Properties

Label 76.6.i.a.5.5
Level $76$
Weight $6$
Character 76.5
Analytic conductor $12.189$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [76,6,Mod(5,76)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(76, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 16]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("76.5");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 76.i (of order \(9\), degree \(6\), minimal)

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: no
Analytic conductor: \(12.1891703058\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(8\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 5.5
Character \(\chi\) \(=\) 76.5
Dual form 76.6.i.a.61.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.50126 - 8.51408i) q^{3} +(-8.90022 - 7.46817i) q^{5} +(70.8987 + 122.800i) q^{7} +(158.110 + 57.5472i) q^{9} +O(q^{10})\) \(q+(1.50126 - 8.51408i) q^{3} +(-8.90022 - 7.46817i) q^{5} +(70.8987 + 122.800i) q^{7} +(158.110 + 57.5472i) q^{9} +(194.817 - 337.433i) q^{11} +(-114.779 - 650.941i) q^{13} +(-76.9461 + 64.5655i) q^{15} +(368.551 - 134.142i) q^{17} +(1147.26 - 1076.98i) q^{19} +(1151.97 - 419.282i) q^{21} +(-396.668 + 332.844i) q^{23} +(-519.210 - 2944.59i) q^{25} +(1777.74 - 3079.14i) q^{27} +(6195.96 + 2255.15i) q^{29} +(-306.669 - 531.166i) q^{31} +(-2580.46 - 2165.26i) q^{33} +(286.079 - 1622.43i) q^{35} +9518.19 q^{37} -5714.48 q^{39} +(-2681.23 + 15206.0i) q^{41} +(779.136 + 653.773i) q^{43} +(-977.438 - 1692.97i) q^{45} +(-15932.9 - 5799.09i) q^{47} +(-1649.76 + 2857.46i) q^{49} +(-588.800 - 3339.25i) q^{51} +(-20338.2 + 17065.8i) q^{53} +(-4253.92 + 1548.30i) q^{55} +(-7447.15 - 11384.7i) q^{57} +(18836.8 - 6856.03i) q^{59} +(-38667.8 + 32446.1i) q^{61} +(4142.96 + 23495.9i) q^{63} +(-3839.79 + 6650.71i) q^{65} +(33834.2 + 12314.7i) q^{67} +(2238.36 + 3876.95i) q^{69} +(-19090.6 - 16018.9i) q^{71} +(-5135.69 + 29125.9i) q^{73} -25849.9 q^{75} +55249.1 q^{77} +(5030.54 - 28529.6i) q^{79} +(7773.60 + 6522.83i) q^{81} +(-36878.7 - 63875.8i) q^{83} +(-4281.98 - 1558.51i) q^{85} +(28502.2 - 49367.3i) q^{87} +(4801.09 + 27228.3i) q^{89} +(71798.1 - 60245.7i) q^{91} +(-4982.78 + 1813.58i) q^{93} +(-18254.0 + 1017.40i) q^{95} +(13600.4 - 4950.16i) q^{97} +(50220.7 - 42140.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 33 q^{3} - 177 q^{7} + 33 q^{9} - 237 q^{11} + 2049 q^{13} + 2085 q^{15} - 609 q^{17} - 6012 q^{19} + 3591 q^{21} + 14100 q^{23} + 11802 q^{25} - 861 q^{27} - 10575 q^{29} - 6546 q^{31} - 21234 q^{33} - 231 q^{35} + 20052 q^{37} + 72204 q^{39} - 3249 q^{41} - 34677 q^{43} - 34956 q^{45} + 4461 q^{47} - 41139 q^{49} + 12099 q^{51} - 24291 q^{53} - 61767 q^{55} - 64470 q^{57} - 20100 q^{59} + 95490 q^{61} + 86403 q^{63} - 57915 q^{65} - 64452 q^{67} - 99315 q^{69} - 115536 q^{71} - 16362 q^{73} + 236250 q^{75} + 26688 q^{77} + 29799 q^{79} + 180327 q^{81} + 52347 q^{83} + 204618 q^{85} + 69414 q^{87} + 47394 q^{89} - 249384 q^{91} - 462126 q^{93} + 412869 q^{95} - 229974 q^{97} - 692274 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.50126 8.51408i 0.0963059 0.546178i −0.898033 0.439927i \(-0.855004\pi\)
0.994339 0.106251i \(-0.0338847\pi\)
\(4\) 0 0
\(5\) −8.90022 7.46817i −0.159212 0.133595i 0.559701 0.828694i \(-0.310916\pi\)
−0.718913 + 0.695100i \(0.755360\pi\)
\(6\) 0 0
\(7\) 70.8987 + 122.800i 0.546882 + 0.947227i 0.998486 + 0.0550084i \(0.0175186\pi\)
−0.451604 + 0.892218i \(0.649148\pi\)
\(8\) 0 0
\(9\) 158.110 + 57.5472i 0.650657 + 0.236820i
\(10\) 0 0
\(11\) 194.817 337.433i 0.485450 0.840825i −0.514410 0.857544i \(-0.671989\pi\)
0.999860 + 0.0167197i \(0.00532230\pi\)
\(12\) 0 0
\(13\) −114.779 650.941i −0.188366 1.06828i −0.921554 0.388250i \(-0.873080\pi\)
0.733188 0.680026i \(-0.238032\pi\)
\(14\) 0 0
\(15\) −76.9461 + 64.5655i −0.0882996 + 0.0740921i
\(16\) 0 0
\(17\) 368.551 134.142i 0.309297 0.112575i −0.182708 0.983167i \(-0.558486\pi\)
0.492005 + 0.870592i \(0.336264\pi\)
\(18\) 0 0
\(19\) 1147.26 1076.98i 0.729087 0.684421i
\(20\) 0 0
\(21\) 1151.97 419.282i 0.570023 0.207471i
\(22\) 0 0
\(23\) −396.668 + 332.844i −0.156353 + 0.131196i −0.717608 0.696447i \(-0.754763\pi\)
0.561255 + 0.827643i \(0.310319\pi\)
\(24\) 0 0
\(25\) −519.210 2944.59i −0.166147 0.942268i
\(26\) 0 0
\(27\) 1777.74 3079.14i 0.469310 0.812868i
\(28\) 0 0
\(29\) 6195.96 + 2255.15i 1.36809 + 0.497943i 0.918545 0.395316i \(-0.129365\pi\)
0.449542 + 0.893259i \(0.351587\pi\)
\(30\) 0 0
\(31\) −306.669 531.166i −0.0573146 0.0992718i 0.835945 0.548814i \(-0.184920\pi\)
−0.893259 + 0.449542i \(0.851587\pi\)
\(32\) 0 0
\(33\) −2580.46 2165.26i −0.412488 0.346119i
\(34\) 0 0
\(35\) 286.079 1622.43i 0.0394744 0.223870i
\(36\) 0 0
\(37\) 9518.19 1.14301 0.571505 0.820598i \(-0.306360\pi\)
0.571505 + 0.820598i \(0.306360\pi\)
\(38\) 0 0
\(39\) −5714.48 −0.601610
\(40\) 0 0
\(41\) −2681.23 + 15206.0i −0.249100 + 1.41272i 0.561674 + 0.827359i \(0.310158\pi\)
−0.810774 + 0.585359i \(0.800953\pi\)
\(42\) 0 0
\(43\) 779.136 + 653.773i 0.0642602 + 0.0539207i 0.674352 0.738410i \(-0.264423\pi\)
−0.610092 + 0.792331i \(0.708867\pi\)
\(44\) 0 0
\(45\) −977.438 1692.97i −0.0719545 0.124629i
\(46\) 0 0
\(47\) −15932.9 5799.09i −1.05208 0.382926i −0.242633 0.970118i \(-0.578011\pi\)
−0.809448 + 0.587192i \(0.800233\pi\)
\(48\) 0 0
\(49\) −1649.76 + 2857.46i −0.0981590 + 0.170016i
\(50\) 0 0
\(51\) −588.800 3339.25i −0.0316988 0.179773i
\(52\) 0 0
\(53\) −20338.2 + 17065.8i −0.994543 + 0.834521i −0.986219 0.165445i \(-0.947094\pi\)
−0.00832396 + 0.999965i \(0.502650\pi\)
\(54\) 0 0
\(55\) −4253.92 + 1548.30i −0.189619 + 0.0690158i
\(56\) 0 0
\(57\) −7447.15 11384.7i −0.303601 0.464125i
