Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1258372982\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} - 19 x^{12} + 36 x^{11} + 134 x^{10} - 237 x^{9} - 438 x^{8} + 716 x^{7} + 662 x^{6} - 1007 x^{5} - 384 x^{4} + 579 x^{3} + 44 x^{2} - 112 x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 861) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.442251\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.442251 | −0.312718 | −0.156359 | − | 0.987700i | \(-0.549976\pi\) | ||||
−0.156359 | + | 0.987700i | \(0.549976\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.80441 | −0.902207 | ||||||||
\(5\) | −4.29274 | −1.91977 | −0.959887 | − | 0.280387i | \(-0.909537\pi\) | ||||
−0.959887 | + | 0.280387i | \(0.909537\pi\) | |||||||
\(6\) | −0.442251 | −0.180548 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.68250 | 0.594855 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.89847 | 0.600349 | ||||||||
\(11\) | −2.21212 | −0.666979 | −0.333489 | − | 0.942754i | \(-0.608226\pi\) | ||||
−0.333489 | + | 0.942754i | \(0.608226\pi\) | |||||||
\(12\) | −1.80441 | −0.520890 | ||||||||
\(13\) | −3.11687 | −0.864463 | −0.432231 | − | 0.901763i | \(-0.642274\pi\) | ||||
−0.432231 | + | 0.901763i | \(0.642274\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.29274 | −1.10838 | ||||||||
\(16\) | 2.86474 | 0.716185 | ||||||||
\(17\) | −6.92396 | −1.67931 | −0.839654 | − | 0.543122i | \(-0.817242\pi\) | ||||
−0.839654 | + | 0.543122i | \(0.817242\pi\) | |||||||
\(18\) | −0.442251 | −0.104239 | ||||||||
\(19\) | 7.72487 | 1.77221 | 0.886104 | − | 0.463487i | \(-0.153402\pi\) | ||||
0.886104 | + | 0.463487i | \(0.153402\pi\) | |||||||
\(20\) | 7.74589 | 1.73203 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.978311 | 0.208577 | ||||||||
\(23\) | 0.0381692 | 0.00795883 | 0.00397941 | − | 0.999992i | \(-0.498733\pi\) | ||||
0.00397941 | + | 0.999992i | \(0.498733\pi\) | |||||||
\(24\) | 1.68250 | 0.343440 | ||||||||
\(25\) | 13.4277 | 2.68553 | ||||||||
\(26\) | 1.37844 | 0.270334 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.66709 | 0.495266 | 0.247633 | − | 0.968854i | \(-0.420347\pi\) | ||||
0.247633 | + | 0.968854i | \(0.420347\pi\) | |||||||
\(30\) | 1.89847 | 0.346612 | ||||||||
\(31\) | 4.69959 | 0.844072 | 0.422036 | − | 0.906579i | \(-0.361316\pi\) | ||||
0.422036 | + | 0.906579i | \(0.361316\pi\) | |||||||
\(32\) | −4.63194 | −0.818820 | ||||||||
\(33\) | −2.21212 | −0.385080 | ||||||||
\(34\) | 3.06213 | 0.525151 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.80441 | −0.300736 | ||||||||
\(37\) | −0.0300718 | −0.00494377 | −0.00247189 | − | 0.999997i | \(-0.500787\pi\) | ||||
−0.00247189 | + | 0.999997i | \(0.500787\pi\) | |||||||
\(38\) | −3.41633 | −0.554202 | ||||||||
\(39\) | −3.11687 | −0.499098 | ||||||||
\(40\) | −7.22256 | −1.14199 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.0093 | 1.67890 | 0.839449 | − | 0.543438i | \(-0.182878\pi\) | ||||
0.839449 | + | 0.543438i | \(0.182878\pi\) | |||||||
\(44\) | 3.99158 | 0.601753 | ||||||||
\(45\) | −4.29274 | −0.639925 | ||||||||
\(46\) | −0.0168804 | −0.00248887 | ||||||||
\(47\) | −3.78108 | −0.551527 | −0.275763 | − | 0.961226i | \(-0.588931\pi\) | ||||
−0.275763 | + | 0.961226i | \(0.588931\pi\) | |||||||
\(48\) | 2.86474 | 0.413490 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.93839 | −0.839815 | ||||||||
\(51\) | −6.92396 | −0.969549 | ||||||||
\(52\) | 5.62412 | 0.779925 | ||||||||
\(53\) | −0.546137 | −0.0750176 | −0.0375088 | − | 0.999296i | \(-0.511942\pi\) | ||||
−0.0375088 | + | 0.999296i | \(0.511942\pi\) | |||||||
\(54\) | −0.442251 | −0.0601827 | ||||||||
\(55\) | 9.49606 | 1.28045 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.72487 | 1.02318 | ||||||||
\(58\) | −1.17952 | −0.154879 | ||||||||
\(59\) | −9.55909 | −1.24449 | −0.622243 | − | 0.782824i | \(-0.713779\pi\) | ||||
−0.622243 | + | 0.782824i | \(0.713779\pi\) | |||||||
\(60\) | 7.74589 | 0.999990 | ||||||||
\(61\) | 6.02077 | 0.770881 | 0.385441 | − | 0.922733i | \(-0.374049\pi\) | ||||
0.385441 | + | 0.922733i | \(0.374049\pi\) | |||||||
\(62\) | −2.07840 | −0.263957 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.68100 | −0.460125 | ||||||||
\(65\) | 13.3799 | 1.65957 | ||||||||
\(66\) | 0.978311 | 0.120422 | ||||||||
\(67\) | −8.97673 | −1.09668 | −0.548341 | − | 0.836255i | \(-0.684741\pi\) | ||||
−0.548341 | + | 0.836255i | \(0.684741\pi\) | |||||||
\(68\) | 12.4937 | 1.51508 | ||||||||
\(69\) | 0.0381692 | 0.00459503 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.6199 | 1.85374 | 0.926868 | − | 0.375386i | \(-0.122490\pi\) | ||||
0.926868 | + | 0.375386i | \(0.122490\pi\) | |||||||
\(72\) | 1.68250 | 0.198285 | ||||||||
\(73\) | −2.42299 | −0.283590 | −0.141795 | − | 0.989896i | \(-0.545287\pi\) | ||||
−0.141795 | + | 0.989896i | \(0.545287\pi\) | |||||||
\(74\) | 0.0132993 | 0.00154601 | ||||||||
\(75\) | 13.4277 | 1.55049 | ||||||||
\(76\) | −13.9389 | −1.59890 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.37844 | 0.156077 | ||||||||
\(79\) | 2.16136 | 0.243172 | 0.121586 | − | 0.992581i | \(-0.461202\pi\) | ||||
0.121586 | + | 0.992581i | \(0.461202\pi\) | |||||||
\(80\) | −12.2976 | −1.37491 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.442251 | 0.0488384 | ||||||||
\(83\) | 17.0488 | 1.87135 | 0.935675 | − | 0.352862i | \(-0.114792\pi\) | ||||
0.935675 | + | 0.352862i | \(0.114792\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 29.7228 | 3.22389 | ||||||||
\(86\) | −4.86886 | −0.525023 | ||||||||
\(87\) | 2.66709 | 0.285942 | ||||||||
\(88\) | −3.72190 | −0.396756 | ||||||||
\(89\) | −8.69193 | −0.921343 | −0.460672 | − | 0.887571i | \(-0.652391\pi\) | ||||
−0.460672 | + | 0.887571i | \(0.652391\pi\) | |||||||
\(90\) | 1.89847 | 0.200116 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.0688730 | −0.00718051 | ||||||||
\(93\) | 4.69959 | 0.487325 | ||||||||
\(94\) | 1.67218 | 0.172473 | ||||||||
\(95\) | −33.1609 | −3.40224 | ||||||||
\(96\) | −4.63194 | −0.472746 | ||||||||
\(97\) | 0.216724 | 0.0220050 | 0.0110025 | − | 0.999939i | \(-0.496498\pi\) | ||||
0.0110025 | + | 0.999939i | \(0.496498\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.21212 | −0.222326 | ||||||||
\(100\) | −24.2291 | −2.42291 | ||||||||
\(101\) | −2.53326 | −0.252069 | −0.126034 | − | 0.992026i | \(-0.540225\pi\) | ||||
−0.126034 | + | 0.992026i | \(0.540225\pi\) | |||||||
\(102\) | 3.06213 | 0.303196 | ||||||||
\(103\) | −0.709634 | −0.0699223 | −0.0349612 | − | 0.999389i | \(-0.511131\pi\) | ||||
−0.0349612 | + | 0.999389i | \(0.511131\pi\) | |||||||
\(104\) | −5.24414 | −0.514230 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.241529 | 0.0234594 | ||||||||
\(107\) | 6.42089 | 0.620731 | 0.310366 | − | 0.950617i | \(-0.399549\pi\) | ||||
0.310366 | + | 0.950617i | \(0.399549\pi\) | |||||||
\(108\) | −1.80441 | −0.173630 | ||||||||
\(109\) | −2.52449 | −0.241802 | −0.120901 | − | 0.992665i | \(-0.538578\pi\) | ||||
−0.120901 | + | 0.992665i | \(0.538578\pi\) | |||||||
