Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [354,6,Mod(1,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("354.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.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: | \(56.7758722138\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 290x^{3} - 616x^{2} + 4720x + 11900 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(4.22515\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 354.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | −3.84671 | −0.0688121 | −0.0344061 | − | 0.999408i | \(-0.510954\pi\) | ||||
−0.0344061 | + | 0.999408i | \(0.510954\pi\) | |||||||
\(6\) | −36.0000 | −0.408248 | ||||||||
\(7\) | 56.0281 | 0.432176 | 0.216088 | − | 0.976374i | \(-0.430670\pi\) | ||||
0.216088 | + | 0.976374i | \(0.430670\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 15.3869 | 0.0486575 | ||||||||
\(11\) | 11.9353 | 0.0297408 | 0.0148704 | − | 0.999889i | \(-0.495266\pi\) | ||||
0.0148704 | + | 0.999889i | \(0.495266\pi\) | |||||||
\(12\) | 144.000 | 0.288675 | ||||||||
\(13\) | −332.703 | −0.546007 | −0.273003 | − | 0.962013i | \(-0.588017\pi\) | ||||
−0.273003 | + | 0.962013i | \(0.588017\pi\) | |||||||
\(14\) | −224.112 | −0.305594 | ||||||||
\(15\) | −34.6204 | −0.0397287 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −542.091 | −0.454935 | −0.227468 | − | 0.973786i | \(-0.573045\pi\) | ||||
−0.227468 | + | 0.973786i | \(0.573045\pi\) | |||||||
\(18\) | −324.000 | −0.235702 | ||||||||
\(19\) | −1034.60 | −0.657489 | −0.328745 | − | 0.944419i | \(-0.606626\pi\) | ||||
−0.328745 | + | 0.944419i | \(0.606626\pi\) | |||||||
\(20\) | −61.5474 | −0.0344061 | ||||||||
\(21\) | 504.253 | 0.249517 | ||||||||
\(22\) | −47.7414 | −0.0210299 | ||||||||
\(23\) | 2801.09 | 1.10410 | 0.552049 | − | 0.833812i | \(-0.313846\pi\) | ||||
0.552049 | + | 0.833812i | \(0.313846\pi\) | |||||||
\(24\) | −576.000 | −0.204124 | ||||||||
\(25\) | −3110.20 | −0.995265 | ||||||||
\(26\) | 1330.81 | 0.386085 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 896.449 | 0.216088 | ||||||||
\(29\) | −7312.03 | −1.61452 | −0.807259 | − | 0.590197i | \(-0.799050\pi\) | ||||
−0.807259 | + | 0.590197i | \(0.799050\pi\) | |||||||
\(30\) | 138.482 | 0.0280924 | ||||||||
\(31\) | 6976.21 | 1.30381 | 0.651907 | − | 0.758299i | \(-0.273969\pi\) | ||||
0.651907 | + | 0.758299i | \(0.273969\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | 107.418 | 0.0171709 | ||||||||
\(34\) | 2168.36 | 0.321688 | ||||||||
\(35\) | −215.524 | −0.0297389 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | −14335.3 | −1.72148 | −0.860742 | − | 0.509042i | \(-0.830000\pi\) | ||||
−0.860742 | + | 0.509042i | \(0.830000\pi\) | |||||||
\(38\) | 4138.40 | 0.464915 | ||||||||
\(39\) | −2994.33 | −0.315237 | ||||||||
\(40\) | 246.190 | 0.0243288 | ||||||||
\(41\) | 8937.40 | 0.830332 | 0.415166 | − | 0.909746i | \(-0.363724\pi\) | ||||
0.415166 | + | 0.909746i | \(0.363724\pi\) | |||||||
\(42\) | −2017.01 | −0.176435 | ||||||||
\(43\) | −7695.38 | −0.634686 | −0.317343 | − | 0.948311i | \(-0.602791\pi\) | ||||
−0.317343 | + | 0.948311i | \(0.602791\pi\) | |||||||
\(44\) | 190.965 | 0.0148704 | ||||||||
\(45\) | −311.584 | −0.0229374 | ||||||||
\(46\) | −11204.4 | −0.780715 | ||||||||
\(47\) | 2137.88 | 0.141169 | 0.0705845 | − | 0.997506i | \(-0.477514\pi\) | ||||
0.0705845 | + | 0.997506i | \(0.477514\pi\) | |||||||
\(48\) | 2304.00 | 0.144338 | ||||||||
\(49\) | −13667.9 | −0.813224 | ||||||||
\(50\) | 12440.8 | 0.703759 | ||||||||
\(51\) | −4878.82 | −0.262657 | ||||||||
\(52\) | −5323.24 | −0.273003 | ||||||||
\(53\) | 12834.6 | 0.627616 | 0.313808 | − | 0.949486i | \(-0.398395\pi\) | ||||
0.313808 | + | 0.949486i | \(0.398395\pi\) | |||||||
\(54\) | −2916.00 | −0.136083 | ||||||||
\(55\) | −45.9118 | −0.00204653 | ||||||||
\(56\) | −3585.80 | −0.152797 | ||||||||
\(57\) | −9311.40 | −0.379601 | ||||||||
\(58\) | 29248.1 | 1.14164 | ||||||||
\(59\) | 3481.00 | 0.130189 | ||||||||
\(60\) | −553.927 | −0.0198644 | ||||||||
\(61\) | 15716.6 | 0.540797 | 0.270398 | − | 0.962749i | \(-0.412845\pi\) | ||||
0.270398 | + | 0.962749i | \(0.412845\pi\) | |||||||
\(62\) | −27904.8 | −0.921935 | ||||||||
\(63\) | 4538.27 | 0.144059 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 1279.81 | 0.0375719 | ||||||||
\(66\) | −429.672 | −0.0121416 | ||||||||
\(67\) | 18747.6 | 0.510220 | 0.255110 | − | 0.966912i | \(-0.417888\pi\) | ||||
0.255110 | + | 0.966912i | \(0.417888\pi\) | |||||||
\(68\) | −8673.45 | −0.227468 | ||||||||
\(69\) | 25209.8 | 0.637451 | ||||||||
\(70\) | 862.096 | 0.0210286 | ||||||||
\(71\) | −33560.5 | −0.790100 | −0.395050 | − | 0.918660i | \(-0.629273\pi\) | ||||
−0.395050 | + | 0.918660i | \(0.629273\pi\) | |||||||
\(72\) | −5184.00 | −0.117851 | ||||||||
\(73\) | −3937.01 | −0.0864687 | −0.0432344 | − | 0.999065i | \(-0.513766\pi\) | ||||
−0.0432344 | + | 0.999065i | \(0.513766\pi\) | |||||||
\(74\) | 57341.2 | 1.21727 | ||||||||
\(75\) | −27991.8 | −0.574616 | ||||||||
\(76\) | −16553.6 | −0.328745 | ||||||||
\(77\) | 668.714 | 0.0128533 | ||||||||
\(78\) | 11977.3 | 0.222906 | ||||||||
\(79\) | −58173.8 | −1.04872 | −0.524360 | − | 0.851497i | \(-0.675695\pi\) | ||||
−0.524360 | + | 0.851497i | \(0.675695\pi\) | |||||||
\(80\) | −984.759 | −0.0172030 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −35749.6 | −0.587133 | ||||||||
\(83\) | 62011.5 | 0.988046 | 0.494023 | − | 0.869449i | \(-0.335526\pi\) | ||||
0.494023 | + | 0.869449i | \(0.335526\pi\) | |||||||
\(84\) | 8068.04 | 0.124758 | ||||||||
\(85\) | 2085.27 | 0.0313051 | ||||||||
\(86\) | 30781.5 | 0.448791 | ||||||||
\(87\) | −65808.2 | −0.932142 | ||||||||
\(88\) | −763.862 | −0.0105150 | ||||||||
\(89\) | −49765.1 | −0.665962 | −0.332981 | − | 0.942933i | \(-0.608055\pi\) | ||||
−0.332981 | + | 0.942933i | \(0.608055\pi\) | |||||||
\(90\) | 1246.34 | 0.0162192 | ||||||||
\(91\) | −18640.7 | −0.235971 | ||||||||
\(92\) | 44817.5 | 0.552049 | ||||||||
\(93\) | 62785.9 | 0.752757 | ||||||||
\(94\) | −8551.53 | −0.0998215 | ||||||||
\(95\) | 3979.81 | 0.0452432 | ||||||||
\(96\) | −9216.00 | −0.102062 | ||||||||
\(97\) | −137225. | −1.48082 | −0.740412 | − | 0.672153i | \(-0.765370\pi\) | ||||
−0.740412 | + | 0.672153i | \(0.765370\pi\) | |||||||
\(98\) | 54671.4 | 0.575036 | ||||||||
\(99\) | 966.763 | 0.00991361 | ||||||||
\(100\) | −49763.2 | −0.497632 | ||||||||
\(101\) | 2248.79 | 0.0219354 | 0.0109677 | − | 0.999940i | \(-0.496509\pi\) | ||||
0.0109677 | + | 0.999940i | \(0.496509\pi\) | |||||||
\(102\) | 19515.3 | 0.185727 | ||||||||
\(103\) | 24776.8 | 0.230119 | 0.115059 | − | 0.993359i | \(-0.463294\pi\) | ||||
0.115059 | + | 0.993359i | \(0.463294\pi\) | |||||||
\(104\) | 21293.0 | 0.193043 | ||||||||
\(105\) | −1939.72 | −0.0171698 | ||||||||
\(106\) | −51338.6 | −0.443792 | ||||||||
\(107\) | −132705. | −1.12054 | −0.560271 | − | 0.828310i | \(-0.689303\pi\) | ||||
−0.560271 | + | 0.828310i | \(0.689303\pi\) | |||||||
\(108\) | 11664.0 | 0.0962250 | ||||||||
\(109\) | −118241. | −0.953237 | −0.476618 | − | 0.879110i | \(-0.658138\pi\) | ||||
−0.476618 | + | 0.879110i | \(0.658138\pi\) | |||||||
\(110\) | 183.647 | 0.00144712 | ||||||||
\(111\) | −129018. | −0.993899 | ||||||||
\(112\) | 14343.2 | 0.108044 | ||||||||
