Properties

Label 29.10.b.a.28.10
Level $29$
Weight $10$
Character 29.28
Analytic conductor $14.936$
Analytic rank $0$
Dimension $22$
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] = [29,10,Mod(28,29)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(29, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("29.28");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 29.b (of order \(2\), degree \(1\), 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: \(14.9360392488\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 28.10
Character \(\chi\) \(=\) 29.28
Dual form 29.10.b.a.28.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-9.11441i q^{2} +171.314i q^{3} +428.927 q^{4} +2218.10 q^{5} +1561.43 q^{6} -1871.46 q^{7} -8576.00i q^{8} -9665.49 q^{9} +O(q^{10})\) \(q-9.11441i q^{2} +171.314i q^{3} +428.927 q^{4} +2218.10 q^{5} +1561.43 q^{6} -1871.46 q^{7} -8576.00i q^{8} -9665.49 q^{9} -20216.7i q^{10} +7045.14i q^{11} +73481.3i q^{12} +42558.5 q^{13} +17057.2i q^{14} +379992. i q^{15} +141446. q^{16} -88283.5i q^{17} +88095.2i q^{18} -8133.60i q^{19} +951404. q^{20} -320607. i q^{21} +64212.3 q^{22} +117858. q^{23} +1.46919e6 q^{24} +2.96684e6 q^{25} -387896. i q^{26} +1.71614e6i q^{27} -802720. q^{28} +(-3.17798e6 + 2.09943e6i) q^{29} +3.46340e6 q^{30} +7.39306e6i q^{31} -5.68011e6i q^{32} -1.20693e6 q^{33} -804653. q^{34} -4.15108e6 q^{35} -4.14579e6 q^{36} +1.28436e7i q^{37} -74133.0 q^{38} +7.29087e6i q^{39} -1.90224e7i q^{40} -2.51109e7i q^{41} -2.92214e6 q^{42} -3.64484e7i q^{43} +3.02186e6i q^{44} -2.14390e7 q^{45} -1.07421e6i q^{46} +5.99932e6i q^{47} +2.42316e7i q^{48} -3.68513e7 q^{49} -2.70410e7i q^{50} +1.51242e7 q^{51} +1.82545e7 q^{52} -5.45801e7 q^{53} +1.56416e7 q^{54} +1.56268e7i q^{55} +1.60496e7i q^{56} +1.39340e6 q^{57} +(1.91350e7 + 2.89654e7i) q^{58} -2.16595e7 q^{59} +1.62989e8i q^{60} -1.42627e8i q^{61} +6.73834e7 q^{62} +1.80886e7 q^{63} +2.06493e7 q^{64} +9.43990e7 q^{65} +1.10005e7i q^{66} -7.07911e7 q^{67} -3.78672e7i q^{68} +2.01907e7i q^{69} +3.78347e7i q^{70} +3.47332e8 q^{71} +8.28912e7i q^{72} -2.96925e8i q^{73} +1.17061e8 q^{74} +5.08261e8i q^{75} -3.48872e6i q^{76} -1.31847e7i q^{77} +6.64520e7 q^{78} +3.79683e8i q^{79} +3.13741e8 q^{80} -4.84245e8 q^{81} -2.28871e8 q^{82} +1.33956e8 q^{83} -1.37517e8i q^{84} -1.95822e8i q^{85} -3.32206e8 q^{86} +(-3.59661e8 - 5.44432e8i) q^{87} +6.04192e7 q^{88} -8.73876e8i q^{89} +1.95404e8i q^{90} -7.96465e7 q^{91} +5.05525e7 q^{92} -1.26654e9 q^{93} +5.46803e7 q^{94} -1.80411e7i q^{95} +9.73082e8 q^{96} -2.02736e8i q^{97} +3.35878e8i