Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4017,2,Mod(1,4017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4017, 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("4017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4017 = 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4017.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: | \(32.0759064919\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 4017.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.389331 | −0.275299 | −0.137649 | − | 0.990481i | \(-0.543955\pi\) | ||||
−0.137649 | + | 0.990481i | \(0.543955\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.84842 | −0.924211 | ||||||||
\(5\) | 0.642702 | 0.287425 | 0.143712 | − | 0.989619i | \(-0.454096\pi\) | ||||
0.143712 | + | 0.989619i | \(0.454096\pi\) | |||||||
\(6\) | 0.389331 | 0.158944 | ||||||||
\(7\) | −1.35418 | −0.511833 | −0.255917 | − | 0.966699i | \(-0.582377\pi\) | ||||
−0.255917 | + | 0.966699i | \(0.582377\pi\) | |||||||
\(8\) | 1.49831 | 0.529733 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.250224 | −0.0791278 | ||||||||
\(11\) | −3.00376 | −0.905669 | −0.452835 | − | 0.891595i | \(-0.649587\pi\) | ||||
−0.452835 | + | 0.891595i | \(0.649587\pi\) | |||||||
\(12\) | 1.84842 | 0.533593 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0.527226 | 0.140907 | ||||||||
\(15\) | −0.642702 | −0.165945 | ||||||||
\(16\) | 3.11350 | 0.778376 | ||||||||
\(17\) | 3.71693 | 0.901489 | 0.450745 | − | 0.892653i | \(-0.351159\pi\) | ||||
0.450745 | + | 0.892653i | \(0.351159\pi\) | |||||||
\(18\) | −0.389331 | −0.0917663 | ||||||||
\(19\) | −2.28396 | −0.523977 | −0.261989 | − | 0.965071i | \(-0.584378\pi\) | ||||
−0.261989 | + | 0.965071i | \(0.584378\pi\) | |||||||
\(20\) | −1.18798 | −0.265641 | ||||||||
\(21\) | 1.35418 | 0.295507 | ||||||||
\(22\) | 1.16946 | 0.249330 | ||||||||
\(23\) | 1.06872 | 0.222844 | 0.111422 | − | 0.993773i | \(-0.464459\pi\) | ||||
0.111422 | + | 0.993773i | \(0.464459\pi\) | |||||||
\(24\) | −1.49831 | −0.305841 | ||||||||
\(25\) | −4.58693 | −0.917387 | ||||||||
\(26\) | 0.389331 | 0.0763541 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.50310 | 0.473042 | ||||||||
\(29\) | −5.70126 | −1.05870 | −0.529349 | − | 0.848404i | \(-0.677564\pi\) | ||||
−0.529349 | + | 0.848404i | \(0.677564\pi\) | |||||||
\(30\) | 0.250224 | 0.0456844 | ||||||||
\(31\) | 7.17094 | 1.28794 | 0.643969 | − | 0.765051i | \(-0.277286\pi\) | ||||
0.643969 | + | 0.765051i | \(0.277286\pi\) | |||||||
\(32\) | −4.20881 | −0.744019 | ||||||||
\(33\) | 3.00376 | 0.522888 | ||||||||
\(34\) | −1.44712 | −0.248179 | ||||||||
\(35\) | −0.870336 | −0.147114 | ||||||||
\(36\) | −1.84842 | −0.308070 | ||||||||
\(37\) | −0.297591 | −0.0489236 | −0.0244618 | − | 0.999701i | \(-0.507787\pi\) | ||||
−0.0244618 | + | 0.999701i | \(0.507787\pi\) | |||||||
\(38\) | 0.889218 | 0.144250 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0.962967 | 0.152258 | ||||||||
\(41\) | 2.02015 | 0.315494 | 0.157747 | − | 0.987480i | \(-0.449577\pi\) | ||||
0.157747 | + | 0.987480i | \(0.449577\pi\) | |||||||
\(42\) | −0.527226 | −0.0813528 | ||||||||
\(43\) | −2.05274 | −0.313040 | −0.156520 | − | 0.987675i | \(-0.550028\pi\) | ||||
−0.156520 | + | 0.987675i | \(0.550028\pi\) | |||||||
\(44\) | 5.55222 | 0.837029 | ||||||||
\(45\) | 0.642702 | 0.0958083 | ||||||||
\(46\) | −0.416088 | −0.0613488 | ||||||||
\(47\) | −10.0660 | −1.46828 | −0.734140 | − | 0.678998i | \(-0.762415\pi\) | ||||
−0.734140 | + | 0.678998i | \(0.762415\pi\) | |||||||
\(48\) | −3.11350 | −0.449395 | ||||||||
\(49\) | −5.16619 | −0.738027 | ||||||||
\(50\) | 1.78584 | 0.252556 | ||||||||
\(51\) | −3.71693 | −0.520475 | ||||||||
\(52\) | 1.84842 | 0.256330 | ||||||||
\(53\) | −10.1464 | −1.39372 | −0.696859 | − | 0.717208i | \(-0.745420\pi\) | ||||
−0.696859 | + | 0.717208i | \(0.745420\pi\) | |||||||
\(54\) | 0.389331 | 0.0529813 | ||||||||
\(55\) | −1.93052 | −0.260312 | ||||||||
\(56\) | −2.02899 | −0.271135 | ||||||||
\(57\) | 2.28396 | 0.302518 | ||||||||
\(58\) | 2.21968 | 0.291458 | ||||||||
\(59\) | 9.99931 | 1.30180 | 0.650900 | − | 0.759164i | \(-0.274392\pi\) | ||||
0.650900 | + | 0.759164i | \(0.274392\pi\) | |||||||
\(60\) | 1.18798 | 0.153368 | ||||||||
\(61\) | 3.25912 | 0.417287 | 0.208643 | − | 0.977992i | \(-0.433095\pi\) | ||||
0.208643 | + | 0.977992i | \(0.433095\pi\) | |||||||
\(62\) | −2.79187 | −0.354568 | ||||||||
\(63\) | −1.35418 | −0.170611 | ||||||||
\(64\) | −4.58839 | −0.573548 | ||||||||
\(65\) | −0.642702 | −0.0797173 | ||||||||
\(66\) | −1.16946 | −0.143951 | ||||||||
\(67\) | 1.23432 | 0.150796 | 0.0753981 | − | 0.997154i | \(-0.475977\pi\) | ||||
0.0753981 | + | 0.997154i | \(0.475977\pi\) | |||||||
\(68\) | −6.87046 | −0.833166 | ||||||||
\(69\) | −1.06872 | −0.128659 | ||||||||
\(70\) | 0.338849 | 0.0405002 | ||||||||
\(71\) | −1.30716 | −0.155131 | −0.0775656 | − | 0.996987i | \(-0.524715\pi\) | ||||
−0.0775656 | + | 0.996987i | \(0.524715\pi\) | |||||||
\(72\) | 1.49831 | 0.176578 | ||||||||
\(73\) | 10.2716 | 1.20219 | 0.601097 | − | 0.799176i | \(-0.294730\pi\) | ||||
0.601097 | + | 0.799176i | \(0.294730\pi\) | |||||||
\(74\) | 0.115861 | 0.0134686 | ||||||||
\(75\) | 4.58693 | 0.529654 | ||||||||
\(76\) | 4.22173 | 0.484265 | ||||||||
\(77\) | 4.06765 | 0.463552 | ||||||||
\(78\) | −0.389331 | −0.0440831 | ||||||||
\(79\) | −1.65729 | −0.186460 | −0.0932299 | − | 0.995645i | \(-0.529719\pi\) | ||||
−0.0932299 | + | 0.995645i | \(0.529719\pi\) | |||||||
\(80\) | 2.00105 | 0.223725 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.786507 | −0.0868552 | ||||||||
\(83\) | 12.8074 | 1.40580 | 0.702900 | − | 0.711289i | \(-0.251888\pi\) | ||||
0.702900 | + | 0.711289i | \(0.251888\pi\) | |||||||
\(84\) | −2.50310 | −0.273111 | ||||||||
\(85\) | 2.38888 | 0.259110 | ||||||||
\(86\) | 0.799197 | 0.0861796 | ||||||||
\(87\) | 5.70126 | 0.611239 | ||||||||
\(88\) | −4.50057 | −0.479763 | ||||||||
\(89\) | −11.2589 | −1.19344 | −0.596720 | − | 0.802450i | \(-0.703529\pi\) | ||||
−0.596720 | + | 0.802450i | \(0.703529\pi\) | |||||||
\(90\) | −0.250224 | −0.0263759 | ||||||||
\(91\) | 1.35418 | 0.141957 | ||||||||
\(92\) | −1.97545 | −0.205955 | ||||||||
\(93\) | −7.17094 | −0.743592 | ||||||||
\(94\) | 3.91902 | 0.404216 | ||||||||
\(95\) | −1.46791 | −0.150604 | ||||||||
\(96\) | 4.20881 | 0.429559 | ||||||||
\(97\) | −4.32334 | −0.438969 | −0.219484 | − | 0.975616i | \(-0.570437\pi\) | ||||
−0.219484 | + | 0.975616i | \(0.570437\pi\) | |||||||
\(98\) | 2.01136 | 0.203178 | ||||||||
\(99\) | −3.00376 | −0.301890 | ||||||||
\(100\) | 8.47859 | 0.847859 | ||||||||
\(101\) | −8.69672 | −0.865356 | −0.432678 | − | 0.901549i | \(-0.642431\pi\) | ||||
−0.432678 | + | 0.901549i | \(0.642431\pi\) | |||||||
\(102\) | 1.44712 | 0.143286 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | −1.49831 | −0.146921 | ||||||||
\(105\) | 0.870336 | 0.0849361 | ||||||||
\(106\) | 3.95032 | 0.383689 | ||||||||
\(107\) | −0.866480 | −0.0837658 | −0.0418829 | − | 0.999123i | \(-0.513336\pi\) | ||||
−0.0418829 | + | 0.999123i | \(0.513336\pi\) | |||||||
\(108\) | 1.84842 | 0.177864 | ||||||||