\(110\) | −4.19964 | −0.400420 | ||||||||
\(111\) | −0.0300718 | −0.00285429 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.71911 | 0.161721 | 0.0808603 | − | 0.996725i | \(-0.474233\pi\) | ||||
0.0808603 | + | 0.996725i | \(0.474233\pi\) | |||||||
\(114\) | −3.41633 | −0.319969 | ||||||||
\(115\) | −0.163851 | −0.0152791 | ||||||||
\(116\) | −4.81253 | −0.446832 | ||||||||
\(117\) | −3.11687 | −0.288154 | ||||||||
\(118\) | 4.22751 | 0.389174 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −7.22256 | −0.659327 | ||||||||
\(121\) | −6.10653 | −0.555139 | ||||||||
\(122\) | −2.66269 | −0.241069 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | −8.48001 | −0.761527 | ||||||||
\(125\) | −36.1778 | −3.23584 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.8770 | −1.67506 | −0.837529 | − | 0.546392i | \(-0.816001\pi\) | ||||
−0.837529 | + | 0.546392i | \(0.816001\pi\) | |||||||
\(128\) | 10.8918 | 0.962709 | ||||||||
\(129\) | 11.0093 | 0.969313 | ||||||||
\(130\) | −5.91727 | −0.518979 | ||||||||
\(131\) | −9.69220 | −0.846811 | −0.423406 | − | 0.905940i | \(-0.639166\pi\) | ||||
−0.423406 | + | 0.905940i | \(0.639166\pi\) | |||||||
\(132\) | 3.99158 | 0.347422 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.96997 | 0.342953 | ||||||||
\(135\) | −4.29274 | −0.369461 | ||||||||
\(136\) | −11.6496 | −0.998945 | ||||||||
\(137\) | 6.05845 | 0.517608 | 0.258804 | − | 0.965930i | \(-0.416672\pi\) | ||||
0.258804 | + | 0.965930i | \(0.416672\pi\) | |||||||
\(138\) | −0.0168804 | −0.00143695 | ||||||||
\(139\) | 1.67013 | 0.141658 | 0.0708291 | − | 0.997488i | \(-0.477435\pi\) | ||||
0.0708291 | + | 0.997488i | \(0.477435\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.78108 | −0.318424 | ||||||||
\(142\) | −6.90790 | −0.579698 | ||||||||
\(143\) | 6.89487 | 0.576578 | ||||||||
\(144\) | 2.86474 | 0.238728 | ||||||||
\(145\) | −11.4491 | −0.950798 | ||||||||
\(146\) | 1.07157 | 0.0886837 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.0542620 | 0.00446031 | ||||||||
\(149\) | 2.69542 | 0.220817 | 0.110409 | − | 0.993886i | \(-0.464784\pi\) | ||||
0.110409 | + | 0.993886i | \(0.464784\pi\) | |||||||
\(150\) | −5.93839 | −0.484868 | ||||||||
\(151\) | −1.70580 | −0.138816 | −0.0694082 | − | 0.997588i | \(-0.522111\pi\) | ||||
−0.0694082 | + | 0.997588i | \(0.522111\pi\) | |||||||
\(152\) | 12.9971 | 1.05421 | ||||||||
\(153\) | −6.92396 | −0.559769 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20.1741 | −1.62043 | ||||||||
\(156\) | 5.62412 | 0.450290 | ||||||||
\(157\) | −11.6850 | −0.932562 | −0.466281 | − | 0.884637i | \(-0.654406\pi\) | ||||
−0.466281 | + | 0.884637i | \(0.654406\pi\) | |||||||
\(158\) | −0.955865 | −0.0760445 | ||||||||
\(159\) | −0.546137 | −0.0433114 | ||||||||
\(160\) | 19.8837 | 1.57195 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.442251 | −0.0347465 | ||||||||
\(163\) | −12.3332 | −0.966009 | −0.483005 | − | 0.875618i | \(-0.660455\pi\) | ||||
−0.483005 | + | 0.875618i | \(0.660455\pi\) | |||||||
\(164\) | 1.80441 | 0.140901 | ||||||||
\(165\) | 9.49606 | 0.739267 | ||||||||
\(166\) | −7.53985 | −0.585206 | ||||||||
\(167\) | −6.35364 | −0.491659 | −0.245830 | − | 0.969313i | \(-0.579060\pi\) | ||||
−0.245830 | + | 0.969313i | \(0.579060\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.28515 | −0.252704 | ||||||||
\(170\) | −13.1449 | −1.00817 | ||||||||
\(171\) | 7.72487 | 0.590736 | ||||||||
\(172\) | −19.8653 | −1.51471 | ||||||||
\(173\) | 0.579038 | 0.0440235 | 0.0220117 | − | 0.999758i | \(-0.492993\pi\) | ||||
0.0220117 | + | 0.999758i | \(0.492993\pi\) | |||||||
\(174\) | −1.17952 | −0.0894193 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.33714 | −0.477680 | ||||||||
\(177\) | −9.55909 | −0.718505 | ||||||||
\(178\) | 3.84401 | 0.288121 | ||||||||
\(179\) | 21.2907 | 1.59134 | 0.795672 | − | 0.605727i | \(-0.207118\pi\) | ||||
0.795672 | + | 0.605727i | \(0.207118\pi\) | |||||||
\(180\) | 7.74589 | 0.577345 | ||||||||
\(181\) | 21.3004 | 1.58325 | 0.791623 | − | 0.611010i | \(-0.209237\pi\) | ||||
0.791623 | + | 0.611010i | \(0.209237\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.02077 | 0.445068 | ||||||||
\(184\) | 0.0642198 | 0.00473435 | ||||||||
\(185\) | 0.129091 | 0.00949093 | ||||||||
\(186\) | −2.07840 | −0.152396 | ||||||||
\(187\) | 15.3166 | 1.12006 | ||||||||
\(188\) | 6.82263 | 0.497591 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 14.6654 | 1.06394 | ||||||||
\(191\) | −2.25947 | −0.163490 | −0.0817448 | − | 0.996653i | \(-0.526049\pi\) | ||||
−0.0817448 | + | 0.996653i | \(0.526049\pi\) | |||||||
\(192\) | −3.68100 | −0.265653 | ||||||||
\(193\) | −19.8775 | −1.43081 | −0.715406 | − | 0.698709i | \(-0.753758\pi\) | ||||
−0.715406 | + | 0.698709i | \(0.753758\pi\) | |||||||
\(194\) | −0.0958464 | −0.00688137 | ||||||||
\(195\) | 13.3799 | 0.958155 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.13650 | −0.508455 | −0.254227 | − | 0.967144i | \(-0.581821\pi\) | ||||
−0.254227 | + | 0.967144i | \(0.581821\pi\) | |||||||
\(198\) | 0.978311 | 0.0695255 | ||||||||
\(199\) | 13.9705 | 0.990343 | 0.495172 | − | 0.868795i | \(-0.335105\pi\) | ||||
0.495172 | + | 0.868795i | \(0.335105\pi\) | |||||||
\(200\) | 22.5921 | 1.59750 | ||||||||
\(201\) | −8.97673 | −0.633170 | ||||||||
\(202\) | 1.12034 | 0.0788265 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 12.4937 | 0.874734 | ||||||||
\(205\) | 4.29274 | 0.299818 | ||||||||
\(206\) | 0.313836 | 0.0218660 | ||||||||
\(207\) | 0.0381692 | 0.00265294 | ||||||||
\(208\) | −8.92901 | −0.619115 | ||||||||
\(209\) | −17.0883 | −1.18202 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.3091 | 1.60466 | 0.802332 | − | 0.596878i | \(-0.203592\pi\) | ||||
0.802332 | + | 0.596878i | \(0.203592\pi\) | |||||||
\(212\) | 0.985457 | 0.0676814 | ||||||||
\(213\) | 15.6199 | 1.07026 | ||||||||
\(214\) | −2.83964 | −0.194114 | ||||||||
\(215\) | −47.2600 | −3.22311 | ||||||||
\(216\) | 1.68250 | 0.114480 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.11646 | 0.0756159 | ||||||||
\(219\) | −2.42299 | −0.163731 | ||||||||
\(220\) | −17.1348 | −1.15523 | ||||||||
\(221\) | 21.5811 | 1.45170 | ||||||||
\(222\) | 0.0132993 | 0.000892589 0 | ||||||||
\(223\) | −24.6795 | −1.65266 | −0.826330 | − | 0.563186i | \(-0.809575\pi\) | ||||
−0.826330 | + | 0.563186i | \(0.809575\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.4277 | 0.895177 | ||||||||
\(226\) | −0.760279 | −0.0505730 | ||||||||
\(227\) | −11.7407 | −0.779259 | −0.389630 | − | 0.920972i | \(-0.627397\pi\) | ||||
−0.389630 | + | 0.920972i | \(0.627397\pi\) | |||||||
\(228\) | −13.9389 | −0.923124 | ||||||||
\(229\) | 15.4411 | 1.02037 | 0.510187 | − | 0.860063i | \(-0.329576\pi\) | ||||
0.510187 | + | 0.860063i | \(0.329576\pi\) | |||||||
\(230\) | 0.0724630 | 0.00477807 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.48739 | 0.294611 | ||||||||
\(233\) | −7.24116 | −0.474384 | −0.237192 | − | 0.971463i | \(-0.576227\pi\) | ||||