\(113\) | −194270. | −1.43123 | −0.715616 | − | 0.698494i | \(-0.753854\pi\) | ||||
−0.715616 | + | 0.698494i | \(0.753854\pi\) | |||||||
\(114\) | 37245.6 | 0.268419 | ||||||||
\(115\) | −10775.0 | −0.0759754 | ||||||||
\(116\) | −116992. | −0.807259 | ||||||||
\(117\) | −26948.9 | −0.182002 | ||||||||
\(118\) | −13924.0 | −0.0920575 | ||||||||
\(119\) | −30372.3 | −0.196612 | ||||||||
\(120\) | 2215.71 | 0.0140462 | ||||||||
\(121\) | −160909. | −0.999115 | ||||||||
\(122\) | −62866.4 | −0.382401 | ||||||||
\(123\) | 80436.6 | 0.479392 | ||||||||
\(124\) | 111619. | 0.651907 | ||||||||
\(125\) | 23985.0 | 0.137298 | ||||||||
\(126\) | −18153.1 | −0.101865 | ||||||||
\(127\) | −165554. | −0.910818 | −0.455409 | − | 0.890282i | \(-0.650507\pi\) | ||||
−0.455409 | + | 0.890282i | \(0.650507\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | −69258.4 | −0.366436 | ||||||||
\(130\) | −5119.25 | −0.0265673 | ||||||||
\(131\) | 222967. | 1.13518 | 0.567588 | − | 0.823313i | \(-0.307877\pi\) | ||||
0.567588 | + | 0.823313i | \(0.307877\pi\) | |||||||
\(132\) | 1718.69 | 0.00858544 | ||||||||
\(133\) | −57966.6 | −0.284151 | ||||||||
\(134\) | −74990.3 | −0.360780 | ||||||||
\(135\) | −2804.26 | −0.0132429 | ||||||||
\(136\) | 34693.8 | 0.160844 | ||||||||
\(137\) | −332097. | −1.51169 | −0.755846 | − | 0.654750i | \(-0.772774\pi\) | ||||
−0.755846 | + | 0.654750i | \(0.772774\pi\) | |||||||
\(138\) | −100839. | −0.450746 | ||||||||
\(139\) | 112233. | 0.492701 | 0.246351 | − | 0.969181i | \(-0.420769\pi\) | ||||
0.246351 | + | 0.969181i | \(0.420769\pi\) | |||||||
\(140\) | −3448.38 | −0.0148695 | ||||||||
\(141\) | 19240.9 | 0.0815039 | ||||||||
\(142\) | 134242. | 0.558685 | ||||||||
\(143\) | −3970.92 | −0.0162387 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | 28127.3 | 0.111098 | ||||||||
\(146\) | 15748.0 | 0.0611426 | ||||||||
\(147\) | −123011. | −0.469515 | ||||||||
\(148\) | −229365. | −0.860742 | ||||||||
\(149\) | −411071. | −1.51688 | −0.758440 | − | 0.651743i | \(-0.774038\pi\) | ||||
−0.758440 | + | 0.651743i | \(0.774038\pi\) | |||||||
\(150\) | 111967. | 0.406315 | ||||||||
\(151\) | −415434. | −1.48272 | −0.741362 | − | 0.671106i | \(-0.765820\pi\) | ||||
−0.741362 | + | 0.671106i | \(0.765820\pi\) | |||||||
\(152\) | 66214.4 | 0.232457 | ||||||||
\(153\) | −43909.3 | −0.151645 | ||||||||
\(154\) | −2674.86 | −0.00908863 | ||||||||
\(155\) | −26835.5 | −0.0897182 | ||||||||
\(156\) | −47909.2 | −0.157619 | ||||||||
\(157\) | −235393. | −0.762157 | −0.381078 | − | 0.924543i | \(-0.624447\pi\) | ||||
−0.381078 | + | 0.924543i | \(0.624447\pi\) | |||||||
\(158\) | 232695. | 0.741557 | ||||||||
\(159\) | 115512. | 0.362354 | ||||||||
\(160\) | 3939.04 | 0.0121644 | ||||||||
\(161\) | 156940. | 0.477165 | ||||||||
\(162\) | −26244.0 | −0.0785674 | ||||||||
\(163\) | −665502. | −1.96192 | −0.980958 | − | 0.194218i | \(-0.937783\pi\) | ||||
−0.980958 | + | 0.194218i | \(0.937783\pi\) | |||||||
\(164\) | 142998. | 0.415166 | ||||||||
\(165\) | −413.207 | −0.00118156 | ||||||||
\(166\) | −248046. | −0.698654 | ||||||||
\(167\) | 605932. | 1.68125 | 0.840626 | − | 0.541616i | \(-0.182187\pi\) | ||||
0.840626 | + | 0.541616i | \(0.182187\pi\) | |||||||
\(168\) | −32272.2 | −0.0882175 | ||||||||
\(169\) | −260602. | −0.701877 | ||||||||
\(170\) | −8341.07 | −0.0221360 | ||||||||
\(171\) | −83802.6 | −0.219163 | ||||||||
\(172\) | −123126. | −0.317343 | ||||||||
\(173\) | 373287. | 0.948261 | 0.474131 | − | 0.880454i | \(-0.342762\pi\) | ||||
0.474131 | + | 0.880454i | \(0.342762\pi\) | |||||||
\(174\) | 263233. | 0.659124 | ||||||||
\(175\) | −174259. | −0.430129 | ||||||||
\(176\) | 3055.45 | 0.00743521 | ||||||||
\(177\) | 31329.0 | 0.0751646 | ||||||||
\(178\) | 199060. | 0.470907 | ||||||||
\(179\) | 94160.1 | 0.219652 | 0.109826 | − | 0.993951i | \(-0.464971\pi\) | ||||
0.109826 | + | 0.993951i | \(0.464971\pi\) | |||||||
\(180\) | −4985.34 | −0.0114687 | ||||||||
\(181\) | 609176. | 1.38212 | 0.691061 | − | 0.722797i | \(-0.257144\pi\) | ||||
0.691061 | + | 0.722797i | \(0.257144\pi\) | |||||||
\(182\) | 74562.8 | 0.166857 | ||||||||
\(183\) | 141449. | 0.312229 | ||||||||
\(184\) | −179270. | −0.390358 | ||||||||
\(185\) | 55143.9 | 0.118459 | ||||||||
\(186\) | −251144. | −0.532280 | ||||||||
\(187\) | −6470.04 | −0.0135302 | ||||||||
\(188\) | 34206.1 | 0.0705845 | ||||||||
\(189\) | 40844.5 | 0.0831723 | ||||||||
\(190\) | −15919.2 | −0.0319918 | ||||||||
\(191\) | −513137. | −1.01777 | −0.508886 | − | 0.860834i | \(-0.669942\pi\) | ||||
−0.508886 | + | 0.860834i | \(0.669942\pi\) | |||||||
\(192\) | 36864.0 | 0.0721688 | ||||||||
\(193\) | −45011.2 | −0.0869815 | −0.0434908 | − | 0.999054i | \(-0.513848\pi\) | ||||
−0.0434908 | + | 0.999054i | \(0.513848\pi\) | |||||||
\(194\) | 548900. | 1.04710 | ||||||||
\(195\) | 11518.3 | 0.0216921 | ||||||||
\(196\) | −218686. | −0.406612 | ||||||||
\(197\) | 765004. | 1.40442 | 0.702212 | − | 0.711968i | \(-0.252196\pi\) | ||||
0.702212 | + | 0.711968i | \(0.252196\pi\) | |||||||
\(198\) | −3867.05 | −0.00700998 | ||||||||
\(199\) | 592525. | 1.06066 | 0.530328 | − | 0.847793i | \(-0.322069\pi\) | ||||
0.530328 | + | 0.847793i | \(0.322069\pi\) | |||||||
\(200\) | 199053. | 0.351879 | ||||||||
\(201\) | 168728. | 0.294576 | ||||||||
\(202\) | −8995.17 | −0.0155107 | ||||||||
\(203\) | −409679. | −0.697756 | ||||||||
\(204\) | −78061.1 | −0.131329 | ||||||||
\(205\) | −34379.6 | −0.0571369 | ||||||||
\(206\) | −99107.1 | −0.162718 | ||||||||
\(207\) | 226888. | 0.368033 | ||||||||
\(208\) | −85171.9 | −0.136502 | ||||||||
\(209\) | −12348.3 | −0.0195543 | ||||||||
\(210\) | 7758.86 | 0.0121409 | ||||||||
\(211\) | 942164. | 1.45687 | 0.728435 | − | 0.685115i | \(-0.240248\pi\) | ||||
0.728435 | + | 0.685115i | \(0.240248\pi\) | |||||||
\(212\) | 205354. | 0.313808 | ||||||||
\(213\) | −302044. | −0.456165 | ||||||||
\(214\) | 530820. | 0.792342 | ||||||||
\(215\) | 29601.9 | 0.0436741 | ||||||||
\(216\) | −46656.0 | −0.0680414 | ||||||||
\(217\) | 390864. | 0.563477 | ||||||||
\(218\) | 472963. | 0.674040 | ||||||||
\(219\) | −35433.1 | −0.0499227 | ||||||||
\(220\) | −734.590 | −0.00102326 | ||||||||
\(221\) | 180355. | 0.248398 | ||||||||
\(222\) | 516071. | 0.702793 | ||||||||
\(223\) | −834107. | −1.12321 | −0.561603 | − | 0.827407i | \(-0.689815\pi\) | ||||
−0.561603 | + | 0.827407i | \(0.689815\pi\) | |||||||
\(224\) | −57372.7 | −0.0763986 | ||||||||
\(225\) | −251926. | −0.331755 | ||||||||
\(226\) | 777081. | 1.01203 | ||||||||
\(227\) | −160293. | −0.206467 | −0.103233 | − | 0.994657i | \(-0.532919\pi\) | ||||
−0.103233 | + | 0.994657i | \(0.532919\pi\) | |||||||
\(228\) | −148982. | −0.189801 | ||||||||
\(229\) | −1.45056e6 | −1.82787 | −0.913937 | − | 0.405857i | \(-0.866973\pi\) | ||||
−0.913937 | + | 0.405857i | \(0.866973\pi\) | |||||||
\(230\) | 43100.0 | 0.0537227 | ||||||||
\(231\) | 6018.43 | 0.00742084 | ||||||||
\(232\) | 467970. | 0.570818 | ||||||||
\(233\) | 29109.3 | 0.0351271 | 0.0175635 | − | 0.999846i | \(-0.494409\pi\) | ||||
0.0175635 | + | 0.999846i | \(0.494409\pi\) | |||||||
\(234\) | 107796. | 0.128695 | ||||||||
\(235\) | −8223.82 | −0.00971414 | ||||||||
\(236\) | 55696.0 | 0.0650945 | ||||||||
\(237\) | −523564. | −0.605479 | ||||||||
\(238\) | 121489. | 0.139026 | ||||||||
