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: | \(0\) |
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: | \( x^{14} - 3 x^{13} - 36 x^{12} + 108 x^{11} + 434 x^{10} - 1239 x^{9} - 2404 x^{8} + 6204 x^{7} + \cdots + 1552 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(-2.28948\) 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 | ||||||||
\(5\) | 2.28948 | 1.02389 | 0.511944 | − | 0.859019i | \(-0.328925\pi\) | ||||
0.511944 | + | 0.859019i | \(0.328925\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.19378 | −0.451206 | −0.225603 | − | 0.974219i | \(-0.572435\pi\) | ||||
−0.225603 | + | 0.974219i | \(0.572435\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.28948 | −0.723998 | ||||||||
\(11\) | 4.27905 | 1.29018 | 0.645091 | − | 0.764106i | \(-0.276819\pi\) | ||||
0.645091 | + | 0.764106i | \(0.276819\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 1.19378 | 0.319051 | ||||||||
\(15\) | −2.28948 | −0.591142 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.59570 | −0.872086 | −0.436043 | − | 0.899926i | \(-0.643621\pi\) | ||||
−0.436043 | + | 0.899926i | \(0.643621\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.35770 | −0.311478 | −0.155739 | − | 0.987798i | \(-0.549776\pi\) | ||||
−0.155739 | + | 0.987798i | \(0.549776\pi\) | |||||||
\(20\) | 2.28948 | 0.511944 | ||||||||
\(21\) | 1.19378 | 0.260504 | ||||||||
\(22\) | −4.27905 | −0.912297 | ||||||||
\(23\) | −6.42459 | −1.33962 | −0.669810 | − | 0.742532i | \(-0.733625\pi\) | ||||
−0.669810 | + | 0.742532i | \(0.733625\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0.241736 | 0.0483473 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.19378 | −0.225603 | ||||||||
\(29\) | −6.53525 | −1.21357 | −0.606783 | − | 0.794867i | \(-0.707540\pi\) | ||||
−0.606783 | + | 0.794867i | \(0.707540\pi\) | |||||||
\(30\) | 2.28948 | 0.418001 | ||||||||
\(31\) | −1.25937 | −0.226189 | −0.113095 | − | 0.993584i | \(-0.536076\pi\) | ||||
−0.113095 | + | 0.993584i | \(0.536076\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.27905 | −0.744887 | ||||||||
\(34\) | 3.59570 | 0.616658 | ||||||||
\(35\) | −2.73314 | −0.461985 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −6.96050 | −1.14430 | −0.572149 | − | 0.820150i | \(-0.693890\pi\) | ||||
−0.572149 | + | 0.820150i | \(0.693890\pi\) | |||||||
\(38\) | 1.35770 | 0.220248 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −2.28948 | −0.361999 | ||||||||
\(41\) | 7.36952 | 1.15093 | 0.575463 | − | 0.817828i | \(-0.304822\pi\) | ||||
0.575463 | + | 0.817828i | \(0.304822\pi\) | |||||||
\(42\) | −1.19378 | −0.184204 | ||||||||
\(43\) | 1.70506 | 0.260020 | 0.130010 | − | 0.991513i | \(-0.458499\pi\) | ||||
0.130010 | + | 0.991513i | \(0.458499\pi\) | |||||||
\(44\) | 4.27905 | 0.645091 | ||||||||
\(45\) | 2.28948 | 0.341296 | ||||||||
\(46\) | 6.42459 | 0.947255 | ||||||||
\(47\) | 1.19672 | 0.174560 | 0.0872800 | − | 0.996184i | \(-0.472183\pi\) | ||||
0.0872800 | + | 0.996184i | \(0.472183\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −5.57489 | −0.796413 | ||||||||
\(50\) | −0.241736 | −0.0341867 | ||||||||
\(51\) | 3.59570 | 0.503499 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 2.84069 | 0.390199 | 0.195100 | − | 0.980783i | \(-0.437497\pi\) | ||||
0.195100 | + | 0.980783i | \(0.437497\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 9.79682 | 1.32100 | ||||||||
\(56\) | 1.19378 | 0.159525 | ||||||||
\(57\) | 1.35770 | 0.179832 | ||||||||
\(58\) | 6.53525 | 0.858121 | ||||||||
\(59\) | 14.3018 | 1.86194 | 0.930971 | − | 0.365093i | \(-0.118963\pi\) | ||||
0.930971 | + | 0.365093i | \(0.118963\pi\) | |||||||
\(60\) | −2.28948 | −0.295571 | ||||||||
\(61\) | 3.12763 | 0.400453 | 0.200226 | − | 0.979750i | \(-0.435832\pi\) | ||||
0.200226 | + | 0.979750i | \(0.435832\pi\) | |||||||
\(62\) | 1.25937 | 0.159940 | ||||||||
\(63\) | −1.19378 | −0.150402 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.28948 | 0.283976 | ||||||||
\(66\) | 4.27905 | 0.526715 | ||||||||
\(67\) | 10.3747 | 1.26748 | 0.633738 | − | 0.773548i | \(-0.281520\pi\) | ||||
0.633738 | + | 0.773548i | \(0.281520\pi\) | |||||||
\(68\) | −3.59570 | −0.436043 | ||||||||
\(69\) | 6.42459 | 0.773430 | ||||||||
\(70\) | 2.73314 | 0.326672 | ||||||||
\(71\) | 1.20531 | 0.143044 | 0.0715222 | − | 0.997439i | \(-0.477214\pi\) | ||||
0.0715222 | + | 0.997439i | \(0.477214\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 10.1318 | 1.18584 | 0.592919 | − | 0.805262i | \(-0.297975\pi\) | ||||
0.592919 | + | 0.805262i | \(0.297975\pi\) | |||||||
\(74\) | 6.96050 | 0.809141 | ||||||||
\(75\) | −0.241736 | −0.0279133 | ||||||||
\(76\) | −1.35770 | −0.155739 | ||||||||
\(77\) | −5.10824 | −0.582138 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | −2.00621 | −0.225716 | −0.112858 | − | 0.993611i | \(-0.536000\pi\) | ||||
−0.112858 | + | 0.993611i | \(0.536000\pi\) | |||||||
\(80\) | 2.28948 | 0.255972 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −7.36952 | −0.813828 | ||||||||
\(83\) | 4.49374 | 0.493252 | 0.246626 | − | 0.969111i | \(-0.420678\pi\) | ||||
0.246626 | + | 0.969111i | \(0.420678\pi\) | |||||||
\(84\) | 1.19378 | 0.130252 | ||||||||
\(85\) | −8.23231 | −0.892919 | ||||||||
\(86\) | −1.70506 | −0.183862 | ||||||||
\(87\) | 6.53525 | 0.700653 | ||||||||
\(88\) | −4.27905 | −0.456148 | ||||||||
\(89\) | 5.55082 | 0.588386 | 0.294193 | − | 0.955746i | \(-0.404949\pi\) | ||||
0.294193 | + | 0.955746i | \(0.404949\pi\) | |||||||
\(90\) | −2.28948 | −0.241333 | ||||||||
\(91\) | −1.19378 | −0.125142 | ||||||||
\(92\) | −6.42459 | −0.669810 | ||||||||
\(93\) | 1.25937 | 0.130590 | ||||||||
\(94\) | −1.19672 | −0.123433 | ||||||||
\(95\) | −3.10843 | −0.318919 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 7.35332 | 0.746616 | 0.373308 | − | 0.927707i | \(-0.378223\pi\) | ||||
0.373308 | + | 0.927707i | \(0.378223\pi\) | |||||||
\(98\) | 5.57489 | 0.563149 | ||||||||
\(99\) | 4.27905 | 0.430061 | ||||||||
\(100\) | 0.241736 | 0.0241736 | ||||||||
\(101\) | 11.1470 | 1.10917 | 0.554584 | − | 0.832128i | \(-0.312878\pi\) | ||||
0.554584 | + | 0.832128i | \(0.312878\pi\) | |||||||
\(102\) | −3.59570 | −0.356028 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 2.73314 | 0.266727 | ||||||||
\(106\) | −2.84069 | −0.275912 | ||||||||
\(107\) | −4.78496 | −0.462580 | −0.231290 | − | 0.972885i | \(-0.574295\pi\) | ||||
−0.231290 | + | 0.972885i | \(0.574295\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 2.92640 | 0.280298 | 0.140149 | − | 0.990130i | \(-0.455242\pi\) | ||||
0.140149 | + | 0.990130i | \(0.455242\pi\) | |||||||
\(110\) | −9.79682 | −0.934090 | ||||||||
\(111\) | 6.96050 | 0.660661 | ||||||||
\(112\) | −1.19378 | −0.112801 | ||||||||
\(113\) | 2.55170 | 0.240044 | 0.120022 | − | 0.992771i | \(-0.461704\pi\) | ||||
0.120022 | + | 0.992771i | \(0.461704\pi\) | |||||||
\(114\) | −1.35770 | −0.127160 | ||||||||
\(115\) | −14.7090 | −1.37162 | ||||||||
\(116\) | −6.53525 | −0.606783 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −14.3018 | −1.31659 | ||||||||
