Properties

Label 84.9.m.a.73.2
Level $84$
Weight $9$
Character 84.73
Analytic conductor $34.220$
Analytic rank $0$
Dimension $10$
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] = [84,9,Mod(61,84)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(84, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 5]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("84.61");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 84.m (of order \(6\), degree \(2\), 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: \(34.2198032451\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 38255 x^{8} + 1483053595 x^{6} - 139470625170 x^{5} + 5194605060018 x^{4} - 71600654137860 x^{3} + 119846615988780 x^{2} + \cdots + 15\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{10}\cdot 3^{8}\cdot 7^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 73.2
Root \(38.0902 + 21.9914i\) of defining polynomial
Character \(\chi\) \(=\) 84.73
Dual form 84.9.m.a.61.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-40.5000 - 23.3827i) q^{3} +(-374.307 + 216.106i) q^{5} +(83.7630 - 2399.54i) q^{7} +(1093.50 + 1894.00i) q^{9} +O(q^{10})\) \(q+(-40.5000 - 23.3827i) q^{3} +(-374.307 + 216.106i) q^{5} +(83.7630 - 2399.54i) q^{7} +(1093.50 + 1894.00i) q^{9} +(6902.31 - 11955.2i) q^{11} -3223.79i q^{13} +20212.6 q^{15} +(-21339.9 - 12320.6i) q^{17} +(29141.7 - 16825.0i) q^{19} +(-59500.1 + 95222.7i) q^{21} +(-112905. - 195558. i) q^{23} +(-101909. + 176511. i) q^{25} -102276. i q^{27} -908389. q^{29} +(925773. + 534495. i) q^{31} +(-559087. + 322789. i) q^{33} +(487202. + 916265. i) q^{35} +(979412. + 1.69639e6i) q^{37} +(-75380.8 + 130563. i) q^{39} +2.90040e6i q^{41} -4.01000e6 q^{43} +(-818609. - 472624. i) q^{45} +(-4.29428e6 + 2.47930e6i) q^{47} +(-5.75077e6 - 401985. i) q^{49} +(576177. + 997968. i) q^{51} +(-3.98900e6 + 6.90915e6i) q^{53} +5.96653e6i q^{55} -1.57365e6 q^{57} +(4.69735e6 + 2.71201e6i) q^{59} +(1.84448e6 - 1.06491e6i) q^{61} +(4.63631e6 - 2.46525e6i) q^{63} +(696680. + 1.20669e6i) q^{65} +(-9.53767e6 + 1.65197e7i) q^{67} +1.05601e7i q^{69} -2.08687e7 q^{71} +(-9.66235e6 - 5.57856e6i) q^{73} +(8.25461e6 - 4.76580e6i) q^{75} +(-2.81087e7 - 1.75638e7i) q^{77} +(1.21508e7 + 2.10458e7i) q^{79} +(-2.39148e6 + 4.14217e6i) q^{81} +3.92213e7i q^{83} +1.06502e7 q^{85} +(3.67898e7 + 2.12406e7i) q^{87} +(1.02177e7 - 5.89920e6i) q^{89} +(-7.73560e6 - 270034. i) q^{91} +(-2.49959e7 - 4.32941e7i) q^{93} +(-7.27196e6 + 1.25954e7i) q^{95} -7.80671e7i q^{97} +3.01907e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 405 q^{3} + 1389 q^{5} + 1217 q^{7} + 10935 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 405 q^{3} + 1389 q^{5} + 1217 q^{7} + 10935 q^{9} - 879 q^{11} - 75006 q^{15} - 13674 q^{17} - 29268 q^{19} - 42363 q^{21} + 312732 q^{23} - 22052 q^{25} - 289794 q^{29} + 242787 q^{31} + 71199 q^{33} + 1209372 q^{35} + 1913308 q^{37} - 1232334 q^{39} - 861848 q^{43} + 3037743 q^{45} - 305448 q^{47} + 9821659 q^{49} + 369198 q^{51} - 10663233 q^{53} + 1580472 q^{57} + 18410871 q^{59} - 13937808 q^{61} + 769824 q^{63} - 14966808 q^{65} - 20722822 q^{67} + 113032584 q^{71} + 43436322 q^{73} + 1786212 q^{75} - 98823405 q^{77} - 42189637 q^{79} - 23914845 q^{81} + 142602108 q^{85} + 11736657 q^{87} + 67171914 q^{89} - 246091266 q^{91} - 6555249 q^{93} - 140649894 q^{95} - 3844746 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(43\) \(73\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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
\(3\) −40.5000 23.3827i −0.500000 0.288675i
\(4\) 0 0
\(5\) −374.307 + 216.106i −0.598891 + 0.345770i −0.768605 0.639724i \(-0.779049\pi\)
0.169714 + 0.985493i \(0.445716\pi\)
\(6\) 0 0
\(7\) 83.7630 2399.54i 0.0348867 0.999391i
\(8\) 0 0
\(9\) 1093.50 + 1894.00i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) 6902.31 11955.2i 0.471437 0.816553i −0.528029 0.849226i \(-0.677069\pi\)
0.999466 + 0.0326733i \(0.0104021\pi\)
\(12\) 0 0
\(13\) 3223.79i 0.112874i −0.998406 0.0564369i \(-0.982026\pi\)
0.998406 0.0564369i \(-0.0179740\pi\)
\(14\) 0 0
\(15\) 20212.6 0.399261
\(16\) 0 0
\(17\) −21339.9 12320.6i −0.255503 0.147515i 0.366778 0.930308i \(-0.380461\pi\)
−0.622282 + 0.782794i \(0.713794\pi\)
\(18\) 0 0
\(19\) 29141.7 16825.0i 0.223615 0.129104i −0.384008 0.923330i \(-0.625457\pi\)
0.607623 + 0.794226i \(0.292123\pi\)
\(20\) 0 0
\(21\) −59500.1 + 95222.7i −0.305943 + 0.489625i
\(22\) 0 0
\(23\) −112905. 195558.i −0.403462 0.698817i 0.590679 0.806907i \(-0.298860\pi\)
−0.994141 + 0.108090i \(0.965527\pi\)
\(24\) 0 0
\(25\) −101909. + 176511.i −0.260887 + 0.451869i
\(26\) 0 0
\(27\) 102276.i 0.192450i
\(28\) 0 0
\(29\) −908389. −1.28434 −0.642170 0.766562i \(-0.721966\pi\)
−0.642170 + 0.766562i \(0.721966\pi\)
\(30\) 0 0
\(31\) 925773. + 534495.i 1.00244 + 0.578758i 0.908969 0.416864i \(-0.136871\pi\)
0.0934693 + 0.995622i \(0.470204\pi\)
\(32\) 0 0
\(33\) −559087. + 322789.i −0.471437 + 0.272184i
\(34\) 0 0
\(35\) 487202. + 916265.i 0.324666 + 0.610589i
\(36\) 0 0
\(37\) 979412. + 1.69639e6i 0.522587 + 0.905147i 0.999655 + 0.0262808i \(0.00836640\pi\)
−0.477067 + 0.878867i \(0.658300\pi\)
\(38\) 0 0
\(39\) −75380.8 + 130563.i −0.0325838 + 0.0564369i
\(40\) 0 0
\(41\) 2.90040e6i 1.02641i 0.858265 + 0.513207i \(0.171543\pi\)
−0.858265 + 0.513207i \(0.828457\pi\)
\(42\) 0 0
\(43\) −4.01000e6 −1.17293 −0.586463 0.809976i \(-0.699480\pi\)
−0.586463 + 0.809976i \(0.699480\pi\)
\(44\) 0 0
\(45\) −818609. 472624.i −0.199630 0.115257i
\(46\) 0 0
\(47\) −4.29428e6 + 2.47930e6i −0.880033 + 0.508087i −0.870669 0.491869i \(-0.836314\pi\)
