36.7786 | −1.16421 | ||||||||
\(999\) | −52.1161 | −1.64888 |
(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 | 6026.2.a.f.1.7 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.f.1.7 | ✓ | 20 | 1.1 | even | 1 | trivial |