\(109\) | −10.7007 | −1.02495 | −0.512473 | − | 0.858704i | \(-0.671270\pi\) | ||||
−0.512473 | + | 0.858704i | \(0.671270\pi\) | |||||||
\(110\) | 0.751614 | 0.0716636 | ||||||||
\(111\) | 0.297591 | 0.0282461 | ||||||||
\(112\) | −4.21626 | −0.398399 | ||||||||
\(113\) | 8.80892 | 0.828674 | 0.414337 | − | 0.910124i | \(-0.364014\pi\) | ||||
0.414337 | + | 0.910124i | \(0.364014\pi\) | |||||||
\(114\) | −0.889218 | −0.0832829 | ||||||||
\(115\) | 0.686871 | 0.0640510 | ||||||||
\(116\) | 10.5383 | 0.978459 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −3.89304 | −0.358384 | ||||||||
\(119\) | −5.03341 | −0.461412 | ||||||||
\(120\) | −0.962967 | −0.0879065 | ||||||||
\(121\) | −1.97740 | −0.179764 | ||||||||
\(122\) | −1.26888 | −0.114879 | ||||||||
\(123\) | −2.02015 | −0.182151 | ||||||||
\(124\) | −13.2549 | −1.19033 | ||||||||
\(125\) | −6.16154 | −0.551105 | ||||||||
\(126\) | 0.527226 | 0.0469690 | ||||||||
\(127\) | 15.7150 | 1.39449 | 0.697243 | − | 0.716835i | \(-0.254410\pi\) | ||||
0.697243 | + | 0.716835i | \(0.254410\pi\) | |||||||
\(128\) | 10.2040 | 0.901916 | ||||||||
\(129\) | 2.05274 | 0.180734 | ||||||||
\(130\) | 0.250224 | 0.0219461 | ||||||||
\(131\) | 11.2112 | 0.979523 | 0.489762 | − | 0.871856i | \(-0.337084\pi\) | ||||
0.489762 | + | 0.871856i | \(0.337084\pi\) | |||||||
\(132\) | −5.55222 | −0.483259 | ||||||||
\(133\) | 3.09291 | 0.268189 | ||||||||
\(134\) | −0.480560 | −0.0415140 | ||||||||
\(135\) | −0.642702 | −0.0553150 | ||||||||
\(136\) | 5.56912 | 0.477548 | ||||||||
\(137\) | −13.9300 | −1.19012 | −0.595058 | − | 0.803682i | \(-0.702871\pi\) | ||||
−0.595058 | + | 0.803682i | \(0.702871\pi\) | |||||||
\(138\) | 0.416088 | 0.0354197 | ||||||||
\(139\) | 4.30921 | 0.365502 | 0.182751 | − | 0.983159i | \(-0.441500\pi\) | ||||
0.182751 | + | 0.983159i | \(0.441500\pi\) | |||||||
\(140\) | 1.60875 | 0.135964 | ||||||||
\(141\) | 10.0660 | 0.847712 | ||||||||
\(142\) | 0.508918 | 0.0427074 | ||||||||
\(143\) | 3.00376 | 0.251187 | ||||||||
\(144\) | 3.11350 | 0.259459 | ||||||||
\(145\) | −3.66421 | −0.304296 | ||||||||
\(146\) | −3.99904 | −0.330963 | ||||||||
\(147\) | 5.16619 | 0.426100 | ||||||||
\(148\) | 0.550073 | 0.0452157 | ||||||||
\(149\) | 20.3044 | 1.66340 | 0.831699 | − | 0.555227i | \(-0.187369\pi\) | ||||
0.831699 | + | 0.555227i | \(0.187369\pi\) | |||||||
\(150\) | −1.78584 | −0.145813 | ||||||||
\(151\) | 14.1623 | 1.15251 | 0.576254 | − | 0.817270i | \(-0.304514\pi\) | ||||
0.576254 | + | 0.817270i | \(0.304514\pi\) | |||||||
\(152\) | −3.42209 | −0.277568 | ||||||||
\(153\) | 3.71693 | 0.300496 | ||||||||
\(154\) | −1.58366 | −0.127615 | ||||||||
\(155\) | 4.60877 | 0.370186 | ||||||||
\(156\) | −1.84842 | −0.147992 | ||||||||
\(157\) | 19.3082 | 1.54096 | 0.770481 | − | 0.637462i | \(-0.220016\pi\) | ||||
0.770481 | + | 0.637462i | \(0.220016\pi\) | |||||||
\(158\) | 0.645235 | 0.0513322 | ||||||||
\(159\) | 10.1464 | 0.804664 | ||||||||
\(160\) | −2.70501 | −0.213850 | ||||||||
\(161\) | −1.44725 | −0.114059 | ||||||||
\(162\) | −0.389331 | −0.0305888 | ||||||||
\(163\) | −6.41726 | −0.502638 | −0.251319 | − | 0.967904i | \(-0.580864\pi\) | ||||
−0.251319 | + | 0.967904i | \(0.580864\pi\) | |||||||
\(164\) | −3.73409 | −0.291583 | ||||||||
\(165\) | 1.93052 | 0.150291 | ||||||||
\(166\) | −4.98634 | −0.387015 | ||||||||
\(167\) | −0.717268 | −0.0555039 | −0.0277519 | − | 0.999615i | \(-0.508835\pi\) | ||||
−0.0277519 | + | 0.999615i | \(0.508835\pi\) | |||||||
\(168\) | 2.02899 | 0.156540 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −0.930066 | −0.0713328 | ||||||||
\(171\) | −2.28396 | −0.174659 | ||||||||
\(172\) | 3.79433 | 0.289315 | ||||||||
\(173\) | 19.2602 | 1.46433 | 0.732164 | − | 0.681129i | \(-0.238511\pi\) | ||||
0.732164 | + | 0.681129i | \(0.238511\pi\) | |||||||
\(174\) | −2.21968 | −0.168273 | ||||||||
\(175\) | 6.21155 | 0.469549 | ||||||||
\(176\) | −9.35223 | −0.704951 | ||||||||
\(177\) | −9.99931 | −0.751594 | ||||||||
\(178\) | 4.38343 | 0.328552 | ||||||||
\(179\) | 4.43432 | 0.331436 | 0.165718 | − | 0.986173i | \(-0.447006\pi\) | ||||
0.165718 | + | 0.986173i | \(0.447006\pi\) | |||||||
\(180\) | −1.18798 | −0.0885471 | ||||||||
\(181\) | −9.60571 | −0.713987 | −0.356993 | − | 0.934107i | \(-0.616198\pi\) | ||||
−0.356993 | + | 0.934107i | \(0.616198\pi\) | |||||||
\(182\) | −0.527226 | −0.0390806 | ||||||||
\(183\) | −3.25912 | −0.240921 | ||||||||
\(184\) | 1.60128 | 0.118048 | ||||||||
\(185\) | −0.191262 | −0.0140619 | ||||||||
\(186\) | 2.79187 | 0.204710 | ||||||||
\(187\) | −11.1648 | −0.816451 | ||||||||
\(188\) | 18.6063 | 1.35700 | ||||||||
\(189\) | 1.35418 | 0.0985024 | ||||||||
\(190\) | 0.571502 | 0.0414611 | ||||||||
\(191\) | −0.0595551 | −0.00430925 | −0.00215463 | − | 0.999998i | \(-0.500686\pi\) | ||||
−0.00215463 | + | 0.999998i | \(0.500686\pi\) | |||||||
\(192\) | 4.58839 | 0.331138 | ||||||||
\(193\) | −18.3402 | −1.32016 | −0.660079 | − | 0.751196i | \(-0.729477\pi\) | ||||
−0.660079 | + | 0.751196i | \(0.729477\pi\) | |||||||
\(194\) | 1.68321 | 0.120848 | ||||||||
\(195\) | 0.642702 | 0.0460248 | ||||||||
\(196\) | 9.54929 | 0.682092 | ||||||||
\(197\) | −2.20431 | −0.157051 | −0.0785253 | − | 0.996912i | \(-0.525021\pi\) | ||||
−0.0785253 | + | 0.996912i | \(0.525021\pi\) | |||||||
\(198\) | 1.16946 | 0.0831099 | ||||||||
\(199\) | 23.4036 | 1.65904 | 0.829519 | − | 0.558478i | \(-0.188615\pi\) | ||||
0.829519 | + | 0.558478i | \(0.188615\pi\) | |||||||
\(200\) | −6.87265 | −0.485970 | ||||||||
\(201\) | −1.23432 | −0.0870623 | ||||||||
\(202\) | 3.38591 | 0.238231 | ||||||||
\(203\) | 7.72055 | 0.541877 | ||||||||
\(204\) | 6.87046 | 0.481028 | ||||||||
\(205\) | 1.29835 | 0.0906810 | ||||||||
\(206\) | −0.389331 | −0.0271260 | ||||||||
\(207\) | 1.06872 | 0.0742814 | ||||||||
\(208\) | −3.11350 | −0.215883 | ||||||||
\(209\) | 6.86049 | 0.474550 | ||||||||
\(210\) | −0.338849 | −0.0233828 | ||||||||
\(211\) | −8.24603 | −0.567680 | −0.283840 | − | 0.958872i | \(-0.591608\pi\) | ||||
−0.283840 | + | 0.958872i | \(0.591608\pi\) | |||||||
\(212\) | 18.7549 | 1.28809 | ||||||||
\(213\) | 1.30716 | 0.0895650 | ||||||||
\(214\) | 0.337348 | 0.0230606 | ||||||||
\(215\) | −1.31930 | −0.0899756 | ||||||||
\(216\) | −1.49831 | −0.101947 | ||||||||
\(217\) | −9.71077 | −0.659210 | ||||||||
\(218\) | 4.16613 | 0.282166 | ||||||||
\(219\) | −10.2716 | −0.694087 | ||||||||
\(220\) | 3.56842 | 0.240583 | ||||||||
\(221\) | −3.71693 | −0.250028 | ||||||||
\(222\) | −0.115861 | −0.00777611 | ||||||||
\(223\) | 0.526175 | 0.0352353 | 0.0176177 | − | 0.999845i | \(-0.494392\pi\) | ||||
0.0176177 | + | 0.999845i | \(0.494392\pi\) | |||||||
\(224\) | 5.69950 | 0.380814 | ||||||||
\(225\) | −4.58693 | −0.305796 | ||||||||
\(226\) | −3.42959 | −0.228133 | ||||||||
\(227\) | 11.1873 | 0.742526 | 0.371263 | − | 0.928528i | \(-0.378925\pi\) | ||||
0.371263 | + | 0.928528i | \(0.378925\pi\) | |||||||
\(228\) | −4.22173 | −0.279591 | ||||||||
\(229\) | −11.9515 | −0.789780 | −0.394890 | − | 0.918728i | \(-0.629217\pi\) | ||||
−0.394890 | + | 0.918728i | \(0.629217\pi\) | |||||||
\(230\) | −0.267420 | −0.0176332 | ||||||||
\(231\) | −4.06765 | −0.267632 | ||||||||
\(232\) | −8.54226 | −0.560827 | ||||||||
