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 | 1.13 | ||
Root | \(-2.41893\) 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 | ||||||||
\(5\) | 2.41893 | 1.08178 | 0.540890 | − | 0.841093i | \(-0.318088\pi\) | ||||
0.540890 | + | 0.841093i | \(0.318088\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −0.257176 | −0.0972034 | −0.0486017 | − | 0.998818i | \(-0.515476\pi\) | ||||
−0.0486017 | + | 0.998818i | \(0.515476\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.41893 | −0.764934 | ||||||||
\(11\) | 1.56925 | 0.473146 | 0.236573 | − | 0.971614i | \(-0.423976\pi\) | ||||
0.236573 | + | 0.971614i | \(0.423976\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0.257176 | 0.0687332 | ||||||||
\(15\) | −2.41893 | −0.624566 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.26992 | 1.03561 | 0.517804 | − | 0.855500i | \(-0.326750\pi\) | ||||
0.517804 | + | 0.855500i | \(0.326750\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 1.38482 | 0.317699 | 0.158849 | − | 0.987303i | \(-0.449222\pi\) | ||||
0.158849 | + | 0.987303i | \(0.449222\pi\) | |||||||
\(20\) | 2.41893 | 0.540890 | ||||||||
\(21\) | 0.257176 | 0.0561204 | ||||||||
\(22\) | −1.56925 | −0.334565 | ||||||||
\(23\) | 8.56848 | 1.78665 | 0.893326 | − | 0.449409i | \(-0.148365\pi\) | ||||
0.893326 | + | 0.449409i | \(0.148365\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0.851240 | 0.170248 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.257176 | −0.0486017 | ||||||||
\(29\) | 10.3349 | 1.91915 | 0.959573 | − | 0.281459i | \(-0.0908182\pi\) | ||||
0.959573 | + | 0.281459i | \(0.0908182\pi\) | |||||||
\(30\) | 2.41893 | 0.441635 | ||||||||
\(31\) | 7.55065 | 1.35614 | 0.678069 | − | 0.734998i | \(-0.262817\pi\) | ||||
0.678069 | + | 0.734998i | \(0.262817\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.56925 | −0.273171 | ||||||||
\(34\) | −4.26992 | −0.732285 | ||||||||
\(35\) | −0.622092 | −0.105153 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −2.82902 | −0.465088 | −0.232544 | − | 0.972586i | \(-0.574705\pi\) | ||||
−0.232544 | + | 0.972586i | \(0.574705\pi\) | |||||||
\(38\) | −1.38482 | −0.224647 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −2.41893 | −0.382467 | ||||||||
\(41\) | 10.3277 | 1.61291 | 0.806455 | − | 0.591296i | \(-0.201384\pi\) | ||||
0.806455 | + | 0.591296i | \(0.201384\pi\) | |||||||
\(42\) | −0.257176 | −0.0396831 | ||||||||
\(43\) | −6.51464 | −0.993474 | −0.496737 | − | 0.867901i | \(-0.665469\pi\) | ||||
−0.496737 | + | 0.867901i | \(0.665469\pi\) | |||||||
\(44\) | 1.56925 | 0.236573 | ||||||||
\(45\) | 2.41893 | 0.360593 | ||||||||
\(46\) | −8.56848 | −1.26335 | ||||||||
\(47\) | 9.53966 | 1.39150 | 0.695751 | − | 0.718283i | \(-0.255072\pi\) | ||||
0.695751 | + | 0.718283i | \(0.255072\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.93386 | −0.990552 | ||||||||
\(50\) | −0.851240 | −0.120384 | ||||||||
\(51\) | −4.26992 | −0.597908 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | −12.5020 | −1.71728 | −0.858640 | − | 0.512580i | \(-0.828690\pi\) | ||||
−0.858640 | + | 0.512580i | \(0.828690\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 3.79591 | 0.511840 | ||||||||
\(56\) | 0.257176 | 0.0343666 | ||||||||
\(57\) | −1.38482 | −0.183423 | ||||||||
\(58\) | −10.3349 | −1.35704 | ||||||||
\(59\) | −4.00889 | −0.521913 | −0.260957 | − | 0.965351i | \(-0.584038\pi\) | ||||
−0.260957 | + | 0.965351i | \(0.584038\pi\) | |||||||
\(60\) | −2.41893 | −0.312283 | ||||||||
\(61\) | 12.4048 | 1.58827 | 0.794134 | − | 0.607743i | \(-0.207925\pi\) | ||||
0.794134 | + | 0.607743i | \(0.207925\pi\) | |||||||
\(62\) | −7.55065 | −0.958934 | ||||||||
\(63\) | −0.257176 | −0.0324011 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.41893 | 0.300032 | ||||||||
\(66\) | 1.56925 | 0.193161 | ||||||||
\(67\) | 9.28134 | 1.13390 | 0.566948 | − | 0.823753i | \(-0.308124\pi\) | ||||
0.566948 | + | 0.823753i | \(0.308124\pi\) | |||||||
\(68\) | 4.26992 | 0.517804 | ||||||||
\(69\) | −8.56848 | −1.03152 | ||||||||
\(70\) | 0.622092 | 0.0743542 | ||||||||
\(71\) | −0.286350 | −0.0339834 | −0.0169917 | − | 0.999856i | \(-0.505409\pi\) | ||||
−0.0169917 | + | 0.999856i | \(0.505409\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −15.7947 | −1.84863 | −0.924313 | − | 0.381635i | \(-0.875361\pi\) | ||||
−0.924313 | + | 0.381635i | \(0.875361\pi\) | |||||||
\(74\) | 2.82902 | 0.328867 | ||||||||
\(75\) | −0.851240 | −0.0982928 | ||||||||
\(76\) | 1.38482 | 0.158849 | ||||||||
\(77\) | −0.403573 | −0.0459914 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 9.06214 | 1.01957 | 0.509785 | − | 0.860302i | \(-0.329725\pi\) | ||||
0.509785 | + | 0.860302i | \(0.329725\pi\) | |||||||
\(80\) | 2.41893 | 0.270445 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −10.3277 | −1.14050 | ||||||||
\(83\) | −6.84929 | −0.751808 | −0.375904 | − | 0.926659i | \(-0.622668\pi\) | ||||
−0.375904 | + | 0.926659i | \(0.622668\pi\) | |||||||
\(84\) | 0.257176 | 0.0280602 | ||||||||
\(85\) | 10.3286 | 1.12030 | ||||||||
\(86\) | 6.51464 | 0.702492 | ||||||||
\(87\) | −10.3349 | −1.10802 | ||||||||
\(88\) | −1.56925 | −0.167282 | ||||||||
\(89\) | −14.0981 | −1.49440 | −0.747199 | − | 0.664600i | \(-0.768602\pi\) | ||||
−0.747199 | + | 0.664600i | \(0.768602\pi\) | |||||||
\(90\) | −2.41893 | −0.254978 | ||||||||
\(91\) | −0.257176 | −0.0269594 | ||||||||
\(92\) | 8.56848 | 0.893326 | ||||||||
\(93\) | −7.55065 | −0.782966 | ||||||||
\(94\) | −9.53966 | −0.983940 | ||||||||
\(95\) | 3.34978 | 0.343680 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 13.3988 | 1.36044 | 0.680220 | − | 0.733008i | \(-0.261884\pi\) | ||||
0.680220 | + | 0.733008i | \(0.261884\pi\) | |||||||
\(98\) | 6.93386 | 0.700426 | ||||||||
\(99\) | 1.56925 | 0.157715 | ||||||||
\(100\) | 0.851240 | 0.0851240 | ||||||||
\(101\) | −3.46177 | −0.344459 | −0.172229 | − | 0.985057i | \(-0.555097\pi\) | ||||
−0.172229 | + | 0.985057i | \(0.555097\pi\) | |||||||
\(102\) | 4.26992 | 0.422785 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0.622092 | 0.0607099 | ||||||||
\(106\) | 12.5020 | 1.21430 | ||||||||
\(107\) | −14.7757 | −1.42842 | −0.714209 | − | 0.699932i | \(-0.753213\pi\) | ||||
−0.714209 | + | 0.699932i | \(0.753213\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −7.20934 | −0.690530 | −0.345265 | − | 0.938505i | \(-0.612211\pi\) | ||||
−0.345265 | + | 0.938505i | \(0.612211\pi\) | |||||||
\(110\) | −3.79591 | −0.361926 | ||||||||
\(111\) | 2.82902 | 0.268519 | ||||||||
\(112\) | −0.257176 | −0.0243008 | ||||||||
\(113\) | 9.35198 | 0.879760 | 0.439880 | − | 0.898057i | \(-0.355021\pi\) | ||||
0.439880 | + | 0.898057i | \(0.355021\pi\) | |||||||
\(114\) | 1.38482 | 0.129700 | ||||||||
\(115\) | 20.7266 | 1.93276 | ||||||||
\(116\) | 10.3349 | 0.959573 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 4.00889 | 0.369048 | ||||||||
\(119\) | −1.09812 | −0.100664 | ||||||||
\(120\) | 2.41893 | 0.220817 | ||||||||
\(121\) | −8.53746 | −0.776133 | ||||||||
