Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4001,2,Mod(1,4001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4001.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: | \(31.9481458487\) |
Analytic rank: | \(0\) |
Dimension: | \(184\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.99 | ||
Character | \(\chi\) | \(=\) | 4001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.273610 | 0.193471 | 0.0967356 | − | 0.995310i | \(-0.469160\pi\) | ||||
0.0967356 | + | 0.995310i | \(0.469160\pi\) | |||||||
\(3\) | −1.75031 | −1.01054 | −0.505272 | − | 0.862960i | \(-0.668608\pi\) | ||||
−0.505272 | + | 0.862960i | \(0.668608\pi\) | |||||||
\(4\) | −1.92514 | −0.962569 | ||||||||
\(5\) | −3.00014 | −1.34170 | −0.670852 | − | 0.741592i | \(-0.734071\pi\) | ||||
−0.670852 | + | 0.741592i | \(0.734071\pi\) | |||||||
\(6\) | −0.478902 | −0.195511 | ||||||||
\(7\) | 1.86672 | 0.705555 | 0.352778 | − | 0.935707i | \(-0.385237\pi\) | ||||
0.352778 | + | 0.935707i | \(0.385237\pi\) | |||||||
\(8\) | −1.07396 | −0.379700 | ||||||||
\(9\) | 0.0635960 | 0.0211987 | ||||||||
\(10\) | −0.820867 | −0.259581 | ||||||||
\(11\) | 3.70792 | 1.11798 | 0.558991 | − | 0.829174i | \(-0.311189\pi\) | ||||
0.558991 | + | 0.829174i | \(0.311189\pi\) | |||||||
\(12\) | 3.36959 | 0.972718 | ||||||||
\(13\) | −5.97047 | −1.65591 | −0.827956 | − | 0.560793i | \(-0.810496\pi\) | ||||
−0.827956 | + | 0.560793i | \(0.810496\pi\) | |||||||
\(14\) | 0.510753 | 0.136505 | ||||||||
\(15\) | 5.25118 | 1.35585 | ||||||||
\(16\) | 3.55643 | 0.889108 | ||||||||
\(17\) | −4.58955 | −1.11313 | −0.556565 | − | 0.830804i | \(-0.687881\pi\) | ||||
−0.556565 | + | 0.830804i | \(0.687881\pi\) | |||||||
\(18\) | 0.0174005 | 0.00410133 | ||||||||
\(19\) | 1.73061 | 0.397029 | 0.198514 | − | 0.980098i | \(-0.436388\pi\) | ||||
0.198514 | + | 0.980098i | \(0.436388\pi\) | |||||||
\(20\) | 5.77568 | 1.29148 | ||||||||
\(21\) | −3.26735 | −0.712994 | ||||||||
\(22\) | 1.01452 | 0.216297 | ||||||||
\(23\) | −8.34614 | −1.74029 | −0.870146 | − | 0.492795i | \(-0.835975\pi\) | ||||
−0.870146 | + | 0.492795i | \(0.835975\pi\) | |||||||
\(24\) | 1.87976 | 0.383704 | ||||||||
\(25\) | 4.00084 | 0.800167 | ||||||||
\(26\) | −1.63358 | −0.320371 | ||||||||
\(27\) | 5.13963 | 0.989122 | ||||||||
\(28\) | −3.59370 | −0.679145 | ||||||||
\(29\) | 3.53627 | 0.656669 | 0.328335 | − | 0.944561i | \(-0.393513\pi\) | ||||
0.328335 | + | 0.944561i | \(0.393513\pi\) | |||||||
\(30\) | 1.43677 | 0.262318 | ||||||||
\(31\) | −7.77624 | −1.39665 | −0.698327 | − | 0.715779i | \(-0.746072\pi\) | ||||
−0.698327 | + | 0.715779i | \(0.746072\pi\) | |||||||
\(32\) | 3.12098 | 0.551717 | ||||||||
\(33\) | −6.49003 | −1.12977 | ||||||||
\(34\) | −1.25575 | −0.215359 | ||||||||
\(35\) | −5.60043 | −0.946646 | ||||||||
\(36\) | −0.122431 | −0.0204052 | ||||||||
\(37\) | −11.3660 | −1.86856 | −0.934278 | − | 0.356547i | \(-0.883954\pi\) | ||||
−0.934278 | + | 0.356547i | \(0.883954\pi\) | |||||||
\(38\) | 0.473511 | 0.0768136 | ||||||||
\(39\) | 10.4502 | 1.67337 | ||||||||
\(40\) | 3.22202 | 0.509445 | ||||||||
\(41\) | −4.43689 | −0.692926 | −0.346463 | − | 0.938064i | \(-0.612617\pi\) | ||||
−0.346463 | + | 0.938064i | \(0.612617\pi\) | |||||||
\(42\) | −0.893978 | −0.137944 | ||||||||
\(43\) | −9.20892 | −1.40435 | −0.702173 | − | 0.712006i | \(-0.747787\pi\) | ||||
−0.702173 | + | 0.712006i | \(0.747787\pi\) | |||||||
\(44\) | −7.13827 | −1.07613 | ||||||||
\(45\) | −0.190797 | −0.0284423 | ||||||||
\(46\) | −2.28358 | −0.336696 | ||||||||
\(47\) | 0.180289 | 0.0262978 | 0.0131489 | − | 0.999914i | \(-0.495814\pi\) | ||||
0.0131489 | + | 0.999914i | \(0.495814\pi\) | |||||||
\(48\) | −6.22487 | −0.898482 | ||||||||
\(49\) | −3.51534 | −0.502192 | ||||||||
\(50\) | 1.09467 | 0.154809 | ||||||||
\(51\) | 8.03316 | 1.12487 | ||||||||
\(52\) | 11.4940 | 1.59393 | ||||||||
\(53\) | 0.827330 | 0.113642 | 0.0568212 | − | 0.998384i | \(-0.481903\pi\) | ||||
0.0568212 | + | 0.998384i | \(0.481903\pi\) | |||||||
\(54\) | 1.40625 | 0.191367 | ||||||||
\(55\) | −11.1243 | −1.50000 | ||||||||
\(56\) | −2.00478 | −0.267900 | ||||||||
\(57\) | −3.02911 | −0.401215 | ||||||||
\(58\) | 0.967558 | 0.127047 | ||||||||
\(59\) | −2.17404 | −0.283036 | −0.141518 | − | 0.989936i | \(-0.545198\pi\) | ||||
−0.141518 | + | 0.989936i | \(0.545198\pi\) | |||||||
\(60\) | −10.1093 | −1.30510 | ||||||||
\(61\) | −1.81133 | −0.231918 | −0.115959 | − | 0.993254i | \(-0.536994\pi\) | ||||
−0.115959 | + | 0.993254i | \(0.536994\pi\) | |||||||
\(62\) | −2.12765 | −0.270212 | ||||||||
\(63\) | 0.118716 | 0.0149568 | ||||||||
\(64\) | −6.25893 | −0.782366 | ||||||||
\(65\) | 17.9123 | 2.22174 | ||||||||
\(66\) | −1.77573 | −0.218578 | ||||||||
\(67\) | −7.78855 | −0.951522 | −0.475761 | − | 0.879574i | \(-0.657827\pi\) | ||||
−0.475761 | + | 0.879574i | \(0.657827\pi\) | |||||||
\(68\) | 8.83552 | 1.07146 | ||||||||
\(69\) | 14.6084 | 1.75864 | ||||||||
\(70\) | −1.53233 | −0.183149 | ||||||||
\(71\) | −0.381705 | −0.0453000 | −0.0226500 | − | 0.999743i | \(-0.507210\pi\) | ||||
−0.0226500 | + | 0.999743i | \(0.507210\pi\) | |||||||
\(72\) | −0.0682993 | −0.00804915 | ||||||||
\(73\) | −6.72766 | −0.787413 | −0.393706 | − | 0.919236i | \(-0.628807\pi\) | ||||
−0.393706 | + | 0.919236i | \(0.628807\pi\) | |||||||
\(74\) | −3.10984 | −0.361512 | ||||||||
\(75\) | −7.00272 | −0.808604 | ||||||||
\(76\) | −3.33166 | −0.382168 | ||||||||
\(77\) | 6.92167 | 0.788797 | ||||||||
\(78\) | 2.85927 | 0.323749 | ||||||||
\(79\) | −3.55275 | −0.399716 | −0.199858 | − | 0.979825i | \(-0.564048\pi\) | ||||
−0.199858 | + | 0.979825i | \(0.564048\pi\) | |||||||
\(80\) | −10.6698 | −1.19292 | ||||||||
\(81\) | −9.18674 | −1.02075 | ||||||||
\(82\) | −1.21398 | −0.134061 | ||||||||
\(83\) | −6.70350 | −0.735804 | −0.367902 | − | 0.929865i | \(-0.619924\pi\) | ||||
−0.367902 | + | 0.929865i | \(0.619924\pi\) | |||||||
\(84\) | 6.29010 | 0.686306 | ||||||||
\(85\) | 13.7693 | 1.49349 | ||||||||
\(86\) | −2.51965 | −0.271701 | ||||||||
\(87\) | −6.18958 | −0.663593 | ||||||||
\(88\) | −3.98214 | −0.424498 | ||||||||
\(89\) | 6.69890 | 0.710082 | 0.355041 | − | 0.934851i | \(-0.384467\pi\) | ||||
0.355041 | + | 0.934851i | \(0.384467\pi\) | |||||||
\(90\) | −0.0522039 | −0.00550277 | ||||||||
\(91\) | −11.1452 | −1.16834 | ||||||||
\(92\) | 16.0675 | 1.67515 | ||||||||
\(93\) | 13.6109 | 1.41138 | ||||||||
\(94\) | 0.0493287 | 0.00508787 | ||||||||
\(95\) | −5.19207 | −0.532695 | ||||||||
\(96\) | −5.46270 | −0.557534 | ||||||||
\(97\) | 16.9117 | 1.71712 | 0.858561 | − | 0.512711i | \(-0.171359\pi\) | ||||
0.858561 | + | 0.512711i | \(0.171359\pi\) | |||||||
\(98\) | −0.961831 | −0.0971597 | ||||||||
\(99\) | 0.235809 | 0.0236997 | ||||||||
\(100\) | −7.70216 | −0.770216 | ||||||||
\(101\) | 11.8744 | 1.18154 | 0.590772 | − | 0.806839i | \(-0.298823\pi\) | ||||
0.590772 | + | 0.806839i | \(0.298823\pi\) | |||||||
\(102\) | 2.19795 | 0.217629 | ||||||||
\(103\) | 14.8105 | 1.45933 | 0.729663 | − | 0.683807i | \(-0.239677\pi\) | ||||
0.729663 | + | 0.683807i | \(0.239677\pi\) | |||||||
\(104\) | 6.41202 | 0.628750 | ||||||||
\(105\) | 9.80251 | 0.956627 | ||||||||
\(106\) | 0.226365 | 0.0219865 | ||||||||