\(58\) 0 0
\(59\) 18836.8 6856.03i 0.704493 0.256414i 0.0351650 0.999382i \(-0.488804\pi\)
0.669328 + 0.742967i \(0.266582\pi\)
\(60\) 0 0
\(61\) −38667.8 + 32446.1i −1.33053 + 1.11645i −0.346575 + 0.938022i \(0.612655\pi\)
−0.983954 + 0.178424i \(0.942900\pi\)
\(62\) 0 0
\(63\) 4142.96 + 23495.9i 0.131510 + 0.745832i
\(64\) 0 0
\(65\) −3839.79 + 6650.71i −0.112726 + 0.195247i
\(66\) 0 0
\(67\) 33834.2 + 12314.7i 0.920809 + 0.335147i 0.758560 0.651603i \(-0.225903\pi\)
0.162248 + 0.986750i \(0.448125\pi\)
\(68\) 0 0
\(69\) 2238.36 + 3876.95i 0.0565987 + 0.0980318i
\(70\) 0 0
\(71\) −19090.6 16018.9i −0.449442 0.377127i 0.389787 0.920905i \(-0.372549\pi\)
−0.839229 + 0.543779i \(0.816993\pi\)
\(72\) 0 0
\(73\) −5135.69 + 29125.9i −0.112795 + 0.639695i 0.875023 + 0.484082i \(0.160846\pi\)
−0.987818 + 0.155613i \(0.950265\pi\)
\(74\) 0 0
\(75\) −25849.9 −0.530647
\(76\) 0 0
\(77\) 55249.1 1.06194
\(78\) 0 0
\(79\) 5030.54 28529.6i 0.0906873 0.514313i −0.905297 0.424780i \(-0.860351\pi\)
0.995984 0.0895331i \(-0.0285375\pi\)
\(80\) 0 0
\(81\) 7773.60 + 6522.83i 0.131647 + 0.110465i
\(82\) 0 0
\(83\) −36878.7 63875.8i −0.587599 1.01775i −0.994546 0.104299i \(-0.966740\pi\)
0.406947 0.913452i \(-0.366593\pi\)
\(84\) 0 0
\(85\) −4281.98 1558.51i −0.0642831 0.0233971i
\(86\) 0 0
\(87\) 28502.2 49367.3i 0.403720 0.699264i
\(88\) 0 0
\(89\) 4801.09 + 27228.3i 0.0642487 + 0.364373i 0.999933 + 0.0115355i \(0.00367193\pi\)
−0.935685 + 0.352837i \(0.885217\pi\)
\(90\) 0 0
\(91\) 71798.1 60245.7i 0.908886 0.762646i
\(92\) 0 0
\(93\) −4982.78 + 1813.58i −0.0597398 + 0.0217435i
\(94\) 0 0
\(95\) −18254.0 + 1017.40i −0.207514 + 0.0115660i
\(96\) 0 0
\(97\) 13600.4 4950.16i 0.146765 0.0534182i −0.267593 0.963532i \(-0.586228\pi\)
0.414358 + 0.910114i \(0.364006\pi\)
\(98\) 0 0
\(99\) 50220.7 42140.2i 0.514986 0.432124i
\(100\) 0 0
\(101\) 17060.8 + 96756.9i 0.166417 + 0.943796i 0.947592 + 0.319484i \(0.103510\pi\)
−0.781175 + 0.624312i \(0.785379\pi\)
\(102\) 0 0
\(103\) 52648.8 91190.3i 0.488985 0.846946i −0.510935 0.859619i \(-0.670701\pi\)
0.999920 + 0.0126732i \(0.00403411\pi\)
\(104\) 0 0
\(105\) −13384.0 4871.39i −0.118471 0.0431201i
\(106\) 0 0
\(107\) −31764.1 55017.0i −0.268211 0.464555i 0.700189 0.713958i \(-0.253099\pi\)
−0.968400 + 0.249402i \(0.919766\pi\)
\(108\) 0 0
\(109\) −10028.1 8414.60i −0.0808451 0.0678371i 0.601470 0.798896i \(-0.294582\pi\)
−0.682315 + 0.731059i \(0.739027\pi\)
\(110\) 0 0
\(111\) 14289.3 81038.6i 0.110079 0.624287i
\(112\) 0 0
\(113\) 43980.7 0.324016 0.162008 0.986789i \(-0.448203\pi\)
0.162008 + 0.986789i \(0.448203\pi\)
\(114\) 0 0
\(115\) 6016.17 0.0424205
\(116\) 0 0
\(117\) 19312.3 109525.i 0.130427 0.739690i
\(118\) 0 0
\(119\) 42602.4 + 35747.6i 0.275782 + 0.231409i
\(120\) 0 0
\(121\) 4618.27 + 7999.08i 0.0286758 + 0.0496680i
\(122\) 0 0
\(123\) 125440. + 45656.4i 0.747606 + 0.272106i
\(124\) 0 0
\(125\) −35523.4 + 61528.3i −0.203348 + 0.352208i
\(126\) 0 0
\(127\) 42814.2 + 242811.i 0.235548 + 1.33586i 0.841457 + 0.540323i \(0.181698\pi\)
−0.605910 + 0.795533i \(0.707191\pi\)
\(128\) 0 0
\(129\) 6735.96 5652.14i 0.0356390 0.0299047i
\(130\) 0 0
\(131\) −277294. + 100927.i −1.41176 + 0.513840i −0.931647 0.363365i \(-0.881628\pi\)
−0.480117 + 0.877205i \(0.659406\pi\)
\(132\) 0 0
\(133\) 213593. + 64527.7i 1.04703 + 0.316313i
\(134\) 0 0
\(135\) −38817.9 + 14128.5i −0.183315 + 0.0667211i
\(136\) 0 0
\(137\) −221298. + 185691.i −1.00734 + 0.845257i −0.987984 0.154556i \(-0.950605\pi\)
−0.0193539 + 0.999813i \(0.506161\pi\)
\(138\) 0 0
\(139\) −67554.3 383120.i −0.296562 1.68189i −0.660784 0.750576i \(-0.729776\pi\)
0.364221 0.931312i \(-0.381335\pi\)
\(140\) 0 0
\(141\) −73293.2 + 126948.i −0.310467 + 0.537745i
\(142\) 0 0
\(143\) −242010. 88084.4i −0.989675 0.360212i
\(144\) 0 0
\(145\) −38303.6 66343.8i −0.151293 0.262048i
\(146\) 0 0
\(147\) 21851.9 + 18336.0i 0.0834059 + 0.0699859i
\(148\) 0 0
\(149\) −18638.0 + 105701.i −0.0687753 + 0.390044i 0.930917 + 0.365231i \(0.119010\pi\)
−0.999692 + 0.0248128i \(0.992101\pi\)
\(150\) 0 0
\(151\) −164771. −0.588082 −0.294041 0.955793i \(-0.595000\pi\)
−0.294041 + 0.955793i \(0.595000\pi\)
\(152\) 0 0
\(153\) 65990.9 0.227906
\(154\) 0 0
\(155\) −1237.42 + 7017.75i −0.00413702 + 0.0234622i
\(156\) 0 0
\(157\) −2382.87 1999.46i −0.00771527 0.00647388i 0.638922 0.769272i \(-0.279381\pi\)
−0.646637 + 0.762798i \(0.723825\pi\)
\(158\) 0 0
\(159\) 114767. + 198781.i 0.360017 + 0.623567i
\(160\) 0 0
\(161\) −68996.6 25112.7i −0.209779 0.0763534i
\(162\) 0 0
\(163\) −235705. + 408254.i −0.694865 + 1.20354i 0.275361 + 0.961341i \(0.411203\pi\)
−0.970226 + 0.242201i \(0.922131\pi\)
\(164\) 0 0
\(165\) 6796.10 + 38542.6i 0.0194334 + 0.110213i
\(166\) 0 0
\(167\) −277637. + 232965.i −0.770346 + 0.646397i −0.940797 0.338969i \(-0.889922\pi\)
0.170452 + 0.985366i \(0.445477\pi\)
\(168\) 0 0
\(169\) −61649.4 + 22438.6i −0.166040 + 0.0604336i
\(170\) 0 0
\(171\) 243371. 104259.i 0.636470 0.272661i
\(172\) 0 0
\(173\) −464197. + 168954.i −1.17920 + 0.429193i −0.855919 0.517110i \(-0.827008\pi\)
−0.323280 + 0.946303i \(0.604786\pi\)
\(174\) 0 0
\(175\) 324785. 272527.i 0.801679 0.672688i
\(176\) 0 0
\(177\) −30093.8 170670.i −0.0722011 0.409473i
\(178\) 0 0
\(179\) 146354. 253492.i 0.341406 0.591333i −0.643288 0.765624i \(-0.722430\pi\)
0.984694 + 0.174291i \(0.0557635\pi\)
\(180\) 0 0
\(181\) 358542. + 130499.i 0.813475 + 0.296081i 0.715058 0.699065i \(-0.246400\pi\)
0.0984165 + 0.995145i \(0.468622\pi\)
\(182\) 0 0
\(183\) 218198. + 377930.i 0.481641 + 0.834226i
\(184\) 0 0
\(185\) −84714.0 71083.5i −0.181981 0.152700i
\(186\) 0 0
\(187\) 26536.2 150494.i 0.0554925 0.314714i