\(122\) | −12.4048 | −1.12307 | ||||||||
\(123\) | −10.3277 | −0.931214 | ||||||||
\(124\) | 7.55065 | 0.678069 | ||||||||
\(125\) | −10.0356 | −0.897609 | ||||||||
\(126\) | 0.257176 | 0.0229111 | ||||||||
\(127\) | −10.9282 | −0.969723 | −0.484862 | − | 0.874591i | \(-0.661130\pi\) | ||||
−0.484862 | + | 0.874591i | \(0.661130\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 6.51464 | 0.573582 | ||||||||
\(130\) | −2.41893 | −0.212155 | ||||||||
\(131\) | 19.8225 | 1.73190 | 0.865949 | − | 0.500132i | \(-0.166715\pi\) | ||||
0.865949 | + | 0.500132i | \(0.166715\pi\) | |||||||
\(132\) | −1.56925 | −0.136586 | ||||||||
\(133\) | −0.356141 | −0.0308814 | ||||||||
\(134\) | −9.28134 | −0.801786 | ||||||||
\(135\) | −2.41893 | −0.208189 | ||||||||
\(136\) | −4.26992 | −0.366142 | ||||||||
\(137\) | −7.15001 | −0.610867 | −0.305433 | − | 0.952213i | \(-0.598801\pi\) | ||||
−0.305433 | + | 0.952213i | \(0.598801\pi\) | |||||||
\(138\) | 8.56848 | 0.729398 | ||||||||
\(139\) | 3.85007 | 0.326559 | 0.163279 | − | 0.986580i | \(-0.447793\pi\) | ||||
0.163279 | + | 0.986580i | \(0.447793\pi\) | |||||||
\(140\) | −0.622092 | −0.0525763 | ||||||||
\(141\) | −9.53966 | −0.803384 | ||||||||
\(142\) | 0.286350 | 0.0240299 | ||||||||
\(143\) | 1.56925 | 0.131227 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 24.9995 | 2.07609 | ||||||||
\(146\) | 15.7947 | 1.30718 | ||||||||
\(147\) | 6.93386 | 0.571895 | ||||||||
\(148\) | −2.82902 | −0.232544 | ||||||||
\(149\) | −10.1252 | −0.829490 | −0.414745 | − | 0.909938i | \(-0.636129\pi\) | ||||
−0.414745 | + | 0.909938i | \(0.636129\pi\) | |||||||
\(150\) | 0.851240 | 0.0695035 | ||||||||
\(151\) | 15.0201 | 1.22232 | 0.611159 | − | 0.791508i | \(-0.290704\pi\) | ||||
0.611159 | + | 0.791508i | \(0.290704\pi\) | |||||||
\(152\) | −1.38482 | −0.112323 | ||||||||
\(153\) | 4.26992 | 0.345202 | ||||||||
\(154\) | 0.403573 | 0.0325208 | ||||||||
\(155\) | 18.2645 | 1.46704 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | 22.4063 | 1.78822 | 0.894109 | − | 0.447849i | \(-0.147810\pi\) | ||||
0.894109 | + | 0.447849i | \(0.147810\pi\) | |||||||
\(158\) | −9.06214 | −0.720946 | ||||||||
\(159\) | 12.5020 | 0.991472 | ||||||||
\(160\) | −2.41893 | −0.191234 | ||||||||
\(161\) | −2.20361 | −0.173669 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 3.77020 | 0.295305 | 0.147652 | − | 0.989039i | \(-0.452828\pi\) | ||||
0.147652 | + | 0.989039i | \(0.452828\pi\) | |||||||
\(164\) | 10.3277 | 0.806455 | ||||||||
\(165\) | −3.79591 | −0.295511 | ||||||||
\(166\) | 6.84929 | 0.531608 | ||||||||
\(167\) | 11.1628 | 0.863801 | 0.431900 | − | 0.901921i | \(-0.357843\pi\) | ||||
0.431900 | + | 0.901921i | \(0.357843\pi\) | |||||||
\(168\) | −0.257176 | −0.0198416 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −10.3286 | −0.792171 | ||||||||
\(171\) | 1.38482 | 0.105900 | ||||||||
\(172\) | −6.51464 | −0.496737 | ||||||||
\(173\) | −13.9420 | −1.05999 | −0.529994 | − | 0.848001i | \(-0.677806\pi\) | ||||
−0.529994 | + | 0.848001i | \(0.677806\pi\) | |||||||
\(174\) | 10.3349 | 0.783488 | ||||||||
\(175\) | −0.218919 | −0.0165487 | ||||||||
\(176\) | 1.56925 | 0.118287 | ||||||||
\(177\) | 4.00889 | 0.301327 | ||||||||
\(178\) | 14.0981 | 1.05670 | ||||||||
\(179\) | −1.46855 | −0.109765 | −0.0548824 | − | 0.998493i | \(-0.517478\pi\) | ||||
−0.0548824 | + | 0.998493i | \(0.517478\pi\) | |||||||
\(180\) | 2.41893 | 0.180297 | ||||||||
\(181\) | −16.8574 | −1.25300 | −0.626499 | − | 0.779422i | \(-0.715513\pi\) | ||||
−0.626499 | + | 0.779422i | \(0.715513\pi\) | |||||||
\(182\) | 0.257176 | 0.0190631 | ||||||||
\(183\) | −12.4048 | −0.916987 | ||||||||
\(184\) | −8.56848 | −0.631677 | ||||||||
\(185\) | −6.84321 | −0.503123 | ||||||||
\(186\) | 7.55065 | 0.553641 | ||||||||
\(187\) | 6.70056 | 0.489993 | ||||||||
\(188\) | 9.53966 | 0.695751 | ||||||||
\(189\) | 0.257176 | 0.0187068 | ||||||||
\(190\) | −3.34978 | −0.243018 | ||||||||
\(191\) | 10.5816 | 0.765660 | 0.382830 | − | 0.923819i | \(-0.374949\pi\) | ||||
0.382830 | + | 0.923819i | \(0.374949\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 6.61573 | 0.476210 | 0.238105 | − | 0.971239i | \(-0.423474\pi\) | ||||
0.238105 | + | 0.971239i | \(0.423474\pi\) | |||||||
\(194\) | −13.3988 | −0.961976 | ||||||||
\(195\) | −2.41893 | −0.173223 | ||||||||
\(196\) | −6.93386 | −0.495276 | ||||||||
\(197\) | −18.2594 | −1.30093 | −0.650463 | − | 0.759538i | \(-0.725425\pi\) | ||||
−0.650463 | + | 0.759538i | \(0.725425\pi\) | |||||||
\(198\) | −1.56925 | −0.111522 | ||||||||
\(199\) | −5.58471 | −0.395890 | −0.197945 | − | 0.980213i | \(-0.563427\pi\) | ||||
−0.197945 | + | 0.980213i | \(0.563427\pi\) | |||||||
\(200\) | −0.851240 | −0.0601918 | ||||||||
\(201\) | −9.28134 | −0.654655 | ||||||||
\(202\) | 3.46177 | 0.243569 | ||||||||
\(203\) | −2.65789 | −0.186548 | ||||||||
\(204\) | −4.26992 | −0.298954 | ||||||||
\(205\) | 24.9819 | 1.74481 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | 8.56848 | 0.595551 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 2.17312 | 0.150318 | ||||||||
\(210\) | −0.622092 | −0.0429284 | ||||||||
\(211\) | −15.0750 | −1.03780 | −0.518902 | − | 0.854834i | \(-0.673659\pi\) | ||||
−0.518902 | + | 0.854834i | \(0.673659\pi\) | |||||||
\(212\) | −12.5020 | −0.858640 | ||||||||
\(213\) | 0.286350 | 0.0196204 | ||||||||
\(214\) | 14.7757 | 1.01004 | ||||||||
\(215\) | −15.7585 | −1.07472 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −1.94185 | −0.131821 | ||||||||
\(218\) | 7.20934 | 0.488278 | ||||||||
\(219\) | 15.7947 | 1.06730 | ||||||||
\(220\) | 3.79591 | 0.255920 | ||||||||
\(221\) | 4.26992 | 0.287226 | ||||||||
\(222\) | −2.82902 | −0.189871 | ||||||||
\(223\) | −22.1745 | −1.48492 | −0.742458 | − | 0.669892i | \(-0.766340\pi\) | ||||
−0.742458 | + | 0.669892i | \(0.766340\pi\) | |||||||
\(224\) | 0.257176 | 0.0171833 | ||||||||
\(225\) | 0.851240 | 0.0567493 | ||||||||
\(226\) | −9.35198 | −0.622084 | ||||||||
\(227\) | 15.2505 | 1.01221 | 0.506107 | − | 0.862471i | \(-0.331084\pi\) | ||||
0.506107 | + | 0.862471i | \(0.331084\pi\) | |||||||
\(228\) | −1.38482 | −0.0917117 | ||||||||
\(229\) | −2.61103 | −0.172542 | −0.0862708 | − | 0.996272i | \(-0.527495\pi\) | ||||
−0.0862708 | + | 0.996272i | \(0.527495\pi\) | |||||||
\(230\) | −20.7266 | −1.36667 | ||||||||
\(231\) | 0.403573 | 0.0265531 | ||||||||
\(232\) | −10.3349 | −0.678521 | ||||||||
\(233\) | 12.0453 | 0.789112 | 0.394556 | − | 0.918872i | \(-0.370898\pi\) | ||||
0.394556 | + | 0.918872i | \(0.370898\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | 23.0758 | 1.50530 | ||||||||
\(236\) | −4.00889 | −0.260957 | ||||||||
\(237\) | −9.06214 | −0.588650 | ||||||||
\(238\) | 1.09812 | 0.0711805 | ||||||||
\(239\) | −16.0683 | −1.03937 | −0.519685 | − | 0.854358i | \(-0.673951\pi\) | ||||
−0.519685 | + | 0.854358i | \(0.673951\pi\) | |||||||
\(240\) | −2.41893 | −0.156141 | ||||||||
\(241\) | 3.41064 | 0.219699 | 0.109849 | − | 0.993948i | \(-0.464963\pi\) | ||||
0.109849 | + | 0.993948i | \(0.464963\pi\) | |||||||