\(107\) | −9.58696 | −0.926806 | −0.463403 | − | 0.886148i | \(-0.653372\pi\) | ||||
−0.463403 | + | 0.886148i | \(0.653372\pi\) | |||||||
\(108\) | −9.89449 | −0.952098 | ||||||||
\(109\) | 9.92829 | 0.950958 | 0.475479 | − | 0.879727i | \(-0.342275\pi\) | ||||
0.475479 | + | 0.879727i | \(0.342275\pi\) | |||||||
\(110\) | −3.04371 | −0.290207 | ||||||||
\(111\) | 19.8940 | 1.88826 | ||||||||
\(112\) | 6.63887 | 0.627315 | ||||||||
\(113\) | −18.6924 | −1.75843 | −0.879215 | − | 0.476425i | \(-0.841932\pi\) | ||||
−0.879215 | + | 0.476425i | \(0.841932\pi\) | |||||||
\(114\) | −0.828792 | −0.0776235 | ||||||||
\(115\) | 25.0396 | 2.33495 | ||||||||
\(116\) | −6.80781 | −0.632089 | ||||||||
\(117\) | −0.379698 | −0.0351031 | ||||||||
\(118\) | −0.594839 | −0.0547594 | ||||||||
\(119\) | −8.56743 | −0.785375 | ||||||||
\(120\) | −5.63954 | −0.514817 | ||||||||
\(121\) | 2.74870 | 0.249882 | ||||||||
\(122\) | −0.495599 | −0.0448694 | ||||||||
\(123\) | 7.76595 | 0.700233 | ||||||||
\(124\) | 14.9703 | 1.34438 | ||||||||
\(125\) | 2.99763 | 0.268116 | ||||||||
\(126\) | 0.0324819 | 0.00289372 | ||||||||
\(127\) | −8.12664 | −0.721122 | −0.360561 | − | 0.932736i | \(-0.617415\pi\) | ||||
−0.360561 | + | 0.932736i | \(0.617415\pi\) | |||||||
\(128\) | −7.95447 | −0.703083 | ||||||||
\(129\) | 16.1185 | 1.41915 | ||||||||
\(130\) | 4.90096 | 0.429843 | ||||||||
\(131\) | −9.79055 | −0.855404 | −0.427702 | − | 0.903920i | \(-0.640677\pi\) | ||||
−0.427702 | + | 0.903920i | \(0.640677\pi\) | |||||||
\(132\) | 12.4942 | 1.08748 | ||||||||
\(133\) | 3.23057 | 0.280126 | ||||||||
\(134\) | −2.13102 | −0.184092 | ||||||||
\(135\) | −15.4196 | −1.32711 | ||||||||
\(136\) | 4.92897 | 0.422656 | ||||||||
\(137\) | 2.83725 | 0.242402 | 0.121201 | − | 0.992628i | \(-0.461325\pi\) | ||||
0.121201 | + | 0.992628i | \(0.461325\pi\) | |||||||
\(138\) | 3.99699 | 0.340246 | ||||||||
\(139\) | 17.4355 | 1.47886 | 0.739431 | − | 0.673232i | \(-0.235095\pi\) | ||||
0.739431 | + | 0.673232i | \(0.235095\pi\) | |||||||
\(140\) | 10.7816 | 0.911212 | ||||||||
\(141\) | −0.315562 | −0.0265751 | ||||||||
\(142\) | −0.104438 | −0.00876425 | ||||||||
\(143\) | −22.1381 | −1.85128 | ||||||||
\(144\) | 0.226175 | 0.0188479 | ||||||||
\(145\) | −10.6093 | −0.881055 | ||||||||
\(146\) | −1.84075 | −0.152342 | ||||||||
\(147\) | 6.15295 | 0.507487 | ||||||||
\(148\) | 21.8811 | 1.79861 | ||||||||
\(149\) | −8.42407 | −0.690126 | −0.345063 | − | 0.938579i | \(-0.612143\pi\) | ||||
−0.345063 | + | 0.938579i | \(0.612143\pi\) | |||||||
\(150\) | −1.91601 | −0.156442 | ||||||||
\(151\) | 7.91976 | 0.644501 | 0.322251 | − | 0.946654i | \(-0.395561\pi\) | ||||
0.322251 | + | 0.946654i | \(0.395561\pi\) | |||||||
\(152\) | −1.85860 | −0.150752 | ||||||||
\(153\) | −0.291877 | −0.0235969 | ||||||||
\(154\) | 1.89383 | 0.152610 | ||||||||
\(155\) | 23.3298 | 1.87390 | ||||||||
\(156\) | −20.1181 | −1.61074 | ||||||||
\(157\) | −15.0434 | −1.20059 | −0.600296 | − | 0.799778i | \(-0.704951\pi\) | ||||
−0.600296 | + | 0.799778i | \(0.704951\pi\) | |||||||
\(158\) | −0.972067 | −0.0773335 | ||||||||
\(159\) | −1.44809 | −0.114841 | ||||||||
\(160\) | −9.36339 | −0.740241 | ||||||||
\(161\) | −15.5799 | −1.22787 | ||||||||
\(162\) | −2.51358 | −0.197486 | ||||||||
\(163\) | −1.50863 | −0.118165 | −0.0590826 | − | 0.998253i | \(-0.518818\pi\) | ||||
−0.0590826 | + | 0.998253i | \(0.518818\pi\) | |||||||
\(164\) | 8.54163 | 0.666989 | ||||||||
\(165\) | 19.4710 | 1.51581 | ||||||||
\(166\) | −1.83414 | −0.142357 | ||||||||
\(167\) | −1.91199 | −0.147954 | −0.0739772 | − | 0.997260i | \(-0.523569\pi\) | ||||
−0.0739772 | + | 0.997260i | \(0.523569\pi\) | |||||||
\(168\) | 3.50899 | 0.270724 | ||||||||
\(169\) | 22.6466 | 1.74204 | ||||||||
\(170\) | 3.76741 | 0.288947 | ||||||||
\(171\) | 0.110060 | 0.00841648 | ||||||||
\(172\) | 17.7284 | 1.35178 | ||||||||
\(173\) | −6.19158 | −0.470737 | −0.235368 | − | 0.971906i | \(-0.575630\pi\) | ||||
−0.235368 | + | 0.971906i | \(0.575630\pi\) | |||||||
\(174\) | −1.69353 | −0.128386 | ||||||||
\(175\) | 7.46845 | 0.564562 | ||||||||
\(176\) | 13.1870 | 0.994006 | ||||||||
\(177\) | 3.80526 | 0.286021 | ||||||||
\(178\) | 1.83288 | 0.137380 | ||||||||
\(179\) | 0.988273 | 0.0738670 | 0.0369335 | − | 0.999318i | \(-0.488241\pi\) | ||||
0.0369335 | + | 0.999318i | \(0.488241\pi\) | |||||||
\(180\) | 0.367310 | 0.0273777 | ||||||||
\(181\) | 17.2474 | 1.28199 | 0.640993 | − | 0.767547i | \(-0.278523\pi\) | ||||
0.640993 | + | 0.767547i | \(0.278523\pi\) | |||||||
\(182\) | −3.04944 | −0.226040 | ||||||||
\(183\) | 3.17040 | 0.234363 | ||||||||
\(184\) | 8.96338 | 0.660789 | ||||||||
\(185\) | 34.0995 | 2.50705 | ||||||||
\(186\) | 3.72406 | 0.273061 | ||||||||
\(187\) | −17.0177 | −1.24446 | ||||||||
\(188\) | −0.347081 | −0.0253135 | ||||||||
\(189\) | 9.59426 | 0.697880 | ||||||||
\(190\) | −1.42060 | −0.103061 | ||||||||
\(191\) | −18.6835 | −1.35189 | −0.675945 | − | 0.736952i | \(-0.736264\pi\) | ||||
−0.675945 | + | 0.736952i | \(0.736264\pi\) | |||||||
\(192\) | 10.9551 | 0.790616 | ||||||||
\(193\) | 9.46633 | 0.681401 | 0.340701 | − | 0.940172i | \(-0.389336\pi\) | ||||
0.340701 | + | 0.940172i | \(0.389336\pi\) | |||||||
\(194\) | 4.62720 | 0.332214 | ||||||||
\(195\) | −31.3521 | −2.24517 | ||||||||
\(196\) | 6.76752 | 0.483394 | ||||||||
\(197\) | −4.19098 | −0.298595 | −0.149298 | − | 0.988792i | \(-0.547701\pi\) | ||||
−0.149298 | + | 0.988792i | \(0.547701\pi\) | |||||||
\(198\) | 0.0645197 | 0.00458521 | ||||||||
\(199\) | 14.5931 | 1.03448 | 0.517239 | − | 0.855841i | \(-0.326960\pi\) | ||||
0.517239 | + | 0.855841i | \(0.326960\pi\) | |||||||
\(200\) | −4.29672 | −0.303824 | ||||||||
\(201\) | 13.6324 | 0.961555 | ||||||||
\(202\) | 3.24894 | 0.228595 | ||||||||
\(203\) | 6.60124 | 0.463316 | ||||||||
\(204\) | −15.4649 | −1.08276 | ||||||||
\(205\) | 13.3113 | 0.929702 | ||||||||
\(206\) | 4.05231 | 0.282338 | ||||||||
\(207\) | −0.530781 | −0.0368919 | ||||||||
\(208\) | −21.2336 | −1.47228 | ||||||||
\(209\) | 6.41696 | 0.443871 | ||||||||
\(210\) | 2.68206 | 0.185080 | ||||||||
\(211\) | −22.0389 | −1.51722 | −0.758609 | − | 0.651546i | \(-0.774121\pi\) | ||||
−0.758609 | + | 0.651546i | \(0.774121\pi\) | |||||||
\(212\) | −1.59272 | −0.109389 | ||||||||
\(213\) | 0.668103 | 0.0457777 | ||||||||
\(214\) | −2.62308 | −0.179310 | ||||||||
\(215\) | 27.6280 | 1.88422 | ||||||||
\(216\) | −5.51973 | −0.375570 | ||||||||
\(217\) | −14.5161 | −0.985417 | ||||||||
\(218\) | 2.71648 | 0.183983 | ||||||||
\(219\) | 11.7755 | 0.795715 | ||||||||
\(220\) | 21.4158 | 1.44385 | ||||||||
\(221\) | 27.4018 | 1.84325 | ||||||||
\(222\) | 5.44319 | 0.365323 | ||||||||
\(223\) | −20.6864 | −1.38526 | −0.692631 | − | 0.721292i | \(-0.743548\pi\) | ||||
−0.692631 | + | 0.721292i | \(0.743548\pi\) | |||||||
\(224\) | 5.82601 | 0.389267 | ||||||||
\(225\) | 0.254437 | 0.0169625 | ||||||||
\(226\) | −5.11441 | −0.340206 | ||||||||
\(227\) | 5.37200 | 0.356552 | 0.178276 | − | 0.983981i | \(-0.442948\pi\) | ||||
0.178276 | + | 0.983981i | \(0.442948\pi\) | |||||||
\(228\) | 5.83145 | 0.386197 | ||||||||
\(229\) | 22.0031 | 1.45400 | 0.727001 | − | 0.686636i | \(-0.240913\pi\) | ||||