−0.00936356 + 0.999956i \(0.502981\pi\)
\(48\) 0 0
\(49\) −5.75077e6 401985.i −0.997566 0.0697309i
\(50\) 0 0
\(51\) 576177. + 997968.i 0.0851677 + 0.147515i
\(52\) 0 0
\(53\) −3.98900e6 + 6.90915e6i −0.505546 + 0.875631i 0.494434 + 0.869215i \(0.335376\pi\)
−0.999979 + 0.00641571i \(0.997958\pi\)
\(54\) 0 0
\(55\) 5.96653e6i 0.652035i
\(56\) 0 0
\(57\) −1.57365e6 −0.149077
\(58\) 0 0
\(59\) 4.69735e6 + 2.71201e6i 0.387654 + 0.223812i 0.681143 0.732150i \(-0.261483\pi\)
−0.293489 + 0.955962i \(0.594816\pi\)
\(60\) 0 0
\(61\) 1.84448e6 1.06491e6i 0.133216 0.0769120i −0.431911 0.901916i \(-0.642161\pi\)
0.565127 + 0.825004i \(0.308827\pi\)
\(62\) 0 0
\(63\) 4.63631e6 2.46525e6i 0.294314 0.156494i
\(64\) 0 0
\(65\) 696680. + 1.20669e6i 0.0390283 + 0.0675991i
\(66\) 0 0
\(67\) −9.53767e6 + 1.65197e7i −0.473307 + 0.819792i −0.999533 0.0305527i \(-0.990273\pi\)
0.526226 + 0.850345i \(0.323607\pi\)
\(68\) 0 0
\(69\) 1.05601e7i 0.465878i
\(70\) 0 0
\(71\) −2.08687e7 −0.821223 −0.410612 0.911810i \(-0.634685\pi\)
−0.410612 + 0.911810i \(0.634685\pi\)
\(72\) 0 0
\(73\) −9.66235e6 5.57856e6i −0.340245 0.196440i 0.320136 0.947372i \(-0.396272\pi\)
−0.660380 + 0.750931i \(0.729605\pi\)
\(74\) 0 0
\(75\) 8.25461e6 4.76580e6i 0.260887 0.150623i
\(76\) 0 0
\(77\) −2.81087e7 1.75638e7i −0.799609 0.499637i
\(78\) 0 0
\(79\) 1.21508e7 + 2.10458e7i 0.311958 + 0.540328i 0.978786 0.204884i \(-0.0656817\pi\)
−0.666828 + 0.745212i \(0.732348\pi\)
\(80\) 0 0
\(81\) −2.39148e6 + 4.14217e6i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 3.92213e7i 0.826436i 0.910632 + 0.413218i \(0.135595\pi\)
−0.910632 + 0.413218i \(0.864405\pi\)
\(84\) 0 0
\(85\) 1.06502e7 0.204025
\(86\) 0 0
\(87\) 3.67898e7 + 2.12406e7i 0.642170 + 0.370757i
\(88\) 0 0
\(89\) 1.02177e7 5.89920e6i 0.162852 0.0940228i −0.416359 0.909200i \(-0.636694\pi\)
0.579211 + 0.815178i \(0.303361\pi\)
\(90\) 0 0
\(91\) −7.73560e6 270034.i −0.112805 0.00393779i
\(92\) 0 0
\(93\) −2.49959e7 4.32941e7i −0.334146 0.578758i
\(94\) 0 0
\(95\) −7.27196e6 + 1.25954e7i −0.0892806 + 0.154638i
\(96\) 0 0
\(97\) 7.80671e7i 0.881822i −0.897551 0.440911i \(-0.854655\pi\)
0.897551 0.440911i \(-0.145345\pi\)
\(98\) 0 0
\(99\) 3.01907e7 0.314291
\(100\) 0 0
\(101\) 3.07926e7 + 1.77781e7i 0.295911 + 0.170844i 0.640604 0.767871i \(-0.278684\pi\)
−0.344694 + 0.938715i \(0.612017\pi\)
\(102\) 0 0
\(103\) 1.83451e8 1.05915e8i 1.62994 0.941044i 0.645826 0.763485i \(-0.276513\pi\)
0.984110 0.177560i \(-0.0568202\pi\)
\(104\) 0 0
\(105\) 1.69306e6 4.85008e7i 0.0139289 0.399017i
\(106\) 0 0
\(107\) −6.59050e7 1.14151e8i −0.502786 0.870851i −0.999995 0.00322029i \(-0.998975\pi\)
0.497209 0.867631i \(-0.334358\pi\)
\(108\) 0 0
\(109\) 9.29656e7 1.61021e8i 0.658591 1.14071i −0.322389 0.946607i \(-0.604486\pi\)
0.980980 0.194107i \(-0.0621808\pi\)
\(110\) 0 0
\(111\) 9.16052e7i 0.603432i
\(112\) 0 0
\(113\) −4.85733e7 −0.297909 −0.148955 0.988844i \(-0.547591\pi\)
−0.148955 + 0.988844i \(0.547591\pi\)
\(114\) 0 0
\(115\) 8.45224e7 + 4.87990e7i 0.483260 + 0.279010i
\(116\) 0 0
\(117\) 6.10585e6 3.52521e6i 0.0325838 0.0188123i
\(118\) 0 0
\(119\) −3.13512e7 + 5.01739e7i −0.156339 + 0.250201i
\(120\) 0 0
\(121\) 1.18956e7 + 2.06038e7i 0.0554940 + 0.0961184i
\(122\) 0 0
\(123\) 6.78191e7 1.17466e8i 0.296300 0.513207i
\(124\) 0 0
\(125\) 2.56925e8i 1.05237i
\(126\) 0 0
\(127\) 1.32804e8 0.510502 0.255251 0.966875i \(-0.417842\pi\)
0.255251 + 0.966875i \(0.417842\pi\)
\(128\) 0 0
\(129\) 1.62405e8 + 9.37646e7i 0.586463 + 0.338595i
\(130\) 0 0
\(131\) −2.33780e8 + 1.34973e8i −0.793821 + 0.458313i −0.841306 0.540559i \(-0.818213\pi\)
0.0474851 + 0.998872i \(0.484879\pi\)
\(132\) 0 0
\(133\) −3.79312e7 7.13360e7i −0.121224 0.227983i
\(134\) 0 0
\(135\) 2.21024e7 + 3.82825e7i 0.0665434 + 0.115257i
\(136\) 0 0
\(137\) −2.88322e8 + 4.99388e8i −0.818456 + 1.41761i 0.0883640 + 0.996088i \(0.471836\pi\)
−0.906820 + 0.421519i \(0.861497\pi\)
\(138\) 0 0
\(139\) 1.98197e8i 0.530930i −0.964120 0.265465i \(-0.914475\pi\)
0.964120 0.265465i \(-0.0855255\pi\)
\(140\) 0 0
\(141\) 2.31891e8 0.586689
\(142\) 0 0
\(143\) −3.85409e7 2.22516e7i −0.0921674 0.0532129i
\(144\) 0 0
\(145\) 3.40016e8 1.96308e8i 0.769179 0.444086i
\(146\) 0 0
\(147\) 2.23507e8 + 1.50749e8i 0.478653 + 0.322838i
\(148\) 0 0
\(149\) −1.00595e8 1.74236e8i −0.204095 0.353504i 0.745749 0.666227i \(-0.232092\pi\)
−0.949844 + 0.312724i \(0.898759\pi\)
\(150\) 0 0
\(151\) −4.83143e8 + 8.36828e8i −0.929326 + 1.60964i −0.144874 + 0.989450i \(0.546278\pi\)
−0.784452 + 0.620190i \(0.787056\pi\)
\(152\) 0 0
\(153\) 5.38903e7i 0.0983432i
\(154\) 0 0
\(155\) −4.62031e8 −0.800468
\(156\) 0 0
\(157\) −3.13710e8 1.81120e8i −0.516332 0.298105i 0.219100 0.975702i \(-0.429688\pi\)
−0.735433 + 0.677598i \(0.763021\pi\)
\(158\) 0 0
\(159\) 3.23109e8 1.86547e8i 0.505546 0.291877i
\(160\) 0 0
\(161\) −4.78705e8 + 2.54540e8i −0.712467 + 0.378837i
\(162\) 0 0
\(163\) −3.14898e7 5.45419e7i −0.0446087 0.0772645i 0.842859 0.538135i \(-0.180871\pi\)
−0.887468 + 0.460870i \(0.847537\pi\)
\(164\) 0 0
\(165\) 1.39513e8 2.41644e8i 0.188226 0.326017i
\(166\) 0 0
\(167\) 9.92784e8i 1.27641i 0.769868 + 0.638203i \(0.220322\pi\)
−0.769868 + 0.638203i \(0.779678\pi\)
\(168\) 0 0
\(169\) 8.05338e8 0.987260
\(170\) 0 0
\(171\) 6.37329e7 + 3.67962e7i 0.0745383 + 0.0430347i
\(172\) 0 0
\(173\) −1.20331e9 + 6.94731e8i −1.34336 + 0.775590i −0.987299 0.158872i \(-0.949214\pi\)
−0.356062 + 0.934462i \(0.615881\pi\)
\(174\) 0 0
\(175\) 4.15009e8 + 2.59319e8i 0.442492 + 0.276492i
\(176\) 0 0
\(177\) −1.26828e8 2.19673e8i −0.129218 0.223812i
\(178\) 0 0
\(179\) −4.36947e8 + 7.56814e8i −0.425614 + 0.737186i −0.996478 0.0838594i \(-0.973275\pi\)
