Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
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: | \( x^{14} - 6 x^{13} - 29 x^{12} + 207 x^{11} + 269 x^{10} - 2601 x^{9} - 847 x^{8} + 14851 x^{7} + 678 x^{6} - 39390 x^{5} - 3280 x^{4} + 42456 x^{3} + 10816 x^{2} + \cdots - 2048 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(2.22430\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.22430 | −0.994736 | −0.497368 | − | 0.867540i | \(-0.665700\pi\) | ||||
−0.497368 | + | 0.867540i | \(0.665700\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.37131 | 0.518308 | 0.259154 | − | 0.965836i | \(-0.416556\pi\) | ||||
0.259154 | + | 0.965836i | \(0.416556\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.22430 | 0.703385 | ||||||||
\(11\) | 3.97219 | 1.19766 | 0.598830 | − | 0.800876i | \(-0.295632\pi\) | ||||
0.598830 | + | 0.800876i | \(0.295632\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −1.37131 | −0.366499 | ||||||||
\(15\) | −2.22430 | −0.574311 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.05875 | 0.499321 | 0.249660 | − | 0.968333i | \(-0.419681\pi\) | ||||
0.249660 | + | 0.968333i | \(0.419681\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −6.55850 | −1.50462 | −0.752311 | − | 0.658808i | \(-0.771061\pi\) | ||||
−0.752311 | + | 0.658808i | \(0.771061\pi\) | |||||||
\(20\) | −2.22430 | −0.497368 | ||||||||
\(21\) | 1.37131 | 0.299245 | ||||||||
\(22\) | −3.97219 | −0.846874 | ||||||||
\(23\) | −0.577248 | −0.120365 | −0.0601823 | − | 0.998187i | \(-0.519168\pi\) | ||||
−0.0601823 | + | 0.998187i | \(0.519168\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −0.0525006 | −0.0105001 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.37131 | 0.259154 | ||||||||
\(29\) | −3.79856 | −0.705375 | −0.352687 | − | 0.935741i | \(-0.614732\pi\) | ||||
−0.352687 | + | 0.935741i | \(0.614732\pi\) | |||||||
\(30\) | 2.22430 | 0.406099 | ||||||||
\(31\) | 2.84411 | 0.510818 | 0.255409 | − | 0.966833i | \(-0.417790\pi\) | ||||
0.255409 | + | 0.966833i | \(0.417790\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.97219 | 0.691470 | ||||||||
\(34\) | −2.05875 | −0.353073 | ||||||||
\(35\) | −3.05021 | −0.515579 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −3.41291 | −0.561079 | −0.280540 | − | 0.959842i | \(-0.590513\pi\) | ||||
−0.280540 | + | 0.959842i | \(0.590513\pi\) | |||||||
\(38\) | 6.55850 | 1.06393 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 2.22430 | 0.351692 | ||||||||
\(41\) | −6.35321 | −0.992205 | −0.496103 | − | 0.868264i | \(-0.665236\pi\) | ||||
−0.496103 | + | 0.868264i | \(0.665236\pi\) | |||||||
\(42\) | −1.37131 | −0.211598 | ||||||||
\(43\) | 12.0059 | 1.83088 | 0.915438 | − | 0.402460i | \(-0.131845\pi\) | ||||
0.915438 | + | 0.402460i | \(0.131845\pi\) | |||||||
\(44\) | 3.97219 | 0.598830 | ||||||||
\(45\) | −2.22430 | −0.331579 | ||||||||
\(46\) | 0.577248 | 0.0851106 | ||||||||
\(47\) | 2.35194 | 0.343066 | 0.171533 | − | 0.985178i | \(-0.445128\pi\) | ||||
0.171533 | + | 0.985178i | \(0.445128\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −5.11950 | −0.731357 | ||||||||
\(50\) | 0.0525006 | 0.00742471 | ||||||||
\(51\) | 2.05875 | 0.288283 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | −9.83809 | −1.35137 | −0.675683 | − | 0.737192i | \(-0.736151\pi\) | ||||
−0.675683 | + | 0.737192i | \(0.736151\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −8.83534 | −1.19136 | ||||||||
\(56\) | −1.37131 | −0.183249 | ||||||||
\(57\) | −6.55850 | −0.868694 | ||||||||
\(58\) | 3.79856 | 0.498775 | ||||||||
\(59\) | 5.32093 | 0.692727 | 0.346363 | − | 0.938100i | \(-0.387416\pi\) | ||||
0.346363 | + | 0.938100i | \(0.387416\pi\) | |||||||
\(60\) | −2.22430 | −0.287156 | ||||||||
\(61\) | 4.72419 | 0.604870 | 0.302435 | − | 0.953170i | \(-0.402200\pi\) | ||||
0.302435 | + | 0.953170i | \(0.402200\pi\) | |||||||
\(62\) | −2.84411 | −0.361203 | ||||||||
\(63\) | 1.37131 | 0.172769 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.22430 | 0.275890 | ||||||||
\(66\) | −3.97219 | −0.488943 | ||||||||
\(67\) | 2.48532 | 0.303630 | 0.151815 | − | 0.988409i | \(-0.451488\pi\) | ||||
0.151815 | + | 0.988409i | \(0.451488\pi\) | |||||||
\(68\) | 2.05875 | 0.249660 | ||||||||
\(69\) | −0.577248 | −0.0694925 | ||||||||
\(70\) | 3.05021 | 0.364570 | ||||||||
\(71\) | −9.14181 | −1.08493 | −0.542466 | − | 0.840077i | \(-0.682509\pi\) | ||||
−0.542466 | + | 0.840077i | \(0.682509\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 9.71266 | 1.13678 | 0.568390 | − | 0.822759i | \(-0.307566\pi\) | ||||
0.568390 | + | 0.822759i | \(0.307566\pi\) | |||||||
\(74\) | 3.41291 | 0.396743 | ||||||||
\(75\) | −0.0525006 | −0.00606225 | ||||||||
\(76\) | −6.55850 | −0.752311 | ||||||||
\(77\) | 5.44712 | 0.620757 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | −1.40658 | −0.158252 | −0.0791261 | − | 0.996865i | \(-0.525213\pi\) | ||||
−0.0791261 | + | 0.996865i | \(0.525213\pi\) | |||||||
\(80\) | −2.22430 | −0.248684 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.35321 | 0.701595 | ||||||||
\(83\) | −12.3179 | −1.35207 | −0.676034 | − | 0.736870i | \(-0.736303\pi\) | ||||
−0.676034 | + | 0.736870i | \(0.736303\pi\) | |||||||
\(84\) | 1.37131 | 0.149623 | ||||||||
\(85\) | −4.57928 | −0.496693 | ||||||||
\(86\) | −12.0059 | −1.29462 | ||||||||
\(87\) | −3.79856 | −0.407248 | ||||||||
\(88\) | −3.97219 | −0.423437 | ||||||||
\(89\) | −17.1581 | −1.81875 | −0.909377 | − | 0.415974i | \(-0.863441\pi\) | ||||
−0.909377 | + | 0.415974i | \(0.863441\pi\) | |||||||
\(90\) | 2.22430 | 0.234462 | ||||||||
\(91\) | −1.37131 | −0.143753 | ||||||||
\(92\) | −0.577248 | −0.0601823 | ||||||||
\(93\) | 2.84411 | 0.294921 | ||||||||
\(94\) | −2.35194 | −0.242584 | ||||||||
\(95\) | 14.5881 | 1.49670 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −14.8494 | −1.50773 | −0.753863 | − | 0.657032i | \(-0.771812\pi\) | ||||
−0.753863 | + | 0.657032i | \(0.771812\pi\) | |||||||
\(98\) | 5.11950 | 0.517148 | ||||||||
\(99\) | 3.97219 | 0.399220 | ||||||||
\(100\) | −0.0525006 | −0.00525006 | ||||||||
\(101\) | 7.50888 | 0.747161 | 0.373581 | − | 0.927598i | \(-0.378130\pi\) | ||||
0.373581 | + | 0.927598i | \(0.378130\pi\) | |||||||
\(102\) | −2.05875 | −0.203847 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | −3.05021 | −0.297670 | ||||||||
\(106\) | 9.83809 | 0.955560 | ||||||||
\(107\) | −10.7285 | −1.03716 | −0.518582 | − | 0.855028i | \(-0.673540\pi\) | ||||
−0.518582 | + | 0.855028i | \(0.673540\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −14.9243 | −1.42949 | −0.714745 | − | 0.699385i | \(-0.753457\pi\) | ||||
−0.714745 | + | 0.699385i | \(0.753457\pi\) | |||||||
\(110\) | 8.83534 | 0.842416 | ||||||||
\(111\) | −3.41291 | −0.323939 | ||||||||
\(112\) | 1.37131 | 0.129577 | ||||||||
\(113\) | −5.51653 | −0.518952 | −0.259476 | − | 0.965750i | \(-0.583550\pi\) | ||||
−0.259476 | + | 0.965750i | \(0.583550\pi\) | |||||||
\(114\) | 6.55850 | 0.614260 | ||||||||
\(115\) | 1.28397 | 0.119731 | ||||||||