\(233\) | −12.4646 | −0.816582 | −0.408291 | − | 0.912852i | \(-0.633875\pi\) | ||||
−0.408291 | + | 0.912852i | \(0.633875\pi\) | |||||||
\(234\) | 0.389331 | 0.0254514 | ||||||||
\(235\) | −6.46945 | −0.422021 | ||||||||
\(236\) | −18.4829 | −1.20314 | ||||||||
\(237\) | 1.65729 | 0.107653 | ||||||||
\(238\) | 1.95967 | 0.127026 | ||||||||
\(239\) | 14.8738 | 0.962109 | 0.481054 | − | 0.876691i | \(-0.340254\pi\) | ||||
0.481054 | + | 0.876691i | \(0.340254\pi\) | |||||||
\(240\) | −2.00105 | −0.129167 | ||||||||
\(241\) | 21.4433 | 1.38128 | 0.690641 | − | 0.723198i | \(-0.257329\pi\) | ||||
0.690641 | + | 0.723198i | \(0.257329\pi\) | |||||||
\(242\) | 0.769863 | 0.0494887 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −6.02422 | −0.385661 | ||||||||
\(245\) | −3.32032 | −0.212127 | ||||||||
\(246\) | 0.786507 | 0.0501459 | ||||||||
\(247\) | 2.28396 | 0.145325 | ||||||||
\(248\) | 10.7443 | 0.682263 | ||||||||
\(249\) | −12.8074 | −0.811639 | ||||||||
\(250\) | 2.39888 | 0.151719 | ||||||||
\(251\) | 19.2691 | 1.21625 | 0.608126 | − | 0.793840i | \(-0.291921\pi\) | ||||
0.608126 | + | 0.793840i | \(0.291921\pi\) | |||||||
\(252\) | 2.50310 | 0.157681 | ||||||||
\(253\) | −3.21019 | −0.201823 | ||||||||
\(254\) | −6.11836 | −0.383900 | ||||||||
\(255\) | −2.38888 | −0.149598 | ||||||||
\(256\) | 5.20403 | 0.325252 | ||||||||
\(257\) | 10.4324 | 0.650758 | 0.325379 | − | 0.945584i | \(-0.394508\pi\) | ||||
0.325379 | + | 0.945584i | \(0.394508\pi\) | |||||||
\(258\) | −0.799197 | −0.0497558 | ||||||||
\(259\) | 0.402993 | 0.0250408 | ||||||||
\(260\) | 1.18798 | 0.0736756 | ||||||||
\(261\) | −5.70126 | −0.352899 | ||||||||
\(262\) | −4.36485 | −0.269662 | ||||||||
\(263\) | −1.46328 | −0.0902294 | −0.0451147 | − | 0.998982i | \(-0.514365\pi\) | ||||
−0.0451147 | + | 0.998982i | \(0.514365\pi\) | |||||||
\(264\) | 4.50057 | 0.276991 | ||||||||
\(265\) | −6.52112 | −0.400589 | ||||||||
\(266\) | −1.20417 | −0.0738321 | ||||||||
\(267\) | 11.2589 | 0.689032 | ||||||||
\(268\) | −2.28154 | −0.139367 | ||||||||
\(269\) | −3.88191 | −0.236684 | −0.118342 | − | 0.992973i | \(-0.537758\pi\) | ||||
−0.118342 | + | 0.992973i | \(0.537758\pi\) | |||||||
\(270\) | 0.250224 | 0.0152281 | ||||||||
\(271\) | 29.7812 | 1.80908 | 0.904541 | − | 0.426387i | \(-0.140214\pi\) | ||||
0.904541 | + | 0.426387i | \(0.140214\pi\) | |||||||
\(272\) | 11.5727 | 0.701697 | ||||||||
\(273\) | −1.35418 | −0.0819589 | ||||||||
\(274\) | 5.42337 | 0.327638 | ||||||||
\(275\) | 13.7781 | 0.830849 | ||||||||
\(276\) | 1.97545 | 0.118908 | ||||||||
\(277\) | 6.18027 | 0.371336 | 0.185668 | − | 0.982613i | \(-0.440555\pi\) | ||||
0.185668 | + | 0.982613i | \(0.440555\pi\) | |||||||
\(278\) | −1.67771 | −0.100622 | ||||||||
\(279\) | 7.17094 | 0.429313 | ||||||||
\(280\) | −1.30403 | −0.0779310 | ||||||||
\(281\) | 16.3655 | 0.976286 | 0.488143 | − | 0.872764i | \(-0.337674\pi\) | ||||
0.488143 | + | 0.872764i | \(0.337674\pi\) | |||||||
\(282\) | −3.91902 | −0.233374 | ||||||||
\(283\) | 1.26540 | 0.0752200 | 0.0376100 | − | 0.999292i | \(-0.488026\pi\) | ||||
0.0376100 | + | 0.999292i | \(0.488026\pi\) | |||||||
\(284\) | 2.41618 | 0.143374 | ||||||||
\(285\) | 1.46791 | 0.0869513 | ||||||||
\(286\) | −1.16946 | −0.0691516 | ||||||||
\(287\) | −2.73565 | −0.161481 | ||||||||
\(288\) | −4.20881 | −0.248006 | ||||||||
\(289\) | −3.18440 | −0.187317 | ||||||||
\(290\) | 1.42659 | 0.0837723 | ||||||||
\(291\) | 4.32334 | 0.253439 | ||||||||
\(292\) | −18.9862 | −1.11108 | ||||||||
\(293\) | 22.0012 | 1.28532 | 0.642662 | − | 0.766150i | \(-0.277830\pi\) | ||||
0.642662 | + | 0.766150i | \(0.277830\pi\) | |||||||
\(294\) | −2.01136 | −0.117305 | ||||||||
\(295\) | 6.42657 | 0.374170 | ||||||||
\(296\) | −0.445884 | −0.0259165 | ||||||||
\(297\) | 3.00376 | 0.174296 | ||||||||
\(298\) | −7.90512 | −0.457931 | ||||||||
\(299\) | −1.06872 | −0.0618059 | ||||||||
\(300\) | −8.47859 | −0.489511 | ||||||||
\(301\) | 2.77979 | 0.160224 | ||||||||
\(302\) | −5.51381 | −0.317284 | ||||||||
\(303\) | 8.69672 | 0.499613 | ||||||||
\(304\) | −7.11113 | −0.407851 | ||||||||
\(305\) | 2.09464 | 0.119939 | ||||||||
\(306\) | −1.44712 | −0.0827263 | ||||||||
\(307\) | −6.06291 | −0.346029 | −0.173014 | − | 0.984919i | \(-0.555351\pi\) | ||||
−0.173014 | + | 0.984919i | \(0.555351\pi\) | |||||||
\(308\) | −7.51873 | −0.428419 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | −1.79434 | −0.101912 | ||||||||
\(311\) | 21.4358 | 1.21551 | 0.607756 | − | 0.794123i | \(-0.292070\pi\) | ||||
0.607756 | + | 0.794123i | \(0.292070\pi\) | |||||||
\(312\) | 1.49831 | 0.0848251 | ||||||||
\(313\) | 22.0335 | 1.24541 | 0.622705 | − | 0.782457i | \(-0.286034\pi\) | ||||
0.622705 | + | 0.782457i | \(0.286034\pi\) | |||||||
\(314\) | −7.51729 | −0.424225 | ||||||||
\(315\) | −0.870336 | −0.0490379 | ||||||||
\(316\) | 3.06337 | 0.172328 | ||||||||
\(317\) | 5.82156 | 0.326971 | 0.163486 | − | 0.986546i | \(-0.447726\pi\) | ||||
0.163486 | + | 0.986546i | \(0.447726\pi\) | |||||||
\(318\) | −3.95032 | −0.221523 | ||||||||
\(319\) | 17.1252 | 0.958829 | ||||||||
\(320\) | −2.94896 | −0.164852 | ||||||||
\(321\) | 0.866480 | 0.0483622 | ||||||||
\(322\) | 0.563459 | 0.0314004 | ||||||||
\(323\) | −8.48934 | −0.472360 | ||||||||
\(324\) | −1.84842 | −0.102690 | ||||||||
\(325\) | 4.58693 | 0.254437 | ||||||||
\(326\) | 2.49844 | 0.138376 | ||||||||
\(327\) | 10.7007 | 0.591752 | ||||||||
\(328\) | 3.02681 | 0.167128 | ||||||||
\(329\) | 13.6313 | 0.751515 | ||||||||
\(330\) | −0.751614 | −0.0413750 | ||||||||
\(331\) | −9.74349 | −0.535551 | −0.267775 | − | 0.963481i | \(-0.586289\pi\) | ||||
−0.267775 | + | 0.963481i | \(0.586289\pi\) | |||||||
\(332\) | −23.6736 | −1.29925 | ||||||||
\(333\) | −0.297591 | −0.0163079 | ||||||||
\(334\) | 0.279255 | 0.0152802 | ||||||||
\(335\) | 0.793300 | 0.0433426 | ||||||||
\(336\) | 4.21626 | 0.230016 | ||||||||
\(337\) | 31.4773 | 1.71468 | 0.857339 | − | 0.514752i | \(-0.172116\pi\) | ||||
0.857339 | + | 0.514752i | \(0.172116\pi\) | |||||||
\(338\) | −0.389331 | −0.0211768 | ||||||||
\(339\) | −8.80892 | −0.478435 | ||||||||
\(340\) | −4.41566 | −0.239473 | ||||||||
\(341\) | −21.5398 | −1.16645 | ||||||||
\(342\) | 0.889218 | 0.0480834 | ||||||||
\(343\) | 16.4753 | 0.889580 | ||||||||
\(344\) | −3.07565 | −0.165828 | ||||||||
\(345\) | −0.686871 | −0.0369799 | ||||||||
\(346\) | −7.49860 | −0.403127 | ||||||||
\(347\) | 4.48252 | 0.240634 | 0.120317 | − | 0.992736i | \(-0.461609\pi\) | ||||
0.120317 | + | 0.992736i | \(0.461609\pi\) | |||||||
\(348\) | −10.5383 | −0.564914 | ||||||||
\(349\) | 11.1704 | 0.597935 | 0.298968 | − | 0.954263i | \(-0.403358\pi\) | ||||
0.298968 | + | 0.954263i | \(0.403358\pi\) | |||||||
\(350\) | −2.41835 | −0.129266 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 12.6423 | 0.673835 | ||||||||
\(353\) | 28.2802 | 1.50520 | 0.752602 | − | 0.658476i | \(-0.228798\pi\) | ||||
0.752602 | + | 0.658476i | \(0.228798\pi\) | |||||||
\(354\) | 3.89304 | 0.206913 | ||||||||
\(355\) | −0.840113 | −0.0445886 | ||||||||
\(356\) | 20.8112 | 1.10299 | ||||||||
\(357\) | 5.03341 | 0.266396 | ||||||||
\(358\) | −1.72642 | −0.0912441 | ||||||||