−0.237192 | + | 0.971463i | \(0.576227\pi\) | |||||||
\(234\) | 1.37844 | 0.0901112 | ||||||||
\(235\) | 16.2312 | 1.05881 | ||||||||
\(236\) | 17.2486 | 1.12279 | ||||||||
\(237\) | 2.16136 | 0.140396 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.7858 | −0.891726 | −0.445863 | − | 0.895101i | \(-0.647103\pi\) | ||||
−0.445863 | + | 0.895101i | \(0.647103\pi\) | |||||||
\(240\) | −12.2976 | −0.793806 | ||||||||
\(241\) | −3.50900 | −0.226035 | −0.113017 | − | 0.993593i | \(-0.536052\pi\) | ||||
−0.113017 | + | 0.993593i | \(0.536052\pi\) | |||||||
\(242\) | 2.70062 | 0.173602 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −10.8640 | −0.695494 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.442251 | 0.0281969 | ||||||||
\(247\) | −24.0774 | −1.53201 | ||||||||
\(248\) | 7.90709 | 0.502100 | ||||||||
\(249\) | 17.0488 | 1.08042 | ||||||||
\(250\) | 15.9997 | 1.01191 | ||||||||
\(251\) | −14.8746 | −0.938876 | −0.469438 | − | 0.882965i | \(-0.655543\pi\) | ||||
−0.469438 | + | 0.882965i | \(0.655543\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.0844348 | −0.00530837 | ||||||||
\(254\) | 8.34835 | 0.523822 | ||||||||
\(255\) | 29.7228 | 1.86131 | ||||||||
\(256\) | 2.54509 | 0.159068 | ||||||||
\(257\) | 21.7559 | 1.35709 | 0.678547 | − | 0.734557i | \(-0.262610\pi\) | ||||
0.678547 | + | 0.734557i | \(0.262610\pi\) | |||||||
\(258\) | −4.86886 | −0.303122 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −24.1429 | −1.49728 | ||||||||
\(261\) | 2.66709 | 0.165089 | ||||||||
\(262\) | 4.28638 | 0.264814 | ||||||||
\(263\) | 2.27801 | 0.140468 | 0.0702340 | − | 0.997531i | \(-0.477625\pi\) | ||||
0.0702340 | + | 0.997531i | \(0.477625\pi\) | |||||||
\(264\) | −3.72190 | −0.229067 | ||||||||
\(265\) | 2.34442 | 0.144017 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.69193 | −0.531938 | ||||||||
\(268\) | 16.1977 | 0.989435 | ||||||||
\(269\) | −2.03093 | −0.123828 | −0.0619141 | − | 0.998081i | \(-0.519720\pi\) | ||||
−0.0619141 | + | 0.998081i | \(0.519720\pi\) | |||||||
\(270\) | 1.89847 | 0.115537 | ||||||||
\(271\) | −15.8435 | −0.962427 | −0.481214 | − | 0.876603i | \(-0.659804\pi\) | ||||
−0.481214 | + | 0.876603i | \(0.659804\pi\) | |||||||
\(272\) | −19.8354 | −1.20269 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.67935 | −0.161866 | ||||||||
\(275\) | −29.7036 | −1.79119 | ||||||||
\(276\) | −0.0688730 | −0.00414567 | ||||||||
\(277\) | −3.50000 | −0.210294 | −0.105147 | − | 0.994457i | \(-0.533531\pi\) | ||||
−0.105147 | + | 0.994457i | \(0.533531\pi\) | |||||||
\(278\) | −0.738614 | −0.0442992 | ||||||||
\(279\) | 4.69959 | 0.281357 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.7164 | 1.59377 | 0.796883 | − | 0.604134i | \(-0.206481\pi\) | ||||
0.796883 | + | 0.604134i | \(0.206481\pi\) | |||||||
\(282\) | 1.67218 | 0.0995771 | ||||||||
\(283\) | −15.6917 | −0.932774 | −0.466387 | − | 0.884581i | \(-0.654445\pi\) | ||||
−0.466387 | + | 0.884581i | \(0.654445\pi\) | |||||||
\(284\) | −28.1847 | −1.67245 | ||||||||
\(285\) | −33.1609 | −1.96428 | ||||||||
\(286\) | −3.04926 | −0.180307 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4.63194 | −0.272940 | ||||||||
\(289\) | 30.9413 | 1.82007 | ||||||||
\(290\) | 5.06338 | 0.297332 | ||||||||
\(291\) | 0.216724 | 0.0127046 | ||||||||
\(292\) | 4.37208 | 0.255857 | ||||||||
\(293\) | −14.4844 | −0.846189 | −0.423095 | − | 0.906085i | \(-0.639056\pi\) | ||||
−0.423095 | + | 0.906085i | \(0.639056\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 41.0347 | 2.38913 | ||||||||
\(296\) | −0.0505959 | −0.00294083 | ||||||||
\(297\) | −2.21212 | −0.128360 | ||||||||
\(298\) | −1.19205 | −0.0690537 | ||||||||
\(299\) | −0.118968 | −0.00688011 | ||||||||
\(300\) | −24.2291 | −1.39887 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.754393 | 0.0434105 | ||||||||
\(303\) | −2.53326 | −0.145532 | ||||||||
\(304\) | 22.1297 | 1.26923 | ||||||||
\(305\) | −25.8456 | −1.47992 | ||||||||
\(306\) | 3.06213 | 0.175050 | ||||||||
\(307\) | 19.7492 | 1.12715 | 0.563573 | − | 0.826066i | \(-0.309426\pi\) | ||||
0.563573 | + | 0.826066i | \(0.309426\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.709634 | −0.0403697 | ||||||||
\(310\) | 8.92203 | 0.506737 | ||||||||
\(311\) | −18.1355 | −1.02837 | −0.514184 | − | 0.857680i | \(-0.671905\pi\) | ||||
−0.514184 | + | 0.857680i | \(0.671905\pi\) | |||||||
\(312\) | −5.24414 | −0.296891 | ||||||||
\(313\) | 3.28237 | 0.185531 | 0.0927653 | − | 0.995688i | \(-0.470429\pi\) | ||||
0.0927653 | + | 0.995688i | \(0.470429\pi\) | |||||||
\(314\) | 5.16769 | 0.291629 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.90000 | −0.219392 | ||||||||
\(317\) | −0.440700 | −0.0247522 | −0.0123761 | − | 0.999923i | \(-0.503940\pi\) | ||||
−0.0123761 | + | 0.999923i | \(0.503940\pi\) | |||||||
\(318\) | 0.241529 | 0.0135443 | ||||||||
\(319\) | −5.89991 | −0.330332 | ||||||||
\(320\) | 15.8016 | 0.883336 | ||||||||
\(321\) | 6.42089 | 0.358379 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −53.4867 | −2.97608 | ||||||||
\(324\) | −1.80441 | −0.100245 | ||||||||
\(325\) | −41.8522 | −2.32154 | ||||||||
\(326\) | 5.45436 | 0.302089 | ||||||||
\(327\) | −2.52449 | −0.139604 | ||||||||
\(328\) | −1.68250 | −0.0929008 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.19964 | −0.231183 | ||||||||
\(331\) | −3.26805 | −0.179628 | −0.0898141 | − | 0.995959i | \(-0.528627\pi\) | ||||
−0.0898141 | + | 0.995959i | \(0.528627\pi\) | |||||||
\(332\) | −30.7631 | −1.68835 | ||||||||
\(333\) | −0.0300718 | −0.00164792 | ||||||||
\(334\) | 2.80990 | 0.153751 | ||||||||
\(335\) | 38.5348 | 2.10538 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.8129 | −1.02481 | −0.512403 | − | 0.858745i | \(-0.671244\pi\) | ||||
−0.512403 | + | 0.858745i | \(0.671244\pi\) | |||||||
\(338\) | 1.45286 | 0.0790252 | ||||||||
\(339\) | 1.71911 | 0.0933694 | ||||||||
\(340\) | −53.6323 | −2.90862 | ||||||||
\(341\) | −10.3961 | −0.562978 | ||||||||
\(342\) | −3.41633 | −0.184734 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 18.5232 | 0.998702 | ||||||||
\(345\) | −0.163851 | −0.00882142 | ||||||||
\(346\) | −0.256080 | −0.0137669 | ||||||||
\(347\) | −24.8798 | −1.33562 | −0.667809 | − | 0.744332i | \(-0.732768\pi\) | ||||
−0.667809 | + | 0.744332i | \(0.732768\pi\) | |||||||
\(348\) | −4.81253 | −0.257979 | ||||||||
\(349\) | −34.7651 | −1.86094 | −0.930468 | − | 0.366374i | \(-0.880599\pi\) | ||||
−0.930468 | + | 0.366374i | \(0.880599\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.11687 | −0.166366 | ||||||||
\(352\) | 10.2464 | 0.546135 | ||||||||
\(353\) | 16.6295 | 0.885098 | 0.442549 | − | 0.896744i | \(-0.354074\pi\) | ||||
0.442549 | + | 0.896744i | \(0.354074\pi\) | |||||||
\(354\) | 4.22751 | 0.224690 | ||||||||
\(355\) | −67.0521 | −3.55876 | ||||||||
\(356\) | 15.6839 | 0.831242 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.41584 | −0.497643 | ||||||||
\(359\) | −25.2772 | −1.33408 | −0.667041 | − | 0.745021i | \(-0.732439\pi\) | ||||