\(116\) | −3.79856 | −0.352687 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −5.32093 | −0.489832 | ||||||||
\(119\) | 2.82320 | 0.258802 | ||||||||
\(120\) | 2.22430 | 0.203050 | ||||||||
\(121\) | 4.77831 | 0.434392 | ||||||||
\(122\) | −4.72419 | −0.427708 | ||||||||
\(123\) | −6.35321 | −0.572850 | ||||||||
\(124\) | 2.84411 | 0.255409 | ||||||||
\(125\) | 11.2383 | 1.00518 | ||||||||
\(126\) | −1.37131 | −0.122166 | ||||||||
\(127\) | −0.708893 | −0.0629041 | −0.0314520 | − | 0.999505i | \(-0.510013\pi\) | ||||
−0.0314520 | + | 0.999505i | \(0.510013\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 12.0059 | 1.05706 | ||||||||
\(130\) | −2.22430 | −0.195084 | ||||||||
\(131\) | 9.30987 | 0.813407 | 0.406704 | − | 0.913560i | \(-0.366678\pi\) | ||||
0.406704 | + | 0.913560i | \(0.366678\pi\) | |||||||
\(132\) | 3.97219 | 0.345735 | ||||||||
\(133\) | −8.99376 | −0.779858 | ||||||||
\(134\) | −2.48532 | −0.214699 | ||||||||
\(135\) | −2.22430 | −0.191437 | ||||||||
\(136\) | −2.05875 | −0.176537 | ||||||||
\(137\) | −10.1749 | −0.869302 | −0.434651 | − | 0.900599i | \(-0.643128\pi\) | ||||
−0.434651 | + | 0.900599i | \(0.643128\pi\) | |||||||
\(138\) | 0.577248 | 0.0491386 | ||||||||
\(139\) | 4.75647 | 0.403438 | 0.201719 | − | 0.979443i | \(-0.435347\pi\) | ||||
0.201719 | + | 0.979443i | \(0.435347\pi\) | |||||||
\(140\) | −3.05021 | −0.257790 | ||||||||
\(141\) | 2.35194 | 0.198069 | ||||||||
\(142\) | 9.14181 | 0.767163 | ||||||||
\(143\) | −3.97219 | −0.332171 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 8.44913 | 0.701662 | ||||||||
\(146\) | −9.71266 | −0.803826 | ||||||||
\(147\) | −5.11950 | −0.422249 | ||||||||
\(148\) | −3.41291 | −0.280540 | ||||||||
\(149\) | 12.5814 | 1.03071 | 0.515355 | − | 0.856977i | \(-0.327660\pi\) | ||||
0.515355 | + | 0.856977i | \(0.327660\pi\) | |||||||
\(150\) | 0.0525006 | 0.00428666 | ||||||||
\(151\) | 16.7636 | 1.36420 | 0.682102 | − | 0.731257i | \(-0.261066\pi\) | ||||
0.682102 | + | 0.731257i | \(0.261066\pi\) | |||||||
\(152\) | 6.55850 | 0.531965 | ||||||||
\(153\) | 2.05875 | 0.166440 | ||||||||
\(154\) | −5.44712 | −0.438941 | ||||||||
\(155\) | −6.32616 | −0.508129 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | −0.478623 | −0.0381983 | −0.0190991 | − | 0.999818i | \(-0.506080\pi\) | ||||
−0.0190991 | + | 0.999818i | \(0.506080\pi\) | |||||||
\(158\) | 1.40658 | 0.111901 | ||||||||
\(159\) | −9.83809 | −0.780211 | ||||||||
\(160\) | 2.22430 | 0.175846 | ||||||||
\(161\) | −0.791588 | −0.0623859 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −2.15078 | −0.168462 | −0.0842310 | − | 0.996446i | \(-0.526843\pi\) | ||||
−0.0842310 | + | 0.996446i | \(0.526843\pi\) | |||||||
\(164\) | −6.35321 | −0.496103 | ||||||||
\(165\) | −8.83534 | −0.687830 | ||||||||
\(166\) | 12.3179 | 0.956057 | ||||||||
\(167\) | −6.59412 | −0.510268 | −0.255134 | − | 0.966906i | \(-0.582120\pi\) | ||||
−0.255134 | + | 0.966906i | \(0.582120\pi\) | |||||||
\(168\) | −1.37131 | −0.105799 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 4.57928 | 0.351215 | ||||||||
\(171\) | −6.55850 | −0.501541 | ||||||||
\(172\) | 12.0059 | 0.915438 | ||||||||
\(173\) | −19.9171 | −1.51427 | −0.757134 | − | 0.653260i | \(-0.773401\pi\) | ||||
−0.757134 | + | 0.653260i | \(0.773401\pi\) | |||||||
\(174\) | 3.79856 | 0.287968 | ||||||||
\(175\) | −0.0719948 | −0.00544230 | ||||||||
\(176\) | 3.97219 | 0.299415 | ||||||||
\(177\) | 5.32093 | 0.399946 | ||||||||
\(178\) | 17.1581 | 1.28605 | ||||||||
\(179\) | −5.92624 | −0.442948 | −0.221474 | − | 0.975166i | \(-0.571087\pi\) | ||||
−0.221474 | + | 0.975166i | \(0.571087\pi\) | |||||||
\(180\) | −2.22430 | −0.165789 | ||||||||
\(181\) | 8.59434 | 0.638812 | 0.319406 | − | 0.947618i | \(-0.396517\pi\) | ||||
0.319406 | + | 0.947618i | \(0.396517\pi\) | |||||||
\(182\) | 1.37131 | 0.101649 | ||||||||
\(183\) | 4.72419 | 0.349222 | ||||||||
\(184\) | 0.577248 | 0.0425553 | ||||||||
\(185\) | 7.59133 | 0.558126 | ||||||||
\(186\) | −2.84411 | −0.208541 | ||||||||
\(187\) | 8.17776 | 0.598017 | ||||||||
\(188\) | 2.35194 | 0.171533 | ||||||||
\(189\) | 1.37131 | 0.0997484 | ||||||||
\(190\) | −14.5881 | −1.05833 | ||||||||
\(191\) | −7.69976 | −0.557135 | −0.278567 | − | 0.960417i | \(-0.589860\pi\) | ||||
−0.278567 | + | 0.960417i | \(0.589860\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 16.7819 | 1.20799 | 0.603993 | − | 0.796989i | \(-0.293575\pi\) | ||||
0.603993 | + | 0.796989i | \(0.293575\pi\) | |||||||
\(194\) | 14.8494 | 1.06612 | ||||||||
\(195\) | 2.22430 | 0.159285 | ||||||||
\(196\) | −5.11950 | −0.365679 | ||||||||
\(197\) | −19.5782 | −1.39489 | −0.697445 | − | 0.716639i | \(-0.745680\pi\) | ||||
−0.697445 | + | 0.716639i | \(0.745680\pi\) | |||||||
\(198\) | −3.97219 | −0.282291 | ||||||||
\(199\) | 19.3299 | 1.37026 | 0.685130 | − | 0.728421i | \(-0.259745\pi\) | ||||
0.685130 | + | 0.728421i | \(0.259745\pi\) | |||||||
\(200\) | 0.0525006 | 0.00371236 | ||||||||
\(201\) | 2.48532 | 0.175301 | ||||||||
\(202\) | −7.50888 | −0.528323 | ||||||||
\(203\) | −5.20902 | −0.365601 | ||||||||
\(204\) | 2.05875 | 0.144142 | ||||||||
\(205\) | 14.1314 | 0.986982 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | −0.577248 | −0.0401215 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | −26.0516 | −1.80203 | ||||||||
\(210\) | 3.05021 | 0.210484 | ||||||||
\(211\) | 15.3213 | 1.05476 | 0.527380 | − | 0.849629i | \(-0.323174\pi\) | ||||
0.527380 | + | 0.849629i | \(0.323174\pi\) | |||||||
\(212\) | −9.83809 | −0.675683 | ||||||||
\(213\) | −9.14181 | −0.626386 | ||||||||
\(214\) | 10.7285 | 0.733386 | ||||||||
\(215\) | −26.7046 | −1.82124 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 3.90017 | 0.264761 | ||||||||
\(218\) | 14.9243 | 1.01080 | ||||||||
\(219\) | 9.71266 | 0.656321 | ||||||||
\(220\) | −8.83534 | −0.595678 | ||||||||
\(221\) | −2.05875 | −0.138487 | ||||||||
\(222\) | 3.41291 | 0.229060 | ||||||||
\(223\) | 3.09661 | 0.207364 | 0.103682 | − | 0.994610i | \(-0.466938\pi\) | ||||
0.103682 | + | 0.994610i | \(0.466938\pi\) | |||||||
\(224\) | −1.37131 | −0.0916247 | ||||||||
\(225\) | −0.0525006 | −0.00350004 | ||||||||
\(226\) | 5.51653 | 0.366954 | ||||||||
\(227\) | 6.51896 | 0.432679 | 0.216339 | − | 0.976318i | \(-0.430588\pi\) | ||||
0.216339 | + | 0.976318i | \(0.430588\pi\) | |||||||
\(228\) | −6.55850 | −0.434347 | ||||||||
\(229\) | −2.09643 | −0.138536 | −0.0692678 | − | 0.997598i | \(-0.522066\pi\) | ||||
−0.0692678 | + | 0.997598i | \(0.522066\pi\) | |||||||
\(230\) | −1.28397 | −0.0846626 | ||||||||
\(231\) | 5.44712 | 0.358394 | ||||||||
\(232\) | 3.79856 | 0.249388 | ||||||||
\(233\) | 16.0235 | 1.04973 | 0.524866 | − | 0.851185i | \(-0.324116\pi\) | ||||
0.524866 | + | 0.851185i | \(0.324116\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | −5.23142 | −0.341260 | ||||||||
\(236\) | 5.32093 | 0.346363 | ||||||||
\(237\) | −1.40658 | −0.0913669 | ||||||||
\(238\) | −2.82320 | −0.183001 | ||||||||
\(239\) | 3.86885 | 0.250255 | 0.125128 | − | 0.992141i | \(-0.460066\pi\) | ||||
0.125128 | + | 0.992141i | \(0.460066\pi\) | |||||||