q^{98} -6.80947e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q - 5804 q^{4} - 1374 q^{5} - 8304 q^{6} - 4956 q^{7} - 112244 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 22 q - 5804 q^{4} - 1374 q^{5} - 8304 q^{6} - 4956 q^{7} - 112244 q^{9} - 244222 q^{13} + 1246804 q^{16} - 1658748 q^{20} + 822328 q^{22} - 874956 q^{23} + 8668172 q^{24} + 5307748 q^{25} - 620352 q^{28} - 2425374 q^{29} - 8942448 q^{30} + 10134274 q^{33} - 37785784 q^{34} - 20790348 q^{35} + 34550680 q^{36} - 30663552 q^{38} + 56872008 q^{42} - 43877176 q^{45} - 131743922 q^{49} - 6194732 q^{51} + 342496580 q^{52} + 34886610 q^{53} + 116488784 q^{54} - 308361676 q^{57} + 342193888 q^{58} + 175799052 q^{59} - 484313328 q^{62} - 190643424 q^{63} - 419498924 q^{64} - 149739966 q^{65} - 508277640 q^{67} + 263144256 q^{71} + 435201408 q^{74} + 1065897336 q^{78} + 2990464236 q^{80} - 129895134 q^{81} - 527065064 q^{82} + 1555989756 q^{83} - 3422424120 q^{86} + 2176720604 q^{87} - 387386068 q^{88} - 1493579244 q^{91} - 1262849472 q^{92} + 2042413382 q^{93} + 166226488 q^{94} - 6686432820 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 9.11441i 0.402804i −0.979509 0.201402i \(-0.935450\pi\)
0.979509 0.201402i \(-0.0645498\pi\)
\(3\) 171.314i 1.22109i 0.791982 + 0.610544i \(0.209049\pi\)
−0.791982 + 0.610544i \(0.790951\pi\)
\(4\) 428.927 0.837749
\(5\) 2218.10 1.58714 0.793571 0.608477i \(-0.208219\pi\)
0.793571 + 0.608477i \(0.208219\pi\)
\(6\) 1561.43 0.491859
\(7\) −1871.46 −0.294604 −0.147302 0.989092i \(-0.547059\pi\)
−0.147302 + 0.989092i \(0.547059\pi\)
\(8\) 8576.00i 0.740253i
\(9\) −9665.49 −0.491058
\(10\) 20216.7i 0.639307i
\(11\) 7045.14i 0.145085i 0.997365 + 0.0725425i \(0.0231113\pi\)
−0.997365 + 0.0725425i \(0.976889\pi\)
\(12\) 73481.3i 1.02297i
\(13\) 42558.5 0.413277 0.206639 0.978417i \(-0.433748\pi\)
0.206639 + 0.978417i \(0.433748\pi\)
\(14\) 17057.2i 0.118668i
\(15\) 379992.i 1.93804i
\(16\) 141446. 0.539572
\(17\) 88283.5i 0.256366i −0.991751 0.128183i \(-0.959086\pi\)
0.991751 0.128183i \(-0.0409144\pi\)
\(18\) 88095.2i 0.197800i
\(19\) 8133.60i 0.0143183i −0.999974 0.00715915i \(-0.997721\pi\)
0.999974 0.00715915i \(-0.00227885\pi\)
\(20\) 951404. 1.32963
\(21\) 320607.i 0.359738i
\(22\) 64212.3 0.0584408
\(23\) 117858. 0.0878180 0.0439090 0.999036i \(-0.486019\pi\)
0.0439090 + 0.999036i \(0.486019\pi\)
\(24\) 1.46919e6 0.903914
\(25\) 2.96684e6 1.51902
\(26\) 387896.i 0.166470i
\(27\) 1.71614e6i 0.621464i
\(28\) −802720. −0.246804
\(29\) −3.17798e6 + 2.09943e6i −0.834373 + 0.551200i
\(30\) 3.46340e6 0.780651