−0.667041 | + | 0.745021i | \(0.732439\pi\) | |||||||
\(360\) | −7.22256 | −0.380663 | ||||||||
\(361\) | 40.6736 | 2.14072 | ||||||||
\(362\) | −9.42011 | −0.495110 | ||||||||
\(363\) | −6.10653 | −0.320510 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.4013 | 0.544428 | ||||||||
\(366\) | −2.66269 | −0.139181 | ||||||||
\(367\) | −33.2183 | −1.73398 | −0.866992 | − | 0.498322i | \(-0.833950\pi\) | ||||
−0.866992 | + | 0.498322i | \(0.833950\pi\) | |||||||
\(368\) | 0.109345 | 0.00569999 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | −0.0570904 | −0.00296799 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −8.48001 | −0.439668 | ||||||||
\(373\) | 25.9809 | 1.34524 | 0.672619 | − | 0.739989i | \(-0.265169\pi\) | ||||
0.672619 | + | 0.739989i | \(0.265169\pi\) | |||||||
\(374\) | −6.77379 | −0.350264 | ||||||||
\(375\) | −36.1778 | −1.86821 | ||||||||
\(376\) | −6.36168 | −0.328079 | ||||||||
\(377\) | −8.31295 | −0.428139 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.2601 | 0.527028 | 0.263514 | − | 0.964656i | \(-0.415118\pi\) | ||||
0.263514 | + | 0.964656i | \(0.415118\pi\) | |||||||
\(380\) | 59.8360 | 3.06952 | ||||||||
\(381\) | −18.8770 | −0.967096 | ||||||||
\(382\) | 0.999253 | 0.0511262 | ||||||||
\(383\) | 2.59188 | 0.132439 | 0.0662194 | − | 0.997805i | \(-0.478906\pi\) | ||||
0.0662194 | + | 0.997805i | \(0.478906\pi\) | |||||||
\(384\) | 10.8918 | 0.555820 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.79083 | 0.447441 | ||||||||
\(387\) | 11.0093 | 0.559633 | ||||||||
\(388\) | −0.391060 | −0.0198531 | ||||||||
\(389\) | −8.65407 | −0.438779 | −0.219390 | − | 0.975637i | \(-0.570407\pi\) | ||||
−0.219390 | + | 0.975637i | \(0.570407\pi\) | |||||||
\(390\) | −5.91727 | −0.299633 | ||||||||
\(391\) | −0.264282 | −0.0133653 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.69220 | −0.488907 | ||||||||
\(394\) | 3.15612 | 0.159003 | ||||||||
\(395\) | −9.27818 | −0.466836 | ||||||||
\(396\) | 3.99158 | 0.200584 | ||||||||
\(397\) | −30.0428 | −1.50780 | −0.753902 | − | 0.656987i | \(-0.771830\pi\) | ||||
−0.753902 | + | 0.656987i | \(0.771830\pi\) | |||||||
\(398\) | −6.17847 | −0.309699 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 38.4667 | 1.92334 | ||||||||
\(401\) | 12.0942 | 0.603955 | 0.301978 | − | 0.953315i | \(-0.402353\pi\) | ||||
0.301978 | + | 0.953315i | \(0.402353\pi\) | |||||||
\(402\) | 3.96997 | 0.198004 | ||||||||
\(403\) | −14.6480 | −0.729669 | ||||||||
\(404\) | 4.57105 | 0.227418 | ||||||||
\(405\) | −4.29274 | −0.213308 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.0665224 | 0.00329739 | ||||||||
\(408\) | −11.6496 | −0.576741 | ||||||||
\(409\) | 13.5140 | 0.668222 | 0.334111 | − | 0.942534i | \(-0.391564\pi\) | ||||
0.334111 | + | 0.942534i | \(0.391564\pi\) | |||||||
\(410\) | −1.89847 | −0.0937587 | ||||||||
\(411\) | 6.05845 | 0.298841 | ||||||||
\(412\) | 1.28047 | 0.0630844 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.0168804 | −0.000829624 0 | ||||||||
\(415\) | −73.1862 | −3.59257 | ||||||||
\(416\) | 14.4371 | 0.707839 | ||||||||
\(417\) | 1.67013 | 0.0817864 | ||||||||
\(418\) | 7.55733 | 0.369641 | ||||||||
\(419\) | −32.1763 | −1.57191 | −0.785957 | − | 0.618281i | \(-0.787829\pi\) | ||||
−0.785957 | + | 0.618281i | \(0.787829\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.2673 | −1.57261 | −0.786307 | − | 0.617836i | \(-0.788010\pi\) | ||||
−0.786307 | + | 0.617836i | \(0.788010\pi\) | |||||||
\(422\) | −10.3085 | −0.501808 | ||||||||
\(423\) | −3.78108 | −0.183842 | ||||||||
\(424\) | −0.918877 | −0.0446246 | ||||||||
\(425\) | −92.9726 | −4.50983 | ||||||||
\(426\) | −6.90790 | −0.334689 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −11.5859 | −0.560028 | ||||||||
\(429\) | 6.89487 | 0.332888 | ||||||||
\(430\) | 20.9008 | 1.00792 | ||||||||
\(431\) | 10.4482 | 0.503271 | 0.251635 | − | 0.967822i | \(-0.419032\pi\) | ||||
0.251635 | + | 0.967822i | \(0.419032\pi\) | |||||||
\(432\) | 2.86474 | 0.137830 | ||||||||
\(433\) | −3.79123 | −0.182195 | −0.0910975 | − | 0.995842i | \(-0.529037\pi\) | ||||
−0.0910975 | + | 0.995842i | \(0.529037\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.4491 | −0.548943 | ||||||||
\(436\) | 4.55522 | 0.218155 | ||||||||
\(437\) | 0.294852 | 0.0141047 | ||||||||
\(438\) | 1.07157 | 0.0512016 | ||||||||
\(439\) | 4.49268 | 0.214424 | 0.107212 | − | 0.994236i | \(-0.465808\pi\) | ||||
0.107212 | + | 0.994236i | \(0.465808\pi\) | |||||||
\(440\) | 15.9772 | 0.761682 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.54424 | −0.453973 | ||||||||
\(443\) | −8.19908 | −0.389550 | −0.194775 | − | 0.980848i | \(-0.562398\pi\) | ||||
−0.194775 | + | 0.980848i | \(0.562398\pi\) | |||||||
\(444\) | 0.0542620 | 0.00257516 | ||||||||
\(445\) | 37.3123 | 1.76877 | ||||||||
\(446\) | 10.9145 | 0.516817 | ||||||||
\(447\) | 2.69542 | 0.127489 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 32.0190 | 1.51107 | 0.755535 | − | 0.655109i | \(-0.227377\pi\) | ||||
0.755535 | + | 0.655109i | \(0.227377\pi\) | |||||||
\(450\) | −5.93839 | −0.279938 | ||||||||
\(451\) | 2.21212 | 0.104165 | ||||||||
\(452\) | −3.10199 | −0.145906 | ||||||||
\(453\) | −1.70580 | −0.0801457 | ||||||||
\(454\) | 5.19234 | 0.243689 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 12.9971 | 0.608647 | ||||||||
\(457\) | 3.92379 | 0.183547 | 0.0917736 | − | 0.995780i | \(-0.470746\pi\) | ||||
0.0917736 | + | 0.995780i | \(0.470746\pi\) | |||||||
\(458\) | −6.82882 | −0.319090 | ||||||||
\(459\) | −6.92396 | −0.323183 | ||||||||
\(460\) | 0.295654 | 0.0137850 | ||||||||
\(461\) | −26.4099 | −1.23003 | −0.615016 | − | 0.788514i | \(-0.710851\pi\) | ||||
−0.615016 | + | 0.788514i | \(0.710851\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.27988 | 0.245377 | 0.122688 | − | 0.992445i | \(-0.460848\pi\) | ||||
0.122688 | + | 0.992445i | \(0.460848\pi\) | |||||||
\(464\) | 7.64051 | 0.354702 | ||||||||
\(465\) | −20.1741 | −0.935554 | ||||||||
\(466\) | 3.20241 | 0.148349 | ||||||||
\(467\) | −20.1035 | −0.930280 | −0.465140 | − | 0.885237i | \(-0.653996\pi\) | ||||
−0.465140 | + | 0.885237i | \(0.653996\pi\) | |||||||
\(468\) | 5.62412 | 0.259975 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −7.17826 | −0.331108 | ||||||||
\(471\) | −11.6850 | −0.538415 | ||||||||
\(472\) | −16.0832 | −0.740290 | ||||||||
\(473\) | −24.3538 | −1.11979 | ||||||||
\(474\) | −0.955865 | −0.0439043 | ||||||||
\(475\) | 103.727 | 4.75932 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.546137 | −0.0250059 | ||||||||
\(478\) | 6.09676 | 0.278859 | ||||||||
\(479\) | 23.4552 | 1.07170 | 0.535848 | − | 0.844315i | \(-0.319992\pi\) | ||||
0.535848 | + | 0.844315i | \(0.319992\pi\) | |||||||
\(480\) | 19.8837 | 0.907565 | ||||||||
\(481\) | 0.0937297 | 0.00427371 | ||||||||
\(482\) | 1.55186 | 0.0706852 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.0187 | 0.500851 | ||||||||
\(485\) | −0.930341 | −0.0422446 | ||||||||
\(486\) | −0.442251 | −0.0200609 | ||||||||