\(119\) | 4.29248 | 0.393491 | ||||||||
\(120\) | 2.28948 | 0.209000 | ||||||||
\(121\) | 7.31027 | 0.664570 | ||||||||
\(122\) | −3.12763 | −0.283163 | ||||||||
\(123\) | −7.36952 | −0.664487 | ||||||||
\(124\) | −1.25937 | −0.113095 | ||||||||
\(125\) | −10.8940 | −0.974386 | ||||||||
\(126\) | 1.19378 | 0.106350 | ||||||||
\(127\) | −3.49577 | −0.310200 | −0.155100 | − | 0.987899i | \(-0.549570\pi\) | ||||
−0.155100 | + | 0.987899i | \(0.549570\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.70506 | −0.150123 | ||||||||
\(130\) | −2.28948 | −0.200801 | ||||||||
\(131\) | −18.1097 | −1.58226 | −0.791128 | − | 0.611651i | \(-0.790506\pi\) | ||||
−0.791128 | + | 0.611651i | \(0.790506\pi\) | |||||||
\(132\) | −4.27905 | −0.372444 | ||||||||
\(133\) | 1.62079 | 0.140541 | ||||||||
\(134\) | −10.3747 | −0.896241 | ||||||||
\(135\) | −2.28948 | −0.197047 | ||||||||
\(136\) | 3.59570 | 0.308329 | ||||||||
\(137\) | 0.772432 | 0.0659933 | 0.0329967 | − | 0.999455i | \(-0.489495\pi\) | ||||
0.0329967 | + | 0.999455i | \(0.489495\pi\) | |||||||
\(138\) | −6.42459 | −0.546898 | ||||||||
\(139\) | 14.3030 | 1.21317 | 0.606583 | − | 0.795020i | \(-0.292540\pi\) | ||||
0.606583 | + | 0.795020i | \(0.292540\pi\) | |||||||
\(140\) | −2.73314 | −0.230992 | ||||||||
\(141\) | −1.19672 | −0.100782 | ||||||||
\(142\) | −1.20531 | −0.101148 | ||||||||
\(143\) | 4.27905 | 0.357832 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −14.9624 | −1.24256 | ||||||||
\(146\) | −10.1318 | −0.838515 | ||||||||
\(147\) | 5.57489 | 0.459809 | ||||||||
\(148\) | −6.96050 | −0.572149 | ||||||||
\(149\) | 17.3427 | 1.42077 | 0.710385 | − | 0.703813i | \(-0.248521\pi\) | ||||
0.710385 | + | 0.703813i | \(0.248521\pi\) | |||||||
\(150\) | 0.241736 | 0.0197377 | ||||||||
\(151\) | 14.7147 | 1.19746 | 0.598731 | − | 0.800950i | \(-0.295672\pi\) | ||||
0.598731 | + | 0.800950i | \(0.295672\pi\) | |||||||
\(152\) | 1.35770 | 0.110124 | ||||||||
\(153\) | −3.59570 | −0.290695 | ||||||||
\(154\) | 5.10824 | 0.411634 | ||||||||
\(155\) | −2.88331 | −0.231593 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | 22.0695 | 1.76134 | 0.880671 | − | 0.473729i | \(-0.157092\pi\) | ||||
0.880671 | + | 0.473729i | \(0.157092\pi\) | |||||||
\(158\) | 2.00621 | 0.159605 | ||||||||
\(159\) | −2.84069 | −0.225282 | ||||||||
\(160\) | −2.28948 | −0.181000 | ||||||||
\(161\) | 7.66954 | 0.604445 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −5.41189 | −0.423892 | −0.211946 | − | 0.977281i | \(-0.567980\pi\) | ||||
−0.211946 | + | 0.977281i | \(0.567980\pi\) | |||||||
\(164\) | 7.36952 | 0.575463 | ||||||||
\(165\) | −9.79682 | −0.762681 | ||||||||
\(166\) | −4.49374 | −0.348782 | ||||||||
\(167\) | 24.2697 | 1.87805 | 0.939025 | − | 0.343850i | \(-0.111731\pi\) | ||||
0.939025 | + | 0.343850i | \(0.111731\pi\) | |||||||
\(168\) | −1.19378 | −0.0921020 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 8.23231 | 0.631389 | ||||||||
\(171\) | −1.35770 | −0.103826 | ||||||||
\(172\) | 1.70506 | 0.130010 | ||||||||
\(173\) | −9.74264 | −0.740720 | −0.370360 | − | 0.928888i | \(-0.620766\pi\) | ||||
−0.370360 | + | 0.928888i | \(0.620766\pi\) | |||||||
\(174\) | −6.53525 | −0.495436 | ||||||||
\(175\) | −0.288580 | −0.0218146 | ||||||||
\(176\) | 4.27905 | 0.322546 | ||||||||
\(177\) | −14.3018 | −1.07499 | ||||||||
\(178\) | −5.55082 | −0.416052 | ||||||||
\(179\) | 5.63260 | 0.421000 | 0.210500 | − | 0.977594i | \(-0.432491\pi\) | ||||
0.210500 | + | 0.977594i | \(0.432491\pi\) | |||||||
\(180\) | 2.28948 | 0.170648 | ||||||||
\(181\) | −6.35214 | −0.472151 | −0.236075 | − | 0.971735i | \(-0.575861\pi\) | ||||
−0.236075 | + | 0.971735i | \(0.575861\pi\) | |||||||
\(182\) | 1.19378 | 0.0884888 | ||||||||
\(183\) | −3.12763 | −0.231201 | ||||||||
\(184\) | 6.42459 | 0.473627 | ||||||||
\(185\) | −15.9359 | −1.17163 | ||||||||
\(186\) | −1.25937 | −0.0923414 | ||||||||
\(187\) | −15.3862 | −1.12515 | ||||||||
\(188\) | 1.19672 | 0.0872800 | ||||||||
\(189\) | 1.19378 | 0.0868346 | ||||||||
\(190\) | 3.10843 | 0.225509 | ||||||||
\(191\) | 0.0280475 | 0.00202944 | 0.00101472 | − | 0.999999i | \(-0.499677\pi\) | ||||
0.00101472 | + | 0.999999i | \(0.499677\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −16.8861 | −1.21549 | −0.607743 | − | 0.794134i | \(-0.707925\pi\) | ||||
−0.607743 | + | 0.794134i | \(0.707925\pi\) | |||||||
\(194\) | −7.35332 | −0.527937 | ||||||||
\(195\) | −2.28948 | −0.163953 | ||||||||
\(196\) | −5.57489 | −0.398207 | ||||||||
\(197\) | 11.9854 | 0.853928 | 0.426964 | − | 0.904269i | \(-0.359583\pi\) | ||||
0.426964 | + | 0.904269i | \(0.359583\pi\) | |||||||
\(198\) | −4.27905 | −0.304099 | ||||||||
\(199\) | 16.7843 | 1.18980 | 0.594902 | − | 0.803798i | \(-0.297191\pi\) | ||||
0.594902 | + | 0.803798i | \(0.297191\pi\) | |||||||
\(200\) | −0.241736 | −0.0170933 | ||||||||
\(201\) | −10.3747 | −0.731778 | ||||||||
\(202\) | −11.1470 | −0.784300 | ||||||||
\(203\) | 7.80165 | 0.547568 | ||||||||
\(204\) | 3.59570 | 0.251750 | ||||||||
\(205\) | 16.8724 | 1.17842 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | −6.42459 | −0.446540 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | −5.80967 | −0.401863 | ||||||||
\(210\) | −2.73314 | −0.188604 | ||||||||
\(211\) | −5.85650 | −0.403178 | −0.201589 | − | 0.979470i | \(-0.564611\pi\) | ||||
−0.201589 | + | 0.979470i | \(0.564611\pi\) | |||||||
\(212\) | 2.84069 | 0.195100 | ||||||||
\(213\) | −1.20531 | −0.0825867 | ||||||||
\(214\) | 4.78496 | 0.327093 | ||||||||
\(215\) | 3.90372 | 0.266231 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 1.50341 | 0.102058 | ||||||||
\(218\) | −2.92640 | −0.198201 | ||||||||
\(219\) | −10.1318 | −0.684644 | ||||||||
\(220\) | 9.79682 | 0.660501 | ||||||||
\(221\) | −3.59570 | −0.241873 | ||||||||
\(222\) | −6.96050 | −0.467158 | ||||||||
\(223\) | 2.27388 | 0.152270 | 0.0761351 | − | 0.997098i | \(-0.475742\pi\) | ||||
0.0761351 | + | 0.997098i | \(0.475742\pi\) | |||||||
\(224\) | 1.19378 | 0.0797627 | ||||||||
\(225\) | 0.241736 | 0.0161158 | ||||||||
\(226\) | −2.55170 | −0.169736 | ||||||||
\(227\) | 24.4840 | 1.62506 | 0.812530 | − | 0.582919i | \(-0.198090\pi\) | ||||
0.812530 | + | 0.582919i | \(0.198090\pi\) | |||||||
\(228\) | 1.35770 | 0.0899159 | ||||||||
\(229\) | 18.1528 | 1.19957 | 0.599786 | − | 0.800161i | \(-0.295252\pi\) | ||||
0.599786 | + | 0.800161i | \(0.295252\pi\) | |||||||
\(230\) | 14.7090 | 0.969883 | ||||||||
\(231\) | 5.10824 | 0.336097 | ||||||||
\(232\) | 6.53525 | 0.429060 | ||||||||
\(233\) | −12.6906 | −0.831392 | −0.415696 | − | 0.909504i | \(-0.636462\pi\) | ||||
−0.415696 | + | 0.909504i | \(0.636462\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | 2.73988 | 0.178730 | ||||||||
\(236\) | 14.3018 | 0.930971 | ||||||||
\(237\) | 2.00621 | 0.130317 | ||||||||
\(238\) | −4.29248 | −0.278240 | ||||||||
\(239\) | 17.9914 | 1.16377 | 0.581883 | − | 0.813273i | \(-0.302316\pi\) | ||||
0.581883 | + | 0.813273i | \(0.302316\pi\) | |||||||
\(240\) | −2.28948 | −0.147786 | ||||||||