\(240\) | −2.22430 | −0.143578 | ||||||||
\(241\) | 18.4872 | 1.19086 | 0.595432 | − | 0.803406i | \(-0.296981\pi\) | ||||
0.595432 | + | 0.803406i | \(0.296981\pi\) | |||||||
\(242\) | −4.77831 | −0.307161 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 4.72419 | 0.302435 | ||||||||
\(245\) | 11.3873 | 0.727507 | ||||||||
\(246\) | 6.35321 | 0.405066 | ||||||||
\(247\) | 6.55850 | 0.417307 | ||||||||
\(248\) | −2.84411 | −0.180601 | ||||||||
\(249\) | −12.3179 | −0.780617 | ||||||||
\(250\) | −11.2383 | −0.710770 | ||||||||
\(251\) | −13.1469 | −0.829822 | −0.414911 | − | 0.909862i | \(-0.636187\pi\) | ||||
−0.414911 | + | 0.909862i | \(0.636187\pi\) | |||||||
\(252\) | 1.37131 | 0.0863846 | ||||||||
\(253\) | −2.29294 | −0.144156 | ||||||||
\(254\) | 0.708893 | 0.0444799 | ||||||||
\(255\) | −4.57928 | −0.286766 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −13.3601 | −0.833379 | −0.416690 | − | 0.909049i | \(-0.636810\pi\) | ||||
−0.416690 | + | 0.909049i | \(0.636810\pi\) | |||||||
\(258\) | −12.0059 | −0.747452 | ||||||||
\(259\) | −4.68017 | −0.290812 | ||||||||
\(260\) | 2.22430 | 0.137945 | ||||||||
\(261\) | −3.79856 | −0.235125 | ||||||||
\(262\) | −9.30987 | −0.575166 | ||||||||
\(263\) | 9.94191 | 0.613045 | 0.306522 | − | 0.951863i | \(-0.400835\pi\) | ||||
0.306522 | + | 0.951863i | \(0.400835\pi\) | |||||||
\(264\) | −3.97219 | −0.244472 | ||||||||
\(265\) | 21.8828 | 1.34425 | ||||||||
\(266\) | 8.99376 | 0.551443 | ||||||||
\(267\) | −17.1581 | −1.05006 | ||||||||
\(268\) | 2.48532 | 0.151815 | ||||||||
\(269\) | 15.0666 | 0.918628 | 0.459314 | − | 0.888274i | \(-0.348095\pi\) | ||||
0.459314 | + | 0.888274i | \(0.348095\pi\) | |||||||
\(270\) | 2.22430 | 0.135366 | ||||||||
\(271\) | 9.46422 | 0.574910 | 0.287455 | − | 0.957794i | \(-0.407191\pi\) | ||||
0.287455 | + | 0.957794i | \(0.407191\pi\) | |||||||
\(272\) | 2.05875 | 0.124830 | ||||||||
\(273\) | −1.37131 | −0.0829957 | ||||||||
\(274\) | 10.1749 | 0.614689 | ||||||||
\(275\) | −0.208543 | −0.0125756 | ||||||||
\(276\) | −0.577248 | −0.0347463 | ||||||||
\(277\) | −25.7673 | −1.54821 | −0.774104 | − | 0.633059i | \(-0.781799\pi\) | ||||
−0.774104 | + | 0.633059i | \(0.781799\pi\) | |||||||
\(278\) | −4.75647 | −0.285274 | ||||||||
\(279\) | 2.84411 | 0.170273 | ||||||||
\(280\) | 3.05021 | 0.182285 | ||||||||
\(281\) | −0.119722 | −0.00714203 | −0.00357102 | − | 0.999994i | \(-0.501137\pi\) | ||||
−0.00357102 | + | 0.999994i | \(0.501137\pi\) | |||||||
\(282\) | −2.35194 | −0.140056 | ||||||||
\(283\) | 30.8366 | 1.83304 | 0.916522 | − | 0.399985i | \(-0.130985\pi\) | ||||
0.916522 | + | 0.399985i | \(0.130985\pi\) | |||||||
\(284\) | −9.14181 | −0.542466 | ||||||||
\(285\) | 14.5881 | 0.864122 | ||||||||
\(286\) | 3.97219 | 0.234881 | ||||||||
\(287\) | −8.71224 | −0.514268 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −12.7615 | −0.750679 | ||||||||
\(290\) | −8.44913 | −0.496150 | ||||||||
\(291\) | −14.8494 | −0.870486 | ||||||||
\(292\) | 9.71266 | 0.568390 | ||||||||
\(293\) | −6.70517 | −0.391720 | −0.195860 | − | 0.980632i | \(-0.562750\pi\) | ||||
−0.195860 | + | 0.980632i | \(0.562750\pi\) | |||||||
\(294\) | 5.11950 | 0.298575 | ||||||||
\(295\) | −11.8353 | −0.689080 | ||||||||
\(296\) | 3.41291 | 0.198371 | ||||||||
\(297\) | 3.97219 | 0.230490 | ||||||||
\(298\) | −12.5814 | −0.728822 | ||||||||
\(299\) | 0.577248 | 0.0333831 | ||||||||
\(300\) | −0.0525006 | −0.00303113 | ||||||||
\(301\) | 16.4638 | 0.948957 | ||||||||
\(302\) | −16.7636 | −0.964637 | ||||||||
\(303\) | 7.50888 | 0.431374 | ||||||||
\(304\) | −6.55850 | −0.376156 | ||||||||
\(305\) | −10.5080 | −0.601686 | ||||||||
\(306\) | −2.05875 | −0.117691 | ||||||||
\(307\) | −28.1100 | −1.60432 | −0.802161 | − | 0.597108i | \(-0.796316\pi\) | ||||
−0.802161 | + | 0.597108i | \(0.796316\pi\) | |||||||
\(308\) | 5.44712 | 0.310378 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 6.32616 | 0.359301 | ||||||||
\(311\) | −34.2660 | −1.94305 | −0.971525 | − | 0.236939i | \(-0.923856\pi\) | ||||
−0.971525 | + | 0.236939i | \(0.923856\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | −10.9600 | −0.619495 | −0.309747 | − | 0.950819i | \(-0.600244\pi\) | ||||
−0.309747 | + | 0.950819i | \(0.600244\pi\) | |||||||
\(314\) | 0.478623 | 0.0270103 | ||||||||
\(315\) | −3.05021 | −0.171860 | ||||||||
\(316\) | −1.40658 | −0.0791261 | ||||||||
\(317\) | −22.3459 | −1.25507 | −0.627536 | − | 0.778588i | \(-0.715936\pi\) | ||||
−0.627536 | + | 0.778588i | \(0.715936\pi\) | |||||||
\(318\) | 9.83809 | 0.551693 | ||||||||
\(319\) | −15.0886 | −0.844800 | ||||||||
\(320\) | −2.22430 | −0.124342 | ||||||||
\(321\) | −10.7285 | −0.598807 | ||||||||
\(322\) | 0.791588 | 0.0441135 | ||||||||
\(323\) | −13.5023 | −0.751290 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0.0525006 | 0.00291221 | ||||||||
\(326\) | 2.15078 | 0.119121 | ||||||||
\(327\) | −14.9243 | −0.825317 | ||||||||
\(328\) | 6.35321 | 0.350797 | ||||||||
\(329\) | 3.22525 | 0.177814 | ||||||||
\(330\) | 8.83534 | 0.486369 | ||||||||
\(331\) | −2.52085 | −0.138559 | −0.0692793 | − | 0.997597i | \(-0.522070\pi\) | ||||
−0.0692793 | + | 0.997597i | \(0.522070\pi\) | |||||||
\(332\) | −12.3179 | −0.676034 | ||||||||
\(333\) | −3.41291 | −0.187026 | ||||||||
\(334\) | 6.59412 | 0.360814 | ||||||||
\(335\) | −5.52809 | −0.302032 | ||||||||
\(336\) | 1.37131 | 0.0748113 | ||||||||
\(337\) | −14.6487 | −0.797963 | −0.398981 | − | 0.916959i | \(-0.630636\pi\) | ||||
−0.398981 | + | 0.916959i | \(0.630636\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | −5.51653 | −0.299617 | ||||||||
\(340\) | −4.57928 | −0.248346 | ||||||||
\(341\) | 11.2974 | 0.611787 | ||||||||
\(342\) | 6.55850 | 0.354643 | ||||||||
\(343\) | −16.6196 | −0.897376 | ||||||||
\(344\) | −12.0059 | −0.647312 | ||||||||
\(345\) | 1.28397 | 0.0691267 | ||||||||
\(346\) | 19.9171 | 1.07075 | ||||||||
\(347\) | 6.95858 | 0.373556 | 0.186778 | − | 0.982402i | \(-0.440195\pi\) | ||||
0.186778 | + | 0.982402i | \(0.440195\pi\) | |||||||
\(348\) | −3.79856 | −0.203624 | ||||||||
\(349\) | −35.8925 | −1.92128 | −0.960640 | − | 0.277797i | \(-0.910396\pi\) | ||||
−0.960640 | + | 0.277797i | \(0.910396\pi\) | |||||||
\(350\) | 0.0719948 | 0.00384829 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −3.97219 | −0.211719 | ||||||||
\(353\) | 9.40353 | 0.500499 | 0.250250 | − | 0.968181i | \(-0.419487\pi\) | ||||
0.250250 | + | 0.968181i | \(0.419487\pi\) | |||||||
\(354\) | −5.32093 | −0.282804 | ||||||||
\(355\) | 20.3341 | 1.07922 | ||||||||
\(356\) | −17.1581 | −0.909377 | ||||||||
\(357\) | 2.82320 | 0.149419 | ||||||||
\(358\) | 5.92624 | 0.313212 | ||||||||
\(359\) | −1.19957 | −0.0633108 | −0.0316554 | − | 0.999499i | \(-0.510078\pi\) | ||||
−0.0316554 | + | 0.999499i | \(0.510078\pi\) | |||||||
\(360\) | 2.22430 | 0.117231 | ||||||||
\(361\) | 24.0139 | 1.26389 | ||||||||
\(362\) | −8.59434 | −0.451708 | ||||||||
\(363\) | 4.77831 | 0.250796 | ||||||||
\(364\) | −1.37131 | −0.0718763 | ||||||||
\(365\) | −21.6038 | −1.13080 | ||||||||