\(487\) | 39.6797 | 1.79806 | 0.899030 | − | 0.437886i | \(-0.144273\pi\) | ||||
0.899030 | + | 0.437886i | \(0.144273\pi\) | |||||||
\(488\) | 10.1300 | 0.458563 | ||||||||
\(489\) | −12.3332 | −0.557726 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 42.0432 | 1.89738 | 0.948691 | − | 0.316204i | \(-0.102408\pi\) | ||||
0.948691 | + | 0.316204i | \(0.102408\pi\) | |||||||
\(492\) | 1.80441 | 0.0813493 | ||||||||
\(493\) | −18.4668 | −0.831703 | ||||||||
\(494\) | 10.6482 | 0.479087 | ||||||||
\(495\) | 9.49606 | 0.426816 | ||||||||
\(496\) | 13.4631 | 0.604511 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −7.53985 | −0.337869 | ||||||||
\(499\) | −5.70934 | −0.255585 | −0.127793 | − | 0.991801i | \(-0.540789\pi\) | ||||
−0.127793 | + | 0.991801i | \(0.540789\pi\) | |||||||
\(500\) | 65.2797 | 2.91940 | ||||||||
\(501\) | −6.35364 | −0.283860 | ||||||||
\(502\) | 6.57830 | 0.293604 | ||||||||
\(503\) | −5.71736 | −0.254924 | −0.127462 | − | 0.991843i | \(-0.540683\pi\) | ||||
−0.127462 | + | 0.991843i | \(0.540683\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.8746 | 0.483915 | ||||||||
\(506\) | 0.0373413 | 0.00166002 | ||||||||
\(507\) | −3.28515 | −0.145899 | ||||||||
\(508\) | 34.0618 | 1.51125 | ||||||||
\(509\) | −35.4392 | −1.57081 | −0.785407 | − | 0.618980i | \(-0.787546\pi\) | ||||
−0.785407 | + | 0.618980i | \(0.787546\pi\) | |||||||
\(510\) | −13.1449 | −0.582067 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.9092 | −1.01245 | ||||||||
\(513\) | 7.72487 | 0.341061 | ||||||||
\(514\) | −9.62155 | −0.424388 | ||||||||
\(515\) | 3.04628 | 0.134235 | ||||||||
\(516\) | −19.8653 | −0.874521 | ||||||||
\(517\) | 8.36419 | 0.367857 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.579038 | 0.0254170 | ||||||||
\(520\) | 22.5118 | 0.987206 | ||||||||
\(521\) | 4.21069 | 0.184474 | 0.0922368 | − | 0.995737i | \(-0.470598\pi\) | ||||
0.0922368 | + | 0.995737i | \(0.470598\pi\) | |||||||
\(522\) | −1.17952 | −0.0516262 | ||||||||
\(523\) | −12.4112 | −0.542703 | −0.271352 | − | 0.962480i | \(-0.587471\pi\) | ||||
−0.271352 | + | 0.962480i | \(0.587471\pi\) | |||||||
\(524\) | 17.4887 | 0.763999 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.00745 | −0.0439269 | ||||||||
\(527\) | −32.5398 | −1.41746 | ||||||||
\(528\) | −6.33714 | −0.275789 | ||||||||
\(529\) | −22.9985 | −0.999937 | ||||||||
\(530\) | −1.03682 | −0.0450367 | ||||||||
\(531\) | −9.55909 | −0.414829 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.11687 | 0.135006 | ||||||||
\(534\) | 3.84401 | 0.166347 | ||||||||
\(535\) | −27.5632 | −1.19166 | ||||||||
\(536\) | −15.1034 | −0.652367 | ||||||||
\(537\) | 21.2907 | 0.918763 | ||||||||
\(538\) | 0.898182 | 0.0387234 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 7.74589 | 0.333330 | ||||||||
\(541\) | 29.7330 | 1.27832 | 0.639162 | − | 0.769072i | \(-0.279282\pi\) | ||||
0.639162 | + | 0.769072i | \(0.279282\pi\) | |||||||
\(542\) | 7.00682 | 0.300969 | ||||||||
\(543\) | 21.3004 | 0.914087 | ||||||||
\(544\) | 32.0714 | 1.37505 | ||||||||
\(545\) | 10.8370 | 0.464205 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.76774 | −0.0755829 | −0.0377915 | − | 0.999286i | \(-0.512032\pi\) | ||||
−0.0377915 | + | 0.999286i | \(0.512032\pi\) | |||||||
\(548\) | −10.9320 | −0.466990 | ||||||||
\(549\) | 6.02077 | 0.256960 | ||||||||
\(550\) | 13.1364 | 0.560139 | ||||||||
\(551\) | 20.6029 | 0.877713 | ||||||||
\(552\) | 0.0642198 | 0.00273338 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.54788 | 0.0657630 | ||||||||
\(555\) | 0.129091 | 0.00547959 | ||||||||
\(556\) | −3.01360 | −0.127805 | ||||||||
\(557\) | −37.5462 | −1.59088 | −0.795442 | − | 0.606029i | \(-0.792761\pi\) | ||||
−0.795442 | + | 0.606029i | \(0.792761\pi\) | |||||||
\(558\) | −2.07840 | −0.0879856 | ||||||||
\(559\) | −34.3144 | −1.45135 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.3166 | 0.646668 | ||||||||
\(562\) | −11.8153 | −0.498400 | ||||||||
\(563\) | 7.50392 | 0.316253 | 0.158126 | − | 0.987419i | \(-0.449455\pi\) | ||||
0.158126 | + | 0.987419i | \(0.449455\pi\) | |||||||
\(564\) | 6.82263 | 0.287284 | ||||||||
\(565\) | −7.37972 | −0.310467 | ||||||||
\(566\) | 6.93966 | 0.291696 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 26.2805 | 1.10271 | ||||||||
\(569\) | −2.92823 | −0.122758 | −0.0613790 | − | 0.998115i | \(-0.519550\pi\) | ||||
−0.0613790 | + | 0.998115i | \(0.519550\pi\) | |||||||
\(570\) | 14.6654 | 0.614267 | ||||||||
\(571\) | 14.3396 | 0.600095 | 0.300047 | − | 0.953924i | \(-0.402997\pi\) | ||||
0.300047 | + | 0.953924i | \(0.402997\pi\) | |||||||
\(572\) | −12.4412 | −0.520193 | ||||||||
\(573\) | −2.25947 | −0.0943908 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.512523 | 0.0213737 | ||||||||
\(576\) | −3.68100 | −0.153375 | ||||||||
\(577\) | 15.3261 | 0.638036 | 0.319018 | − | 0.947749i | \(-0.396647\pi\) | ||||
0.319018 | + | 0.947749i | \(0.396647\pi\) | |||||||
\(578\) | −13.6838 | −0.569171 | ||||||||
\(579\) | −19.8775 | −0.826080 | ||||||||
\(580\) | 20.6590 | 0.857817 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.0958464 | −0.00397296 | ||||||||
\(583\) | 1.20812 | 0.0500352 | ||||||||
\(584\) | −4.07670 | −0.168695 | ||||||||
\(585\) | 13.3799 | 0.553191 | ||||||||
\(586\) | 6.40575 | 0.264619 | ||||||||
\(587\) | 18.1300 | 0.748306 | 0.374153 | − | 0.927367i | \(-0.377934\pi\) | ||||
0.374153 | + | 0.927367i | \(0.377934\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 36.3037 | 1.49587 | ||||||||
\(590\) | −18.1476 | −0.747126 | ||||||||
\(591\) | −7.13650 | −0.293556 | ||||||||
\(592\) | −0.0861479 | −0.00354066 | ||||||||
\(593\) | 14.6521 | 0.601691 | 0.300845 | − | 0.953673i | \(-0.402731\pi\) | ||||
0.300845 | + | 0.953673i | \(0.402731\pi\) | |||||||
\(594\) | 0.978311 | 0.0401406 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.86366 | −0.199223 | ||||||||
\(597\) | 13.9705 | 0.571775 | ||||||||
\(598\) | 0.0526138 | 0.00215154 | ||||||||
\(599\) | 4.58262 | 0.187241 | 0.0936205 | − | 0.995608i | \(-0.470156\pi\) | ||||
0.0936205 | + | 0.995608i | \(0.470156\pi\) | |||||||
\(600\) | 22.5921 | 0.922319 | ||||||||
\(601\) | −0.579777 | −0.0236496 | −0.0118248 | − | 0.999930i | \(-0.503764\pi\) | ||||
−0.0118248 | + | 0.999930i | \(0.503764\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.97673 | −0.365561 | ||||||||
\(604\) | 3.07798 | 0.125241 | ||||||||
\(605\) | 26.2138 | 1.06574 | ||||||||
\(606\) | 1.12034 | 0.0455105 | ||||||||
\(607\) | −11.2678 | −0.457345 | −0.228672 | − | 0.973503i | \(-0.573438\pi\) | ||||
−0.228672 | + | 0.973503i | \(0.573438\pi\) | |||||||
\(608\) | −35.7812 | −1.45112 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 11.4303 | 0.462798 | ||||||||
\(611\) | 11.7851 | 0.476774 | ||||||||
\(612\) | 12.4937 | 0.505028 | ||||||||
\(613\) | 41.6317 | 1.68149 | 0.840745 | − | 0.541431i | \(-0.182117\pi\) | ||||
0.840745 | + | 0.541431i | \(0.182117\pi\) | |||||||
\(614\) | −8.73410 | −0.352479 | ||||||||