\(188\) 0 0
\(189\) 504159. 1.02663
\(190\) 0 0
\(191\) 107928. 0.214067 0.107033 0.994255i \(-0.465865\pi\)
0.107033 + 0.994255i \(0.465865\pi\)
\(192\) 0 0
\(193\) 126314. 716364.i 0.244095 1.38433i −0.578490 0.815690i \(-0.696358\pi\)
0.822585 0.568643i \(-0.192531\pi\)
\(194\) 0 0
\(195\) 50860.1 + 42676.7i 0.0957835 + 0.0803719i
\(196\) 0 0
\(197\) −244831. 424060.i −0.449470 0.778505i 0.548881 0.835900i \(-0.315054\pi\)
−0.998352 + 0.0573952i \(0.981720\pi\)
\(198\) 0 0
\(199\) −354815. 129142.i −0.635140 0.231172i 0.00432687 0.999991i \(-0.498623\pi\)
−0.639467 + 0.768819i \(0.720845\pi\)
\(200\) 0 0
\(201\) 155642. 269580.i 0.271729 0.470649i
\(202\) 0 0
\(203\) 162353. + 920752.i 0.276517 + 1.56820i
\(204\) 0 0
\(205\) 137425. 115313.i 0.228391 0.191643i
\(206\) 0 0
\(207\) −81871.3 + 29798.7i −0.132802 + 0.0483361i
\(208\) 0 0
\(209\) −139902. 596938.i −0.221543 0.945287i
\(210\) 0 0
\(211\) 627262. 228305.i 0.969936 0.353028i 0.192016 0.981392i \(-0.438497\pi\)
0.777920 + 0.628364i \(0.216275\pi\)
\(212\) 0 0
\(213\) −165046. + 138490.i −0.249262 + 0.209156i
\(214\) 0 0
\(215\) −2052.00 11637.4i −0.00302747 0.0171697i
\(216\) 0 0
\(217\) 43484.8 75317.9i 0.0626886 0.108580i
\(218\) 0 0
\(219\) 240270. + 87451.3i 0.338524 + 0.123213i
\(220\) 0 0
\(221\) −129620. 224508.i −0.178522 0.309209i
\(222\) 0 0
\(223\) 433966. + 364140.i 0.584377 + 0.490350i 0.886381 0.462956i \(-0.153211\pi\)
−0.302004 + 0.953307i \(0.597656\pi\)
\(224\) 0 0
\(225\) 87360.6 495447.i 0.115043 0.652440i
\(226\) 0 0
\(227\) −468869. −0.603930 −0.301965 0.953319i \(-0.597643\pi\)
−0.301965 + 0.953319i \(0.597643\pi\)
\(228\) 0 0
\(229\) 937113. 1.18087 0.590437 0.807084i \(-0.298956\pi\)
0.590437 + 0.807084i \(0.298956\pi\)
\(230\) 0 0
\(231\) 82943.3 470395.i 0.102271 0.580006i
\(232\) 0 0
\(233\) −448581. 376404.i −0.541317 0.454219i 0.330671 0.943746i \(-0.392725\pi\)
−0.871988 + 0.489527i \(0.837169\pi\)
\(234\) 0 0
\(235\) 98497.4 + 170602.i 0.116347 + 0.201519i
\(236\) 0 0
\(237\) −235351. 85660.7i −0.272173 0.0990629i
\(238\) 0 0
\(239\) 118788. 205746.i 0.134517 0.232990i −0.790896 0.611951i \(-0.790385\pi\)
0.925413 + 0.378961i \(0.123718\pi\)
\(240\) 0 0
\(241\) −2934.13 16640.3i −0.00325415 0.0184552i 0.983137 0.182868i \(-0.0585381\pi\)
−0.986392 + 0.164413i \(0.947427\pi\)
\(242\) 0 0
\(243\) 729056. 611750.i 0.792036 0.664597i
\(244\) 0 0
\(245\) 36023.2 13111.4i 0.0383414 0.0139551i
\(246\) 0 0
\(247\) −832732. 623187.i −0.868486 0.649944i
\(248\) 0 0
\(249\) −599208. + 218094.i −0.612462 + 0.222918i
\(250\) 0 0
\(251\) −1.37034e6 + 1.14985e6i −1.37292 + 1.15201i −0.401166 + 0.916005i \(0.631395\pi\)
−0.971751 + 0.236009i \(0.924161\pi\)
\(252\) 0 0
\(253\) 35034.8 + 198692.i 0.0344111 + 0.195155i
\(254\) 0 0
\(255\) −19697.6 + 34117.3i −0.0189699 + 0.0328567i
\(256\) 0 0
\(257\) 326623. + 118881.i 0.308470 + 0.112274i 0.491617 0.870812i \(-0.336406\pi\)
−0.183146 + 0.983086i \(0.558628\pi\)
\(258\) 0 0
\(259\) 674828. + 1.16884e6i 0.625091 + 1.08269i
\(260\) 0 0
\(261\) 849864. + 713120.i 0.772232 + 0.647980i
\(262\) 0 0
\(263\) −222265. + 1.26053e6i −0.198144 + 1.12373i 0.709725 + 0.704479i \(0.248819\pi\)
−0.907869 + 0.419253i \(0.862292\pi\)
\(264\) 0 0
\(265\) 308465. 0.269831
\(266\) 0 0
\(267\) 239032. 0.205200
\(268\) 0 0
\(269\) −269600. + 1.52898e6i −0.227164 + 1.28831i 0.631342 + 0.775504i \(0.282504\pi\)
−0.858506 + 0.512804i \(0.828607\pi\)
\(270\) 0 0
\(271\) 355499. + 298299.i 0.294046 + 0.246734i 0.777861 0.628436i \(-0.216305\pi\)
−0.483815 + 0.875170i \(0.660749\pi\)
\(272\) 0 0
\(273\) −405149. 701739.i −0.329009 0.569861i
\(274\) 0 0
\(275\) −1.09475e6 398457.i −0.872939 0.317724i
\(276\) 0 0
\(277\) 856730. 1.48390e6i 0.670880 1.16200i −0.306776 0.951782i \(-0.599250\pi\)
0.977655 0.210216i \(-0.0674166\pi\)
\(278\) 0 0
\(279\) −17920.2 101630.i −0.0137826 0.0781651i
\(280\) 0 0
\(281\) −183817. + 154240.i −0.138873 + 0.116529i −0.709578 0.704627i \(-0.751114\pi\)
0.570705 + 0.821155i \(0.306670\pi\)
\(282\) 0 0
\(283\) −1.97635e6 + 719332.i −1.46689 + 0.533904i −0.947254 0.320484i \(-0.896154\pi\)
−0.519635 + 0.854388i \(0.673932\pi\)
\(284\) 0 0
\(285\) −18741.8 + 156943.i −0.0136678 + 0.114454i
\(286\) 0 0
\(287\) −2.05740e6 + 748831.i −1.47439 + 0.536635i
\(288\) 0 0
\(289\) −969838. + 813791.i −0.683053 + 0.573150i
\(290\) 0 0
\(291\) −21728.2 123227.i −0.0150415 0.0853045i
\(292\) 0 0
\(293\) 442562. 766539.i 0.301165 0.521633i −0.675235 0.737603i \(-0.735958\pi\)
0.976400 + 0.215969i \(0.0692911\pi\)
\(294\) 0 0
\(295\) −218853. 79656.2i −0.146419 0.0532923i
\(296\) 0 0
\(297\) −692669. 1.19974e6i −0.455653 0.789215i
\(298\) 0 0
\(299\) 262191. + 220004.i 0.169605 + 0.142316i
\(300\) 0 0
\(301\) −25043.7 + 142030.i −0.0159324 + 0.0903573i
\(302\) 0 0
\(303\) 849408. 0.531508
\(304\) 0 0
\(305\) 586465. 0.360987
\(306\) 0 0
\(307\) −40981.2 + 232416.i −0.0248164 + 0.140741i −0.994699 0.102834i \(-0.967209\pi\)
0.969882 + 0.243575i \(0.0783201\pi\)
\(308\) 0 0
\(309\) −697362. 585156.i −0.415491 0.348639i
\(310\) 0 0
\(311\) 1.05972e6 + 1.83549e6i 0.621284 + 1.07610i 0.989247 + 0.146255i \(0.0467221\pi\)
−0.367963 + 0.929841i \(0.619945\pi\)
\(312\) 0 0
\(313\) −1.93620e6 704720.i −1.11709 0.406589i −0.283504 0.958971i \(-0.591497\pi\)
−0.833591 + 0.552382i \(0.813719\pi\)
\(314\) 0 0
\(315\) 138598. 240059.i 0.0787012 0.136314i
\(316\) 0 0
\(317\) 569321. + 3.22878e6i 0.318207 + 1.80464i 0.553648 + 0.832751i \(0.313235\pi\)
−0.235442 + 0.971888i \(0.575654\pi\)
\(318\) 0 0
\(319\) 1.96804e6 1.65138e6i 1.08282 0.908595i
\(320\) 0 0
\(321\) −516105. + 187847.i −0.279560 + 0.101752i