0.727001 | + | 0.686636i | \(0.240913\pi\) | |||||||
\(230\) | 6.85107 | 0.451746 | ||||||||
\(231\) | −12.1151 | −0.797114 | ||||||||
\(232\) | −3.79780 | −0.249338 | ||||||||
\(233\) | −7.68655 | −0.503563 | −0.251781 | − | 0.967784i | \(-0.581016\pi\) | ||||
−0.251781 | + | 0.967784i | \(0.581016\pi\) | |||||||
\(234\) | −0.103889 | −0.00679144 | ||||||||
\(235\) | −0.540891 | −0.0352839 | ||||||||
\(236\) | 4.18533 | 0.272442 | ||||||||
\(237\) | 6.21843 | 0.403930 | ||||||||
\(238\) | −2.34413 | −0.151947 | ||||||||
\(239\) | 10.7005 | 0.692156 | 0.346078 | − | 0.938206i | \(-0.387513\pi\) | ||||
0.346078 | + | 0.938206i | \(0.387513\pi\) | |||||||
\(240\) | 18.6755 | 1.20550 | ||||||||
\(241\) | 22.6716 | 1.46041 | 0.730203 | − | 0.683230i | \(-0.239426\pi\) | ||||
0.730203 | + | 0.683230i | \(0.239426\pi\) | |||||||
\(242\) | 0.752072 | 0.0483450 | ||||||||
\(243\) | 0.660799 | 0.0423902 | ||||||||
\(244\) | 3.48707 | 0.223237 | ||||||||
\(245\) | 10.5465 | 0.673792 | ||||||||
\(246\) | 2.12484 | 0.135475 | ||||||||
\(247\) | −10.3326 | −0.657445 | ||||||||
\(248\) | 8.35134 | 0.530310 | ||||||||
\(249\) | 11.7332 | 0.743562 | ||||||||
\(250\) | 0.820181 | 0.0518728 | ||||||||
\(251\) | 7.98553 | 0.504042 | 0.252021 | − | 0.967722i | \(-0.418905\pi\) | ||||
0.252021 | + | 0.967722i | \(0.418905\pi\) | |||||||
\(252\) | −0.228545 | −0.0143970 | ||||||||
\(253\) | −30.9469 | −1.94561 | ||||||||
\(254\) | −2.22353 | −0.139516 | ||||||||
\(255\) | −24.1006 | −1.50924 | ||||||||
\(256\) | 10.3414 | 0.646340 | ||||||||
\(257\) | −1.90960 | −0.119117 | −0.0595587 | − | 0.998225i | \(-0.518969\pi\) | ||||
−0.0595587 | + | 0.998225i | \(0.518969\pi\) | |||||||
\(258\) | 4.41017 | 0.274565 | ||||||||
\(259\) | −21.2171 | −1.31837 | ||||||||
\(260\) | −34.4836 | −2.13858 | ||||||||
\(261\) | 0.224893 | 0.0139205 | ||||||||
\(262\) | −2.67879 | −0.165496 | ||||||||
\(263\) | 11.5263 | 0.710742 | 0.355371 | − | 0.934725i | \(-0.384355\pi\) | ||||
0.355371 | + | 0.934725i | \(0.384355\pi\) | |||||||
\(264\) | 6.97000 | 0.428974 | ||||||||
\(265\) | −2.48210 | −0.152474 | ||||||||
\(266\) | 0.883914 | 0.0541962 | ||||||||
\(267\) | −11.7252 | −0.717569 | ||||||||
\(268\) | 14.9940 | 0.915906 | ||||||||
\(269\) | −17.1075 | −1.04306 | −0.521532 | − | 0.853232i | \(-0.674639\pi\) | ||||
−0.521532 | + | 0.853232i | \(0.674639\pi\) | |||||||
\(270\) | −4.21895 | −0.256757 | ||||||||
\(271\) | 3.84391 | 0.233501 | 0.116750 | − | 0.993161i | \(-0.462752\pi\) | ||||
0.116750 | + | 0.993161i | \(0.462752\pi\) | |||||||
\(272\) | −16.3224 | −0.989693 | ||||||||
\(273\) | 19.5076 | 1.18066 | ||||||||
\(274\) | 0.776298 | 0.0468979 | ||||||||
\(275\) | 14.8348 | 0.894572 | ||||||||
\(276\) | −28.1231 | −1.69281 | ||||||||
\(277\) | 9.85454 | 0.592102 | 0.296051 | − | 0.955172i | \(-0.404330\pi\) | ||||
0.296051 | + | 0.955172i | \(0.404330\pi\) | |||||||
\(278\) | 4.77053 | 0.286117 | ||||||||
\(279\) | −0.494538 | −0.0296072 | ||||||||
\(280\) | 6.01461 | 0.359442 | ||||||||
\(281\) | 26.8883 | 1.60402 | 0.802011 | − | 0.597309i | \(-0.203764\pi\) | ||||
0.802011 | + | 0.597309i | \(0.203764\pi\) | |||||||
\(282\) | −0.0863407 | −0.00514151 | ||||||||
\(283\) | 3.29380 | 0.195796 | 0.0978980 | − | 0.995196i | \(-0.468788\pi\) | ||||
0.0978980 | + | 0.995196i | \(0.468788\pi\) | |||||||
\(284\) | 0.734834 | 0.0436044 | ||||||||
\(285\) | 9.08774 | 0.538311 | ||||||||
\(286\) | −6.05719 | −0.358169 | ||||||||
\(287\) | −8.28245 | −0.488898 | ||||||||
\(288\) | 0.198482 | 0.0116957 | ||||||||
\(289\) | 4.06400 | 0.239059 | ||||||||
\(290\) | −2.90281 | −0.170459 | ||||||||
\(291\) | −29.6008 | −1.73523 | ||||||||
\(292\) | 12.9517 | 0.757939 | ||||||||
\(293\) | −2.01585 | −0.117768 | −0.0588838 | − | 0.998265i | \(-0.518754\pi\) | ||||
−0.0588838 | + | 0.998265i | \(0.518754\pi\) | |||||||
\(294\) | 1.68351 | 0.0981841 | ||||||||
\(295\) | 6.52243 | 0.379751 | ||||||||
\(296\) | 12.2065 | 0.709491 | ||||||||
\(297\) | 19.0573 | 1.10582 | ||||||||
\(298\) | −2.30490 | −0.133520 | ||||||||
\(299\) | 49.8304 | 2.88177 | ||||||||
\(300\) | 13.4812 | 0.778337 | ||||||||
\(301\) | −17.1905 | −0.990844 | ||||||||
\(302\) | 2.16692 | 0.124692 | ||||||||
\(303\) | −20.7839 | −1.19400 | ||||||||
\(304\) | 6.15479 | 0.353001 | ||||||||
\(305\) | 5.43426 | 0.311165 | ||||||||
\(306\) | −0.0798604 | −0.00456532 | ||||||||
\(307\) | 3.49294 | 0.199353 | 0.0996763 | − | 0.995020i | \(-0.468219\pi\) | ||||
0.0996763 | + | 0.995020i | \(0.468219\pi\) | |||||||
\(308\) | −13.3252 | −0.759272 | ||||||||
\(309\) | −25.9231 | −1.47471 | ||||||||
\(310\) | 6.38326 | 0.362545 | ||||||||
\(311\) | 2.08613 | 0.118293 | 0.0591467 | − | 0.998249i | \(-0.481162\pi\) | ||||
0.0591467 | + | 0.998249i | \(0.481162\pi\) | |||||||
\(312\) | −11.2230 | −0.635380 | ||||||||
\(313\) | 19.4399 | 1.09881 | 0.549405 | − | 0.835556i | \(-0.314854\pi\) | ||||
0.549405 | + | 0.835556i | \(0.314854\pi\) | |||||||
\(314\) | −4.11601 | −0.232280 | ||||||||
\(315\) | −0.356165 | −0.0200676 | ||||||||
\(316\) | 6.83954 | 0.384754 | ||||||||
\(317\) | 1.15367 | 0.0647964 | 0.0323982 | − | 0.999475i | \(-0.489686\pi\) | ||||
0.0323982 | + | 0.999475i | \(0.489686\pi\) | |||||||
\(318\) | −0.396210 | −0.0222184 | ||||||||
\(319\) | 13.1122 | 0.734144 | ||||||||
\(320\) | 18.7777 | 1.04970 | ||||||||
\(321\) | 16.7802 | 0.936578 | ||||||||
\(322\) | −4.26282 | −0.237558 | ||||||||
\(323\) | −7.94272 | −0.441945 | ||||||||
\(324\) | 17.6857 | 0.982542 | ||||||||
\(325\) | −23.8869 | −1.32501 | ||||||||
\(326\) | −0.412776 | −0.0228616 | ||||||||
\(327\) | −17.3776 | −0.960985 | ||||||||
\(328\) | 4.76503 | 0.263105 | ||||||||
\(329\) | 0.336549 | 0.0185546 | ||||||||
\(330\) | 5.32745 | 0.293266 | ||||||||
\(331\) | −21.7620 | −1.19615 | −0.598075 | − | 0.801440i | \(-0.704067\pi\) | ||||
−0.598075 | + | 0.801440i | \(0.704067\pi\) | |||||||
\(332\) | 12.9052 | 0.708262 | ||||||||
\(333\) | −0.722831 | −0.0396109 | ||||||||
\(334\) | −0.523139 | −0.0286249 | ||||||||
\(335\) | 23.3667 | 1.27666 | ||||||||
\(336\) | −11.6201 | −0.633929 | ||||||||
\(337\) | −1.23573 | −0.0673147 | −0.0336573 | − | 0.999433i | \(-0.510715\pi\) | ||||
−0.0336573 | + | 0.999433i | \(0.510715\pi\) | |||||||
\(338\) | 6.19632 | 0.337035 | ||||||||
\(339\) | 32.7175 | 1.77697 | ||||||||
\(340\) | −26.5078 | −1.43759 | ||||||||
\(341\) | −28.8337 | −1.56143 | ||||||||
\(342\) | 0.0301134 | 0.00162835 | ||||||||
\(343\) | −19.6292 | −1.05988 | ||||||||
\(344\) | 9.88996 | 0.533231 | ||||||||
\(345\) | −43.8271 | −2.35957 | ||||||||
\(346\) | −1.69407 | −0.0910740 | ||||||||
\(347\) | −26.1681 | −1.40478 | −0.702389 | − | 0.711793i | \(-0.747883\pi\) | ||||
−0.702389 | + | 0.711793i | \(0.747883\pi\) | |||||||
\(348\) | 11.9158 | 0.638754 | ||||||||
\(349\) | −32.5117 | −1.74031 | −0.870155 | − | 0.492778i | \(-0.835982\pi\) | ||||
−0.870155 | + | 0.492778i | \(0.835982\pi\) | |||||||
\(350\) | 2.04344 | 0.109226 | ||||||||
\(351\) | −30.6860 | −1.63790 | ||||||||
\(352\) | 11.5724 | 0.616810 | ||||||||
\(353\) | −25.4204 | −1.35299 | −0.676495 | − | 0.736447i | \(-0.736502\pi\) | ||||
−0.676495 | + | 0.736447i | \(0.736502\pi\) | |||||||
\(354\) | 1.04115 | 0.0553367 | ||||||||