\(239\) | 652150. | 0.738504 | 0.369252 | − | 0.929329i | \(-0.379614\pi\) | ||||
0.369252 | + | 0.929329i | \(0.379614\pi\) | |||||||
\(240\) | −8862.83 | −0.00993218 | ||||||||
\(241\) | −62780.9 | −0.0696281 | −0.0348141 | − | 0.999394i | \(-0.511084\pi\) | ||||
−0.0348141 | + | 0.999394i | \(0.511084\pi\) | |||||||
\(242\) | 643634. | 0.706481 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 251466. | 0.270398 | ||||||||
\(245\) | 52576.3 | 0.0559597 | ||||||||
\(246\) | −321746. | −0.338982 | ||||||||
\(247\) | 344214. | 0.358993 | ||||||||
\(248\) | −446478. | −0.460968 | ||||||||
\(249\) | 558104. | 0.570449 | ||||||||
\(250\) | −95940.2 | −0.0970846 | ||||||||
\(251\) | 951482. | 0.953271 | 0.476636 | − | 0.879101i | \(-0.341856\pi\) | ||||
0.476636 | + | 0.879101i | \(0.341856\pi\) | |||||||
\(252\) | 72612.4 | 0.0720293 | ||||||||
\(253\) | 33432.0 | 0.0328368 | ||||||||
\(254\) | 662218. | 0.644046 | ||||||||
\(255\) | 18767.4 | 0.0180740 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 1.82587e6 | 1.72440 | 0.862199 | − | 0.506570i | \(-0.169087\pi\) | ||||
0.862199 | + | 0.506570i | \(0.169087\pi\) | |||||||
\(258\) | 277034. | 0.259109 | ||||||||
\(259\) | −803180. | −0.743983 | ||||||||
\(260\) | 20477.0 | 0.0187859 | ||||||||
\(261\) | −592274. | −0.538173 | ||||||||
\(262\) | −891869. | −0.802690 | ||||||||
\(263\) | 1.79365e6 | 1.59900 | 0.799500 | − | 0.600666i | \(-0.205098\pi\) | ||||
0.799500 | + | 0.600666i | \(0.205098\pi\) | |||||||
\(264\) | −6874.76 | −0.00607082 | ||||||||
\(265\) | −49371.2 | −0.0431876 | ||||||||
\(266\) | 231867. | 0.200925 | ||||||||
\(267\) | −447886. | −0.384494 | ||||||||
\(268\) | 299961. | 0.255110 | ||||||||
\(269\) | 1.18796e6 | 1.00097 | 0.500485 | − | 0.865745i | \(-0.333155\pi\) | ||||
0.500485 | + | 0.865745i | \(0.333155\pi\) | |||||||
\(270\) | 11217.0 | 0.00936414 | ||||||||
\(271\) | 1.40374e6 | 1.16109 | 0.580543 | − | 0.814230i | \(-0.302840\pi\) | ||||
0.580543 | + | 0.814230i | \(0.302840\pi\) | |||||||
\(272\) | −138775. | −0.113734 | ||||||||
\(273\) | −167766. | −0.136238 | ||||||||
\(274\) | 1.32839e6 | 1.06893 | ||||||||
\(275\) | −37121.3 | −0.0296000 | ||||||||
\(276\) | 403357. | 0.318726 | ||||||||
\(277\) | −72688.1 | −0.0569199 | −0.0284599 | − | 0.999595i | \(-0.509060\pi\) | ||||
−0.0284599 | + | 0.999595i | \(0.509060\pi\) | |||||||
\(278\) | −448932. | −0.348392 | ||||||||
\(279\) | 565073. | 0.434604 | ||||||||
\(280\) | 13793.5 | 0.0105143 | ||||||||
\(281\) | −2.26275e6 | −1.70950 | −0.854751 | − | 0.519038i | \(-0.826290\pi\) | ||||
−0.854751 | + | 0.519038i | \(0.826290\pi\) | |||||||
\(282\) | −76963.8 | −0.0576320 | ||||||||
\(283\) | −244837. | −0.181723 | −0.0908616 | − | 0.995864i | \(-0.528962\pi\) | ||||
−0.0908616 | + | 0.995864i | \(0.528962\pi\) | |||||||
\(284\) | −536967. | −0.395050 | ||||||||
\(285\) | 35818.3 | 0.0261212 | ||||||||
\(286\) | 15883.7 | 0.0114825 | ||||||||
\(287\) | 500745. | 0.358849 | ||||||||
\(288\) | −82944.0 | −0.0589256 | ||||||||
\(289\) | −1.12599e6 | −0.793034 | ||||||||
\(290\) | −112509. | −0.0785584 | ||||||||
\(291\) | −1.23502e6 | −0.854954 | ||||||||
\(292\) | −62992.1 | −0.0432344 | ||||||||
\(293\) | 869270. | 0.591542 | 0.295771 | − | 0.955259i | \(-0.404423\pi\) | ||||
0.295771 | + | 0.955259i | \(0.404423\pi\) | |||||||
\(294\) | 492043. | 0.331997 | ||||||||
\(295\) | −13390.4 | −0.00895858 | ||||||||
\(296\) | 917460. | 0.608636 | ||||||||
\(297\) | 8700.86 | 0.00572363 | ||||||||
\(298\) | 1.64428e6 | 1.07260 | ||||||||
\(299\) | −931931. | −0.602845 | ||||||||
\(300\) | −447869. | −0.287308 | ||||||||
\(301\) | −431157. | −0.274296 | ||||||||
\(302\) | 1.66174e6 | 1.04844 | ||||||||
\(303\) | 20239.1 | 0.0126644 | ||||||||
\(304\) | −264858. | −0.164372 | ||||||||
\(305\) | −60457.3 | −0.0372134 | ||||||||
\(306\) | 175637. | 0.107229 | ||||||||
\(307\) | 1.90712e6 | 1.15486 | 0.577432 | − | 0.816439i | \(-0.304055\pi\) | ||||
0.577432 | + | 0.816439i | \(0.304055\pi\) | |||||||
\(308\) | 10699.4 | 0.00642663 | ||||||||
\(309\) | 222991. | 0.132859 | ||||||||
\(310\) | 107342. | 0.0634403 | ||||||||
\(311\) | −1.95290e6 | −1.14493 | −0.572465 | − | 0.819929i | \(-0.694013\pi\) | ||||
−0.572465 | + | 0.819929i | \(0.694013\pi\) | |||||||
\(312\) | 191637. | 0.111453 | ||||||||
\(313\) | −915889. | −0.528423 | −0.264212 | − | 0.964465i | \(-0.585112\pi\) | ||||
−0.264212 | + | 0.964465i | \(0.585112\pi\) | |||||||
\(314\) | 941572. | 0.538926 | ||||||||
\(315\) | −17457.4 | −0.00991298 | ||||||||
\(316\) | −930781. | −0.524360 | ||||||||
\(317\) | 732828. | 0.409594 | 0.204797 | − | 0.978804i | \(-0.434346\pi\) | ||||
0.204797 | + | 0.978804i | \(0.434346\pi\) | |||||||
\(318\) | −462047. | −0.256223 | ||||||||
\(319\) | −87271.5 | −0.0480171 | ||||||||
\(320\) | −15756.1 | −0.00860152 | ||||||||
\(321\) | −1.19434e6 | −0.646945 | ||||||||
\(322\) | −627759. | −0.337406 | ||||||||
\(323\) | 560847. | 0.299115 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | 1.03477e6 | 0.543421 | ||||||||
\(326\) | 2.66201e6 | 1.38728 | ||||||||
\(327\) | −1.06417e6 | −0.550351 | ||||||||
\(328\) | −571994. | −0.293567 | ||||||||
\(329\) | 119781. | 0.0610098 | ||||||||
\(330\) | 1652.83 | 0.000835492 0 | ||||||||
\(331\) | 1.54652e6 | 0.775862 | 0.387931 | − | 0.921688i | \(-0.373190\pi\) | ||||
0.387931 | + | 0.921688i | \(0.373190\pi\) | |||||||
\(332\) | 992185. | 0.494023 | ||||||||
\(333\) | −1.16116e6 | −0.573828 | ||||||||
\(334\) | −2.42373e6 | −1.18882 | ||||||||
\(335\) | −72116.5 | −0.0351094 | ||||||||
\(336\) | 129089. | 0.0623792 | ||||||||
\(337\) | 1.72789e6 | 0.828785 | 0.414393 | − | 0.910098i | \(-0.363994\pi\) | ||||
0.414393 | + | 0.910098i | \(0.363994\pi\) | |||||||
\(338\) | 1.04241e6 | 0.496302 | ||||||||
\(339\) | −1.74843e6 | −0.826322 | ||||||||
\(340\) | 33364.3 | 0.0156525 | ||||||||
\(341\) | 83263.5 | 0.0387765 | ||||||||
\(342\) | 335210. | 0.154972 | ||||||||
\(343\) | −1.70745e6 | −0.783632 | ||||||||
\(344\) | 492504. | 0.224395 | ||||||||
\(345\) | −96975.0 | −0.0438644 | ||||||||
\(346\) | −1.49315e6 | −0.670522 | ||||||||
\(347\) | 1.69181e6 | 0.754272 | 0.377136 | − | 0.926158i | \(-0.376909\pi\) | ||||
0.377136 | + | 0.926158i | \(0.376909\pi\) | |||||||
\(348\) | −1.05293e6 | −0.466071 | ||||||||
\(349\) | −703883. | −0.309340 | −0.154670 | − | 0.987966i | \(-0.549431\pi\) | ||||
−0.154670 | + | 0.987966i | \(0.549431\pi\) | |||||||
\(350\) | 697035. | 0.304147 | ||||||||
\(351\) | −242540. | −0.105079 | ||||||||
\(352\) | −12221.8 | −0.00525749 | ||||||||
\(353\) | 907096. | 0.387451 | 0.193725 | − | 0.981056i | \(-0.437943\pi\) | ||||
0.193725 | + | 0.981056i | \(0.437943\pi\) | |||||||
\(354\) | −125316. | −0.0531494 | ||||||||
\(355\) | 129098. | 0.0543685 | ||||||||
\(356\) | −796241. | −0.332981 | ||||||||
\(357\) | −273351. | −0.113514 | ||||||||
\(358\) | −376641. | −0.155317 | ||||||||
\(359\) | −3.02098e6 | −1.23712 | −0.618560 | − | 0.785738i | \(-0.712283\pi\) | ||||
−0.618560 | + | 0.785738i | \(0.712283\pi\) | |||||||
\(360\) | 19941.4 | 0.00810959 | ||||||||
\(361\) | −1.40570e6 | −0.567708 | ||||||||
\(362\) | −2.43670e6 | −0.977307 | ||||||||
\(363\) | −1.44818e6 | −0.576840 | ||||||||
\(364\) | −298251. | −0.117985 | ||||||||
\(365\) | 15144.5 | 0.00595010 | ||||||||