\(242\) | 8.53746 | 0.548809 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 12.4048 | 0.794134 | ||||||||
\(245\) | −16.7725 | −1.07156 | ||||||||
\(246\) | 10.3277 | 0.658467 | ||||||||
\(247\) | 1.38482 | 0.0881137 | ||||||||
\(248\) | −7.55065 | −0.479467 | ||||||||
\(249\) | 6.84929 | 0.434056 | ||||||||
\(250\) | 10.0356 | 0.634705 | ||||||||
\(251\) | 18.3812 | 1.16021 | 0.580106 | − | 0.814541i | \(-0.303011\pi\) | ||||
0.580106 | + | 0.814541i | \(0.303011\pi\) | |||||||
\(252\) | −0.257176 | −0.0162006 | ||||||||
\(253\) | 13.4461 | 0.845348 | ||||||||
\(254\) | 10.9282 | 0.685698 | ||||||||
\(255\) | −10.3286 | −0.646805 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 27.4438 | 1.71190 | 0.855950 | − | 0.517059i | \(-0.172973\pi\) | ||||
0.855950 | + | 0.517059i | \(0.172973\pi\) | |||||||
\(258\) | −6.51464 | −0.405584 | ||||||||
\(259\) | 0.727555 | 0.0452081 | ||||||||
\(260\) | 2.41893 | 0.150016 | ||||||||
\(261\) | 10.3349 | 0.639716 | ||||||||
\(262\) | −19.8225 | −1.22464 | ||||||||
\(263\) | −24.1083 | −1.48658 | −0.743290 | − | 0.668969i | \(-0.766736\pi\) | ||||
−0.743290 | + | 0.668969i | \(0.766736\pi\) | |||||||
\(264\) | 1.56925 | 0.0965805 | ||||||||
\(265\) | −30.2415 | −1.85772 | ||||||||
\(266\) | 0.356141 | 0.0218364 | ||||||||
\(267\) | 14.0981 | 0.862791 | ||||||||
\(268\) | 9.28134 | 0.566948 | ||||||||
\(269\) | −11.7471 | −0.716233 | −0.358117 | − | 0.933677i | \(-0.616581\pi\) | ||||
−0.358117 | + | 0.933677i | \(0.616581\pi\) | |||||||
\(270\) | 2.41893 | 0.147212 | ||||||||
\(271\) | 20.2824 | 1.23207 | 0.616035 | − | 0.787719i | \(-0.288738\pi\) | ||||
0.616035 | + | 0.787719i | \(0.288738\pi\) | |||||||
\(272\) | 4.26992 | 0.258902 | ||||||||
\(273\) | 0.257176 | 0.0155650 | ||||||||
\(274\) | 7.15001 | 0.431948 | ||||||||
\(275\) | 1.33581 | 0.0805522 | ||||||||
\(276\) | −8.56848 | −0.515762 | ||||||||
\(277\) | −26.9165 | −1.61725 | −0.808627 | − | 0.588322i | \(-0.799789\pi\) | ||||
−0.808627 | + | 0.588322i | \(0.799789\pi\) | |||||||
\(278\) | −3.85007 | −0.230912 | ||||||||
\(279\) | 7.55065 | 0.452046 | ||||||||
\(280\) | 0.622092 | 0.0371771 | ||||||||
\(281\) | −18.6951 | −1.11526 | −0.557628 | − | 0.830091i | \(-0.688289\pi\) | ||||
−0.557628 | + | 0.830091i | \(0.688289\pi\) | |||||||
\(282\) | 9.53966 | 0.568078 | ||||||||
\(283\) | −23.9981 | −1.42654 | −0.713270 | − | 0.700889i | \(-0.752787\pi\) | ||||
−0.713270 | + | 0.700889i | \(0.752787\pi\) | |||||||
\(284\) | −0.286350 | −0.0169917 | ||||||||
\(285\) | −3.34978 | −0.198424 | ||||||||
\(286\) | −1.56925 | −0.0927916 | ||||||||
\(287\) | −2.65603 | −0.156780 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 1.23219 | 0.0724819 | ||||||||
\(290\) | −24.9995 | −1.46802 | ||||||||
\(291\) | −13.3988 | −0.785450 | ||||||||
\(292\) | −15.7947 | −0.924313 | ||||||||
\(293\) | −16.2925 | −0.951815 | −0.475908 | − | 0.879495i | \(-0.657880\pi\) | ||||
−0.475908 | + | 0.879495i | \(0.657880\pi\) | |||||||
\(294\) | −6.93386 | −0.404391 | ||||||||
\(295\) | −9.69724 | −0.564595 | ||||||||
\(296\) | 2.82902 | 0.164433 | ||||||||
\(297\) | −1.56925 | −0.0910570 | ||||||||
\(298\) | 10.1252 | 0.586538 | ||||||||
\(299\) | 8.56848 | 0.495528 | ||||||||
\(300\) | −0.851240 | −0.0491464 | ||||||||
\(301\) | 1.67541 | 0.0965690 | ||||||||
\(302\) | −15.0201 | −0.864309 | ||||||||
\(303\) | 3.46177 | 0.198873 | ||||||||
\(304\) | 1.38482 | 0.0794247 | ||||||||
\(305\) | 30.0063 | 1.71816 | ||||||||
\(306\) | −4.26992 | −0.244095 | ||||||||
\(307\) | −9.48598 | −0.541393 | −0.270697 | − | 0.962665i | \(-0.587254\pi\) | ||||
−0.270697 | + | 0.962665i | \(0.587254\pi\) | |||||||
\(308\) | −0.403573 | −0.0229957 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | −18.2645 | −1.03736 | ||||||||
\(311\) | 5.00459 | 0.283784 | 0.141892 | − | 0.989882i | \(-0.454681\pi\) | ||||
0.141892 | + | 0.989882i | \(0.454681\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 17.0166 | 0.961835 | 0.480917 | − | 0.876766i | \(-0.340304\pi\) | ||||
0.480917 | + | 0.876766i | \(0.340304\pi\) | |||||||
\(314\) | −22.4063 | −1.26446 | ||||||||
\(315\) | −0.622092 | −0.0350509 | ||||||||
\(316\) | 9.06214 | 0.509785 | ||||||||
\(317\) | −23.2420 | −1.30540 | −0.652701 | − | 0.757615i | \(-0.726364\pi\) | ||||
−0.652701 | + | 0.757615i | \(0.726364\pi\) | |||||||
\(318\) | −12.5020 | −0.701076 | ||||||||
\(319\) | 16.2181 | 0.908037 | ||||||||
\(320\) | 2.41893 | 0.135223 | ||||||||
\(321\) | 14.7757 | 0.824698 | ||||||||
\(322\) | 2.20361 | 0.122802 | ||||||||
\(323\) | 5.91305 | 0.329011 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0.851240 | 0.0472183 | ||||||||
\(326\) | −3.77020 | −0.208812 | ||||||||
\(327\) | 7.20934 | 0.398678 | ||||||||
\(328\) | −10.3277 | −0.570250 | ||||||||
\(329\) | −2.45337 | −0.135259 | ||||||||
\(330\) | 3.79591 | 0.208958 | ||||||||
\(331\) | −0.342089 | −0.0188029 | −0.00940146 | − | 0.999956i | \(-0.502993\pi\) | ||||
−0.00940146 | + | 0.999956i | \(0.502993\pi\) | |||||||
\(332\) | −6.84929 | −0.375904 | ||||||||
\(333\) | −2.82902 | −0.155029 | ||||||||
\(334\) | −11.1628 | −0.610799 | ||||||||
\(335\) | 22.4509 | 1.22663 | ||||||||
\(336\) | 0.257176 | 0.0140301 | ||||||||
\(337\) | 25.7894 | 1.40484 | 0.702418 | − | 0.711764i | \(-0.252104\pi\) | ||||
0.702418 | + | 0.711764i | \(0.252104\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | −9.35198 | −0.507930 | ||||||||
\(340\) | 10.3286 | 0.560150 | ||||||||
\(341\) | 11.8488 | 0.641651 | ||||||||
\(342\) | −1.38482 | −0.0748823 | ||||||||
\(343\) | 3.58345 | 0.193488 | ||||||||
\(344\) | 6.51464 | 0.351246 | ||||||||
\(345\) | −20.7266 | −1.11588 | ||||||||
\(346\) | 13.9420 | 0.749525 | ||||||||
\(347\) | 18.4618 | 0.991079 | 0.495540 | − | 0.868585i | \(-0.334970\pi\) | ||||
0.495540 | + | 0.868585i | \(0.334970\pi\) | |||||||
\(348\) | −10.3349 | −0.554010 | ||||||||
\(349\) | −20.4645 | −1.09544 | −0.547719 | − | 0.836662i | \(-0.684504\pi\) | ||||
−0.547719 | + | 0.836662i | \(0.684504\pi\) | |||||||
\(350\) | 0.218919 | 0.0117017 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −1.56925 | −0.0836412 | ||||||||
\(353\) | 10.0583 | 0.535351 | 0.267676 | − | 0.963509i | \(-0.413744\pi\) | ||||
0.267676 | + | 0.963509i | \(0.413744\pi\) | |||||||
\(354\) | −4.00889 | −0.213070 | ||||||||
\(355\) | −0.692661 | −0.0367626 | ||||||||
\(356\) | −14.0981 | −0.747199 | ||||||||
\(357\) | 1.09812 | 0.0581187 | ||||||||
\(358\) | 1.46855 | 0.0776155 | ||||||||
\(359\) | 14.8765 | 0.785149 | 0.392575 | − | 0.919720i | \(-0.371584\pi\) | ||||
0.392575 | + | 0.919720i | \(0.371584\pi\) | |||||||
\(360\) | −2.41893 | −0.127489 | ||||||||
\(361\) | −17.0823 | −0.899068 | ||||||||
\(362\) | 16.8574 | 0.886004 | ||||||||
\(363\) | 8.53746 | 0.448100 | ||||||||
\(364\) | −0.257176 | −0.0134797 | ||||||||
\(365\) | −38.2063 | −1.99981 | ||||||||
\(366\) | 12.4048 | 0.648407 | ||||||||
\(367\) | −10.7987 | −0.563688 | −0.281844 | − | 0.959460i | \(-0.590946\pi\) | ||||