\(615\) | 4.29274 | 0.173100 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.5914 | −0.587427 | −0.293713 | − | 0.955894i | \(-0.594891\pi\) | ||||
−0.293713 | + | 0.955894i | \(0.594891\pi\) | |||||||
\(618\) | 0.313836 | 0.0126243 | ||||||||
\(619\) | −20.3756 | −0.818965 | −0.409482 | − | 0.912318i | \(-0.634291\pi\) | ||||
−0.409482 | + | 0.912318i | \(0.634291\pi\) | |||||||
\(620\) | 36.4025 | 1.46196 | ||||||||
\(621\) | 0.0381692 | 0.00153168 | ||||||||
\(622\) | 8.02043 | 0.321590 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −8.92901 | −0.357446 | ||||||||
\(625\) | 88.1637 | 3.52655 | ||||||||
\(626\) | −1.45163 | −0.0580189 | ||||||||
\(627\) | −17.0883 | −0.682442 | ||||||||
\(628\) | 21.0845 | 0.841364 | ||||||||
\(629\) | 0.208216 | 0.00830212 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.23277 | 0.367551 | 0.183775 | − | 0.982968i | \(-0.441168\pi\) | ||||
0.183775 | + | 0.982968i | \(0.441168\pi\) | |||||||
\(632\) | 3.63651 | 0.144652 | ||||||||
\(633\) | 23.3091 | 0.926453 | ||||||||
\(634\) | 0.194900 | 0.00774047 | ||||||||
\(635\) | 81.0339 | 3.21573 | ||||||||
\(636\) | 0.985457 | 0.0390759 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.60924 | 0.103301 | ||||||||
\(639\) | 15.6199 | 0.617912 | ||||||||
\(640\) | −46.7558 | −1.84818 | ||||||||
\(641\) | 5.12329 | 0.202358 | 0.101179 | − | 0.994868i | \(-0.467739\pi\) | ||||
0.101179 | + | 0.994868i | \(0.467739\pi\) | |||||||
\(642\) | −2.83964 | −0.112072 | ||||||||
\(643\) | −15.5518 | −0.613302 | −0.306651 | − | 0.951822i | \(-0.599208\pi\) | ||||
−0.306651 | + | 0.951822i | \(0.599208\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −47.2600 | −1.86086 | ||||||||
\(646\) | 23.6545 | 0.930675 | ||||||||
\(647\) | −20.5466 | −0.807768 | −0.403884 | − | 0.914810i | \(-0.632340\pi\) | ||||
−0.403884 | + | 0.914810i | \(0.632340\pi\) | |||||||
\(648\) | 1.68250 | 0.0660950 | ||||||||
\(649\) | 21.1458 | 0.830046 | ||||||||
\(650\) | 18.5092 | 0.725989 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 22.2542 | 0.871540 | ||||||||
\(653\) | 22.6686 | 0.887091 | 0.443546 | − | 0.896252i | \(-0.353720\pi\) | ||||
0.443546 | + | 0.896252i | \(0.353720\pi\) | |||||||
\(654\) | 1.11646 | 0.0436569 | ||||||||
\(655\) | 41.6061 | 1.62569 | ||||||||
\(656\) | −2.86474 | −0.111849 | ||||||||
\(657\) | −2.42299 | −0.0945299 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −38.2328 | −1.48934 | −0.744669 | − | 0.667434i | \(-0.767393\pi\) | ||||
−0.744669 | + | 0.667434i | \(0.767393\pi\) | |||||||
\(660\) | −17.1348 | −0.666972 | ||||||||
\(661\) | −25.8102 | −1.00390 | −0.501951 | − | 0.864896i | \(-0.667384\pi\) | ||||
−0.501951 | + | 0.864896i | \(0.667384\pi\) | |||||||
\(662\) | 1.44530 | 0.0561731 | ||||||||
\(663\) | 21.5811 | 0.838139 | ||||||||
\(664\) | 28.6847 | 1.11318 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.0132993 | 0.000515336 0 | ||||||||
\(667\) | 0.101801 | 0.00394173 | ||||||||
\(668\) | 11.4646 | 0.443579 | ||||||||
\(669\) | −24.6795 | −0.954164 | ||||||||
\(670\) | −17.0421 | −0.658392 | ||||||||
\(671\) | −13.3187 | −0.514161 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.21950 | −0.278291 | −0.139146 | − | 0.990272i | \(-0.544436\pi\) | ||||
−0.139146 | + | 0.990272i | \(0.544436\pi\) | |||||||
\(674\) | 8.32003 | 0.320476 | ||||||||
\(675\) | 13.4277 | 0.516831 | ||||||||
\(676\) | 5.92777 | 0.227991 | ||||||||
\(677\) | −11.7898 | −0.453119 | −0.226560 | − | 0.973997i | \(-0.572748\pi\) | ||||
−0.226560 | + | 0.973997i | \(0.572748\pi\) | |||||||
\(678\) | −0.760279 | −0.0291983 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 50.0088 | 1.91775 | ||||||||
\(681\) | −11.7407 | −0.449906 | ||||||||
\(682\) | 4.59766 | 0.176054 | ||||||||
\(683\) | 27.1434 | 1.03861 | 0.519307 | − | 0.854588i | \(-0.326190\pi\) | ||||
0.519307 | + | 0.854588i | \(0.326190\pi\) | |||||||
\(684\) | −13.9389 | −0.532966 | ||||||||
\(685\) | −26.0074 | −0.993691 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.4411 | 0.589114 | ||||||||
\(688\) | 31.5387 | 1.20240 | ||||||||
\(689\) | 1.70223 | 0.0648500 | ||||||||
\(690\) | 0.0724630 | 0.00275862 | ||||||||
\(691\) | 2.26956 | 0.0863380 | 0.0431690 | − | 0.999068i | \(-0.486255\pi\) | ||||
0.0431690 | + | 0.999068i | \(0.486255\pi\) | |||||||
\(692\) | −1.04482 | −0.0397183 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.0031 | 0.417673 | ||||||||
\(695\) | −7.16943 | −0.271952 | ||||||||
\(696\) | 4.48739 | 0.170094 | ||||||||
\(697\) | 6.92396 | 0.262264 | ||||||||
\(698\) | 15.3749 | 0.581949 | ||||||||
\(699\) | −7.24116 | −0.273886 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.9632 | 1.20723 | 0.603616 | − | 0.797275i | \(-0.293726\pi\) | ||||
0.603616 | + | 0.797275i | \(0.293726\pi\) | |||||||
\(702\) | 1.37844 | 0.0520257 | ||||||||
\(703\) | −0.232301 | −0.00876139 | ||||||||
\(704\) | 8.14281 | 0.306894 | ||||||||
\(705\) | 16.2312 | 0.611302 | ||||||||
\(706\) | −7.35440 | −0.276786 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 17.2486 | 0.648240 | ||||||||
\(709\) | −17.4623 | −0.655812 | −0.327906 | − | 0.944710i | \(-0.606343\pi\) | ||||
−0.327906 | + | 0.944710i | \(0.606343\pi\) | |||||||
\(710\) | 29.6538 | 1.11289 | ||||||||
\(711\) | 2.16136 | 0.0810575 | ||||||||
\(712\) | −14.6242 | −0.548066 | ||||||||
\(713\) | 0.179380 | 0.00671782 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −29.5979 | −1.10690 | ||||||||
\(716\) | −38.4173 | −1.43572 | ||||||||
\(717\) | −13.7858 | −0.514838 | ||||||||
\(718\) | 11.1789 | 0.417192 | ||||||||
\(719\) | 15.8378 | 0.590649 | 0.295325 | − | 0.955397i | \(-0.404572\pi\) | ||||
0.295325 | + | 0.955397i | \(0.404572\pi\) | |||||||
\(720\) | −12.2976 | −0.458304 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −17.9879 | −0.669442 | ||||||||
\(723\) | −3.50900 | −0.130501 | ||||||||
\(724\) | −38.4347 | −1.42842 | ||||||||
\(725\) | 35.8127 | 1.33005 | ||||||||
\(726\) | 2.70062 | 0.100229 | ||||||||
\(727\) | 14.3866 | 0.533568 | 0.266784 | − | 0.963756i | \(-0.414039\pi\) | ||||
0.266784 | + | 0.963756i | \(0.414039\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −4.59998 | −0.170253 | ||||||||
\(731\) | −76.2278 | −2.81939 | ||||||||
\(732\) | −10.8640 | −0.401544 | ||||||||
\(733\) | −43.3409 | −1.60083 | −0.800416 | − | 0.599444i | \(-0.795388\pi\) | ||||
−0.800416 | + | 0.599444i | \(0.795388\pi\) | |||||||
\(734\) | 14.6908 | 0.542249 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.176798 | −0.00651684 | ||||||||
\(737\) | 19.8576 | 0.731464 | ||||||||
\(738\) | 0.442251 | 0.0162795 | ||||||||
\(739\) | 7.73562 | 0.284560 | 0.142280 | − | 0.989826i | \(-0.454557\pi\) | ||||
0.142280 | + | 0.989826i | \(0.454557\pi\) | |||||||
\(740\) | −0.232933 | −0.00856278 | ||||||||
\(741\) | −24.0774 | −0.884505 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.4859 | 1.08173 | 0.540867 | − | 0.841108i | \(-0.318096\pi\) | ||||
0.540867 | + | 0.841108i | \(0.318096\pi\) | |||||||
\(744\) | 7.90709 | 0.289888 | ||||||||