0.570863 + 0.821045i \(0.306609\pi\)
\(180\) 0 0
\(181\) 3.49705e8i 0.325827i −0.986640 0.162913i \(-0.947911\pi\)
0.986640 0.162913i \(-0.0520891\pi\)
\(182\) 0 0
\(183\) −9.96020e7 −0.0888104
\(184\) 0 0
\(185\) −7.33201e8 4.23314e8i −0.625945 0.361390i
\(186\) 0 0
\(187\) −2.94589e8 + 1.70081e8i −0.240907 + 0.139088i
\(188\) 0 0
\(189\) −2.45415e8 8.56693e6i −0.192333 0.00671395i
\(190\) 0 0
\(191\) 2.50191e8 + 4.33344e8i 0.187992 + 0.325611i 0.944580 0.328280i \(-0.106469\pi\)
−0.756589 + 0.653891i \(0.773136\pi\)
\(192\) 0 0
\(193\) −2.34010e8 + 4.05317e8i −0.168657 + 0.292123i −0.937948 0.346776i \(-0.887276\pi\)
0.769291 + 0.638899i \(0.220610\pi\)
\(194\) 0 0
\(195\) 6.51610e7i 0.0450660i
\(196\) 0 0
\(197\) −2.45218e9 −1.62812 −0.814062 0.580779i \(-0.802748\pi\)
−0.814062 + 0.580779i \(0.802748\pi\)
\(198\) 0 0
\(199\) 8.11486e8 + 4.68511e8i 0.517450 + 0.298750i 0.735891 0.677100i \(-0.236764\pi\)
−0.218441 + 0.975850i \(0.570097\pi\)
\(200\) 0 0
\(201\) 7.72551e8 4.46033e8i 0.473307 0.273264i
\(202\) 0 0
\(203\) −7.60894e7 + 2.17971e9i −0.0448064 + 1.28356i
\(204\) 0 0
\(205\) −6.26794e8 1.08564e9i −0.354903 0.614709i
\(206\) 0 0
\(207\) 2.46924e8 4.27685e8i 0.134487 0.232939i
\(208\) 0 0
\(209\) 4.64525e8i 0.243458i
\(210\) 0 0
\(211\) 1.15290e9 0.581648 0.290824 0.956777i \(-0.406071\pi\)
0.290824 + 0.956777i \(0.406071\pi\)
\(212\) 0 0
\(213\) 8.45181e8 + 4.87966e8i 0.410612 + 0.237067i
\(214\) 0 0
\(215\) 1.50097e9 8.66586e8i 0.702455 0.405563i
\(216\) 0 0
\(217\) 1.36009e9 2.17666e9i 0.613377 0.981637i
\(218\) 0 0
\(219\) 2.60883e8 + 4.51863e8i 0.113415 + 0.196440i
\(220\) 0 0
\(221\) −3.97190e7 + 6.87953e7i −0.0166506 + 0.0288396i
\(222\) 0 0
\(223\) 4.36603e9i 1.76550i 0.469844 + 0.882749i \(0.344310\pi\)
−0.469844 + 0.882749i \(0.655690\pi\)
\(224\) 0 0
\(225\) −4.45749e8 −0.173924
\(226\) 0 0
\(227\) 1.97909e7 + 1.14263e7i 0.00745352 + 0.00430329i 0.503722 0.863866i \(-0.331964\pi\)
−0.496269 + 0.868169i \(0.665297\pi\)
\(228\) 0 0
\(229\) 2.21311e9 1.27774e9i 0.804749 0.464622i −0.0403802 0.999184i \(-0.512857\pi\)
0.845129 + 0.534563i \(0.179524\pi\)
\(230\) 0 0
\(231\) 7.27714e8 + 1.36859e9i 0.255572 + 0.480646i
\(232\) 0 0
\(233\) −2.38427e9 4.12968e9i −0.808970 1.40118i −0.913578 0.406663i \(-0.866692\pi\)
0.104608 0.994513i \(-0.466641\pi\)
\(234\) 0 0
\(235\) 1.07159e9 1.85604e9i 0.351362 0.608577i
\(236\) 0 0
\(237\) 1.13647e9i 0.360219i
\(238\) 0 0
\(239\) −1.03549e9 −0.317360 −0.158680 0.987330i \(-0.550724\pi\)
−0.158680 + 0.987330i \(0.550724\pi\)
\(240\) 0 0
\(241\) −3.22795e9 1.86366e9i −0.956884 0.552457i −0.0616712 0.998097i \(-0.519643\pi\)
−0.895213 + 0.445639i \(0.852976\pi\)
\(242\) 0 0
\(243\) 1.93710e8 1.11839e8i 0.0555556 0.0320750i
\(244\) 0 0
\(245\) 2.23942e9 1.09231e9i 0.621544 0.303167i
\(246\) 0 0
\(247\) −5.42401e7 9.39467e7i −0.0145725 0.0252402i
\(248\) 0 0
\(249\) 9.17099e8 1.58846e9i 0.238572 0.413218i
\(250\) 0 0
\(251\) 6.14337e8i 0.154779i 0.997001 + 0.0773894i \(0.0246585\pi\)
−0.997001 + 0.0773894i \(0.975342\pi\)
\(252\) 0 0
\(253\) −3.11723e9 −0.760828
\(254\) 0 0
\(255\) −4.31334e8 2.49031e8i −0.102012 0.0588969i
\(256\) 0 0
\(257\) 5.99301e9 3.46007e9i 1.37377 0.793144i 0.382365 0.924011i \(-0.375110\pi\)
0.991400 + 0.130868i \(0.0417763\pi\)
\(258\) 0 0
\(259\) 4.15260e9 2.20804e9i 0.922828 0.490691i
\(260\) 0 0
\(261\) −9.93324e8 1.72049e9i −0.214057 0.370757i
\(262\) 0 0
\(263\) 1.64705e9 2.85277e9i 0.344257 0.596271i −0.640961 0.767573i \(-0.721464\pi\)
0.985219 + 0.171302i \(0.0547974\pi\)
\(264\) 0 0
\(265\) 3.44819e9i 0.699210i
\(266\) 0 0
\(267\) −5.51757e8 −0.108568
\(268\) 0 0
\(269\) 7.32809e8 + 4.23087e8i 0.139953 + 0.0808018i 0.568341 0.822793i \(-0.307585\pi\)
−0.428389 + 0.903595i \(0.640919\pi\)
\(270\) 0 0
\(271\) 5.00561e9 2.88999e9i 0.928067 0.535820i 0.0418675 0.999123i \(-0.486669\pi\)
0.886200 + 0.463303i \(0.153336\pi\)
\(272\) 0 0
\(273\) 3.06978e8 + 1.91816e8i 0.0552658 + 0.0345329i
\(274\) 0 0
\(275\) 1.40681e9 + 2.43667e9i 0.245983 + 0.426055i
\(276\) 0 0
\(277\) −4.52504e9 + 7.83759e9i −0.768604 + 1.33126i 0.169715 + 0.985493i \(0.445715\pi\)
−0.938320 + 0.345769i \(0.887618\pi\)
\(278\) 0 0
\(279\) 2.33788e9i 0.385839i
\(280\) 0 0
\(281\) 3.48332e9 0.558687 0.279343 0.960191i \(-0.409883\pi\)
0.279343 + 0.960191i \(0.409883\pi\)
\(282\) 0 0
\(283\) −5.09155e9 2.93961e9i −0.793788 0.458294i 0.0475064 0.998871i \(-0.484873\pi\)
−0.841294 + 0.540577i \(0.818206\pi\)
\(284\) 0 0
\(285\) 5.89029e8 3.40076e8i 0.0892806 0.0515462i
\(286\) 0 0
\(287\) 6.95962e9 + 2.42946e8i 1.02579 + 0.0358082i
\(288\) 0 0
\(289\) −3.18428e9 5.51534e9i −0.456479 0.790644i
\(290\) 0 0
\(291\) −1.82542e9 + 3.16172e9i −0.254560 + 0.440911i
\(292\) 0 0
\(293\) 5.84504e9i 0.793080i 0.918017 + 0.396540i \(0.129789\pi\)
−0.918017 + 0.396540i \(0.870211\pi\)
\(294\) 0 0
\(295\) −2.34433e9 −0.309550
\(296\) 0 0
\(297\) −1.22272e9 7.05940e8i −0.157146 0.0907281i
\(298\) 0 0
\(299\) −6.30436e8 + 3.63983e8i −0.0788781 + 0.0455403i
\(300\) 0 0
\(301\) −3.35890e8 + 9.62215e9i −0.0409195 + 1.17221i
\(302\) 0 0
\(303\) −8.31400e8 1.44003e9i −0.0986370 0.170844i
\(304\) 0 0
\(305\) −4.60268e8 + 7.97207e8i −0.0531877 + 0.0921238i
\(306\) 0 0
\(307\) 9.48408e9i 1.06768i 0.845585 + 0.533841i \(0.179252\pi\)
−0.845585 + 0.533841i \(0.820748\pi\)
\(308\) 0 0
\(309\) −9.90634e9 −1.08662
\(310\) 0 0
\(311\) −3.11264e9 1.79708e9i −0.332726 0.192099i 0.324325 0.945946i \(-0.394863\pi\)
−0.657051 + 0.753846i \(0.728196\pi\)
\(312\) 0 0
\(313\) 7.72906e8 4.46237e8i 0.0805284 0.0464931i −0.459195 0.888335i \(-0.651862\pi\)
