Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6028,2,Mod(1,6028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6028, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6028.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6028 = 2^{2} \cdot 11 \cdot 137 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6028.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: | \(48.1338223384\) |
Analytic rank: | \(0\) |
Dimension: | \(29\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 6028.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.191141 | −0.110356 | −0.0551778 | − | 0.998477i | \(-0.517573\pi\) | ||||
−0.0551778 | + | 0.998477i | \(0.517573\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.65958 | −1.63662 | −0.818308 | − | 0.574780i | \(-0.805087\pi\) | ||||
−0.818308 | + | 0.574780i | \(0.805087\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.84676 | 1.07598 | 0.537988 | − | 0.842953i | \(-0.319185\pi\) | ||||
0.537988 | + | 0.842953i | \(0.319185\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.96346 | −0.987822 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.64616 | 0.733912 | 0.366956 | − | 0.930238i | \(-0.380400\pi\) | ||||
0.366956 | + | 0.930238i | \(0.380400\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.699498 | 0.180610 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.79088 | 0.919424 | 0.459712 | − | 0.888068i | \(-0.347953\pi\) | ||||
0.459712 | + | 0.888068i | \(0.347953\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.211026 | −0.0484127 | −0.0242064 | − | 0.999707i | \(-0.507706\pi\) | ||||
−0.0242064 | + | 0.999707i | \(0.507706\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.544135 | −0.118740 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.37500 | 1.32928 | 0.664640 | − | 0.747164i | \(-0.268585\pi\) | ||||
0.664640 | + | 0.747164i | \(0.268585\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.39255 | 1.67851 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.13987 | 0.219367 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.95225 | −0.362524 | −0.181262 | − | 0.983435i | \(-0.558018\pi\) | ||||
−0.181262 | + | 0.983435i | \(0.558018\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.76637 | −0.496855 | −0.248428 | − | 0.968650i | \(-0.579914\pi\) | ||||
−0.248428 | + | 0.968650i | \(0.579914\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.191141 | −0.0332735 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −10.4180 | −1.76096 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.91058 | −0.971693 | −0.485847 | − | 0.874044i | \(-0.661489\pi\) | ||||
−0.485847 | + | 0.874044i | \(0.661489\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.505791 | −0.0809913 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.71559 | −1.51732 | −0.758660 | − | 0.651486i | \(-0.774146\pi\) | ||||
−0.758660 | + | 0.651486i | \(0.774146\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.53429 | −1.14897 | −0.574484 | − | 0.818516i | \(-0.694797\pi\) | ||||
−0.574484 | + | 0.818516i | \(0.694797\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.8450 | 1.61668 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.2920 | 1.79297 | 0.896486 | − | 0.443073i | \(-0.146112\pi\) | ||||
0.896486 | + | 0.443073i | \(0.146112\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.10407 | 0.157724 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.724595 | −0.101464 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.38024 | 0.739032 | 0.369516 | − | 0.929224i | \(-0.379523\pi\) | ||||
0.369516 | + | 0.929224i | \(0.379523\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.65958 | −0.493458 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.0403359 | 0.00534261 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.674804 | 0.0878520 | 0.0439260 | − | 0.999035i | \(-0.486013\pi\) | ||||
0.0439260 | + | 0.999035i | \(0.486013\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.33389 | −0.682934 | −0.341467 | − | 0.939894i | \(-0.610924\pi\) | ||||
−0.341467 | + | 0.939894i | \(0.610924\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.43629 | −1.06287 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.68384 | −1.20113 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.6147 | −1.54113 | −0.770566 | − | 0.637360i | \(-0.780026\pi\) | ||||
−0.770566 | + | 0.637360i | \(0.780026\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.21853 | −0.146693 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.49942 | 0.415304 | 0.207652 | − | 0.978203i | \(-0.433418\pi\) | ||||
0.207652 | + | 0.978203i | \(0.433418\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.90946 | 0.340527 | 0.170263 | − | 0.985399i | \(-0.445538\pi\) | ||||
0.170263 | + | 0.985399i | \(0.445538\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.60416 | −0.185233 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.84676 | 0.324419 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.712964 | 0.0802147 | 0.0401074 | − | 0.999195i | \(-0.487230\pi\) | ||||
0.0401074 | + | 0.999195i | \(0.487230\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.67252 | 0.963613 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.7980 | −1.73406 | −0.867031 | − | 0.498255i | \(-0.833974\pi\) | ||||
−0.867031 | + | 0.498255i | \(0.833974\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.8730 | −1.50474 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.373156 | 0.0400065 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.85344 | 0.196464 | 0.0982321 | − | 0.995164i | \(-0.468681\pi\) | ||||
0.0982321 | + | 0.995164i | \(0.468681\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.53299 | 0.789672 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.528768 | 0.0548307 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.772268 | 0.0792330 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.5406 | 1.88252 | 0.941259 | − | 0.337686i | \(-0.109644\pi\) | ||||
0.941259 | + | 0.337686i | \(0.109644\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.96346 | −0.297839 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.4478 | 1.33810 | 0.669052 | − | 0.743216i | \(-0.266700\pi\) | ||||
0.669052 | + | 0.743216i | \(0.266700\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.8383 | −1.36353 | −0.681765 | − | 0.731571i | \(-0.738787\pi\) | ||||