−0.281844 | + | 0.959460i | \(0.590946\pi\) | |||||||
\(368\) | 8.56848 | 0.446663 | ||||||||
\(369\) | 10.3277 | 0.537636 | ||||||||
\(370\) | 6.84321 | 0.355761 | ||||||||
\(371\) | 3.21521 | 0.166925 | ||||||||
\(372\) | −7.55065 | −0.391483 | ||||||||
\(373\) | 27.3303 | 1.41511 | 0.707554 | − | 0.706659i | \(-0.249799\pi\) | ||||
0.707554 | + | 0.706659i | \(0.249799\pi\) | |||||||
\(374\) | −6.70056 | −0.346478 | ||||||||
\(375\) | 10.0356 | 0.518235 | ||||||||
\(376\) | −9.53966 | −0.491970 | ||||||||
\(377\) | 10.3349 | 0.532276 | ||||||||
\(378\) | −0.257176 | −0.0132277 | ||||||||
\(379\) | 8.62300 | 0.442934 | 0.221467 | − | 0.975168i | \(-0.428916\pi\) | ||||
0.221467 | + | 0.975168i | \(0.428916\pi\) | |||||||
\(380\) | 3.34978 | 0.171840 | ||||||||
\(381\) | 10.9282 | 0.559870 | ||||||||
\(382\) | −10.5816 | −0.541403 | ||||||||
\(383\) | 5.34302 | 0.273015 | 0.136508 | − | 0.990639i | \(-0.456412\pi\) | ||||
0.136508 | + | 0.990639i | \(0.456412\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −0.976216 | −0.0497526 | ||||||||
\(386\) | −6.61573 | −0.336732 | ||||||||
\(387\) | −6.51464 | −0.331158 | ||||||||
\(388\) | 13.3988 | 0.680220 | ||||||||
\(389\) | −30.3993 | −1.54131 | −0.770654 | − | 0.637254i | \(-0.780070\pi\) | ||||
−0.770654 | + | 0.637254i | \(0.780070\pi\) | |||||||
\(390\) | 2.41893 | 0.122487 | ||||||||
\(391\) | 36.5867 | 1.85027 | ||||||||
\(392\) | 6.93386 | 0.350213 | ||||||||
\(393\) | −19.8225 | −0.999912 | ||||||||
\(394\) | 18.2594 | 0.919893 | ||||||||
\(395\) | 21.9207 | 1.10295 | ||||||||
\(396\) | 1.56925 | 0.0788577 | ||||||||
\(397\) | −35.9897 | −1.80627 | −0.903136 | − | 0.429354i | \(-0.858741\pi\) | ||||
−0.903136 | + | 0.429354i | \(0.858741\pi\) | |||||||
\(398\) | 5.58471 | 0.279936 | ||||||||
\(399\) | 0.356141 | 0.0178294 | ||||||||
\(400\) | 0.851240 | 0.0425620 | ||||||||
\(401\) | −15.2475 | −0.761423 | −0.380712 | − | 0.924694i | \(-0.624321\pi\) | ||||
−0.380712 | + | 0.924694i | \(0.624321\pi\) | |||||||
\(402\) | 9.28134 | 0.462911 | ||||||||
\(403\) | 7.55065 | 0.376125 | ||||||||
\(404\) | −3.46177 | −0.172229 | ||||||||
\(405\) | 2.41893 | 0.120198 | ||||||||
\(406\) | 2.65789 | 0.131909 | ||||||||
\(407\) | −4.43943 | −0.220054 | ||||||||
\(408\) | 4.26992 | 0.211392 | ||||||||
\(409\) | 18.7585 | 0.927550 | 0.463775 | − | 0.885953i | \(-0.346495\pi\) | ||||
0.463775 | + | 0.885953i | \(0.346495\pi\) | |||||||
\(410\) | −24.9819 | −1.23377 | ||||||||
\(411\) | 7.15001 | 0.352684 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | 1.03099 | 0.0507317 | ||||||||
\(414\) | −8.56848 | −0.421118 | ||||||||
\(415\) | −16.5680 | −0.813291 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −3.85007 | −0.188539 | ||||||||
\(418\) | −2.17312 | −0.106291 | ||||||||
\(419\) | 12.8880 | 0.629621 | 0.314811 | − | 0.949154i | \(-0.398059\pi\) | ||||
0.314811 | + | 0.949154i | \(0.398059\pi\) | |||||||
\(420\) | 0.622092 | 0.0303550 | ||||||||
\(421\) | −13.2438 | −0.645462 | −0.322731 | − | 0.946491i | \(-0.604601\pi\) | ||||
−0.322731 | + | 0.946491i | \(0.604601\pi\) | |||||||
\(422\) | 15.0750 | 0.733839 | ||||||||
\(423\) | 9.53966 | 0.463834 | ||||||||
\(424\) | 12.5020 | 0.607150 | ||||||||
\(425\) | 3.63473 | 0.176310 | ||||||||
\(426\) | −0.286350 | −0.0138737 | ||||||||
\(427\) | −3.19021 | −0.154385 | ||||||||
\(428\) | −14.7757 | −0.714209 | ||||||||
\(429\) | −1.56925 | −0.0757640 | ||||||||
\(430\) | 15.7585 | 0.759942 | ||||||||
\(431\) | −13.7422 | −0.661937 | −0.330969 | − | 0.943642i | \(-0.607375\pi\) | ||||
−0.330969 | + | 0.943642i | \(0.607375\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 21.5048 | 1.03346 | 0.516729 | − | 0.856149i | \(-0.327150\pi\) | ||||
0.516729 | + | 0.856149i | \(0.327150\pi\) | |||||||
\(434\) | 1.94185 | 0.0932116 | ||||||||
\(435\) | −24.9995 | −1.19863 | ||||||||
\(436\) | −7.20934 | −0.345265 | ||||||||
\(437\) | 11.8658 | 0.567617 | ||||||||
\(438\) | −15.7947 | −0.754699 | ||||||||
\(439\) | 2.91356 | 0.139057 | 0.0695283 | − | 0.997580i | \(-0.477851\pi\) | ||||
0.0695283 | + | 0.997580i | \(0.477851\pi\) | |||||||
\(440\) | −3.79591 | −0.180963 | ||||||||
\(441\) | −6.93386 | −0.330184 | ||||||||
\(442\) | −4.26992 | −0.203099 | ||||||||
\(443\) | −29.2420 | −1.38933 | −0.694664 | − | 0.719335i | \(-0.744447\pi\) | ||||
−0.694664 | + | 0.719335i | \(0.744447\pi\) | |||||||
\(444\) | 2.82902 | 0.134259 | ||||||||
\(445\) | −34.1024 | −1.61661 | ||||||||
\(446\) | 22.1745 | 1.04999 | ||||||||
\(447\) | 10.1252 | 0.478906 | ||||||||
\(448\) | −0.257176 | −0.0121504 | ||||||||
\(449\) | 34.2300 | 1.61541 | 0.807706 | − | 0.589585i | \(-0.200709\pi\) | ||||
0.807706 | + | 0.589585i | \(0.200709\pi\) | |||||||
\(450\) | −0.851240 | −0.0401279 | ||||||||
\(451\) | 16.2067 | 0.763142 | ||||||||
\(452\) | 9.35198 | 0.439880 | ||||||||
\(453\) | −15.0201 | −0.705706 | ||||||||
\(454\) | −15.2505 | −0.715743 | ||||||||
\(455\) | −0.622092 | −0.0291641 | ||||||||
\(456\) | 1.38482 | 0.0648500 | ||||||||
\(457\) | −4.90047 | −0.229234 | −0.114617 | − | 0.993410i | \(-0.536564\pi\) | ||||
−0.114617 | + | 0.993410i | \(0.536564\pi\) | |||||||
\(458\) | 2.61103 | 0.122005 | ||||||||
\(459\) | −4.26992 | −0.199303 | ||||||||
\(460\) | 20.7266 | 0.966382 | ||||||||
\(461\) | 12.2479 | 0.570443 | 0.285221 | − | 0.958462i | \(-0.407933\pi\) | ||||
0.285221 | + | 0.958462i | \(0.407933\pi\) | |||||||
\(462\) | −0.403573 | −0.0187759 | ||||||||
\(463\) | 33.1408 | 1.54018 | 0.770091 | − | 0.637934i | \(-0.220211\pi\) | ||||
0.770091 | + | 0.637934i | \(0.220211\pi\) | |||||||
\(464\) | 10.3349 | 0.479787 | ||||||||
\(465\) | −18.2645 | −0.846997 | ||||||||
\(466\) | −12.0453 | −0.557987 | ||||||||
\(467\) | −23.1797 | −1.07263 | −0.536314 | − | 0.844019i | \(-0.680184\pi\) | ||||
−0.536314 | + | 0.844019i | \(0.680184\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | −2.38694 | −0.110219 | ||||||||
\(470\) | −23.0758 | −1.06441 | ||||||||
\(471\) | −22.4063 | −1.03243 | ||||||||
\(472\) | 4.00889 | 0.184524 | ||||||||
\(473\) | −10.2231 | −0.470058 | ||||||||
\(474\) | 9.06214 | 0.416238 | ||||||||
\(475\) | 1.17881 | 0.0540876 | ||||||||
\(476\) | −1.09812 | −0.0503322 | ||||||||
\(477\) | −12.5020 | −0.572427 | ||||||||
\(478\) | 16.0683 | 0.734946 | ||||||||
\(479\) | −7.47120 | −0.341368 | −0.170684 | − | 0.985326i | \(-0.554598\pi\) | ||||
−0.170684 | + | 0.985326i | \(0.554598\pi\) | |||||||
\(480\) | 2.41893 | 0.110409 | ||||||||
\(481\) | −2.82902 | −0.128992 | ||||||||
\(482\) | −3.41064 | −0.155351 | ||||||||
\(483\) | 2.20361 | 0.100268 | ||||||||
\(484\) | −8.53746 | −0.388066 | ||||||||
\(485\) | 32.4107 | 1.47170 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −13.0822 | −0.592813 | −0.296406 | − | 0.955062i | \(-0.595788\pi\) | ||||
−0.296406 | + | 0.955062i | \(0.595788\pi\) | |||||||
\(488\) | −12.4048 | −0.561537 | ||||||||
\(489\) | −3.77020 | −0.170494 | ||||||||
\(490\) | 16.7725 | 0.757707 | ||||||||
\(491\) | −29.2439 | −1.31976 | −0.659879 | − | 0.751372i | \(-0.729392\pi\) | ||||