\(366\) | −565798. | −0.220779 | ||||||||
\(367\) | −3.28381e6 | −1.27266 | −0.636331 | − | 0.771416i | \(-0.719549\pi\) | ||||
−0.636331 | + | 0.771416i | \(0.719549\pi\) | |||||||
\(368\) | 717079. | 0.276025 | ||||||||
\(369\) | 723930. | 0.276777 | ||||||||
\(370\) | −220575. | −0.0837631 | ||||||||
\(371\) | 719100. | 0.271241 | ||||||||
\(372\) | 1.00457e6 | 0.376378 | ||||||||
\(373\) | −362447. | −0.134888 | −0.0674439 | − | 0.997723i | \(-0.521484\pi\) | ||||
−0.0674439 | + | 0.997723i | \(0.521484\pi\) | |||||||
\(374\) | 25880.1 | 0.00956726 | ||||||||
\(375\) | 215865. | 0.0792693 | ||||||||
\(376\) | −136824. | −0.0499108 | ||||||||
\(377\) | 2.43273e6 | 0.881538 | ||||||||
\(378\) | −163378. | −0.0588117 | ||||||||
\(379\) | 5.30531e6 | 1.89720 | 0.948600 | − | 0.316479i | \(-0.102501\pi\) | ||||
0.948600 | + | 0.316479i | \(0.102501\pi\) | |||||||
\(380\) | 63677.0 | 0.0226216 | ||||||||
\(381\) | −1.48999e6 | −0.525861 | ||||||||
\(382\) | 2.05255e6 | 0.719673 | ||||||||
\(383\) | −1.96109e6 | −0.683126 | −0.341563 | − | 0.939859i | \(-0.610956\pi\) | ||||
−0.341563 | + | 0.939859i | \(0.610956\pi\) | |||||||
\(384\) | −147456. | −0.0510310 | ||||||||
\(385\) | −2572.35 | −0.000884461 0 | ||||||||
\(386\) | 180045. | 0.0615052 | ||||||||
\(387\) | −623325. | −0.211562 | ||||||||
\(388\) | −2.19560e6 | −0.740412 | ||||||||
\(389\) | −1.17218e6 | −0.392753 | −0.196376 | − | 0.980529i | \(-0.562917\pi\) | ||||
−0.196376 | + | 0.980529i | \(0.562917\pi\) | |||||||
\(390\) | −46073.3 | −0.0153387 | ||||||||
\(391\) | −1.51845e6 | −0.502293 | ||||||||
\(392\) | 874743. | 0.287518 | ||||||||
\(393\) | 2.00671e6 | 0.655394 | ||||||||
\(394\) | −3.06001e6 | −0.993077 | ||||||||
\(395\) | 223778. | 0.0721647 | ||||||||
\(396\) | 15468.2 | 0.00495680 | ||||||||
\(397\) | −4.60634e6 | −1.46683 | −0.733415 | − | 0.679781i | \(-0.762075\pi\) | ||||
−0.733415 | + | 0.679781i | \(0.762075\pi\) | |||||||
\(398\) | −2.37010e6 | −0.749996 | ||||||||
\(399\) | −521700. | −0.164055 | ||||||||
\(400\) | −796212. | −0.248816 | ||||||||
\(401\) | 405384. | 0.125894 | 0.0629472 | − | 0.998017i | \(-0.479950\pi\) | ||||
0.0629472 | + | 0.998017i | \(0.479950\pi\) | |||||||
\(402\) | −674912. | −0.208297 | ||||||||
\(403\) | −2.32101e6 | −0.711891 | ||||||||
\(404\) | 35980.7 | 0.0109677 | ||||||||
\(405\) | −25238.3 | −0.00764579 | ||||||||
\(406\) | 1.63871e6 | 0.493388 | ||||||||
\(407\) | −171097. | −0.0511983 | ||||||||
\(408\) | 312244. | 0.0928633 | ||||||||
\(409\) | 2.78581e6 | 0.823461 | 0.411730 | − | 0.911306i | \(-0.364925\pi\) | ||||
0.411730 | + | 0.911306i | \(0.364925\pi\) | |||||||
\(410\) | 137519. | 0.0404019 | ||||||||
\(411\) | −2.98887e6 | −0.872775 | ||||||||
\(412\) | 396428. | 0.115059 | ||||||||
\(413\) | 195034. | 0.0562645 | ||||||||
\(414\) | −907554. | −0.260238 | ||||||||
\(415\) | −238541. | −0.0679896 | ||||||||
\(416\) | 340688. | 0.0965213 | ||||||||
\(417\) | 1.01010e6 | 0.284461 | ||||||||
\(418\) | 49393.2 | 0.0138270 | ||||||||
\(419\) | 349547. | 0.0972682 | 0.0486341 | − | 0.998817i | \(-0.484513\pi\) | ||||
0.0486341 | + | 0.998817i | \(0.484513\pi\) | |||||||
\(420\) | −31035.5 | −0.00858489 | ||||||||
\(421\) | 6.25957e6 | 1.72123 | 0.860616 | − | 0.509254i | \(-0.170079\pi\) | ||||
0.860616 | + | 0.509254i | \(0.170079\pi\) | |||||||
\(422\) | −3.76866e6 | −1.03016 | ||||||||
\(423\) | 173168. | 0.0470563 | ||||||||
\(424\) | −821417. | −0.221896 | ||||||||
\(425\) | 1.68601e6 | 0.452781 | ||||||||
\(426\) | 1.20818e6 | 0.322557 | ||||||||
\(427\) | 880571. | 0.233719 | ||||||||
\(428\) | −2.12328e6 | −0.560271 | ||||||||
\(429\) | −35738.3 | −0.00937542 | ||||||||
\(430\) | −118408. | −0.0308822 | ||||||||
\(431\) | −2.14092e6 | −0.555145 | −0.277572 | − | 0.960705i | \(-0.589530\pi\) | ||||
−0.277572 | + | 0.960705i | \(0.589530\pi\) | |||||||
\(432\) | 186624. | 0.0481125 | ||||||||
\(433\) | −2.50951e6 | −0.643234 | −0.321617 | − | 0.946870i | \(-0.604226\pi\) | ||||
−0.321617 | + | 0.946870i | \(0.604226\pi\) | |||||||
\(434\) | −1.56345e6 | −0.398438 | ||||||||
\(435\) | 253146. | 0.0641427 | ||||||||
\(436\) | −1.89185e6 | −0.476618 | ||||||||
\(437\) | −2.89801e6 | −0.725933 | ||||||||
\(438\) | 141732. | 0.0353007 | ||||||||
\(439\) | 1.07166e6 | 0.265398 | 0.132699 | − | 0.991156i | \(-0.457636\pi\) | ||||
0.132699 | + | 0.991156i | \(0.457636\pi\) | |||||||
\(440\) | 2938.36 | 0.000723558 0 | ||||||||
\(441\) | −1.10710e6 | −0.271075 | ||||||||
\(442\) | −721420. | −0.175644 | ||||||||
\(443\) | 7.83320e6 | 1.89640 | 0.948199 | − | 0.317676i | \(-0.102902\pi\) | ||||
0.948199 | + | 0.317676i | \(0.102902\pi\) | |||||||
\(444\) | −2.06428e6 | −0.496949 | ||||||||
\(445\) | 191432. | 0.0458263 | ||||||||
\(446\) | 3.33643e6 | 0.794227 | ||||||||
\(447\) | −3.69964e6 | −0.875771 | ||||||||
\(448\) | 229491. | 0.0540220 | ||||||||
\(449\) | −1.13368e6 | −0.265384 | −0.132692 | − | 0.991157i | \(-0.542362\pi\) | ||||
−0.132692 | + | 0.991157i | \(0.542362\pi\) | |||||||
\(450\) | 1.00771e6 | 0.234586 | ||||||||
\(451\) | 106671. | 0.0246948 | ||||||||
\(452\) | −3.10832e6 | −0.715616 | ||||||||
\(453\) | −3.73891e6 | −0.856051 | ||||||||
\(454\) | 641172. | 0.145994 | ||||||||
\(455\) | 71705.4 | 0.0162377 | ||||||||
\(456\) | 595930. | 0.134209 | ||||||||
\(457\) | 5.90765e6 | 1.32320 | 0.661599 | − | 0.749858i | \(-0.269878\pi\) | ||||
0.661599 | + | 0.749858i | \(0.269878\pi\) | |||||||
\(458\) | 5.80223e6 | 1.29250 | ||||||||
\(459\) | −395184. | −0.0875523 | ||||||||
\(460\) | −172400. | −0.0379877 | ||||||||
\(461\) | 5.61621e6 | 1.23081 | 0.615405 | − | 0.788211i | \(-0.288993\pi\) | ||||
0.615405 | + | 0.788211i | \(0.288993\pi\) | |||||||
\(462\) | −24073.7 | −0.00524732 | ||||||||
\(463\) | −647744. | −0.140427 | −0.0702136 | − | 0.997532i | \(-0.522368\pi\) | ||||
−0.0702136 | + | 0.997532i | \(0.522368\pi\) | |||||||
\(464\) | −1.87188e6 | −0.403629 | ||||||||
\(465\) | −241519. | −0.0517988 | ||||||||
\(466\) | −116437. | −0.0248386 | ||||||||
\(467\) | −2.37034e6 | −0.502942 | −0.251471 | − | 0.967865i | \(-0.580914\pi\) | ||||
−0.251471 | + | 0.967865i | \(0.580914\pi\) | |||||||
\(468\) | −431183. | −0.0910011 | ||||||||
\(469\) | 1.05039e6 | 0.220505 | ||||||||
\(470\) | 32895.3 | 0.00686893 | ||||||||
\(471\) | −2.11854e6 | −0.440031 | ||||||||
\(472\) | −222784. | −0.0460287 | ||||||||
\(473\) | −91846.9 | −0.0188761 | ||||||||
\(474\) | 2.09426e6 | 0.428138 | ||||||||
\(475\) | 3.21782e6 | 0.654376 | ||||||||
\(476\) | −485957. | −0.0983060 | ||||||||
\(477\) | 1.03961e6 | 0.209205 | ||||||||
\(478\) | −2.60860e6 | −0.522201 | ||||||||
\(479\) | 9.37809e6 | 1.86756 | 0.933782 | − | 0.357843i | \(-0.116488\pi\) | ||||
0.933782 | + | 0.357843i | \(0.116488\pi\) | |||||||
\(480\) | 35451.3 | 0.00702311 | ||||||||
\(481\) | 4.76940e6 | 0.939942 | ||||||||
\(482\) | 251123. | 0.0492345 | ||||||||
\(483\) | 1.41246e6 | 0.275491 | ||||||||
\(484\) | −2.57454e6 | −0.499558 | ||||||||
\(485\) | 527865. | 0.101899 | ||||||||
\(486\) | −236196. | −0.0453609 | ||||||||
\(487\) | −5.99993e6 | −1.14637 | −0.573183 | − | 0.819427i | \(-0.694292\pi\) | ||||
−0.573183 | + | 0.819427i | \(0.694292\pi\) | |||||||
\(488\) | −1.00586e6 | −0.191201 | ||||||||
\(489\) | −5.98952e6 | −1.13271 | ||||||||
\(490\) | −210305. | −0.0395695 | ||||||||