\(31\) 7.39306e6i 1.43779i 0.695116 + 0.718897i \(0.255353\pi\)
−0.695116 + 0.718897i \(0.744647\pi\)
\(32\) 5.68011e6i 0.957594i
\(33\) −1.20693e6 −0.177162
\(34\) −804653. −0.103265
\(35\) −4.15108e6 −0.467579
\(36\) −4.14579e6 −0.411383
\(37\) 1.28436e7i 1.12662i 0.826246 + 0.563310i \(0.190472\pi\)
−0.826246 + 0.563310i \(0.809528\pi\)
\(38\) −74133.0 −0.00576747
\(39\) 7.29087e6i 0.504648i
\(40\) 1.90224e7i 1.17489i
\(41\) 2.51109e7i 1.38782i −0.720060 0.693912i \(-0.755886\pi\)
0.720060 0.693912i \(-0.244114\pi\)
\(42\) −2.92214e6 −0.144904
\(43\) 3.64484e7i 1.62581i −0.582393 0.812907i \(-0.697884\pi\)
0.582393 0.812907i \(-0.302116\pi\)
\(44\) 3.02186e6i 0.121545i
\(45\) −2.14390e7 −0.779378
\(46\) 1.07421e6i 0.0353734i
\(47\) 5.99932e6i 0.179334i 0.995972 + 0.0896668i \(0.0285802\pi\)
−0.995972 + 0.0896668i \(0.971420\pi\)
\(48\) 2.42316e7i 0.658866i
\(49\) −3.68513e7 −0.913208
\(50\) 2.70410e7i 0.611868i
\(51\) 1.51242e7 0.313045
\(52\) 1.82545e7 0.346223
\(53\) −5.45801e7 −0.950152 −0.475076 0.879945i \(-0.657579\pi\)
−0.475076 + 0.879945i \(0.657579\pi\)
\(54\) 1.56416e7 0.250328
\(55\) 1.56268e7i 0.230271i
\(56\) 1.60496e7i 0.218082i
\(57\) 1.39340e6 0.0174839
\(58\) 1.91350e7 + 2.89654e7i 0.222026 + 0.336089i
\(59\) −2.16595e7 −0.232710 −0.116355 0.993208i \(-0.537121\pi\)
−0.116355 + 0.993208i \(0.537121\pi\)
\(60\) 1.62989e8i 1.62359i
\(61\) 1.42627e8i 1.31892i −0.751739 0.659460i \(-0.770785\pi\)
0.751739 0.659460i \(-0.229215\pi\)
\(62\) 6.73834e7 0.579149
\(63\) 1.80886e7 0.144668
\(64\) 2.06493e7 0.153849
\(65\) 9.43990e7 0.655930
\(66\) 1.10005e7i 0.0713614i
\(67\) −7.07911e7 −0.429183 −0.214591 0.976704i \(-0.568842\pi\)
−0.214591 + 0.976704i \(0.568842\pi\)
\(68\) 3.78672e7i 0.214770i
\(69\) 2.01907e7i 0.107234i
\(70\) 3.78347e7i 0.188343i
\(71\) 3.47332e8 1.62212 0.811058 0.584966i \(-0.198892\pi\)
0.811058 + 0.584966i \(0.198892\pi\)
\(72\) 8.28912e7i 0.363507i
\(73\) 2.96925e8i 1.22375i −0.790953 0.611877i \(-0.790415\pi\)
0.790953 0.611877i \(-0.209585\pi\)
\(74\) 1.17061e8 0.453807
\(75\) 5.08261e8i 1.85486i
\(76\) 3.48872e6i 0.0119951i
\(77\) 1.31847e7i 0.0427427i
\(78\) 6.64520e7 0.203274
\(79\) 3.79683e8i 1.09673i 0.836240 + 0.548364i \(0.184749\pi\)
−0.836240 + 0.548364i \(0.815251\pi\)
\(80\) 3.13741e8 0.856378
\(81\) −4.84245e8 −1.24992
\(82\) −2.28871e8 −0.559021
\(83\) 1.33956e8 0.309822 0.154911 0.987928i \(-0.450491\pi\)
0.154911 + 0.987928i \(0.450491\pi\)
\(84\) 1.37517e8i 0.301370i
\(85\) 1.95822e8i 0.406889i
\(86\) −3.32206e8 −0.654885
\(87\) −3.59661e8 5.44432e8i −0.673065 1.01884i