−0.659879 | + | 0.751372i | \(0.729392\pi\) | |||||||
\(492\) | −10.3277 | −0.465607 | ||||||||
\(493\) | 44.1293 | 1.98748 | ||||||||
\(494\) | −1.38482 | −0.0623058 | ||||||||
\(495\) | 3.79591 | 0.170613 | ||||||||
\(496\) | 7.55065 | 0.339034 | ||||||||
\(497\) | 0.0736422 | 0.00330331 | ||||||||
\(498\) | −6.84929 | −0.306924 | ||||||||
\(499\) | 20.8225 | 0.932142 | 0.466071 | − | 0.884747i | \(-0.345669\pi\) | ||||
0.466071 | + | 0.884747i | \(0.345669\pi\) | |||||||
\(500\) | −10.0356 | −0.448805 | ||||||||
\(501\) | −11.1628 | −0.498715 | ||||||||
\(502\) | −18.3812 | −0.820393 | ||||||||
\(503\) | 12.1548 | 0.541957 | 0.270978 | − | 0.962585i | \(-0.412653\pi\) | ||||
0.270978 | + | 0.962585i | \(0.412653\pi\) | |||||||
\(504\) | 0.257176 | 0.0114555 | ||||||||
\(505\) | −8.37379 | −0.372629 | ||||||||
\(506\) | −13.4461 | −0.597751 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −10.9282 | −0.484862 | ||||||||
\(509\) | 5.21062 | 0.230957 | 0.115478 | − | 0.993310i | \(-0.463160\pi\) | ||||
0.115478 | + | 0.993310i | \(0.463160\pi\) | |||||||
\(510\) | 10.3286 | 0.457360 | ||||||||
\(511\) | 4.06201 | 0.179693 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.38482 | −0.0611411 | ||||||||
\(514\) | −27.4438 | −1.21050 | ||||||||
\(515\) | −2.41893 | −0.106591 | ||||||||
\(516\) | 6.51464 | 0.286791 | ||||||||
\(517\) | 14.9701 | 0.658384 | ||||||||
\(518\) | −0.727555 | −0.0319670 | ||||||||
\(519\) | 13.9420 | 0.611984 | ||||||||
\(520\) | −2.41893 | −0.106077 | ||||||||
\(521\) | −33.9850 | −1.48891 | −0.744456 | − | 0.667672i | \(-0.767291\pi\) | ||||
−0.744456 | + | 0.667672i | \(0.767291\pi\) | |||||||
\(522\) | −10.3349 | −0.452347 | ||||||||
\(523\) | 37.6173 | 1.64489 | 0.822444 | − | 0.568846i | \(-0.192610\pi\) | ||||
0.822444 | + | 0.568846i | \(0.192610\pi\) | |||||||
\(524\) | 19.8225 | 0.865949 | ||||||||
\(525\) | 0.218919 | 0.00955439 | ||||||||
\(526\) | 24.1083 | 1.05117 | ||||||||
\(527\) | 32.2407 | 1.40443 | ||||||||
\(528\) | −1.56925 | −0.0682928 | ||||||||
\(529\) | 50.4189 | 2.19213 | ||||||||
\(530\) | 30.2415 | 1.31361 | ||||||||
\(531\) | −4.00889 | −0.173971 | ||||||||
\(532\) | −0.356141 | −0.0154407 | ||||||||
\(533\) | 10.3277 | 0.447341 | ||||||||
\(534\) | −14.0981 | −0.610085 | ||||||||
\(535\) | −35.7414 | −1.54523 | ||||||||
\(536\) | −9.28134 | −0.400893 | ||||||||
\(537\) | 1.46855 | 0.0633728 | ||||||||
\(538\) | 11.7471 | 0.506453 | ||||||||
\(539\) | −10.8809 | −0.468676 | ||||||||
\(540\) | −2.41893 | −0.104094 | ||||||||
\(541\) | 29.9167 | 1.28622 | 0.643110 | − | 0.765774i | \(-0.277644\pi\) | ||||
0.643110 | + | 0.765774i | \(0.277644\pi\) | |||||||
\(542\) | −20.2824 | −0.871205 | ||||||||
\(543\) | 16.8574 | 0.723419 | ||||||||
\(544\) | −4.26992 | −0.183071 | ||||||||
\(545\) | −17.4389 | −0.747001 | ||||||||
\(546\) | −0.257176 | −0.0110061 | ||||||||
\(547\) | 31.6336 | 1.35255 | 0.676276 | − | 0.736648i | \(-0.263592\pi\) | ||||
0.676276 | + | 0.736648i | \(0.263592\pi\) | |||||||
\(548\) | −7.15001 | −0.305433 | ||||||||
\(549\) | 12.4048 | 0.529422 | ||||||||
\(550\) | −1.33581 | −0.0569590 | ||||||||
\(551\) | 14.3120 | 0.609710 | ||||||||
\(552\) | 8.56848 | 0.364699 | ||||||||
\(553\) | −2.33057 | −0.0991057 | ||||||||
\(554\) | 26.9165 | 1.14357 | ||||||||
\(555\) | 6.84321 | 0.290478 | ||||||||
\(556\) | 3.85007 | 0.163279 | ||||||||
\(557\) | 13.8220 | 0.585659 | 0.292829 | − | 0.956165i | \(-0.405403\pi\) | ||||
0.292829 | + | 0.956165i | \(0.405403\pi\) | |||||||
\(558\) | −7.55065 | −0.319645 | ||||||||
\(559\) | −6.51464 | −0.275540 | ||||||||
\(560\) | −0.622092 | −0.0262882 | ||||||||
\(561\) | −6.70056 | −0.282898 | ||||||||
\(562\) | 18.6951 | 0.788606 | ||||||||
\(563\) | 0.435298 | 0.0183456 | 0.00917281 | − | 0.999958i | \(-0.497080\pi\) | ||||
0.00917281 | + | 0.999958i | \(0.497080\pi\) | |||||||
\(564\) | −9.53966 | −0.401692 | ||||||||
\(565\) | 22.6218 | 0.951707 | ||||||||
\(566\) | 23.9981 | 1.00872 | ||||||||
\(567\) | −0.257176 | −0.0108004 | ||||||||
\(568\) | 0.286350 | 0.0120150 | ||||||||
\(569\) | 10.2054 | 0.427831 | 0.213916 | − | 0.976852i | \(-0.431378\pi\) | ||||
0.213916 | + | 0.976852i | \(0.431378\pi\) | |||||||
\(570\) | 3.34978 | 0.140307 | ||||||||
\(571\) | 22.7820 | 0.953396 | 0.476698 | − | 0.879067i | \(-0.341834\pi\) | ||||
0.476698 | + | 0.879067i | \(0.341834\pi\) | |||||||
\(572\) | 1.56925 | 0.0656136 | ||||||||
\(573\) | −10.5816 | −0.442054 | ||||||||
\(574\) | 2.65603 | 0.110860 | ||||||||
\(575\) | 7.29384 | 0.304174 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 16.3459 | 0.680490 | 0.340245 | − | 0.940337i | \(-0.389490\pi\) | ||||
0.340245 | + | 0.940337i | \(0.389490\pi\) | |||||||
\(578\) | −1.23219 | −0.0512525 | ||||||||
\(579\) | −6.61573 | −0.274940 | ||||||||
\(580\) | 24.9995 | 1.03805 | ||||||||
\(581\) | 1.76147 | 0.0730782 | ||||||||
\(582\) | 13.3988 | 0.555397 | ||||||||
\(583\) | −19.6187 | −0.812524 | ||||||||
\(584\) | 15.7947 | 0.653588 | ||||||||
\(585\) | 2.41893 | 0.100011 | ||||||||
\(586\) | 16.2925 | 0.673035 | ||||||||
\(587\) | −45.6887 | −1.88577 | −0.942887 | − | 0.333112i | \(-0.891901\pi\) | ||||
−0.942887 | + | 0.333112i | \(0.891901\pi\) | |||||||
\(588\) | 6.93386 | 0.285948 | ||||||||
\(589\) | 10.4563 | 0.430843 | ||||||||
\(590\) | 9.69724 | 0.399229 | ||||||||
\(591\) | 18.2594 | 0.751089 | ||||||||
\(592\) | −2.82902 | −0.116272 | ||||||||
\(593\) | −5.09918 | −0.209398 | −0.104699 | − | 0.994504i | \(-0.533388\pi\) | ||||
−0.104699 | + | 0.994504i | \(0.533388\pi\) | |||||||
\(594\) | 1.56925 | 0.0643870 | ||||||||
\(595\) | −2.65628 | −0.108897 | ||||||||
\(596\) | −10.1252 | −0.414745 | ||||||||
\(597\) | 5.58471 | 0.228567 | ||||||||
\(598\) | −8.56848 | −0.350391 | ||||||||
\(599\) | −2.52897 | −0.103331 | −0.0516654 | − | 0.998664i | \(-0.516453\pi\) | ||||
−0.0516654 | + | 0.998664i | \(0.516453\pi\) | |||||||
\(600\) | 0.851240 | 0.0347517 | ||||||||
\(601\) | −13.9478 | −0.568943 | −0.284471 | − | 0.958685i | \(-0.591818\pi\) | ||||
−0.284471 | + | 0.958685i | \(0.591818\pi\) | |||||||
\(602\) | −1.67541 | −0.0682846 | ||||||||
\(603\) | 9.28134 | 0.377965 | ||||||||
\(604\) | 15.0201 | 0.611159 | ||||||||
\(605\) | −20.6516 | −0.839605 | ||||||||
\(606\) | −3.46177 | −0.140625 | ||||||||
\(607\) | −26.2324 | −1.06474 | −0.532371 | − | 0.846511i | \(-0.678699\pi\) | ||||
−0.532371 | + | 0.846511i | \(0.678699\pi\) | |||||||
\(608\) | −1.38482 | −0.0561617 | ||||||||
\(609\) | 2.65789 | 0.107703 | ||||||||
\(610\) | −30.0063 | −1.21492 | ||||||||
\(611\) | 9.53966 | 0.385933 | ||||||||
\(612\) | 4.26992 | 0.172601 | ||||||||
\(613\) | −18.5862 | −0.750688 | −0.375344 | − | 0.926886i | \(-0.622475\pi\) | ||||
−0.375344 | + | 0.926886i | \(0.622475\pi\) | |||||||
\(614\) | 9.48598 | 0.382823 | ||||||||
\(615\) | −24.9819 | −1.00737 | ||||||||
\(616\) | 0.403573 | 0.0162604 | ||||||||
\(617\) | 8.44285 | 0.339896 | 0.169948 | − | 0.985453i | \(-0.445640\pi\) | ||||