−0.681765 | + | 0.731571i | \(0.738787\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.99131 | 0.194332 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.10269 | 0.106601 | 0.0533006 | − | 0.998579i | \(-0.483026\pi\) | ||||
0.0533006 | + | 0.998579i | \(0.483026\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.29086 | 0.794121 | 0.397060 | − | 0.917792i | \(-0.370030\pi\) | ||||
0.397060 | + | 0.917792i | \(0.370030\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.12976 | 0.107232 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.72302 | 0.350232 | 0.175116 | − | 0.984548i | \(-0.443970\pi\) | ||||
0.175116 | + | 0.984548i | \(0.443970\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −23.3298 | −2.17552 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.84180 | −0.724974 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.7917 | 0.989278 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.85705 | 0.167445 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.4153 | −1.11046 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.32564 | 0.827517 | 0.413758 | − | 0.910387i | \(-0.364216\pi\) | ||||
0.413758 | + | 0.910387i | \(0.364216\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.44012 | 0.126795 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.6262 | 1.45264 | 0.726318 | − | 0.687359i | \(-0.241230\pi\) | ||||
0.726318 | + | 0.687359i | \(0.241230\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.600742 | −0.0520909 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.17143 | −0.359020 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.00000 | 0.0854358 | ||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.57515 | 0.303241 | 0.151620 | − | 0.988439i | \(-0.451551\pi\) | ||||
0.151620 | + | 0.988439i | \(0.451551\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.34951 | −0.197864 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.64616 | 0.221283 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.14442 | 0.593312 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.211033 | −0.0174057 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.84531 | 0.642713 | 0.321356 | − | 0.946958i | \(-0.395861\pi\) | ||||
0.321356 | + | 0.946958i | \(0.395861\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.1896 | 0.991979 | 0.495989 | − | 0.868329i | \(-0.334805\pi\) | ||||
0.495989 | + | 0.868329i | \(0.334805\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.2341 | −0.908227 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.1238 | 0.813161 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.9694 | 1.35431 | 0.677154 | − | 0.735842i | \(-0.263213\pi\) | ||||
0.677154 | + | 0.735842i | \(0.263213\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.02839 | −0.0815563 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.1481 | 1.43027 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.337480 | −0.0264335 | −0.0132167 | − | 0.999913i | \(-0.504207\pi\) | ||||
−0.0132167 | + | 0.999913i | \(0.504207\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.699498 | 0.0544558 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.251999 | 0.0195003 | 0.00975014 | − | 0.999952i | \(-0.496896\pi\) | ||||
0.00975014 | + | 0.999952i | \(0.496896\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.99785 | −0.461373 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.625369 | 0.0478231 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.1881 | 1.00267 | 0.501337 | − | 0.865252i | \(-0.332842\pi\) | ||||
0.501337 | + | 0.865252i | \(0.332842\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 23.8916 | 1.80604 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.128983 | −0.00969496 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 24.0856 | 1.80024 | 0.900120 | − | 0.435643i | \(-0.143479\pi\) | ||||
0.900120 | + | 0.435643i | \(0.143479\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.0171 | −1.11621 | −0.558106 | − | 0.829770i | \(-0.688472\pi\) | ||||
−0.558106 | + | 0.829770i | \(0.688472\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.01953 | 0.0753656 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 21.6303 | 1.59029 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.79088 | 0.277217 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.24493 | 0.236034 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.10029 | 0.441401 | 0.220701 | − | 0.975342i | \(-0.429166\pi\) | ||||
0.220701 | + | 0.975342i | \(0.429166\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.5020 | 0.755947 | 0.377973 | − | 0.925816i | \(-0.376621\pi\) | ||||
0.377973 | + | 0.925816i | \(0.376621\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.85098 | 0.132552 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.85868 | 0.274920 | 0.137460 | − | 0.990507i | \(-0.456106\pi\) | ||||
0.137460 | + | 0.990507i | \(0.456106\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.33355 | −0.307197 | −0.153599 | − | 0.988133i | \(-0.549086\pi\) | ||||
−0.153599 | + | 0.988133i | \(0.549086\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.41119 | 0.170072 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.55759 | −0.390067 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 35.5550 | 2.48327 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −18.8921 | −1.31309 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.211026 | −0.0145970 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.9057 | −1.02615 | −0.513074 | − | 0.858345i | \(-0.671493\pi\) | ||||
−0.513074 | + | 0.858345i | \(0.671493\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.668884 | −0.0458312 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 27.5724 | 1.88042 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.87521 | −0.534604 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.556119 | −0.0375790 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.0313 | 0.674776 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.8953 | −1.19836 | −0.599179 | − | 0.800615i | \(-0.704506\pi\) | ||||
−0.599179 | + | 0.800615i | \(0.704506\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −24.8710 | −1.65807 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.3987 | −1.22117 | −0.610583 | − | 0.791953i | \(-0.709065\pi\) | ||||
−0.610583 | + | 0.791953i | \(0.709065\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.6620 | 0.836728 | 0.418364 | − | 0.908280i | \(-0.362604\pi\) | ||||