\(241\) | 3.62121 | 0.233262 | 0.116631 | − | 0.993175i | \(-0.462790\pi\) | ||||
0.116631 | + | 0.993175i | \(0.462790\pi\) | |||||||
\(242\) | −7.31027 | −0.469922 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 3.12763 | 0.200226 | ||||||||
\(245\) | −12.7636 | −0.815438 | ||||||||
\(246\) | 7.36952 | 0.469864 | ||||||||
\(247\) | −1.35770 | −0.0863884 | ||||||||
\(248\) | 1.25937 | 0.0799700 | ||||||||
\(249\) | −4.49374 | −0.284779 | ||||||||
\(250\) | 10.8940 | 0.688995 | ||||||||
\(251\) | 9.61212 | 0.606712 | 0.303356 | − | 0.952877i | \(-0.401893\pi\) | ||||
0.303356 | + | 0.952877i | \(0.401893\pi\) | |||||||
\(252\) | −1.19378 | −0.0752010 | ||||||||
\(253\) | −27.4912 | −1.72835 | ||||||||
\(254\) | 3.49577 | 0.219344 | ||||||||
\(255\) | 8.23231 | 0.515527 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.38700 | −0.273654 | −0.136827 | − | 0.990595i | \(-0.543690\pi\) | ||||
−0.136827 | + | 0.990595i | \(0.543690\pi\) | |||||||
\(258\) | 1.70506 | 0.106153 | ||||||||
\(259\) | 8.30929 | 0.516314 | ||||||||
\(260\) | 2.28948 | 0.141988 | ||||||||
\(261\) | −6.53525 | −0.404522 | ||||||||
\(262\) | 18.1097 | 1.11882 | ||||||||
\(263\) | −28.0116 | −1.72727 | −0.863635 | − | 0.504118i | \(-0.831818\pi\) | ||||
−0.863635 | + | 0.504118i | \(0.831818\pi\) | |||||||
\(264\) | 4.27905 | 0.263357 | ||||||||
\(265\) | 6.50372 | 0.399520 | ||||||||
\(266\) | −1.62079 | −0.0993773 | ||||||||
\(267\) | −5.55082 | −0.339705 | ||||||||
\(268\) | 10.3747 | 0.633738 | ||||||||
\(269\) | −7.77286 | −0.473920 | −0.236960 | − | 0.971519i | \(-0.576151\pi\) | ||||
−0.236960 | + | 0.971519i | \(0.576151\pi\) | |||||||
\(270\) | 2.28948 | 0.139334 | ||||||||
\(271\) | 11.6289 | 0.706406 | 0.353203 | − | 0.935547i | \(-0.385093\pi\) | ||||
0.353203 | + | 0.935547i | \(0.385093\pi\) | |||||||
\(272\) | −3.59570 | −0.218022 | ||||||||
\(273\) | 1.19378 | 0.0722508 | ||||||||
\(274\) | −0.772432 | −0.0466643 | ||||||||
\(275\) | 1.03440 | 0.0623768 | ||||||||
\(276\) | 6.42459 | 0.386715 | ||||||||
\(277\) | 15.6095 | 0.937883 | 0.468941 | − | 0.883229i | \(-0.344636\pi\) | ||||
0.468941 | + | 0.883229i | \(0.344636\pi\) | |||||||
\(278\) | −14.3030 | −0.857837 | ||||||||
\(279\) | −1.25937 | −0.0753965 | ||||||||
\(280\) | 2.73314 | 0.163336 | ||||||||
\(281\) | −14.6040 | −0.871199 | −0.435599 | − | 0.900141i | \(-0.643464\pi\) | ||||
−0.435599 | + | 0.900141i | \(0.643464\pi\) | |||||||
\(282\) | 1.19672 | 0.0712638 | ||||||||
\(283\) | 14.0678 | 0.836245 | 0.418122 | − | 0.908391i | \(-0.362688\pi\) | ||||
0.418122 | + | 0.908391i | \(0.362688\pi\) | |||||||
\(284\) | 1.20531 | 0.0715222 | ||||||||
\(285\) | 3.10843 | 0.184128 | ||||||||
\(286\) | −4.27905 | −0.253026 | ||||||||
\(287\) | −8.79758 | −0.519305 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −4.07091 | −0.239465 | ||||||||
\(290\) | 14.9624 | 0.878620 | ||||||||
\(291\) | −7.35332 | −0.431059 | ||||||||
\(292\) | 10.1318 | 0.592919 | ||||||||
\(293\) | −24.4565 | −1.42876 | −0.714381 | − | 0.699757i | \(-0.753292\pi\) | ||||
−0.714381 | + | 0.699757i | \(0.753292\pi\) | |||||||
\(294\) | −5.57489 | −0.325134 | ||||||||
\(295\) | 32.7438 | 1.90642 | ||||||||
\(296\) | 6.96050 | 0.404571 | ||||||||
\(297\) | −4.27905 | −0.248296 | ||||||||
\(298\) | −17.3427 | −1.00464 | ||||||||
\(299\) | −6.42459 | −0.371544 | ||||||||
\(300\) | −0.241736 | −0.0139566 | ||||||||
\(301\) | −2.03547 | −0.117323 | ||||||||
\(302\) | −14.7147 | −0.846733 | ||||||||
\(303\) | −11.1470 | −0.640378 | ||||||||
\(304\) | −1.35770 | −0.0778695 | ||||||||
\(305\) | 7.16067 | 0.410019 | ||||||||
\(306\) | 3.59570 | 0.205553 | ||||||||
\(307\) | −4.95540 | −0.282820 | −0.141410 | − | 0.989951i | \(-0.545164\pi\) | ||||
−0.141410 | + | 0.989951i | \(0.545164\pi\) | |||||||
\(308\) | −5.10824 | −0.291069 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 2.88331 | 0.163761 | ||||||||
\(311\) | 0.541516 | 0.0307066 | 0.0153533 | − | 0.999882i | \(-0.495113\pi\) | ||||
0.0153533 | + | 0.999882i | \(0.495113\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | −21.4984 | −1.21516 | −0.607580 | − | 0.794258i | \(-0.707860\pi\) | ||||
−0.607580 | + | 0.794258i | \(0.707860\pi\) | |||||||
\(314\) | −22.0695 | −1.24546 | ||||||||
\(315\) | −2.73314 | −0.153995 | ||||||||
\(316\) | −2.00621 | −0.112858 | ||||||||
\(317\) | 1.44767 | 0.0813094 | 0.0406547 | − | 0.999173i | \(-0.487056\pi\) | ||||
0.0406547 | + | 0.999173i | \(0.487056\pi\) | |||||||
\(318\) | 2.84069 | 0.159298 | ||||||||
\(319\) | −27.9647 | −1.56572 | ||||||||
\(320\) | 2.28948 | 0.127986 | ||||||||
\(321\) | 4.78496 | 0.267070 | ||||||||
\(322\) | −7.66954 | −0.427407 | ||||||||
\(323\) | 4.88189 | 0.271636 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0.241736 | 0.0134091 | ||||||||
\(326\) | 5.41189 | 0.299737 | ||||||||
\(327\) | −2.92640 | −0.161830 | ||||||||
\(328\) | −7.36952 | −0.406914 | ||||||||
\(329\) | −1.42862 | −0.0787625 | ||||||||
\(330\) | 9.79682 | 0.539297 | ||||||||
\(331\) | 28.5941 | 1.57167 | 0.785836 | − | 0.618435i | \(-0.212233\pi\) | ||||
0.785836 | + | 0.618435i | \(0.212233\pi\) | |||||||
\(332\) | 4.49374 | 0.246626 | ||||||||
\(333\) | −6.96050 | −0.381433 | ||||||||
\(334\) | −24.2697 | −1.32798 | ||||||||
\(335\) | 23.7528 | 1.29775 | ||||||||
\(336\) | 1.19378 | 0.0651260 | ||||||||
\(337\) | −32.2295 | −1.75565 | −0.877827 | − | 0.478978i | \(-0.841007\pi\) | ||||
−0.877827 | + | 0.478978i | \(0.841007\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | −2.55170 | −0.138589 | ||||||||
\(340\) | −8.23231 | −0.446460 | ||||||||
\(341\) | −5.38890 | −0.291825 | ||||||||
\(342\) | 1.35770 | 0.0734160 | ||||||||
\(343\) | 15.0116 | 0.810552 | ||||||||
\(344\) | −1.70506 | −0.0919309 | ||||||||
\(345\) | 14.7090 | 0.791906 | ||||||||
\(346\) | 9.74264 | 0.523768 | ||||||||
\(347\) | 22.3484 | 1.19973 | 0.599863 | − | 0.800103i | \(-0.295222\pi\) | ||||
0.599863 | + | 0.800103i | \(0.295222\pi\) | |||||||
\(348\) | 6.53525 | 0.350326 | ||||||||
\(349\) | 9.93972 | 0.532061 | 0.266030 | − | 0.963965i | \(-0.414288\pi\) | ||||
0.266030 | + | 0.963965i | \(0.414288\pi\) | |||||||
\(350\) | 0.288580 | 0.0154252 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −4.27905 | −0.228074 | ||||||||
\(353\) | −17.0214 | −0.905958 | −0.452979 | − | 0.891521i | \(-0.649639\pi\) | ||||
−0.452979 | + | 0.891521i | \(0.649639\pi\) | |||||||
\(354\) | 14.3018 | 0.760135 | ||||||||
\(355\) | 2.75955 | 0.146462 | ||||||||
\(356\) | 5.55082 | 0.294193 | ||||||||
\(357\) | −4.29248 | −0.227182 | ||||||||
\(358\) | −5.63260 | −0.297692 | ||||||||
\(359\) | 0.00561075 | 0.000296124 0 | 0.000148062 | − | 1.00000i | \(-0.499953\pi\) | ||||
0.000148062 | 1.00000i | \(0.499953\pi\) | ||||||||
\(360\) | −2.28948 | −0.120666 | ||||||||
\(361\) | −17.1566 | −0.902982 | ||||||||
\(362\) | 6.35214 | 0.333861 | ||||||||
\(363\) | −7.31027 | −0.383690 | ||||||||
\(364\) | −1.19378 | −0.0625710 | ||||||||
\(365\) | 23.1966 | 1.21417 | ||||||||
\(366\) | 3.12763 | 0.163484 | ||||||||