\(366\) | −4.72419 | −0.246937 | ||||||||
\(367\) | −27.4623 | −1.43352 | −0.716761 | − | 0.697319i | \(-0.754376\pi\) | ||||
−0.716761 | + | 0.697319i | \(0.754376\pi\) | |||||||
\(368\) | −0.577248 | −0.0300912 | ||||||||
\(369\) | −6.35321 | −0.330735 | ||||||||
\(370\) | −7.59133 | −0.394654 | ||||||||
\(371\) | −13.4911 | −0.700423 | ||||||||
\(372\) | 2.84411 | 0.147460 | ||||||||
\(373\) | −22.2010 | −1.14952 | −0.574762 | − | 0.818321i | \(-0.694905\pi\) | ||||
−0.574762 | + | 0.818321i | \(0.694905\pi\) | |||||||
\(374\) | −8.17776 | −0.422862 | ||||||||
\(375\) | 11.2383 | 0.580341 | ||||||||
\(376\) | −2.35194 | −0.121292 | ||||||||
\(377\) | 3.79856 | 0.195636 | ||||||||
\(378\) | −1.37131 | −0.0705327 | ||||||||
\(379\) | 31.0945 | 1.59722 | 0.798609 | − | 0.601851i | \(-0.205570\pi\) | ||||
0.798609 | + | 0.601851i | \(0.205570\pi\) | |||||||
\(380\) | 14.5881 | 0.748351 | ||||||||
\(381\) | −0.708893 | −0.0363177 | ||||||||
\(382\) | 7.69976 | 0.393954 | ||||||||
\(383\) | −10.7140 | −0.547457 | −0.273729 | − | 0.961807i | \(-0.588257\pi\) | ||||
−0.273729 | + | 0.961807i | \(0.588257\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −12.1160 | −0.617489 | ||||||||
\(386\) | −16.7819 | −0.854175 | ||||||||
\(387\) | 12.0059 | 0.610292 | ||||||||
\(388\) | −14.8494 | −0.753863 | ||||||||
\(389\) | −17.8987 | −0.907499 | −0.453749 | − | 0.891129i | \(-0.649914\pi\) | ||||
−0.453749 | + | 0.891129i | \(0.649914\pi\) | |||||||
\(390\) | −2.22430 | −0.112632 | ||||||||
\(391\) | −1.18841 | −0.0601006 | ||||||||
\(392\) | 5.11950 | 0.258574 | ||||||||
\(393\) | 9.30987 | 0.469621 | ||||||||
\(394\) | 19.5782 | 0.986336 | ||||||||
\(395\) | 3.12864 | 0.157419 | ||||||||
\(396\) | 3.97219 | 0.199610 | ||||||||
\(397\) | −13.3530 | −0.670170 | −0.335085 | − | 0.942188i | \(-0.608765\pi\) | ||||
−0.335085 | + | 0.942188i | \(0.608765\pi\) | |||||||
\(398\) | −19.3299 | −0.968920 | ||||||||
\(399\) | −8.99376 | −0.450251 | ||||||||
\(400\) | −0.0525006 | −0.00262503 | ||||||||
\(401\) | −4.34378 | −0.216918 | −0.108459 | − | 0.994101i | \(-0.534592\pi\) | ||||
−0.108459 | + | 0.994101i | \(0.534592\pi\) | |||||||
\(402\) | −2.48532 | −0.123956 | ||||||||
\(403\) | −2.84411 | −0.141675 | ||||||||
\(404\) | 7.50888 | 0.373581 | ||||||||
\(405\) | −2.22430 | −0.110526 | ||||||||
\(406\) | 5.20902 | 0.258519 | ||||||||
\(407\) | −13.5567 | −0.671982 | ||||||||
\(408\) | −2.05875 | −0.101923 | ||||||||
\(409\) | −16.6202 | −0.821817 | −0.410909 | − | 0.911677i | \(-0.634788\pi\) | ||||
−0.410909 | + | 0.911677i | \(0.634788\pi\) | |||||||
\(410\) | −14.1314 | −0.697902 | ||||||||
\(411\) | −10.1749 | −0.501891 | ||||||||
\(412\) | 1.00000 | 0.0492665 | ||||||||
\(413\) | 7.29667 | 0.359046 | ||||||||
\(414\) | 0.577248 | 0.0283702 | ||||||||
\(415\) | 27.3987 | 1.34495 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | 4.75647 | 0.232925 | ||||||||
\(418\) | 26.0516 | 1.27423 | ||||||||
\(419\) | −7.77507 | −0.379837 | −0.189919 | − | 0.981800i | \(-0.560822\pi\) | ||||
−0.189919 | + | 0.981800i | \(0.560822\pi\) | |||||||
\(420\) | −3.05021 | −0.148835 | ||||||||
\(421\) | −18.9950 | −0.925760 | −0.462880 | − | 0.886421i | \(-0.653184\pi\) | ||||
−0.462880 | + | 0.886421i | \(0.653184\pi\) | |||||||
\(422\) | −15.3213 | −0.745829 | ||||||||
\(423\) | 2.35194 | 0.114355 | ||||||||
\(424\) | 9.83809 | 0.477780 | ||||||||
\(425\) | −0.108086 | −0.00524293 | ||||||||
\(426\) | 9.14181 | 0.442922 | ||||||||
\(427\) | 6.47834 | 0.313509 | ||||||||
\(428\) | −10.7285 | −0.518582 | ||||||||
\(429\) | −3.97219 | −0.191779 | ||||||||
\(430\) | 26.7046 | 1.28781 | ||||||||
\(431\) | −34.1073 | −1.64289 | −0.821445 | − | 0.570288i | \(-0.806832\pi\) | ||||
−0.821445 | + | 0.570288i | \(0.806832\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 24.8426 | 1.19386 | 0.596929 | − | 0.802294i | \(-0.296387\pi\) | ||||
0.596929 | + | 0.802294i | \(0.296387\pi\) | |||||||
\(434\) | −3.90017 | −0.187214 | ||||||||
\(435\) | 8.44913 | 0.405105 | ||||||||
\(436\) | −14.9243 | −0.714745 | ||||||||
\(437\) | 3.78588 | 0.181103 | ||||||||
\(438\) | −9.71266 | −0.464089 | ||||||||
\(439\) | −6.63461 | −0.316652 | −0.158326 | − | 0.987387i | \(-0.550610\pi\) | ||||
−0.158326 | + | 0.987387i | \(0.550610\pi\) | |||||||
\(440\) | 8.83534 | 0.421208 | ||||||||
\(441\) | −5.11950 | −0.243786 | ||||||||
\(442\) | 2.05875 | 0.0979249 | ||||||||
\(443\) | 27.9899 | 1.32984 | 0.664921 | − | 0.746914i | \(-0.268465\pi\) | ||||
0.664921 | + | 0.746914i | \(0.268465\pi\) | |||||||
\(444\) | −3.41291 | −0.161970 | ||||||||
\(445\) | 38.1647 | 1.80918 | ||||||||
\(446\) | −3.09661 | −0.146629 | ||||||||
\(447\) | 12.5814 | 0.595081 | ||||||||
\(448\) | 1.37131 | 0.0647885 | ||||||||
\(449\) | −32.4440 | −1.53113 | −0.765564 | − | 0.643360i | \(-0.777540\pi\) | ||||
−0.765564 | + | 0.643360i | \(0.777540\pi\) | |||||||
\(450\) | 0.0525006 | 0.00247490 | ||||||||
\(451\) | −25.2362 | −1.18833 | ||||||||
\(452\) | −5.51653 | −0.259476 | ||||||||
\(453\) | 16.7636 | 0.787623 | ||||||||
\(454\) | −6.51896 | −0.305950 | ||||||||
\(455\) | 3.05021 | 0.142996 | ||||||||
\(456\) | 6.55850 | 0.307130 | ||||||||
\(457\) | −5.24245 | −0.245232 | −0.122616 | − | 0.992454i | \(-0.539128\pi\) | ||||
−0.122616 | + | 0.992454i | \(0.539128\pi\) | |||||||
\(458\) | 2.09643 | 0.0979595 | ||||||||
\(459\) | 2.05875 | 0.0960944 | ||||||||
\(460\) | 1.28397 | 0.0598655 | ||||||||
\(461\) | −29.4265 | −1.37053 | −0.685265 | − | 0.728294i | \(-0.740314\pi\) | ||||
−0.685265 | + | 0.728294i | \(0.740314\pi\) | |||||||
\(462\) | −5.44712 | −0.253423 | ||||||||
\(463\) | −2.03166 | −0.0944193 | −0.0472097 | − | 0.998885i | \(-0.515033\pi\) | ||||
−0.0472097 | + | 0.998885i | \(0.515033\pi\) | |||||||
\(464\) | −3.79856 | −0.176344 | ||||||||
\(465\) | −6.32616 | −0.293368 | ||||||||
\(466\) | −16.0235 | −0.742272 | ||||||||
\(467\) | 19.0090 | 0.879630 | 0.439815 | − | 0.898089i | \(-0.355044\pi\) | ||||
0.439815 | + | 0.898089i | \(0.355044\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | 3.40815 | 0.157374 | ||||||||
\(470\) | 5.23142 | 0.241308 | ||||||||
\(471\) | −0.478623 | −0.0220538 | ||||||||
\(472\) | −5.32093 | −0.244916 | ||||||||
\(473\) | 47.6895 | 2.19277 | ||||||||
\(474\) | 1.40658 | 0.0646062 | ||||||||
\(475\) | 0.344325 | 0.0157987 | ||||||||
\(476\) | 2.82320 | 0.129401 | ||||||||
\(477\) | −9.83809 | −0.450455 | ||||||||
\(478\) | −3.86885 | −0.176957 | ||||||||
\(479\) | 12.3832 | 0.565804 | 0.282902 | − | 0.959149i | \(-0.408703\pi\) | ||||
0.282902 | + | 0.959149i | \(0.408703\pi\) | |||||||
\(480\) | 2.22430 | 0.101525 | ||||||||
\(481\) | 3.41291 | 0.155615 | ||||||||
\(482\) | −18.4872 | −0.842068 | ||||||||
\(483\) | −0.791588 | −0.0360185 | ||||||||
\(484\) | 4.77831 | 0.217196 | ||||||||
\(485\) | 33.0294 | 1.49979 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 9.91311 | 0.449206 | 0.224603 | − | 0.974450i | \(-0.427892\pi\) | ||||
0.224603 | + | 0.974450i | \(0.427892\pi\) | |||||||
\(488\) | −4.72419 | −0.213854 | ||||||||