\(491\) | 361791. | 0.0677258 | 0.0338629 | − | 0.999426i | \(-0.489219\pi\) | ||||
0.0338629 | + | 0.999426i | \(0.489219\pi\) | |||||||
\(492\) | 1.28699e6 | 0.239696 | ||||||||
\(493\) | 3.96378e6 | 0.734501 | ||||||||
\(494\) | −1.37686e6 | −0.253847 | ||||||||
\(495\) | −3718.86 | −0.000682177 0 | ||||||||
\(496\) | 1.78591e6 | 0.325953 | ||||||||
\(497\) | −1.88033e6 | −0.341462 | ||||||||
\(498\) | −2.23242e6 | −0.403368 | ||||||||
\(499\) | −1.36591e6 | −0.245568 | −0.122784 | − | 0.992433i | \(-0.539182\pi\) | ||||
−0.122784 | + | 0.992433i | \(0.539182\pi\) | |||||||
\(500\) | 383761. | 0.0686492 | ||||||||
\(501\) | 5.45339e6 | 0.970672 | ||||||||
\(502\) | −3.80593e6 | −0.674064 | ||||||||
\(503\) | −1.04525e7 | −1.84204 | −0.921020 | − | 0.389514i | \(-0.872643\pi\) | ||||
−0.921020 | + | 0.389514i | \(0.872643\pi\) | |||||||
\(504\) | −290449. | −0.0509324 | ||||||||
\(505\) | −8650.46 | −0.00150942 | ||||||||
\(506\) | −133728. | −0.0232191 | ||||||||
\(507\) | −2.34542e6 | −0.405229 | ||||||||
\(508\) | −2.64887e6 | −0.455409 | ||||||||
\(509\) | −2.22371e6 | −0.380437 | −0.190219 | − | 0.981742i | \(-0.560920\pi\) | ||||
−0.190219 | + | 0.981742i | \(0.560920\pi\) | |||||||
\(510\) | −75069.7 | −0.0127802 | ||||||||
\(511\) | −220583. | −0.0373697 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | −754223. | −0.126534 | ||||||||
\(514\) | −7.30348e6 | −1.21933 | ||||||||
\(515\) | −95309.2 | −0.0158349 | ||||||||
\(516\) | −1.10813e6 | −0.183218 | ||||||||
\(517\) | 25516.4 | 0.00419848 | ||||||||
\(518\) | 3.21272e6 | 0.526076 | ||||||||
\(519\) | 3.35959e6 | 0.547479 | ||||||||
\(520\) | −81908.0 | −0.0132837 | ||||||||
\(521\) | −4.81180e6 | −0.776628 | −0.388314 | − | 0.921527i | \(-0.626942\pi\) | ||||
−0.388314 | + | 0.921527i | \(0.626942\pi\) | |||||||
\(522\) | 2.36910e6 | 0.380545 | ||||||||
\(523\) | −1.48640e6 | −0.237620 | −0.118810 | − | 0.992917i | \(-0.537908\pi\) | ||||
−0.118810 | + | 0.992917i | \(0.537908\pi\) | |||||||
\(524\) | 3.56748e6 | 0.567588 | ||||||||
\(525\) | −1.56833e6 | −0.248335 | ||||||||
\(526\) | −7.17460e6 | −1.13066 | ||||||||
\(527\) | −3.78174e6 | −0.593151 | ||||||||
\(528\) | 27499.0 | 0.00429272 | ||||||||
\(529\) | 1.40977e6 | 0.219033 | ||||||||
\(530\) | 197485. | 0.0305383 | ||||||||
\(531\) | 281961. | 0.0433963 | ||||||||
\(532\) | −927466. | −0.142075 | ||||||||
\(533\) | −2.97350e6 | −0.453367 | ||||||||
\(534\) | 1.79154e6 | 0.271878 | ||||||||
\(535\) | 510478. | 0.0771068 | ||||||||
\(536\) | −1.19984e6 | −0.180390 | ||||||||
\(537\) | 847441. | 0.126816 | ||||||||
\(538\) | −4.75184e6 | −0.707793 | ||||||||
\(539\) | −163131. | −0.0241860 | ||||||||
\(540\) | −44868.1 | −0.00662145 | ||||||||
\(541\) | 1.03121e7 | 1.51480 | 0.757398 | − | 0.652954i | \(-0.226470\pi\) | ||||
0.757398 | + | 0.652954i | \(0.226470\pi\) | |||||||
\(542\) | −5.61497e6 | −0.821011 | ||||||||
\(543\) | 5.48258e6 | 0.797968 | ||||||||
\(544\) | 555101. | 0.0804220 | ||||||||
\(545\) | 454838. | 0.0655942 | ||||||||
\(546\) | 671065. | 0.0963347 | ||||||||
\(547\) | 9.49949e6 | 1.35748 | 0.678738 | − | 0.734380i | \(-0.262527\pi\) | ||||
0.678738 | + | 0.734380i | \(0.262527\pi\) | |||||||
\(548\) | −5.31355e6 | −0.755846 | ||||||||
\(549\) | 1.27304e6 | 0.180266 | ||||||||
\(550\) | 148485. | 0.0209304 | ||||||||
\(551\) | 7.56502e6 | 1.06153 | ||||||||
\(552\) | −1.61343e6 | −0.225373 | ||||||||
\(553\) | −3.25936e6 | −0.453232 | ||||||||
\(554\) | 290753. | 0.0402484 | ||||||||
\(555\) | 496295. | 0.0683923 | ||||||||
\(556\) | 1.79573e6 | 0.246351 | ||||||||
\(557\) | 3.48276e6 | 0.475648 | 0.237824 | − | 0.971308i | \(-0.423566\pi\) | ||||
0.237824 | + | 0.971308i | \(0.423566\pi\) | |||||||
\(558\) | −2.26029e6 | −0.307312 | ||||||||
\(559\) | 2.56027e6 | 0.346543 | ||||||||
\(560\) | −55174.1 | −0.00743474 | ||||||||
\(561\) | −58230.3 | −0.00781164 | ||||||||
\(562\) | 9.05098e6 | 1.20880 | ||||||||
\(563\) | −1.93601e6 | −0.257417 | −0.128709 | − | 0.991682i | \(-0.541083\pi\) | ||||
−0.128709 | + | 0.991682i | \(0.541083\pi\) | |||||||
\(564\) | 307855. | 0.0407520 | ||||||||
\(565\) | 747302. | 0.0984862 | ||||||||
\(566\) | 979346. | 0.128498 | ||||||||
\(567\) | 367600. | 0.0480195 | ||||||||
\(568\) | 2.14787e6 | 0.279343 | ||||||||
\(569\) | −2.29564e6 | −0.297251 | −0.148625 | − | 0.988894i | \(-0.547485\pi\) | ||||
−0.148625 | + | 0.988894i | \(0.547485\pi\) | |||||||
\(570\) | −143273. | −0.0184705 | ||||||||
\(571\) | −9.98740e6 | −1.28192 | −0.640962 | − | 0.767573i | \(-0.721464\pi\) | ||||
−0.640962 | + | 0.767573i | \(0.721464\pi\) | |||||||
\(572\) | −63534.7 | −0.00811935 | ||||||||
\(573\) | −4.61823e6 | −0.587610 | ||||||||
\(574\) | −2.00298e6 | −0.253745 | ||||||||
\(575\) | −8.71196e6 | −1.09887 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | 9.12529e6 | 1.14106 | 0.570528 | − | 0.821278i | \(-0.306738\pi\) | ||||
0.570528 | + | 0.821278i | \(0.306738\pi\) | |||||||
\(578\) | 4.50398e6 | 0.560760 | ||||||||
\(579\) | −405100. | −0.0502188 | ||||||||
\(580\) | 450037. | 0.0555492 | ||||||||
\(581\) | 3.47439e6 | 0.427010 | ||||||||
\(582\) | 4.94010e6 | 0.604544 | ||||||||
\(583\) | 153186. | 0.0186658 | ||||||||
\(584\) | 251968. | 0.0305713 | ||||||||
\(585\) | 103665. | 0.0125240 | ||||||||
\(586\) | −3.47708e6 | −0.418283 | ||||||||
\(587\) | −1.49765e7 | −1.79397 | −0.896987 | − | 0.442056i | \(-0.854249\pi\) | ||||
−0.896987 | + | 0.442056i | \(0.854249\pi\) | |||||||
\(588\) | −1.96817e6 | −0.234758 | ||||||||
\(589\) | −7.21759e6 | −0.857243 | ||||||||
\(590\) | 53561.7 | 0.00633467 | ||||||||
\(591\) | 6.88503e6 | 0.810844 | ||||||||
\(592\) | −3.66984e6 | −0.430371 | ||||||||
\(593\) | −65101.7 | −0.00760248 | −0.00380124 | − | 0.999993i | \(-0.501210\pi\) | ||||
−0.00380124 | + | 0.999993i | \(0.501210\pi\) | |||||||
\(594\) | −34803.5 | −0.00404721 | ||||||||
\(595\) | 116834. | 0.0135293 | ||||||||
\(596\) | −6.57714e6 | −0.758440 | ||||||||
\(597\) | 5.33273e6 | 0.612370 | ||||||||
\(598\) | 3.72772e6 | 0.426276 | ||||||||
\(599\) | 7.19805e6 | 0.819687 | 0.409843 | − | 0.912156i | \(-0.365583\pi\) | ||||
0.409843 | + | 0.912156i | \(0.365583\pi\) | |||||||
\(600\) | 1.79148e6 | 0.203158 | ||||||||
\(601\) | −5.24745e6 | −0.592600 | −0.296300 | − | 0.955095i | \(-0.595753\pi\) | ||||
−0.296300 | + | 0.955095i | \(0.595753\pi\) | |||||||
\(602\) | 1.72463e6 | 0.193956 | ||||||||
\(603\) | 1.51855e6 | 0.170073 | ||||||||
\(604\) | −6.64695e6 | −0.741362 | ||||||||
\(605\) | 618969. | 0.0687513 | ||||||||
\(606\) | −80956.5 | −0.00895510 | ||||||||
\(607\) | 1.44188e7 | 1.58839 | 0.794196 | − | 0.607661i | \(-0.207892\pi\) | ||||
0.794196 | + | 0.607661i | \(0.207892\pi\) | |||||||
\(608\) | 1.05943e6 | 0.116229 | ||||||||
\(609\) | −3.68711e6 | −0.402849 | ||||||||
\(610\) | 241829. | 0.0263138 | ||||||||
\(611\) | −711280. | −0.0770792 | ||||||||
\(612\) | −702550. | −0.0758226 | ||||||||
\(613\) | −7.19815e6 | −0.773695 | −0.386847 | − | 0.922144i | \(-0.626436\pi\) | ||||
−0.386847 | + | 0.922144i | \(0.626436\pi\) | |||||||
\(614\) | −7.62846e6 | −0.816613 | ||||||||
\(615\) | −309417. | −0.0329880 | ||||||||
\(616\) | −42797.7 | −0.00454432 | ||||||||
\(617\) | 578775. | 0.0612064 | 0.0306032 | − | 0.999532i | \(-0.490257\pi\) | ||||
0.0306032 | + | 0.999532i | \(0.490257\pi\) | |||||||