\(359\) | 12.2438 | 0.646201 | 0.323100 | − | 0.946365i | \(-0.395275\pi\) | ||||
0.323100 | + | 0.946365i | \(0.395275\pi\) | |||||||
\(360\) | 0.962967 | 0.0507528 | ||||||||
\(361\) | −13.7835 | −0.725448 | ||||||||
\(362\) | 3.73980 | 0.196560 | ||||||||
\(363\) | 1.97740 | 0.103787 | ||||||||
\(364\) | −2.50310 | −0.131198 | ||||||||
\(365\) | 6.60155 | 0.345541 | ||||||||
\(366\) | 1.26888 | 0.0663252 | ||||||||
\(367\) | −2.60849 | −0.136162 | −0.0680811 | − | 0.997680i | \(-0.521688\pi\) | ||||
−0.0680811 | + | 0.997680i | \(0.521688\pi\) | |||||||
\(368\) | 3.32748 | 0.173457 | ||||||||
\(369\) | 2.02015 | 0.105165 | ||||||||
\(370\) | 0.0744644 | 0.00387122 | ||||||||
\(371\) | 13.7401 | 0.713352 | ||||||||
\(372\) | 13.2549 | 0.687235 | ||||||||
\(373\) | −13.4756 | −0.697740 | −0.348870 | − | 0.937171i | \(-0.613435\pi\) | ||||
−0.348870 | + | 0.937171i | \(0.613435\pi\) | |||||||
\(374\) | 4.34680 | 0.224768 | ||||||||
\(375\) | 6.16154 | 0.318181 | ||||||||
\(376\) | −15.0820 | −0.777797 | ||||||||
\(377\) | 5.70126 | 0.293630 | ||||||||
\(378\) | −0.527226 | −0.0271176 | ||||||||
\(379\) | −22.3063 | −1.14580 | −0.572899 | − | 0.819626i | \(-0.694181\pi\) | ||||
−0.572899 | + | 0.819626i | \(0.694181\pi\) | |||||||
\(380\) | 2.71331 | 0.139190 | ||||||||
\(381\) | −15.7150 | −0.805106 | ||||||||
\(382\) | 0.0231866 | 0.00118633 | ||||||||
\(383\) | 33.1365 | 1.69320 | 0.846599 | − | 0.532232i | \(-0.178647\pi\) | ||||
0.846599 | + | 0.532232i | \(0.178647\pi\) | |||||||
\(384\) | −10.2040 | −0.520721 | ||||||||
\(385\) | 2.61429 | 0.133236 | ||||||||
\(386\) | 7.14042 | 0.363438 | ||||||||
\(387\) | −2.05274 | −0.104347 | ||||||||
\(388\) | 7.99135 | 0.405699 | ||||||||
\(389\) | −1.12469 | −0.0570242 | −0.0285121 | − | 0.999593i | \(-0.509077\pi\) | ||||
−0.0285121 | + | 0.999593i | \(0.509077\pi\) | |||||||
\(390\) | −0.250224 | −0.0126706 | ||||||||
\(391\) | 3.97238 | 0.200892 | ||||||||
\(392\) | −7.74055 | −0.390957 | ||||||||
\(393\) | −11.2112 | −0.565528 | ||||||||
\(394\) | 0.858207 | 0.0432358 | ||||||||
\(395\) | −1.06514 | −0.0535932 | ||||||||
\(396\) | 5.55222 | 0.279010 | ||||||||
\(397\) | −23.8859 | −1.19880 | −0.599401 | − | 0.800449i | \(-0.704594\pi\) | ||||
−0.599401 | + | 0.800449i | \(0.704594\pi\) | |||||||
\(398\) | −9.11176 | −0.456731 | ||||||||
\(399\) | −3.09291 | −0.154839 | ||||||||
\(400\) | −14.2814 | −0.714072 | ||||||||
\(401\) | −23.3086 | −1.16398 | −0.581988 | − | 0.813197i | \(-0.697725\pi\) | ||||
−0.581988 | + | 0.813197i | \(0.697725\pi\) | |||||||
\(402\) | 0.480560 | 0.0239681 | ||||||||
\(403\) | −7.17094 | −0.357210 | ||||||||
\(404\) | 16.0752 | 0.799771 | ||||||||
\(405\) | 0.642702 | 0.0319361 | ||||||||
\(406\) | −3.00585 | −0.149178 | ||||||||
\(407\) | 0.893893 | 0.0443086 | ||||||||
\(408\) | −5.56912 | −0.275713 | ||||||||
\(409\) | 21.1034 | 1.04350 | 0.521748 | − | 0.853100i | \(-0.325280\pi\) | ||||
0.521748 | + | 0.853100i | \(0.325280\pi\) | |||||||
\(410\) | −0.505490 | −0.0249644 | ||||||||
\(411\) | 13.9300 | 0.687114 | ||||||||
\(412\) | −1.84842 | −0.0910652 | ||||||||
\(413\) | −13.5409 | −0.666304 | ||||||||
\(414\) | −0.416088 | −0.0204496 | ||||||||
\(415\) | 8.23137 | 0.404062 | ||||||||
\(416\) | 4.20881 | 0.206354 | ||||||||
\(417\) | −4.30921 | −0.211023 | ||||||||
\(418\) | −2.67100 | −0.130643 | ||||||||
\(419\) | −10.1892 | −0.497774 | −0.248887 | − | 0.968532i | \(-0.580065\pi\) | ||||
−0.248887 | + | 0.968532i | \(0.580065\pi\) | |||||||
\(420\) | −1.60875 | −0.0784989 | ||||||||
\(421\) | 12.4669 | 0.607598 | 0.303799 | − | 0.952736i | \(-0.401745\pi\) | ||||
0.303799 | + | 0.952736i | \(0.401745\pi\) | |||||||
\(422\) | 3.21044 | 0.156282 | ||||||||
\(423\) | −10.0660 | −0.489427 | ||||||||
\(424\) | −15.2025 | −0.738298 | ||||||||
\(425\) | −17.0493 | −0.827014 | ||||||||
\(426\) | −0.508918 | −0.0246571 | ||||||||
\(427\) | −4.41344 | −0.213581 | ||||||||
\(428\) | 1.60162 | 0.0774172 | ||||||||
\(429\) | −3.00376 | −0.145023 | ||||||||
\(430\) | 0.513645 | 0.0247702 | ||||||||
\(431\) | 14.2559 | 0.686682 | 0.343341 | − | 0.939211i | \(-0.388441\pi\) | ||||
0.343341 | + | 0.939211i | \(0.388441\pi\) | |||||||
\(432\) | −3.11350 | −0.149798 | ||||||||
\(433\) | −7.41028 | −0.356116 | −0.178058 | − | 0.984020i | \(-0.556981\pi\) | ||||
−0.178058 | + | 0.984020i | \(0.556981\pi\) | |||||||
\(434\) | 3.78071 | 0.181480 | ||||||||
\(435\) | 3.66421 | 0.175685 | ||||||||
\(436\) | 19.7795 | 0.947265 | ||||||||
\(437\) | −2.44093 | −0.116765 | ||||||||
\(438\) | 3.99904 | 0.191081 | ||||||||
\(439\) | 5.97218 | 0.285036 | 0.142518 | − | 0.989792i | \(-0.454480\pi\) | ||||
0.142518 | + | 0.989792i | \(0.454480\pi\) | |||||||
\(440\) | −2.89253 | −0.137896 | ||||||||
\(441\) | −5.16619 | −0.246009 | ||||||||
\(442\) | 1.44712 | 0.0688324 | ||||||||
\(443\) | 0.244976 | 0.0116391 | 0.00581957 | − | 0.999983i | \(-0.498148\pi\) | ||||
0.00581957 | + | 0.999983i | \(0.498148\pi\) | |||||||
\(444\) | −0.550073 | −0.0261053 | ||||||||
\(445\) | −7.23610 | −0.343024 | ||||||||
\(446\) | −0.204856 | −0.00970024 | ||||||||
\(447\) | −20.3044 | −0.960363 | ||||||||
\(448\) | 6.21352 | 0.293561 | ||||||||
\(449\) | 4.69213 | 0.221435 | 0.110718 | − | 0.993852i | \(-0.464685\pi\) | ||||
0.110718 | + | 0.993852i | \(0.464685\pi\) | |||||||
\(450\) | 1.78584 | 0.0841852 | ||||||||
\(451\) | −6.06805 | −0.285733 | ||||||||
\(452\) | −16.2826 | −0.765869 | ||||||||
\(453\) | −14.1623 | −0.665401 | ||||||||
\(454\) | −4.35556 | −0.204417 | ||||||||
\(455\) | 0.870336 | 0.0408020 | ||||||||
\(456\) | 3.42209 | 0.160254 | ||||||||
\(457\) | −21.8979 | −1.02434 | −0.512169 | − | 0.858885i | \(-0.671158\pi\) | ||||
−0.512169 | + | 0.858885i | \(0.671158\pi\) | |||||||
\(458\) | 4.65311 | 0.217425 | ||||||||
\(459\) | −3.71693 | −0.173492 | ||||||||
\(460\) | −1.26963 | −0.0591966 | ||||||||
\(461\) | 13.7694 | 0.641306 | 0.320653 | − | 0.947197i | \(-0.396098\pi\) | ||||
0.320653 | + | 0.947197i | \(0.396098\pi\) | |||||||
\(462\) | 1.58366 | 0.0736787 | ||||||||
\(463\) | −34.9696 | −1.62517 | −0.812587 | − | 0.582840i | \(-0.801942\pi\) | ||||
−0.812587 | + | 0.582840i | \(0.801942\pi\) | |||||||
\(464\) | −17.7509 | −0.824064 | ||||||||
\(465\) | −4.60877 | −0.213727 | ||||||||
\(466\) | 4.85286 | 0.224804 | ||||||||
\(467\) | −16.0893 | −0.744524 | −0.372262 | − | 0.928128i | \(-0.621418\pi\) | ||||
−0.372262 | + | 0.928128i | \(0.621418\pi\) | |||||||
\(468\) | 1.84842 | 0.0854433 | ||||||||
\(469\) | −1.67150 | −0.0771826 | ||||||||
\(470\) | 2.51876 | 0.116182 | ||||||||
\(471\) | −19.3082 | −0.889675 | ||||||||
\(472\) | 14.9821 | 0.689606 | ||||||||
\(473\) | 6.16595 | 0.283511 | ||||||||
\(474\) | −0.645235 | −0.0296366 | ||||||||
\(475\) | 10.4764 | 0.480690 | ||||||||
\(476\) | 9.30387 | 0.426442 | ||||||||
\(477\) | −10.1464 | −0.464573 | ||||||||
\(478\) | −5.79085 | −0.264867 | ||||||||
\(479\) | 21.0086 | 0.959906 | 0.479953 | − | 0.877294i | \(-0.340654\pi\) | ||||
0.479953 | + | 0.877294i | \(0.340654\pi\) | |||||||
\(480\) | 2.70501 | 0.123466 | ||||||||
\(481\) | 0.297591 | 0.0135690 | ||||||||
\(482\) | −8.34853 | −0.380265 | ||||||||
\(483\) | 1.44725 | 0.0658521 | ||||||||