\(355\) | 1.14517 | 0.0607792 | ||||||||
\(356\) | −12.8963 | −0.683503 | ||||||||
\(357\) | 14.9957 | 0.793656 | ||||||||
\(358\) | 0.270401 | 0.0142911 | ||||||||
\(359\) | 18.8771 | 0.996293 | 0.498147 | − | 0.867093i | \(-0.334014\pi\) | ||||
0.498147 | + | 0.867093i | \(0.334014\pi\) | |||||||
\(360\) | 0.204907 | 0.0107996 | ||||||||
\(361\) | −16.0050 | −0.842368 | ||||||||
\(362\) | 4.71904 | 0.248027 | ||||||||
\(363\) | −4.81109 | −0.252517 | ||||||||
\(364\) | 21.4561 | 1.12460 | ||||||||
\(365\) | 20.1839 | 1.05647 | ||||||||
\(366\) | 0.867453 | 0.0453425 | ||||||||
\(367\) | 22.6084 | 1.18015 | 0.590075 | − | 0.807349i | \(-0.299098\pi\) | ||||
0.590075 | + | 0.807349i | \(0.299098\pi\) | |||||||
\(368\) | −29.6825 | −1.54731 | ||||||||
\(369\) | −0.282169 | −0.0146891 | ||||||||
\(370\) | 9.32995 | 0.485041 | ||||||||
\(371\) | 1.54440 | 0.0801810 | ||||||||
\(372\) | −26.2028 | −1.35855 | ||||||||
\(373\) | −4.22807 | −0.218921 | −0.109461 | − | 0.993991i | \(-0.534912\pi\) | ||||
−0.109461 | + | 0.993991i | \(0.534912\pi\) | |||||||
\(374\) | −4.65621 | −0.240767 | ||||||||
\(375\) | −5.24679 | −0.270943 | ||||||||
\(376\) | −0.193622 | −0.00998529 | ||||||||
\(377\) | −21.1132 | −1.08739 | ||||||||
\(378\) | 2.62508 | 0.135020 | ||||||||
\(379\) | −0.0938411 | −0.00482029 | −0.00241015 | − | 0.999997i | \(-0.500767\pi\) | ||||
−0.00241015 | + | 0.999997i | \(0.500767\pi\) | |||||||
\(380\) | 9.99544 | 0.512755 | ||||||||
\(381\) | 14.2242 | 0.728726 | ||||||||
\(382\) | −5.11198 | −0.261552 | ||||||||
\(383\) | 11.0532 | 0.564791 | 0.282396 | − | 0.959298i | \(-0.408871\pi\) | ||||
0.282396 | + | 0.959298i | \(0.408871\pi\) | |||||||
\(384\) | 13.9228 | 0.710496 | ||||||||
\(385\) | −20.7660 | −1.05833 | ||||||||
\(386\) | 2.59008 | 0.131831 | ||||||||
\(387\) | −0.585650 | −0.0297703 | ||||||||
\(388\) | −32.5573 | −1.65285 | ||||||||
\(389\) | −4.14102 | −0.209958 | −0.104979 | − | 0.994474i | \(-0.533478\pi\) | ||||
−0.104979 | + | 0.994474i | \(0.533478\pi\) | |||||||
\(390\) | −8.57822 | −0.434375 | ||||||||
\(391\) | 38.3051 | 1.93717 | ||||||||
\(392\) | 3.77532 | 0.190683 | ||||||||
\(393\) | 17.1365 | 0.864424 | ||||||||
\(394\) | −1.14669 | −0.0577695 | ||||||||
\(395\) | 10.6587 | 0.536300 | ||||||||
\(396\) | −0.453965 | −0.0228126 | ||||||||
\(397\) | 33.3372 | 1.67314 | 0.836572 | − | 0.547857i | \(-0.184556\pi\) | ||||
0.836572 | + | 0.547857i | \(0.184556\pi\) | |||||||
\(398\) | 3.99282 | 0.200142 | ||||||||
\(399\) | −5.65450 | −0.283079 | ||||||||
\(400\) | 14.2287 | 0.711435 | ||||||||
\(401\) | −26.5022 | −1.32346 | −0.661729 | − | 0.749743i | \(-0.730177\pi\) | ||||
−0.661729 | + | 0.749743i | \(0.730177\pi\) | |||||||
\(402\) | 3.72995 | 0.186033 | ||||||||
\(403\) | 46.4279 | 2.31274 | ||||||||
\(404\) | −22.8598 | −1.13732 | ||||||||
\(405\) | 27.5615 | 1.36954 | ||||||||
\(406\) | 1.80616 | 0.0896383 | ||||||||
\(407\) | −42.1442 | −2.08901 | ||||||||
\(408\) | −8.62725 | −0.427112 | ||||||||
\(409\) | 30.1507 | 1.49086 | 0.745428 | − | 0.666586i | \(-0.232245\pi\) | ||||
0.745428 | + | 0.666586i | \(0.232245\pi\) | |||||||
\(410\) | 3.64210 | 0.179870 | ||||||||
\(411\) | −4.96607 | −0.244958 | ||||||||
\(412\) | −28.5123 | −1.40470 | ||||||||
\(413\) | −4.05834 | −0.199698 | ||||||||
\(414\) | −0.145227 | −0.00713751 | ||||||||
\(415\) | 20.1114 | 0.987231 | ||||||||
\(416\) | −18.6338 | −0.913595 | ||||||||
\(417\) | −30.5176 | −1.49446 | ||||||||
\(418\) | 1.75574 | 0.0858762 | ||||||||
\(419\) | −4.34784 | −0.212406 | −0.106203 | − | 0.994344i | \(-0.533869\pi\) | ||||
−0.106203 | + | 0.994344i | \(0.533869\pi\) | |||||||
\(420\) | −18.8712 | −0.920819 | ||||||||
\(421\) | 25.6692 | 1.25104 | 0.625520 | − | 0.780208i | \(-0.284887\pi\) | ||||
0.625520 | + | 0.780208i | \(0.284887\pi\) | |||||||
\(422\) | −6.03004 | −0.293538 | ||||||||
\(423\) | 0.0114656 | 0.000557479 0 | ||||||||
\(424\) | −0.888515 | −0.0431501 | ||||||||
\(425\) | −18.3620 | −0.890690 | ||||||||
\(426\) | 0.182799 | 0.00885666 | ||||||||
\(427\) | −3.38126 | −0.163631 | ||||||||
\(428\) | 18.4562 | 0.892115 | ||||||||
\(429\) | 38.7486 | 1.87080 | ||||||||
\(430\) | 7.55929 | 0.364541 | ||||||||
\(431\) | 17.4951 | 0.842708 | 0.421354 | − | 0.906896i | \(-0.361555\pi\) | ||||
0.421354 | + | 0.906896i | \(0.361555\pi\) | |||||||
\(432\) | 18.2787 | 0.879436 | ||||||||
\(433\) | 0.996301 | 0.0478792 | 0.0239396 | − | 0.999713i | \(-0.492379\pi\) | ||||
0.0239396 | + | 0.999713i | \(0.492379\pi\) | |||||||
\(434\) | −3.97174 | −0.190650 | ||||||||
\(435\) | 18.5696 | 0.890345 | ||||||||
\(436\) | −19.1133 | −0.915363 | ||||||||
\(437\) | −14.4439 | −0.690946 | ||||||||
\(438\) | 3.22189 | 0.153948 | ||||||||
\(439\) | 23.5023 | 1.12171 | 0.560853 | − | 0.827916i | \(-0.310473\pi\) | ||||
0.560853 | + | 0.827916i | \(0.310473\pi\) | |||||||
\(440\) | 11.9470 | 0.569550 | ||||||||
\(441\) | −0.223562 | −0.0106458 | ||||||||
\(442\) | 7.49740 | 0.356615 | ||||||||
\(443\) | −39.0629 | −1.85593 | −0.927967 | − | 0.372662i | \(-0.878445\pi\) | ||||
−0.927967 | + | 0.372662i | \(0.878445\pi\) | |||||||
\(444\) | −38.2987 | −1.81758 | ||||||||
\(445\) | −20.0976 | −0.952720 | ||||||||
\(446\) | −5.65999 | −0.268008 | ||||||||
\(447\) | 14.7448 | 0.697403 | ||||||||
\(448\) | −11.6837 | −0.552003 | ||||||||
\(449\) | −30.3220 | −1.43099 | −0.715493 | − | 0.698620i | \(-0.753798\pi\) | ||||
−0.715493 | + | 0.698620i | \(0.753798\pi\) | |||||||
\(450\) | 0.0696165 | 0.00328175 | ||||||||
\(451\) | −16.4517 | −0.774679 | ||||||||
\(452\) | 35.9854 | 1.69261 | ||||||||
\(453\) | −13.8621 | −0.651297 | ||||||||
\(454\) | 1.46983 | 0.0689825 | ||||||||
\(455\) | 33.4372 | 1.56756 | ||||||||
\(456\) | 3.25312 | 0.152342 | ||||||||
\(457\) | 13.1097 | 0.613245 | 0.306623 | − | 0.951831i | \(-0.400801\pi\) | ||||
0.306623 | + | 0.951831i | \(0.400801\pi\) | |||||||
\(458\) | 6.02025 | 0.281308 | ||||||||
\(459\) | −23.5886 | −1.10102 | ||||||||
\(460\) | −48.2047 | −2.24755 | ||||||||
\(461\) | −32.8530 | −1.53011 | −0.765057 | − | 0.643962i | \(-0.777289\pi\) | ||||
−0.765057 | + | 0.643962i | \(0.777289\pi\) | |||||||
\(462\) | −3.31480 | −0.154219 | ||||||||
\(463\) | −3.20561 | −0.148977 | −0.0744886 | − | 0.997222i | \(-0.523732\pi\) | ||||
−0.0744886 | + | 0.997222i | \(0.523732\pi\) | |||||||
\(464\) | 12.5765 | 0.583850 | ||||||||
\(465\) | −40.8345 | −1.89365 | ||||||||
\(466\) | −2.10311 | −0.0974249 | ||||||||
\(467\) | 16.8311 | 0.778851 | 0.389426 | − | 0.921058i | \(-0.372674\pi\) | ||||
0.389426 | + | 0.921058i | \(0.372674\pi\) | |||||||
\(468\) | 0.730972 | 0.0337892 | ||||||||
\(469\) | −14.5391 | −0.671352 | ||||||||
\(470\) | −0.147993 | −0.00682641 | ||||||||
\(471\) | 26.3306 | 1.21325 | ||||||||
\(472\) | 2.33483 | 0.107469 | ||||||||
\(473\) | −34.1460 | −1.57003 | ||||||||
\(474\) | 1.70142 | 0.0781489 | ||||||||
\(475\) | 6.92388 | 0.317689 | ||||||||
\(476\) | 16.4935 | 0.755977 | ||||||||
\(477\) | 0.0526149 | 0.00240907 | ||||||||
\(478\) | 2.92775 | 0.133912 | ||||||||
\(479\) | −1.33542 | −0.0610171 | −0.0305085 | − | 0.999535i | \(-0.509713\pi\) | ||||
−0.0305085 | + | 0.999535i | \(0.509713\pi\) | |||||||
\(480\) | 16.3889 | 0.748046 | ||||||||
\(481\) | 67.8603 | 3.09416 | ||||||||