0.169948 | + | 0.985453i | \(0.445640\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | 33.6205 | 1.35132 | 0.675662 | − | 0.737212i | \(-0.263858\pi\) | ||||
0.675662 | + | 0.737212i | \(0.263858\pi\) | |||||||
\(620\) | 18.2645 | 0.733521 | ||||||||
\(621\) | −8.56848 | −0.343841 | ||||||||
\(622\) | −5.00459 | −0.200666 | ||||||||
\(623\) | 3.62570 | 0.145261 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | −28.5316 | −1.14126 | ||||||||
\(626\) | −17.0166 | −0.680120 | ||||||||
\(627\) | −2.17312 | −0.0867861 | ||||||||
\(628\) | 22.4063 | 0.894109 | ||||||||
\(629\) | −12.0797 | −0.481648 | ||||||||
\(630\) | 0.622092 | 0.0247847 | ||||||||
\(631\) | −27.1072 | −1.07912 | −0.539560 | − | 0.841947i | \(-0.681409\pi\) | ||||
−0.539560 | + | 0.841947i | \(0.681409\pi\) | |||||||
\(632\) | −9.06214 | −0.360473 | ||||||||
\(633\) | 15.0750 | 0.599177 | ||||||||
\(634\) | 23.2420 | 0.923059 | ||||||||
\(635\) | −26.4347 | −1.04903 | ||||||||
\(636\) | 12.5020 | 0.495736 | ||||||||
\(637\) | −6.93386 | −0.274730 | ||||||||
\(638\) | −16.2181 | −0.642079 | ||||||||
\(639\) | −0.286350 | −0.0113278 | ||||||||
\(640\) | −2.41893 | −0.0956168 | ||||||||
\(641\) | −7.16304 | −0.282923 | −0.141462 | − | 0.989944i | \(-0.545180\pi\) | ||||
−0.141462 | + | 0.989944i | \(0.545180\pi\) | |||||||
\(642\) | −14.7757 | −0.583149 | ||||||||
\(643\) | 43.7819 | 1.72659 | 0.863294 | − | 0.504701i | \(-0.168397\pi\) | ||||
0.863294 | + | 0.504701i | \(0.168397\pi\) | |||||||
\(644\) | −2.20361 | −0.0868343 | ||||||||
\(645\) | 15.7585 | 0.620490 | ||||||||
\(646\) | −5.91305 | −0.232646 | ||||||||
\(647\) | −40.6556 | −1.59834 | −0.799169 | − | 0.601107i | \(-0.794727\pi\) | ||||
−0.799169 | + | 0.601107i | \(0.794727\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −6.29095 | −0.246941 | ||||||||
\(650\) | −0.851240 | −0.0333884 | ||||||||
\(651\) | 1.94185 | 0.0761070 | ||||||||
\(652\) | 3.77020 | 0.147652 | ||||||||
\(653\) | −42.1850 | −1.65083 | −0.825413 | − | 0.564530i | \(-0.809058\pi\) | ||||
−0.825413 | + | 0.564530i | \(0.809058\pi\) | |||||||
\(654\) | −7.20934 | −0.281908 | ||||||||
\(655\) | 47.9493 | 1.87353 | ||||||||
\(656\) | 10.3277 | 0.403227 | ||||||||
\(657\) | −15.7947 | −0.616209 | ||||||||
\(658\) | 2.45337 | 0.0956423 | ||||||||
\(659\) | 32.0508 | 1.24852 | 0.624261 | − | 0.781216i | \(-0.285400\pi\) | ||||
0.624261 | + | 0.781216i | \(0.285400\pi\) | |||||||
\(660\) | −3.79591 | −0.147755 | ||||||||
\(661\) | 26.4456 | 1.02861 | 0.514307 | − | 0.857606i | \(-0.328049\pi\) | ||||
0.514307 | + | 0.857606i | \(0.328049\pi\) | |||||||
\(662\) | 0.342089 | 0.0132957 | ||||||||
\(663\) | −4.26992 | −0.165830 | ||||||||
\(664\) | 6.84929 | 0.265804 | ||||||||
\(665\) | −0.861482 | −0.0334069 | ||||||||
\(666\) | 2.82902 | 0.109622 | ||||||||
\(667\) | 88.5546 | 3.42885 | ||||||||
\(668\) | 11.1628 | 0.431900 | ||||||||
\(669\) | 22.1745 | 0.857317 | ||||||||
\(670\) | −22.4509 | −0.867356 | ||||||||
\(671\) | 19.4662 | 0.751483 | ||||||||
\(672\) | −0.257176 | −0.00992078 | ||||||||
\(673\) | −29.5184 | −1.13785 | −0.568925 | − | 0.822390i | \(-0.692640\pi\) | ||||
−0.568925 | + | 0.822390i | \(0.692640\pi\) | |||||||
\(674\) | −25.7894 | −0.993370 | ||||||||
\(675\) | −0.851240 | −0.0327643 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 22.0651 | 0.848030 | 0.424015 | − | 0.905655i | \(-0.360620\pi\) | ||||
0.424015 | + | 0.905655i | \(0.360620\pi\) | |||||||
\(678\) | 9.35198 | 0.359161 | ||||||||
\(679\) | −3.44584 | −0.132239 | ||||||||
\(680\) | −10.3286 | −0.396086 | ||||||||
\(681\) | −15.2505 | −0.584402 | ||||||||
\(682\) | −11.8488 | −0.453716 | ||||||||
\(683\) | −1.67975 | −0.0642737 | −0.0321369 | − | 0.999483i | \(-0.510231\pi\) | ||||
−0.0321369 | + | 0.999483i | \(0.510231\pi\) | |||||||
\(684\) | 1.38482 | 0.0529498 | ||||||||
\(685\) | −17.2954 | −0.660823 | ||||||||
\(686\) | −3.58345 | −0.136817 | ||||||||
\(687\) | 2.61103 | 0.0996169 | ||||||||
\(688\) | −6.51464 | −0.248368 | ||||||||
\(689\) | −12.5020 | −0.476288 | ||||||||
\(690\) | 20.7266 | 0.789048 | ||||||||
\(691\) | −34.2647 | −1.30349 | −0.651745 | − | 0.758438i | \(-0.725963\pi\) | ||||
−0.651745 | + | 0.758438i | \(0.725963\pi\) | |||||||
\(692\) | −13.9420 | −0.529994 | ||||||||
\(693\) | −0.403573 | −0.0153305 | ||||||||
\(694\) | −18.4618 | −0.700799 | ||||||||
\(695\) | 9.31306 | 0.353265 | ||||||||
\(696\) | 10.3349 | 0.391744 | ||||||||
\(697\) | 44.0982 | 1.67034 | ||||||||
\(698\) | 20.4645 | 0.774592 | ||||||||
\(699\) | −12.0453 | −0.455594 | ||||||||
\(700\) | −0.218919 | −0.00827434 | ||||||||
\(701\) | −9.73279 | −0.367602 | −0.183801 | − | 0.982963i | \(-0.558840\pi\) | ||||
−0.183801 | + | 0.982963i | \(0.558840\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | −3.91767 | −0.147758 | ||||||||
\(704\) | 1.56925 | 0.0591433 | ||||||||
\(705\) | −23.0758 | −0.869085 | ||||||||
\(706\) | −10.0583 | −0.378550 | ||||||||
\(707\) | 0.890284 | 0.0334826 | ||||||||
\(708\) | 4.00889 | 0.150663 | ||||||||
\(709\) | 43.2474 | 1.62419 | 0.812096 | − | 0.583524i | \(-0.198327\pi\) | ||||
0.812096 | + | 0.583524i | \(0.198327\pi\) | |||||||
\(710\) | 0.692661 | 0.0259951 | ||||||||
\(711\) | 9.06214 | 0.339857 | ||||||||
\(712\) | 14.0981 | 0.528350 | ||||||||
\(713\) | 64.6977 | 2.42295 | ||||||||
\(714\) | −1.09812 | −0.0410961 | ||||||||
\(715\) | 3.79591 | 0.141959 | ||||||||
\(716\) | −1.46855 | −0.0548824 | ||||||||
\(717\) | 16.0683 | 0.600081 | ||||||||
\(718\) | −14.8765 | −0.555184 | ||||||||
\(719\) | 36.1888 | 1.34961 | 0.674807 | − | 0.737995i | \(-0.264227\pi\) | ||||
0.674807 | + | 0.737995i | \(0.264227\pi\) | |||||||
\(720\) | 2.41893 | 0.0901483 | ||||||||
\(721\) | 0.257176 | 0.00957773 | ||||||||
\(722\) | 17.0823 | 0.635737 | ||||||||
\(723\) | −3.41064 | −0.126843 | ||||||||
\(724\) | −16.8574 | −0.626499 | ||||||||
\(725\) | 8.79750 | 0.326731 | ||||||||
\(726\) | −8.53746 | −0.316855 | ||||||||
\(727\) | 39.2177 | 1.45450 | 0.727252 | − | 0.686370i | \(-0.240797\pi\) | ||||
0.727252 | + | 0.686370i | \(0.240797\pi\) | |||||||
\(728\) | 0.257176 | 0.00953157 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 38.2063 | 1.41408 | ||||||||
\(731\) | −27.8170 | −1.02885 | ||||||||
\(732\) | −12.4048 | −0.458493 | ||||||||
\(733\) | −14.5729 | −0.538261 | −0.269131 | − | 0.963104i | \(-0.586736\pi\) | ||||
−0.269131 | + | 0.963104i | \(0.586736\pi\) | |||||||
\(734\) | 10.7987 | 0.398588 | ||||||||
\(735\) | 16.7725 | 0.618665 | ||||||||
\(736\) | −8.56848 | −0.315839 | ||||||||
\(737\) | 14.5647 | 0.536499 | ||||||||
\(738\) | −10.3277 | −0.380166 | ||||||||
\(739\) | −13.0285 | −0.479261 | −0.239631 | − | 0.970864i | \(-0.577026\pi\) | ||||
−0.239631 | + | 0.970864i | \(0.577026\pi\) | |||||||
\(740\) | −6.84321 | −0.251561 | ||||||||
\(741\) | −1.38482 | −0.0508725 | ||||||||
\(742\) | −3.21521 | −0.118034 | ||||||||
\(743\) | 13.9766 | 0.512751 | 0.256376 | − | 0.966577i | \(-0.417472\pi\) | ||||
0.256376 | + | 0.966577i | \(0.417472\pi\) | |||||||
\(744\) | 7.55065 | 0.276820 | ||||||||