0.539724 + 0.841842i \(0.318529\pi\)
\(314\) 0 0
\(315\) −1.20265e9 + 1.92469e9i −0.122151 + 0.195488i
\(316\) 0 0
\(317\) −6.15360e9 1.06583e10i −0.609386 1.05549i −0.991342 0.131306i \(-0.958083\pi\)
0.381956 0.924180i \(-0.375250\pi\)
\(318\) 0 0
\(319\) −6.26998e9 + 1.08599e10i −0.605486 + 1.04873i
\(320\) 0 0
\(321\) 6.16415e9i 0.580568i
\(322\) 0 0
\(323\) −8.29174e8 −0.0761791
\(324\) 0 0
\(325\) 5.69035e8 + 3.28532e8i 0.0510041 + 0.0294472i
\(326\) 0 0
\(327\) −7.53021e9 + 4.34757e9i −0.658591 + 0.380238i
\(328\) 0 0
\(329\) 5.58948e9 + 1.05120e10i 0.477076 + 0.897223i
\(330\) 0 0
\(331\) 7.20962e8 + 1.24874e9i 0.0600621 + 0.104031i 0.894493 0.447082i \(-0.147537\pi\)
−0.834431 + 0.551113i \(0.814203\pi\)
\(332\) 0 0
\(333\) −2.14198e9 + 3.71001e9i −0.174196 + 0.301716i
\(334\) 0 0
\(335\) 8.24460e9i 0.654621i
\(336\) 0 0
\(337\) −2.10452e9 −0.163168 −0.0815838 0.996666i \(-0.525998\pi\)
−0.0815838 + 0.996666i \(0.525998\pi\)
\(338\) 0 0
\(339\) 1.96722e9 + 1.13577e9i 0.148955 + 0.0859990i
\(340\) 0 0
\(341\) 1.27799e10 7.37850e9i 0.945173 0.545696i
\(342\) 0 0
\(343\) −1.44628e9 + 1.37655e10i −0.104490 + 0.994526i
\(344\) 0 0
\(345\) −2.28210e9 3.95272e9i −0.161087 0.279010i
\(346\) 0 0
\(347\) −3.19525e9 + 5.53434e9i −0.220388 + 0.381723i −0.954926 0.296845i \(-0.904066\pi\)
0.734538 + 0.678567i \(0.237399\pi\)
\(348\) 0 0
\(349\) 1.17252e9i 0.0790346i −0.999219 0.0395173i \(-0.987418\pi\)
0.999219 0.0395173i \(-0.0125820\pi\)
\(350\) 0 0
\(351\) −3.29716e8 −0.0217226
\(352\) 0 0
\(353\) 1.60024e10 + 9.23900e9i 1.03059 + 0.595013i 0.917154 0.398532i \(-0.130480\pi\)
0.113438 + 0.993545i \(0.463814\pi\)
\(354\) 0 0
\(355\) 7.81128e9 4.50985e9i 0.491823 0.283954i
\(356\) 0 0
\(357\) 2.44292e9 1.29897e9i 0.150396 0.0799696i
\(358\) 0 0
\(359\) −1.23847e10 2.14508e10i −0.745600 1.29142i −0.949914 0.312512i \(-0.898830\pi\)
0.204314 0.978905i \(-0.434504\pi\)
\(360\) 0 0
\(361\) −7.92562e9 + 1.37276e10i −0.466664 + 0.808286i
\(362\) 0 0
\(363\) 1.11261e9i 0.0640789i
\(364\) 0 0
\(365\) 4.82224e9 0.271693
\(366\) 0 0
\(367\) −2.07383e10 1.19733e10i −1.14316 0.660006i −0.195952 0.980613i \(-0.562780\pi\)
−0.947212 + 0.320607i \(0.896113\pi\)
\(368\) 0 0
\(369\) −5.49335e9 + 3.17159e9i −0.296300 + 0.171069i
\(370\) 0 0
\(371\) 1.62446e10 + 1.01505e10i 0.857461 + 0.535786i
\(372\) 0 0
\(373\) −1.13190e10 1.96050e10i −0.584751 1.01282i −0.994906 0.100803i \(-0.967859\pi\)
0.410155 0.912016i \(-0.365475\pi\)
\(374\) 0 0
\(375\) −6.00760e9 + 1.04055e10i −0.303792 + 0.526183i
\(376\) 0 0
\(377\) 2.92845e9i 0.144968i
\(378\) 0 0
\(379\) −3.53911e10 −1.71529 −0.857644 0.514245i \(-0.828072\pi\)
−0.857644 + 0.514245i \(0.828072\pi\)
\(380\) 0 0
\(381\) −5.37857e9 3.10532e9i −0.255251 0.147369i
\(382\) 0 0
\(383\) 3.67174e10 2.11988e10i 1.70639 0.985183i 0.767439 0.641122i \(-0.221531\pi\)
0.938947 0.344061i \(-0.111803\pi\)
\(384\) 0 0
\(385\) 1.43169e10 + 4.99774e8i 0.651638 + 0.0227473i
\(386\) 0 0
\(387\) −4.38494e9 7.59493e9i −0.195488 0.338595i
\(388\) 0 0
\(389\) −1.82067e10 + 3.15350e10i −0.795121 + 1.37719i 0.127641 + 0.991820i \(0.459259\pi\)
−0.922762 + 0.385370i \(0.874074\pi\)
\(390\) 0 0
\(391\) 5.56424e9i 0.238067i
\(392\) 0 0
\(393\) 1.26241e10 0.529214
\(394\) 0 0
\(395\) −9.09626e9 5.25173e9i −0.373658 0.215732i
\(396\) 0 0
\(397\) 9.66830e9 5.58199e9i 0.389214 0.224713i −0.292606 0.956233i \(-0.594522\pi\)
0.681819 + 0.731521i \(0.261189\pi\)
\(398\) 0 0
\(399\) −1.31814e8 + 3.77604e9i −0.00520079 + 0.148986i
\(400\) 0 0
\(401\) 6.55936e9 + 1.13611e10i 0.253679 + 0.439384i 0.964536 0.263952i \(-0.0850261\pi\)
−0.710857 + 0.703336i \(0.751693\pi\)
\(402\) 0 0
\(403\) 1.72310e9 2.98449e9i 0.0653266 0.113149i
\(404\) 0 0
\(405\) 2.06726e9i 0.0768377i
\(406\) 0 0
\(407\) 2.70408e10 0.985468
\(408\) 0 0
\(409\) 2.95703e10 + 1.70724e10i 1.05673 + 0.610102i 0.924525 0.381121i \(-0.124462\pi\)
0.132202 + 0.991223i \(0.457795\pi\)
\(410\) 0 0
\(411\) 2.33541e10 1.34835e10i 0.818456 0.472536i
\(412\) 0 0
\(413\) 6.90104e9 1.10443e10i 0.237200 0.379610i
\(414\) 0 0
\(415\) −8.47596e9 1.46808e10i −0.285757 0.494945i
\(416\) 0 0
\(417\) −4.63437e9 + 8.02697e9i −0.153266 + 0.265465i
\(418\) 0 0
\(419\) 3.49852e10i 1.13509i −0.823344 0.567543i \(-0.807894\pi\)
0.823344 0.567543i \(-0.192106\pi\)
\(420\) 0 0
\(421\) 1.41410e10 0.450146 0.225073 0.974342i \(-0.427738\pi\)
0.225073 + 0.974342i \(0.427738\pi\)
\(422\) 0 0
\(423\) −9.39159e9 5.42224e9i −0.293344 0.169362i
\(424\) 0 0
\(425\) 4.34944e9 2.51115e9i 0.133315 0.0769693i
\(426\) 0 0
\(427\) −2.40080e9 4.51510e9i −0.0722178 0.135818i
\(428\) 0 0
\(429\) 1.04060e9 + 1.80238e9i 0.0307225 + 0.0532129i
\(430\) 0 0
\(431\) 7.04983e9 1.22107e10i 0.204301 0.353859i −0.745609 0.666384i \(-0.767841\pi\)
0.949910 + 0.312525i \(0.101175\pi\)
\(432\) 0 0
\(433\) 1.05233e10i 0.299365i −0.988734 0.149683i \(-0.952175\pi\)
0.988734 0.149683i \(-0.0478252\pi\)
\(434\) 0 0
\(435\) −1.83609e10 −0.512786
\(436\) 0 0
\(437\) −6.58050e9 3.79926e9i −0.180440 0.104177i
\(438\) 0 0
\(439\) 5.71624e10 3.30027e10i 1.53905 0.888571i 0.540155 0.841566i \(-0.318366\pi\)
0.998895 0.0470049i \(-0.0149676\pi\)
\(440\) 0 0
\(441\) −5.52711e9 1.13315e10i −0.146131 0.299594i
\(442\) 0 0
\(443\) −3.33675e10 5.77942e10i −0.866380 1.50061i −0.865670 0.500615i \(-0.833107\pi\)
−0.000709897 1.00000i \(-0.500226\pi\)
\(444\) 0 0
\(445\) −2.54971e9 + 4.41622e9i −0.0650205 + 0.112619i
\(446\) 0 0
\(447\) 9.40877e9i 0.235669i
\(448\) 0 0
\(449\) −4.05035e10 −0.996569 −0.498285 0.867014i \(-0.666037\pi\)
−0.498285 + 0.867014i \(0.666037\pi\)
\(450\) 0 0