\(484\) | 3.65507 | 0.166139 | ||||||||
\(485\) | −2.77862 | −0.126171 | ||||||||
\(486\) | 0.389331 | 0.0176604 | ||||||||
\(487\) | −14.5423 | −0.658973 | −0.329486 | − | 0.944160i | \(-0.606876\pi\) | ||||
−0.329486 | + | 0.944160i | \(0.606876\pi\) | |||||||
\(488\) | 4.88317 | 0.221051 | ||||||||
\(489\) | 6.41726 | 0.290198 | ||||||||
\(490\) | 1.29270 | 0.0583984 | ||||||||
\(491\) | 34.1591 | 1.54158 | 0.770789 | − | 0.637090i | \(-0.219862\pi\) | ||||
0.770789 | + | 0.637090i | \(0.219862\pi\) | |||||||
\(492\) | 3.73409 | 0.168346 | ||||||||
\(493\) | −21.1912 | −0.954404 | ||||||||
\(494\) | −0.889218 | −0.0400078 | ||||||||
\(495\) | −1.93052 | −0.0867706 | ||||||||
\(496\) | 22.3267 | 1.00250 | ||||||||
\(497\) | 1.77013 | 0.0794013 | ||||||||
\(498\) | 4.98634 | 0.223443 | ||||||||
\(499\) | −5.80677 | −0.259947 | −0.129973 | − | 0.991517i | \(-0.541489\pi\) | ||||
−0.129973 | + | 0.991517i | \(0.541489\pi\) | |||||||
\(500\) | 11.3891 | 0.509337 | ||||||||
\(501\) | 0.717268 | 0.0320452 | ||||||||
\(502\) | −7.50205 | −0.334833 | ||||||||
\(503\) | 24.7511 | 1.10360 | 0.551798 | − | 0.833978i | \(-0.313942\pi\) | ||||
0.551798 | + | 0.833978i | \(0.313942\pi\) | |||||||
\(504\) | −2.02899 | −0.0903783 | ||||||||
\(505\) | −5.58940 | −0.248725 | ||||||||
\(506\) | 1.24983 | 0.0555617 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −29.0480 | −1.28880 | ||||||||
\(509\) | −29.9406 | −1.32709 | −0.663547 | − | 0.748135i | \(-0.730950\pi\) | ||||
−0.663547 | + | 0.748135i | \(0.730950\pi\) | |||||||
\(510\) | 0.930066 | 0.0411840 | ||||||||
\(511\) | −13.9096 | −0.615323 | ||||||||
\(512\) | −22.4341 | −0.991457 | ||||||||
\(513\) | 2.28396 | 0.100839 | ||||||||
\(514\) | −4.06168 | −0.179153 | ||||||||
\(515\) | 0.642702 | 0.0283208 | ||||||||
\(516\) | −3.79433 | −0.167036 | ||||||||
\(517\) | 30.2360 | 1.32978 | ||||||||
\(518\) | −0.156898 | −0.00689369 | ||||||||
\(519\) | −19.2602 | −0.845430 | ||||||||
\(520\) | −0.962967 | −0.0422289 | ||||||||
\(521\) | 40.3306 | 1.76692 | 0.883458 | − | 0.468509i | \(-0.155209\pi\) | ||||
0.883458 | + | 0.468509i | \(0.155209\pi\) | |||||||
\(522\) | 2.21968 | 0.0971527 | ||||||||
\(523\) | −22.7558 | −0.995041 | −0.497521 | − | 0.867452i | \(-0.665756\pi\) | ||||
−0.497521 | + | 0.867452i | \(0.665756\pi\) | |||||||
\(524\) | −20.7229 | −0.905286 | ||||||||
\(525\) | −6.21155 | −0.271094 | ||||||||
\(526\) | 0.569699 | 0.0248401 | ||||||||
\(527\) | 26.6539 | 1.16106 | ||||||||
\(528\) | 9.35223 | 0.407004 | ||||||||
\(529\) | −21.8578 | −0.950340 | ||||||||
\(530\) | 2.53888 | 0.110282 | ||||||||
\(531\) | 9.99931 | 0.433933 | ||||||||
\(532\) | −5.71699 | −0.247863 | ||||||||
\(533\) | −2.02015 | −0.0875024 | ||||||||
\(534\) | −4.38343 | −0.189690 | ||||||||
\(535\) | −0.556888 | −0.0240764 | ||||||||
\(536\) | 1.84940 | 0.0798817 | ||||||||
\(537\) | −4.43432 | −0.191355 | ||||||||
\(538\) | 1.51135 | 0.0651589 | ||||||||
\(539\) | 15.5180 | 0.668408 | ||||||||
\(540\) | 1.18798 | 0.0511227 | ||||||||
\(541\) | −14.0755 | −0.605153 | −0.302576 | − | 0.953125i | \(-0.597847\pi\) | ||||
−0.302576 | + | 0.953125i | \(0.597847\pi\) | |||||||
\(542\) | −11.5948 | −0.498038 | ||||||||
\(543\) | 9.60571 | 0.412220 | ||||||||
\(544\) | −15.6439 | −0.670725 | ||||||||
\(545\) | −6.87739 | −0.294595 | ||||||||
\(546\) | 0.527226 | 0.0225632 | ||||||||
\(547\) | 12.1714 | 0.520410 | 0.260205 | − | 0.965553i | \(-0.416210\pi\) | ||||
0.260205 | + | 0.965553i | \(0.416210\pi\) | |||||||
\(548\) | 25.7484 | 1.09992 | ||||||||
\(549\) | 3.25912 | 0.139096 | ||||||||
\(550\) | −5.36423 | −0.228732 | ||||||||
\(551\) | 13.0215 | 0.554733 | ||||||||
\(552\) | −1.60128 | −0.0681550 | ||||||||
\(553\) | 2.24428 | 0.0954364 | ||||||||
\(554\) | −2.40617 | −0.102228 | ||||||||
\(555\) | 0.191262 | 0.00811863 | ||||||||
\(556\) | −7.96523 | −0.337801 | ||||||||
\(557\) | −34.6179 | −1.46681 | −0.733403 | − | 0.679794i | \(-0.762069\pi\) | ||||
−0.733403 | + | 0.679794i | \(0.762069\pi\) | |||||||
\(558\) | −2.79187 | −0.118189 | ||||||||
\(559\) | 2.05274 | 0.0868217 | ||||||||
\(560\) | −2.70980 | −0.114510 | ||||||||
\(561\) | 11.1648 | 0.471378 | ||||||||
\(562\) | −6.37161 | −0.268770 | ||||||||
\(563\) | 10.5183 | 0.443292 | 0.221646 | − | 0.975127i | \(-0.428857\pi\) | ||||
0.221646 | + | 0.975127i | \(0.428857\pi\) | |||||||
\(564\) | −18.6063 | −0.783465 | ||||||||
\(565\) | 5.66151 | 0.238182 | ||||||||
\(566\) | −0.492659 | −0.0207080 | ||||||||
\(567\) | −1.35418 | −0.0568704 | ||||||||
\(568\) | −1.95853 | −0.0821781 | ||||||||
\(569\) | −8.84536 | −0.370817 | −0.185408 | − | 0.982662i | \(-0.559361\pi\) | ||||
−0.185408 | + | 0.982662i | \(0.559361\pi\) | |||||||
\(570\) | −0.571502 | −0.0239376 | ||||||||
\(571\) | −11.9955 | −0.501996 | −0.250998 | − | 0.967988i | \(-0.580759\pi\) | ||||
−0.250998 | + | 0.967988i | \(0.580759\pi\) | |||||||
\(572\) | −5.55222 | −0.232150 | ||||||||
\(573\) | 0.0595551 | 0.00248795 | ||||||||
\(574\) | 1.06508 | 0.0444554 | ||||||||
\(575\) | −4.90217 | −0.204434 | ||||||||
\(576\) | −4.58839 | −0.191183 | ||||||||
\(577\) | −33.7368 | −1.40448 | −0.702242 | − | 0.711939i | \(-0.747817\pi\) | ||||
−0.702242 | + | 0.711939i | \(0.747817\pi\) | |||||||
\(578\) | 1.23979 | 0.0515683 | ||||||||
\(579\) | 18.3402 | 0.762194 | ||||||||
\(580\) | 6.77300 | 0.281234 | ||||||||
\(581\) | −17.3436 | −0.719535 | ||||||||
\(582\) | −1.68321 | −0.0697714 | ||||||||
\(583\) | 30.4775 | 1.26225 | ||||||||
\(584\) | 15.3900 | 0.636842 | ||||||||
\(585\) | −0.642702 | −0.0265724 | ||||||||
\(586\) | −8.56576 | −0.353848 | ||||||||
\(587\) | −2.66128 | −0.109843 | −0.0549213 | − | 0.998491i | \(-0.517491\pi\) | ||||
−0.0549213 | + | 0.998491i | \(0.517491\pi\) | |||||||
\(588\) | −9.54929 | −0.393806 | ||||||||
\(589\) | −16.3782 | −0.674850 | ||||||||
\(590\) | −2.50207 | −0.103008 | ||||||||
\(591\) | 2.20431 | 0.0906732 | ||||||||
\(592\) | −0.926550 | −0.0380810 | ||||||||
\(593\) | −1.55005 | −0.0636531 | −0.0318266 | − | 0.999493i | \(-0.510132\pi\) | ||||
−0.0318266 | + | 0.999493i | \(0.510132\pi\) | |||||||
\(594\) | −1.16946 | −0.0479835 | ||||||||
\(595\) | −3.23498 | −0.132621 | ||||||||
\(596\) | −37.5310 | −1.53733 | ||||||||
\(597\) | −23.4036 | −0.957846 | ||||||||
\(598\) | 0.416088 | 0.0170151 | ||||||||
\(599\) | 13.4015 | 0.547571 | 0.273786 | − | 0.961791i | \(-0.411724\pi\) | ||||
0.273786 | + | 0.961791i | \(0.411724\pi\) | |||||||
\(600\) | 6.87265 | 0.280575 | ||||||||
\(601\) | −44.7777 | −1.82652 | −0.913259 | − | 0.407378i | \(-0.866443\pi\) | ||||
−0.913259 | + | 0.407378i | \(0.866443\pi\) | |||||||
\(602\) | −1.08226 | −0.0441096 | ||||||||
\(603\) | 1.23432 | 0.0502654 | ||||||||
\(604\) | −26.1778 | −1.06516 | ||||||||
\(605\) | −1.27088 | −0.0516685 | ||||||||
\(606\) | −3.38591 | −0.137543 | ||||||||
\(607\) | −38.2141 | −1.55106 | −0.775531 | − | 0.631309i | \(-0.782518\pi\) | ||||
−0.775531 | + | 0.631309i | \(0.782518\pi\) | |||||||
\(608\) | 9.61276 | 0.389849 | ||||||||
\(609\) | −7.72055 | −0.312853 | ||||||||
\(610\) | −0.815509 | −0.0330190 | ||||||||
\(611\) | 10.0660 | 0.407228 | ||||||||
\(612\) | −6.87046 | −0.277722 | ||||||||