0.418364 | + | 0.908280i | \(0.362604\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.544135 | −0.0358014 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.7145 | 1.22603 | 0.613014 | − | 0.790072i | \(-0.289957\pi\) | ||||
0.613014 | + | 0.790072i | \(0.289957\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −44.9836 | −2.93440 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.136277 | −0.00885214 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.91435 | 0.123829 | 0.0619146 | − | 0.998081i | \(-0.480279\pi\) | ||||
0.0619146 | + | 0.998081i | \(0.480279\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.2997 | 1.43645 | 0.718226 | − | 0.695810i | \(-0.244954\pi\) | ||||
0.718226 | + | 0.695810i | \(0.244954\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.07727 | −0.325707 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.04043 | −0.258133 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.558409 | −0.0355307 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.01966 | 0.191363 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.62088 | 0.102309 | 0.0511546 | − | 0.998691i | \(-0.483710\pi\) | ||||
0.0511546 | + | 0.998691i | \(0.483710\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.37500 | 0.400793 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.65171 | 0.166057 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.37871 | 0.397893 | 0.198946 | − | 0.980010i | \(-0.436248\pi\) | ||||
0.198946 | + | 0.980010i | \(0.436248\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.8260 | −1.04552 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.78542 | 0.358109 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.257630 | 0.0158862 | 0.00794308 | − | 0.999968i | \(-0.497472\pi\) | ||||
0.00794308 | + | 0.999968i | \(0.497472\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −19.6894 | −1.20951 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.354269 | −0.0216809 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.8603 | −1.02799 | −0.513996 | − | 0.857792i | \(-0.671835\pi\) | ||||
−0.513996 | + | 0.857792i | \(0.671835\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.26050 | −0.441044 | −0.220522 | − | 0.975382i | \(-0.570776\pi\) | ||||
−0.220522 | + | 0.975382i | \(0.570776\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.43987 | −0.0871447 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.39255 | 0.506090 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.5461 | −0.934072 | −0.467036 | − | 0.884238i | \(-0.654678\pi\) | ||||
−0.467036 | + | 0.884238i | \(0.654678\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.19805 | 0.490804 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.48160 | 0.327005 | 0.163503 | − | 0.986543i | \(-0.447721\pi\) | ||||
0.163503 | + | 0.986543i | \(0.447721\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31.8976 | 1.89612 | 0.948058 | − | 0.318098i | \(-0.103044\pi\) | ||||
0.948058 | + | 0.318098i | \(0.103044\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.147612 | −0.00874380 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −27.6580 | −1.63260 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.62922 | −0.154660 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.54389 | −0.207746 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.40112 | −0.549219 | −0.274610 | − | 0.961556i | \(-0.588549\pi\) | ||||
−0.274610 | + | 0.961556i | \(0.588549\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.46950 | −0.143780 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.13987 | 0.0661417 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.8693 | 0.975574 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.4484 | −1.23626 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.57043 | −0.147667 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19.5198 | 1.11770 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.40735 | 0.194468 | 0.0972339 | − | 0.995262i | \(-0.469000\pi\) | ||||
0.0972339 | + | 0.995262i | \(0.469000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.64508 | 0.150473 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.1348 | 1.31186 | 0.655928 | − | 0.754823i | \(-0.272277\pi\) | ||||
0.655928 | + | 0.754823i | \(0.272277\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.00793 | 0.170018 | 0.0850092 | − | 0.996380i | \(-0.472908\pi\) | ||||
0.0850092 | + | 0.996380i | \(0.472908\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 30.8733 | 1.73951 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.7809 | −1.05484 | −0.527419 | − | 0.849605i | \(-0.676840\pi\) | ||||
−0.527419 | + | 0.849605i | \(0.676840\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.95225 | −0.109305 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.210770 | −0.0117640 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.799975 | −0.0445118 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.2080 | 1.23188 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.58473 | −0.0876357 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 34.9924 | 1.92919 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.1658 | 1.38324 | 0.691618 | − | 0.722264i | \(-0.256898\pi\) | ||||
0.691618 | + | 0.722264i | \(0.256898\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 17.5158 | 0.959860 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 46.1646 | 2.52224 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.4772 | 0.679676 | 0.339838 | − | 0.940484i | \(-0.389628\pi\) | ||||
0.339838 | + | 0.940484i | \(0.389628\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.711624 | −0.0386501 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.76637 | −0.149807 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.7843 | −0.906269 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.45930 | 0.240081 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.49616 | −0.348732 | −0.174366 | − | 0.984681i | \(-0.555788\pi\) | ||||
−0.174366 | + | 0.984681i | \(0.555788\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.7997 | 1.27397 | 0.636983 | − | 0.770878i | \(-0.280182\pi\) | ||||
0.636983 | + | 0.770878i | \(0.280182\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.01626 | 0.160996 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.41945 | −0.448122 | −0.224061 | − | 0.974575i | \(-0.571932\pi\) | ||||