\(489\) | −2.15078 | −0.0972616 | ||||||||
\(490\) | −11.3873 | −0.514425 | ||||||||
\(491\) | −11.9387 | −0.538785 | −0.269393 | − | 0.963030i | \(-0.586823\pi\) | ||||
−0.269393 | + | 0.963030i | \(0.586823\pi\) | |||||||
\(492\) | −6.35321 | −0.286425 | ||||||||
\(493\) | −7.82030 | −0.352208 | ||||||||
\(494\) | −6.55850 | −0.295081 | ||||||||
\(495\) | −8.83534 | −0.397119 | ||||||||
\(496\) | 2.84411 | 0.127704 | ||||||||
\(497\) | −12.5363 | −0.562329 | ||||||||
\(498\) | 12.3179 | 0.551980 | ||||||||
\(499\) | 3.11589 | 0.139486 | 0.0697432 | − | 0.997565i | \(-0.477782\pi\) | ||||
0.0697432 | + | 0.997565i | \(0.477782\pi\) | |||||||
\(500\) | 11.2383 | 0.502590 | ||||||||
\(501\) | −6.59412 | −0.294603 | ||||||||
\(502\) | 13.1469 | 0.586773 | ||||||||
\(503\) | −4.28793 | −0.191190 | −0.0955948 | − | 0.995420i | \(-0.530475\pi\) | ||||
−0.0955948 | + | 0.995420i | \(0.530475\pi\) | |||||||
\(504\) | −1.37131 | −0.0610832 | ||||||||
\(505\) | −16.7020 | −0.743228 | ||||||||
\(506\) | 2.29294 | 0.101934 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | −0.708893 | −0.0314520 | ||||||||
\(509\) | −16.1716 | −0.716792 | −0.358396 | − | 0.933570i | \(-0.616676\pi\) | ||||
−0.358396 | + | 0.933570i | \(0.616676\pi\) | |||||||
\(510\) | 4.57928 | 0.202774 | ||||||||
\(511\) | 13.3191 | 0.589202 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −6.55850 | −0.289565 | ||||||||
\(514\) | 13.3601 | 0.589288 | ||||||||
\(515\) | −2.22430 | −0.0980143 | ||||||||
\(516\) | 12.0059 | 0.528528 | ||||||||
\(517\) | 9.34237 | 0.410877 | ||||||||
\(518\) | 4.68017 | 0.205635 | ||||||||
\(519\) | −19.9171 | −0.874263 | ||||||||
\(520\) | −2.22430 | −0.0975419 | ||||||||
\(521\) | −17.2663 | −0.756452 | −0.378226 | − | 0.925713i | \(-0.623466\pi\) | ||||
−0.378226 | + | 0.925713i | \(0.623466\pi\) | |||||||
\(522\) | 3.79856 | 0.166258 | ||||||||
\(523\) | 6.78924 | 0.296873 | 0.148436 | − | 0.988922i | \(-0.452576\pi\) | ||||
0.148436 | + | 0.988922i | \(0.452576\pi\) | |||||||
\(524\) | 9.30987 | 0.406704 | ||||||||
\(525\) | −0.0719948 | −0.00314211 | ||||||||
\(526\) | −9.94191 | −0.433488 | ||||||||
\(527\) | 5.85533 | 0.255062 | ||||||||
\(528\) | 3.97219 | 0.172867 | ||||||||
\(529\) | −22.6668 | −0.985512 | ||||||||
\(530\) | −21.8828 | −0.950530 | ||||||||
\(531\) | 5.32093 | 0.230909 | ||||||||
\(532\) | −8.99376 | −0.389929 | ||||||||
\(533\) | 6.35321 | 0.275188 | ||||||||
\(534\) | 17.1581 | 0.742503 | ||||||||
\(535\) | 23.8634 | 1.03171 | ||||||||
\(536\) | −2.48532 | −0.107349 | ||||||||
\(537\) | −5.92624 | −0.255736 | ||||||||
\(538\) | −15.0666 | −0.649568 | ||||||||
\(539\) | −20.3356 | −0.875918 | ||||||||
\(540\) | −2.22430 | −0.0957185 | ||||||||
\(541\) | −36.7453 | −1.57980 | −0.789901 | − | 0.613234i | \(-0.789868\pi\) | ||||
−0.789901 | + | 0.613234i | \(0.789868\pi\) | |||||||
\(542\) | −9.46422 | −0.406523 | ||||||||
\(543\) | 8.59434 | 0.368818 | ||||||||
\(544\) | −2.05875 | −0.0882683 | ||||||||
\(545\) | 33.1961 | 1.42197 | ||||||||
\(546\) | 1.37131 | 0.0586868 | ||||||||
\(547\) | 11.4650 | 0.490209 | 0.245105 | − | 0.969497i | \(-0.421178\pi\) | ||||
0.245105 | + | 0.969497i | \(0.421178\pi\) | |||||||
\(548\) | −10.1749 | −0.434651 | ||||||||
\(549\) | 4.72419 | 0.201623 | ||||||||
\(550\) | 0.208543 | 0.00889229 | ||||||||
\(551\) | 24.9128 | 1.06132 | ||||||||
\(552\) | 0.577248 | 0.0245693 | ||||||||
\(553\) | −1.92886 | −0.0820233 | ||||||||
\(554\) | 25.7673 | 1.09475 | ||||||||
\(555\) | 7.59133 | 0.322234 | ||||||||
\(556\) | 4.75647 | 0.201719 | ||||||||
\(557\) | −19.2122 | −0.814046 | −0.407023 | − | 0.913418i | \(-0.633433\pi\) | ||||
−0.407023 | + | 0.913418i | \(0.633433\pi\) | |||||||
\(558\) | −2.84411 | −0.120401 | ||||||||
\(559\) | −12.0059 | −0.507793 | ||||||||
\(560\) | −3.05021 | −0.128895 | ||||||||
\(561\) | 8.17776 | 0.345265 | ||||||||
\(562\) | 0.119722 | 0.00505018 | ||||||||
\(563\) | −5.72057 | −0.241093 | −0.120547 | − | 0.992708i | \(-0.538465\pi\) | ||||
−0.120547 | + | 0.992708i | \(0.538465\pi\) | |||||||
\(564\) | 2.35194 | 0.0990347 | ||||||||
\(565\) | 12.2704 | 0.516220 | ||||||||
\(566\) | −30.8366 | −1.29616 | ||||||||
\(567\) | 1.37131 | 0.0575897 | ||||||||
\(568\) | 9.14181 | 0.383582 | ||||||||
\(569\) | 23.7134 | 0.994115 | 0.497058 | − | 0.867717i | \(-0.334414\pi\) | ||||
0.497058 | + | 0.867717i | \(0.334414\pi\) | |||||||
\(570\) | −14.5881 | −0.611026 | ||||||||
\(571\) | 28.7940 | 1.20499 | 0.602495 | − | 0.798122i | \(-0.294173\pi\) | ||||
0.602495 | + | 0.798122i | \(0.294173\pi\) | |||||||
\(572\) | −3.97219 | −0.166086 | ||||||||
\(573\) | −7.69976 | −0.321662 | ||||||||
\(574\) | 8.71224 | 0.363642 | ||||||||
\(575\) | 0.0303059 | 0.00126384 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −5.33926 | −0.222276 | −0.111138 | − | 0.993805i | \(-0.535450\pi\) | ||||
−0.111138 | + | 0.993805i | \(0.535450\pi\) | |||||||
\(578\) | 12.7615 | 0.530810 | ||||||||
\(579\) | 16.7819 | 0.697431 | ||||||||
\(580\) | 8.44913 | 0.350831 | ||||||||
\(581\) | −16.8917 | −0.700788 | ||||||||
\(582\) | 14.8494 | 0.615527 | ||||||||
\(583\) | −39.0788 | −1.61848 | ||||||||
\(584\) | −9.71266 | −0.401913 | ||||||||
\(585\) | 2.22430 | 0.0919634 | ||||||||
\(586\) | 6.70517 | 0.276988 | ||||||||
\(587\) | −31.3094 | −1.29228 | −0.646139 | − | 0.763220i | \(-0.723617\pi\) | ||||
−0.646139 | + | 0.763220i | \(0.723617\pi\) | |||||||
\(588\) | −5.11950 | −0.211125 | ||||||||
\(589\) | −18.6531 | −0.768588 | ||||||||
\(590\) | 11.8353 | 0.487253 | ||||||||
\(591\) | −19.5782 | −0.805340 | ||||||||
\(592\) | −3.41291 | −0.140270 | ||||||||
\(593\) | −25.0646 | −1.02928 | −0.514640 | − | 0.857406i | \(-0.672074\pi\) | ||||
−0.514640 | + | 0.857406i | \(0.672074\pi\) | |||||||
\(594\) | −3.97219 | −0.162981 | ||||||||
\(595\) | −6.27963 | −0.257440 | ||||||||
\(596\) | 12.5814 | 0.515355 | ||||||||
\(597\) | 19.3299 | 0.791120 | ||||||||
\(598\) | −0.577248 | −0.0236054 | ||||||||
\(599\) | −1.11554 | −0.0455796 | −0.0227898 | − | 0.999740i | \(-0.507255\pi\) | ||||
−0.0227898 | + | 0.999740i | \(0.507255\pi\) | |||||||
\(600\) | 0.0525006 | 0.00214333 | ||||||||
\(601\) | 0.614374 | 0.0250608 | 0.0125304 | − | 0.999921i | \(-0.496011\pi\) | ||||
0.0125304 | + | 0.999921i | \(0.496011\pi\) | |||||||
\(602\) | −16.4638 | −0.671014 | ||||||||
\(603\) | 2.48532 | 0.101210 | ||||||||
\(604\) | 16.7636 | 0.682102 | ||||||||
\(605\) | −10.6284 | −0.432105 | ||||||||
\(606\) | −7.50888 | −0.305027 | ||||||||
\(607\) | −22.2310 | −0.902329 | −0.451165 | − | 0.892441i | \(-0.648991\pi\) | ||||
−0.451165 | + | 0.892441i | \(0.648991\pi\) | |||||||
\(608\) | 6.55850 | 0.265982 | ||||||||
\(609\) | −5.20902 | −0.211080 | ||||||||
\(610\) | 10.5080 | 0.425456 | ||||||||
\(611\) | −2.35194 | −0.0951495 | ||||||||
\(612\) | 2.05875 | 0.0832201 | ||||||||
\(613\) | −13.4733 | −0.544180 | −0.272090 | − | 0.962272i | \(-0.587715\pi\) | ||||
−0.272090 | + | 0.962272i | \(0.587715\pi\) | |||||||
\(614\) | 28.1100 | 1.13443 | ||||||||
\(615\) | 14.1314 | 0.569834 | ||||||||
\(616\) | −5.44712 | −0.219471 | ||||||||