\(613\) | −21.8566 | −0.882779 | −0.441389 | − | 0.897316i | \(-0.645514\pi\) | ||||
−0.441389 | + | 0.897316i | \(0.645514\pi\) | |||||||
\(614\) | 2.36048 | 0.0952612 | ||||||||
\(615\) | −1.29835 | −0.0523547 | ||||||||
\(616\) | 6.09460 | 0.245559 | ||||||||
\(617\) | 32.7065 | 1.31671 | 0.658357 | − | 0.752706i | \(-0.271252\pi\) | ||||
0.658357 | + | 0.752706i | \(0.271252\pi\) | |||||||
\(618\) | 0.389331 | 0.0156612 | ||||||||
\(619\) | −24.2386 | −0.974233 | −0.487117 | − | 0.873337i | \(-0.661951\pi\) | ||||
−0.487117 | + | 0.873337i | \(0.661951\pi\) | |||||||
\(620\) | −8.51896 | −0.342130 | ||||||||
\(621\) | −1.06872 | −0.0428864 | ||||||||
\(622\) | −8.34563 | −0.334629 | ||||||||
\(623\) | 15.2466 | 0.610842 | ||||||||
\(624\) | 3.11350 | 0.124640 | ||||||||
\(625\) | 18.9746 | 0.758986 | ||||||||
\(626\) | −8.57835 | −0.342860 | ||||||||
\(627\) | −6.86049 | −0.273981 | ||||||||
\(628\) | −35.6897 | −1.42417 | ||||||||
\(629\) | −1.10613 | −0.0441041 | ||||||||
\(630\) | 0.338849 | 0.0135001 | ||||||||
\(631\) | −7.96732 | −0.317174 | −0.158587 | − | 0.987345i | \(-0.550694\pi\) | ||||
−0.158587 | + | 0.987345i | \(0.550694\pi\) | |||||||
\(632\) | −2.48314 | −0.0987739 | ||||||||
\(633\) | 8.24603 | 0.327750 | ||||||||
\(634\) | −2.26651 | −0.0900148 | ||||||||
\(635\) | 10.1001 | 0.400810 | ||||||||
\(636\) | −18.7549 | −0.743679 | ||||||||
\(637\) | 5.16619 | 0.204692 | ||||||||
\(638\) | −6.66739 | −0.263965 | ||||||||
\(639\) | −1.30716 | −0.0517104 | ||||||||
\(640\) | 6.55814 | 0.259233 | ||||||||
\(641\) | 33.0630 | 1.30591 | 0.652955 | − | 0.757397i | \(-0.273529\pi\) | ||||
0.652955 | + | 0.757397i | \(0.273529\pi\) | |||||||
\(642\) | −0.337348 | −0.0133141 | ||||||||
\(643\) | 3.82237 | 0.150739 | 0.0753697 | − | 0.997156i | \(-0.475986\pi\) | ||||
0.0753697 | + | 0.997156i | \(0.475986\pi\) | |||||||
\(644\) | 2.67513 | 0.105415 | ||||||||
\(645\) | 1.31930 | 0.0519474 | ||||||||
\(646\) | 3.30517 | 0.130040 | ||||||||
\(647\) | 6.43456 | 0.252969 | 0.126484 | − | 0.991969i | \(-0.459631\pi\) | ||||
0.126484 | + | 0.991969i | \(0.459631\pi\) | |||||||
\(648\) | 1.49831 | 0.0588592 | ||||||||
\(649\) | −30.0356 | −1.17900 | ||||||||
\(650\) | −1.78584 | −0.0700463 | ||||||||
\(651\) | 9.71077 | 0.380595 | ||||||||
\(652\) | 11.8618 | 0.464544 | ||||||||
\(653\) | −14.9742 | −0.585986 | −0.292993 | − | 0.956115i | \(-0.594651\pi\) | ||||
−0.292993 | + | 0.956115i | \(0.594651\pi\) | |||||||
\(654\) | −4.16613 | −0.162909 | ||||||||
\(655\) | 7.20543 | 0.281539 | ||||||||
\(656\) | 6.28974 | 0.245573 | ||||||||
\(657\) | 10.2716 | 0.400731 | ||||||||
\(658\) | −5.30707 | −0.206891 | ||||||||
\(659\) | 32.1155 | 1.25104 | 0.625522 | − | 0.780207i | \(-0.284886\pi\) | ||||
0.625522 | + | 0.780207i | \(0.284886\pi\) | |||||||
\(660\) | −3.56842 | −0.138901 | ||||||||
\(661\) | −49.4261 | −1.92245 | −0.961226 | − | 0.275760i | \(-0.911070\pi\) | ||||
−0.961226 | + | 0.275760i | \(0.911070\pi\) | |||||||
\(662\) | 3.79345 | 0.147436 | ||||||||
\(663\) | 3.71693 | 0.144354 | ||||||||
\(664\) | 19.1895 | 0.744698 | ||||||||
\(665\) | 1.98782 | 0.0770842 | ||||||||
\(666\) | 0.115861 | 0.00448954 | ||||||||
\(667\) | −6.09307 | −0.235925 | ||||||||
\(668\) | 1.32581 | 0.0512973 | ||||||||
\(669\) | −0.526175 | −0.0203431 | ||||||||
\(670\) | −0.308857 | −0.0119322 | ||||||||
\(671\) | −9.78961 | −0.377924 | ||||||||
\(672\) | −5.69950 | −0.219863 | ||||||||
\(673\) | 23.2243 | 0.895232 | 0.447616 | − | 0.894226i | \(-0.352273\pi\) | ||||
0.447616 | + | 0.894226i | \(0.352273\pi\) | |||||||
\(674\) | −12.2551 | −0.472049 | ||||||||
\(675\) | 4.58693 | 0.176551 | ||||||||
\(676\) | −1.84842 | −0.0710931 | ||||||||
\(677\) | −14.1618 | −0.544282 | −0.272141 | − | 0.962257i | \(-0.587732\pi\) | ||||
−0.272141 | + | 0.962257i | \(0.587732\pi\) | |||||||
\(678\) | 3.42959 | 0.131713 | ||||||||
\(679\) | 5.85460 | 0.224679 | ||||||||
\(680\) | 3.57929 | 0.137259 | ||||||||
\(681\) | −11.1873 | −0.428698 | ||||||||
\(682\) | 8.38612 | 0.321121 | ||||||||
\(683\) | 14.3440 | 0.548858 | 0.274429 | − | 0.961607i | \(-0.411511\pi\) | ||||
0.274429 | + | 0.961607i | \(0.411511\pi\) | |||||||
\(684\) | 4.22173 | 0.161422 | ||||||||
\(685\) | −8.95281 | −0.342069 | ||||||||
\(686\) | −6.41433 | −0.244900 | ||||||||
\(687\) | 11.9515 | 0.455980 | ||||||||
\(688\) | −6.39122 | −0.243663 | ||||||||
\(689\) | 10.1464 | 0.386548 | ||||||||
\(690\) | 0.267420 | 0.0101805 | ||||||||
\(691\) | 25.9061 | 0.985515 | 0.492758 | − | 0.870167i | \(-0.335989\pi\) | ||||
0.492758 | + | 0.870167i | \(0.335989\pi\) | |||||||
\(692\) | −35.6010 | −1.35335 | ||||||||
\(693\) | 4.06765 | 0.154517 | ||||||||
\(694\) | −1.74519 | −0.0662464 | ||||||||
\(695\) | 2.76954 | 0.105054 | ||||||||
\(696\) | 8.54226 | 0.323793 | ||||||||
\(697\) | 7.50876 | 0.284415 | ||||||||
\(698\) | −4.34897 | −0.164611 | ||||||||
\(699\) | 12.4646 | 0.471454 | ||||||||
\(700\) | −11.4816 | −0.433962 | ||||||||
\(701\) | 9.97933 | 0.376914 | 0.188457 | − | 0.982081i | \(-0.439651\pi\) | ||||
0.188457 | + | 0.982081i | \(0.439651\pi\) | |||||||
\(702\) | −0.389331 | −0.0146944 | ||||||||
\(703\) | 0.679687 | 0.0256349 | ||||||||
\(704\) | 13.7824 | 0.519445 | ||||||||
\(705\) | 6.46945 | 0.243654 | ||||||||
\(706\) | −11.0104 | −0.414381 | ||||||||
\(707\) | 11.7770 | 0.442918 | ||||||||
\(708\) | 18.4829 | 0.694631 | ||||||||
\(709\) | 12.0282 | 0.451728 | 0.225864 | − | 0.974159i | \(-0.427480\pi\) | ||||
0.225864 | + | 0.974159i | \(0.427480\pi\) | |||||||
\(710\) | 0.327082 | 0.0122752 | ||||||||
\(711\) | −1.65729 | −0.0621533 | ||||||||
\(712\) | −16.8693 | −0.632204 | ||||||||
\(713\) | 7.66375 | 0.287010 | ||||||||
\(714\) | −1.95967 | −0.0733386 | ||||||||
\(715\) | 1.93052 | 0.0721975 | ||||||||
\(716\) | −8.19649 | −0.306317 | ||||||||
\(717\) | −14.8738 | −0.555474 | ||||||||
\(718\) | −4.76688 | −0.177898 | ||||||||
\(719\) | −16.6861 | −0.622288 | −0.311144 | − | 0.950363i | \(-0.600712\pi\) | ||||
−0.311144 | + | 0.950363i | \(0.600712\pi\) | |||||||
\(720\) | 2.00105 | 0.0745749 | ||||||||
\(721\) | −1.35418 | −0.0504324 | ||||||||
\(722\) | 5.36635 | 0.199715 | ||||||||
\(723\) | −21.4433 | −0.797483 | ||||||||
\(724\) | 17.7554 | 0.659874 | ||||||||
\(725\) | 26.1513 | 0.971235 | ||||||||
\(726\) | −0.769863 | −0.0285723 | ||||||||
\(727\) | 36.2715 | 1.34523 | 0.672617 | − | 0.739991i | \(-0.265170\pi\) | ||||
0.672617 | + | 0.739991i | \(0.265170\pi\) | |||||||
\(728\) | 2.02899 | 0.0751993 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −2.57019 | −0.0951269 | ||||||||
\(731\) | −7.62991 | −0.282202 | ||||||||
\(732\) | 6.02422 | 0.222661 | ||||||||
\(733\) | 28.1998 | 1.04158 | 0.520792 | − | 0.853684i | \(-0.325637\pi\) | ||||
0.520792 | + | 0.853684i | \(0.325637\pi\) | |||||||
\(734\) | 1.01557 | 0.0374853 | ||||||||
\(735\) | 3.32032 | 0.122472 | ||||||||
\(736\) | −4.49805 | −0.165800 | ||||||||
\(737\) | −3.70761 | −0.136572 | ||||||||
\(738\) | −0.786507 | −0.0289517 | ||||||||
\(739\) | 8.08229 | 0.297312 | 0.148656 | − | 0.988889i | \(-0.452505\pi\) | ||||
0.148656 | + | 0.988889i | \(0.452505\pi\) | |||||||
\(740\) | 0.353533 | 0.0129961 | ||||||||
\(741\) | −2.28396 | −0.0839035 | ||||||||