−0.224061 | + | 0.974575i | \(0.571932\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.8064 | −0.679694 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.06275 | −0.109172 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.1786 | 1.17054 | 0.585271 | − | 0.810838i | \(-0.300988\pi\) | ||||
0.585271 | + | 0.810838i | \(0.300988\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9555 | −0.997656 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.191141 | −0.0100323 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.6474 | −0.557311 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.3739 | −0.541516 | −0.270758 | − | 0.962647i | \(-0.587274\pi\) | ||||
−0.270758 | + | 0.962647i | \(0.587274\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 28.7918 | 1.49884 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.3163 | 0.795181 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.49700 | −0.439958 | −0.219979 | − | 0.975505i | \(-0.570599\pi\) | ||||
−0.219979 | + | 0.975505i | \(0.570599\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.37308 | 0.122545 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.16596 | −0.266061 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.7991 | 1.63341 | 0.816704 | − | 0.577057i | \(-0.195799\pi\) | ||||
0.816704 | + | 0.577057i | \(0.195799\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.78252 | −0.0913211 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.2404 | 0.574358 | 0.287179 | − | 0.957877i | \(-0.407283\pi\) | ||||
0.287179 | + | 0.957877i | \(0.407283\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.4180 | −0.530949 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 22.3276 | 1.13498 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.9964 | 1.11526 | 0.557630 | − | 0.830090i | \(-0.311711\pi\) | ||||
0.557630 | + | 0.830090i | \(0.311711\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.1669 | 1.22217 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.17795 | −0.160306 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.60915 | −0.131281 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.3947 | −1.17414 | −0.587072 | − | 0.809534i | \(-0.699720\pi\) | ||||
−0.587072 | + | 0.809534i | \(0.699720\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.114827 | 0.00574852 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.57728 | 0.178641 | 0.0893205 | − | 0.996003i | \(-0.471530\pi\) | ||||
0.0893205 | + | 0.996003i | \(0.471530\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.32026 | −0.364648 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −31.7378 | −1.57706 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.91058 | −0.292977 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.6237 | −0.624202 | −0.312101 | − | 0.950049i | \(-0.601033\pi\) | ||||
−0.312101 | + | 0.950049i | \(0.601033\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.191141 | −0.00942831 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.92101 | 0.0945266 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 57.8143 | 2.83799 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.683360 | −0.0334643 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.0823 | 0.687966 | 0.343983 | − | 0.938976i | \(-0.388224\pi\) | ||||
0.343983 | + | 0.938976i | \(0.388224\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.9202 | 1.31201 | 0.656004 | − | 0.754757i | \(-0.272245\pi\) | ||||
0.656004 | + | 0.754757i | \(0.272245\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −36.4269 | −1.77114 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 31.8152 | 1.54326 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.1843 | −0.734821 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.505791 | −0.0244198 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.7618 | −1.14457 | −0.572284 | − | 0.820056i | \(-0.693942\pi\) | ||||
−0.572284 | + | 0.820056i | \(0.693942\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.2300 | 1.02025 | 0.510125 | − | 0.860101i | \(-0.329599\pi\) | ||||
0.510125 | + | 0.860101i | \(0.329599\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.36559 | −0.0654753 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.34529 | −0.0643540 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.5133 | −0.788139 | −0.394069 | − | 0.919081i | \(-0.628933\pi\) | ||||
−0.394069 | + | 0.919081i | \(0.628933\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.27186 | −0.155803 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.90666 | 0.185611 | 0.0928054 | − | 0.995684i | \(-0.470417\pi\) | ||||
0.0928054 | + | 0.995684i | \(0.470417\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.78281 | −0.321536 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.49956 | −0.0709270 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.2784 | 1.00419 | 0.502095 | − | 0.864812i | \(-0.332563\pi\) | ||||
0.502095 | + | 0.864812i | \(0.332563\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.71559 | −0.457489 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.32995 | −0.109470 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −27.5676 | −1.29239 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.4251 | 0.908668 | 0.454334 | − | 0.890831i | \(-0.349877\pi\) | ||||
0.454334 | + | 0.890831i | \(0.349877\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.32109 | 0.201691 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.47388 | −0.254944 | −0.127472 | − | 0.991842i | \(-0.540686\pi\) | ||||
−0.127472 | + | 0.991842i | \(0.540686\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.1130 | −1.67831 | −0.839156 | − | 0.543890i | \(-0.816951\pi\) | ||||
−0.839156 | + | 0.543890i | \(0.816951\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.93507 | −0.0897368 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.1946 | 0.888219 | 0.444110 | − | 0.895972i | \(-0.353520\pi\) | ||||
0.444110 | + | 0.895972i | \(0.353520\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −35.9111 | −1.65822 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.24356 | −0.149455 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.53429 | −0.346427 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.77105 | −0.0812612 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −15.9441 | −0.730032 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.14526 | −0.0523281 | −0.0261640 | − | 0.999658i | \(-0.508329\pi\) | ||||