\(482\) | 6.20316 | 0.282546 | ||||||||
\(483\) | 27.2698 | 1.24082 | ||||||||
\(484\) | −5.29163 | −0.240529 | ||||||||
\(485\) | −50.7374 | −2.30387 | ||||||||
\(486\) | 0.180801 | 0.00820129 | ||||||||
\(487\) | 2.38892 | 0.108252 | 0.0541261 | − | 0.998534i | \(-0.482763\pi\) | ||||
0.0541261 | + | 0.998534i | \(0.482763\pi\) | |||||||
\(488\) | 1.94529 | 0.0880593 | ||||||||
\(489\) | 2.64058 | 0.119411 | ||||||||
\(490\) | 2.88563 | 0.130359 | ||||||||
\(491\) | −27.3128 | −1.23261 | −0.616304 | − | 0.787508i | \(-0.711371\pi\) | ||||
−0.616304 | + | 0.787508i | \(0.711371\pi\) | |||||||
\(492\) | −14.9505 | −0.674022 | ||||||||
\(493\) | −16.2299 | −0.730958 | ||||||||
\(494\) | −2.82708 | −0.127197 | ||||||||
\(495\) | −0.707461 | −0.0317980 | ||||||||
\(496\) | −27.6557 | −1.24178 | ||||||||
\(497\) | −0.712537 | −0.0319617 | ||||||||
\(498\) | 3.21032 | 0.143858 | ||||||||
\(499\) | −28.1844 | −1.26171 | −0.630853 | − | 0.775902i | \(-0.717295\pi\) | ||||
−0.630853 | + | 0.775902i | \(0.717295\pi\) | |||||||
\(500\) | −5.77085 | −0.258080 | ||||||||
\(501\) | 3.34658 | 0.149514 | ||||||||
\(502\) | 2.18492 | 0.0975177 | ||||||||
\(503\) | 29.3083 | 1.30679 | 0.653395 | − | 0.757017i | \(-0.273344\pi\) | ||||
0.653395 | + | 0.757017i | \(0.273344\pi\) | |||||||
\(504\) | −0.127496 | −0.00567912 | ||||||||
\(505\) | −35.6247 | −1.58528 | ||||||||
\(506\) | −8.46736 | −0.376420 | ||||||||
\(507\) | −39.6386 | −1.76041 | ||||||||
\(508\) | 15.6449 | 0.694130 | ||||||||
\(509\) | −7.79102 | −0.345331 | −0.172665 | − | 0.984981i | \(-0.555238\pi\) | ||||
−0.172665 | + | 0.984981i | \(0.555238\pi\) | |||||||
\(510\) | −6.59415 | −0.291994 | ||||||||
\(511\) | −12.5587 | −0.555563 | ||||||||
\(512\) | 18.7385 | 0.828131 | ||||||||
\(513\) | 8.89468 | 0.392710 | ||||||||
\(514\) | −0.522484 | −0.0230458 | ||||||||
\(515\) | −44.4337 | −1.95798 | ||||||||
\(516\) | −31.0303 | −1.36603 | ||||||||
\(517\) | 0.668497 | 0.0294005 | ||||||||
\(518\) | −5.80521 | −0.255066 | ||||||||
\(519\) | 10.8372 | 0.475700 | ||||||||
\(520\) | −19.2370 | −0.843596 | ||||||||
\(521\) | −14.4354 | −0.632428 | −0.316214 | − | 0.948688i | \(-0.602412\pi\) | ||||
−0.316214 | + | 0.948688i | \(0.602412\pi\) | |||||||
\(522\) | 0.0615328 | 0.00269322 | ||||||||
\(523\) | −9.85239 | −0.430815 | −0.215407 | − | 0.976524i | \(-0.569108\pi\) | ||||
−0.215407 | + | 0.976524i | \(0.569108\pi\) | |||||||
\(524\) | 18.8482 | 0.823386 | ||||||||
\(525\) | −13.0721 | −0.570515 | ||||||||
\(526\) | 3.15370 | 0.137508 | ||||||||
\(527\) | 35.6895 | 1.55466 | ||||||||
\(528\) | −23.0813 | −1.00449 | ||||||||
\(529\) | 46.6581 | 2.02861 | ||||||||
\(530\) | −0.679127 | −0.0294994 | ||||||||
\(531\) | −0.138260 | −0.00599999 | ||||||||
\(532\) | −6.21929 | −0.269640 | ||||||||
\(533\) | 26.4904 | 1.14743 | ||||||||
\(534\) | −3.20812 | −0.138829 | ||||||||
\(535\) | 28.7622 | 1.24350 | ||||||||
\(536\) | 8.36455 | 0.361294 | ||||||||
\(537\) | −1.72979 | −0.0746459 | ||||||||
\(538\) | −4.68078 | −0.201803 | ||||||||
\(539\) | −13.0346 | −0.561441 | ||||||||
\(540\) | 29.6848 | 1.27743 | ||||||||
\(541\) | −31.4079 | −1.35033 | −0.675166 | − | 0.737666i | \(-0.735928\pi\) | ||||
−0.675166 | + | 0.737666i | \(0.735928\pi\) | |||||||
\(542\) | 1.05173 | 0.0451757 | ||||||||
\(543\) | −30.1883 | −1.29550 | ||||||||
\(544\) | −14.3239 | −0.614133 | ||||||||
\(545\) | −29.7863 | −1.27590 | ||||||||
\(546\) | 5.33747 | 0.228423 | ||||||||
\(547\) | −17.2727 | −0.738527 | −0.369264 | − | 0.929325i | \(-0.620390\pi\) | ||||
−0.369264 | + | 0.929325i | \(0.620390\pi\) | |||||||
\(548\) | −5.46209 | −0.233329 | ||||||||
\(549\) | −0.115194 | −0.00491635 | ||||||||
\(550\) | 4.05894 | 0.173074 | ||||||||
\(551\) | 6.11990 | 0.260717 | ||||||||
\(552\) | −15.6887 | −0.667757 | ||||||||
\(553\) | −6.63200 | −0.282022 | ||||||||
\(554\) | 2.69630 | 0.114555 | ||||||||
\(555\) | −59.6848 | −2.53348 | ||||||||
\(556\) | −33.5658 | −1.42351 | ||||||||
\(557\) | 5.57348 | 0.236156 | 0.118078 | − | 0.993004i | \(-0.462327\pi\) | ||||
0.118078 | + | 0.993004i | \(0.462327\pi\) | |||||||
\(558\) | −0.135310 | −0.00572814 | ||||||||
\(559\) | 54.9816 | 2.32547 | ||||||||
\(560\) | −19.9175 | −0.841670 | ||||||||
\(561\) | 29.7863 | 1.25758 | ||||||||
\(562\) | 7.35690 | 0.310332 | ||||||||
\(563\) | 10.7904 | 0.454763 | 0.227381 | − | 0.973806i | \(-0.426984\pi\) | ||||
0.227381 | + | 0.973806i | \(0.426984\pi\) | |||||||
\(564\) | 0.607500 | 0.0255804 | ||||||||
\(565\) | 56.0797 | 2.35929 | ||||||||
\(566\) | 0.901214 | 0.0378809 | ||||||||
\(567\) | −17.1491 | −0.720195 | ||||||||
\(568\) | 0.409934 | 0.0172004 | ||||||||
\(569\) | −26.7148 | −1.11994 | −0.559971 | − | 0.828512i | \(-0.689188\pi\) | ||||
−0.559971 | + | 0.828512i | \(0.689188\pi\) | |||||||
\(570\) | 2.48649 | 0.104148 | ||||||||
\(571\) | −17.6386 | −0.738154 | −0.369077 | − | 0.929399i | \(-0.620326\pi\) | ||||
−0.369077 | + | 0.929399i | \(0.620326\pi\) | |||||||
\(572\) | 42.6188 | 1.78198 | ||||||||
\(573\) | 32.7020 | 1.36614 | ||||||||
\(574\) | −2.26616 | −0.0945876 | ||||||||
\(575\) | −33.3915 | −1.39252 | ||||||||
\(576\) | −0.398043 | −0.0165851 | ||||||||
\(577\) | −25.1722 | −1.04793 | −0.523967 | − | 0.851738i | \(-0.675549\pi\) | ||||
−0.523967 | + | 0.851738i | \(0.675549\pi\) | |||||||
\(578\) | 1.11195 | 0.0462510 | ||||||||
\(579\) | −16.5690 | −0.688586 | ||||||||
\(580\) | 20.4244 | 0.848076 | ||||||||
\(581\) | −12.5136 | −0.519150 | ||||||||
\(582\) | −8.09905 | −0.335716 | ||||||||
\(583\) | 3.06768 | 0.127050 | ||||||||
\(584\) | 7.22520 | 0.298981 | ||||||||
\(585\) | 1.13915 | 0.0470980 | ||||||||
\(586\) | −0.551557 | −0.0227846 | ||||||||
\(587\) | −6.77946 | −0.279818 | −0.139909 | − | 0.990164i | \(-0.544681\pi\) | ||||
−0.139909 | + | 0.990164i | \(0.544681\pi\) | |||||||
\(588\) | −11.8453 | −0.488491 | ||||||||
\(589\) | −13.4576 | −0.554512 | ||||||||
\(590\) | 1.78460 | 0.0734708 | ||||||||
\(591\) | 7.33553 | 0.301743 | ||||||||
\(592\) | −40.4223 | −1.66135 | ||||||||
\(593\) | 33.0057 | 1.35538 | 0.677691 | − | 0.735347i | \(-0.262981\pi\) | ||||
0.677691 | + | 0.735347i | \(0.262981\pi\) | |||||||
\(594\) | 5.21427 | 0.213944 | ||||||||
\(595\) | 25.7035 | 1.05374 | ||||||||
\(596\) | 16.2175 | 0.664294 | ||||||||
\(597\) | −25.5425 | −1.04539 | ||||||||
\(598\) | 13.6341 | 0.557539 | ||||||||
\(599\) | −4.88130 | −0.199445 | −0.0997223 | − | 0.995015i | \(-0.531795\pi\) | ||||
−0.0997223 | + | 0.995015i | \(0.531795\pi\) | |||||||
\(600\) | 7.52060 | 0.307027 | ||||||||
\(601\) | −26.7936 | −1.09293 | −0.546466 | − | 0.837481i | \(-0.684027\pi\) | ||||
−0.546466 | + | 0.837481i | \(0.684027\pi\) | |||||||
\(602\) | −4.70348 | −0.191700 | ||||||||
\(603\) | −0.495321 | −0.0201710 | ||||||||
\(604\) | −15.2466 | −0.620377 | ||||||||
\(605\) | −8.24649 | −0.335268 | ||||||||
\(606\) | −5.68666 | −0.231005 | ||||||||
\(607\) | 16.7752 | 0.680885 | 0.340443 | − | 0.940265i | \(-0.389423\pi\) | ||||
0.340443 | + | 0.940265i | \(0.389423\pi\) | |||||||
\(608\) | 5.40120 | 0.219048 | ||||||||
\(609\) | −11.5542 | −0.468201 | ||||||||
\(610\) | 1.48686 | 0.0602014 | ||||||||
\(611\) | −1.07641 | −0.0435469 | ||||||||