\(451\) 3.46747e10 + 2.00195e10i 0.838121 + 0.483889i
\(452\) 0 0
\(453\) 3.91346e10 2.25944e10i 0.929326 0.536547i
\(454\) 0 0
\(455\) 2.95384e9 1.57064e9i 0.0689195 0.0366463i
\(456\) 0 0
\(457\) −3.16521e10 5.48230e10i −0.725667 1.25689i −0.958699 0.284423i \(-0.908198\pi\)
0.233032 0.972469i \(-0.425135\pi\)
\(458\) 0 0
\(459\) −1.26010e9 + 2.18256e9i −0.0283892 + 0.0491716i
\(460\) 0 0
\(461\) 4.09845e10i 0.907436i 0.891145 + 0.453718i \(0.149903\pi\)
−0.891145 + 0.453718i \(0.850097\pi\)
\(462\) 0 0
\(463\) −1.54289e10 −0.335745 −0.167873 0.985809i \(-0.553690\pi\)
−0.167873 + 0.985809i \(0.553690\pi\)
\(464\) 0 0
\(465\) 1.87122e10 + 1.08035e10i 0.400234 + 0.231075i
\(466\) 0 0
\(467\) 2.98997e10 1.72626e10i 0.628636 0.362943i −0.151588 0.988444i \(-0.548439\pi\)
0.780224 + 0.625501i \(0.215105\pi\)
\(468\) 0 0
\(469\) 3.88408e10 + 2.42697e10i 0.802781 + 0.501619i
\(470\) 0 0
\(471\) 8.47016e9 + 1.46707e10i 0.172111 + 0.298105i
\(472\) 0 0
\(473\) −2.76783e10 + 4.79402e10i −0.552961 + 0.957757i
\(474\) 0 0
\(475\) 6.85845e9i 0.134726i
\(476\) 0 0
\(477\) −1.74479e10 −0.337031
\(478\) 0 0
\(479\) −5.19585e10 2.99983e10i −0.986994 0.569842i −0.0826199 0.996581i \(-0.526329\pi\)
−0.904375 + 0.426740i \(0.859662\pi\)
\(480\) 0 0
\(481\) 5.46881e9 3.15742e9i 0.102167 0.0589864i
\(482\) 0 0
\(483\) 2.53394e10 + 8.84546e8i 0.465594 + 0.0162529i
\(484\) 0 0
\(485\) 1.68708e10 + 2.92210e10i 0.304907 + 0.528115i
\(486\) 0 0
\(487\) 7.27140e8 1.25944e9i 0.0129271 0.0223904i −0.859489 0.511153i \(-0.829218\pi\)
0.872417 + 0.488763i \(0.162552\pi\)
\(488\) 0 0
\(489\) 2.94526e9i 0.0515097i
\(490\) 0 0
\(491\) −6.42504e10 −1.10548 −0.552739 0.833355i \(-0.686417\pi\)
−0.552739 + 0.833355i \(0.686417\pi\)
\(492\) 0 0
\(493\) 1.93849e10 + 1.11919e10i 0.328153 + 0.189459i
\(494\) 0 0
\(495\) −1.13006e10 + 6.52440e9i −0.188226 + 0.108672i
\(496\) 0 0
\(497\) −1.74802e9 + 5.00752e10i −0.0286498 + 0.820724i
\(498\) 0 0
\(499\) −1.47773e10 2.55951e10i −0.238338 0.412813i 0.721900 0.691998i \(-0.243269\pi\)
−0.960238 + 0.279184i \(0.909936\pi\)
\(500\) 0 0
\(501\) 2.32140e10 4.02077e10i 0.368467 0.638203i
\(502\) 0 0
\(503\) 3.65527e10i 0.571015i 0.958376 + 0.285508i \(0.0921622\pi\)
−0.958376 + 0.285508i \(0.907838\pi\)
\(504\) 0 0
\(505\) −1.53678e10 −0.236291
\(506\) 0 0
\(507\) −3.26162e10 1.88310e10i −0.493630 0.284997i
\(508\) 0 0
\(509\) −6.42278e10 + 3.70819e10i −0.956867 + 0.552447i −0.895207 0.445650i \(-0.852973\pi\)
−0.0616596 + 0.998097i \(0.519639\pi\)
\(510\) 0 0
\(511\) −1.41953e10 + 2.27179e10i −0.208191 + 0.333184i
\(512\) 0 0
\(513\) −1.72079e9 2.98049e9i −0.0248461 0.0430347i
\(514\) 0 0
\(515\) −4.57779e10 + 7.92897e10i −0.650769 + 1.12717i
\(516\) 0 0
\(517\) 6.84517e10i 0.958125i
\(518\) 0 0
\(519\) 6.49787e10 0.895574
\(520\) 0 0
\(521\) 1.33656e10 + 7.71665e9i 0.181401 + 0.104732i 0.587951 0.808897i \(-0.299935\pi\)
−0.406550 + 0.913629i \(0.633268\pi\)
\(522\) 0 0
\(523\) −3.44919e10 + 1.99139e10i −0.461010 + 0.266164i −0.712469 0.701704i \(-0.752423\pi\)
0.251459 + 0.967868i \(0.419090\pi\)
\(524\) 0 0
\(525\) −1.07443e10 2.02065e10i −0.141430 0.265982i
\(526\) 0 0
\(527\) −1.31706e10 2.28121e10i −0.170751 0.295749i
\(528\) 0 0
\(529\) 1.36603e10 2.36603e10i 0.174437 0.302133i
\(530\) 0 0
\(531\) 1.18623e10i 0.149208i
\(532\) 0 0
\(533\) 9.35027e9 0.115855
\(534\) 0 0
\(535\) 4.93374e10 + 2.84850e10i 0.602228 + 0.347697i
\(536\) 0 0
\(537\) 3.53927e10 2.04340e10i 0.425614 0.245729i
\(538\) 0 0
\(539\) −4.44994e10 + 6.59767e10i −0.527229 + 0.781692i
\(540\) 0 0
\(541\) 3.80963e9 + 6.59847e9i 0.0444727 + 0.0770290i 0.887405 0.460991i \(-0.152506\pi\)
−0.842932 + 0.538020i \(0.819173\pi\)
\(542\) 0 0
\(543\) −8.17703e9 + 1.41630e10i −0.0940582 + 0.162913i
\(544\) 0 0
\(545\) 8.03617e10i 0.910884i
\(546\) 0 0
\(547\) −9.03887e10 −1.00964 −0.504818 0.863226i \(-0.668441\pi\)
−0.504818 + 0.863226i \(0.668441\pi\)
\(548\) 0 0
\(549\) 4.03388e9 + 2.32896e9i 0.0444052 + 0.0256373i
\(550\) 0 0
\(551\) −2.64720e10 + 1.52836e10i −0.287197 + 0.165814i
\(552\) 0 0
\(553\) 5.15180e10 2.73935e10i 0.550882 0.292918i
\(554\) 0 0
\(555\) 1.97964e10 + 3.42884e10i 0.208648 + 0.361390i
\(556\) 0 0
\(557\) −4.86872e10 + 8.43287e10i −0.505817 + 0.876101i 0.494160 + 0.869371i \(0.335476\pi\)
−0.999977 + 0.00673046i \(0.997858\pi\)
\(558\) 0 0
\(559\) 1.29274e10i 0.132393i
\(560\) 0 0
\(561\) 1.59078e10 0.160605
\(562\) 0 0
\(563\) −1.63982e11 9.46751e10i −1.63216 0.942329i −0.983425 0.181315i \(-0.941965\pi\)
−0.648736 0.761014i \(-0.724702\pi\)
\(564\) 0 0
\(565\) 1.81813e10 1.04970e10i 0.178415 0.103008i
\(566\) 0 0
\(567\) 9.73898e9 + 6.08542e9i 0.0942283 + 0.0588787i
\(568\) 0 0
\(569\) 5.52884e9 + 9.57622e9i 0.0527454 + 0.0913577i 0.891193 0.453625i \(-0.149869\pi\)
−0.838447 + 0.544983i \(0.816536\pi\)
\(570\) 0 0
\(571\) 2.80453e9 4.85758e9i 0.0263824 0.0456957i −0.852533 0.522674i \(-0.824935\pi\)
0.878915 + 0.476978i \(0.158268\pi\)
\(572\) 0 0
\(573\) 2.34006e10i 0.217074i
\(574\) 0 0
\(575\) 4.60242e10 0.421031
\(576\) 0 0
\(577\) −1.30662e11 7.54375e10i −1.17881 0.680587i −0.223072 0.974802i \(-0.571609\pi\)
−0.955739 + 0.294215i \(0.904942\pi\)
\(578\) 0 0
\(579\) 1.89548e10 1.09435e10i 0.168657 0.0973742i
\(580\) 0 0
\(581\) 9.41130e10 + 3.28529e9i 0.825933 + 0.0288316i
\(582\) 0 0
\(583\) 5.50666e10 + 9.53782e10i 0.476666 + 0.825610i
\(584\) 0 0
\(585\) −1.52364e9 + 2.63902e9i −0.0130094 + 0.0225330i
\(586\) 0 0
\(587\) 2.18697e11i 1.84201i −0.389556 0.921003i \(-0.627371\pi\)
0.389556 0.921003i \(-0.372629\pi\)
\(588\) 0 0
\(589\) 3.59715e10 0.298880
\(590\) 0 0
\(591\) 9.93132e10 + 5.73385e10i 0.814062 + 0.469999i