−0.0261640 | + | 0.999658i | \(0.508329\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.6403 | −0.713138 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.46886 | −0.157839 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −67.8510 | −3.08096 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.5610 | 1.47548 | 0.737739 | − | 0.675086i | \(-0.235893\pi\) | ||||
0.737739 | + | 0.675086i | \(0.235893\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.0645064 | 0.00291708 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.129597 | 0.00584862 | 0.00292431 | − | 0.999996i | \(-0.499069\pi\) | ||||
0.00292431 | + | 0.999996i | \(0.499069\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.40075 | −0.333313 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10.8450 | 0.487449 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.96202 | 0.446857 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.3346 | −1.35796 | −0.678982 | − | 0.734155i | \(-0.737579\pi\) | ||||
−0.678982 | + | 0.734155i | \(0.737579\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.0481675 | −0.00215196 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.62787 | −0.161759 | −0.0808794 | − | 0.996724i | \(-0.525773\pi\) | ||||
−0.0808794 | + | 0.996724i | \(0.525773\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −49.2133 | −2.18996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.14644 | 0.0509151 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.2882 | −0.544667 | −0.272333 | − | 0.962203i | \(-0.587795\pi\) | ||||
−0.272333 | + | 0.962203i | \(0.587795\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.28255 | 0.366398 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.240541 | −0.0106202 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 50.6425 | 2.23157 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.2920 | 0.540601 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.52080 | −0.110651 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.02854 | 0.176493 | 0.0882467 | − | 0.996099i | \(-0.471874\pi\) | ||||
0.0882467 | + | 0.996099i | \(0.471874\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.7789 | −1.38960 | −0.694798 | − | 0.719205i | \(-0.744506\pi\) | ||||
−0.694798 | + | 0.719205i | \(0.744506\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.56668 | −0.199306 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.4870 | −0.456820 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.6406 | 0.766984 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.99976 | −0.0867821 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −25.7090 | −1.11358 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.03539 | −0.174465 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.60375 | −0.198666 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.10407 | 0.0475555 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.7235 | 0.590018 | 0.295009 | − | 0.955495i | \(-0.404677\pi\) | ||||
0.295009 | + | 0.955495i | \(0.404677\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.87039 | 0.123180 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −30.3411 | −1.29967 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.56232 | −0.0668000 | −0.0334000 | − | 0.999442i | \(-0.510634\pi\) | ||||
−0.0334000 | + | 0.999442i | \(0.510634\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.8068 | 0.674617 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.411976 | 0.0175508 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.02964 | 0.0863091 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.13444 | −0.175497 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.03434 | 0.170941 | 0.0854703 | − | 0.996341i | \(-0.472761\pi\) | ||||
0.0854703 | + | 0.996341i | \(0.472761\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.9369 | −0.843242 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.724595 | −0.0305924 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.04172 | −0.212483 | −0.106242 | − | 0.994340i | \(-0.533882\pi\) | ||||
−0.106242 | + | 0.994340i | \(0.533882\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.6247 | −0.573196 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 24.6886 | 1.03682 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.97227 | 0.418059 | 0.209030 | − | 0.977909i | \(-0.432969\pi\) | ||||
0.209030 | + | 0.977909i | \(0.432969\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.0679 | −0.463176 | −0.231588 | − | 0.972814i | \(-0.574392\pi\) | ||||
−0.231588 | + | 0.972814i | \(0.574392\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.16602 | −0.0487111 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 53.5025 | 2.23121 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.3322 | −1.55416 | −0.777081 | − | 0.629401i | \(-0.783300\pi\) | ||||
−0.777081 | + | 0.629401i | \(0.783300\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.00736 | −0.0834230 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −44.9733 | −1.86581 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.38024 | 0.222827 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 28.6977 | 1.18650 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.3727 | 1.08852 | 0.544259 | − | 0.838917i | \(-0.316811\pi\) | ||||
0.544259 | + | 0.838917i | \(0.316811\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.583777 | 0.0240541 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.737554 | −0.0303389 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.1058 | 0.743517 | 0.371758 | − | 0.928329i | \(-0.378755\pi\) | ||||
0.371758 | + | 0.928329i | \(0.378755\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −39.4933 | −1.61907 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.828321 | 0.0339009 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.3505 | 0.586344 | 0.293172 | − | 0.956060i | \(-0.405289\pi\) | ||||
0.293172 | + | 0.956060i | \(0.405289\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.7363 | 0.519525 | 0.259762 | − | 0.965673i | \(-0.416356\pi\) | ||||
0.259762 | + | 0.965673i | \(0.416356\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 37.3832 | 1.52236 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.65958 | −0.148783 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.6628 | 1.24456 | 0.622282 | − | 0.782794i | \(-0.286206\pi\) | ||||
0.622282 | + | 0.782794i | \(0.286206\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.06229 | 0.0430460 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.5266 | 1.31588 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.1110 | 1.29695 | 0.648476 | − | 0.761235i | \(-0.275407\pi\) | ||||