\(367\) | −4.96085 | −0.258954 | −0.129477 | − | 0.991582i | \(-0.541330\pi\) | ||||
−0.129477 | + | 0.991582i | \(0.541330\pi\) | |||||||
\(368\) | −6.42459 | −0.334905 | ||||||||
\(369\) | 7.36952 | 0.383642 | ||||||||
\(370\) | 15.9359 | 0.828470 | ||||||||
\(371\) | −3.39116 | −0.176060 | ||||||||
\(372\) | 1.25937 | 0.0652952 | ||||||||
\(373\) | 11.5261 | 0.596801 | 0.298400 | − | 0.954441i | \(-0.403547\pi\) | ||||
0.298400 | + | 0.954441i | \(0.403547\pi\) | |||||||
\(374\) | 15.3862 | 0.795601 | ||||||||
\(375\) | 10.8940 | 0.562562 | ||||||||
\(376\) | −1.19672 | −0.0617163 | ||||||||
\(377\) | −6.53525 | −0.336583 | ||||||||
\(378\) | −1.19378 | −0.0614014 | ||||||||
\(379\) | 19.0110 | 0.976532 | 0.488266 | − | 0.872695i | \(-0.337630\pi\) | ||||
0.488266 | + | 0.872695i | \(0.337630\pi\) | |||||||
\(380\) | −3.10843 | −0.159459 | ||||||||
\(381\) | 3.49577 | 0.179094 | ||||||||
\(382\) | −0.0280475 | −0.00143503 | ||||||||
\(383\) | 8.99836 | 0.459795 | 0.229897 | − | 0.973215i | \(-0.426161\pi\) | ||||
0.229897 | + | 0.973215i | \(0.426161\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −11.6952 | −0.596044 | ||||||||
\(386\) | 16.8861 | 0.859478 | ||||||||
\(387\) | 1.70506 | 0.0866733 | ||||||||
\(388\) | 7.35332 | 0.373308 | ||||||||
\(389\) | 34.9429 | 1.77168 | 0.885838 | − | 0.463995i | \(-0.153584\pi\) | ||||
0.885838 | + | 0.463995i | \(0.153584\pi\) | |||||||
\(390\) | 2.28948 | 0.115933 | ||||||||
\(391\) | 23.1009 | 1.16826 | ||||||||
\(392\) | 5.57489 | 0.281575 | ||||||||
\(393\) | 18.1097 | 0.913516 | ||||||||
\(394\) | −11.9854 | −0.603818 | ||||||||
\(395\) | −4.59318 | −0.231108 | ||||||||
\(396\) | 4.27905 | 0.215030 | ||||||||
\(397\) | 7.48202 | 0.375512 | 0.187756 | − | 0.982216i | \(-0.439879\pi\) | ||||
0.187756 | + | 0.982216i | \(0.439879\pi\) | |||||||
\(398\) | −16.7843 | −0.841319 | ||||||||
\(399\) | −1.62079 | −0.0811412 | ||||||||
\(400\) | 0.241736 | 0.0120868 | ||||||||
\(401\) | −13.7786 | −0.688071 | −0.344036 | − | 0.938957i | \(-0.611794\pi\) | ||||
−0.344036 | + | 0.938957i | \(0.611794\pi\) | |||||||
\(402\) | 10.3747 | 0.517445 | ||||||||
\(403\) | −1.25937 | −0.0627336 | ||||||||
\(404\) | 11.1470 | 0.554584 | ||||||||
\(405\) | 2.28948 | 0.113765 | ||||||||
\(406\) | −7.80165 | −0.387189 | ||||||||
\(407\) | −29.7843 | −1.47635 | ||||||||
\(408\) | −3.59570 | −0.178014 | ||||||||
\(409\) | 18.5833 | 0.918885 | 0.459443 | − | 0.888207i | \(-0.348049\pi\) | ||||
0.459443 | + | 0.888207i | \(0.348049\pi\) | |||||||
\(410\) | −16.8724 | −0.833269 | ||||||||
\(411\) | −0.772432 | −0.0381013 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | −17.0732 | −0.840119 | ||||||||
\(414\) | 6.42459 | 0.315752 | ||||||||
\(415\) | 10.2883 | 0.505035 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −14.3030 | −0.700421 | ||||||||
\(418\) | 5.80967 | 0.284160 | ||||||||
\(419\) | −16.9895 | −0.829991 | −0.414996 | − | 0.909823i | \(-0.636217\pi\) | ||||
−0.414996 | + | 0.909823i | \(0.636217\pi\) | |||||||
\(420\) | 2.73314 | 0.133363 | ||||||||
\(421\) | 26.6550 | 1.29908 | 0.649542 | − | 0.760326i | \(-0.274961\pi\) | ||||
0.649542 | + | 0.760326i | \(0.274961\pi\) | |||||||
\(422\) | 5.85650 | 0.285090 | ||||||||
\(423\) | 1.19672 | 0.0581867 | ||||||||
\(424\) | −2.84069 | −0.137956 | ||||||||
\(425\) | −0.869212 | −0.0421630 | ||||||||
\(426\) | 1.20531 | 0.0583977 | ||||||||
\(427\) | −3.73370 | −0.180687 | ||||||||
\(428\) | −4.78496 | −0.231290 | ||||||||
\(429\) | −4.27905 | −0.206594 | ||||||||
\(430\) | −3.90372 | −0.188254 | ||||||||
\(431\) | −31.1412 | −1.50002 | −0.750011 | − | 0.661426i | \(-0.769952\pi\) | ||||
−0.750011 | + | 0.661426i | \(0.769952\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −4.81223 | −0.231261 | −0.115631 | − | 0.993292i | \(-0.536889\pi\) | ||||
−0.115631 | + | 0.993292i | \(0.536889\pi\) | |||||||
\(434\) | −1.50341 | −0.0721659 | ||||||||
\(435\) | 14.9624 | 0.717390 | ||||||||
\(436\) | 2.92640 | 0.140149 | ||||||||
\(437\) | 8.72268 | 0.417262 | ||||||||
\(438\) | 10.1318 | 0.484117 | ||||||||
\(439\) | 40.6140 | 1.93840 | 0.969200 | − | 0.246275i | \(-0.0792067\pi\) | ||||
0.969200 | + | 0.246275i | \(0.0792067\pi\) | |||||||
\(440\) | −9.79682 | −0.467045 | ||||||||
\(441\) | −5.57489 | −0.265471 | ||||||||
\(442\) | 3.59570 | 0.171030 | ||||||||
\(443\) | −12.7887 | −0.607611 | −0.303806 | − | 0.952734i | \(-0.598257\pi\) | ||||
−0.303806 | + | 0.952734i | \(0.598257\pi\) | |||||||
\(444\) | 6.96050 | 0.330331 | ||||||||
\(445\) | 12.7085 | 0.602442 | ||||||||
\(446\) | −2.27388 | −0.107671 | ||||||||
\(447\) | −17.3427 | −0.820282 | ||||||||
\(448\) | −1.19378 | −0.0564007 | ||||||||
\(449\) | −41.2330 | −1.94591 | −0.972953 | − | 0.231002i | \(-0.925800\pi\) | ||||
−0.972953 | + | 0.231002i | \(0.925800\pi\) | |||||||
\(450\) | −0.241736 | −0.0113956 | ||||||||
\(451\) | 31.5346 | 1.48490 | ||||||||
\(452\) | 2.55170 | 0.120022 | ||||||||
\(453\) | −14.7147 | −0.691355 | ||||||||
\(454\) | −24.4840 | −1.14909 | ||||||||
\(455\) | −2.73314 | −0.128131 | ||||||||
\(456\) | −1.35770 | −0.0635802 | ||||||||
\(457\) | −13.7388 | −0.642675 | −0.321338 | − | 0.946965i | \(-0.604132\pi\) | ||||
−0.321338 | + | 0.946965i | \(0.604132\pi\) | |||||||
\(458\) | −18.1528 | −0.848225 | ||||||||
\(459\) | 3.59570 | 0.167833 | ||||||||
\(460\) | −14.7090 | −0.685811 | ||||||||
\(461\) | −10.4692 | −0.487601 | −0.243801 | − | 0.969825i | \(-0.578394\pi\) | ||||
−0.243801 | + | 0.969825i | \(0.578394\pi\) | |||||||
\(462\) | −5.10824 | −0.237657 | ||||||||
\(463\) | 19.0331 | 0.884545 | 0.442272 | − | 0.896881i | \(-0.354172\pi\) | ||||
0.442272 | + | 0.896881i | \(0.354172\pi\) | |||||||
\(464\) | −6.53525 | −0.303392 | ||||||||
\(465\) | 2.88331 | 0.133710 | ||||||||
\(466\) | 12.6906 | 0.587883 | ||||||||
\(467\) | −4.60131 | −0.212923 | −0.106462 | − | 0.994317i | \(-0.533952\pi\) | ||||
−0.106462 | + | 0.994317i | \(0.533952\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | −12.3851 | −0.571893 | ||||||||
\(470\) | −2.73988 | −0.126381 | ||||||||
\(471\) | −22.0695 | −1.01691 | ||||||||
\(472\) | −14.3018 | −0.658296 | ||||||||
\(473\) | 7.29606 | 0.335473 | ||||||||
\(474\) | −2.00621 | −0.0921481 | ||||||||
\(475\) | −0.328206 | −0.0150591 | ||||||||
\(476\) | 4.29248 | 0.196745 | ||||||||
\(477\) | 2.84069 | 0.130066 | ||||||||
\(478\) | −17.9914 | −0.822907 | ||||||||
\(479\) | 8.25442 | 0.377154 | 0.188577 | − | 0.982058i | \(-0.439613\pi\) | ||||
0.188577 | + | 0.982058i | \(0.439613\pi\) | |||||||
\(480\) | 2.28948 | 0.104500 | ||||||||
\(481\) | −6.96050 | −0.317371 | ||||||||
\(482\) | −3.62121 | −0.164941 | ||||||||
\(483\) | −7.66954 | −0.348976 | ||||||||
\(484\) | 7.31027 | 0.332285 | ||||||||
\(485\) | 16.8353 | 0.764451 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 30.9469 | 1.40234 | 0.701169 | − | 0.712996i | \(-0.252662\pi\) | ||||
0.701169 | + | 0.712996i | \(0.252662\pi\) | |||||||
\(488\) | −3.12763 | −0.141581 | ||||||||
\(489\) | 5.41189 | 0.244734 | ||||||||
\(490\) | 12.7636 | 0.576602 | ||||||||