\(592\) 0 0
\(593\) −1.98077e11 + 1.14360e11i −1.60183 + 0.924816i −0.610708 + 0.791856i \(0.709115\pi\)
−0.991121 + 0.132960i \(0.957552\pi\)
\(594\) 0 0
\(595\) 8.92094e8 2.55556e10i 0.00711775 0.203901i
\(596\) 0 0
\(597\) −2.19101e10 3.79494e10i −0.172483 0.298750i
\(598\) 0 0
\(599\) 8.69028e10 1.50520e11i 0.675036 1.16920i −0.301423 0.953491i \(-0.597462\pi\)
0.976458 0.215705i \(-0.0692051\pi\)
\(600\) 0 0
\(601\) 3.36846e10i 0.258187i −0.991632 0.129093i \(-0.958793\pi\)
0.991632 0.129093i \(-0.0412067\pi\)
\(602\) 0 0
\(603\) −4.17178e10 −0.315538
\(604\) 0 0
\(605\) −8.90523e9 5.14144e9i −0.0664697 0.0383763i
\(606\) 0 0
\(607\) 9.20478e10 5.31438e10i 0.678045 0.391470i −0.121073 0.992644i \(-0.538633\pi\)
0.799118 + 0.601174i \(0.205300\pi\)
\(608\) 0 0
\(609\) 5.40492e10 8.64993e10i 0.392934 0.628845i
\(610\) 0 0
\(611\) 7.99275e9 + 1.38438e10i 0.0573497 + 0.0993326i
\(612\) 0 0
\(613\) 5.34031e10 9.24969e10i 0.378203 0.655066i −0.612598 0.790395i \(-0.709876\pi\)
0.990801 + 0.135328i \(0.0432089\pi\)
\(614\) 0 0
\(615\) 5.86245e10i 0.409806i
\(616\) 0 0
\(617\) 1.04431e11 0.720593 0.360297 0.932838i \(-0.382675\pi\)
0.360297 + 0.932838i \(0.382675\pi\)
\(618\) 0 0
\(619\) −1.91873e10 1.10778e10i −0.130693 0.0754554i 0.433228 0.901284i \(-0.357374\pi\)
−0.563921 + 0.825829i \(0.690708\pi\)
\(620\) 0 0
\(621\) −2.00008e10 + 1.15475e10i −0.134487 + 0.0776463i
\(622\) 0 0
\(623\) −1.32995e10 2.50119e10i −0.0882842 0.166033i
\(624\) 0 0
\(625\) 1.57150e10 + 2.72192e10i 0.102990 + 0.178384i
\(626\) 0 0
\(627\) −1.08618e10 + 1.88133e10i −0.0702802 + 0.121729i
\(628\) 0 0
\(629\) 4.82677e10i 0.308357i
\(630\) 0 0
\(631\) 2.53563e11 1.59944 0.799722 0.600371i \(-0.204980\pi\)
0.799722 + 0.600371i \(0.204980\pi\)
\(632\) 0 0
\(633\) −4.66923e10 2.69578e10i −0.290824 0.167907i
\(634\) 0 0
\(635\) −4.97095e10 + 2.86998e10i −0.305735 + 0.176516i
\(636\) 0 0
\(637\) −1.29591e9 + 1.85393e10i −0.00787079 + 0.112599i
\(638\) 0 0
\(639\) −2.28199e10 3.95252e10i −0.136871 0.237067i
\(640\) 0 0
\(641\) 4.44352e10 7.69641e10i 0.263206 0.455886i −0.703886 0.710313i \(-0.748554\pi\)
0.967092 + 0.254427i \(0.0818869\pi\)
\(642\) 0 0
\(643\) 1.06138e10i 0.0620909i −0.999518 0.0310455i \(-0.990116\pi\)
0.999518 0.0310455i \(-0.00988367\pi\)
\(644\) 0 0
\(645\) −8.10524e10 −0.468303
\(646\) 0 0
\(647\) 2.13261e11 + 1.23126e11i 1.21701 + 0.702642i 0.964278 0.264894i \(-0.0853369\pi\)
0.252734 + 0.967536i \(0.418670\pi\)
\(648\) 0 0
\(649\) 6.48451e10 3.74383e10i 0.365509 0.211027i
\(650\) 0 0
\(651\) −1.05980e11 + 5.63521e10i −0.590063 + 0.313752i
\(652\) 0 0
\(653\) −3.72691e10 6.45521e10i −0.204973 0.355024i 0.745151 0.666896i \(-0.232377\pi\)
−0.950124 + 0.311872i \(0.899044\pi\)
\(654\) 0 0
\(655\) 5.83370e10 1.01043e11i 0.316941 0.548958i
\(656\) 0 0
\(657\) 2.44006e10i 0.130960i
\(658\) 0 0
\(659\) 1.29564e11 0.686975 0.343488 0.939157i \(-0.388392\pi\)
0.343488 + 0.939157i \(0.388392\pi\)
\(660\) 0 0
\(661\) −2.62586e10 1.51604e10i −0.137552 0.0794155i 0.429645 0.902998i \(-0.358639\pi\)
−0.567197 + 0.823582i \(0.691972\pi\)
\(662\) 0 0
\(663\) 3.21724e9 1.85747e9i 0.0166506 0.00961320i
\(664\) 0 0
\(665\) 2.96140e10 + 1.85044e10i 0.151430 + 0.0946211i
\(666\) 0 0
\(667\) 1.02562e11 + 1.77642e11i 0.518183 + 0.897519i
\(668\) 0 0
\(669\) 1.02090e11 1.76824e11i 0.509655 0.882749i
\(670\) 0 0
\(671\) 2.94014e10i 0.145037i
\(672\) 0 0
\(673\) −2.10696e11 −1.02706 −0.513530 0.858071i \(-0.671663\pi\)
−0.513530 + 0.858071i \(0.671663\pi\)
\(674\) 0 0
\(675\) 1.80528e10 + 1.04228e10i 0.0869622 + 0.0502076i
\(676\) 0 0
\(677\) 3.82781e10 2.20999e10i 0.182220 0.105205i −0.406115 0.913822i \(-0.633117\pi\)
0.588335 + 0.808617i \(0.299784\pi\)
\(678\) 0 0
\(679\) −1.87325e11 6.53913e9i −0.881285 0.0307639i
\(680\) 0 0
\(681\) −5.34354e8 9.25528e8i −0.00248451 0.00430329i
\(682\) 0 0
\(683\) 6.69506e10 1.15962e11i 0.307660 0.532883i −0.670190 0.742190i \(-0.733787\pi\)
0.977850 + 0.209307i \(0.0671206\pi\)
\(684\) 0 0
\(685\) 2.49232e11i 1.13199i
\(686\) 0 0
\(687\) −1.19508e11 −0.536499
\(688\) 0 0
\(689\) 2.22736e10 + 1.28597e10i 0.0988358 + 0.0570629i
\(690\) 0 0
\(691\) −3.36307e11 + 1.94167e11i −1.47511 + 0.851653i −0.999606 0.0280622i \(-0.991066\pi\)
−0.475501 + 0.879715i \(0.657733\pi\)
\(692\) 0 0
\(693\) 2.52886e9 7.24438e10i 0.0109646 0.314100i
\(694\) 0 0
\(695\) 4.28315e10 + 7.41864e10i 0.183580 + 0.317969i
\(696\) 0 0
\(697\) 3.57346e10 6.18942e10i 0.151411 0.262252i
\(698\) 0 0
\(699\) 2.23003e11i 0.934118i
\(700\) 0 0
\(701\) 1.53431e11 0.635392 0.317696 0.948193i \(-0.397091\pi\)
0.317696 + 0.948193i \(0.397091\pi\)
\(702\) 0 0
\(703\) 5.70835e10 + 3.29572e10i 0.233716 + 0.134936i
\(704\) 0 0
\(705\) −8.67984e10 + 5.01131e10i −0.351362 + 0.202859i
\(706\) 0 0
\(707\) 4.52386e10 7.23989e10i 0.181064 0.289771i
\(708\) 0 0
\(709\) −5.25372e10 9.09971e10i −0.207913 0.360116i 0.743144 0.669132i \(-0.233334\pi\)
−0.951057 + 0.309016i \(0.900000\pi\)
\(710\) 0 0
\(711\) −2.65738e10 + 4.60272e10i −0.103986 + 0.180109i
\(712\) 0 0
\(713\) 2.41389e11i 0.934028i
\(714\) 0 0
\(715\) 1.92348e10 0.0735976
\(716\) 0 0
\(717\) 4.19372e10 + 2.42124e10i 0.158680 + 0.0916140i
\(718\) 0 0
\(719\) 1.52234e11 8.78923e10i 0.569634 0.328878i −0.187369 0.982290i \(-0.559996\pi\)
0.757003 + 0.653411i \(0.226663\pi\)
\(720\) 0 0
\(721\) −2.38782e11 4.49069e11i −0.883608 1.66177i
\(722\) 0 0
\(723\) 8.71548e10 + 1.50956e11i 0.318961 + 0.552457i
\(724\) 0 0
\(725\) 9.25729e10 1.60341e11i 0.335067 0.580353i
\(726\) 0 0
\(727\) 3.71190e11i 1.32880i 0.747379 + 0.664398i \(0.231312\pi\)
−0.747379 + 0.664398i \(0.768688\pi\)