\(88\) 6.04192e7 0.107400
\(89\) 8.73876e8i 1.47637i −0.674599 0.738185i \(-0.735683\pi\)
0.674599 0.738185i \(-0.264317\pi\)
\(90\) 1.95404e8i 0.313937i
\(91\) −7.96465e7 −0.121753
\(92\) 5.05525e7 0.0735695
\(93\) −1.26654e9 −1.75567
\(94\) 5.46803e7 0.0722363
\(95\) 1.80411e7i 0.0227252i
\(96\) 9.73082e8 1.16931
\(97\) 2.02736e8i 0.232519i −0.993219 0.116259i \(-0.962910\pi\)
0.993219 0.116259i \(-0.0370904\pi\)
\(98\) 3.35878e8i 0.367844i
\(99\) 6.80947e7i 0.0712451i
\(100\) 1.27256e9 1.27256
\(101\) 5.18428e8i 0.495726i 0.968795 + 0.247863i \(0.0797283\pi\)
−0.968795 + 0.247863i \(0.920272\pi\)
\(102\) 1.37848e8i 0.126096i
\(103\) −2.00795e9 −1.75786 −0.878931 0.476949i \(-0.841743\pi\)
−0.878931 + 0.476949i \(0.841743\pi\)
\(104\) 3.64982e8i 0.305930i
\(105\) 7.11138e8i 0.570955i
\(106\) 4.97466e8i 0.382725i
\(107\) −2.74837e8 −0.202697 −0.101349 0.994851i \(-0.532316\pi\)
−0.101349 + 0.994851i \(0.532316\pi\)
\(108\) 7.36100e8i 0.520631i
\(109\) 3.29796e8 0.223783 0.111891 0.993720i \(-0.464309\pi\)
0.111891 + 0.993720i \(0.464309\pi\)
\(110\) 1.42429e8 0.0927540
\(111\) −2.20028e9 −1.37570
\(112\) −2.64710e8 −0.158960
\(113\) 8.04680e8i 0.464270i −0.972684 0.232135i \(-0.925429\pi\)
0.972684 0.232135i \(-0.0745711\pi\)
\(114\) 1.27000e7i 0.00704259i
\(115\) 2.61421e8 0.139380
\(116\) −1.36312e9 + 9.00501e8i −0.698995 + 0.461768i
\(117\) −4.11349e8 −0.202943
\(118\) 1.97414e8i 0.0937363i
\(119\) 1.65219e8i 0.0755264i
\(120\) 3.25881e9 1.43464
\(121\) 2.30831e9 0.978950
\(122\) −1.29996e9 −0.531266
\(123\) 4.30185e9 1.69466
\(124\) 3.17109e9i 1.20451i
\(125\) 2.24852e9 0.823763
\(126\) 1.64867e8i 0.0582727i
\(127\) 1.60518e9i 0.547530i −0.961797 0.273765i \(-0.911731\pi\)
0.961797 0.273765i \(-0.0882691\pi\)
\(128\) 3.09642e9i 1.01957i
\(129\) 6.24413e9 1.98526
\(130\) 8.60392e8i 0.264211i
\(131\) 4.65180e9i 1.38007i 0.723777 + 0.690034i \(0.242404\pi\)
−0.723777 + 0.690034i \(0.757596\pi\)
\(132\) −5.17686e8 −0.148417
\(133\) 1.52217e7i 0.00421823i
\(134\) 6.45220e8i 0.172877i
\(135\) 3.80657e9i 0.986352i
\(136\) −7.57120e8 −0.189775
\(137\) 4.52630e9i 1.09774i −0.835906 0.548872i \(-0.815057\pi\)
0.835906 0.548872i \(-0.184943\pi\)
\(138\) 1.84027e8 0.0431941
\(139\) −7.21815e9 −1.64006 −0.820029 0.572323i \(-0.806043\pi\)
−0.820029 + 0.572323i \(0.806043\pi\)
\(140\) −1.78051e9 −0.391714
\(141\) −1.02777e9 −0.218982
\(142\) 3.16572e9i 0.653395i
\(143\) 2.99831e8i 0.0599604i
\(144\) −1.36714e9 −0.264961
\(145\) −7.04908e9 + 4.65674e9i −1.32427 + 0.874834i
\(146\) −2.70630e9 −0.492933
\(147\) 6.31314e9i 1.11511i
\(148\) 5.50895e9i 0.943825i