\(491\) | 2.62104 | 0.118286 | 0.0591429 | − | 0.998250i | \(-0.481163\pi\) | ||||
0.0591429 | + | 0.998250i | \(0.481163\pi\) | |||||||
\(492\) | −7.36952 | −0.332244 | ||||||||
\(493\) | 23.4988 | 1.05833 | ||||||||
\(494\) | 1.35770 | 0.0610858 | ||||||||
\(495\) | 9.79682 | 0.440334 | ||||||||
\(496\) | −1.25937 | −0.0565473 | ||||||||
\(497\) | −1.43888 | −0.0645425 | ||||||||
\(498\) | 4.49374 | 0.201369 | ||||||||
\(499\) | −10.9828 | −0.491657 | −0.245829 | − | 0.969313i | \(-0.579060\pi\) | ||||
−0.245829 | + | 0.969313i | \(0.579060\pi\) | |||||||
\(500\) | −10.8940 | −0.487193 | ||||||||
\(501\) | −24.2697 | −1.08429 | ||||||||
\(502\) | −9.61212 | −0.429010 | ||||||||
\(503\) | −2.99356 | −0.133476 | −0.0667382 | − | 0.997771i | \(-0.521259\pi\) | ||||
−0.0667382 | + | 0.997771i | \(0.521259\pi\) | |||||||
\(504\) | 1.19378 | 0.0531751 | ||||||||
\(505\) | 25.5209 | 1.13566 | ||||||||
\(506\) | 27.4912 | 1.22213 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −3.49577 | −0.155100 | ||||||||
\(509\) | 19.6098 | 0.869188 | 0.434594 | − | 0.900626i | \(-0.356892\pi\) | ||||
0.434594 | + | 0.900626i | \(0.356892\pi\) | |||||||
\(510\) | −8.23231 | −0.364533 | ||||||||
\(511\) | −12.0951 | −0.535058 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.35770 | 0.0599440 | ||||||||
\(514\) | 4.38700 | 0.193502 | ||||||||
\(515\) | −2.28948 | −0.100887 | ||||||||
\(516\) | −1.70506 | −0.0750613 | ||||||||
\(517\) | 5.12084 | 0.225214 | ||||||||
\(518\) | −8.30929 | −0.365089 | ||||||||
\(519\) | 9.74264 | 0.427655 | ||||||||
\(520\) | −2.28948 | −0.100401 | ||||||||
\(521\) | 22.8030 | 0.999017 | 0.499509 | − | 0.866309i | \(-0.333514\pi\) | ||||
0.499509 | + | 0.866309i | \(0.333514\pi\) | |||||||
\(522\) | 6.53525 | 0.286040 | ||||||||
\(523\) | −25.2714 | −1.10504 | −0.552522 | − | 0.833499i | \(-0.686334\pi\) | ||||
−0.552522 | + | 0.833499i | \(0.686334\pi\) | |||||||
\(524\) | −18.1097 | −0.791128 | ||||||||
\(525\) | 0.288580 | 0.0125946 | ||||||||
\(526\) | 28.0116 | 1.22136 | ||||||||
\(527\) | 4.52832 | 0.197257 | ||||||||
\(528\) | −4.27905 | −0.186222 | ||||||||
\(529\) | 18.2754 | 0.794583 | ||||||||
\(530\) | −6.50372 | −0.282504 | ||||||||
\(531\) | 14.3018 | 0.620647 | ||||||||
\(532\) | 1.62079 | 0.0702703 | ||||||||
\(533\) | 7.36952 | 0.319209 | ||||||||
\(534\) | 5.55082 | 0.240208 | ||||||||
\(535\) | −10.9551 | −0.473630 | ||||||||
\(536\) | −10.3747 | −0.448121 | ||||||||
\(537\) | −5.63260 | −0.243065 | ||||||||
\(538\) | 7.77286 | 0.335112 | ||||||||
\(539\) | −23.8552 | −1.02752 | ||||||||
\(540\) | −2.28948 | −0.0985237 | ||||||||
\(541\) | 4.86481 | 0.209154 | 0.104577 | − | 0.994517i | \(-0.466651\pi\) | ||||
0.104577 | + | 0.994517i | \(0.466651\pi\) | |||||||
\(542\) | −11.6289 | −0.499504 | ||||||||
\(543\) | 6.35214 | 0.272596 | ||||||||
\(544\) | 3.59570 | 0.154165 | ||||||||
\(545\) | 6.69995 | 0.286994 | ||||||||
\(546\) | −1.19378 | −0.0510890 | ||||||||
\(547\) | 25.2611 | 1.08009 | 0.540043 | − | 0.841638i | \(-0.318408\pi\) | ||||
0.540043 | + | 0.841638i | \(0.318408\pi\) | |||||||
\(548\) | 0.772432 | 0.0329967 | ||||||||
\(549\) | 3.12763 | 0.133484 | ||||||||
\(550\) | −1.03440 | −0.0441070 | ||||||||
\(551\) | 8.87292 | 0.377999 | ||||||||
\(552\) | −6.42459 | −0.273449 | ||||||||
\(553\) | 2.39497 | 0.101844 | ||||||||
\(554\) | −15.6095 | −0.663183 | ||||||||
\(555\) | 15.9359 | 0.676443 | ||||||||
\(556\) | 14.3030 | 0.606583 | ||||||||
\(557\) | 10.1532 | 0.430205 | 0.215102 | − | 0.976591i | \(-0.430991\pi\) | ||||
0.215102 | + | 0.976591i | \(0.430991\pi\) | |||||||
\(558\) | 1.25937 | 0.0533133 | ||||||||
\(559\) | 1.70506 | 0.0721166 | ||||||||
\(560\) | −2.73314 | −0.115496 | ||||||||
\(561\) | 15.3862 | 0.649606 | ||||||||
\(562\) | 14.6040 | 0.616031 | ||||||||
\(563\) | −5.09473 | −0.214717 | −0.107359 | − | 0.994220i | \(-0.534239\pi\) | ||||
−0.107359 | + | 0.994220i | \(0.534239\pi\) | |||||||
\(564\) | −1.19672 | −0.0503911 | ||||||||
\(565\) | 5.84207 | 0.245778 | ||||||||
\(566\) | −14.0678 | −0.591314 | ||||||||
\(567\) | −1.19378 | −0.0501340 | ||||||||
\(568\) | −1.20531 | −0.0505738 | ||||||||
\(569\) | −42.8195 | −1.79509 | −0.897543 | − | 0.440926i | \(-0.854650\pi\) | ||||
−0.897543 | + | 0.440926i | \(0.854650\pi\) | |||||||
\(570\) | −3.10843 | −0.130198 | ||||||||
\(571\) | 32.0885 | 1.34286 | 0.671430 | − | 0.741068i | \(-0.265680\pi\) | ||||
0.671430 | + | 0.741068i | \(0.265680\pi\) | |||||||
\(572\) | 4.27905 | 0.178916 | ||||||||
\(573\) | −0.0280475 | −0.00117170 | ||||||||
\(574\) | 8.79758 | 0.367204 | ||||||||
\(575\) | −1.55306 | −0.0647670 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 13.9671 | 0.581458 | 0.290729 | − | 0.956805i | \(-0.406102\pi\) | ||||
0.290729 | + | 0.956805i | \(0.406102\pi\) | |||||||
\(578\) | 4.07091 | 0.169327 | ||||||||
\(579\) | 16.8861 | 0.701761 | ||||||||
\(580\) | −14.9624 | −0.621278 | ||||||||
\(581\) | −5.36453 | −0.222558 | ||||||||
\(582\) | 7.35332 | 0.304805 | ||||||||
\(583\) | 12.1555 | 0.503428 | ||||||||
\(584\) | −10.1318 | −0.419257 | ||||||||
\(585\) | 2.28948 | 0.0946585 | ||||||||
\(586\) | 24.4565 | 1.01029 | ||||||||
\(587\) | −13.4259 | −0.554147 | −0.277073 | − | 0.960849i | \(-0.589365\pi\) | ||||
−0.277073 | + | 0.960849i | \(0.589365\pi\) | |||||||
\(588\) | 5.57489 | 0.229905 | ||||||||
\(589\) | 1.70985 | 0.0704530 | ||||||||
\(590\) | −32.7438 | −1.34804 | ||||||||
\(591\) | −11.9854 | −0.493016 | ||||||||
\(592\) | −6.96050 | −0.286075 | ||||||||
\(593\) | −31.2213 | −1.28210 | −0.641052 | − | 0.767497i | \(-0.721502\pi\) | ||||
−0.641052 | + | 0.767497i | \(0.721502\pi\) | |||||||
\(594\) | 4.27905 | 0.175572 | ||||||||
\(595\) | 9.82755 | 0.402890 | ||||||||
\(596\) | 17.3427 | 0.710385 | ||||||||
\(597\) | −16.7843 | −0.686934 | ||||||||
\(598\) | 6.42459 | 0.262721 | ||||||||
\(599\) | −30.1210 | −1.23071 | −0.615356 | − | 0.788250i | \(-0.710988\pi\) | ||||
−0.615356 | + | 0.788250i | \(0.710988\pi\) | |||||||
\(600\) | 0.241736 | 0.00986884 | ||||||||
\(601\) | 32.1632 | 1.31197 | 0.655983 | − | 0.754776i | \(-0.272254\pi\) | ||||
0.655983 | + | 0.754776i | \(0.272254\pi\) | |||||||
\(602\) | 2.03547 | 0.0829596 | ||||||||
\(603\) | 10.3747 | 0.422492 | ||||||||
\(604\) | 14.7147 | 0.598731 | ||||||||
\(605\) | 16.7367 | 0.680445 | ||||||||
\(606\) | 11.1470 | 0.452816 | ||||||||
\(607\) | 26.2385 | 1.06499 | 0.532494 | − | 0.846434i | \(-0.321255\pi\) | ||||
0.532494 | + | 0.846434i | \(0.321255\pi\) | |||||||
\(608\) | 1.35770 | 0.0550620 | ||||||||
\(609\) | −7.80165 | −0.316139 | ||||||||
\(610\) | −7.16067 | −0.289927 | ||||||||
\(611\) | 1.19672 | 0.0484142 | ||||||||
\(612\) | −3.59570 | −0.145348 | ||||||||
\(613\) | −15.6293 | −0.631262 | −0.315631 | − | 0.948882i | \(-0.602216\pi\) | ||||
−0.315631 | + | 0.948882i | \(0.602216\pi\) | |||||||
\(614\) | 4.95540 | 0.199984 | ||||||||
\(615\) | −16.8724 | −0.680361 | ||||||||
\(616\) | 5.10824 | 0.205817 | ||||||||
\(617\) | −1.25068 | −0.0503505 | −0.0251753 | − | 0.999683i | \(-0.508014\pi\) | ||||