\(745\) | −24.4922 | −0.897326 | ||||||||
\(746\) | −27.3303 | −1.00063 | ||||||||
\(747\) | −6.84929 | −0.250603 | ||||||||
\(748\) | 6.70056 | 0.244997 | ||||||||
\(749\) | 3.79995 | 0.138847 | ||||||||
\(750\) | −10.0356 | −0.366447 | ||||||||
\(751\) | −6.09636 | −0.222459 | −0.111230 | − | 0.993795i | \(-0.535479\pi\) | ||||
−0.111230 | + | 0.993795i | \(0.535479\pi\) | |||||||
\(752\) | 9.53966 | 0.347875 | ||||||||
\(753\) | −18.3812 | −0.669848 | ||||||||
\(754\) | −10.3349 | −0.376376 | ||||||||
\(755\) | 36.3326 | 1.32228 | ||||||||
\(756\) | 0.257176 | 0.00935340 | ||||||||
\(757\) | 35.0595 | 1.27426 | 0.637130 | − | 0.770756i | \(-0.280121\pi\) | ||||
0.637130 | + | 0.770756i | \(0.280121\pi\) | |||||||
\(758\) | −8.62300 | −0.313202 | ||||||||
\(759\) | −13.4461 | −0.488062 | ||||||||
\(760\) | −3.34978 | −0.121509 | ||||||||
\(761\) | −18.3039 | −0.663515 | −0.331758 | − | 0.943365i | \(-0.607642\pi\) | ||||
−0.331758 | + | 0.943365i | \(0.607642\pi\) | |||||||
\(762\) | −10.9282 | −0.395888 | ||||||||
\(763\) | 1.85407 | 0.0671218 | ||||||||
\(764\) | 10.5816 | 0.382830 | ||||||||
\(765\) | 10.3286 | 0.373433 | ||||||||
\(766\) | −5.34302 | −0.193051 | ||||||||
\(767\) | −4.00889 | −0.144753 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −28.0075 | −1.00998 | −0.504989 | − | 0.863126i | \(-0.668503\pi\) | ||||
−0.504989 | + | 0.863126i | \(0.668503\pi\) | |||||||
\(770\) | 0.976216 | 0.0351804 | ||||||||
\(771\) | −27.4438 | −0.988365 | ||||||||
\(772\) | 6.61573 | 0.238105 | ||||||||
\(773\) | 16.9295 | 0.608910 | 0.304455 | − | 0.952527i | \(-0.401526\pi\) | ||||
0.304455 | + | 0.952527i | \(0.401526\pi\) | |||||||
\(774\) | 6.51464 | 0.234164 | ||||||||
\(775\) | 6.42742 | 0.230880 | ||||||||
\(776\) | −13.3988 | −0.480988 | ||||||||
\(777\) | −0.727555 | −0.0261009 | ||||||||
\(778\) | 30.3993 | 1.08987 | ||||||||
\(779\) | 14.3019 | 0.512419 | ||||||||
\(780\) | −2.41893 | −0.0866117 | ||||||||
\(781\) | −0.449354 | −0.0160791 | ||||||||
\(782\) | −36.5867 | −1.30834 | ||||||||
\(783\) | −10.3349 | −0.369340 | ||||||||
\(784\) | −6.93386 | −0.247638 | ||||||||
\(785\) | 54.1994 | 1.93446 | ||||||||
\(786\) | 19.8225 | 0.707044 | ||||||||
\(787\) | 4.30348 | 0.153402 | 0.0767012 | − | 0.997054i | \(-0.475561\pi\) | ||||
0.0767012 | + | 0.997054i | \(0.475561\pi\) | |||||||
\(788\) | −18.2594 | −0.650463 | ||||||||
\(789\) | 24.1083 | 0.858278 | ||||||||
\(790\) | −21.9207 | −0.779904 | ||||||||
\(791\) | −2.40510 | −0.0855156 | ||||||||
\(792\) | −1.56925 | −0.0557608 | ||||||||
\(793\) | 12.4048 | 0.440506 | ||||||||
\(794\) | 35.9897 | 1.27723 | ||||||||
\(795\) | 30.2415 | 1.07255 | ||||||||
\(796\) | −5.58471 | −0.197945 | ||||||||
\(797\) | 9.26665 | 0.328242 | 0.164121 | − | 0.986440i | \(-0.447521\pi\) | ||||
0.164121 | + | 0.986440i | \(0.447521\pi\) | |||||||
\(798\) | −0.356141 | −0.0126073 | ||||||||
\(799\) | 40.7335 | 1.44105 | ||||||||
\(800\) | −0.851240 | −0.0300959 | ||||||||
\(801\) | −14.0981 | −0.498133 | ||||||||
\(802\) | 15.2475 | 0.538408 | ||||||||
\(803\) | −24.7858 | −0.874670 | ||||||||
\(804\) | −9.28134 | −0.327328 | ||||||||
\(805\) | −5.33038 | −0.187871 | ||||||||
\(806\) | −7.55065 | −0.265960 | ||||||||
\(807\) | 11.7471 | 0.413517 | ||||||||
\(808\) | 3.46177 | 0.121785 | ||||||||
\(809\) | −25.8177 | −0.907701 | −0.453850 | − | 0.891078i | \(-0.649950\pi\) | ||||
−0.453850 | + | 0.891078i | \(0.649950\pi\) | |||||||
\(810\) | −2.41893 | −0.0849927 | ||||||||
\(811\) | 27.7188 | 0.973339 | 0.486669 | − | 0.873586i | \(-0.338212\pi\) | ||||
0.486669 | + | 0.873586i | \(0.338212\pi\) | |||||||
\(812\) | −2.65789 | −0.0932738 | ||||||||
\(813\) | −20.2824 | −0.711336 | ||||||||
\(814\) | 4.43943 | 0.155602 | ||||||||
\(815\) | 9.11986 | 0.319455 | ||||||||
\(816\) | −4.26992 | −0.149477 | ||||||||
\(817\) | −9.02158 | −0.315625 | ||||||||
\(818\) | −18.7585 | −0.655877 | ||||||||
\(819\) | −0.257176 | −0.00898645 | ||||||||
\(820\) | 24.9819 | 0.872406 | ||||||||
\(821\) | 8.58538 | 0.299632 | 0.149816 | − | 0.988714i | \(-0.452132\pi\) | ||||
0.149816 | + | 0.988714i | \(0.452132\pi\) | |||||||
\(822\) | −7.15001 | −0.249385 | ||||||||
\(823\) | −25.0310 | −0.872527 | −0.436263 | − | 0.899819i | \(-0.643698\pi\) | ||||
−0.436263 | + | 0.899819i | \(0.643698\pi\) | |||||||
\(824\) | 1.00000 | 0.0348367 | ||||||||
\(825\) | −1.33581 | −0.0465068 | ||||||||
\(826\) | −1.03099 | −0.0358727 | ||||||||
\(827\) | 3.21644 | 0.111847 | 0.0559233 | − | 0.998435i | \(-0.482190\pi\) | ||||
0.0559233 | + | 0.998435i | \(0.482190\pi\) | |||||||
\(828\) | 8.56848 | 0.297775 | ||||||||
\(829\) | −27.9871 | −0.972034 | −0.486017 | − | 0.873949i | \(-0.661551\pi\) | ||||
−0.486017 | + | 0.873949i | \(0.661551\pi\) | |||||||
\(830\) | 16.5680 | 0.575083 | ||||||||
\(831\) | 26.9165 | 0.933721 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | −29.6070 | −1.02582 | ||||||||
\(834\) | 3.85007 | 0.133317 | ||||||||
\(835\) | 27.0020 | 0.934442 | ||||||||
\(836\) | 2.17312 | 0.0751589 | ||||||||
\(837\) | −7.55065 | −0.260989 | ||||||||
\(838\) | −12.8880 | −0.445209 | ||||||||
\(839\) | 28.7827 | 0.993688 | 0.496844 | − | 0.867840i | \(-0.334492\pi\) | ||||
0.496844 | + | 0.867840i | \(0.334492\pi\) | |||||||
\(840\) | −0.622092 | −0.0214642 | ||||||||
\(841\) | 77.8106 | 2.68312 | ||||||||
\(842\) | 13.2438 | 0.456411 | ||||||||
\(843\) | 18.6951 | 0.643894 | ||||||||
\(844\) | −15.0750 | −0.518902 | ||||||||
\(845\) | 2.41893 | 0.0832138 | ||||||||
\(846\) | −9.53966 | −0.327980 | ||||||||
\(847\) | 2.19563 | 0.0754427 | ||||||||
\(848\) | −12.5020 | −0.429320 | ||||||||
\(849\) | 23.9981 | 0.823614 | ||||||||
\(850\) | −3.63473 | −0.124670 | ||||||||
\(851\) | −24.2404 | −0.830950 | ||||||||
\(852\) | 0.286350 | 0.00981018 | ||||||||
\(853\) | 6.26327 | 0.214450 | 0.107225 | − | 0.994235i | \(-0.465803\pi\) | ||||
0.107225 | + | 0.994235i | \(0.465803\pi\) | |||||||
\(854\) | 3.19021 | 0.109167 | ||||||||
\(855\) | 3.34978 | 0.114560 | ||||||||
\(856\) | 14.7757 | 0.505022 | ||||||||
\(857\) | −38.6866 | −1.32151 | −0.660755 | − | 0.750601i | \(-0.729764\pi\) | ||||
−0.660755 | + | 0.750601i | \(0.729764\pi\) | |||||||
\(858\) | 1.56925 | 0.0535732 | ||||||||
\(859\) | 3.86346 | 0.131820 | 0.0659098 | − | 0.997826i | \(-0.479005\pi\) | ||||
0.0659098 | + | 0.997826i | \(0.479005\pi\) | |||||||
\(860\) | −15.7585 | −0.537360 | ||||||||
\(861\) | 2.65603 | 0.0905171 | ||||||||
\(862\) | 13.7422 | 0.468060 | ||||||||
\(863\) | 1.04093 | 0.0354336 | 0.0177168 | − | 0.999843i | \(-0.494360\pi\) | ||||
0.0177168 | + | 0.999843i | \(0.494360\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −33.7247 | −1.14667 | ||||||||
\(866\) | −21.5048 | −0.730764 | ||||||||
\(867\) | −1.23219 | −0.0418475 | ||||||||
\(868\) | −1.94185 | −0.0659106 | ||||||||
\(869\) | 14.2208 | 0.482406 | ||||||||
\(870\) | 24.9995 | 0.847562 | ||||||||
\(871\) | 9.28134 | 0.314486 | ||||||||
\(872\) | 7.20934 | 0.244139 | ||||||||
\(873\) | 13.3988 | 0.453480 | ||||||||