\(322\) 0 0
\(323\) 278357. 550817.i 0.148455 0.293766i
\(324\) 0 0
\(325\) −1.85716e6 + 675951.i −0.975306 + 0.354982i
\(326\) 0 0
\(327\) −86697.4 + 72747.7i −0.0448370 + 0.0376227i
\(328\) 0 0
\(329\) −417490. 2.36771e6i −0.212646 1.20597i
\(330\) 0 0
\(331\) 1.09997e6 1.90521e6i 0.551838 0.955811i −0.446304 0.894881i \(-0.647260\pi\)
0.998142 0.0609297i \(-0.0194065\pi\)
\(332\) 0 0
\(333\) 1.50492e6 + 547745.i 0.743708 + 0.270687i
\(334\) 0 0
\(335\) −209164. 362283.i −0.101830 0.176375i
\(336\) 0 0
\(337\) 1.38586e6 + 1.16288e6i 0.664730 + 0.557775i 0.911500 0.411299i \(-0.134925\pi\)
−0.246770 + 0.969074i \(0.579369\pi\)
\(338\) 0 0
\(339\) 66026.5 374455.i 0.0312046 0.176970i
\(340\) 0 0
\(341\) −238977. −0.111294
\(342\) 0 0
\(343\) 1.91533e6 0.879038
\(344\) 0 0
\(345\) 9031.84 51222.1i 0.00408534 0.0231691i
\(346\) 0 0
\(347\) −571789. 479788.i −0.254925 0.213907i 0.506365 0.862319i \(-0.330989\pi\)
−0.761289 + 0.648412i \(0.775433\pi\)
\(348\) 0 0
\(349\) 2.10644e6 + 3.64847e6i 0.925734 + 1.60342i 0.790377 + 0.612621i \(0.209885\pi\)
0.135357 + 0.990797i \(0.456782\pi\)
\(350\) 0 0
\(351\) −2.20839e6 803787.i −0.956770 0.348236i
\(352\) 0 0
\(353\) 1.41425e6 2.44955e6i 0.604071 1.04628i −0.388126 0.921606i \(-0.626877\pi\)
0.992197 0.124676i \(-0.0397892\pi\)
\(354\) 0 0
\(355\) 50278.5 + 285144.i 0.0211744 + 0.120086i
\(356\) 0 0
\(357\) 368315. 309053.i 0.152950 0.128340i
\(358\) 0 0
\(359\) 4.10605e6 1.49448e6i 1.68147 0.612004i 0.687957 0.725751i \(-0.258508\pi\)
0.993510 + 0.113748i \(0.0362856\pi\)
\(360\) 0 0
\(361\) 156328. 2.47116e6i 0.0631348 0.998005i
\(362\) 0 0
\(363\) 75038.0 27311.6i 0.0298892 0.0108788i
\(364\) 0 0
\(365\) 263226. 220873.i 0.103418 0.0867782i
\(366\) 0 0
\(367\) −712246. 4.03935e6i −0.276035 1.56547i −0.735654 0.677358i \(-0.763125\pi\)
0.459618 0.888116i \(-0.347986\pi\)
\(368\) 0 0
\(369\) −1.29899e6 + 2.24992e6i −0.496638 + 0.860203i
\(370\) 0 0
\(371\) −3.53764e6 1.28760e6i −1.33438 0.485674i
\(372\) 0 0
\(373\) 2.48064e6 + 4.29659e6i 0.923190 + 1.59901i 0.794447 + 0.607334i \(0.207761\pi\)
0.128743 + 0.991678i \(0.458906\pi\)
\(374\) 0 0
\(375\) 470527. + 394819.i 0.172785 + 0.144984i
\(376\) 0 0
\(377\) 756804. 4.29205e6i 0.274240 1.55529i
\(378\) 0 0
\(379\) 867337. 0.310163 0.155081 0.987902i \(-0.450436\pi\)
0.155081 + 0.987902i \(0.450436\pi\)
\(380\) 0 0
\(381\) 2.13159e6 0.752300
\(382\) 0 0
\(383\) 281973. 1.59915e6i 0.0982223 0.557046i −0.895490 0.445082i \(-0.853175\pi\)
0.993712 0.111964i \(-0.0357143\pi\)
\(384\) 0 0
\(385\) −491729. 412610.i −0.169073 0.141869i
\(386\) 0 0
\(387\) 85566.1 + 148205.i 0.0290419 + 0.0503020i
\(388\) 0 0
\(389\) 475214. + 172964.i 0.159226 + 0.0579537i 0.420404 0.907337i \(-0.361888\pi\)
−0.261177 + 0.965291i \(0.584111\pi\)
\(390\) 0 0
\(391\) −101544. + 175880.i −0.0335902 + 0.0581800i
\(392\) 0 0
\(393\) 443007. + 2.51242e6i 0.144687 + 0.820560i
\(394\) 0 0
\(395\) −257837. + 216351.i −0.0831480 + 0.0697695i
\(396\) 0 0
\(397\) −3.13354e6 + 1.14052e6i −0.997837 + 0.363183i −0.788750 0.614714i \(-0.789271\pi\)
−0.209087 + 0.977897i \(0.567049\pi\)
\(398\) 0 0
\(399\) 870052. 1.72167e6i 0.273598 0.541400i
\(400\) 0 0
\(401\) −5.77310e6 + 2.10124e6i −1.79287 + 0.652550i −0.793855 + 0.608107i \(0.791929\pi\)
−0.999012 + 0.0444431i \(0.985849\pi\)
\(402\) 0 0
\(403\) −310559. + 260590.i −0.0952536 + 0.0799272i
\(404\) 0 0
\(405\) −20473.2 116109.i −0.00620223 0.0351746i
\(406\) 0 0
\(407\) 1.85430e6 3.21175e6i 0.554875 0.961071i
\(408\) 0 0
\(409\) −732420. 266579.i −0.216497 0.0787985i 0.231495 0.972836i \(-0.425638\pi\)
−0.447992 + 0.894038i \(0.647861\pi\)
\(410\) 0 0
\(411\) 1.24876e6 + 2.16291e6i 0.364648 + 0.631589i
\(412\) 0 0
\(413\) 2.17743e6 + 1.82708e6i 0.628157 + 0.527086i
\(414\) 0 0
\(415\) −148807. + 843926.i −0.0424134 + 0.240538i
\(416\) 0 0
\(417\) −3.36333e6 −0.947172
\(418\) 0 0
\(419\) 6.32803e6 1.76089 0.880447 0.474144i \(-0.157242\pi\)
0.880447 + 0.474144i \(0.157242\pi\)
\(420\) 0 0
\(421\) 458810. 2.60204e6i 0.126162 0.715498i −0.854449 0.519534i \(-0.826105\pi\)
0.980611 0.195964i \(-0.0627835\pi\)
\(422\) 0 0
\(423\) −2.18542e6 1.83378e6i −0.593859 0.498307i
\(424\) 0 0
\(425\) −586347. 1.01558e6i −0.157464 0.272736i
\(426\) 0 0
\(427\) −6.72588e6 2.44802e6i −1.78517 0.649749i
\(428\) 0 0
\(429\) −1.11328e6 + 1.92825e6i −0.292052 + 0.505849i
\(430\) 0 0
\(431\) 1.09334e6 + 6.20062e6i 0.283505 + 1.60784i 0.710578 + 0.703619i \(0.248434\pi\)
−0.427073 + 0.904217i \(0.640455\pi\)
\(432\) 0 0
\(433\) 191609. 160779.i 0.0491129 0.0412106i −0.617901 0.786256i \(-0.712017\pi\)
0.667014 + 0.745045i \(0.267572\pi\)
\(434\) 0 0
\(435\) −622360. + 226520.i −0.157695 + 0.0573963i
\(436\) 0 0
\(437\) −96616.5 + 809063.i −0.0242018 + 0.202665i
\(438\) 0 0
\(439\) −5.11989e6 + 1.86349e6i −1.26794 + 0.461493i −0.886427 0.462869i \(-0.846820\pi\)
−0.381516 + 0.924362i \(0.624598\pi\)
\(440\) 0 0
\(441\) −425282. + 356854.i −0.104131 + 0.0873763i
\(442\) 0 0
\(443\) −129202. 732739.i −0.0312794 0.177395i 0.965166 0.261640i \(-0.0842632\pi\)
−0.996445 + 0.0842452i \(0.973152\pi\)
\(444\) 0 0
\(445\) 160615. 278193.i 0.0384491 0.0665958i
\(446\) 0 0
\(447\) 871967. + 317370.i 0.206410 + 0.0751271i
\(448\) 0 0
\(449\) 3.70632e6 + 6.41953e6i 0.867614 + 1.50275i 0.864428 + 0.502757i \(0.167681\pi\)
0.00318678 + 0.999995i \(0.498986\pi\)
\(450\) 0 0
\(451\) 4.60866e6 + 3.86712e6i 1.06692 + 0.895254i
\(452\) 0 0
\(453\) −247364. + 1.40287e6i −0.0566358 + 0.321197i
\(454\) 0 0
\(455\) −1.08894e6 −0.246591
\(456\) 0 0
\(457\) −5.14993e6 −1.15348 −0.576741 0.816927i \(-0.695676\pi\)
−0.576741 + 0.816927i \(0.695676\pi\)
\(458\) 0 0