\(745\) | −11.5708 | −0.423920 | ||||||||
\(746\) | −11.4901 | −0.420681 | ||||||||
\(747\) | 17.0488 | 0.623783 | ||||||||
\(748\) | −27.6375 | −1.01053 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 15.9997 | 0.584225 | ||||||||
\(751\) | −16.3584 | −0.596926 | −0.298463 | − | 0.954421i | \(-0.596474\pi\) | ||||
−0.298463 | + | 0.954421i | \(0.596474\pi\) | |||||||
\(752\) | −10.8318 | −0.394995 | ||||||||
\(753\) | −14.8746 | −0.542060 | ||||||||
\(754\) | 3.67641 | 0.133887 | ||||||||
\(755\) | 7.32259 | 0.266496 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −47.1225 | −1.71270 | −0.856349 | − | 0.516397i | \(-0.827273\pi\) | ||||
−0.856349 | + | 0.516397i | \(0.827273\pi\) | |||||||
\(758\) | −4.53755 | −0.164811 | ||||||||
\(759\) | −0.0844348 | −0.00306479 | ||||||||
\(760\) | −55.7934 | −2.02384 | ||||||||
\(761\) | 39.2835 | 1.42403 | 0.712013 | − | 0.702166i | \(-0.247784\pi\) | ||||
0.712013 | + | 0.702166i | \(0.247784\pi\) | |||||||
\(762\) | 8.34835 | 0.302429 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4.07702 | 0.147502 | ||||||||
\(765\) | 29.7228 | 1.07463 | ||||||||
\(766\) | −1.14626 | −0.0414161 | ||||||||
\(767\) | 29.7944 | 1.07581 | ||||||||
\(768\) | 2.54509 | 0.0918380 | ||||||||
\(769\) | 25.4482 | 0.917687 | 0.458843 | − | 0.888517i | \(-0.348264\pi\) | ||||
0.458843 | + | 0.888517i | \(0.348264\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.7559 | 0.783519 | ||||||||
\(772\) | 35.8672 | 1.29089 | ||||||||
\(773\) | −1.77505 | −0.0638440 | −0.0319220 | − | 0.999490i | \(-0.510163\pi\) | ||||
−0.0319220 | + | 0.999490i | \(0.510163\pi\) | |||||||
\(774\) | −4.86886 | −0.175008 | ||||||||
\(775\) | 63.1045 | 2.26678 | ||||||||
\(776\) | 0.364639 | 0.0130898 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.82727 | 0.137214 | ||||||||
\(779\) | −7.72487 | −0.276772 | ||||||||
\(780\) | −24.1429 | −0.864454 | ||||||||
\(781\) | −34.5530 | −1.23640 | ||||||||
\(782\) | 0.116879 | 0.00417958 | ||||||||
\(783\) | 2.66709 | 0.0953139 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 50.1606 | 1.79031 | ||||||||
\(786\) | 4.28638 | 0.152890 | ||||||||
\(787\) | −48.7760 | −1.73868 | −0.869338 | − | 0.494218i | \(-0.835455\pi\) | ||||
−0.869338 | + | 0.494218i | \(0.835455\pi\) | |||||||
\(788\) | 12.8772 | 0.458731 | ||||||||
\(789\) | 2.27801 | 0.0810992 | ||||||||
\(790\) | 4.10328 | 0.145988 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −3.72190 | −0.132252 | ||||||||
\(793\) | −18.7659 | −0.666398 | ||||||||
\(794\) | 13.2864 | 0.471518 | ||||||||
\(795\) | 2.34442 | 0.0831482 | ||||||||
\(796\) | −25.2086 | −0.893495 | ||||||||
\(797\) | −12.9486 | −0.458665 | −0.229332 | − | 0.973348i | \(-0.573654\pi\) | ||||
−0.229332 | + | 0.973348i | \(0.573654\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.1800 | 0.926183 | ||||||||
\(800\) | −62.1961 | −2.19897 | ||||||||
\(801\) | −8.69193 | −0.307114 | ||||||||
\(802\) | −5.34866 | −0.188868 | ||||||||
\(803\) | 5.35994 | 0.189148 | ||||||||
\(804\) | 16.1977 | 0.571251 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.47809 | 0.228181 | ||||||||
\(807\) | −2.03093 | −0.0714923 | ||||||||
\(808\) | −4.26222 | −0.149944 | ||||||||
\(809\) | −34.2717 | −1.20493 | −0.602464 | − | 0.798146i | \(-0.705814\pi\) | ||||
−0.602464 | + | 0.798146i | \(0.705814\pi\) | |||||||
\(810\) | 1.89847 | 0.0667054 | ||||||||
\(811\) | −39.7411 | −1.39550 | −0.697749 | − | 0.716342i | \(-0.745815\pi\) | ||||
−0.697749 | + | 0.716342i | \(0.745815\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15.8435 | −0.555657 | ||||||||
\(814\) | −0.0294196 | −0.00103116 | ||||||||
\(815\) | 52.9432 | 1.85452 | ||||||||
\(816\) | −19.8354 | −0.694376 | ||||||||
\(817\) | 85.0452 | 2.97536 | ||||||||
\(818\) | −5.97656 | −0.208965 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.74589 | −0.270498 | ||||||||
\(821\) | −42.6305 | −1.48782 | −0.743908 | − | 0.668282i | \(-0.767030\pi\) | ||||
−0.743908 | + | 0.668282i | \(0.767030\pi\) | |||||||
\(822\) | −2.67935 | −0.0934532 | ||||||||
\(823\) | 11.8760 | 0.413973 | 0.206986 | − | 0.978344i | \(-0.433634\pi\) | ||||
0.206986 | + | 0.978344i | \(0.433634\pi\) | |||||||
\(824\) | −1.19396 | −0.0415937 | ||||||||
\(825\) | −29.7036 | −1.03415 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.5702 | −0.645751 | −0.322875 | − | 0.946442i | \(-0.604649\pi\) | ||||
−0.322875 | + | 0.946442i | \(0.604649\pi\) | |||||||
\(828\) | −0.0688730 | −0.00239350 | ||||||||
\(829\) | 45.5475 | 1.58193 | 0.790966 | − | 0.611860i | \(-0.209579\pi\) | ||||
0.790966 | + | 0.611860i | \(0.209579\pi\) | |||||||
\(830\) | 32.3667 | 1.12346 | ||||||||
\(831\) | −3.50000 | −0.121414 | ||||||||
\(832\) | 11.4732 | 0.397761 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −0.738614 | −0.0255761 | ||||||||
\(835\) | 27.2745 | 0.943875 | ||||||||
\(836\) | 30.8344 | 1.06643 | ||||||||
\(837\) | 4.69959 | 0.162442 | ||||||||
\(838\) | 14.2300 | 0.491566 | ||||||||
\(839\) | 0.520222 | 0.0179601 | 0.00898004 | − | 0.999960i | \(-0.497142\pi\) | ||||
0.00898004 | + | 0.999960i | \(0.497142\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.8866 | −0.754712 | ||||||||
\(842\) | 14.2703 | 0.491785 | ||||||||
\(843\) | 26.7164 | 0.920161 | ||||||||
\(844\) | −42.0593 | −1.44774 | ||||||||
\(845\) | 14.1023 | 0.485134 | ||||||||
\(846\) | 1.67218 | 0.0574909 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.56454 | −0.0537265 | ||||||||
\(849\) | −15.6917 | −0.538537 | ||||||||
\(850\) | 41.1172 | 1.41031 | ||||||||
\(851\) | −0.00114782 | −3.93466e−5 0 | ||||||||
\(852\) | −28.1847 | −0.965592 | ||||||||
\(853\) | 26.2375 | 0.898356 | 0.449178 | − | 0.893442i | \(-0.351717\pi\) | ||||
0.449178 | + | 0.893442i | \(0.351717\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −33.1609 | −1.13408 | ||||||||
\(856\) | 10.8032 | 0.369245 | ||||||||
\(857\) | 37.6320 | 1.28548 | 0.642742 | − | 0.766083i | \(-0.277797\pi\) | ||||
0.642742 | + | 0.766083i | \(0.277797\pi\) | |||||||
\(858\) | −3.04926 | −0.104100 | ||||||||
\(859\) | 21.6450 | 0.738518 | 0.369259 | − | 0.929327i | \(-0.379612\pi\) | ||||
0.369259 | + | 0.929327i | \(0.379612\pi\) | |||||||
\(860\) | 85.2766 | 2.90791 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.62071 | −0.157382 | ||||||||
\(863\) | −33.1370 | −1.12800 | −0.563998 | − | 0.825776i | \(-0.690737\pi\) | ||||
−0.563998 | + | 0.825776i | \(0.690737\pi\) | |||||||
\(864\) | −4.63194 | −0.157582 | ||||||||
\(865\) | −2.48566 | −0.0845151 | ||||||||
\(866\) | 1.67668 | 0.0569757 | ||||||||
\(867\) | 30.9413 | 1.05082 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.78119 | −0.162191 | ||||||||
\(870\) | 5.06338 | 0.171665 | ||||||||
\(871\) | 27.9793 | 0.948041 | ||||||||
\(872\) | −4.24746 | −0.143837 | ||||||||
\(873\) | 0.216724 | 0.00733500 | ||||||||
\(874\) | −0.130399 | −0.00441080 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.37208 | 0.147719 | ||||||||
\(877\) | 2.91954 | 0.0985857 | 0.0492929 | − | 0.998784i | \(-0.484303\pi\) | ||||