\(617\) | 10.0914 | 0.406264 | 0.203132 | − | 0.979151i | \(-0.434888\pi\) | ||||
0.203132 | + | 0.979151i | \(0.434888\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | 35.9985 | 1.44690 | 0.723451 | − | 0.690376i | \(-0.242555\pi\) | ||||
0.723451 | + | 0.690376i | \(0.242555\pi\) | |||||||
\(620\) | −6.32616 | −0.254065 | ||||||||
\(621\) | −0.577248 | −0.0231642 | ||||||||
\(622\) | 34.2660 | 1.37394 | ||||||||
\(623\) | −23.5291 | −0.942674 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | −24.7347 | −0.989390 | ||||||||
\(626\) | 10.9600 | 0.438049 | ||||||||
\(627\) | −26.0516 | −1.04040 | ||||||||
\(628\) | −0.478623 | −0.0190991 | ||||||||
\(629\) | −7.02634 | −0.280158 | ||||||||
\(630\) | 3.05021 | 0.121523 | ||||||||
\(631\) | −20.5110 | −0.816530 | −0.408265 | − | 0.912863i | \(-0.633866\pi\) | ||||
−0.408265 | + | 0.912863i | \(0.633866\pi\) | |||||||
\(632\) | 1.40658 | 0.0559506 | ||||||||
\(633\) | 15.3213 | 0.608966 | ||||||||
\(634\) | 22.3459 | 0.887470 | ||||||||
\(635\) | 1.57679 | 0.0625729 | ||||||||
\(636\) | −9.83809 | −0.390106 | ||||||||
\(637\) | 5.11950 | 0.202842 | ||||||||
\(638\) | 15.0886 | 0.597364 | ||||||||
\(639\) | −9.14181 | −0.361644 | ||||||||
\(640\) | 2.22430 | 0.0879231 | ||||||||
\(641\) | −44.1698 | −1.74460 | −0.872302 | − | 0.488968i | \(-0.837374\pi\) | ||||
−0.872302 | + | 0.488968i | \(0.837374\pi\) | |||||||
\(642\) | 10.7285 | 0.423421 | ||||||||
\(643\) | −19.1123 | −0.753715 | −0.376858 | − | 0.926271i | \(-0.622995\pi\) | ||||
−0.376858 | + | 0.926271i | \(0.622995\pi\) | |||||||
\(644\) | −0.791588 | −0.0311930 | ||||||||
\(645\) | −26.7046 | −1.05149 | ||||||||
\(646\) | 13.5023 | 0.531242 | ||||||||
\(647\) | 46.3714 | 1.82305 | 0.911524 | − | 0.411248i | \(-0.134907\pi\) | ||||
0.911524 | + | 0.411248i | \(0.134907\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 21.1358 | 0.829652 | ||||||||
\(650\) | −0.0525006 | −0.00205924 | ||||||||
\(651\) | 3.90017 | 0.152860 | ||||||||
\(652\) | −2.15078 | −0.0842310 | ||||||||
\(653\) | 13.3132 | 0.520987 | 0.260494 | − | 0.965476i | \(-0.416115\pi\) | ||||
0.260494 | + | 0.965476i | \(0.416115\pi\) | |||||||
\(654\) | 14.9243 | 0.583587 | ||||||||
\(655\) | −20.7079 | −0.809126 | ||||||||
\(656\) | −6.35321 | −0.248051 | ||||||||
\(657\) | 9.71266 | 0.378927 | ||||||||
\(658\) | −3.22525 | −0.125733 | ||||||||
\(659\) | 35.4348 | 1.38034 | 0.690172 | − | 0.723645i | \(-0.257535\pi\) | ||||
0.690172 | + | 0.723645i | \(0.257535\pi\) | |||||||
\(660\) | −8.83534 | −0.343915 | ||||||||
\(661\) | −20.1520 | −0.783822 | −0.391911 | − | 0.920003i | \(-0.628186\pi\) | ||||
−0.391911 | + | 0.920003i | \(0.628186\pi\) | |||||||
\(662\) | 2.52085 | 0.0979757 | ||||||||
\(663\) | −2.05875 | −0.0799553 | ||||||||
\(664\) | 12.3179 | 0.478028 | ||||||||
\(665\) | 20.0048 | 0.775753 | ||||||||
\(666\) | 3.41291 | 0.132248 | ||||||||
\(667\) | 2.19271 | 0.0849022 | ||||||||
\(668\) | −6.59412 | −0.255134 | ||||||||
\(669\) | 3.09661 | 0.119722 | ||||||||
\(670\) | 5.52809 | 0.213569 | ||||||||
\(671\) | 18.7654 | 0.724430 | ||||||||
\(672\) | −1.37131 | −0.0528996 | ||||||||
\(673\) | −11.0538 | −0.426092 | −0.213046 | − | 0.977042i | \(-0.568338\pi\) | ||||
−0.213046 | + | 0.977042i | \(0.568338\pi\) | |||||||
\(674\) | 14.6487 | 0.564245 | ||||||||
\(675\) | −0.0525006 | −0.00202075 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 42.5938 | 1.63701 | 0.818506 | − | 0.574498i | \(-0.194803\pi\) | ||||
0.818506 | + | 0.574498i | \(0.194803\pi\) | |||||||
\(678\) | 5.51653 | 0.211861 | ||||||||
\(679\) | −20.3632 | −0.781466 | ||||||||
\(680\) | 4.57928 | 0.175607 | ||||||||
\(681\) | 6.51896 | 0.249807 | ||||||||
\(682\) | −11.2974 | −0.432599 | ||||||||
\(683\) | 44.8926 | 1.71777 | 0.858884 | − | 0.512171i | \(-0.171159\pi\) | ||||
0.858884 | + | 0.512171i | \(0.171159\pi\) | |||||||
\(684\) | −6.55850 | −0.250770 | ||||||||
\(685\) | 22.6320 | 0.864726 | ||||||||
\(686\) | 16.6196 | 0.634540 | ||||||||
\(687\) | −2.09643 | −0.0799836 | ||||||||
\(688\) | 12.0059 | 0.457719 | ||||||||
\(689\) | 9.83809 | 0.374801 | ||||||||
\(690\) | −1.28397 | −0.0488800 | ||||||||
\(691\) | 41.5886 | 1.58211 | 0.791053 | − | 0.611748i | \(-0.209533\pi\) | ||||
0.791053 | + | 0.611748i | \(0.209533\pi\) | |||||||
\(692\) | −19.9171 | −0.757134 | ||||||||
\(693\) | 5.44712 | 0.206919 | ||||||||
\(694\) | −6.95858 | −0.264144 | ||||||||
\(695\) | −10.5798 | −0.401315 | ||||||||
\(696\) | 3.79856 | 0.143984 | ||||||||
\(697\) | −13.0797 | −0.495429 | ||||||||
\(698\) | 35.8925 | 1.35855 | ||||||||
\(699\) | 16.0235 | 0.606063 | ||||||||
\(700\) | −0.0719948 | −0.00272115 | ||||||||
\(701\) | 39.7054 | 1.49965 | 0.749827 | − | 0.661634i | \(-0.230137\pi\) | ||||
0.749827 | + | 0.661634i | \(0.230137\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | 22.3836 | 0.844212 | ||||||||
\(704\) | 3.97219 | 0.149708 | ||||||||
\(705\) | −5.23142 | −0.197027 | ||||||||
\(706\) | −9.40353 | −0.353906 | ||||||||
\(707\) | 10.2970 | 0.387260 | ||||||||
\(708\) | 5.32093 | 0.199973 | ||||||||
\(709\) | −45.0868 | −1.69327 | −0.846635 | − | 0.532174i | \(-0.821375\pi\) | ||||
−0.846635 | + | 0.532174i | \(0.821375\pi\) | |||||||
\(710\) | −20.3341 | −0.763125 | ||||||||
\(711\) | −1.40658 | −0.0527507 | ||||||||
\(712\) | 17.1581 | 0.643026 | ||||||||
\(713\) | −1.64176 | −0.0614844 | ||||||||
\(714\) | −2.82320 | −0.105655 | ||||||||
\(715\) | 8.83534 | 0.330423 | ||||||||
\(716\) | −5.92624 | −0.221474 | ||||||||
\(717\) | 3.86885 | 0.144485 | ||||||||
\(718\) | 1.19957 | 0.0447675 | ||||||||
\(719\) | 36.2868 | 1.35327 | 0.676634 | − | 0.736319i | \(-0.263438\pi\) | ||||
0.676634 | + | 0.736319i | \(0.263438\pi\) | |||||||
\(720\) | −2.22430 | −0.0828947 | ||||||||
\(721\) | 1.37131 | 0.0510704 | ||||||||
\(722\) | −24.0139 | −0.893705 | ||||||||
\(723\) | 18.4872 | 0.687546 | ||||||||
\(724\) | 8.59434 | 0.319406 | ||||||||
\(725\) | 0.199427 | 0.00740653 | ||||||||
\(726\) | −4.77831 | −0.177340 | ||||||||
\(727\) | −2.53230 | −0.0939179 | −0.0469590 | − | 0.998897i | \(-0.514953\pi\) | ||||
−0.0469590 | + | 0.998897i | \(0.514953\pi\) | |||||||
\(728\) | 1.37131 | 0.0508243 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 21.6038 | 0.799594 | ||||||||
\(731\) | 24.7171 | 0.914194 | ||||||||
\(732\) | 4.72419 | 0.174611 | ||||||||
\(733\) | 50.6304 | 1.87007 | 0.935037 | − | 0.354549i | \(-0.115366\pi\) | ||||
0.935037 | + | 0.354549i | \(0.115366\pi\) | |||||||
\(734\) | 27.4623 | 1.01365 | ||||||||
\(735\) | 11.3873 | 0.420027 | ||||||||
\(736\) | 0.577248 | 0.0212777 | ||||||||
\(737\) | 9.87217 | 0.363646 | ||||||||
\(738\) | 6.35321 | 0.233865 | ||||||||
\(739\) | 9.78320 | 0.359881 | 0.179940 | − | 0.983678i | \(-0.442410\pi\) | ||||
0.179940 | + | 0.983678i | \(0.442410\pi\) | |||||||
\(740\) | 7.59133 | 0.279063 | ||||||||
\(741\) | 6.55850 | 0.240932 | ||||||||
\(742\) | 13.4911 | 0.495274 | ||||||||
\(743\) | −31.9241 | −1.17118 | −0.585590 | − | 0.810607i | \(-0.699137\pi\) | ||||
−0.585590 | + | 0.810607i | \(0.699137\pi\) | |||||||