\(459\) 242148. 1.37329e6i 0.0536475 0.304250i
\(460\) 0 0
\(461\) 1.22701e6 + 1.02959e6i 0.268904 + 0.225637i 0.767262 0.641334i \(-0.221619\pi\)
−0.498357 + 0.866972i \(0.666063\pi\)
\(462\) 0 0
\(463\) 434748. + 753006.i 0.0942509 + 0.163247i 0.909296 0.416151i \(-0.136621\pi\)
−0.815045 + 0.579398i \(0.803288\pi\)
\(464\) 0 0
\(465\) 57891.9 + 21070.9i 0.0124161 + 0.00451910i
\(466\) 0 0
\(467\) 1.60301e6 2.77649e6i 0.340129 0.589121i −0.644327 0.764750i \(-0.722863\pi\)
0.984456 + 0.175629i \(0.0561959\pi\)
\(468\) 0 0
\(469\) 886562. + 5.02794e6i 0.186113 + 1.05550i
\(470\) 0 0
\(471\) −20600.9 + 17286.2i −0.00427892 + 0.00359044i
\(472\) 0 0
\(473\) 372393. 135540.i 0.0765331 0.0278558i
\(474\) 0 0
\(475\) −3.76693e6 2.81904e6i −0.766044 0.573280i
\(476\) 0 0
\(477\) −4.19776e6 + 1.52786e6i −0.844737 + 0.307459i
\(478\) 0 0
\(479\) −6.71800e6 + 5.63707e6i −1.33783 + 1.12257i −0.355652 + 0.934618i \(0.615741\pi\)
−0.982178 + 0.187954i \(0.939814\pi\)
\(480\) 0 0
\(481\) −1.09248e6 6.19579e6i −0.215304 1.22105i
\(482\) 0 0
\(483\) −317393. + 549741.i −0.0619056 + 0.107224i
\(484\) 0 0
\(485\) −158016. 57512.9i −0.0305032 0.0111023i
\(486\) 0 0
\(487\) −2.14673e6 3.71825e6i −0.410162 0.710422i 0.584745 0.811217i \(-0.301195\pi\)
−0.994907 + 0.100795i \(0.967861\pi\)
\(488\) 0 0
\(489\) 3.12205e6 + 2.61971e6i 0.590429 + 0.495428i
\(490\) 0 0
\(491\) 846598. 4.80129e6i 0.158480 0.898783i −0.797056 0.603906i \(-0.793610\pi\)
0.955535 0.294877i \(-0.0952786\pi\)
\(492\) 0 0
\(493\) 2.58603e6 0.479200
\(494\) 0 0
\(495\) −761686. −0.139721
\(496\) 0 0
\(497\) 613627. 3.48005e6i 0.111433 0.631967i
\(498\) 0 0
\(499\) 2.13120e6 + 1.78829e6i 0.383153 + 0.321504i 0.813939 0.580951i \(-0.197319\pi\)
−0.430786 + 0.902454i \(0.641763\pi\)
\(500\) 0 0
\(501\) 1.56667e6 + 2.71356e6i 0.278859 + 0.482998i
\(502\) 0 0
\(503\) −2.71225e6 987179.i −0.477980 0.173971i 0.0917837 0.995779i \(-0.470743\pi\)
−0.569764 + 0.821808i \(0.692965\pi\)
\(504\) 0 0
\(505\) 570752. 988571.i 0.0995907 0.172496i
\(506\) 0 0
\(507\) 98491.7 + 558574.i 0.0170169 + 0.0965074i
\(508\) 0 0
\(509\) 6.43422e6 5.39895e6i 1.10078 0.923666i 0.103305 0.994650i \(-0.467058\pi\)
0.997477 + 0.0709840i \(0.0226139\pi\)
\(510\) 0 0
\(511\) −3.94078e6 + 1.43433e6i −0.667622 + 0.242994i
\(512\) 0 0
\(513\) −1.27663e6 5.44718e6i −0.214177 0.913857i
\(514\) 0 0
\(515\) −1.14961e6 + 418424.i −0.191000 + 0.0695182i
\(516\) 0 0
\(517\) −5.06079e6 + 4.24651e6i −0.832707 + 0.698724i
\(518\) 0 0
\(519\) 741605. + 4.20585e6i 0.120852 + 0.685387i
\(520\) 0 0
\(521\) 5.29254e6 9.16695e6i 0.854220 1.47955i −0.0231464 0.999732i \(-0.507368\pi\)
0.877367 0.479821i \(-0.159298\pi\)
\(522\) 0 0
\(523\) 4.98548e6 + 1.81457e6i 0.796990 + 0.290081i 0.708239 0.705973i \(-0.249490\pi\)
0.0887515 + 0.996054i \(0.471712\pi\)
\(524\) 0 0
\(525\) −1.83273e6 3.17437e6i −0.290201 0.502643i
\(526\) 0 0
\(527\) −184274. 154625.i −0.0289027 0.0242522i
\(528\) 0 0
\(529\) −1.07110e6 + 6.07450e6i −0.166414 + 0.943782i
\(530\) 0 0
\(531\) 3.37282e6 0.519107
\(532\) 0 0
\(533\) 1.02060e7 1.55610
\(534\) 0 0
\(535\) −128169. + 726883.i −0.0193597 + 0.109794i
\(536\) 0 0
\(537\) −1.93854e6 1.62663e6i −0.290094 0.243418i
\(538\) 0 0
\(539\) 642801. + 1.11336e6i 0.0953026 + 0.165069i
\(540\) 0 0
\(541\) 135462. + 49304.3i 0.0198988 + 0.00724255i 0.351950 0.936019i \(-0.385519\pi\)
−0.332052 + 0.943261i \(0.607741\pi\)
\(542\) 0 0
\(543\) 1.64934e6 2.85675e6i 0.240055 0.415788i
\(544\) 0 0
\(545\) 26410.9 + 149784.i 0.00380883 + 0.0216009i
\(546\) 0 0
\(547\) 3.83552e6 3.21838e6i 0.548095 0.459907i −0.326200 0.945301i \(-0.605768\pi\)
0.874295 + 0.485394i \(0.161324\pi\)
\(548\) 0 0
\(549\) −7.98093e6 + 2.90482e6i −1.13011 + 0.411328i
\(550\) 0 0
\(551\) 9.53714e6 4.08568e6i 1.33826 0.573304i
\(552\) 0 0
\(553\) 3.86010e6 1.40496e6i 0.536767 0.195367i
\(554\) 0 0
\(555\) −732388. + 614547.i −0.100927 + 0.0846881i
\(556\) 0 0
\(557\) −1.37928e6 7.82228e6i −0.188371 1.06831i −0.921547 0.388266i \(-0.873074\pi\)
0.733176 0.680039i \(-0.238037\pi\)
\(558\) 0 0
\(559\) 336140. 582211.i 0.0454978 0.0788045i
\(560\) 0 0
\(561\) −1.24148e6 451862.i −0.166545 0.0606176i
\(562\) 0 0
\(563\) −1.88834e6 3.27070e6i −0.251078 0.434880i 0.712745 0.701423i \(-0.247452\pi\)
−0.963823 + 0.266543i \(0.914118\pi\)
\(564\) 0 0
\(565\) −391438. 328455.i −0.0515872 0.0432868i
\(566\) 0 0
\(567\) −249866. + 1.41706e6i −0.0326399 + 0.185110i
\(568\) 0 0
\(569\) 1.06210e7 1.37526 0.687630 0.726061i \(-0.258651\pi\)
0.687630 + 0.726061i \(0.258651\pi\)
\(570\) 0 0
\(571\) 7.71674e6 0.990476 0.495238 0.868757i \(-0.335081\pi\)
0.495238 + 0.868757i \(0.335081\pi\)
\(572\) 0 0
\(573\) 162028. 918904.i 0.0206159 0.116919i
\(574\) 0 0
\(575\) 1.18604e6 + 995208.i 0.149600 + 0.125529i
\(576\) 0 0
\(577\) −4.76850e6 8.25928e6i −0.596269 1.03277i −0.993366 0.114991i \(-0.963316\pi\)
0.397098 0.917776i \(-0.370017\pi\)
\(578\) 0 0
\(579\) −5.90955e6 2.15090e6i −0.732584 0.266639i
\(580\) 0 0
\(581\) 5.22931e6 9.05743e6i 0.642694 1.11318i
\(582\) 0 0
\(583\) 1.79633e6 + 1.01875e7i 0.218884 + 1.24135i
\(584\) 0 0
\(585\) −989837. + 830572.i −0.119584 + 0.100343i
\(586\) 0 0
\(587\) −3.87713e6 + 1.41116e6i −0.464424 + 0.169037i −0.563625 0.826031i \(-0.690594\pi\)
0.0992006 + 0.995067i \(0.468371\pi\)
\(588\) 0 0
\(589\) −923885. 279111.i −0.109731 0.0331504i
\(590\) 0 0
\(591\) −3.97803e6 + 1.44788e6i −0.468489 + 0.170516i
\(592\) 0 0
\(593\) −2.15399e6 + 1.80742e6i −0.251540 + 0.211068i −0.759835 0.650116i \(-0.774720\pi\)
0.508295 + 0.861183i \(0.330276\pi\)
\(594\) 0 0
\(595\) −112201. 636324.i −0.0129929 0.0736861i
\(596\) 0 0