\(149\) 1.01411e10 1.68557 0.842783 0.538254i \(-0.180916\pi\)
0.842783 + 0.538254i \(0.180916\pi\)
\(150\) 4.63250e9 0.747145
\(151\) −8.28140e9 −1.29631 −0.648153 0.761510i \(-0.724458\pi\)
−0.648153 + 0.761510i \(0.724458\pi\)
\(152\) −6.97538e7 −0.0105992
\(153\) 8.53303e8i 0.125890i
\(154\) −1.20171e8 −0.0172169
\(155\) 1.63986e10i 2.28199i
\(156\) 3.12725e9i 0.422768i
\(157\) 4.78086e9i 0.627997i −0.949423 0.313999i \(-0.898331\pi\)
0.949423 0.313999i \(-0.101669\pi\)
\(158\) 3.46059e9 0.441767
\(159\) 9.35033e9i 1.16022i
\(160\) 1.25990e10i 1.51984i
\(161\) −2.20566e8 −0.0258716
\(162\) 4.41361e9i 0.503473i
\(163\) 7.68815e9i 0.853056i −0.904474 0.426528i \(-0.859737\pi\)
0.904474 0.426528i \(-0.140263\pi\)
\(164\) 1.07707e10i 1.16265i
\(165\) −2.67709e9 −0.281181
\(166\) 1.22093e9i 0.124797i
\(167\) 9.12487e8 0.0907826 0.0453913 0.998969i \(-0.485547\pi\)
0.0453913 + 0.998969i \(0.485547\pi\)
\(168\) −2.74953e9 −0.266297
\(169\) −8.79327e9 −0.829202
\(170\) −1.78480e9 −0.163896
\(171\) 7.86152e7i 0.00703111i
\(172\) 1.56337e10i 1.36202i
\(173\) −4.69144e9 −0.398197 −0.199099 0.979979i \(-0.563801\pi\)
−0.199099 + 0.979979i \(0.563801\pi\)
\(174\) −4.96218e9 + 3.27810e9i −0.410394 + 0.271113i
\(175\) −5.55232e9 −0.447510
\(176\) 9.96505e8i 0.0782839i
\(177\) 3.71057e9i 0.284159i
\(178\) −7.96487e9 −0.594687
\(179\) 2.28637e10 1.66459 0.832297 0.554330i \(-0.187026\pi\)
0.832297 + 0.554330i \(0.187026\pi\)
\(180\) −9.19578e9 −0.652923
\(181\) 2.88439e9 0.199756 0.0998780 0.995000i \(-0.468155\pi\)
0.0998780 + 0.995000i \(0.468155\pi\)
\(182\) 7.25931e8i 0.0490427i
\(183\) 2.44341e10 1.61052
\(184\) 1.01075e9i 0.0650075i
\(185\) 2.84883e10i 1.78811i
\(186\) 1.15437e10i 0.707193i
\(187\) 6.21970e8 0.0371948
\(188\) 2.57327e9i 0.150237i
\(189\) 3.21169e9i 0.183086i
\(190\) −1.64434e8 −0.00915380
\(191\) 3.49991e10i 1.90286i 0.307866 + 0.951430i \(0.400385\pi\)
−0.307866 + 0.951430i \(0.599615\pi\)
\(192\) 3.53752e9i 0.187864i
\(193\) 9.82019e9i 0.509462i 0.967012 + 0.254731i \(0.0819870\pi\)
−0.967012 + 0.254731i \(0.918013\pi\)
\(194\) −1.84782e9 −0.0936595
\(195\) 1.61719e10i 0.800949i
\(196\) −1.58065e10 −0.765039
\(197\) 2.87802e10 1.36143 0.680715 0.732548i \(-0.261669\pi\)
0.680715 + 0.732548i \(0.261669\pi\)
\(198\) −6.20643e8 −0.0286978
\(199\) 1.15729e10 0.523122 0.261561 0.965187i \(-0.415763\pi\)
0.261561 + 0.965187i \(0.415763\pi\)
\(200\) 2.54436e10i 1.12446i
\(201\) 1.21275e10i 0.524070i
\(202\) 4.72516e9 0.199680
\(203\) 5.94746e9 3.92899e9i 0.245810 0.162386i
\(204\) 6.48719e9 0.262253