0.648476 | + | 0.761235i | \(0.275407\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.79604 | −0.274043 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.45258 | 0.380547 | 0.190273 | − | 0.981731i | \(-0.439063\pi\) | ||||
0.190273 | + | 0.981731i | \(0.439063\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.8478 | 1.23988 | 0.619939 | − | 0.784650i | \(-0.287157\pi\) | ||||
0.619939 | + | 0.784650i | \(0.287157\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.26664 | 0.291600 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.27630 | 0.211391 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.47212 | 0.138885 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.0403359 | 0.00161086 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22.4063 | −0.893398 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.99764 | 0.398000 | 0.199000 | − | 0.980000i | \(-0.436231\pi\) | ||||
0.199000 | + | 0.980000i | \(0.436231\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.84909 | 0.113241 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −34.1280 | −1.35433 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.92154 | 0.115756 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.3704 | −0.410247 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.67922 | −0.0663251 | −0.0331625 | − | 0.999450i | \(-0.510558\pi\) | ||||
−0.0331625 | + | 0.999450i | \(0.510558\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.23418 | 0.166980 | 0.0834899 | − | 0.996509i | \(-0.473393\pi\) | ||||
0.0834899 | + | 0.996509i | \(0.473393\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.27022 | −0.207515 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.0959 | 0.593481 | 0.296741 | − | 0.954958i | \(-0.404100\pi\) | ||||
0.296741 | + | 0.954958i | \(0.404100\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.674804 | 0.0264884 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.50528 | 0.0589965 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.2754 | 0.441242 | 0.220621 | − | 0.975360i | \(-0.429192\pi\) | ||||
0.220621 | + | 0.975360i | \(0.429192\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −60.8449 | −2.37741 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.62209 | −0.336380 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.2708 | 0.711730 | 0.355865 | − | 0.934537i | \(-0.384186\pi\) | ||||
0.355865 | + | 0.934537i | \(0.384186\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.2041 | 0.785847 | 0.392924 | − | 0.919571i | \(-0.371464\pi\) | ||||
0.392924 | + | 0.919571i | \(0.371464\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.91739 | −0.0744653 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.19846 | 0.0852528 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.4456 | −0.481895 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.42054 | 0.132246 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.33389 | −0.205912 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.3590 | −0.823328 | −0.411664 | − | 0.911336i | \(-0.635052\pi\) | ||||
−0.411664 | + | 0.911336i | \(0.635052\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.56637 | 0.368210 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 35.3233 | 1.35758 | 0.678792 | − | 0.734331i | \(-0.262504\pi\) | ||||
0.678792 | + | 0.734331i | \(0.262504\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 52.7809 | 2.02554 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.51676 | 0.134762 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.07478 | −0.194181 | −0.0970905 | − | 0.995276i | \(-0.530954\pi\) | ||||
−0.0970905 | + | 0.995276i | \(0.530954\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.65958 | −0.139825 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.42023 | −0.0923375 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.2370 | 0.542385 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.74824 | 0.180631 | 0.0903157 | − | 0.995913i | \(-0.471212\pi\) | ||||
0.0903157 | + | 0.995913i | \(0.471212\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.43629 | −0.320468 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.0836 | −0.496288 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −36.8307 | −1.39506 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.57712 | −0.135299 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.9423 | −1.47083 | −0.735416 | − | 0.677616i | \(-0.763013\pi\) | ||||
−0.735416 | + | 0.677616i | \(0.763013\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.24729 | 0.0470423 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.59823 | 0.323828 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 38.2827 | 1.43977 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −51.2779 | −1.92578 | −0.962890 | − | 0.269893i | \(-0.913012\pi\) | ||||
−0.962890 | + | 0.269893i | \(0.913012\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.11284 | −0.0792378 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.6356 | −0.660459 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.68384 | −0.362155 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.365913 | −0.0136653 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.5913 | 0.618749 | 0.309375 | − | 0.950940i | \(-0.399880\pi\) | ||||
0.309375 | + | 0.950940i | \(0.399880\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −39.3944 | −1.46712 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.26241 | −0.158521 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16.3843 | −0.608499 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.7610 | 1.25213 | 0.626063 | − | 0.779773i | \(-0.284665\pi\) | ||||
0.626063 | + | 0.779773i | \(0.284665\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.0471 | −0.927670 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −28.5616 | −1.05639 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.1316 | −0.928256 | −0.464128 | − | 0.885768i | \(-0.653632\pi\) | ||||
−0.464128 | + | 0.885768i | \(0.653632\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.772293 | 0.0284865 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.6147 | −0.464669 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.55248 | −0.204251 | −0.102126 | − | 0.994771i | \(-0.532564\pi\) | ||||