\(597\) −1.63220e6 + 2.82705e6i −0.187429 + 0.324636i
\(598\) 0 0
\(599\) 1.17608e7 + 4.28056e6i 1.33927 + 0.487454i 0.909582 0.415524i \(-0.136402\pi\)
0.429687 + 0.902978i \(0.358624\pi\)
\(600\) 0 0
\(601\) 3.49522e6 + 6.05389e6i 0.394719 + 0.683673i 0.993065 0.117565i \(-0.0375087\pi\)
−0.598346 + 0.801237i \(0.704175\pi\)
\(602\) 0 0
\(603\) 4.64084e6 + 3.89413e6i 0.519761 + 0.436131i
\(604\) 0 0
\(605\) 18634.9 105684.i 0.00206985 0.0117387i
\(606\) 0 0
\(607\) −7.20698e6 −0.793929 −0.396964 0.917834i \(-0.629936\pi\)
−0.396964 + 0.917834i \(0.629936\pi\)
\(608\) 0 0
\(609\) 8.08309e6 0.883149
\(610\) 0 0
\(611\) −1.94612e6 + 1.10370e7i −0.210895 + 1.19604i
\(612\) 0 0
\(613\) −9.57240e6 8.03220e6i −1.02889 0.863343i −0.0381730 0.999271i \(-0.512154\pi\)
−0.990719 + 0.135929i \(0.956598\pi\)
\(614\) 0 0
\(615\) −775473. 1.34316e6i −0.0826759 0.143199i
\(616\) 0 0
\(617\) −1.32473e7 4.82164e6i −1.40093 0.509896i −0.472475 0.881344i \(-0.656639\pi\)
−0.928454 + 0.371448i \(0.878861\pi\)
\(618\) 0 0
\(619\) −3.00321e6 + 5.20170e6i −0.315035 + 0.545656i −0.979445 0.201712i \(-0.935349\pi\)
0.664410 + 0.747368i \(0.268683\pi\)
\(620\) 0 0
\(621\) 319700. + 1.81311e6i 0.0332670 + 0.188666i
\(622\) 0 0
\(623\) −3.00325e6 + 2.52003e6i −0.310007 + 0.260127i
\(624\) 0 0
\(625\) −8.00462e6 + 2.91344e6i −0.819673 + 0.298337i
\(626\) 0 0
\(627\) −5.29241e6 + 294976.i −0.537631 + 0.0299652i
\(628\) 0 0
\(629\) 3.50794e6 1.27678e6i 0.353529 0.128674i
\(630\) 0 0
\(631\) 28000.5 23495.2i 0.00279957 0.00234912i −0.641387 0.767218i \(-0.721641\pi\)
0.644186 + 0.764869i \(0.277196\pi\)
\(632\) 0 0
\(633\) −1.00212e6 5.68330e6i −0.0994055 0.563757i
\(634\) 0 0
\(635\) 1.43230e6 2.48082e6i 0.140961 0.244152i
\(636\) 0 0
\(637\) 2.04940e6 + 745920.i 0.200114 + 0.0728356i
\(638\) 0 0
\(639\) −2.09656e6 3.63135e6i −0.203121 0.351817i
\(640\) 0 0
\(641\) −1.17087e7 9.82481e6i −1.12555 0.944450i −0.126680 0.991944i \(-0.540432\pi\)
−0.998872 + 0.0474937i \(0.984877\pi\)
\(642\) 0 0
\(643\) 123239. 698923.i 0.0117549 0.0666656i −0.978366 0.206881i \(-0.933669\pi\)
0.990121 + 0.140216i \(0.0447797\pi\)
\(644\) 0 0
\(645\) −102163. −0.00966926
\(646\) 0 0
\(647\) 774794. 0.0727655 0.0363827 0.999338i \(-0.488416\pi\)
0.0363827 + 0.999338i \(0.488416\pi\)
\(648\) 0 0
\(649\) 1.35627e6 7.69182e6i 0.126397 0.716832i
\(650\) 0 0
\(651\) −575981. 483305.i −0.0532666 0.0446960i
\(652\) 0 0
\(653\) 6.68597e6 + 1.15804e7i 0.613595 + 1.06278i 0.990629 + 0.136578i \(0.0436104\pi\)
−0.377035 + 0.926199i \(0.623056\pi\)
\(654\) 0 0
\(655\) 3.22171e6 + 1.17261e6i 0.293416 + 0.106795i
\(656\) 0 0
\(657\) −2.48812e6 + 4.30955e6i −0.224883 + 0.389509i
\(658\) 0 0
\(659\) 2.32818e6 + 1.32038e7i 0.208835 + 1.18436i 0.891290 + 0.453433i \(0.149801\pi\)
−0.682455 + 0.730927i \(0.739088\pi\)
\(660\) 0 0
\(661\) −4.81984e6 + 4.04432e6i −0.429071 + 0.360033i −0.831601 0.555374i \(-0.812575\pi\)
0.402530 + 0.915407i \(0.368131\pi\)
\(662\) 0 0
\(663\) −2.10608e6 + 766549.i −0.186076 + 0.0677261i
\(664\) 0 0
\(665\) −1.41912e6 2.16946e6i −0.124441 0.190238i
\(666\) 0 0
\(667\) −3.20835e6 + 1.16774e6i −0.279233 + 0.101633i
\(668\) 0 0
\(669\) 3.75181e6 3.14815e6i 0.324098 0.271950i
\(670\) 0 0
\(671\) 3.41524e6 + 1.93688e7i 0.292830 + 1.66072i
\(672\) 0 0
\(673\) −8.18441e6 + 1.41758e7i −0.696545 + 1.20645i 0.273111 + 0.961982i \(0.411947\pi\)
−0.969657 + 0.244470i \(0.921386\pi\)
\(674\) 0 0
\(675\) −9.98982e6 3.63600e6i −0.843914 0.307160i
\(676\) 0 0
\(677\) −696613. 1.20657e6i −0.0584144 0.101177i 0.835339 0.549735i \(-0.185271\pi\)
−0.893754 + 0.448558i \(0.851938\pi\)
\(678\) 0 0
\(679\) 1.57213e6 + 1.31918e6i 0.130862 + 0.109807i
\(680\) 0 0
\(681\) −703895. + 3.99199e6i −0.0581621 + 0.329854i
\(682\) 0 0
\(683\) −1.26107e7 −1.03440 −0.517198 0.855866i \(-0.673025\pi\)
−0.517198 + 0.855866i \(0.673025\pi\)
\(684\) 0 0
\(685\) 3.35637e6 0.273302
\(686\) 0 0
\(687\) 1.40685e6 7.97865e6i 0.113725 0.644967i
\(688\) 0 0
\(689\) 1.34432e7 + 1.12802e7i 1.07884 + 0.905251i
\(690\) 0 0
\(691\) −1.72975e6 2.99601e6i −0.137812 0.238698i 0.788856 0.614578i \(-0.210674\pi\)
−0.926668 + 0.375880i \(0.877340\pi\)
\(692\) 0 0
\(693\) 8.73541e6 + 3.17943e6i 0.690956 + 0.251487i
\(694\) 0 0
\(695\) −2.25995e6 + 3.91436e6i −0.177475 + 0.307396i
\(696\) 0 0
\(697\) 1.05159e6 + 5.96385e6i 0.0819905 + 0.464991i
\(698\) 0 0
\(699\) −3.87817e6 + 3.25417e6i −0.300216 + 0.251911i
\(700\) 0 0
\(701\) −6.75018e6 + 2.45686e6i −0.518824 + 0.188837i −0.588141 0.808758i \(-0.700140\pi\)
0.0693173 + 0.997595i \(0.477918\pi\)
\(702\) 0 0
\(703\) 1.09199e7 1.02509e7i 0.833354 0.782301i
\(704\) 0 0
\(705\) 1.60039e6 582495.i 0.121270 0.0441387i
\(706\) 0 0
\(707\) −1.06722e7 + 8.95501e6i −0.802979 + 0.673779i
\(708\) 0 0
\(709\) −1.71457e6 9.72378e6i −0.128097 0.726473i −0.979420 0.201832i \(-0.935311\pi\)
0.851323 0.524641i \(-0.175801\pi\)
\(710\) 0 0
\(711\) 2.43717e6 4.22131e6i 0.180806 0.313165i
\(712\) 0 0
\(713\) 298441. + 108624.i 0.0219854 + 0.00800204i
\(714\) 0 0
\(715\) 1.49611e6 + 2.59134e6i 0.109446 + 0.189566i
\(716\) 0 0
\(717\) −1.57341e6 1.32025e6i −0.114299 0.0959085i
\(718\) 0 0
\(719\) 1.80846e6 1.02563e7i 0.130463 0.739892i −0.847449 0.530876i \(-0.821863\pi\)
0.977912 0.209016i \(-0.0670260\pi\)
\(720\) 0 0
\(721\) 1.49309e7 1.06967
\(722\) 0 0
\(723\) −146082. −0.0103932
\(724\) 0 0
\(725\) 3.42347e6 1.94154e7i 0.241892 1.37184i
\(726\) 0 0
\(727\) −5.38410e6 4.51780e6i −0.377813 0.317023i 0.434030 0.900898i \(-0.357091\pi\)
−0.811843 + 0.583875i \(0.801536\pi\)
\(728\) 0 0
\(729\) −2.88104e6 4.99010e6i −0.200784 0.347769i
\(730\) 0 0
\(731\) 374849. + 136434.i 0.0259456 + 0.00944342i