−0.0251753 | + | 0.999683i | \(0.508014\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | 31.7077 | 1.27444 | 0.637221 | − | 0.770681i | \(-0.280084\pi\) | ||||
0.637221 | + | 0.770681i | \(0.280084\pi\) | |||||||
\(620\) | −2.88331 | −0.115796 | ||||||||
\(621\) | 6.42459 | 0.257810 | ||||||||
\(622\) | −0.541516 | −0.0217128 | ||||||||
\(623\) | −6.62646 | −0.265483 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | −26.1502 | −1.04601 | ||||||||
\(626\) | 21.4984 | 0.859248 | ||||||||
\(627\) | 5.80967 | 0.232016 | ||||||||
\(628\) | 22.0695 | 0.880671 | ||||||||
\(629\) | 25.0279 | 0.997927 | ||||||||
\(630\) | 2.73314 | 0.108891 | ||||||||
\(631\) | −15.6313 | −0.622273 | −0.311137 | − | 0.950365i | \(-0.600710\pi\) | ||||
−0.311137 | + | 0.950365i | \(0.600710\pi\) | |||||||
\(632\) | 2.00621 | 0.0798026 | ||||||||
\(633\) | 5.85650 | 0.232775 | ||||||||
\(634\) | −1.44767 | −0.0574944 | ||||||||
\(635\) | −8.00352 | −0.317610 | ||||||||
\(636\) | −2.84069 | −0.112641 | ||||||||
\(637\) | −5.57489 | −0.220885 | ||||||||
\(638\) | 27.9647 | 1.10713 | ||||||||
\(639\) | 1.20531 | 0.0476815 | ||||||||
\(640\) | −2.28948 | −0.0904998 | ||||||||
\(641\) | −33.4222 | −1.32010 | −0.660048 | − | 0.751223i | \(-0.729464\pi\) | ||||
−0.660048 | + | 0.751223i | \(0.729464\pi\) | |||||||
\(642\) | −4.78496 | −0.188847 | ||||||||
\(643\) | −8.92919 | −0.352133 | −0.176067 | − | 0.984378i | \(-0.556337\pi\) | ||||
−0.176067 | + | 0.984378i | \(0.556337\pi\) | |||||||
\(644\) | 7.66954 | 0.302222 | ||||||||
\(645\) | −3.90372 | −0.153709 | ||||||||
\(646\) | −4.88189 | −0.192075 | ||||||||
\(647\) | −42.6542 | −1.67691 | −0.838455 | − | 0.544970i | \(-0.816541\pi\) | ||||
−0.838455 | + | 0.544970i | \(0.816541\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 61.1983 | 2.40224 | ||||||||
\(650\) | −0.241736 | −0.00948168 | ||||||||
\(651\) | −1.50341 | −0.0589232 | ||||||||
\(652\) | −5.41189 | −0.211946 | ||||||||
\(653\) | 15.3018 | 0.598806 | 0.299403 | − | 0.954127i | \(-0.403213\pi\) | ||||
0.299403 | + | 0.954127i | \(0.403213\pi\) | |||||||
\(654\) | 2.92640 | 0.114431 | ||||||||
\(655\) | −41.4620 | −1.62005 | ||||||||
\(656\) | 7.36952 | 0.287732 | ||||||||
\(657\) | 10.1318 | 0.395280 | ||||||||
\(658\) | 1.42862 | 0.0556935 | ||||||||
\(659\) | 4.82352 | 0.187898 | 0.0939489 | − | 0.995577i | \(-0.470051\pi\) | ||||
0.0939489 | + | 0.995577i | \(0.470051\pi\) | |||||||
\(660\) | −9.79682 | −0.381341 | ||||||||
\(661\) | 24.6784 | 0.959880 | 0.479940 | − | 0.877301i | \(-0.340658\pi\) | ||||
0.479940 | + | 0.877301i | \(0.340658\pi\) | |||||||
\(662\) | −28.5941 | −1.11134 | ||||||||
\(663\) | 3.59570 | 0.139646 | ||||||||
\(664\) | −4.49374 | −0.174391 | ||||||||
\(665\) | 3.71078 | 0.143898 | ||||||||
\(666\) | 6.96050 | 0.269714 | ||||||||
\(667\) | 41.9864 | 1.62572 | ||||||||
\(668\) | 24.2697 | 0.939025 | ||||||||
\(669\) | −2.27388 | −0.0879133 | ||||||||
\(670\) | −23.7528 | −0.917651 | ||||||||
\(671\) | 13.3833 | 0.516657 | ||||||||
\(672\) | −1.19378 | −0.0460510 | ||||||||
\(673\) | −7.82552 | −0.301652 | −0.150826 | − | 0.988560i | \(-0.548193\pi\) | ||||
−0.150826 | + | 0.988560i | \(0.548193\pi\) | |||||||
\(674\) | 32.2295 | 1.24143 | ||||||||
\(675\) | −0.241736 | −0.00930443 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 20.1050 | 0.772699 | 0.386350 | − | 0.922352i | \(-0.373736\pi\) | ||||
0.386350 | + | 0.922352i | \(0.373736\pi\) | |||||||
\(678\) | 2.55170 | 0.0979974 | ||||||||
\(679\) | −8.77823 | −0.336878 | ||||||||
\(680\) | 8.23231 | 0.315695 | ||||||||
\(681\) | −24.4840 | −0.938229 | ||||||||
\(682\) | 5.38890 | 0.206352 | ||||||||
\(683\) | 4.60842 | 0.176336 | 0.0881681 | − | 0.996106i | \(-0.471899\pi\) | ||||
0.0881681 | + | 0.996106i | \(0.471899\pi\) | |||||||
\(684\) | −1.35770 | −0.0519130 | ||||||||
\(685\) | 1.76847 | 0.0675698 | ||||||||
\(686\) | −15.0116 | −0.573147 | ||||||||
\(687\) | −18.1528 | −0.692573 | ||||||||
\(688\) | 1.70506 | 0.0650050 | ||||||||
\(689\) | 2.84069 | 0.108222 | ||||||||
\(690\) | −14.7090 | −0.559962 | ||||||||
\(691\) | −2.68257 | −0.102050 | −0.0510249 | − | 0.998697i | \(-0.516249\pi\) | ||||
−0.0510249 | + | 0.998697i | \(0.516249\pi\) | |||||||
\(692\) | −9.74264 | −0.370360 | ||||||||
\(693\) | −5.10824 | −0.194046 | ||||||||
\(694\) | −22.3484 | −0.848335 | ||||||||
\(695\) | 32.7465 | 1.24215 | ||||||||
\(696\) | −6.53525 | −0.247718 | ||||||||
\(697\) | −26.4986 | −1.00371 | ||||||||
\(698\) | −9.93972 | −0.376224 | ||||||||
\(699\) | 12.6906 | 0.480004 | ||||||||
\(700\) | −0.288580 | −0.0109073 | ||||||||
\(701\) | −35.8678 | −1.35471 | −0.677354 | − | 0.735657i | \(-0.736873\pi\) | ||||
−0.677354 | + | 0.735657i | \(0.736873\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | 9.45027 | 0.356424 | ||||||||
\(704\) | 4.27905 | 0.161273 | ||||||||
\(705\) | −2.73988 | −0.103190 | ||||||||
\(706\) | 17.0214 | 0.640609 | ||||||||
\(707\) | −13.3070 | −0.500463 | ||||||||
\(708\) | −14.3018 | −0.537496 | ||||||||
\(709\) | 4.94712 | 0.185793 | 0.0928965 | − | 0.995676i | \(-0.470387\pi\) | ||||
0.0928965 | + | 0.995676i | \(0.470387\pi\) | |||||||
\(710\) | −2.75955 | −0.103564 | ||||||||
\(711\) | −2.00621 | −0.0752386 | ||||||||
\(712\) | −5.55082 | −0.208026 | ||||||||
\(713\) | 8.09093 | 0.303008 | ||||||||
\(714\) | 4.29248 | 0.160642 | ||||||||
\(715\) | 9.79682 | 0.366380 | ||||||||
\(716\) | 5.63260 | 0.210500 | ||||||||
\(717\) | −17.9914 | −0.671900 | ||||||||
\(718\) | −0.00561075 | −0.000209391 0 | ||||||||
\(719\) | 11.8733 | 0.442800 | 0.221400 | − | 0.975183i | \(-0.428937\pi\) | ||||
0.221400 | + | 0.975183i | \(0.428937\pi\) | |||||||
\(720\) | 2.28948 | 0.0853240 | ||||||||
\(721\) | 1.19378 | 0.0444586 | ||||||||
\(722\) | 17.1566 | 0.638504 | ||||||||
\(723\) | −3.62121 | −0.134674 | ||||||||
\(724\) | −6.35214 | −0.236075 | ||||||||
\(725\) | −1.57981 | −0.0586726 | ||||||||
\(726\) | 7.31027 | 0.271310 | ||||||||
\(727\) | 30.5078 | 1.13147 | 0.565736 | − | 0.824587i | \(-0.308592\pi\) | ||||
0.565736 | + | 0.824587i | \(0.308592\pi\) | |||||||
\(728\) | 1.19378 | 0.0442444 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −23.1966 | −0.858545 | ||||||||
\(731\) | −6.13091 | −0.226760 | ||||||||
\(732\) | −3.12763 | −0.115601 | ||||||||
\(733\) | −4.82880 | −0.178356 | −0.0891779 | − | 0.996016i | \(-0.528424\pi\) | ||||
−0.0891779 | + | 0.996016i | \(0.528424\pi\) | |||||||
\(734\) | 4.96085 | 0.183108 | ||||||||
\(735\) | 12.7636 | 0.470793 | ||||||||
\(736\) | 6.42459 | 0.236814 | ||||||||
\(737\) | 44.3940 | 1.63528 | ||||||||
\(738\) | −7.36952 | −0.271276 | ||||||||
\(739\) | −3.09730 | −0.113936 | −0.0569681 | − | 0.998376i | \(-0.518143\pi\) | ||||
−0.0569681 | + | 0.998376i | \(0.518143\pi\) | |||||||
\(740\) | −15.9359 | −0.585817 | ||||||||
\(741\) | 1.35770 | 0.0498764 | ||||||||
\(742\) | 3.39116 | 0.124493 | ||||||||
\(743\) | 16.3166 | 0.598597 | 0.299299 | − | 0.954159i | \(-0.403247\pi\) | ||||
0.299299 | + | 0.954159i | \(0.403247\pi\) | |||||||