\(618\) | −891964. | −0.0939455 | ||||||||
\(619\) | −4.16767e6 | −0.437187 | −0.218593 | − | 0.975816i | \(-0.570147\pi\) | ||||
−0.218593 | + | 0.975816i | \(0.570147\pi\) | |||||||
\(620\) | −429368. | −0.0448591 | ||||||||
\(621\) | 2.04200e6 | 0.212484 | ||||||||
\(622\) | 7.81159e6 | 0.809587 | ||||||||
\(623\) | −2.78824e6 | −0.287813 | ||||||||
\(624\) | −766547. | −0.0788093 | ||||||||
\(625\) | 9.62712e6 | 0.985817 | ||||||||
\(626\) | 3.66356e6 | 0.373652 | ||||||||
\(627\) | −111135. | −0.0112897 | ||||||||
\(628\) | −3.76629e6 | −0.381078 | ||||||||
\(629\) | 7.77104e6 | 0.783163 | ||||||||
\(630\) | 69829.8 | 0.00700954 | ||||||||
\(631\) | −3.67485e6 | −0.367423 | −0.183711 | − | 0.982980i | \(-0.558811\pi\) | ||||
−0.183711 | + | 0.982980i | \(0.558811\pi\) | |||||||
\(632\) | 3.72312e6 | 0.370779 | ||||||||
\(633\) | 8.47948e6 | 0.841124 | ||||||||
\(634\) | −2.93131e6 | −0.289627 | ||||||||
\(635\) | 636841. | 0.0626753 | ||||||||
\(636\) | 1.84819e6 | 0.181177 | ||||||||
\(637\) | 4.54733e6 | 0.444026 | ||||||||
\(638\) | 349086. | 0.0339532 | ||||||||
\(639\) | −2.71840e6 | −0.263367 | ||||||||
\(640\) | 63024.6 | 0.00608219 | ||||||||
\(641\) | 1.05758e7 | 1.01664 | 0.508321 | − | 0.861168i | \(-0.330267\pi\) | ||||
0.508321 | + | 0.861168i | \(0.330267\pi\) | |||||||
\(642\) | 4.77738e6 | 0.457459 | ||||||||
\(643\) | 7.95735e6 | 0.758999 | 0.379499 | − | 0.925192i | \(-0.376096\pi\) | ||||
0.379499 | + | 0.925192i | \(0.376096\pi\) | |||||||
\(644\) | 2.51104e6 | 0.238582 | ||||||||
\(645\) | 266417. | 0.0252152 | ||||||||
\(646\) | −2.24339e6 | −0.211506 | ||||||||
\(647\) | 9.86680e6 | 0.926649 | 0.463325 | − | 0.886189i | \(-0.346656\pi\) | ||||
0.463325 | + | 0.886189i | \(0.346656\pi\) | |||||||
\(648\) | −419904. | −0.0392837 | ||||||||
\(649\) | 41546.9 | 0.00387193 | ||||||||
\(650\) | −4.13909e6 | −0.384257 | ||||||||
\(651\) | 3.51777e6 | 0.325323 | ||||||||
\(652\) | −1.06480e7 | −0.980958 | ||||||||
\(653\) | −5.93484e6 | −0.544661 | −0.272331 | − | 0.962204i | \(-0.587794\pi\) | ||||
−0.272331 | + | 0.962204i | \(0.587794\pi\) | |||||||
\(654\) | 4.25667e6 | 0.389157 | ||||||||
\(655\) | −857692. | −0.0781138 | ||||||||
\(656\) | 2.28798e6 | 0.207583 | ||||||||
\(657\) | −318897. | −0.0288229 | ||||||||
\(658\) | −479126. | −0.0431405 | ||||||||
\(659\) | −1.88160e7 | −1.68777 | −0.843887 | − | 0.536522i | \(-0.819738\pi\) | ||||
−0.843887 | + | 0.536522i | \(0.819738\pi\) | |||||||
\(660\) | −6611.31 | −0.000590782 0 | ||||||||
\(661\) | 1.17369e7 | 1.04484 | 0.522420 | − | 0.852689i | \(-0.325029\pi\) | ||||
0.522420 | + | 0.852689i | \(0.325029\pi\) | |||||||
\(662\) | −6.18607e6 | −0.548617 | ||||||||
\(663\) | 1.62320e6 | 0.143413 | ||||||||
\(664\) | −3.96874e6 | −0.349327 | ||||||||
\(665\) | 222981. | 0.0195530 | ||||||||
\(666\) | 4.64464e6 | 0.405757 | ||||||||
\(667\) | −2.04817e7 | −1.78259 | ||||||||
\(668\) | 9.69492e6 | 0.840626 | ||||||||
\(669\) | −7.50696e6 | −0.648483 | ||||||||
\(670\) | 288466. | 0.0248261 | ||||||||
\(671\) | 187583. | 0.0160837 | ||||||||
\(672\) | −516355. | −0.0441088 | ||||||||
\(673\) | 1.29616e7 | 1.10312 | 0.551559 | − | 0.834136i | \(-0.314033\pi\) | ||||
0.551559 | + | 0.834136i | \(0.314033\pi\) | |||||||
\(674\) | −6.91157e6 | −0.586040 | ||||||||
\(675\) | −2.26734e6 | −0.191539 | ||||||||
\(676\) | −4.16963e6 | −0.350938 | ||||||||
\(677\) | −4.72777e6 | −0.396447 | −0.198223 | − | 0.980157i | \(-0.563517\pi\) | ||||
−0.198223 | + | 0.980157i | \(0.563517\pi\) | |||||||
\(678\) | 6.99373e6 | 0.584298 | ||||||||
\(679\) | −7.68845e6 | −0.639977 | ||||||||
\(680\) | −133457. | −0.0110680 | ||||||||
\(681\) | −1.44264e6 | −0.119204 | ||||||||
\(682\) | −333054. | −0.0274191 | ||||||||
\(683\) | 8.57737e6 | 0.703562 | 0.351781 | − | 0.936082i | \(-0.385576\pi\) | ||||
0.351781 | + | 0.936082i | \(0.385576\pi\) | |||||||
\(684\) | −1.34084e6 | −0.109582 | ||||||||
\(685\) | 1.27748e6 | 0.104023 | ||||||||
\(686\) | 6.82979e6 | 0.554111 | ||||||||
\(687\) | −1.30550e7 | −1.05532 | ||||||||
\(688\) | −1.97002e6 | −0.158671 | ||||||||
\(689\) | −4.27012e6 | −0.342683 | ||||||||
\(690\) | 387900. | 0.0310168 | ||||||||
\(691\) | −1.77711e7 | −1.41586 | −0.707929 | − | 0.706284i | \(-0.750370\pi\) | ||||
−0.707929 | + | 0.706284i | \(0.750370\pi\) | |||||||
\(692\) | 5.97260e6 | 0.474131 | ||||||||
\(693\) | 54165.8 | 0.00428442 | ||||||||
\(694\) | −6.76724e6 | −0.533351 | ||||||||
\(695\) | −431729. | −0.0339038 | ||||||||
\(696\) | 4.21173e6 | 0.329562 | ||||||||
\(697\) | −4.84488e6 | −0.377747 | ||||||||
\(698\) | 2.81553e6 | 0.218737 | ||||||||
\(699\) | 261984. | 0.0202806 | ||||||||
\(700\) | −2.78814e6 | −0.215065 | ||||||||
\(701\) | −2.48795e6 | −0.191226 | −0.0956129 | − | 0.995419i | \(-0.530481\pi\) | ||||
−0.0956129 | + | 0.995419i | \(0.530481\pi\) | |||||||
\(702\) | 970161. | 0.0743021 | ||||||||
\(703\) | 1.48313e7 | 1.13186 | ||||||||
\(704\) | 48887.2 | 0.00371760 | ||||||||
\(705\) | −74014.4 | −0.00560846 | ||||||||
\(706\) | −3.62838e6 | −0.273969 | ||||||||
\(707\) | 125995. | 0.00947996 | ||||||||
\(708\) | 501264. | 0.0375823 | ||||||||
\(709\) | 8.75924e6 | 0.654411 | 0.327206 | − | 0.944953i | \(-0.393893\pi\) | ||||
0.327206 | + | 0.944953i | \(0.393893\pi\) | |||||||
\(710\) | −516390. | −0.0384443 | ||||||||
\(711\) | −4.71208e6 | −0.349573 | ||||||||
\(712\) | 3.18497e6 | 0.235453 | ||||||||
\(713\) | 1.95410e7 | 1.43954 | ||||||||
\(714\) | 1.09340e6 | 0.0802665 | ||||||||
\(715\) | 15275.0 | 0.00111742 | ||||||||
\(716\) | 1.50656e6 | 0.109826 | ||||||||
\(717\) | 5.86935e6 | 0.426375 | ||||||||
\(718\) | 1.20839e7 | 0.874775 | ||||||||
\(719\) | −1.83297e7 | −1.32231 | −0.661156 | − | 0.750249i | \(-0.729934\pi\) | ||||
−0.661156 | + | 0.750249i | \(0.729934\pi\) | |||||||
\(720\) | −79765.5 | −0.00573434 | ||||||||
\(721\) | 1.38819e6 | 0.0994517 | ||||||||
\(722\) | 5.62281e6 | 0.401430 | ||||||||
\(723\) | −565028. | −0.0401998 | ||||||||
\(724\) | 9.74681e6 | 0.691061 | ||||||||
\(725\) | 2.27419e7 | 1.60687 | ||||||||
\(726\) | 5.79271e6 | 0.407887 | ||||||||
\(727\) | −6.86359e6 | −0.481632 | −0.240816 | − | 0.970571i | \(-0.577415\pi\) | ||||
−0.240816 | + | 0.970571i | \(0.577415\pi\) | |||||||
\(728\) | 1.19300e6 | 0.0834283 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −60578.2 | −0.00420735 | ||||||||
\(731\) | 4.17159e6 | 0.288741 | ||||||||
\(732\) | 2.26319e6 | 0.156115 | ||||||||
\(733\) | 2.58595e7 | 1.77770 | 0.888852 | − | 0.458194i | \(-0.151503\pi\) | ||||
0.888852 | + | 0.458194i | \(0.151503\pi\) | |||||||
\(734\) | 1.31352e7 | 0.899907 | ||||||||
\(735\) | 473187. | 0.0323083 | ||||||||
\(736\) | −2.86832e6 | −0.195179 | ||||||||
\(737\) | 223759. | 0.0151744 | ||||||||
\(738\) | −2.89572e6 | −0.195711 | ||||||||
\(739\) | 1.09072e7 | 0.734686 | 0.367343 | − | 0.930085i | \(-0.380267\pi\) | ||||
0.367343 | + | 0.930085i | \(0.380267\pi\) | |||||||
\(740\) | 882302. | 0.0592295 | ||||||||
\(741\) | 3.09793e6 | 0.207265 | ||||||||
\(742\) | −2.87640e6 | −0.191796 | ||||||||
\(743\) | −5.35885e6 | −0.356123 | −0.178061 | − | 0.984019i | \(-0.556983\pi\) | ||||
−0.178061 | + | 0.984019i | \(0.556983\pi\) | |||||||
\(744\) | −4.01830e6 | −0.266140 | ||||||||
\(745\) | 1.58127e6 | 0.104380 | ||||||||