\(612\) | 0.561904 | 0.0227136 | ||||||||
\(613\) | 45.3150 | 1.83025 | 0.915127 | − | 0.403166i | \(-0.132090\pi\) | ||||
0.915127 | + | 0.403166i | \(0.132090\pi\) | |||||||
\(614\) | 0.955702 | 0.0385690 | ||||||||
\(615\) | −23.2989 | −0.939504 | ||||||||
\(616\) | −7.43356 | −0.299507 | ||||||||
\(617\) | −20.9179 | −0.842123 | −0.421062 | − | 0.907032i | \(-0.638342\pi\) | ||||
−0.421062 | + | 0.907032i | \(0.638342\pi\) | |||||||
\(618\) | −7.09280 | −0.285314 | ||||||||
\(619\) | −13.9694 | −0.561479 | −0.280739 | − | 0.959784i | \(-0.590580\pi\) | ||||
−0.280739 | + | 0.959784i | \(0.590580\pi\) | |||||||
\(620\) | −44.9131 | −1.80375 | ||||||||
\(621\) | −42.8961 | −1.72136 | ||||||||
\(622\) | 0.570784 | 0.0228863 | ||||||||
\(623\) | 12.5050 | 0.501002 | ||||||||
\(624\) | 37.1654 | 1.48781 | ||||||||
\(625\) | −28.9975 | −1.15990 | ||||||||
\(626\) | 5.31895 | 0.212588 | ||||||||
\(627\) | −11.2317 | −0.448551 | ||||||||
\(628\) | 28.9606 | 1.15565 | ||||||||
\(629\) | 52.1648 | 2.07995 | ||||||||
\(630\) | −0.0974502 | −0.00388251 | ||||||||
\(631\) | −10.7231 | −0.426879 | −0.213439 | − | 0.976956i | \(-0.568467\pi\) | ||||
−0.213439 | + | 0.976956i | \(0.568467\pi\) | |||||||
\(632\) | 3.81550 | 0.151772 | ||||||||
\(633\) | 38.5749 | 1.53321 | ||||||||
\(634\) | 0.315654 | 0.0125362 | ||||||||
\(635\) | 24.3810 | 0.967532 | ||||||||
\(636\) | 2.78776 | 0.110542 | ||||||||
\(637\) | 20.9883 | 0.831585 | ||||||||
\(638\) | 3.58763 | 0.142036 | ||||||||
\(639\) | −0.0242749 | −0.000960301 0 | ||||||||
\(640\) | 23.8645 | 0.943328 | ||||||||
\(641\) | −22.9098 | −0.904881 | −0.452441 | − | 0.891794i | \(-0.649447\pi\) | ||||
−0.452441 | + | 0.891794i | \(0.649447\pi\) | |||||||
\(642\) | 4.59122 | 0.181201 | ||||||||
\(643\) | 14.0008 | 0.552138 | 0.276069 | − | 0.961138i | \(-0.410968\pi\) | ||||
0.276069 | + | 0.961138i | \(0.410968\pi\) | |||||||
\(644\) | 29.9935 | 1.18191 | ||||||||
\(645\) | −48.3577 | −1.90408 | ||||||||
\(646\) | −2.17320 | −0.0855036 | ||||||||
\(647\) | −8.20116 | −0.322421 | −0.161210 | − | 0.986920i | \(-0.551540\pi\) | ||||
−0.161210 | + | 0.986920i | \(0.551540\pi\) | |||||||
\(648\) | 9.86615 | 0.387579 | ||||||||
\(649\) | −8.06119 | −0.316429 | ||||||||
\(650\) | −6.53568 | −0.256350 | ||||||||
\(651\) | 25.4077 | 0.995807 | ||||||||
\(652\) | 2.90433 | 0.113742 | ||||||||
\(653\) | 33.2558 | 1.30140 | 0.650700 | − | 0.759335i | \(-0.274476\pi\) | ||||
0.650700 | + | 0.759335i | \(0.274476\pi\) | |||||||
\(654\) | −4.75468 | −0.185923 | ||||||||
\(655\) | 29.3730 | 1.14770 | ||||||||
\(656\) | −15.7795 | −0.616086 | ||||||||
\(657\) | −0.427852 | −0.0166921 | ||||||||
\(658\) | 0.0920831 | 0.00358977 | ||||||||
\(659\) | −28.3719 | −1.10521 | −0.552606 | − | 0.833442i | \(-0.686367\pi\) | ||||
−0.552606 | + | 0.833442i | \(0.686367\pi\) | |||||||
\(660\) | −37.4843 | −1.45908 | ||||||||
\(661\) | −24.6344 | −0.958165 | −0.479083 | − | 0.877770i | \(-0.659031\pi\) | ||||
−0.479083 | + | 0.877770i | \(0.659031\pi\) | |||||||
\(662\) | −5.95430 | −0.231420 | ||||||||
\(663\) | −47.9618 | −1.86268 | ||||||||
\(664\) | 7.19925 | 0.279385 | ||||||||
\(665\) | −9.69215 | −0.375845 | ||||||||
\(666\) | −0.197773 | −0.00766356 | ||||||||
\(667\) | −29.5142 | −1.14280 | ||||||||
\(668\) | 3.68085 | 0.142416 | ||||||||
\(669\) | 36.2076 | 1.39987 | ||||||||
\(670\) | 6.39336 | 0.246997 | ||||||||
\(671\) | −6.71629 | −0.259280 | ||||||||
\(672\) | −10.1973 | −0.393371 | ||||||||
\(673\) | 22.6227 | 0.872042 | 0.436021 | − | 0.899936i | \(-0.356387\pi\) | ||||
0.436021 | + | 0.899936i | \(0.356387\pi\) | |||||||
\(674\) | −0.338108 | −0.0130235 | ||||||||
\(675\) | 20.5628 | 0.791463 | ||||||||
\(676\) | −43.5978 | −1.67684 | ||||||||
\(677\) | −32.1683 | −1.23633 | −0.618165 | − | 0.786048i | \(-0.712124\pi\) | ||||
−0.618165 | + | 0.786048i | \(0.712124\pi\) | |||||||
\(678\) | 8.95182 | 0.343793 | ||||||||
\(679\) | 31.5695 | 1.21152 | ||||||||
\(680\) | −14.7876 | −0.567079 | ||||||||
\(681\) | −9.40268 | −0.360311 | ||||||||
\(682\) | −7.88918 | −0.302092 | ||||||||
\(683\) | −41.6390 | −1.59327 | −0.796637 | − | 0.604458i | \(-0.793390\pi\) | ||||
−0.796637 | + | 0.604458i | \(0.793390\pi\) | |||||||
\(684\) | −0.211880 | −0.00810144 | ||||||||
\(685\) | −8.51214 | −0.325232 | ||||||||
\(686\) | −5.37075 | −0.205056 | ||||||||
\(687\) | −38.5122 | −1.46933 | ||||||||
\(688\) | −32.7509 | −1.24862 | ||||||||
\(689\) | −4.93955 | −0.188182 | ||||||||
\(690\) | −11.9915 | −0.456509 | ||||||||
\(691\) | 20.1261 | 0.765632 | 0.382816 | − | 0.923825i | \(-0.374954\pi\) | ||||
0.382816 | + | 0.923825i | \(0.374954\pi\) | |||||||
\(692\) | 11.9196 | 0.453117 | ||||||||
\(693\) | 0.440191 | 0.0167215 | ||||||||
\(694\) | −7.15985 | −0.271784 | ||||||||
\(695\) | −52.3090 | −1.98419 | ||||||||
\(696\) | 6.64733 | 0.251967 | ||||||||
\(697\) | 20.3634 | 0.771317 | ||||||||
\(698\) | −8.89551 | −0.336700 | ||||||||
\(699\) | 13.4539 | 0.508872 | ||||||||
\(700\) | −14.3778 | −0.543430 | ||||||||
\(701\) | 33.1224 | 1.25101 | 0.625507 | − | 0.780219i | \(-0.284892\pi\) | ||||
0.625507 | + | 0.780219i | \(0.284892\pi\) | |||||||
\(702\) | −8.39598 | −0.316886 | ||||||||
\(703\) | −19.6701 | −0.741870 | ||||||||
\(704\) | −23.2076 | −0.874671 | ||||||||
\(705\) | 0.946729 | 0.0356559 | ||||||||
\(706\) | −6.95526 | −0.261765 | ||||||||
\(707\) | 22.1662 | 0.833644 | ||||||||
\(708\) | −7.32564 | −0.275315 | ||||||||
\(709\) | 21.3873 | 0.803216 | 0.401608 | − | 0.915812i | \(-0.368451\pi\) | ||||
0.401608 | + | 0.915812i | \(0.368451\pi\) | |||||||
\(710\) | 0.313329 | 0.0117590 | ||||||||
\(711\) | −0.225941 | −0.00847344 | ||||||||
\(712\) | −7.19432 | −0.269619 | ||||||||
\(713\) | 64.9016 | 2.43059 | ||||||||
\(714\) | 4.10296 | 0.153549 | ||||||||
\(715\) | 66.4173 | 2.48387 | ||||||||
\(716\) | −1.90256 | −0.0711021 | ||||||||
\(717\) | −18.7292 | −0.699453 | ||||||||
\(718\) | 5.16494 | 0.192754 | ||||||||
\(719\) | 26.7348 | 0.997041 | 0.498520 | − | 0.866878i | \(-0.333877\pi\) | ||||
0.498520 | + | 0.866878i | \(0.333877\pi\) | |||||||
\(720\) | −0.678556 | −0.0252883 | ||||||||
\(721\) | 27.6472 | 1.02964 | ||||||||
\(722\) | −4.37912 | −0.162974 | ||||||||
\(723\) | −39.6824 | −1.47580 | ||||||||
\(724\) | −33.2035 | −1.23400 | ||||||||
\(725\) | 14.1480 | 0.525445 | ||||||||
\(726\) | −1.31636 | −0.0488547 | ||||||||
\(727\) | 20.7270 | 0.768724 | 0.384362 | − | 0.923183i | \(-0.374422\pi\) | ||||
0.384362 | + | 0.923183i | \(0.374422\pi\) | |||||||
\(728\) | 11.9695 | 0.443618 | ||||||||
\(729\) | 26.4036 | 0.977912 | ||||||||
\(730\) | 5.52251 | 0.204397 | ||||||||
\(731\) | 42.2648 | 1.56322 | ||||||||
\(732\) | −6.10346 | −0.225590 | ||||||||
\(733\) | −30.0368 | −1.10943 | −0.554717 | − | 0.832039i | \(-0.687173\pi\) | ||||
−0.554717 | + | 0.832039i | \(0.687173\pi\) | |||||||
\(734\) | 6.18588 | 0.228325 | ||||||||
\(735\) | −18.4597 | −0.680897 | ||||||||
\(736\) | −26.0482 | −0.960149 | ||||||||
\(737\) | −28.8793 | −1.06378 | ||||||||
\(738\) | −0.0772041 | −0.00284192 | ||||||||
\(739\) | −44.9552 | −1.65370 | −0.826852 | − | 0.562420i | \(-0.809871\pi\) | ||||
−0.826852 | + | 0.562420i | \(0.809871\pi\) | |||||||
\(740\) | −65.6463 | −2.41320 | ||||||||