\(744\) | −1.25937 | −0.0461707 | ||||||||
\(745\) | 39.7059 | 1.45471 | ||||||||
\(746\) | −11.5261 | −0.422002 | ||||||||
\(747\) | 4.49374 | 0.164417 | ||||||||
\(748\) | −15.3862 | −0.562575 | ||||||||
\(749\) | 5.71218 | 0.208719 | ||||||||
\(750\) | −10.8940 | −0.397791 | ||||||||
\(751\) | 39.3121 | 1.43452 | 0.717259 | − | 0.696807i | \(-0.245396\pi\) | ||||
0.717259 | + | 0.696807i | \(0.245396\pi\) | |||||||
\(752\) | 1.19672 | 0.0436400 | ||||||||
\(753\) | −9.61212 | −0.350285 | ||||||||
\(754\) | 6.53525 | 0.238000 | ||||||||
\(755\) | 33.6890 | 1.22607 | ||||||||
\(756\) | 1.19378 | 0.0434173 | ||||||||
\(757\) | −41.8503 | −1.52107 | −0.760537 | − | 0.649294i | \(-0.775064\pi\) | ||||
−0.760537 | + | 0.649294i | \(0.775064\pi\) | |||||||
\(758\) | −19.0110 | −0.690512 | ||||||||
\(759\) | 27.4912 | 0.997866 | ||||||||
\(760\) | 3.10843 | 0.112755 | ||||||||
\(761\) | −34.0486 | −1.23426 | −0.617131 | − | 0.786861i | \(-0.711705\pi\) | ||||
−0.617131 | + | 0.786861i | \(0.711705\pi\) | |||||||
\(762\) | −3.49577 | −0.126639 | ||||||||
\(763\) | −3.49348 | −0.126472 | ||||||||
\(764\) | 0.0280475 | 0.00101472 | ||||||||
\(765\) | −8.23231 | −0.297640 | ||||||||
\(766\) | −8.99836 | −0.325124 | ||||||||
\(767\) | 14.3018 | 0.516410 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 10.7045 | 0.386014 | 0.193007 | − | 0.981197i | \(-0.438176\pi\) | ||||
0.193007 | + | 0.981197i | \(0.438176\pi\) | |||||||
\(770\) | 11.6952 | 0.421467 | ||||||||
\(771\) | 4.38700 | 0.157994 | ||||||||
\(772\) | −16.8861 | −0.607743 | ||||||||
\(773\) | 23.6267 | 0.849793 | 0.424896 | − | 0.905242i | \(-0.360311\pi\) | ||||
0.424896 | + | 0.905242i | \(0.360311\pi\) | |||||||
\(774\) | −1.70506 | −0.0612873 | ||||||||
\(775\) | −0.304435 | −0.0109356 | ||||||||
\(776\) | −7.35332 | −0.263969 | ||||||||
\(777\) | −8.30929 | −0.298094 | ||||||||
\(778\) | −34.9429 | −1.25276 | ||||||||
\(779\) | −10.0056 | −0.358488 | ||||||||
\(780\) | −2.28948 | −0.0819767 | ||||||||
\(781\) | 5.15760 | 0.184553 | ||||||||
\(782\) | −23.1009 | −0.826088 | ||||||||
\(783\) | 6.53525 | 0.233551 | ||||||||
\(784\) | −5.57489 | −0.199103 | ||||||||
\(785\) | 50.5279 | 1.80342 | ||||||||
\(786\) | −18.1097 | −0.645953 | ||||||||
\(787\) | 19.1971 | 0.684304 | 0.342152 | − | 0.939645i | \(-0.388844\pi\) | ||||
0.342152 | + | 0.939645i | \(0.388844\pi\) | |||||||
\(788\) | 11.9854 | 0.426964 | ||||||||
\(789\) | 28.0116 | 0.997240 | ||||||||
\(790\) | 4.59318 | 0.163418 | ||||||||
\(791\) | −3.04616 | −0.108309 | ||||||||
\(792\) | −4.27905 | −0.152049 | ||||||||
\(793\) | 3.12763 | 0.111066 | ||||||||
\(794\) | −7.48202 | −0.265527 | ||||||||
\(795\) | −6.50372 | −0.230663 | ||||||||
\(796\) | 16.7843 | 0.594902 | ||||||||
\(797\) | −42.4158 | −1.50245 | −0.751223 | − | 0.660049i | \(-0.770536\pi\) | ||||
−0.751223 | + | 0.660049i | \(0.770536\pi\) | |||||||
\(798\) | 1.62079 | 0.0573755 | ||||||||
\(799\) | −4.30306 | −0.152231 | ||||||||
\(800\) | −0.241736 | −0.00854667 | ||||||||
\(801\) | 5.55082 | 0.196129 | ||||||||
\(802\) | 13.7786 | 0.486540 | ||||||||
\(803\) | 43.3545 | 1.52995 | ||||||||
\(804\) | −10.3747 | −0.365889 | ||||||||
\(805\) | 17.5593 | 0.618884 | ||||||||
\(806\) | 1.25937 | 0.0443594 | ||||||||
\(807\) | 7.77286 | 0.273618 | ||||||||
\(808\) | −11.1470 | −0.392150 | ||||||||
\(809\) | −5.02509 | −0.176673 | −0.0883363 | − | 0.996091i | \(-0.528155\pi\) | ||||
−0.0883363 | + | 0.996091i | \(0.528155\pi\) | |||||||
\(810\) | −2.28948 | −0.0804443 | ||||||||
\(811\) | 22.9949 | 0.807462 | 0.403731 | − | 0.914878i | \(-0.367713\pi\) | ||||
0.403731 | + | 0.914878i | \(0.367713\pi\) | |||||||
\(812\) | 7.80165 | 0.273784 | ||||||||
\(813\) | −11.6289 | −0.407844 | ||||||||
\(814\) | 29.7843 | 1.04394 | ||||||||
\(815\) | −12.3904 | −0.434018 | ||||||||
\(816\) | 3.59570 | 0.125875 | ||||||||
\(817\) | −2.31497 | −0.0809905 | ||||||||
\(818\) | −18.5833 | −0.649750 | ||||||||
\(819\) | −1.19378 | −0.0417140 | ||||||||
\(820\) | 16.8724 | 0.589210 | ||||||||
\(821\) | 21.0749 | 0.735519 | 0.367760 | − | 0.929921i | \(-0.380125\pi\) | ||||
0.367760 | + | 0.929921i | \(0.380125\pi\) | |||||||
\(822\) | 0.772432 | 0.0269417 | ||||||||
\(823\) | −42.8530 | −1.49376 | −0.746881 | − | 0.664958i | \(-0.768449\pi\) | ||||
−0.746881 | + | 0.664958i | \(0.768449\pi\) | |||||||
\(824\) | 1.00000 | 0.0348367 | ||||||||
\(825\) | −1.03440 | −0.0360132 | ||||||||
\(826\) | 17.0732 | 0.594054 | ||||||||
\(827\) | 35.1982 | 1.22396 | 0.611980 | − | 0.790873i | \(-0.290373\pi\) | ||||
0.611980 | + | 0.790873i | \(0.290373\pi\) | |||||||
\(828\) | −6.42459 | −0.223270 | ||||||||
\(829\) | −16.5382 | −0.574395 | −0.287197 | − | 0.957871i | \(-0.592724\pi\) | ||||
−0.287197 | + | 0.957871i | \(0.592724\pi\) | |||||||
\(830\) | −10.2883 | −0.357113 | ||||||||
\(831\) | −15.6095 | −0.541487 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 20.0457 | 0.694541 | ||||||||
\(834\) | 14.3030 | 0.495273 | ||||||||
\(835\) | 55.5652 | 1.92291 | ||||||||
\(836\) | −5.80967 | −0.200932 | ||||||||
\(837\) | 1.25937 | 0.0435302 | ||||||||
\(838\) | 16.9895 | 0.586892 | ||||||||
\(839\) | 1.93922 | 0.0669493 | 0.0334747 | − | 0.999440i | \(-0.489343\pi\) | ||||
0.0334747 | + | 0.999440i | \(0.489343\pi\) | |||||||
\(840\) | −2.73314 | −0.0943022 | ||||||||
\(841\) | 13.7095 | 0.472743 | ||||||||
\(842\) | −26.6550 | −0.918591 | ||||||||
\(843\) | 14.6040 | 0.502987 | ||||||||
\(844\) | −5.85650 | −0.201589 | ||||||||
\(845\) | 2.28948 | 0.0787606 | ||||||||
\(846\) | −1.19672 | −0.0411442 | ||||||||
\(847\) | −8.72685 | −0.299858 | ||||||||
\(848\) | 2.84069 | 0.0975498 | ||||||||
\(849\) | −14.0678 | −0.482806 | ||||||||
\(850\) | 0.869212 | 0.0298137 | ||||||||
\(851\) | 44.7184 | 1.53293 | ||||||||
\(852\) | −1.20531 | −0.0412934 | ||||||||
\(853\) | −18.4017 | −0.630064 | −0.315032 | − | 0.949081i | \(-0.602015\pi\) | ||||
−0.315032 | + | 0.949081i | \(0.602015\pi\) | |||||||
\(854\) | 3.73370 | 0.127765 | ||||||||
\(855\) | −3.10843 | −0.106306 | ||||||||
\(856\) | 4.78496 | 0.163547 | ||||||||
\(857\) | 22.7555 | 0.777314 | 0.388657 | − | 0.921383i | \(-0.372939\pi\) | ||||
0.388657 | + | 0.921383i | \(0.372939\pi\) | |||||||
\(858\) | 4.27905 | 0.146084 | ||||||||
\(859\) | −35.4905 | −1.21092 | −0.605461 | − | 0.795875i | \(-0.707011\pi\) | ||||
−0.605461 | + | 0.795875i | \(0.707011\pi\) | |||||||
\(860\) | 3.90372 | 0.133116 | ||||||||
\(861\) | 8.79758 | 0.299821 | ||||||||
\(862\) | 31.1412 | 1.06068 | ||||||||
\(863\) | 16.4055 | 0.558449 | 0.279224 | − | 0.960226i | \(-0.409923\pi\) | ||||
0.279224 | + | 0.960226i | \(0.409923\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −22.3056 | −0.758414 | ||||||||
\(866\) | 4.81223 | 0.163526 | ||||||||
\(867\) | 4.07091 | 0.138255 | ||||||||
\(868\) | 1.50341 | 0.0510290 | ||||||||
\(869\) | −8.58466 | −0.291215 | ||||||||
\(870\) | −14.9624 | −0.507271 | ||||||||
\(871\) | 10.3747 | 0.351535 | ||||||||
\(872\) | −2.92640 | −0.0991005 | ||||||||
\(873\) | 7.35332 | 0.248872 | ||||||||