\(746\) | 1.44979e6 | 0.0953801 | ||||||||
\(747\) | 5.02293e6 | 0.329349 | ||||||||
\(748\) | −103521. | −0.00676508 | ||||||||
\(749\) | −7.43520e6 | −0.484271 | ||||||||
\(750\) | −863462. | −0.0560518 | ||||||||
\(751\) | 2.43107e7 | 1.57289 | 0.786443 | − | 0.617663i | \(-0.211920\pi\) | ||||
0.786443 | + | 0.617663i | \(0.211920\pi\) | |||||||
\(752\) | 547298. | 0.0352922 | ||||||||
\(753\) | 8.56334e6 | 0.550371 | ||||||||
\(754\) | −9.73093e6 | −0.623341 | ||||||||
\(755\) | 1.59806e6 | 0.102029 | ||||||||
\(756\) | 653511. | 0.0415861 | ||||||||
\(757\) | 1.49623e7 | 0.948984 | 0.474492 | − | 0.880260i | \(-0.342632\pi\) | ||||
0.474492 | + | 0.880260i | \(0.342632\pi\) | |||||||
\(758\) | −2.12213e7 | −1.34152 | ||||||||
\(759\) | 300888. | 0.0189583 | ||||||||
\(760\) | −254708. | −0.0159959 | ||||||||
\(761\) | −6.31860e6 | −0.395511 | −0.197756 | − | 0.980251i | \(-0.563365\pi\) | ||||
−0.197756 | + | 0.980251i | \(0.563365\pi\) | |||||||
\(762\) | 5.95996e6 | 0.371840 | ||||||||
\(763\) | −6.62480e6 | −0.411966 | ||||||||
\(764\) | −8.21020e6 | −0.508886 | ||||||||
\(765\) | 168907. | 0.0104350 | ||||||||
\(766\) | 7.84436e6 | 0.483043 | ||||||||
\(767\) | −1.15814e6 | −0.0710840 | ||||||||
\(768\) | 589824. | 0.0360844 | ||||||||
\(769\) | 2.14926e6 | 0.131061 | 0.0655304 | − | 0.997851i | \(-0.479126\pi\) | ||||
0.0655304 | + | 0.997851i | \(0.479126\pi\) | |||||||
\(770\) | 10289.4 | 0.000625408 0 | ||||||||
\(771\) | 1.64328e7 | 0.995581 | ||||||||
\(772\) | −720179. | −0.0434908 | ||||||||
\(773\) | 1.77001e6 | 0.106543 | 0.0532717 | − | 0.998580i | \(-0.483035\pi\) | ||||
0.0532717 | + | 0.998580i | \(0.483035\pi\) | |||||||
\(774\) | 2.49330e6 | 0.149597 | ||||||||
\(775\) | −2.16974e7 | −1.29764 | ||||||||
\(776\) | 8.78239e6 | 0.523551 | ||||||||
\(777\) | −7.22862e6 | −0.429539 | ||||||||
\(778\) | 4.68871e6 | 0.277718 | ||||||||
\(779\) | −9.24664e6 | −0.545934 | ||||||||
\(780\) | 184293. | 0.0108461 | ||||||||
\(781\) | −400556. | −0.0234982 | ||||||||
\(782\) | 6.07378e6 | 0.355175 | ||||||||
\(783\) | −5.33047e6 | −0.310714 | ||||||||
\(784\) | −3.49897e6 | −0.203306 | ||||||||
\(785\) | 905489. | 0.0524456 | ||||||||
\(786\) | −8.02682e6 | −0.463433 | ||||||||
\(787\) | 8.25365e6 | 0.475017 | 0.237509 | − | 0.971385i | \(-0.423669\pi\) | ||||
0.237509 | + | 0.971385i | \(0.423669\pi\) | |||||||
\(788\) | 1.22401e7 | 0.702212 | ||||||||
\(789\) | 1.61429e7 | 0.923183 | ||||||||
\(790\) | −895112. | −0.0510281 | ||||||||
\(791\) | −1.08846e7 | −0.618544 | ||||||||
\(792\) | −61872.8 | −0.00350499 | ||||||||
\(793\) | −5.22896e6 | −0.295279 | ||||||||
\(794\) | 1.84254e7 | 1.03721 | ||||||||
\(795\) | −444341. | −0.0249344 | ||||||||
\(796\) | 9.48040e6 | 0.530328 | ||||||||
\(797\) | −3.45082e7 | −1.92432 | −0.962158 | − | 0.272492i | \(-0.912152\pi\) | ||||
−0.962158 | + | 0.272492i | \(0.912152\pi\) | |||||||
\(798\) | 2.08680e6 | 0.116004 | ||||||||
\(799\) | −1.15893e6 | −0.0642227 | ||||||||
\(800\) | 3.18485e6 | 0.175940 | ||||||||
\(801\) | −4.03097e6 | −0.221987 | ||||||||
\(802\) | −1.62154e6 | −0.0890207 | ||||||||
\(803\) | −46989.5 | −0.00257165 | ||||||||
\(804\) | 2.69965e6 | 0.147288 | ||||||||
\(805\) | −603702. | −0.0328347 | ||||||||
\(806\) | 9.28402e6 | 0.503383 | ||||||||
\(807\) | 1.06916e7 | 0.577910 | ||||||||
\(808\) | −143923. | −0.00775534 | ||||||||
\(809\) | 3.02590e7 | 1.62549 | 0.812743 | − | 0.582622i | \(-0.197973\pi\) | ||||
0.812743 | + | 0.582622i | \(0.197973\pi\) | |||||||
\(810\) | 100953. | 0.00540639 | ||||||||
\(811\) | 2.15332e7 | 1.14963 | 0.574813 | − | 0.818285i | \(-0.305075\pi\) | ||||
0.574813 | + | 0.818285i | \(0.305075\pi\) | |||||||
\(812\) | −6.55486e6 | −0.348878 | ||||||||
\(813\) | 1.26337e7 | 0.670353 | ||||||||
\(814\) | 684387. | 0.0362027 | ||||||||
\(815\) | 2.56000e6 | 0.135004 | ||||||||
\(816\) | −1.24898e6 | −0.0656643 | ||||||||
\(817\) | 7.96164e6 | 0.417299 | ||||||||
\(818\) | −1.11432e7 | −0.582275 | ||||||||
\(819\) | −1.50990e6 | −0.0786570 | ||||||||
\(820\) | −550074. | −0.0285684 | ||||||||
\(821\) | −1.93543e7 | −1.00212 | −0.501060 | − | 0.865412i | \(-0.667056\pi\) | ||||
−0.501060 | + | 0.865412i | \(0.667056\pi\) | |||||||
\(822\) | 1.19555e7 | 0.617145 | ||||||||
\(823\) | −5.27575e6 | −0.271509 | −0.135755 | − | 0.990742i | \(-0.543346\pi\) | ||||
−0.135755 | + | 0.990742i | \(0.543346\pi\) | |||||||
\(824\) | −1.58571e6 | −0.0813592 | ||||||||
\(825\) | −334092. | −0.0170896 | ||||||||
\(826\) | −780135. | −0.0397850 | ||||||||
\(827\) | 8.87915e6 | 0.451448 | 0.225724 | − | 0.974191i | \(-0.427525\pi\) | ||||
0.225724 | + | 0.974191i | \(0.427525\pi\) | |||||||
\(828\) | 3.63021e6 | 0.184016 | ||||||||
\(829\) | −6.08897e6 | −0.307721 | −0.153861 | − | 0.988093i | \(-0.549171\pi\) | ||||
−0.153861 | + | 0.988093i | \(0.549171\pi\) | |||||||
\(830\) | 954163. | 0.0480759 | ||||||||
\(831\) | −654193. | −0.0328627 | ||||||||
\(832\) | −1.36275e6 | −0.0682509 | ||||||||
\(833\) | 7.40922e6 | 0.369964 | ||||||||
\(834\) | −4.04039e6 | −0.201144 | ||||||||
\(835\) | −2.33085e6 | −0.115691 | ||||||||
\(836\) | −197573. | −0.00977713 | ||||||||
\(837\) | 5.08566e6 | 0.250919 | ||||||||
\(838\) | −1.39819e6 | −0.0687790 | ||||||||
\(839\) | 2.92994e6 | 0.143699 | 0.0718494 | − | 0.997415i | \(-0.477110\pi\) | ||||
0.0718494 | + | 0.997415i | \(0.477110\pi\) | |||||||
\(840\) | 124142. | 0.00607044 | ||||||||
\(841\) | 3.29546e7 | 1.60667 | ||||||||
\(842\) | −2.50383e7 | −1.21709 | ||||||||
\(843\) | −2.03647e7 | −0.986982 | ||||||||
\(844\) | 1.50746e7 | 0.728435 | ||||||||
\(845\) | 1.00246e6 | 0.0482976 | ||||||||
\(846\) | −692674. | −0.0332738 | ||||||||
\(847\) | −9.01539e6 | −0.431794 | ||||||||
\(848\) | 3.28567e6 | 0.156904 | ||||||||
\(849\) | −2.20353e6 | −0.104918 | ||||||||
\(850\) | −6.74405e6 | −0.320165 | ||||||||
\(851\) | −4.01545e7 | −1.90069 | ||||||||
\(852\) | −4.83271e6 | −0.228082 | ||||||||
\(853\) | 1.35688e7 | 0.638510 | 0.319255 | − | 0.947669i | \(-0.396567\pi\) | ||||
0.319255 | + | 0.947669i | \(0.396567\pi\) | |||||||
\(854\) | −3.52228e6 | −0.165264 | ||||||||
\(855\) | 322365. | 0.0150811 | ||||||||
\(856\) | 8.49312e6 | 0.396171 | ||||||||
\(857\) | 1.57548e7 | 0.732760 | 0.366380 | − | 0.930465i | \(-0.380597\pi\) | ||||
0.366380 | + | 0.930465i | \(0.380597\pi\) | |||||||
\(858\) | 142953. | 0.00662942 | ||||||||
\(859\) | −2.71282e7 | −1.25441 | −0.627203 | − | 0.778855i | \(-0.715801\pi\) | ||||
−0.627203 | + | 0.778855i | \(0.715801\pi\) | |||||||
\(860\) | 473631. | 0.0218370 | ||||||||
\(861\) | 4.50671e6 | 0.207182 | ||||||||
\(862\) | 8.56366e6 | 0.392547 | ||||||||
\(863\) | −1.37550e6 | −0.0628687 | −0.0314344 | − | 0.999506i | \(-0.510008\pi\) | ||||
−0.0314344 | + | 0.999506i | \(0.510008\pi\) | |||||||
\(864\) | −746496. | −0.0340207 | ||||||||
\(865\) | −1.43593e6 | −0.0652519 | ||||||||
\(866\) | 1.00380e7 | 0.454835 | ||||||||
\(867\) | −1.01340e7 | −0.457858 | ||||||||
\(868\) | 6.25382e6 | 0.281738 | ||||||||
\(869\) | −694324. | −0.0311898 | ||||||||
\(870\) | −1.01258e6 | −0.0453557 | ||||||||
\(871\) | −6.23737e6 | −0.278584 | ||||||||
\(872\) | 7.56741e6 | 0.337020 | ||||||||
\(873\) | −1.11152e7 | −0.493608 | ||||||||
\(874\) | 1.15920e7 | 0.513312 | ||||||||
\(875\) | 1.34384e6 | 0.0593371 | ||||||||