\(742\) | −5.34946 | −0.196385 | ||||||||
\(743\) | −47.3255 | −1.73620 | −0.868101 | − | 0.496387i | \(-0.834660\pi\) | ||||
−0.868101 | + | 0.496387i | \(0.834660\pi\) | |||||||
\(744\) | −10.7443 | −0.393905 | ||||||||
\(745\) | 13.0496 | 0.478102 | ||||||||
\(746\) | 5.24647 | 0.192087 | ||||||||
\(747\) | 12.8074 | 0.468600 | ||||||||
\(748\) | 20.6372 | 0.754572 | ||||||||
\(749\) | 1.17337 | 0.0428741 | ||||||||
\(750\) | −2.39888 | −0.0875947 | ||||||||
\(751\) | 16.3887 | 0.598033 | 0.299016 | − | 0.954248i | \(-0.403341\pi\) | ||||
0.299016 | + | 0.954248i | \(0.403341\pi\) | |||||||
\(752\) | −31.3406 | −1.14287 | ||||||||
\(753\) | −19.2691 | −0.702204 | ||||||||
\(754\) | −2.21968 | −0.0808359 | ||||||||
\(755\) | 9.10211 | 0.331260 | ||||||||
\(756\) | −2.50310 | −0.0910370 | ||||||||
\(757\) | 33.2828 | 1.20968 | 0.604842 | − | 0.796345i | \(-0.293236\pi\) | ||||
0.604842 | + | 0.796345i | \(0.293236\pi\) | |||||||
\(758\) | 8.68454 | 0.315437 | ||||||||
\(759\) | 3.21019 | 0.116523 | ||||||||
\(760\) | −2.19938 | −0.0797799 | ||||||||
\(761\) | −22.2884 | −0.807953 | −0.403976 | − | 0.914769i | \(-0.632372\pi\) | ||||
−0.403976 | + | 0.914769i | \(0.632372\pi\) | |||||||
\(762\) | 6.11836 | 0.221645 | ||||||||
\(763\) | 14.4908 | 0.524601 | ||||||||
\(764\) | 0.110083 | 0.00398266 | ||||||||
\(765\) | 2.38888 | 0.0863702 | ||||||||
\(766\) | −12.9011 | −0.466135 | ||||||||
\(767\) | −9.99931 | −0.361054 | ||||||||
\(768\) | −5.20403 | −0.187784 | ||||||||
\(769\) | 14.8200 | 0.534423 | 0.267212 | − | 0.963638i | \(-0.413898\pi\) | ||||
0.267212 | + | 0.963638i | \(0.413898\pi\) | |||||||
\(770\) | −1.01782 | −0.0366798 | ||||||||
\(771\) | −10.4324 | −0.375715 | ||||||||
\(772\) | 33.9005 | 1.22010 | ||||||||
\(773\) | −21.0194 | −0.756016 | −0.378008 | − | 0.925802i | \(-0.623391\pi\) | ||||
−0.378008 | + | 0.925802i | \(0.623391\pi\) | |||||||
\(774\) | 0.799197 | 0.0287265 | ||||||||
\(775\) | −32.8926 | −1.18154 | ||||||||
\(776\) | −6.47771 | −0.232536 | ||||||||
\(777\) | −0.402993 | −0.0144573 | ||||||||
\(778\) | 0.437878 | 0.0156987 | ||||||||
\(779\) | −4.61395 | −0.165312 | ||||||||
\(780\) | −1.18798 | −0.0425366 | ||||||||
\(781\) | 3.92640 | 0.140498 | ||||||||
\(782\) | −1.54657 | −0.0553053 | ||||||||
\(783\) | 5.70126 | 0.203746 | ||||||||
\(784\) | −16.0849 | −0.574462 | ||||||||
\(785\) | 12.4094 | 0.442911 | ||||||||
\(786\) | 4.36485 | 0.155689 | ||||||||
\(787\) | −29.1852 | −1.04034 | −0.520169 | − | 0.854063i | \(-0.674131\pi\) | ||||
−0.520169 | + | 0.854063i | \(0.674131\pi\) | |||||||
\(788\) | 4.07449 | 0.145148 | ||||||||
\(789\) | 1.46328 | 0.0520940 | ||||||||
\(790\) | 0.414694 | 0.0147541 | ||||||||
\(791\) | −11.9289 | −0.424143 | ||||||||
\(792\) | −4.50057 | −0.159921 | ||||||||
\(793\) | −3.25912 | −0.115735 | ||||||||
\(794\) | 9.29955 | 0.330029 | ||||||||
\(795\) | 6.52112 | 0.231280 | ||||||||
\(796\) | −43.2597 | −1.53330 | ||||||||
\(797\) | 12.4917 | 0.442479 | 0.221240 | − | 0.975219i | \(-0.428990\pi\) | ||||
0.221240 | + | 0.975219i | \(0.428990\pi\) | |||||||
\(798\) | 1.20417 | 0.0426270 | ||||||||
\(799\) | −37.4148 | −1.32364 | ||||||||
\(800\) | 19.3055 | 0.682553 | ||||||||
\(801\) | −11.2589 | −0.397813 | ||||||||
\(802\) | 9.07477 | 0.320441 | ||||||||
\(803\) | −30.8533 | −1.08879 | ||||||||
\(804\) | 2.28154 | 0.0804639 | ||||||||
\(805\) | −0.930149 | −0.0327835 | ||||||||
\(806\) | 2.79187 | 0.0983394 | ||||||||
\(807\) | 3.88191 | 0.136650 | ||||||||
\(808\) | −13.0304 | −0.458407 | ||||||||
\(809\) | 23.0780 | 0.811378 | 0.405689 | − | 0.914011i | \(-0.367032\pi\) | ||||
0.405689 | + | 0.914011i | \(0.367032\pi\) | |||||||
\(810\) | −0.250224 | −0.00879197 | ||||||||
\(811\) | −34.4387 | −1.20930 | −0.604652 | − | 0.796490i | \(-0.706688\pi\) | ||||
−0.604652 | + | 0.796490i | \(0.706688\pi\) | |||||||
\(812\) | −14.2708 | −0.500808 | ||||||||
\(813\) | −29.7812 | −1.04447 | ||||||||
\(814\) | −0.348020 | −0.0121981 | ||||||||
\(815\) | −4.12438 | −0.144471 | ||||||||
\(816\) | −11.5727 | −0.405125 | ||||||||
\(817\) | 4.68839 | 0.164026 | ||||||||
\(818\) | −8.21622 | −0.287273 | ||||||||
\(819\) | 1.35418 | 0.0473190 | ||||||||
\(820\) | −2.39990 | −0.0838083 | ||||||||
\(821\) | −38.8773 | −1.35683 | −0.678413 | − | 0.734681i | \(-0.737332\pi\) | ||||
−0.678413 | + | 0.734681i | \(0.737332\pi\) | |||||||
\(822\) | −5.42337 | −0.189162 | ||||||||
\(823\) | −40.3817 | −1.40762 | −0.703809 | − | 0.710389i | \(-0.748519\pi\) | ||||
−0.703809 | + | 0.710389i | \(0.748519\pi\) | |||||||
\(824\) | 1.49831 | 0.0521961 | ||||||||
\(825\) | −13.7781 | −0.479691 | ||||||||
\(826\) | 5.27190 | 0.183433 | ||||||||
\(827\) | −3.88693 | −0.135162 | −0.0675810 | − | 0.997714i | \(-0.521528\pi\) | ||||
−0.0675810 | + | 0.997714i | \(0.521528\pi\) | |||||||
\(828\) | −1.97545 | −0.0686517 | ||||||||
\(829\) | 31.2107 | 1.08399 | 0.541996 | − | 0.840381i | \(-0.317669\pi\) | ||||
0.541996 | + | 0.840381i | \(0.317669\pi\) | |||||||
\(830\) | −3.20473 | −0.111238 | ||||||||
\(831\) | −6.18027 | −0.214391 | ||||||||
\(832\) | 4.58839 | 0.159074 | ||||||||
\(833\) | −19.2024 | −0.665323 | ||||||||
\(834\) | 1.67771 | 0.0580943 | ||||||||
\(835\) | −0.460990 | −0.0159532 | ||||||||
\(836\) | −12.6811 | −0.438584 | ||||||||
\(837\) | −7.17094 | −0.247864 | ||||||||
\(838\) | 3.96697 | 0.137037 | ||||||||
\(839\) | 55.0313 | 1.89989 | 0.949945 | − | 0.312417i | \(-0.101139\pi\) | ||||
0.949945 | + | 0.312417i | \(0.101139\pi\) | |||||||
\(840\) | 1.30403 | 0.0449935 | ||||||||
\(841\) | 3.50435 | 0.120840 | ||||||||
\(842\) | −4.85374 | −0.167271 | ||||||||
\(843\) | −16.3655 | −0.563659 | ||||||||
\(844\) | 15.2421 | 0.524656 | ||||||||
\(845\) | 0.642702 | 0.0221096 | ||||||||
\(846\) | 3.91902 | 0.134739 | ||||||||
\(847\) | 2.67776 | 0.0920090 | ||||||||
\(848\) | −31.5909 | −1.08484 | ||||||||
\(849\) | −1.26540 | −0.0434283 | ||||||||
\(850\) | 6.63784 | 0.227676 | ||||||||
\(851\) | −0.318042 | −0.0109024 | ||||||||
\(852\) | −2.41618 | −0.0827769 | ||||||||
\(853\) | −7.78015 | −0.266387 | −0.133194 | − | 0.991090i | \(-0.542523\pi\) | ||||
−0.133194 | + | 0.991090i | \(0.542523\pi\) | |||||||
\(854\) | 1.71829 | 0.0587987 | ||||||||
\(855\) | −1.46791 | −0.0502014 | ||||||||
\(856\) | −1.29826 | −0.0443735 | ||||||||
\(857\) | −2.27773 | −0.0778057 | −0.0389029 | − | 0.999243i | \(-0.512386\pi\) | ||||
−0.0389029 | + | 0.999243i | \(0.512386\pi\) | |||||||
\(858\) | 1.16946 | 0.0399247 | ||||||||
\(859\) | −1.10615 | −0.0377413 | −0.0188707 | − | 0.999822i | \(-0.506007\pi\) | ||||
−0.0188707 | + | 0.999822i | \(0.506007\pi\) | |||||||
\(860\) | 2.43862 | 0.0831564 | ||||||||
\(861\) | 2.73565 | 0.0932309 | ||||||||
\(862\) | −5.55027 | −0.189043 | ||||||||
\(863\) | 32.7298 | 1.11414 | 0.557068 | − | 0.830467i | \(-0.311926\pi\) | ||||
0.557068 | + | 0.830467i | \(0.311926\pi\) | |||||||
\(864\) | 4.20881 | 0.143186 | ||||||||
\(865\) | 12.3786 | 0.420884 | ||||||||
\(866\) | 2.88506 | 0.0980382 | ||||||||
\(867\) | 3.18440 | 0.108148 | ||||||||
\(868\) | 17.9496 | 0.609249 | ||||||||
\(869\) | 4.97811 | 0.168871 | ||||||||
\(870\) | −1.42659 | −0.0483660 | ||||||||
\(871\) | −1.23432 | −0.0418234 | ||||||||