\(874\) | −8.72268 | −0.295049 | ||||||||
\(875\) | 13.0050 | 0.439649 | ||||||||
\(876\) | −10.1318 | −0.342322 | ||||||||
\(877\) | 4.73131 | 0.159765 | 0.0798825 | − | 0.996804i | \(-0.474545\pi\) | ||||
0.0798825 | + | 0.996804i | \(0.474545\pi\) | |||||||
\(878\) | −40.6140 | −1.37066 | ||||||||
\(879\) | 24.4565 | 0.824896 | ||||||||
\(880\) | 9.79682 | 0.330251 | ||||||||
\(881\) | −23.2448 | −0.783138 | −0.391569 | − | 0.920149i | \(-0.628067\pi\) | ||||
−0.391569 | + | 0.920149i | \(0.628067\pi\) | |||||||
\(882\) | 5.57489 | 0.187716 | ||||||||
\(883\) | −11.6759 | −0.392925 | −0.196462 | − | 0.980511i | \(-0.562945\pi\) | ||||
−0.196462 | + | 0.980511i | \(0.562945\pi\) | |||||||
\(884\) | −3.59570 | −0.120937 | ||||||||
\(885\) | −32.7438 | −1.10067 | ||||||||
\(886\) | 12.7887 | 0.429646 | ||||||||
\(887\) | −18.4731 | −0.620268 | −0.310134 | − | 0.950693i | \(-0.600374\pi\) | ||||
−0.310134 | + | 0.950693i | \(0.600374\pi\) | |||||||
\(888\) | −6.96050 | −0.233579 | ||||||||
\(889\) | 4.17318 | 0.139964 | ||||||||
\(890\) | −12.7085 | −0.425991 | ||||||||
\(891\) | 4.27905 | 0.143354 | ||||||||
\(892\) | 2.27388 | 0.0761351 | ||||||||
\(893\) | −1.62479 | −0.0543716 | ||||||||
\(894\) | 17.3427 | 0.580027 | ||||||||
\(895\) | 12.8957 | 0.431057 | ||||||||
\(896\) | 1.19378 | 0.0398813 | ||||||||
\(897\) | 6.42459 | 0.214511 | ||||||||
\(898\) | 41.2330 | 1.37596 | ||||||||
\(899\) | 8.23030 | 0.274496 | ||||||||
\(900\) | 0.241736 | 0.00805788 | ||||||||
\(901\) | −10.2143 | −0.340287 | ||||||||
\(902\) | −31.5346 | −1.04999 | ||||||||
\(903\) | 2.03547 | 0.0677362 | ||||||||
\(904\) | −2.55170 | −0.0848682 | ||||||||
\(905\) | −14.5431 | −0.483430 | ||||||||
\(906\) | 14.7147 | 0.488862 | ||||||||
\(907\) | 11.3470 | 0.376770 | 0.188385 | − | 0.982095i | \(-0.439675\pi\) | ||||
0.188385 | + | 0.982095i | \(0.439675\pi\) | |||||||
\(908\) | 24.4840 | 0.812530 | ||||||||
\(909\) | 11.1470 | 0.369723 | ||||||||
\(910\) | 2.73314 | 0.0906026 | ||||||||
\(911\) | 0.347605 | 0.0115167 | 0.00575834 | − | 0.999983i | \(-0.498167\pi\) | ||||
0.00575834 | + | 0.999983i | \(0.498167\pi\) | |||||||
\(912\) | 1.35770 | 0.0449580 | ||||||||
\(913\) | 19.2289 | 0.636385 | ||||||||
\(914\) | 13.7388 | 0.454440 | ||||||||
\(915\) | −7.16067 | −0.236724 | ||||||||
\(916\) | 18.1528 | 0.599786 | ||||||||
\(917\) | 21.6190 | 0.713923 | ||||||||
\(918\) | −3.59570 | −0.118676 | ||||||||
\(919\) | 56.7382 | 1.87162 | 0.935810 | − | 0.352505i | \(-0.114670\pi\) | ||||
0.935810 | + | 0.352505i | \(0.114670\pi\) | |||||||
\(920\) | 14.7090 | 0.484941 | ||||||||
\(921\) | 4.95540 | 0.163286 | ||||||||
\(922\) | 10.4692 | 0.344786 | ||||||||
\(923\) | 1.20531 | 0.0396734 | ||||||||
\(924\) | 5.10824 | 0.168049 | ||||||||
\(925\) | −1.68260 | −0.0553237 | ||||||||
\(926\) | −19.0331 | −0.625468 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 6.53525 | 0.214530 | ||||||||
\(929\) | 29.7076 | 0.974675 | 0.487337 | − | 0.873214i | \(-0.337968\pi\) | ||||
0.487337 | + | 0.873214i | \(0.337968\pi\) | |||||||
\(930\) | −2.88331 | −0.0945473 | ||||||||
\(931\) | 7.56904 | 0.248065 | ||||||||
\(932\) | −12.6906 | −0.415696 | ||||||||
\(933\) | −0.541516 | −0.0177284 | ||||||||
\(934\) | 4.60131 | 0.150560 | ||||||||
\(935\) | −35.2265 | −1.15203 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | 0.370005 | 0.0120875 | 0.00604377 | − | 0.999982i | \(-0.498076\pi\) | ||||
0.00604377 | + | 0.999982i | \(0.498076\pi\) | |||||||
\(938\) | 12.3851 | 0.404389 | ||||||||
\(939\) | 21.4984 | 0.701573 | ||||||||
\(940\) | 2.73988 | 0.0893650 | ||||||||
\(941\) | −10.8330 | −0.353146 | −0.176573 | − | 0.984288i | \(-0.556501\pi\) | ||||
−0.176573 | + | 0.984288i | \(0.556501\pi\) | |||||||
\(942\) | 22.0695 | 0.719065 | ||||||||
\(943\) | −47.3462 | −1.54180 | ||||||||
\(944\) | 14.3018 | 0.465486 | ||||||||
\(945\) | 2.73314 | 0.0889090 | ||||||||
\(946\) | −7.29606 | −0.237215 | ||||||||
\(947\) | 6.65466 | 0.216247 | 0.108124 | − | 0.994137i | \(-0.465516\pi\) | ||||
0.108124 | + | 0.994137i | \(0.465516\pi\) | |||||||
\(948\) | 2.00621 | 0.0651585 | ||||||||
\(949\) | 10.1318 | 0.328893 | ||||||||
\(950\) | 0.328206 | 0.0106484 | ||||||||
\(951\) | −1.44767 | −0.0469440 | ||||||||
\(952\) | −4.29248 | −0.139120 | ||||||||
\(953\) | 24.0843 | 0.780168 | 0.390084 | − | 0.920779i | \(-0.372446\pi\) | ||||
0.390084 | + | 0.920779i | \(0.372446\pi\) | |||||||
\(954\) | −2.84069 | −0.0919708 | ||||||||
\(955\) | 0.0642142 | 0.00207792 | ||||||||
\(956\) | 17.9914 | 0.581883 | ||||||||
\(957\) | 27.9647 | 0.903970 | ||||||||
\(958\) | −8.25442 | −0.266688 | ||||||||
\(959\) | −0.922113 | −0.0297766 | ||||||||
\(960\) | −2.28948 | −0.0738928 | ||||||||
\(961\) | −29.4140 | −0.948838 | ||||||||
\(962\) | 6.96050 | 0.224415 | ||||||||
\(963\) | −4.78496 | −0.154193 | ||||||||
\(964\) | 3.62121 | 0.116631 | ||||||||
\(965\) | −38.6604 | −1.24452 | ||||||||
\(966\) | 7.66954 | 0.246764 | ||||||||
\(967\) | 41.6001 | 1.33777 | 0.668885 | − | 0.743366i | \(-0.266772\pi\) | ||||
0.668885 | + | 0.743366i | \(0.266772\pi\) | |||||||
\(968\) | −7.31027 | −0.234961 | ||||||||
\(969\) | −4.88189 | −0.156829 | ||||||||
\(970\) | −16.8353 | −0.540549 | ||||||||
\(971\) | 28.7867 | 0.923808 | 0.461904 | − | 0.886930i | \(-0.347166\pi\) | ||||
0.461904 | + | 0.886930i | \(0.347166\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −17.0746 | −0.547387 | ||||||||
\(974\) | −30.9469 | −0.991602 | ||||||||
\(975\) | −0.241736 | −0.00774176 | ||||||||
\(976\) | 3.12763 | 0.100113 | ||||||||
\(977\) | −17.8877 | −0.572277 | −0.286138 | − | 0.958188i | \(-0.592372\pi\) | ||||
−0.286138 | + | 0.958188i | \(0.592372\pi\) | |||||||
\(978\) | −5.41189 | −0.173053 | ||||||||
\(979\) | 23.7523 | 0.759125 | ||||||||
\(980\) | −12.7636 | −0.407719 | ||||||||
\(981\) | 2.92640 | 0.0934328 | ||||||||
\(982\) | −2.62104 | −0.0836407 | ||||||||
\(983\) | 7.03181 | 0.224280 | 0.112140 | − | 0.993692i | \(-0.464229\pi\) | ||||
0.112140 | + | 0.993692i | \(0.464229\pi\) | |||||||
\(984\) | 7.36952 | 0.234932 | ||||||||
\(985\) | 27.4405 | 0.874327 | ||||||||
\(986\) | −23.4988 | −0.748356 | ||||||||
\(987\) | 1.42862 | 0.0454736 | ||||||||
\(988\) | −1.35770 | −0.0431942 | ||||||||
\(989\) | −10.9543 | −0.348328 | ||||||||
\(990\) | −9.79682 | −0.311363 | ||||||||
\(991\) | 1.50489 | 0.0478044 | 0.0239022 | − | 0.999714i | \(-0.492391\pi\) | ||||
0.0239022 | + | 0.999714i | \(0.492391\pi\) | |||||||
\(992\) | 1.25937 | 0.0399850 | ||||||||
\(993\) | −28.5941 | −0.907405 | ||||||||
\(994\) | 1.43888 | 0.0456384 | ||||||||
\(995\) | 38.4273 | 1.21823 | ||||||||
\(996\) | −4.49374 | −0.142390 | ||||||||
\(997\) | 26.0217 | 0.824116 | 0.412058 | − | 0.911158i | \(-0.364810\pi\) | ||||
0.412058 | + | 0.911158i | \(0.364810\pi\) | |||||||
\(998\) | 10.9828 | 0.347654 | ||||||||
\(999\) | 6.96050 | 0.220220 |
(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.z.1.12 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.z.1.12 | ✓ | 14 | 1.1 | even | 1 | trivial |