\(732\) 0 0
\(733\) −3.45753e6 + 5.98862e6i −0.237687 + 0.411686i −0.960050 0.279828i \(-0.909723\pi\)
0.722363 + 0.691514i \(0.243056\pi\)
\(734\) 0 0
\(735\) −57551.0 326388.i −0.00392948 0.0222852i
\(736\) 0 0
\(737\) 1.07468e7 9.01768e6i 0.728807 0.611542i
\(738\) 0 0
\(739\) 1.97366e7 7.18353e6i 1.32942 0.483868i 0.422953 0.906152i \(-0.360994\pi\)
0.906464 + 0.422284i \(0.138771\pi\)
\(740\) 0 0
\(741\) −6.55601e6 + 6.15438e6i −0.438626 + 0.411755i
\(742\) 0 0
\(743\) −5.79122e6 + 2.10783e6i −0.384856 + 0.140076i −0.527200 0.849741i \(-0.676758\pi\)
0.142344 + 0.989817i \(0.454536\pi\)
\(744\) 0 0
\(745\) 955276. 801571.i 0.0630577 0.0529117i
\(746\) 0 0
\(747\) −2.15501e6 1.22217e7i −0.141302 0.801361i
\(748\) 0 0
\(749\) 4.50407e6 7.80127e6i 0.293360 0.508114i
\(750\) 0 0
\(751\) −8.83002e6 3.21386e6i −0.571297 0.207935i 0.0401867 0.999192i \(-0.487205\pi\)
−0.611484 + 0.791257i \(0.709427\pi\)
\(752\) 0 0
\(753\) 7.73269e6 + 1.33934e7i 0.496985 + 0.860803i
\(754\) 0 0
\(755\) 1.46650e6 + 1.23054e6i 0.0936297 + 0.0785646i
\(756\) 0 0
\(757\) −45805.4 + 259775.i −0.00290521 + 0.0164762i −0.986226 0.165404i \(-0.947107\pi\)
0.983321 + 0.181880i \(0.0582183\pi\)
\(758\) 0 0
\(759\) 1.74428e6 0.109903
\(760\) 0 0
\(761\) −2.46615e7 −1.54368 −0.771841 0.635815i \(-0.780664\pi\)
−0.771841 + 0.635815i \(0.780664\pi\)
\(762\) 0 0
\(763\) 322333. 1.82804e6i 0.0200444 0.113677i
\(764\) 0 0
\(765\) −587333. 492831.i −0.0362853 0.0304470i
\(766\) 0 0
\(767\) −6.62493e6 1.14747e7i −0.406624 0.704293i
\(768\) 0 0
\(769\) 9.43176e6 + 3.43288e6i 0.575144 + 0.209335i 0.613183 0.789941i \(-0.289889\pi\)
−0.0380388 + 0.999276i \(0.512111\pi\)
\(770\) 0 0
\(771\) 1.50251e6 2.60242e6i 0.0910292 0.157667i
\(772\) 0 0
\(773\) −3.40728e6 1.93236e7i −0.205097 1.16316i −0.897287 0.441447i \(-0.854465\pi\)
0.692191 0.721715i \(-0.256646\pi\)
\(774\) 0 0
\(775\) −1.40484e6 + 1.17880e6i −0.0840180 + 0.0704994i
\(776\) 0 0
\(777\) 1.09646e7 3.99081e6i 0.651542 0.237142i
\(778\) 0 0
\(779\) 1.33005e7 + 2.03329e7i 0.785279 + 1.20048i
\(780\) 0 0
\(781\) −9.12448e6 + 3.32104e6i −0.535279 + 0.194826i
\(782\) 0 0
\(783\) 1.79587e7 1.50692e7i 1.04682 0.878385i
\(784\) 0 0
\(785\) 6275.72 + 35591.4i 0.000363487 + 0.00206144i
\(786\) 0 0
\(787\) 1.45243e7 2.51569e7i 0.835910 1.44784i −0.0573777 0.998353i \(-0.518274\pi\)
0.893288 0.449486i \(-0.148393\pi\)
\(788\) 0 0
\(789\) 1.03985e7 + 3.78476e6i 0.594675 + 0.216444i
\(790\) 0 0
\(791\) 3.11817e6 + 5.40084e6i 0.177198 + 0.306916i
\(792\) 0 0
\(793\) 2.55587e7 + 2.14463e7i 1.44330 + 1.21107i
\(794\) 0 0
\(795\) 463087. 2.62630e6i 0.0259863 0.147376i
\(796\) 0 0
\(797\) −1.83010e7 −1.02054 −0.510269 0.860015i \(-0.670454\pi\)
−0.510269 + 0.860015i \(0.670454\pi\)
\(798\) 0 0
\(799\) −6.64997e6 −0.368513
\(800\) 0 0
\(801\) −807815. + 4.58135e6i −0.0444868 + 0.252297i
\(802\) 0 0
\(803\) 8.82752e6 + 7.40717e6i 0.483114 + 0.405381i
\(804\) 0 0
\(805\) 426539. + 738787.i 0.0231990 + 0.0401818i
\(806\) 0 0
\(807\) 1.26131e7 + 4.59078e6i 0.681769 + 0.248144i
\(808\) 0 0
\(809\) −1.86634e6 + 3.23260e6i −0.100258 + 0.173653i −0.911791 0.410654i \(-0.865300\pi\)
0.811533 + 0.584307i \(0.198634\pi\)
\(810\) 0 0
\(811\) −4.06242e6 2.30391e7i −0.216887 1.23003i −0.877602 0.479390i \(-0.840858\pi\)
0.660715 0.750636i \(-0.270253\pi\)
\(812\) 0 0
\(813\) 3.07344e6 2.57892e6i 0.163079 0.136840i
\(814\) 0 0
\(815\) 5.14674e6 1.87326e6i 0.271418 0.0987879i
\(816\) 0 0
\(817\) 1.59798e6 89064.2i 0.0837558 0.00466819i
\(818\) 0 0
\(819\) 1.48189e7 5.39365e6i 0.771982 0.280979i
\(820\) 0 0
\(821\) −1.78767e6 + 1.50003e6i −0.0925611 + 0.0776680i −0.687894 0.725811i \(-0.741465\pi\)
0.595333 + 0.803479i \(0.297020\pi\)
\(822\) 0 0
\(823\) 12536.8 + 71099.6i 0.000645188 + 0.00365904i 0.985129 0.171818i \(-0.0549642\pi\)
−0.984483 + 0.175477i \(0.943853\pi\)
\(824\) 0 0
\(825\) −5.03600e6 + 8.72261e6i −0.257603 + 0.446181i
\(826\) 0 0
\(827\) −2.63894e7 9.60494e6i −1.34173 0.488350i −0.431373 0.902174i \(-0.641971\pi\)
−0.910357 + 0.413824i \(0.864193\pi\)
\(828\) 0 0
\(829\) −1.65912e7 2.87368e7i −0.838478 1.45229i −0.891167 0.453675i \(-0.850113\pi\)
0.0526892 0.998611i \(-0.483221\pi\)
\(830\) 0 0
\(831\) −1.13479e7 9.52198e6i −0.570048 0.478327i
\(832\) 0 0
\(833\) −224715. + 1.27442e6i −0.0112207 + 0.0636357i
\(834\) 0 0
\(835\) 4.21085e6 0.209003
\(836\) 0 0
\(837\) −2.18071e6 −0.107593
\(838\) 0 0
\(839\) −1.87283e6 + 1.06213e7i −0.0918530 + 0.520924i 0.903813 + 0.427927i \(0.140756\pi\)
−0.995666 + 0.0929975i \(0.970355\pi\)
\(840\) 0 0
\(841\) 1.75918e7 + 1.47613e7i 0.857670 + 0.719670i
\(842\) 0 0
\(843\) 1.03726e6 + 1.79658e6i 0.0502710 + 0.0870720i
\(844\) 0 0
\(845\) 716268. + 260700.i 0.0345091 + 0.0125603i
\(846\) 0 0
\(847\) −654859. + 1.13425e6i −0.0313646 + 0.0543250i
\(848\) 0 0
\(849\) 3.15743e6 + 1.79067e7i 0.150337 + 0.852601i
\(850\) 0 0
\(851\) −3.77556e6 + 3.16807e6i −0.178714 + 0.149959i
\(852\) 0 0
\(853\) −1.18539e7 + 4.31448e6i −0.557815 + 0.203028i −0.605515 0.795834i \(-0.707033\pi\)
0.0477006 + 0.998862i \(0.484811\pi\)
\(854\) 0 0
\(855\) −2.94468e6 889604.i −0.137760 0.0416180i
\(856\) 0 0
\(857\) 9.54596e6 3.47444e6i 0.443984 0.161597i −0.110347 0.993893i \(-0.535196\pi\)
0.554331 + 0.832296i \(0.312974\pi\)
\(858\) 0 0
\(859\) 1.22368e6 1.02679e6i 0.0565828 0.0474786i −0.614058 0.789261i \(-0.710464\pi\)
0.670640 + 0.741783i \(0.266019\pi\)
\(860\) 0 0
\(861\) 3.28691e6 + 1.86410e7i 0.151106 + 0.856962i
\(862\) 0 0
\(863\) −1.13172e7 + 1.96020e7i −0.517265 + 0.895929i 0.482534 + 0.875877i \(0.339717\pi\)
−0.999799 + 0.0200520i \(0.993617\pi\)
\(864\) 0 0
\(865\) 5.39323e6 + 1.96298e6i 0.245081 + 0.0892020i