\(872\) | −16.0330 | −0.542947 | ||||||||
\(873\) | −4.32334 | −0.146323 | ||||||||
\(874\) | 0.950329 | 0.0321454 | ||||||||
\(875\) | 8.34386 | 0.282074 | ||||||||
\(876\) | 18.9862 | 0.641483 | ||||||||
\(877\) | 35.4220 | 1.19611 | 0.598057 | − | 0.801453i | \(-0.295939\pi\) | ||||
0.598057 | + | 0.801453i | \(0.295939\pi\) | |||||||
\(878\) | −2.32516 | −0.0784702 | ||||||||
\(879\) | −22.0012 | −0.742083 | ||||||||
\(880\) | −6.01069 | −0.202620 | ||||||||
\(881\) | −16.0042 | −0.539195 | −0.269598 | − | 0.962973i | \(-0.586891\pi\) | ||||
−0.269598 | + | 0.962973i | \(0.586891\pi\) | |||||||
\(882\) | 2.01136 | 0.0677259 | ||||||||
\(883\) | 39.1782 | 1.31845 | 0.659226 | − | 0.751945i | \(-0.270884\pi\) | ||||
0.659226 | + | 0.751945i | \(0.270884\pi\) | |||||||
\(884\) | 6.87046 | 0.231079 | ||||||||
\(885\) | −6.42657 | −0.216027 | ||||||||
\(886\) | −0.0953767 | −0.00320424 | ||||||||
\(887\) | −23.8804 | −0.801824 | −0.400912 | − | 0.916116i | \(-0.631307\pi\) | ||||
−0.400912 | + | 0.916116i | \(0.631307\pi\) | |||||||
\(888\) | 0.445884 | 0.0149629 | ||||||||
\(889\) | −21.2811 | −0.713744 | ||||||||
\(890\) | 2.81724 | 0.0944341 | ||||||||
\(891\) | −3.00376 | −0.100630 | ||||||||
\(892\) | −0.972593 | −0.0325648 | ||||||||
\(893\) | 22.9904 | 0.769345 | ||||||||
\(894\) | 7.90512 | 0.264387 | ||||||||
\(895\) | 2.84994 | 0.0952631 | ||||||||
\(896\) | −13.8181 | −0.461631 | ||||||||
\(897\) | 1.06872 | 0.0356837 | ||||||||
\(898\) | −1.82679 | −0.0609608 | ||||||||
\(899\) | −40.8834 | −1.36354 | ||||||||
\(900\) | 8.47859 | 0.282620 | ||||||||
\(901\) | −37.7136 | −1.25642 | ||||||||
\(902\) | 2.36248 | 0.0786621 | ||||||||
\(903\) | −2.77979 | −0.0925056 | ||||||||
\(904\) | 13.1985 | 0.438976 | ||||||||
\(905\) | −6.17360 | −0.205218 | ||||||||
\(906\) | 5.51381 | 0.183184 | ||||||||
\(907\) | 33.0754 | 1.09825 | 0.549125 | − | 0.835740i | \(-0.314961\pi\) | ||||
0.549125 | + | 0.835740i | \(0.314961\pi\) | |||||||
\(908\) | −20.6788 | −0.686251 | ||||||||
\(909\) | −8.69672 | −0.288452 | ||||||||
\(910\) | −0.338849 | −0.0112327 | ||||||||
\(911\) | −48.6164 | −1.61073 | −0.805366 | − | 0.592777i | \(-0.798031\pi\) | ||||
−0.805366 | + | 0.592777i | \(0.798031\pi\) | |||||||
\(912\) | 7.11113 | 0.235473 | ||||||||
\(913\) | −38.4705 | −1.27319 | ||||||||
\(914\) | 8.52552 | 0.281999 | ||||||||
\(915\) | −2.09464 | −0.0692466 | ||||||||
\(916\) | 22.0915 | 0.729923 | ||||||||
\(917\) | −15.1820 | −0.501353 | ||||||||
\(918\) | 1.44712 | 0.0477620 | ||||||||
\(919\) | −54.9938 | −1.81408 | −0.907040 | − | 0.421045i | \(-0.861663\pi\) | ||||
−0.907040 | + | 0.421045i | \(0.861663\pi\) | |||||||
\(920\) | 1.02915 | 0.0339299 | ||||||||
\(921\) | 6.06291 | 0.199780 | ||||||||
\(922\) | −5.36086 | −0.176551 | ||||||||
\(923\) | 1.30716 | 0.0430256 | ||||||||
\(924\) | 7.51873 | 0.247348 | ||||||||
\(925\) | 1.36503 | 0.0448819 | ||||||||
\(926\) | 13.6148 | 0.447409 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | 23.9955 | 0.787691 | ||||||||
\(929\) | 20.6765 | 0.678375 | 0.339187 | − | 0.940719i | \(-0.389848\pi\) | ||||
0.339187 | + | 0.940719i | \(0.389848\pi\) | |||||||
\(930\) | 1.79434 | 0.0588387 | ||||||||
\(931\) | 11.7994 | 0.386709 | ||||||||
\(932\) | 23.0398 | 0.754694 | ||||||||
\(933\) | −21.4358 | −0.701777 | ||||||||
\(934\) | 6.26407 | 0.204967 | ||||||||
\(935\) | −7.17563 | −0.234668 | ||||||||
\(936\) | −1.49831 | −0.0489738 | ||||||||
\(937\) | 36.4697 | 1.19141 | 0.595706 | − | 0.803202i | \(-0.296872\pi\) | ||||
0.595706 | + | 0.803202i | \(0.296872\pi\) | |||||||
\(938\) | 0.650766 | 0.0212483 | ||||||||
\(939\) | −22.0335 | −0.719037 | ||||||||
\(940\) | 11.9583 | 0.390036 | ||||||||
\(941\) | −37.1490 | −1.21102 | −0.605512 | − | 0.795836i | \(-0.707032\pi\) | ||||
−0.605512 | + | 0.795836i | \(0.707032\pi\) | |||||||
\(942\) | 7.51729 | 0.244927 | ||||||||
\(943\) | 2.15898 | 0.0703061 | ||||||||
\(944\) | 31.1329 | 1.01329 | ||||||||
\(945\) | 0.870336 | 0.0283120 | ||||||||
\(946\) | −2.40060 | −0.0780502 | ||||||||
\(947\) | 18.1906 | 0.591116 | 0.295558 | − | 0.955325i | \(-0.404494\pi\) | ||||
0.295558 | + | 0.955325i | \(0.404494\pi\) | |||||||
\(948\) | −3.06337 | −0.0994937 | ||||||||
\(949\) | −10.2716 | −0.333429 | ||||||||
\(950\) | −4.07879 | −0.132333 | ||||||||
\(951\) | −5.82156 | −0.188777 | ||||||||
\(952\) | −7.54162 | −0.244425 | ||||||||
\(953\) | 52.7833 | 1.70982 | 0.854909 | − | 0.518778i | \(-0.173613\pi\) | ||||
0.854909 | + | 0.518778i | \(0.173613\pi\) | |||||||
\(954\) | 3.95032 | 0.127896 | ||||||||
\(955\) | −0.0382761 | −0.00123859 | ||||||||
\(956\) | −27.4931 | −0.889191 | ||||||||
\(957\) | −17.1252 | −0.553580 | ||||||||
\(958\) | −8.17929 | −0.264261 | ||||||||
\(959\) | 18.8637 | 0.609142 | ||||||||
\(960\) | 2.94896 | 0.0951774 | ||||||||
\(961\) | 20.4223 | 0.658785 | ||||||||
\(962\) | −0.115861 | −0.00373552 | ||||||||
\(963\) | −0.866480 | −0.0279219 | ||||||||
\(964\) | −39.6362 | −1.27659 | ||||||||
\(965\) | −11.7873 | −0.379446 | ||||||||
\(966\) | −0.563459 | −0.0181290 | ||||||||
\(967\) | 28.3632 | 0.912100 | 0.456050 | − | 0.889954i | \(-0.349264\pi\) | ||||
0.456050 | + | 0.889954i | \(0.349264\pi\) | |||||||
\(968\) | −2.96276 | −0.0952267 | ||||||||
\(969\) | 8.48934 | 0.272717 | ||||||||
\(970\) | 1.08180 | 0.0347346 | ||||||||
\(971\) | 54.2490 | 1.74093 | 0.870467 | − | 0.492226i | \(-0.163817\pi\) | ||||
0.870467 | + | 0.492226i | \(0.163817\pi\) | |||||||
\(972\) | 1.84842 | 0.0592881 | ||||||||
\(973\) | −5.83546 | −0.187076 | ||||||||
\(974\) | 5.66176 | 0.181414 | ||||||||
\(975\) | −4.58693 | −0.146899 | ||||||||
\(976\) | 10.1473 | 0.324806 | ||||||||
\(977\) | 6.90212 | 0.220818 | 0.110409 | − | 0.993886i | \(-0.464784\pi\) | ||||
0.110409 | + | 0.993886i | \(0.464784\pi\) | |||||||
\(978\) | −2.49844 | −0.0798912 | ||||||||
\(979\) | 33.8190 | 1.08086 | ||||||||
\(980\) | 6.13734 | 0.196050 | ||||||||
\(981\) | −10.7007 | −0.341648 | ||||||||
\(982\) | −13.2992 | −0.424395 | ||||||||
\(983\) | 1.20088 | 0.0383023 | 0.0191511 | − | 0.999817i | \(-0.493904\pi\) | ||||
0.0191511 | + | 0.999817i | \(0.493904\pi\) | |||||||
\(984\) | −3.02681 | −0.0964912 | ||||||||
\(985\) | −1.41671 | −0.0451403 | ||||||||
\(986\) | 8.25040 | 0.262746 | ||||||||
\(987\) | −13.6313 | −0.433888 | ||||||||
\(988\) | −4.22173 | −0.134311 | ||||||||
\(989\) | −2.19381 | −0.0697592 | ||||||||
\(990\) | 0.751614 | 0.0238879 | ||||||||
\(991\) | −27.6817 | −0.879339 | −0.439669 | − | 0.898160i | \(-0.644904\pi\) | ||||
−0.439669 | + | 0.898160i | \(0.644904\pi\) | |||||||
\(992\) | −30.1811 | −0.958250 | ||||||||
\(993\) | 9.74349 | 0.309200 | ||||||||
\(994\) | −0.689168 | −0.0218591 | ||||||||
\(995\) | 15.0415 | 0.476849 | ||||||||
\(996\) | 23.6736 | 0.750125 | ||||||||
\(997\) | −17.3294 | −0.548829 | −0.274415 | − | 0.961611i | \(-0.588484\pi\) | ||||
−0.274415 | + | 0.961611i | \(0.588484\pi\) | |||||||
\(998\) | 2.26076 | 0.0715630 | ||||||||
\(999\) | 0.297591 | 0.00941536 |
(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 | 4017.2.a.g.1.11 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4017.2.a.g.1.11 | ✓ | 24 | 1.1 | even | 1 | trivial |