\(728\) 0 0
\(729\) −1.04604e10 −0.0370370
\(730\) 0 0
\(731\) 8.55730e10 + 4.94056e10i 0.299686 + 0.173024i
\(732\) 0 0
\(733\) 3.30816e10 1.90996e10i 0.114596 0.0661621i −0.441606 0.897209i \(-0.645591\pi\)
0.556203 + 0.831047i \(0.312258\pi\)
\(734\) 0 0
\(735\) −1.16238e11 8.12515e9i −0.398289 0.0278408i
\(736\) 0 0
\(737\) 1.31664e11 + 2.28049e11i 0.446269 + 0.772961i
\(738\) 0 0
\(739\) −1.92789e11 + 3.33920e11i −0.646404 + 1.11960i 0.337571 + 0.941300i \(0.390395\pi\)
−0.983975 + 0.178305i \(0.942939\pi\)
\(740\) 0 0
\(741\) 5.07312e9i 0.0168268i
\(742\) 0 0
\(743\) 5.07236e11 1.66439 0.832194 0.554485i \(-0.187085\pi\)
0.832194 + 0.554485i \(0.187085\pi\)
\(744\) 0 0
\(745\) 7.53071e10 + 4.34786e10i 0.244462 + 0.141140i
\(746\) 0 0
\(747\) −7.42850e10 + 4.28885e10i −0.238572 + 0.137739i
\(748\) 0 0
\(749\) −2.79430e11 + 1.48580e11i −0.887862 + 0.472099i
\(750\) 0 0
\(751\) 3.14299e11 + 5.44382e11i 0.988060 + 1.71137i 0.627460 + 0.778649i \(0.284095\pi\)
0.360600 + 0.932721i \(0.382572\pi\)
\(752\) 0 0
\(753\) 1.43648e10 2.48806e10i 0.0446808 0.0773894i
\(754\) 0 0
\(755\) 4.17641e11i 1.28533i
\(756\) 0 0
\(757\) −3.39756e11 −1.03463 −0.517314 0.855796i \(-0.673068\pi\)
−0.517314 + 0.855796i \(0.673068\pi\)
\(758\) 0 0
\(759\) 1.26248e11 + 7.28892e10i 0.380414 + 0.219632i
\(760\) 0 0
\(761\) −5.74796e11 + 3.31859e11i −1.71386 + 0.989497i −0.784655 + 0.619933i \(0.787160\pi\)
−0.929205 + 0.369564i \(0.879507\pi\)
\(762\) 0 0
\(763\) −3.78589e11 2.36562e11i −1.11704 0.697986i
\(764\) 0 0
\(765\) 1.16460e10 + 2.01715e10i 0.0340041 + 0.0588969i
\(766\) 0 0
\(767\) 8.74296e9 1.51432e10i 0.0252625 0.0437560i
\(768\) 0 0
\(769\) 3.99685e11i 1.14291i 0.820633 + 0.571456i \(0.193621\pi\)
−0.820633 + 0.571456i \(0.806379\pi\)
\(770\) 0 0
\(771\) −3.23623e11 −0.915843
\(772\) 0 0
\(773\) −8.18869e10 4.72774e10i −0.229349 0.132415i 0.380923 0.924607i \(-0.375606\pi\)
−0.610272 + 0.792192i \(0.708940\pi\)
\(774\) 0 0
\(775\) −1.88689e11 + 1.08940e11i −0.523045 + 0.301980i
\(776\) 0 0
\(777\) −2.19810e11 7.67312e9i −0.603064 0.0210517i
\(778\) 0 0
\(779\) 4.87991e10 + 8.45226e10i 0.132514 + 0.229521i
\(780\) 0 0
\(781\) −1.44042e11 + 2.49488e11i −0.387155 + 0.670573i
\(782\) 0 0
\(783\) 9.29063e10i 0.247171i
\(784\) 0 0
\(785\) 1.56565e11 0.412302
\(786\) 0 0
\(787\) −2.38365e10 1.37620e10i −0.0621362 0.0358743i 0.468610 0.883405i \(-0.344755\pi\)
−0.530746 + 0.847531i \(0.678088\pi\)
\(788\) 0 0
\(789\) −1.33411e11 + 7.70248e10i −0.344257 + 0.198757i
\(790\) 0 0
\(791\) −4.06864e9 + 1.16554e11i −0.0103931 + 0.297728i
\(792\) 0 0
\(793\) −3.43305e9 5.94622e9i −0.00868135 0.0150365i
\(794\) 0 0
\(795\) −8.06279e10 + 1.39652e11i −0.201845 + 0.349605i
\(796\) 0 0
\(797\) 1.49359e11i 0.370167i −0.982723 0.185084i \(-0.940744\pi\)
0.982723 0.185084i \(-0.0592556\pi\)
\(798\) 0 0
\(799\) 1.22186e11 0.299802
\(800\) 0 0
\(801\) 2.23462e10 + 1.29016e10i 0.0542841 + 0.0313409i
\(802\) 0 0
\(803\) −1.33385e11 + 7.70099e10i −0.320808 + 0.185219i
\(804\) 0 0
\(805\) 1.24175e11 1.98727e11i 0.295700 0.473232i
\(806\) 0 0
\(807\) −1.97858e10 3.42701e10i −0.0466509 0.0808018i
\(808\) 0 0
\(809\) −3.45374e9 + 5.98206e9i −0.00806298 + 0.0139655i −0.870029 0.493001i \(-0.835900\pi\)
0.861966 + 0.506966i \(0.169233\pi\)
\(810\) 0 0
\(811\) 3.74372e11i 0.865406i 0.901537 + 0.432703i \(0.142440\pi\)
−0.901537 + 0.432703i \(0.857560\pi\)
\(812\) 0 0
\(813\) −2.70303e11 −0.618712
\(814\) 0 0
\(815\) 2.35737e10 + 1.36103e10i 0.0534315 + 0.0308487i
\(816\) 0 0
\(817\) −1.16858e11 + 6.74682e10i −0.262284 + 0.151430i
\(818\) 0 0
\(819\) −7.94744e9 1.49465e10i −0.0176641 0.0332203i
\(820\) 0 0
\(821\) 4.25087e11 + 7.36272e11i 0.935632 + 1.62056i 0.773504 + 0.633792i \(0.218502\pi\)
0.162128 + 0.986770i \(0.448164\pi\)
\(822\) 0 0
\(823\) 1.48472e11 2.57161e11i 0.323627 0.560539i −0.657606 0.753362i \(-0.728431\pi\)
0.981234 + 0.192823i \(0.0617642\pi\)
\(824\) 0 0
\(825\) 1.31580e11i 0.284037i
\(826\) 0 0
\(827\) 3.43560e11 0.734482 0.367241 0.930126i \(-0.380302\pi\)
0.367241 + 0.930126i \(0.380302\pi\)
\(828\) 0 0
\(829\) 1.65330e11 + 9.54533e10i 0.350053 + 0.202103i 0.664708 0.747103i \(-0.268556\pi\)
−0.314656 + 0.949206i \(0.601889\pi\)
\(830\) 0 0
\(831\) 3.66528e11 2.11615e11i 0.768604 0.443754i
\(832\) 0 0
\(833\) 1.17768e11 + 7.94312e10i 0.244595 + 0.164972i
\(834\) 0 0
\(835\) −2.14547e11 3.71606e11i −0.441343 0.764428i
\(836\) 0 0
\(837\) 5.46659e10 9.46842e10i 0.111382 0.192919i
\(838\) 0 0
\(839\) 3.92637e11i 0.792399i −0.918164 0.396199i \(-0.870329\pi\)
0.918164 0.396199i \(-0.129671\pi\)
\(840\) 0 0
\(841\) 3.24924e11 0.649529
\(842\) 0 0
\(843\) −1.41075e11 8.14495e10i −0.279343 0.161279i
\(844\) 0 0
\(845\) −3.01443e11 + 1.74038e11i −0.591261 + 0.341364i
\(846\) 0 0
\(847\) 5.04361e10 2.68182e10i 0.0979959 0.0521070i
\(848\) 0 0
\(849\) 1.37472e11 + 2.38108e11i 0.264596 + 0.458294i
\(850\) 0 0
\(851\) 2.21162e11 3.83063e11i 0.421688 0.730386i
\(852\) 0 0
\(853\) 8.40881e11i 1.58832i −0.607707 0.794161i \(-0.707911\pi\)
0.607707 0.794161i \(-0.292089\pi\)
\(854\) 0 0
\(855\) −3.18075e10 −0.0595204
\(856\) 0 0
\(857\) 6.17115e11 + 3.56292e11i 1.14404 + 0.660514i 0.947429 0.319966i \(-0.103672\pi\)
0.196615 + 0.980481i \(0.437005\pi\)
\(858\) 0 0
\(859\) −4.48728e11 + 2.59073e11i −0.824158 + 0.475828i −0.851848 0.523789i \(-0.824518\pi\)
0.0276900 + 0.999617i \(0.491185\pi\)
\(860\) 0 0
\(861\) −2.76184e11 1.72574e11i −0.502557 0.314024i
\(862\) 0 0
\(863\) −3.65673e11 6.33365e11i −0.659250 1.14185i −0.980810 0.194965i \(-0.937541\pi\)
0.321560 0.946889i \(-0.395793\pi\)
\(864\) 0 0