\(744\) | −2.84411 | −0.104270 | ||||||||
\(745\) | −27.9848 | −1.02528 | ||||||||
\(746\) | 22.2010 | 0.812836 | ||||||||
\(747\) | −12.3179 | −0.450690 | ||||||||
\(748\) | 8.17776 | 0.299009 | ||||||||
\(749\) | −14.7122 | −0.537570 | ||||||||
\(750\) | −11.2383 | −0.410363 | ||||||||
\(751\) | −26.1622 | −0.954671 | −0.477336 | − | 0.878721i | \(-0.658397\pi\) | ||||
−0.477336 | + | 0.878721i | \(0.658397\pi\) | |||||||
\(752\) | 2.35194 | 0.0857666 | ||||||||
\(753\) | −13.1469 | −0.479098 | ||||||||
\(754\) | −3.79856 | −0.138335 | ||||||||
\(755\) | −37.2873 | −1.35702 | ||||||||
\(756\) | 1.37131 | 0.0498742 | ||||||||
\(757\) | 9.89410 | 0.359607 | 0.179804 | − | 0.983703i | \(-0.442454\pi\) | ||||
0.179804 | + | 0.983703i | \(0.442454\pi\) | |||||||
\(758\) | −31.0945 | −1.12940 | ||||||||
\(759\) | −2.29294 | −0.0832285 | ||||||||
\(760\) | −14.5881 | −0.529164 | ||||||||
\(761\) | −49.2646 | −1.78584 | −0.892919 | − | 0.450217i | \(-0.851347\pi\) | ||||
−0.892919 | + | 0.450217i | \(0.851347\pi\) | |||||||
\(762\) | 0.708893 | 0.0256805 | ||||||||
\(763\) | −20.4659 | −0.740916 | ||||||||
\(764\) | −7.69976 | −0.278567 | ||||||||
\(765\) | −4.57928 | −0.165564 | ||||||||
\(766\) | 10.7140 | 0.387111 | ||||||||
\(767\) | −5.32093 | −0.192128 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −27.4727 | −0.990690 | −0.495345 | − | 0.868696i | \(-0.664958\pi\) | ||||
−0.495345 | + | 0.868696i | \(0.664958\pi\) | |||||||
\(770\) | 12.1160 | 0.436631 | ||||||||
\(771\) | −13.3601 | −0.481152 | ||||||||
\(772\) | 16.7819 | 0.603993 | ||||||||
\(773\) | 2.07706 | 0.0747067 | 0.0373533 | − | 0.999302i | \(-0.488107\pi\) | ||||
0.0373533 | + | 0.999302i | \(0.488107\pi\) | |||||||
\(774\) | −12.0059 | −0.431541 | ||||||||
\(775\) | −0.149318 | −0.00536365 | ||||||||
\(776\) | 14.8494 | 0.533062 | ||||||||
\(777\) | −4.68017 | −0.167900 | ||||||||
\(778\) | 17.8987 | 0.641699 | ||||||||
\(779\) | 41.6675 | 1.49289 | ||||||||
\(780\) | 2.22430 | 0.0796426 | ||||||||
\(781\) | −36.3130 | −1.29938 | ||||||||
\(782\) | 1.18841 | 0.0424975 | ||||||||
\(783\) | −3.79856 | −0.135749 | ||||||||
\(784\) | −5.11950 | −0.182839 | ||||||||
\(785\) | 1.06460 | 0.0379972 | ||||||||
\(786\) | −9.30987 | −0.332072 | ||||||||
\(787\) | 2.37041 | 0.0844960 | 0.0422480 | − | 0.999107i | \(-0.486548\pi\) | ||||
0.0422480 | + | 0.999107i | \(0.486548\pi\) | |||||||
\(788\) | −19.5782 | −0.697445 | ||||||||
\(789\) | 9.94191 | 0.353942 | ||||||||
\(790\) | −3.12864 | −0.111312 | ||||||||
\(791\) | −7.56490 | −0.268977 | ||||||||
\(792\) | −3.97219 | −0.141146 | ||||||||
\(793\) | −4.72419 | −0.167761 | ||||||||
\(794\) | 13.3530 | 0.473882 | ||||||||
\(795\) | 21.8828 | 0.776104 | ||||||||
\(796\) | 19.3299 | 0.685130 | ||||||||
\(797\) | −25.5196 | −0.903952 | −0.451976 | − | 0.892030i | \(-0.649281\pi\) | ||||
−0.451976 | + | 0.892030i | \(0.649281\pi\) | |||||||
\(798\) | 8.99376 | 0.318376 | ||||||||
\(799\) | 4.84207 | 0.171300 | ||||||||
\(800\) | 0.0525006 | 0.00185618 | ||||||||
\(801\) | −17.1581 | −0.606251 | ||||||||
\(802\) | 4.34378 | 0.153384 | ||||||||
\(803\) | 38.5806 | 1.36148 | ||||||||
\(804\) | 2.48532 | 0.0876505 | ||||||||
\(805\) | 1.76073 | 0.0620575 | ||||||||
\(806\) | 2.84411 | 0.100180 | ||||||||
\(807\) | 15.0666 | 0.530370 | ||||||||
\(808\) | −7.50888 | −0.264161 | ||||||||
\(809\) | 1.08081 | 0.0379991 | 0.0189996 | − | 0.999819i | \(-0.493952\pi\) | ||||
0.0189996 | + | 0.999819i | \(0.493952\pi\) | |||||||
\(810\) | 2.22430 | 0.0781538 | ||||||||
\(811\) | −18.9563 | −0.665645 | −0.332823 | − | 0.942989i | \(-0.608001\pi\) | ||||
−0.332823 | + | 0.942989i | \(0.608001\pi\) | |||||||
\(812\) | −5.20902 | −0.182801 | ||||||||
\(813\) | 9.46422 | 0.331925 | ||||||||
\(814\) | 13.5567 | 0.475163 | ||||||||
\(815\) | 4.78397 | 0.167575 | ||||||||
\(816\) | 2.05875 | 0.0720708 | ||||||||
\(817\) | −78.7404 | −2.75478 | ||||||||
\(818\) | 16.6202 | 0.581113 | ||||||||
\(819\) | −1.37131 | −0.0479176 | ||||||||
\(820\) | 14.1314 | 0.493491 | ||||||||
\(821\) | −11.8047 | −0.411988 | −0.205994 | − | 0.978553i | \(-0.566043\pi\) | ||||
−0.205994 | + | 0.978553i | \(0.566043\pi\) | |||||||
\(822\) | 10.1749 | 0.354891 | ||||||||
\(823\) | 12.5546 | 0.437625 | 0.218812 | − | 0.975767i | \(-0.429782\pi\) | ||||
0.218812 | + | 0.975767i | \(0.429782\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | −0.208543 | −0.00726052 | ||||||||
\(826\) | −7.29667 | −0.253884 | ||||||||
\(827\) | 30.0107 | 1.04357 | 0.521787 | − | 0.853076i | \(-0.325266\pi\) | ||||
0.521787 | + | 0.853076i | \(0.325266\pi\) | |||||||
\(828\) | −0.577248 | −0.0200608 | ||||||||
\(829\) | −8.20653 | −0.285025 | −0.142512 | − | 0.989793i | \(-0.545518\pi\) | ||||
−0.142512 | + | 0.989793i | \(0.545518\pi\) | |||||||
\(830\) | −27.3987 | −0.951024 | ||||||||
\(831\) | −25.7673 | −0.893858 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | −10.5398 | −0.365182 | ||||||||
\(834\) | −4.75647 | −0.164703 | ||||||||
\(835\) | 14.6673 | 0.507582 | ||||||||
\(836\) | −26.0516 | −0.901014 | ||||||||
\(837\) | 2.84411 | 0.0983070 | ||||||||
\(838\) | 7.77507 | 0.268585 | ||||||||
\(839\) | −52.1181 | −1.79932 | −0.899658 | − | 0.436596i | \(-0.856184\pi\) | ||||
−0.899658 | + | 0.436596i | \(0.856184\pi\) | |||||||
\(840\) | 3.05021 | 0.105242 | ||||||||
\(841\) | −14.5709 | −0.502446 | ||||||||
\(842\) | 18.9950 | 0.654611 | ||||||||
\(843\) | −0.119722 | −0.00412345 | ||||||||
\(844\) | 15.3213 | 0.527380 | ||||||||
\(845\) | −2.22430 | −0.0765182 | ||||||||
\(846\) | −2.35194 | −0.0808615 | ||||||||
\(847\) | 6.55256 | 0.225149 | ||||||||
\(848\) | −9.83809 | −0.337841 | ||||||||
\(849\) | 30.8366 | 1.05831 | ||||||||
\(850\) | 0.108086 | 0.00370731 | ||||||||
\(851\) | 1.97010 | 0.0675341 | ||||||||
\(852\) | −9.14181 | −0.313193 | ||||||||
\(853\) | −6.07651 | −0.208056 | −0.104028 | − | 0.994574i | \(-0.533173\pi\) | ||||
−0.104028 | + | 0.994574i | \(0.533173\pi\) | |||||||
\(854\) | −6.47834 | −0.221684 | ||||||||
\(855\) | 14.5881 | 0.498901 | ||||||||
\(856\) | 10.7285 | 0.366693 | ||||||||
\(857\) | −25.3195 | −0.864896 | −0.432448 | − | 0.901659i | \(-0.642350\pi\) | ||||
−0.432448 | + | 0.901659i | \(0.642350\pi\) | |||||||
\(858\) | 3.97219 | 0.135608 | ||||||||
\(859\) | −0.769055 | −0.0262398 | −0.0131199 | − | 0.999914i | \(-0.504176\pi\) | ||||
−0.0131199 | + | 0.999914i | \(0.504176\pi\) | |||||||
\(860\) | −26.7046 | −0.910619 | ||||||||
\(861\) | −8.71224 | −0.296912 | ||||||||
\(862\) | 34.1073 | 1.16170 | ||||||||
\(863\) | −0.772340 | −0.0262908 | −0.0131454 | − | 0.999914i | \(-0.504184\pi\) | ||||
−0.0131454 | + | 0.999914i | \(0.504184\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 44.3015 | 1.50630 | ||||||||
\(866\) | −24.8426 | −0.844185 | ||||||||
\(867\) | −12.7615 | −0.433405 | ||||||||
\(868\) | 3.90017 | 0.132380 | ||||||||
\(869\) | −5.58719 | −0.189532 | ||||||||
\(870\) | −8.44913 | −0.286452 | ||||||||
\(871\) | −2.48532 | −0.0842118 | ||||||||
\(872\) | 14.9243 | 0.505401 | ||||||||
\(873\) | −14.8494 | −0.502575 | ||||||||