−0.102126 | + | 0.994771i | \(0.532564\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.106735 | 0.00392101 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.7155 | 0.796664 | 0.398332 | − | 0.917241i | \(-0.369589\pi\) | ||||
0.398332 | + | 0.917241i | \(0.369589\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −28.7106 | −1.05187 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 46.8170 | 1.71294 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.13910 | 0.114700 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.44058 | −0.0890580 | −0.0445290 | − | 0.999008i | \(-0.514179\pi\) | ||||
−0.0445290 | + | 0.999008i | \(0.514179\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.309818 | −0.0112904 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −44.6090 | −1.62349 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.1738 | −1.38745 | −0.693726 | − | 0.720239i | \(-0.744032\pi\) | ||||
−0.693726 | + | 0.720239i | \(0.744032\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.21853 | −0.0442297 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.2672 | −1.31469 | −0.657343 | − | 0.753592i | \(-0.728320\pi\) | ||||
−0.657343 | + | 0.753592i | \(0.728320\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.6021 | 0.854455 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 41.1123 | 1.48642 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.78564 | 0.0644757 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.6865 | −0.926277 | −0.463139 | − | 0.886286i | \(-0.653277\pi\) | ||||
−0.463139 | + | 0.886286i | \(0.653277\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.21924 | −0.0439097 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.6836 | −0.743936 | −0.371968 | − | 0.928246i | \(-0.621317\pi\) | ||||
−0.371968 | + | 0.928246i | \(0.621317\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −23.2169 | −0.833976 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.21615 | 0.115379 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.05024 | 0.0734576 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.49942 | 0.125219 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.22530 | −0.0795258 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −62.1010 | −2.21648 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.7277 | −0.917092 | −0.458546 | − | 0.888671i | \(-0.651630\pi\) | ||||
−0.458546 | + | 0.888671i | \(0.651630\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.0492438 | −0.00175313 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.5986 | 0.376842 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.1143 | −0.501214 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.76346 | 0.133476 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.0793 | 0.357026 | 0.178513 | − | 0.983938i | \(-0.442871\pi\) | ||||
0.178513 | + | 0.983938i | \(0.442871\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 46.5975 | 1.64850 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.49260 | −0.194072 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.90946 | 0.102673 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −66.4146 | −2.34081 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.22271 | 0.113445 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 52.3577 | 1.84080 | 0.920400 | − | 0.390978i | \(-0.127863\pi\) | ||||
0.920400 | + | 0.390978i | \(0.127863\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.4110 | 1.27856 | 0.639282 | − | 0.768972i | \(-0.279232\pi\) | ||||
0.639282 | + | 0.768972i | \(0.279232\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.38778 | 0.0486717 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.23504 | 0.0432614 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.58993 | 0.0556247 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −22.3237 | −0.780055 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.9504 | −1.08018 | −0.540088 | − | 0.841608i | \(-0.681609\pi\) | ||||
−0.540088 | + | 0.841608i | \(0.681609\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.21942 | −0.216795 | −0.108398 | − | 0.994108i | \(-0.534572\pi\) | ||||
−0.108398 | + | 0.994108i | \(0.534572\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.60416 | −0.0558498 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42.5570 | 1.47985 | 0.739925 | − | 0.672689i | \(-0.234861\pi\) | ||||
0.739925 | + | 0.672689i | \(0.234861\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 48.9373 | 1.69966 | 0.849832 | − | 0.527053i | \(-0.176703\pi\) | ||||
0.849832 | + | 0.527053i | \(0.176703\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.97150 | 0.103080 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.18539 | 0.145015 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.922212 | −0.0319145 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.15329 | −0.108994 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.3258 | 0.529105 | 0.264552 | − | 0.964371i | \(-0.414776\pi\) | ||||
0.264552 | + | 0.964371i | \(0.414776\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.1887 | −0.868577 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.04776 | −0.0360868 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 21.9496 | 0.755090 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.84676 | 0.0978160 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.09695 | −0.209247 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −37.6799 | −1.29165 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.0565 | 1.47423 | 0.737113 | − | 0.675770i | \(-0.236189\pi\) | ||||
0.737113 | + | 0.675770i | \(0.236189\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.28859 | −0.0782681 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 52.7997 | 1.80360 | 0.901801 | − | 0.432152i | \(-0.142245\pi\) | ||||
0.901801 | + | 0.432152i | \(0.142245\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.8128 | 1.39251 | 0.696257 | − | 0.717793i | \(-0.254847\pi\) | ||||
0.696257 | + | 0.717793i | \(0.254847\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.28659 | 0.180167 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.8251 | −0.538694 | −0.269347 | − | 0.963043i | \(-0.586808\pi\) | ||||
−0.269347 | + | 0.963043i | \(0.586808\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −48.2630 | −1.64099 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.502552 | 0.0170676 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.712964 | 0.0241856 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −33.3805 | −1.13106 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −54.9446 | −1.85959 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −35.3435 | −1.19483 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.7156 | −1.03719 | −0.518596 | − | 0.855020i | \(-0.673545\pi\) | ||||