\(866\) 0 0
\(867\) 5.47269e6 + 9.47898e6i 0.247260 + 0.428266i
\(868\) 0 0
\(869\) −8.64678e6 7.25551e6i −0.388423 0.325926i
\(870\) 0 0
\(871\) 4.13268e6 2.34376e7i 0.184581 1.04681i
\(872\) 0 0
\(873\) 2.43523e6 0.108144
\(874\) 0 0
\(875\) −1.00742e7 −0.444828
\(876\) 0 0
\(877\) −4.63706e6 + 2.62981e7i −0.203584 + 1.15458i 0.696069 + 0.717975i \(0.254931\pi\)
−0.899652 + 0.436607i \(0.856180\pi\)
\(878\) 0 0
\(879\) −5.86197e6 4.91878e6i −0.255901 0.214726i
\(880\) 0 0
\(881\) 7.98917e6 + 1.38377e7i 0.346786 + 0.600652i 0.985677 0.168646i \(-0.0539396\pi\)
−0.638890 + 0.769298i \(0.720606\pi\)
\(882\) 0 0
\(883\) 1.36914e7 + 4.98325e6i 0.590942 + 0.215085i 0.620144 0.784488i \(-0.287074\pi\)
−0.0292017 + 0.999574i \(0.509297\pi\)
\(884\) 0 0
\(885\) −1.00675e6 + 1.74375e6i −0.0432081 + 0.0748387i
\(886\) 0 0
\(887\) −3.44258e6 1.95239e7i −0.146918 0.833214i −0.965807 0.259262i \(-0.916521\pi\)
0.818889 0.573952i \(-0.194590\pi\)
\(888\) 0 0
\(889\) −2.67818e7 + 2.24726e7i −1.13654 + 0.953672i
\(890\) 0 0
\(891\) 3.71544e6 1.35231e6i 0.156789 0.0570666i
\(892\) 0 0
\(893\) −2.45247e7 + 1.05063e7i −1.02914 + 0.440880i
\(894\) 0 0
\(895\) −3.19571e6 + 1.16314e6i −0.133355 + 0.0485372i
\(896\) 0 0
\(897\) 2.26675e6 1.90203e6i 0.0940638 0.0789289i
\(898\) 0 0
\(899\) −702251. 3.98266e6i −0.0289797 0.164352i
\(900\) 0 0
\(901\) −5.20644e6 + 9.01782e6i −0.213663 + 0.370075i
\(902\) 0 0
\(903\) 1.17166e6 + 426448.i 0.0478168 + 0.0174039i
\(904\) 0 0
\(905\) −2.21652e6 3.83912e6i −0.0899601 0.155816i
\(906\) 0 0
\(907\) −2.66921e7 2.23973e7i −1.07737 0.904019i −0.0816678 0.996660i \(-0.526025\pi\)
−0.995700 + 0.0926410i \(0.970469\pi\)
\(908\) 0 0
\(909\) −2.87060e6 + 1.62800e7i −0.115229 + 0.653498i
\(910\) 0 0
\(911\) −1.94250e7 −0.775471 −0.387735 0.921771i \(-0.626743\pi\)
−0.387735 + 0.921771i \(0.626743\pi\)
\(912\) 0 0
\(913\) −2.87384e7 −1.14100
\(914\) 0 0
\(915\) 880436. 4.99320e6i 0.0347652 0.197163i
\(916\) 0 0
\(917\) −3.20536e7 2.68962e7i −1.25879 1.05625i
\(918\) 0 0
\(919\) 1.36621e7 + 2.36634e7i 0.533614 + 0.924247i 0.999229 + 0.0392595i \(0.0124999\pi\)
−0.465615 + 0.884988i \(0.654167\pi\)
\(920\) 0 0
\(921\) 1.91729e6 + 697835.i 0.0744797 + 0.0271084i
\(922\) 0 0
\(923\) −8.23618e6 + 1.42655e7i −0.318216 + 0.551166i
\(924\) 0 0
\(925\) −4.94194e6 2.80271e7i −0.189908 1.07702i
\(926\) 0 0
\(927\) 1.35720e7 1.13883e7i 0.518735 0.435270i
\(928\) 0 0
\(929\) 1.70740e7 6.21442e6i 0.649075 0.236244i 0.00356274 0.999994i \(-0.498866\pi\)
0.645513 + 0.763749i \(0.276644\pi\)
\(930\) 0 0
\(931\) 1.18472e6 + 5.05502e6i 0.0447964 + 0.191139i
\(932\) 0 0
\(933\) 1.72184e7 6.26699e6i 0.647574 0.235697i
\(934\) 0 0
\(935\) −1.36009e6 + 1.14125e6i −0.0508791 + 0.0426927i
\(936\) 0 0
\(937\) 7.97107e6 + 4.52062e7i 0.296597 + 1.68209i 0.660638 + 0.750705i \(0.270286\pi\)
−0.364041 + 0.931383i \(0.618603\pi\)
\(938\) 0 0
\(939\) −8.90679e6 + 1.54270e7i −0.329653 + 0.570976i
\(940\) 0 0
\(941\) 3.87085e6 + 1.40887e6i 0.142506 + 0.0518679i 0.412288 0.911053i \(-0.364730\pi\)
−0.269783 + 0.962921i \(0.586952\pi\)
\(942\) 0 0
\(943\) −3.99767e6 6.92417e6i −0.146396 0.253564i
\(944\) 0 0
\(945\) −4.48713e6 3.76515e6i −0.163451 0.137152i
\(946\) 0 0
\(947\) −7.28310e6 + 4.13045e7i −0.263901 + 1.49666i 0.508245 + 0.861213i \(0.330295\pi\)
−0.772146 + 0.635445i \(0.780817\pi\)
\(948\) 0 0
\(949\) 1.95487e7 0.704617
\(950\) 0 0
\(951\) 2.83448e7 1.01630
\(952\) 0 0
\(953\) −8.14225e6 + 4.61770e7i −0.290410 + 1.64700i 0.394883 + 0.918731i \(0.370785\pi\)
−0.685294 + 0.728267i \(0.740326\pi\)
\(954\) 0 0
\(955\) −960580. 806022.i −0.0340820 0.0285982i
\(956\) 0 0
\(957\) −1.11054e7 1.92352e7i −0.391972 0.678916i
\(958\) 0 0
\(959\) −3.84926e7 1.40101e7i −1.35154 0.491922i
\(960\) 0 0
\(961\) 1.41265e7 2.44678e7i 0.493430 0.854646i
\(962\) 0 0
\(963\) −1.85613e6 1.05267e7i −0.0644976 0.365784i
\(964\) 0 0
\(965\) −6.47415e6 + 5.43246e6i −0.223802 + 0.187792i
\(966\) 0 0
\(967\) 4.76089e7 1.73282e7i 1.63728 0.595920i 0.650717 0.759320i \(-0.274468\pi\)
0.986560 + 0.163400i \(0.0522460\pi\)
\(968\) 0 0
\(969\) −4.27181e6 3.19687e6i −0.146151 0.109375i
\(970\) 0 0
\(971\) 2.54102e7 9.24856e6i 0.864889 0.314794i 0.128793 0.991671i \(-0.458890\pi\)
0.736095 + 0.676878i \(0.236667\pi\)
\(972\) 0 0
\(973\) 4.22576e7 3.54584e7i 1.43095 1.20071i
\(974\) 0 0
\(975\) 2.96702e6 + 1.68268e7i 0.0999559 + 0.566878i
\(976\) 0 0
\(977\) −2.21791e7 + 3.84154e7i −0.743375 + 1.28756i 0.207575 + 0.978219i \(0.433443\pi\)
−0.950950 + 0.309345i \(0.899890\pi\)
\(978\) 0 0
\(979\) 1.01231e7 + 3.68449e6i 0.337563 + 0.122863i
\(980\) 0 0
\(981\) −1.10131e6 1.90752e6i −0.0365372 0.0632844i
\(982\) 0 0
\(983\) −1.92569e7 1.61584e7i −0.635626 0.533354i 0.267045 0.963684i \(-0.413953\pi\)
−0.902672 + 0.430330i \(0.858397\pi\)
\(984\) 0 0
\(985\) −987901. + 5.60266e6i −0.0324431 + 0.183994i
\(986\) 0 0
\(987\) −2.07856e7 −0.679156
\(988\) 0 0
\(989\) −526663. −0.0171215
\(990\) 0 0
\(991\) −4.93327e6 + 2.79780e7i −0.159570 + 0.904965i 0.794918 + 0.606716i \(0.207514\pi\)
−0.954488 + 0.298249i \(0.903597\pi\)
\(992\) 0 0
\(993\) −1.45697e7 1.22255e7i −0.468898 0.393452i
\(994\) 0 0
\(995\) 2.19348e6 + 3.79921e6i 0.0702385 + 0.121657i
\(996\) 0 0
\(997\) 2.88890e7 + 1.05147e7i 0.920437 + 0.335012i 0.758412 0.651775i \(-0.225975\pi\)
0.162025 + 0.986787i \(0.448198\pi\)
\(998\) 0 0
\(999\) 1.69209e7 2.93079e7i 0.536426 0.929117i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 76.6.i.a.5.5 48
19.4 even 9 inner 76.6.i.a.61.5 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.6.i.a.5.5 48 1.1 even 1 trivial
76.6.i.a.61.5 yes 48 19.4 even 9 inner