\(865\) 3.00271e11 5.20085e11i 0.536351 0.928987i
\(866\) 0 0
\(867\) 2.97829e11i 0.527096i
\(868\) 0 0
\(869\) 3.35475e11 0.588275
\(870\) 0 0
\(871\) 5.32561e10 + 3.07474e10i 0.0925330 + 0.0534240i
\(872\) 0 0
\(873\) 1.47859e11 8.53663e10i 0.254560 0.146970i
\(874\) 0 0
\(875\) −6.16502e11 2.15208e10i −1.05173 0.0367136i
\(876\) 0 0
\(877\) 3.40974e11 + 5.90584e11i 0.576398 + 0.998351i 0.995888 + 0.0905912i \(0.0288757\pi\)
−0.419490 + 0.907760i \(0.637791\pi\)
\(878\) 0 0
\(879\) 1.36673e11 2.36724e11i 0.228943 0.396540i
\(880\) 0 0
\(881\) 1.12611e12i 1.86929i −0.355580 0.934646i \(-0.615717\pi\)
0.355580 0.934646i \(-0.384283\pi\)
\(882\) 0 0
\(883\) −2.79315e10 −0.0459464 −0.0229732 0.999736i \(-0.507313\pi\)
−0.0229732 + 0.999736i \(0.507313\pi\)
\(884\) 0 0
\(885\) 9.49454e10 + 5.48168e10i 0.154775 + 0.0893594i
\(886\) 0 0
\(887\) −3.70745e11 + 2.14050e11i −0.598937 + 0.345796i −0.768623 0.639702i \(-0.779058\pi\)
0.169687 + 0.985498i \(0.445724\pi\)
\(888\) 0 0
\(889\) 1.11241e10 3.18669e11i 0.0178097 0.510191i
\(890\) 0 0
\(891\) 3.30135e10 + 5.71811e10i 0.0523819 + 0.0907281i
\(892\) 0 0
\(893\) −8.34284e10 + 1.44502e11i −0.131192 + 0.227232i
\(894\) 0 0
\(895\) 3.77707e11i 0.588658i
\(896\) 0 0
\(897\) 3.40436e10 0.0525854
\(898\) 0 0
\(899\) −8.40962e11 4.85530e11i −1.28747 0.743322i
\(900\) 0 0
\(901\) 1.70250e11 9.82937e10i 0.258337 0.149151i
\(902\) 0 0
\(903\) 2.38595e11 3.81843e11i 0.358848 0.574294i
\(904\) 0 0
\(905\) 7.55733e10 + 1.30897e11i 0.112661 + 0.195135i
\(906\) 0 0
\(907\) 3.94184e11 6.82746e11i 0.582465 1.00886i −0.412722 0.910857i \(-0.635422\pi\)
0.995186 0.0980011i \(-0.0312449\pi\)
\(908\) 0 0
\(909\) 7.77615e10i 0.113896i
\(910\) 0 0
\(911\) 8.76508e11 1.27257 0.636286 0.771453i \(-0.280470\pi\)
0.636286 + 0.771453i \(0.280470\pi\)
\(912\) 0 0
\(913\) 4.68897e11 + 2.70718e11i 0.674829 + 0.389613i
\(914\) 0 0
\(915\) 3.72817e10 2.15246e10i 0.0531877 0.0307079i
\(916\) 0 0
\(917\) 3.04291e11 + 5.72270e11i 0.430340 + 0.809327i
\(918\) 0 0
\(919\) 6.03038e10 + 1.04449e11i 0.0845440 + 0.146434i 0.905197 0.424993i \(-0.139723\pi\)
−0.820653 + 0.571427i \(0.806390\pi\)
\(920\) 0 0
\(921\) 2.21763e11 3.84105e11i 0.308213 0.533841i
\(922\) 0 0
\(923\) 6.72761e10i 0.0926946i
\(924\) 0 0
\(925\) −3.99243e11 −0.545344
\(926\) 0 0
\(927\) 4.01207e11 + 2.31637e11i 0.543312 + 0.313681i
\(928\) 0 0
\(929\) −4.76098e11 + 2.74876e11i −0.639196 + 0.369040i −0.784305 0.620376i \(-0.786980\pi\)
0.145109 + 0.989416i \(0.453647\pi\)
\(930\) 0 0
\(931\) −1.74351e11 + 8.50420e10i −0.232073 + 0.113197i
\(932\) 0 0
\(933\) 8.40412e10 + 1.45564e11i 0.110909 + 0.192099i
\(934\) 0 0
\(935\) 7.35111e10 1.27325e11i 0.0961848 0.166597i
\(936\) 0 0
\(937\) 7.46093e11i 0.967909i 0.875093 + 0.483955i \(0.160800\pi\)
−0.875093 + 0.483955i \(0.839200\pi\)
\(938\) 0 0
\(939\) −4.17369e10 −0.0536856
\(940\) 0 0
\(941\) −7.72272e11 4.45871e11i −0.984945 0.568658i −0.0811853 0.996699i \(-0.525871\pi\)
−0.903759 + 0.428041i \(0.859204\pi\)
\(942\) 0 0
\(943\) 5.67195e11 3.27470e11i 0.717275 0.414119i
\(944\) 0 0
\(945\) 9.37118e10 4.98290e10i 0.117508 0.0624820i
\(946\) 0 0
\(947\) −5.89215e11 1.02055e12i −0.732611 1.26892i −0.955764 0.294136i \(-0.904968\pi\)
0.223152 0.974784i \(-0.428365\pi\)
\(948\) 0 0
\(949\) −1.79841e10 + 3.11494e10i −0.0221730 + 0.0384047i
\(950\) 0 0
\(951\) 5.75551e11i 0.703658i
\(952\) 0 0
\(953\) 6.62724e11 0.803454 0.401727 0.915759i \(-0.368410\pi\)
0.401727 + 0.915759i \(0.368410\pi\)
\(954\) 0 0
\(955\) −1.87296e11 1.08136e11i −0.225173 0.130004i
\(956\) 0 0
\(957\) 5.07869e11 2.93218e11i 0.605486 0.349577i
\(958\) 0 0
\(959\) 1.17415e12 + 7.33669e11i 1.38819 + 0.867413i
\(960\) 0 0
\(961\) 1.44924e11 + 2.51016e11i 0.169921 + 0.294312i
\(962\) 0 0
\(963\) 1.44134e11 2.49648e11i 0.167595 0.290284i
\(964\) 0 0
\(965\) 2.02284e11i 0.233266i
\(966\) 0 0
\(967\) 7.71443e11 0.882263 0.441131 0.897443i \(-0.354577\pi\)
0.441131 + 0.897443i \(0.354577\pi\)
\(968\) 0 0
\(969\) 3.35816e10 + 1.93883e10i 0.0380895 + 0.0219910i
\(970\) 0 0
\(971\) −1.42118e12 + 8.20516e11i −1.59871 + 0.923018i −0.606979 + 0.794718i \(0.707619\pi\)
−0.991735 + 0.128301i \(0.959048\pi\)
\(972\) 0 0
\(973\) −4.75581e11 1.66015e10i −0.530607 0.0185224i
\(974\) 0 0
\(975\) −1.53639e10 2.66111e10i −0.0170014 0.0294472i
\(976\) 0 0
\(977\) −5.74522e11 + 9.95102e11i −0.630563 + 1.09217i 0.356874 + 0.934153i \(0.383843\pi\)
−0.987437 + 0.158015i \(0.949491\pi\)
\(978\) 0 0
\(979\) 1.62873e11i 0.177303i
\(980\) 0 0
\(981\) 4.06631e11 0.439061
\(982\) 0 0
\(983\) −9.51092e11 5.49113e11i −1.01861 0.588096i −0.104910 0.994482i \(-0.533456\pi\)
−0.913701 + 0.406386i \(0.866789\pi\)
\(984\) 0 0
\(985\) 9.17867e11 5.29931e11i 0.975068 0.562956i
\(986\) 0 0
\(987\) 1.94239e10 5.56432e11i 0.0204676 0.586331i
\(988\) 0 0
\(989\) 4.52750e11 + 7.84187e11i 0.473231 + 0.819661i
\(990\) 0 0
\(991\) 5.20799e11 9.02050e11i 0.539977 0.935267i −0.458928 0.888474i \(-0.651766\pi\)
0.998905 0.0467938i \(-0.0149004\pi\)
\(992\) 0 0
\(993\) 6.74321e10i 0.0693538i
\(994\) 0 0
\(995\) −4.04993e11 −0.413195
\(996\) 0 0
\(997\) −5.42668e11 3.13310e11i −0.549229 0.317098i 0.199582 0.979881i \(-0.436042\pi\)
−0.748811 + 0.662783i \(0.769375\pi\)
\(998\) 0 0
\(999\) 1.73500e11 1.00170e11i 0.174196 0.100572i
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 84.9.m.a.73.2 yes 10
3.2 odd 2 252.9.z.b.73.4 10
7.5 odd 6 inner 84.9.m.a.61.2 10
21.5 even 6 252.9.z.b.145.4 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.9.m.a.61.2 10 7.5 odd 6 inner
84.9.m.a.73.2 yes 10 1.1 even 1 trivial
252.9.z.b.73.4 10 3.2 odd 2
252.9.z.b.145.4 10 21.5 even 6