\(876\) | −566929. | −0.0249614 | ||||||||
\(877\) | −2.96555e7 | −1.30199 | −0.650993 | − | 0.759084i | \(-0.725647\pi\) | ||||
−0.650993 | + | 0.759084i | \(0.725647\pi\) | |||||||
\(878\) | −4.28665e6 | −0.187664 | ||||||||
\(879\) | 7.82343e6 | 0.341527 | ||||||||
\(880\) | −11753.4 | −0.000511632 0 | ||||||||
\(881\) | −2.42564e7 | −1.05290 | −0.526450 | − | 0.850206i | \(-0.676477\pi\) | ||||
−0.526450 | + | 0.850206i | \(0.676477\pi\) | |||||||
\(882\) | 4.42839e6 | 0.191679 | ||||||||
\(883\) | −2.11783e6 | −0.0914093 | −0.0457046 | − | 0.998955i | \(-0.514553\pi\) | ||||
−0.0457046 | + | 0.998955i | \(0.514553\pi\) | |||||||
\(884\) | 2.88568e6 | 0.124199 | ||||||||
\(885\) | −120514. | −0.00517224 | ||||||||
\(886\) | −3.13328e7 | −1.34096 | ||||||||
\(887\) | −3.18056e7 | −1.35736 | −0.678680 | − | 0.734434i | \(-0.737448\pi\) | ||||
−0.678680 | + | 0.734434i | \(0.737448\pi\) | |||||||
\(888\) | 8.25714e6 | 0.351396 | ||||||||
\(889\) | −9.27570e6 | −0.393634 | ||||||||
\(890\) | −765728. | −0.0324041 | ||||||||
\(891\) | 78307.8 | 0.00330454 | ||||||||
\(892\) | −1.33457e7 | −0.561603 | ||||||||
\(893\) | −2.21185e6 | −0.0928170 | ||||||||
\(894\) | 1.47986e7 | 0.619264 | ||||||||
\(895\) | −362207. | −0.0151147 | ||||||||
\(896\) | −917964. | −0.0381993 | ||||||||
\(897\) | −8.38738e6 | −0.348053 | ||||||||
\(898\) | 4.53471e6 | 0.187655 | ||||||||
\(899\) | −5.10103e7 | −2.10503 | ||||||||
\(900\) | −4.03082e6 | −0.165877 | ||||||||
\(901\) | −6.95754e6 | −0.285525 | ||||||||
\(902\) | −426684. | −0.0174618 | ||||||||
\(903\) | −3.88041e6 | −0.158365 | ||||||||
\(904\) | 1.24333e7 | 0.506017 | ||||||||
\(905\) | −2.34333e6 | −0.0951067 | ||||||||
\(906\) | 1.49556e7 | 0.605319 | ||||||||
\(907\) | 9.64462e6 | 0.389284 | 0.194642 | − | 0.980874i | \(-0.437645\pi\) | ||||
0.194642 | + | 0.980874i | \(0.437645\pi\) | |||||||
\(908\) | −2.56469e6 | −0.103233 | ||||||||
\(909\) | 182152. | 0.00731180 | ||||||||
\(910\) | −286822. | −0.0114818 | ||||||||
\(911\) | −1.61560e7 | −0.644969 | −0.322484 | − | 0.946575i | \(-0.604518\pi\) | ||||
−0.322484 | + | 0.946575i | \(0.604518\pi\) | |||||||
\(912\) | −2.38372e6 | −0.0949004 | ||||||||
\(913\) | 740129. | 0.0293853 | ||||||||
\(914\) | −2.36306e7 | −0.935642 | ||||||||
\(915\) | −544116. | −0.0214852 | ||||||||
\(916\) | −2.32089e7 | −0.913937 | ||||||||
\(917\) | 1.24924e7 | 0.490595 | ||||||||
\(918\) | 1.58074e6 | 0.0619089 | ||||||||
\(919\) | −1.58719e7 | −0.619926 | −0.309963 | − | 0.950749i | \(-0.600317\pi\) | ||||
−0.309963 | + | 0.950749i | \(0.600317\pi\) | |||||||
\(920\) | 689600. | 0.0268613 | ||||||||
\(921\) | 1.71640e7 | 0.666761 | ||||||||
\(922\) | −2.24648e7 | −0.870314 | ||||||||
\(923\) | 1.11657e7 | 0.431400 | ||||||||
\(924\) | 96294.8 | 0.00371042 | ||||||||
\(925\) | 4.45857e7 | 1.71333 | ||||||||
\(926\) | 2.59098e6 | 0.0992970 | ||||||||
\(927\) | 2.00692e6 | 0.0767062 | ||||||||
\(928\) | 7.48752e6 | 0.285409 | ||||||||
\(929\) | 4.10831e6 | 0.156179 | 0.0780897 | − | 0.996946i | \(-0.475118\pi\) | ||||
0.0780897 | + | 0.996946i | \(0.475118\pi\) | |||||||
\(930\) | 966078. | 0.0366273 | ||||||||
\(931\) | 1.41408e7 | 0.534686 | ||||||||
\(932\) | 465749. | 0.0175635 | ||||||||
\(933\) | −1.75761e7 | −0.661025 | ||||||||
\(934\) | 9.48135e6 | 0.355634 | ||||||||
\(935\) | 24888.4 | 0.000931039 0 | ||||||||
\(936\) | 1.72473e6 | 0.0643475 | ||||||||
\(937\) | 1.81013e7 | 0.673536 | 0.336768 | − | 0.941588i | \(-0.390666\pi\) | ||||
0.336768 | + | 0.941588i | \(0.390666\pi\) | |||||||
\(938\) | −4.20156e6 | −0.155921 | ||||||||
\(939\) | −8.24300e6 | −0.305085 | ||||||||
\(940\) | −131581. | −0.00485707 | ||||||||
\(941\) | −4.88376e7 | −1.79796 | −0.898980 | − | 0.437989i | \(-0.855691\pi\) | ||||
−0.898980 | + | 0.437989i | \(0.855691\pi\) | |||||||
\(942\) | 8.47414e6 | 0.311149 | ||||||||
\(943\) | 2.50345e7 | 0.916768 | ||||||||
\(944\) | 891136. | 0.0325472 | ||||||||
\(945\) | −157117. | −0.00572326 | ||||||||
\(946\) | 367388. | 0.0133474 | ||||||||
\(947\) | 2.03944e7 | 0.738985 | 0.369493 | − | 0.929234i | \(-0.379532\pi\) | ||||
0.369493 | + | 0.929234i | \(0.379532\pi\) | |||||||
\(948\) | −8.37703e6 | −0.302739 | ||||||||
\(949\) | 1.30985e6 | 0.0472125 | ||||||||
\(950\) | −1.28713e7 | −0.462714 | ||||||||
\(951\) | 6.59546e6 | 0.236479 | ||||||||
\(952\) | 1.94383e6 | 0.0695129 | ||||||||
\(953\) | −3.11786e7 | −1.11205 | −0.556025 | − | 0.831166i | \(-0.687674\pi\) | ||||
−0.556025 | + | 0.831166i | \(0.687674\pi\) | |||||||
\(954\) | −4.15843e6 | −0.147931 | ||||||||
\(955\) | 1.97389e6 | 0.0700350 | ||||||||
\(956\) | 1.04344e7 | 0.369252 | ||||||||
\(957\) | −785444. | −0.0277227 | ||||||||
\(958\) | −3.75123e7 | −1.32057 | ||||||||
\(959\) | −1.86067e7 | −0.653317 | ||||||||
\(960\) | −141805. | −0.00496609 | ||||||||
\(961\) | 2.00384e7 | 0.699929 | ||||||||
\(962\) | −1.90776e7 | −0.664639 | ||||||||
\(963\) | −1.07491e7 | −0.373514 | ||||||||
\(964\) | −1.00449e6 | −0.0348141 | ||||||||
\(965\) | 173145. | 0.00598538 | ||||||||
\(966\) | −5.64983e6 | −0.194802 | ||||||||
\(967\) | −1.97677e7 | −0.679813 | −0.339906 | − | 0.940459i | \(-0.610395\pi\) | ||||
−0.339906 | + | 0.940459i | \(0.610395\pi\) | |||||||
\(968\) | 1.02981e7 | 0.353241 | ||||||||
\(969\) | 5.04762e6 | 0.172694 | ||||||||
\(970\) | −2.11146e6 | −0.0720533 | ||||||||
\(971\) | −8.01735e6 | −0.272887 | −0.136443 | − | 0.990648i | \(-0.543567\pi\) | ||||
−0.136443 | + | 0.990648i | \(0.543567\pi\) | |||||||
\(972\) | 944784. | 0.0320750 | ||||||||
\(973\) | 6.28820e6 | 0.212934 | ||||||||
\(974\) | 2.39997e7 | 0.810604 | ||||||||
\(975\) | 9.31296e6 | 0.313744 | ||||||||
\(976\) | 4.02345e6 | 0.135199 | ||||||||
\(977\) | 3.83569e7 | 1.28560 | 0.642802 | − | 0.766033i | \(-0.277772\pi\) | ||||
0.642802 | + | 0.766033i | \(0.277772\pi\) | |||||||
\(978\) | 2.39581e7 | 0.800949 | ||||||||
\(979\) | −593963. | −0.0198063 | ||||||||
\(980\) | 841222. | 0.0279798 | ||||||||
\(981\) | −9.57750e6 | −0.317746 | ||||||||
\(982\) | −1.44716e6 | −0.0478894 | ||||||||
\(983\) | −4.39437e7 | −1.45048 | −0.725242 | − | 0.688494i | \(-0.758272\pi\) | ||||
−0.725242 | + | 0.688494i | \(0.758272\pi\) | |||||||
\(984\) | −5.14794e6 | −0.169491 | ||||||||
\(985\) | −2.94275e6 | −0.0966413 | ||||||||
\(986\) | −1.58551e7 | −0.519371 | ||||||||
\(987\) | 1.07803e6 | 0.0352240 | ||||||||
\(988\) | 5.50743e6 | 0.179497 | ||||||||
\(989\) | −2.15555e7 | −0.700755 | ||||||||
\(990\) | 14875.4 | 0.000482372 0 | ||||||||
\(991\) | −4.70351e7 | −1.52138 | −0.760690 | − | 0.649115i | \(-0.775139\pi\) | ||||
−0.760690 | + | 0.649115i | \(0.775139\pi\) | |||||||
\(992\) | −7.14364e6 | −0.230484 | ||||||||
\(993\) | 1.39186e7 | 0.447944 | ||||||||
\(994\) | 7.52131e6 | 0.241450 | ||||||||
\(995\) | −2.27928e6 | −0.0729859 | ||||||||
\(996\) | 8.92966e6 | 0.285224 | ||||||||
\(997\) | −1.58777e7 | −0.505884 | −0.252942 | − | 0.967481i | \(-0.581398\pi\) | ||||
−0.252942 | + | 0.967481i | \(0.581398\pi\) | |||||||
\(998\) | 5.46365e6 | 0.173643 | ||||||||
\(999\) | −1.04504e7 | −0.331300 |
(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 | 354.6.a.c.1.3 | ✓ | 5 | |
3.2 | odd | 2 | 1062.6.a.f.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
354.6.a.c.1.3 | ✓ | 5 | 1.1 | even | 1 | trivial | |
1062.6.a.f.1.3 | 5 | 3.2 | odd | 2 |