\(874\) | −3.78588 | −0.128059 | ||||||||
\(875\) | 15.4112 | 0.520993 | ||||||||
\(876\) | 9.71266 | 0.328160 | ||||||||
\(877\) | −5.65111 | −0.190824 | −0.0954122 | − | 0.995438i | \(-0.530417\pi\) | ||||
−0.0954122 | + | 0.995438i | \(0.530417\pi\) | |||||||
\(878\) | 6.63461 | 0.223907 | ||||||||
\(879\) | −6.70517 | −0.226160 | ||||||||
\(880\) | −8.83534 | −0.297839 | ||||||||
\(881\) | 2.98848 | 0.100684 | 0.0503422 | − | 0.998732i | \(-0.483969\pi\) | ||||
0.0503422 | + | 0.998732i | \(0.483969\pi\) | |||||||
\(882\) | 5.11950 | 0.172383 | ||||||||
\(883\) | 24.2160 | 0.814934 | 0.407467 | − | 0.913220i | \(-0.366412\pi\) | ||||
0.407467 | + | 0.913220i | \(0.366412\pi\) | |||||||
\(884\) | −2.05875 | −0.0692434 | ||||||||
\(885\) | −11.8353 | −0.397841 | ||||||||
\(886\) | −27.9899 | −0.940340 | ||||||||
\(887\) | −11.0954 | −0.372548 | −0.186274 | − | 0.982498i | \(-0.559641\pi\) | ||||
−0.186274 | + | 0.982498i | \(0.559641\pi\) | |||||||
\(888\) | 3.41291 | 0.114530 | ||||||||
\(889\) | −0.972114 | −0.0326037 | ||||||||
\(890\) | −38.1647 | −1.27928 | ||||||||
\(891\) | 3.97219 | 0.133073 | ||||||||
\(892\) | 3.09661 | 0.103682 | ||||||||
\(893\) | −15.4252 | −0.516185 | ||||||||
\(894\) | −12.5814 | −0.420786 | ||||||||
\(895\) | 13.1817 | 0.440617 | ||||||||
\(896\) | −1.37131 | −0.0458124 | ||||||||
\(897\) | 0.577248 | 0.0192738 | ||||||||
\(898\) | 32.4440 | 1.08267 | ||||||||
\(899\) | −10.8035 | −0.360318 | ||||||||
\(900\) | −0.0525006 | −0.00175002 | ||||||||
\(901\) | −20.2542 | −0.674765 | ||||||||
\(902\) | 25.2362 | 0.840273 | ||||||||
\(903\) | 16.4638 | 0.547880 | ||||||||
\(904\) | 5.51653 | 0.183477 | ||||||||
\(905\) | −19.1164 | −0.635449 | ||||||||
\(906\) | −16.7636 | −0.556934 | ||||||||
\(907\) | 6.27707 | 0.208427 | 0.104213 | − | 0.994555i | \(-0.466768\pi\) | ||||
0.104213 | + | 0.994555i | \(0.466768\pi\) | |||||||
\(908\) | 6.51896 | 0.216339 | ||||||||
\(909\) | 7.50888 | 0.249054 | ||||||||
\(910\) | −3.05021 | −0.101113 | ||||||||
\(911\) | 17.7132 | 0.586864 | 0.293432 | − | 0.955980i | \(-0.405203\pi\) | ||||
0.293432 | + | 0.955980i | \(0.405203\pi\) | |||||||
\(912\) | −6.55850 | −0.217174 | ||||||||
\(913\) | −48.9292 | −1.61932 | ||||||||
\(914\) | 5.24245 | 0.173405 | ||||||||
\(915\) | −10.5080 | −0.347384 | ||||||||
\(916\) | −2.09643 | −0.0692678 | ||||||||
\(917\) | 12.7668 | 0.421595 | ||||||||
\(918\) | −2.05875 | −0.0679490 | ||||||||
\(919\) | −39.4541 | −1.30147 | −0.650735 | − | 0.759305i | \(-0.725539\pi\) | ||||
−0.650735 | + | 0.759305i | \(0.725539\pi\) | |||||||
\(920\) | −1.28397 | −0.0423313 | ||||||||
\(921\) | −28.1100 | −0.926255 | ||||||||
\(922\) | 29.4265 | 0.969111 | ||||||||
\(923\) | 9.14181 | 0.300906 | ||||||||
\(924\) | 5.44712 | 0.179197 | ||||||||
\(925\) | 0.179180 | 0.00589140 | ||||||||
\(926\) | 2.03166 | 0.0667646 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | 3.79856 | 0.124694 | ||||||||
\(929\) | 41.4822 | 1.36099 | 0.680493 | − | 0.732755i | \(-0.261766\pi\) | ||||
0.680493 | + | 0.732755i | \(0.261766\pi\) | |||||||
\(930\) | 6.32616 | 0.207443 | ||||||||
\(931\) | 33.5762 | 1.10042 | ||||||||
\(932\) | 16.0235 | 0.524866 | ||||||||
\(933\) | −34.2660 | −1.12182 | ||||||||
\(934\) | −19.0090 | −0.621992 | ||||||||
\(935\) | −18.1898 | −0.594869 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | 17.0382 | 0.556614 | 0.278307 | − | 0.960492i | \(-0.410227\pi\) | ||||
0.278307 | + | 0.960492i | \(0.410227\pi\) | |||||||
\(938\) | −3.40815 | −0.111280 | ||||||||
\(939\) | −10.9600 | −0.357665 | ||||||||
\(940\) | −5.23142 | −0.170630 | ||||||||
\(941\) | −38.5648 | −1.25718 | −0.628589 | − | 0.777738i | \(-0.716367\pi\) | ||||
−0.628589 | + | 0.777738i | \(0.716367\pi\) | |||||||
\(942\) | 0.478623 | 0.0155944 | ||||||||
\(943\) | 3.66738 | 0.119426 | ||||||||
\(944\) | 5.32093 | 0.173182 | ||||||||
\(945\) | −3.05021 | −0.0992233 | ||||||||
\(946\) | −47.6895 | −1.55052 | ||||||||
\(947\) | −49.7548 | −1.61681 | −0.808406 | − | 0.588625i | \(-0.799669\pi\) | ||||
−0.808406 | + | 0.588625i | \(0.799669\pi\) | |||||||
\(948\) | −1.40658 | −0.0456835 | ||||||||
\(949\) | −9.71266 | −0.315286 | ||||||||
\(950\) | −0.344325 | −0.0111714 | ||||||||
\(951\) | −22.3459 | −0.724616 | ||||||||
\(952\) | −2.82320 | −0.0915003 | ||||||||
\(953\) | 23.9960 | 0.777307 | 0.388654 | − | 0.921384i | \(-0.372940\pi\) | ||||
0.388654 | + | 0.921384i | \(0.372940\pi\) | |||||||
\(954\) | 9.83809 | 0.318520 | ||||||||
\(955\) | 17.1265 | 0.554202 | ||||||||
\(956\) | 3.86885 | 0.125128 | ||||||||
\(957\) | −15.0886 | −0.487745 | ||||||||
\(958\) | −12.3832 | −0.400084 | ||||||||
\(959\) | −13.9530 | −0.450566 | ||||||||
\(960\) | −2.22430 | −0.0717889 | ||||||||
\(961\) | −22.9110 | −0.739065 | ||||||||
\(962\) | −3.41291 | −0.110037 | ||||||||
\(963\) | −10.7285 | −0.345722 | ||||||||
\(964\) | 18.4872 | 0.595432 | ||||||||
\(965\) | −37.3279 | −1.20163 | ||||||||
\(966\) | 0.791588 | 0.0254689 | ||||||||
\(967\) | 43.5903 | 1.40177 | 0.700885 | − | 0.713274i | \(-0.252789\pi\) | ||||
0.700885 | + | 0.713274i | \(0.252789\pi\) | |||||||
\(968\) | −4.77831 | −0.153581 | ||||||||
\(969\) | −13.5023 | −0.433757 | ||||||||
\(970\) | −33.0294 | −1.06051 | ||||||||
\(971\) | 41.5288 | 1.33272 | 0.666361 | − | 0.745629i | \(-0.267851\pi\) | ||||
0.666361 | + | 0.745629i | \(0.267851\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 6.52261 | 0.209105 | ||||||||
\(974\) | −9.91311 | −0.317636 | ||||||||
\(975\) | 0.0525006 | 0.00168137 | ||||||||
\(976\) | 4.72419 | 0.151218 | ||||||||
\(977\) | 29.4383 | 0.941814 | 0.470907 | − | 0.882183i | \(-0.343927\pi\) | ||||
0.470907 | + | 0.882183i | \(0.343927\pi\) | |||||||
\(978\) | 2.15078 | 0.0687743 | ||||||||
\(979\) | −68.1552 | −2.17825 | ||||||||
\(980\) | 11.3873 | 0.363754 | ||||||||
\(981\) | −14.9243 | −0.476497 | ||||||||
\(982\) | 11.9387 | 0.380979 | ||||||||
\(983\) | 35.0015 | 1.11638 | 0.558188 | − | 0.829715i | \(-0.311497\pi\) | ||||
0.558188 | + | 0.829715i | \(0.311497\pi\) | |||||||
\(984\) | 6.35321 | 0.202533 | ||||||||
\(985\) | 43.5477 | 1.38755 | ||||||||
\(986\) | 7.82030 | 0.249049 | ||||||||
\(987\) | 3.22525 | 0.102661 | ||||||||
\(988\) | 6.55850 | 0.208654 | ||||||||
\(989\) | −6.93036 | −0.220373 | ||||||||
\(990\) | 8.83534 | 0.280805 | ||||||||
\(991\) | 17.7909 | 0.565146 | 0.282573 | − | 0.959246i | \(-0.408812\pi\) | ||||
0.282573 | + | 0.959246i | \(0.408812\pi\) | |||||||
\(992\) | −2.84411 | −0.0903007 | ||||||||
\(993\) | −2.52085 | −0.0799968 | ||||||||
\(994\) | 12.5363 | 0.397627 | ||||||||
\(995\) | −42.9954 | −1.36305 | ||||||||
\(996\) | −12.3179 | −0.390309 | ||||||||
\(997\) | 16.4268 | 0.520241 | 0.260121 | − | 0.965576i | \(-0.416238\pi\) | ||||
0.260121 | + | 0.965576i | \(0.416238\pi\) | |||||||
\(998\) | −3.11589 | −0.0986318 | ||||||||
\(999\) | −3.41291 | −0.107980 |
(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 | 8034.2.a.bb.1.5 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.bb.1.5 | ✓ | 14 | 1.1 | even | 1 | trivial |