0.0492929 | + | 0.998784i | \(0.484303\pi\) | |||||||
\(878\) | −1.98689 | −0.0670544 | ||||||||
\(879\) | −14.4844 | −0.488548 | ||||||||
\(880\) | 27.2037 | 0.917038 | ||||||||
\(881\) | 24.7028 | 0.832258 | 0.416129 | − | 0.909306i | \(-0.363387\pi\) | ||||
0.416129 | + | 0.909306i | \(0.363387\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.69015 | 0.225141 | 0.112571 | − | 0.993644i | \(-0.464092\pi\) | ||||
0.112571 | + | 0.993644i | \(0.464092\pi\) | |||||||
\(884\) | −38.9412 | −1.30973 | ||||||||
\(885\) | 41.0347 | 1.37937 | ||||||||
\(886\) | 3.62605 | 0.121819 | ||||||||
\(887\) | 9.40760 | 0.315876 | 0.157938 | − | 0.987449i | \(-0.449515\pi\) | ||||
0.157938 | + | 0.987449i | \(0.449515\pi\) | |||||||
\(888\) | −0.0505959 | −0.00169789 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −16.5014 | −0.553127 | ||||||||
\(891\) | −2.21212 | −0.0741088 | ||||||||
\(892\) | 44.5320 | 1.49104 | ||||||||
\(893\) | −29.2083 | −0.977419 | ||||||||
\(894\) | −1.19205 | −0.0398682 | ||||||||
\(895\) | −91.3957 | −3.05502 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.118968 | −0.00397223 | ||||||||
\(898\) | −14.1604 | −0.472539 | ||||||||
\(899\) | 12.5342 | 0.418040 | ||||||||
\(900\) | −24.2291 | −0.807635 | ||||||||
\(901\) | 3.78143 | 0.125978 | ||||||||
\(902\) | −0.978311 | −0.0325742 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.89242 | 0.0962004 | ||||||||
\(905\) | −91.4371 | −3.03947 | ||||||||
\(906\) | 0.754393 | 0.0250630 | ||||||||
\(907\) | 21.7567 | 0.722421 | 0.361210 | − | 0.932484i | \(-0.382364\pi\) | ||||
0.361210 | + | 0.932484i | \(0.382364\pi\) | |||||||
\(908\) | 21.1851 | 0.703053 | ||||||||
\(909\) | −2.53326 | −0.0840229 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.9801 | −1.29147 | −0.645734 | − | 0.763562i | \(-0.723449\pi\) | ||||
−0.645734 | + | 0.763562i | \(0.723449\pi\) | |||||||
\(912\) | 22.1297 | 0.732789 | ||||||||
\(913\) | −37.7140 | −1.24815 | ||||||||
\(914\) | −1.73530 | −0.0573986 | ||||||||
\(915\) | −25.8456 | −0.854431 | ||||||||
\(916\) | −27.8621 | −0.920589 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3.06213 | 0.101065 | ||||||||
\(919\) | −57.3909 | −1.89315 | −0.946576 | − | 0.322480i | \(-0.895483\pi\) | ||||
−0.946576 | + | 0.322480i | \(0.895483\pi\) | |||||||
\(920\) | −0.275679 | −0.00908888 | ||||||||
\(921\) | 19.7492 | 0.650758 | ||||||||
\(922\) | 11.6798 | 0.384654 | ||||||||
\(923\) | −48.6850 | −1.60249 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.403794 | −0.0132767 | ||||||||
\(926\) | −2.33503 | −0.0767338 | ||||||||
\(927\) | −0.709634 | −0.0233074 | ||||||||
\(928\) | −12.3538 | −0.405533 | ||||||||
\(929\) | 35.3944 | 1.16125 | 0.580627 | − | 0.814170i | \(-0.302808\pi\) | ||||
0.580627 | + | 0.814170i | \(0.302808\pi\) | |||||||
\(930\) | 8.92203 | 0.292565 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 13.0661 | 0.427993 | ||||||||
\(933\) | −18.1355 | −0.593729 | ||||||||
\(934\) | 8.89079 | 0.290916 | ||||||||
\(935\) | −65.7504 | −2.15027 | ||||||||
\(936\) | −5.24414 | −0.171410 | ||||||||
\(937\) | 33.9294 | 1.10842 | 0.554212 | − | 0.832376i | \(-0.313020\pi\) | ||||
0.554212 | + | 0.832376i | \(0.313020\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.28237 | 0.107116 | ||||||||
\(940\) | −29.2878 | −0.955263 | ||||||||
\(941\) | 18.0053 | 0.586955 | 0.293477 | − | 0.955966i | \(-0.405187\pi\) | ||||
0.293477 | + | 0.955966i | \(0.405187\pi\) | |||||||
\(942\) | 5.16769 | 0.168372 | ||||||||
\(943\) | −0.0381692 | −0.00124296 | ||||||||
\(944\) | −27.3843 | −0.891283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.7705 | 0.350179 | ||||||||
\(947\) | −28.6412 | −0.930714 | −0.465357 | − | 0.885123i | \(-0.654074\pi\) | ||||
−0.465357 | + | 0.885123i | \(0.654074\pi\) | |||||||
\(948\) | −3.90000 | −0.126666 | ||||||||
\(949\) | 7.55214 | 0.245153 | ||||||||
\(950\) | −45.8733 | −1.48833 | ||||||||
\(951\) | −0.440700 | −0.0142907 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.2041 | 0.330544 | 0.165272 | − | 0.986248i | \(-0.447150\pi\) | ||||
0.165272 | + | 0.986248i | \(0.447150\pi\) | |||||||
\(954\) | 0.241529 | 0.00781980 | ||||||||
\(955\) | 9.69934 | 0.313863 | ||||||||
\(956\) | 24.8752 | 0.804522 | ||||||||
\(957\) | −5.89991 | −0.190717 | ||||||||
\(958\) | −10.3731 | −0.335139 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 15.8016 | 0.509994 | ||||||||
\(961\) | −8.91384 | −0.287543 | ||||||||
\(962\) | −0.0414520 | −0.00133647 | ||||||||
\(963\) | 6.42089 | 0.206910 | ||||||||
\(964\) | 6.33169 | 0.203930 | ||||||||
\(965\) | 85.3289 | 2.74684 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −49.6045 | −1.59517 | −0.797587 | − | 0.603204i | \(-0.793891\pi\) | ||||
−0.797587 | + | 0.603204i | \(0.793891\pi\) | |||||||
\(968\) | −10.2743 | −0.330228 | ||||||||
\(969\) | −53.4867 | −1.71824 | ||||||||
\(970\) | 0.411444 | 0.0132107 | ||||||||
\(971\) | −26.3030 | −0.844102 | −0.422051 | − | 0.906572i | \(-0.638690\pi\) | ||||
−0.422051 | + | 0.906572i | \(0.638690\pi\) | |||||||
\(972\) | −1.80441 | −0.0578766 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −17.5484 | −0.562287 | ||||||||
\(975\) | −41.8522 | −1.34034 | ||||||||
\(976\) | 17.2480 | 0.552093 | ||||||||
\(977\) | 32.8265 | 1.05021 | 0.525106 | − | 0.851037i | \(-0.324026\pi\) | ||||
0.525106 | + | 0.851037i | \(0.324026\pi\) | |||||||
\(978\) | 5.45436 | 0.174411 | ||||||||
\(979\) | 19.2276 | 0.614516 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.52449 | −0.0806006 | ||||||||
\(982\) | −18.5936 | −0.593347 | ||||||||
\(983\) | 12.6918 | 0.404805 | 0.202403 | − | 0.979302i | \(-0.435125\pi\) | ||||
0.202403 | + | 0.979302i | \(0.435125\pi\) | |||||||
\(984\) | −1.68250 | −0.0536363 | ||||||||
\(985\) | 30.6352 | 0.976118 | ||||||||
\(986\) | 8.16696 | 0.260089 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 43.4456 | 1.38219 | ||||||||
\(989\) | 0.420215 | 0.0133621 | ||||||||
\(990\) | −4.19964 | −0.133473 | ||||||||
\(991\) | −52.5027 | −1.66780 | −0.833902 | − | 0.551912i | \(-0.813898\pi\) | ||||
−0.833902 | + | 0.551912i | \(0.813898\pi\) | |||||||
\(992\) | −21.7682 | −0.691142 | ||||||||
\(993\) | −3.26805 | −0.103708 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −59.9718 | −1.90123 | ||||||||
\(996\) | −30.7631 | −0.974767 | ||||||||
\(997\) | −24.7134 | −0.782683 | −0.391341 | − | 0.920246i | \(-0.627989\pi\) | ||||
−0.391341 | + | 0.920246i | \(0.627989\pi\) | |||||||
\(998\) | 2.52496 | 0.0799262 | ||||||||
\(999\) | −0.0300718 | −0.000951430 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6027.2.a.bk.1.7 | 14 | ||
7.3 | odd | 6 | 861.2.i.g.247.8 | ✓ | 28 | ||
7.5 | odd | 6 | 861.2.i.g.739.8 | yes | 28 | ||
7.6 | odd | 2 | 6027.2.a.bj.1.7 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.i.g.247.8 | ✓ | 28 | 7.3 | odd | 6 | ||
861.2.i.g.739.8 | yes | 28 | 7.5 | odd | 6 | ||
6027.2.a.bj.1.7 | 14 | 7.6 | odd | 2 | |||
6027.2.a.bk.1.7 | 14 | 1.1 | even | 1 | trivial |