\(741\) | 18.0852 | 0.664376 | ||||||||
\(742\) | 0.422561 | 0.0155127 | ||||||||
\(743\) | 26.2207 | 0.961946 | 0.480973 | − | 0.876735i | \(-0.340284\pi\) | ||||
0.480973 | + | 0.876735i | \(0.340284\pi\) | |||||||
\(744\) | −14.6175 | −0.535902 | ||||||||
\(745\) | 25.2734 | 0.925945 | ||||||||
\(746\) | −1.15684 | −0.0423550 | ||||||||
\(747\) | −0.426316 | −0.0155981 | ||||||||
\(748\) | 32.7615 | 1.19788 | ||||||||
\(749\) | −17.8962 | −0.653913 | ||||||||
\(750\) | −1.43557 | −0.0524197 | ||||||||
\(751\) | 39.4426 | 1.43928 | 0.719640 | − | 0.694348i | \(-0.244307\pi\) | ||||
0.719640 | + | 0.694348i | \(0.244307\pi\) | |||||||
\(752\) | 0.641185 | 0.0233816 | ||||||||
\(753\) | −13.9772 | −0.509357 | ||||||||
\(754\) | −5.77678 | −0.210378 | ||||||||
\(755\) | −23.7604 | −0.864729 | ||||||||
\(756\) | −18.4703 | −0.671757 | ||||||||
\(757\) | 13.8394 | 0.503000 | 0.251500 | − | 0.967857i | \(-0.419076\pi\) | ||||
0.251500 | + | 0.967857i | \(0.419076\pi\) | |||||||
\(758\) | −0.0256758 | −0.000932588 0 | ||||||||
\(759\) | 54.1667 | 1.96613 | ||||||||
\(760\) | 5.57605 | 0.202264 | ||||||||
\(761\) | 46.6841 | 1.69230 | 0.846149 | − | 0.532946i | \(-0.178915\pi\) | ||||
0.846149 | + | 0.532946i | \(0.178915\pi\) | |||||||
\(762\) | 3.89187 | 0.140987 | ||||||||
\(763\) | 18.5334 | 0.670953 | ||||||||
\(764\) | 35.9683 | 1.30129 | ||||||||
\(765\) | 0.875673 | 0.0316600 | ||||||||
\(766\) | 3.02426 | 0.109271 | ||||||||
\(767\) | 12.9801 | 0.468683 | ||||||||
\(768\) | −18.1008 | −0.653155 | ||||||||
\(769\) | −35.4819 | −1.27951 | −0.639755 | − | 0.768579i | \(-0.720964\pi\) | ||||
−0.639755 | + | 0.768579i | \(0.720964\pi\) | |||||||
\(770\) | −5.68177 | −0.204757 | ||||||||
\(771\) | 3.34239 | 0.120373 | ||||||||
\(772\) | −18.2240 | −0.655896 | ||||||||
\(773\) | 25.1072 | 0.903043 | 0.451522 | − | 0.892260i | \(-0.350881\pi\) | ||||
0.451522 | + | 0.892260i | \(0.350881\pi\) | |||||||
\(774\) | −0.160240 | −0.00575969 | ||||||||
\(775\) | −31.1115 | −1.11756 | ||||||||
\(776\) | −18.1624 | −0.651992 | ||||||||
\(777\) | 37.1366 | 1.33227 | ||||||||
\(778\) | −1.13302 | −0.0406208 | ||||||||
\(779\) | −7.67853 | −0.275112 | ||||||||
\(780\) | 60.3570 | 2.16113 | ||||||||
\(781\) | −1.41533 | −0.0506446 | ||||||||
\(782\) | 10.4806 | 0.374787 | ||||||||
\(783\) | 18.1751 | 0.649526 | ||||||||
\(784\) | −12.5021 | −0.446503 | ||||||||
\(785\) | 45.1323 | 1.61084 | ||||||||
\(786\) | 4.68872 | 0.167241 | ||||||||
\(787\) | −48.6263 | −1.73334 | −0.866670 | − | 0.498882i | \(-0.833744\pi\) | ||||
−0.866670 | + | 0.498882i | \(0.833744\pi\) | |||||||
\(788\) | 8.06822 | 0.287418 | ||||||||
\(789\) | −20.1746 | −0.718235 | ||||||||
\(790\) | 2.91634 | 0.103759 | ||||||||
\(791\) | −34.8935 | −1.24067 | ||||||||
\(792\) | −0.253249 | −0.00899879 | ||||||||
\(793\) | 10.8145 | 0.384035 | ||||||||
\(794\) | 9.12136 | 0.323705 | ||||||||
\(795\) | 4.34446 | 0.154082 | ||||||||
\(796\) | −28.0938 | −0.995757 | ||||||||
\(797\) | 34.9647 | 1.23851 | 0.619257 | − | 0.785189i | \(-0.287434\pi\) | ||||
0.619257 | + | 0.785189i | \(0.287434\pi\) | |||||||
\(798\) | −1.54713 | −0.0547677 | ||||||||
\(799\) | −0.827445 | −0.0292729 | ||||||||
\(800\) | 12.4865 | 0.441466 | ||||||||
\(801\) | 0.426024 | 0.0150528 | ||||||||
\(802\) | −7.25127 | −0.256051 | ||||||||
\(803\) | −24.9457 | −0.880313 | ||||||||
\(804\) | −26.2442 | −0.925563 | ||||||||
\(805\) | 46.7420 | 1.64744 | ||||||||
\(806\) | 12.7031 | 0.447448 | ||||||||
\(807\) | 29.9435 | 1.05406 | ||||||||
\(808\) | −12.7525 | −0.448633 | ||||||||
\(809\) | −5.42646 | −0.190784 | −0.0953921 | − | 0.995440i | \(-0.530411\pi\) | ||||
−0.0953921 | + | 0.995440i | \(0.530411\pi\) | |||||||
\(810\) | 7.54109 | 0.264967 | ||||||||
\(811\) | 12.0367 | 0.422666 | 0.211333 | − | 0.977414i | \(-0.432220\pi\) | ||||
0.211333 | + | 0.977414i | \(0.432220\pi\) | |||||||
\(812\) | −12.7083 | −0.445974 | ||||||||
\(813\) | −6.72805 | −0.235963 | ||||||||
\(814\) | −11.5311 | −0.404163 | ||||||||
\(815\) | 4.52611 | 0.158543 | ||||||||
\(816\) | 28.5694 | 1.00013 | ||||||||
\(817\) | −15.9370 | −0.557566 | ||||||||
\(818\) | 8.24952 | 0.288438 | ||||||||
\(819\) | −0.708792 | −0.0247672 | ||||||||
\(820\) | −25.6261 | −0.894902 | ||||||||
\(821\) | −23.2393 | −0.811056 | −0.405528 | − | 0.914083i | \(-0.632912\pi\) | ||||
−0.405528 | + | 0.914083i | \(0.632912\pi\) | |||||||
\(822\) | −1.35876 | −0.0473923 | ||||||||
\(823\) | 39.5067 | 1.37712 | 0.688558 | − | 0.725181i | \(-0.258244\pi\) | ||||
0.688558 | + | 0.725181i | \(0.258244\pi\) | |||||||
\(824\) | −15.9059 | −0.554107 | ||||||||
\(825\) | −25.9655 | −0.904004 | ||||||||
\(826\) | −1.11040 | −0.0386358 | ||||||||
\(827\) | 28.1602 | 0.979226 | 0.489613 | − | 0.871940i | \(-0.337138\pi\) | ||||
0.489613 | + | 0.871940i | \(0.337138\pi\) | |||||||
\(828\) | 1.02183 | 0.0355110 | ||||||||
\(829\) | −5.43801 | −0.188870 | −0.0944349 | − | 0.995531i | \(-0.530104\pi\) | ||||
−0.0944349 | + | 0.995531i | \(0.530104\pi\) | |||||||
\(830\) | 5.50268 | 0.191001 | ||||||||
\(831\) | −17.2485 | −0.598345 | ||||||||
\(832\) | 37.3688 | 1.29553 | ||||||||
\(833\) | 16.1339 | 0.559005 | ||||||||
\(834\) | −8.34992 | −0.289134 | ||||||||
\(835\) | 5.73624 | 0.198511 | ||||||||
\(836\) | −12.3535 | −0.427256 | ||||||||
\(837\) | −39.9670 | −1.38146 | ||||||||
\(838\) | −1.18961 | −0.0410944 | ||||||||
\(839\) | −18.1956 | −0.628181 | −0.314090 | − | 0.949393i | \(-0.601700\pi\) | ||||
−0.314090 | + | 0.949393i | \(0.601700\pi\) | |||||||
\(840\) | −10.5275 | −0.363232 | ||||||||
\(841\) | −16.4948 | −0.568786 | ||||||||
\(842\) | 7.02334 | 0.242040 | ||||||||
\(843\) | −47.0630 | −1.62093 | ||||||||
\(844\) | 42.4278 | 1.46043 | ||||||||
\(845\) | −67.9429 | −2.33731 | ||||||||
\(846\) | 0.00313711 | 0.000107856 0 | ||||||||
\(847\) | 5.13107 | 0.176306 | ||||||||
\(848\) | 2.94234 | 0.101040 | ||||||||
\(849\) | −5.76518 | −0.197860 | ||||||||
\(850\) | −5.02403 | −0.172323 | ||||||||
\(851\) | 94.8621 | 3.25183 | ||||||||
\(852\) | −1.28619 | −0.0440642 | ||||||||
\(853\) | −15.7779 | −0.540226 | −0.270113 | − | 0.962829i | \(-0.587061\pi\) | ||||
−0.270113 | + | 0.962829i | \(0.587061\pi\) | |||||||
\(854\) | −0.925145 | −0.0316578 | ||||||||
\(855\) | −0.330195 | −0.0112924 | ||||||||
\(856\) | 10.2960 | 0.351909 | ||||||||
\(857\) | 50.4138 | 1.72210 | 0.861051 | − | 0.508519i | \(-0.169807\pi\) | ||||
0.861051 | + | 0.508519i | \(0.169807\pi\) | |||||||
\(858\) | 10.6020 | 0.361945 | ||||||||
\(859\) | 6.69367 | 0.228385 | 0.114193 | − | 0.993459i | \(-0.463572\pi\) | ||||
0.114193 | + | 0.993459i | \(0.463572\pi\) | |||||||
\(860\) | −53.1878 | −1.81369 | ||||||||
\(861\) | 14.4969 | 0.494053 | ||||||||
\(862\) | 4.78682 | 0.163040 | ||||||||
\(863\) | 27.9913 | 0.952835 | 0.476418 | − | 0.879219i | \(-0.341935\pi\) | ||||
0.476418 | + | 0.879219i | \(0.341935\pi\) | |||||||
\(864\) | 16.0407 | 0.545715 | ||||||||
\(865\) | 18.5756 | 0.631589 | ||||||||
\(866\) | 0.272597 | 0.00926324 | ||||||||
\(867\) | −7.11327 | −0.241579 | ||||||||
\(868\) | 27.9455 | 0.948532 | ||||||||
\(869\) | −13.1733 | −0.446875 | ||||||||
\(870\) | 5.08082 | 0.172256 | ||||||||
\(871\) | 46.5013 | 1.57564 | ||||||||