\(874\) | −11.8658 | −0.401366 | ||||||||
\(875\) | 2.58091 | 0.0872506 | ||||||||
\(876\) | 15.7947 | 0.533652 | ||||||||
\(877\) | −22.7979 | −0.769831 | −0.384915 | − | 0.922952i | \(-0.625769\pi\) | ||||
−0.384915 | + | 0.922952i | \(0.625769\pi\) | |||||||
\(878\) | −2.91356 | −0.0983279 | ||||||||
\(879\) | 16.2925 | 0.549531 | ||||||||
\(880\) | 3.79591 | 0.127960 | ||||||||
\(881\) | 26.3482 | 0.887694 | 0.443847 | − | 0.896103i | \(-0.353613\pi\) | ||||
0.443847 | + | 0.896103i | \(0.353613\pi\) | |||||||
\(882\) | 6.93386 | 0.233475 | ||||||||
\(883\) | 22.9812 | 0.773379 | 0.386690 | − | 0.922210i | \(-0.373618\pi\) | ||||
0.386690 | + | 0.922210i | \(0.373618\pi\) | |||||||
\(884\) | 4.26992 | 0.143613 | ||||||||
\(885\) | 9.69724 | 0.325969 | ||||||||
\(886\) | 29.2420 | 0.982403 | ||||||||
\(887\) | 27.5466 | 0.924924 | 0.462462 | − | 0.886639i | \(-0.346966\pi\) | ||||
0.462462 | + | 0.886639i | \(0.346966\pi\) | |||||||
\(888\) | −2.82902 | −0.0949356 | ||||||||
\(889\) | 2.81048 | 0.0942604 | ||||||||
\(890\) | 34.1024 | 1.14312 | ||||||||
\(891\) | 1.56925 | 0.0525718 | ||||||||
\(892\) | −22.1745 | −0.742458 | ||||||||
\(893\) | 13.2107 | 0.442078 | ||||||||
\(894\) | −10.1252 | −0.338638 | ||||||||
\(895\) | −3.55233 | −0.118741 | ||||||||
\(896\) | 0.257176 | 0.00859165 | ||||||||
\(897\) | −8.56848 | −0.286093 | ||||||||
\(898\) | −34.2300 | −1.14227 | ||||||||
\(899\) | 78.0354 | 2.60263 | ||||||||
\(900\) | 0.851240 | 0.0283747 | ||||||||
\(901\) | −53.3824 | −1.77843 | ||||||||
\(902\) | −16.2067 | −0.539623 | ||||||||
\(903\) | −1.67541 | −0.0557541 | ||||||||
\(904\) | −9.35198 | −0.311042 | ||||||||
\(905\) | −40.7769 | −1.35547 | ||||||||
\(906\) | 15.0201 | 0.499009 | ||||||||
\(907\) | −26.5420 | −0.881312 | −0.440656 | − | 0.897676i | \(-0.645254\pi\) | ||||
−0.440656 | + | 0.897676i | \(0.645254\pi\) | |||||||
\(908\) | 15.2505 | 0.506107 | ||||||||
\(909\) | −3.46177 | −0.114820 | ||||||||
\(910\) | 0.622092 | 0.0206221 | ||||||||
\(911\) | 32.1818 | 1.06623 | 0.533115 | − | 0.846043i | \(-0.321021\pi\) | ||||
0.533115 | + | 0.846043i | \(0.321021\pi\) | |||||||
\(912\) | −1.38482 | −0.0458558 | ||||||||
\(913\) | −10.7482 | −0.355715 | ||||||||
\(914\) | 4.90047 | 0.162093 | ||||||||
\(915\) | −30.0063 | −0.991978 | ||||||||
\(916\) | −2.61103 | −0.0862708 | ||||||||
\(917\) | −5.09787 | −0.168346 | ||||||||
\(918\) | 4.26992 | 0.140928 | ||||||||
\(919\) | −37.8115 | −1.24729 | −0.623643 | − | 0.781709i | \(-0.714348\pi\) | ||||
−0.623643 | + | 0.781709i | \(0.714348\pi\) | |||||||
\(920\) | −20.7266 | −0.683336 | ||||||||
\(921\) | 9.48598 | 0.312574 | ||||||||
\(922\) | −12.2479 | −0.403364 | ||||||||
\(923\) | −0.286350 | −0.00942531 | ||||||||
\(924\) | 0.403573 | 0.0132766 | ||||||||
\(925\) | −2.40817 | −0.0791803 | ||||||||
\(926\) | −33.1408 | −1.08907 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | −10.3349 | −0.339260 | ||||||||
\(929\) | −3.13069 | −0.102715 | −0.0513573 | − | 0.998680i | \(-0.516355\pi\) | ||||
−0.0513573 | + | 0.998680i | \(0.516355\pi\) | |||||||
\(930\) | 18.2645 | 0.598918 | ||||||||
\(931\) | −9.60212 | −0.314697 | ||||||||
\(932\) | 12.0453 | 0.394556 | ||||||||
\(933\) | −5.00459 | −0.163843 | ||||||||
\(934\) | 23.1797 | 0.758462 | ||||||||
\(935\) | 16.2082 | 0.530065 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | 32.1463 | 1.05017 | 0.525087 | − | 0.851049i | \(-0.324033\pi\) | ||||
0.525087 | + | 0.851049i | \(0.324033\pi\) | |||||||
\(938\) | 2.38694 | 0.0779363 | ||||||||
\(939\) | −17.0166 | −0.555316 | ||||||||
\(940\) | 23.0758 | 0.752649 | ||||||||
\(941\) | 46.2552 | 1.50788 | 0.753938 | − | 0.656946i | \(-0.228152\pi\) | ||||
0.753938 | + | 0.656946i | \(0.228152\pi\) | |||||||
\(942\) | 22.4063 | 0.730037 | ||||||||
\(943\) | 88.4924 | 2.88171 | ||||||||
\(944\) | −4.00889 | −0.130478 | ||||||||
\(945\) | 0.622092 | 0.0202366 | ||||||||
\(946\) | 10.2231 | 0.332381 | ||||||||
\(947\) | 15.2368 | 0.495129 | 0.247564 | − | 0.968871i | \(-0.420370\pi\) | ||||
0.247564 | + | 0.968871i | \(0.420370\pi\) | |||||||
\(948\) | −9.06214 | −0.294325 | ||||||||
\(949\) | −15.7947 | −0.512717 | ||||||||
\(950\) | −1.17881 | −0.0382457 | ||||||||
\(951\) | 23.2420 | 0.753674 | ||||||||
\(952\) | 1.09812 | 0.0355903 | ||||||||
\(953\) | −7.86823 | −0.254877 | −0.127438 | − | 0.991846i | \(-0.540676\pi\) | ||||
−0.127438 | + | 0.991846i | \(0.540676\pi\) | |||||||
\(954\) | 12.5020 | 0.404767 | ||||||||
\(955\) | 25.5963 | 0.828276 | ||||||||
\(956\) | −16.0683 | −0.519685 | ||||||||
\(957\) | −16.2181 | −0.524255 | ||||||||
\(958\) | 7.47120 | 0.241384 | ||||||||
\(959\) | 1.83881 | 0.0593783 | ||||||||
\(960\) | −2.41893 | −0.0780707 | ||||||||
\(961\) | 26.0124 | 0.839109 | ||||||||
\(962\) | 2.82902 | 0.0912112 | ||||||||
\(963\) | −14.7757 | −0.476139 | ||||||||
\(964\) | 3.41064 | 0.109849 | ||||||||
\(965\) | 16.0030 | 0.515155 | ||||||||
\(966\) | −2.20361 | −0.0708999 | ||||||||
\(967\) | −4.92886 | −0.158501 | −0.0792507 | − | 0.996855i | \(-0.525253\pi\) | ||||
−0.0792507 | + | 0.996855i | \(0.525253\pi\) | |||||||
\(968\) | 8.53746 | 0.274404 | ||||||||
\(969\) | −5.91305 | −0.189955 | ||||||||
\(970\) | −32.4107 | −1.04065 | ||||||||
\(971\) | 12.0048 | 0.385252 | 0.192626 | − | 0.981272i | \(-0.438300\pi\) | ||||
0.192626 | + | 0.981272i | \(0.438300\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −0.990145 | −0.0317426 | ||||||||
\(974\) | 13.0822 | 0.419182 | ||||||||
\(975\) | −0.851240 | −0.0272615 | ||||||||
\(976\) | 12.4048 | 0.397067 | ||||||||
\(977\) | 0.539082 | 0.0172468 | 0.00862339 | − | 0.999963i | \(-0.497255\pi\) | ||||
0.00862339 | + | 0.999963i | \(0.497255\pi\) | |||||||
\(978\) | 3.77020 | 0.120558 | ||||||||
\(979\) | −22.1235 | −0.707069 | ||||||||
\(980\) | −16.7725 | −0.535779 | ||||||||
\(981\) | −7.20934 | −0.230177 | ||||||||
\(982\) | 29.2439 | 0.933210 | ||||||||
\(983\) | −42.9713 | −1.37057 | −0.685286 | − | 0.728274i | \(-0.740323\pi\) | ||||
−0.685286 | + | 0.728274i | \(0.740323\pi\) | |||||||
\(984\) | 10.3277 | 0.329234 | ||||||||
\(985\) | −44.1682 | −1.40731 | ||||||||
\(986\) | −44.1293 | −1.40536 | ||||||||
\(987\) | 2.45337 | 0.0780916 | ||||||||
\(988\) | 1.38482 | 0.0440569 | ||||||||
\(989\) | −55.8206 | −1.77499 | ||||||||
\(990\) | −3.79591 | −0.120642 | ||||||||
\(991\) | 49.6660 | 1.57769 | 0.788846 | − | 0.614592i | \(-0.210679\pi\) | ||||
0.788846 | + | 0.614592i | \(0.210679\pi\) | |||||||
\(992\) | −7.55065 | −0.239734 | ||||||||
\(993\) | 0.342089 | 0.0108559 | ||||||||
\(994\) | −0.0736422 | −0.00233579 | ||||||||
\(995\) | −13.5090 | −0.428265 | ||||||||
\(996\) | 6.84929 | 0.217028 | ||||||||
\(997\) | 46.7267 | 1.47985 | 0.739924 | − | 0.672690i | \(-0.234861\pi\) | ||||
0.739924 | + | 0.672690i | \(0.234861\pi\) | |||||||
\(998\) | −20.8225 | −0.659124 | ||||||||
\(999\) | 2.82902 | 0.0895062 |
(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.1.13 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.z.1.13 | ✓ | 14 | 1.1 | even | 1 | trivial |