−0.518596 | + | 0.855020i | \(0.673545\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.79694 | 0.0606094 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.1326 | 0.476138 | 0.238069 | − | 0.971248i | \(-0.423486\pi\) | ||||
0.238069 | + | 0.971248i | \(0.423486\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.9330 | −0.906368 | −0.453184 | − | 0.891417i | \(-0.649712\pi\) | ||||
−0.453184 | + | 0.891417i | \(0.649712\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.472024 | 0.0158669 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.9362 | −0.434354 | −0.217177 | − | 0.976132i | \(-0.569685\pi\) | ||||
−0.217177 | + | 0.976132i | \(0.569685\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 26.5479 | 0.890388 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.67252 | 0.290540 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.59393 | −0.0868026 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −88.1431 | −2.94630 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.22441 | −0.107660 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.40065 | 0.180122 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.3958 | 0.679484 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.09967 | 0.136428 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 54.9563 | 1.82681 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.4277 | −0.445861 | −0.222930 | − | 0.974834i | \(-0.571562\pi\) | ||||
−0.222930 | + | 0.974834i | \(0.571562\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −39.8520 | −1.32181 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.16499 | 0.104861 | 0.0524303 | − | 0.998625i | \(-0.483303\pi\) | ||||
0.0524303 | + | 0.998625i | \(0.483303\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.7980 | −0.522839 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.73104 | −0.123344 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 47.3308 | 1.56300 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.2242 | 0.766096 | 0.383048 | − | 0.923728i | \(-0.374874\pi\) | ||||
0.383048 | + | 0.923728i | \(0.374874\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.651286 | −0.0214606 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.26001 | 0.304797 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −49.6048 | −1.63100 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 41.0094 | 1.34692 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −38.8402 | −1.27431 | −0.637153 | − | 0.770738i | \(-0.719888\pi\) | ||||
−0.637153 | + | 0.770738i | \(0.719888\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.232987 | −0.00763584 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.42203 | −0.144771 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.8730 | −0.453697 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.8486 | 1.23646 | 0.618230 | − | 0.785997i | \(-0.287850\pi\) | ||||
0.618230 | + | 0.785997i | \(0.287850\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.574941 | −0.0187625 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.3035 | 1.02046 | 0.510232 | − | 0.860037i | \(-0.329559\pi\) | ||||
0.510232 | + | 0.860037i | \(0.329559\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −61.9369 | −2.01694 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −11.8751 | −0.386297 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 49.9866 | 1.62435 | 0.812173 | − | 0.583417i | \(-0.198285\pi\) | ||||
0.812173 | + | 0.583417i | \(0.198285\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.69889 | 0.249917 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.58980 | 0.116407 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32.2830 | −1.04575 | −0.522875 | − | 0.852410i | \(-0.675140\pi\) | ||||
−0.522875 | + | 0.852410i | \(0.675140\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.3245 | −0.722404 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.373156 | 0.0120624 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.84676 | 0.0919268 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.3472 | −0.753135 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.26779 | −0.105303 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −38.4328 | −1.23719 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.3221 | −0.685673 | −0.342836 | − | 0.939395i | \(-0.611388\pi\) | ||||
−0.342836 | + | 0.939395i | \(0.611388\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.152908 | 0.00491213 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.24615 | −0.168357 | −0.0841785 | − | 0.996451i | \(-0.526827\pi\) | ||||
−0.0841785 | + | 0.996451i | \(0.526827\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.1776 | 0.326279 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.24487 | −0.135945 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.8270 | −0.378380 | −0.189190 | − | 0.981941i | \(-0.560586\pi\) | ||||
−0.189190 | + | 0.981941i | \(0.560586\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.85344 | 0.0592362 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −24.5697 | −0.784450 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.0570 | 1.02246 | 0.511230 | − | 0.859444i | \(-0.329190\pi\) | ||||
0.511230 | + | 0.859444i | \(0.329190\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.1212 | −0.449938 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.68850 | −0.212897 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −48.0311 | −1.52730 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.2771 | 0.866484 | 0.433242 | − | 0.901278i | \(-0.357369\pi\) | ||||
0.433242 | + | 0.901278i | \(0.357369\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.81022 | −0.152648 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.8590 | 0.502764 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −62.2844 | −1.97257 | −0.986283 | − | 0.165062i | \(-0.947218\pi\) | ||||
−0.986283 | + | 0.165062i | \(0.947218\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.73726 | −0.213158 |
(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 | 6028.2.a.f.1.12 | ✓ | 29 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6028.2.a.f.1.12 | ✓ | 29 | 1.1 | even | 1 | trivial |