\(872\) | −10.6625 | −0.361079 | ||||||||
\(873\) | 1.07552 | 0.0364007 | ||||||||
\(874\) | −3.95199 | −0.133678 | ||||||||
\(875\) | 5.59575 | 0.189171 | ||||||||
\(876\) | −22.6695 | −0.765931 | ||||||||
\(877\) | 32.1120 | 1.08435 | 0.542173 | − | 0.840267i | \(-0.317602\pi\) | ||||
0.542173 | + | 0.840267i | \(0.317602\pi\) | |||||||
\(878\) | 6.43046 | 0.217018 | ||||||||
\(879\) | 3.52838 | 0.119009 | ||||||||
\(880\) | −39.5628 | −1.33366 | ||||||||
\(881\) | −26.1191 | −0.879976 | −0.439988 | − | 0.898004i | \(-0.645017\pi\) | ||||
−0.439988 | + | 0.898004i | \(0.645017\pi\) | |||||||
\(882\) | −0.0611687 | −0.00205966 | ||||||||
\(883\) | 39.7046 | 1.33617 | 0.668083 | − | 0.744086i | \(-0.267115\pi\) | ||||
0.668083 | + | 0.744086i | \(0.267115\pi\) | |||||||
\(884\) | −52.7523 | −1.77425 | ||||||||
\(885\) | −11.4163 | −0.383755 | ||||||||
\(886\) | −10.6880 | −0.359070 | ||||||||
\(887\) | −33.5353 | −1.12601 | −0.563003 | − | 0.826455i | \(-0.690354\pi\) | ||||
−0.563003 | + | 0.826455i | \(0.690354\pi\) | |||||||
\(888\) | −21.3653 | −0.716972 | ||||||||
\(889\) | −15.1702 | −0.508792 | ||||||||
\(890\) | −5.49891 | −0.184324 | ||||||||
\(891\) | −34.0638 | −1.14118 | ||||||||
\(892\) | 39.8241 | 1.33341 | ||||||||
\(893\) | 0.312009 | 0.0104410 | ||||||||
\(894\) | 4.03431 | 0.134927 | ||||||||
\(895\) | −2.96496 | −0.0991076 | ||||||||
\(896\) | −14.8488 | −0.496064 | ||||||||
\(897\) | −87.2189 | −2.91215 | ||||||||
\(898\) | −8.29640 | −0.276854 | ||||||||
\(899\) | −27.4989 | −0.917140 | ||||||||
\(900\) | −0.489827 | −0.0163276 | ||||||||
\(901\) | −3.79707 | −0.126499 | ||||||||
\(902\) | −4.50133 | −0.149878 | ||||||||
\(903\) | 30.0888 | 1.00129 | ||||||||
\(904\) | 20.0748 | 0.667677 | ||||||||
\(905\) | −51.7445 | −1.72004 | ||||||||
\(906\) | −3.79279 | −0.126007 | ||||||||
\(907\) | 13.3872 | 0.444514 | 0.222257 | − | 0.974988i | \(-0.428658\pi\) | ||||
0.222257 | + | 0.974988i | \(0.428658\pi\) | |||||||
\(908\) | −10.3418 | −0.343206 | ||||||||
\(909\) | 0.755162 | 0.0250472 | ||||||||
\(910\) | 9.14874 | 0.303278 | ||||||||
\(911\) | −15.3096 | −0.507228 | −0.253614 | − | 0.967305i | \(-0.581619\pi\) | ||||
−0.253614 | + | 0.967305i | \(0.581619\pi\) | |||||||
\(912\) | −10.7728 | −0.356723 | ||||||||
\(913\) | −24.8561 | −0.822615 | ||||||||
\(914\) | 3.58694 | 0.118645 | ||||||||
\(915\) | −9.51165 | −0.314445 | ||||||||
\(916\) | −42.3589 | −1.39958 | ||||||||
\(917\) | −18.2763 | −0.603535 | ||||||||
\(918\) | −6.45406 | −0.213016 | ||||||||
\(919\) | −2.27868 | −0.0751667 | −0.0375833 | − | 0.999293i | \(-0.511966\pi\) | ||||
−0.0375833 | + | 0.999293i | \(0.511966\pi\) | |||||||
\(920\) | −26.8914 | −0.886583 | ||||||||
\(921\) | −6.11374 | −0.201455 | ||||||||
\(922\) | −8.98888 | −0.296033 | ||||||||
\(923\) | 2.27896 | 0.0750129 | ||||||||
\(924\) | 23.3232 | 0.767277 | ||||||||
\(925\) | −45.4734 | −1.49516 | ||||||||
\(926\) | −0.877085 | −0.0288228 | ||||||||
\(927\) | 0.941892 | 0.0309358 | ||||||||
\(928\) | 11.0366 | 0.362296 | ||||||||
\(929\) | 54.2380 | 1.77949 | 0.889745 | − | 0.456457i | \(-0.150882\pi\) | ||||
0.889745 | + | 0.456457i | \(0.150882\pi\) | |||||||
\(930\) | −11.1727 | −0.366367 | ||||||||
\(931\) | −6.08368 | −0.199385 | ||||||||
\(932\) | 14.7977 | 0.484714 | ||||||||
\(933\) | −3.65137 | −0.119541 | ||||||||
\(934\) | 4.60515 | 0.150685 | ||||||||
\(935\) | 51.0555 | 1.66969 | ||||||||
\(936\) | 0.407779 | 0.0133287 | ||||||||
\(937\) | −20.7294 | −0.677201 | −0.338601 | − | 0.940930i | \(-0.609954\pi\) | ||||
−0.338601 | + | 0.940930i | \(0.609954\pi\) | |||||||
\(938\) | −3.97803 | −0.129887 | ||||||||
\(939\) | −34.0260 | −1.11040 | ||||||||
\(940\) | 1.04129 | 0.0339632 | ||||||||
\(941\) | −45.6259 | −1.48736 | −0.743681 | − | 0.668535i | \(-0.766922\pi\) | ||||
−0.743681 | + | 0.668535i | \(0.766922\pi\) | |||||||
\(942\) | 7.20431 | 0.234729 | ||||||||
\(943\) | 37.0310 | 1.20589 | ||||||||
\(944\) | −7.73184 | −0.251650 | ||||||||
\(945\) | −28.7841 | −0.936348 | ||||||||
\(946\) | −9.34266 | −0.303756 | ||||||||
\(947\) | 10.4299 | 0.338927 | 0.169464 | − | 0.985536i | \(-0.445796\pi\) | ||||
0.169464 | + | 0.985536i | \(0.445796\pi\) | |||||||
\(948\) | −11.9713 | −0.388811 | ||||||||
\(949\) | 40.1673 | 1.30389 | ||||||||
\(950\) | 1.89444 | 0.0614637 | ||||||||
\(951\) | −2.01928 | −0.0654796 | ||||||||
\(952\) | 9.20103 | 0.298207 | ||||||||
\(953\) | −18.7987 | −0.608949 | −0.304474 | − | 0.952521i | \(-0.598481\pi\) | ||||
−0.304474 | + | 0.952521i | \(0.598481\pi\) | |||||||
\(954\) | 0.0143959 | 0.000466085 0 | ||||||||
\(955\) | 56.0531 | 1.81384 | ||||||||
\(956\) | −20.5999 | −0.666247 | ||||||||
\(957\) | −22.9505 | −0.741884 | ||||||||
\(958\) | −0.365385 | −0.0118050 | ||||||||
\(959\) | 5.29636 | 0.171028 | ||||||||
\(960\) | −32.8668 | −1.06077 | ||||||||
\(961\) | 29.4700 | 0.950644 | ||||||||
\(962\) | 18.5672 | 0.598631 | ||||||||
\(963\) | −0.609692 | −0.0196471 | ||||||||
\(964\) | −43.6459 | −1.40574 | ||||||||
\(965\) | −28.4003 | −0.914238 | ||||||||
\(966\) | 7.46127 | 0.240062 | ||||||||
\(967\) | −13.6049 | −0.437505 | −0.218753 | − | 0.975780i | \(-0.570199\pi\) | ||||
−0.218753 | + | 0.975780i | \(0.570199\pi\) | |||||||
\(968\) | −2.95198 | −0.0948804 | ||||||||
\(969\) | 13.9022 | 0.446604 | ||||||||
\(970\) | −13.8822 | −0.445732 | ||||||||
\(971\) | −7.52515 | −0.241494 | −0.120747 | − | 0.992683i | \(-0.538529\pi\) | ||||
−0.120747 | + | 0.992683i | \(0.538529\pi\) | |||||||
\(972\) | −1.27213 | −0.0408035 | ||||||||
\(973\) | 32.5473 | 1.04342 | ||||||||
\(974\) | 0.653631 | 0.0209437 | ||||||||
\(975\) | 41.8095 | 1.33898 | ||||||||
\(976\) | −6.44189 | −0.206200 | ||||||||
\(977\) | −14.2026 | −0.454381 | −0.227191 | − | 0.973850i | \(-0.572954\pi\) | ||||
−0.227191 | + | 0.973850i | \(0.572954\pi\) | |||||||
\(978\) | 0.722488 | 0.0231026 | ||||||||
\(979\) | 24.8390 | 0.793859 | ||||||||
\(980\) | −20.3035 | −0.648572 | ||||||||
\(981\) | 0.631400 | 0.0201590 | ||||||||
\(982\) | −7.47304 | −0.238474 | ||||||||
\(983\) | −40.4071 | −1.28879 | −0.644393 | − | 0.764695i | \(-0.722890\pi\) | ||||
−0.644393 | + | 0.764695i | \(0.722890\pi\) | |||||||
\(984\) | −8.34029 | −0.265879 | ||||||||
\(985\) | 12.5735 | 0.400626 | ||||||||
\(986\) | −4.44066 | −0.141419 | ||||||||
\(987\) | −0.589067 | −0.0187502 | ||||||||
\(988\) | 19.8916 | 0.632836 | ||||||||
\(989\) | 76.8589 | 2.44397 | ||||||||
\(990\) | −0.193568 | −0.00615199 | ||||||||
\(991\) | 48.6246 | 1.54461 | 0.772306 | − | 0.635251i | \(-0.219103\pi\) | ||||
0.772306 | + | 0.635251i | \(0.219103\pi\) | |||||||
\(992\) | −24.2695 | −0.770558 | ||||||||
\(993\) | 38.0904 | 1.20876 | ||||||||
\(994\) | −0.194957 | −0.00618366 | ||||||||
\(995\) | −43.7814 | −1.38796 | ||||||||
\(996\) | −22.5881 | −0.715730 | ||||||||
\(997\) | 49.0353 | 1.55296 | 0.776482 | − | 0.630140i | \(-0.217002\pi\) | ||||
0.776482 | + | 0.630140i | \(0.217002\pi\) | |||||||
\(998\) | −7.71152 | −0.244104 | ||||||||
\(999\) | −58.4169 | −1.84823 |
(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 | 4001.2.a.b.1.99 | ✓ | 184 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4001.2.a.b.1.99 | ✓ | 184 | 1.1 | even | 1 | trivial |