\(205\) 5.56984e10i 2.20268i
\(206\) 1.83013e10i 0.708074i
\(207\) −1.13915e9 −0.0431237
\(208\) 6.01972e9 0.222993
\(209\) 5.73024e7 0.00207737
\(210\) −6.48161e9 −0.229983
\(211\) 2.26337e10i 0.786113i 0.919514 + 0.393057i \(0.128582\pi\)
−0.919514 + 0.393057i \(0.871418\pi\)
\(212\) −2.34109e10 −0.795989
\(213\) 5.95028e10i 1.98075i
\(214\) 2.50498e9i 0.0816473i
\(215\) 8.08463e10i 2.58040i
\(216\) 1.47176e10 0.460040
\(217\) 1.38358e10i 0.423580i
\(218\) 3.00590e9i 0.0901406i
\(219\) 5.08674e10 1.49431
\(220\) 6.70278e9i 0.192909i
\(221\) 3.75722e9i 0.105950i
\(222\) 2.00543e10i 0.554139i
\(223\) −3.15612e10 −0.854636 −0.427318 0.904101i \(-0.640542\pi\)
−0.427318 + 0.904101i \(0.640542\pi\)
\(224\) 1.06301e10i 0.282111i
\(225\) −2.86760e10 −0.745927
\(226\) −7.33419e9 −0.187010
\(227\) 5.42144e10 1.35518 0.677592 0.735438i \(-0.263024\pi\)
0.677592 + 0.735438i \(0.263024\pi\)
\(228\) 5.97667e8 0.0146471
\(229\) 3.97970e10i 0.956292i −0.878280 0.478146i \(-0.841309\pi\)
0.878280 0.478146i \(-0.158691\pi\)
\(230\) 2.38270e9i 0.0561427i
\(231\) 2.25872e9 0.0521926
\(232\) 1.80047e10 + 2.72544e10i 0.408028 + 0.617647i
\(233\) −5.97296e10 −1.32766 −0.663832 0.747882i \(-0.731071\pi\)
−0.663832 + 0.747882i \(0.731071\pi\)
\(234\) 3.74920e9i 0.0817462i
\(235\) 1.33071e10i 0.284628i
\(236\) −9.29035e9 −0.194952
\(237\) −6.50450e10 −1.33920
\(238\) 1.50587e9 0.0304223
\(239\) −4.96650e10 −0.984601 −0.492300 0.870425i \(-0.663844\pi\)
−0.492300 + 0.870425i \(0.663844\pi\)
\(240\) 5.37481e10i 1.04571i
\(241\) −4.65043e10 −0.888007 −0.444004 0.896025i \(-0.646442\pi\)
−0.444004 + 0.896025i \(0.646442\pi\)
\(242\) 2.10389e10i 0.394325i
\(243\) 4.91791e10i 0.904799i
\(244\) 6.11768e10i 1.10492i
\(245\) −8.17397e10 −1.44939
\(246\) 3.92088e10i 0.682614i
\(247\) 3.46154e8i 0.00591743i
\(248\) 6.34029e10 1.06433
\(249\) 2.29486e10i 0.378320i
\(250\) 2.04940e10i 0.331815i
\(251\) 8.66926e10i 1.37864i 0.724458 + 0.689319i \(0.242090\pi\)
−0.724458 + 0.689319i \(0.757910\pi\)
\(252\) 7.75868e9 0.121195
\(253\) 8.30326e8i 0.0127411i
\(254\) −1.46303e10 −0.220547
\(255\) 3.35470e10 0.496847
\(256\) −1.76496e10 −0.256836
\(257\) 4.62355e10 0.661115 0.330557 0.943786i \(-0.392763\pi\)
0.330557 + 0.943786i \(0.392763\pi\)
\(258\) 5.69116e10i 0.799672i
\(259\) 2.40362e10i 0.331907i
\(260\) 4.04903e10 0.549505
\(261\) 3.07167e10 2.02920e10i 0.409725 0.270671i
\(262\) 4.23984e10 0.555897
\(263\) 5.98443e10i 0.771297i −0.922646 0.385649i \(-0.873978\pi\)
0.922646 0.385649i \(-0.126022\pi\)
\(264\) 1.03506e10i 0.131144i
\(265\) −1.21064e11 −1.50803
\(266\) 1.38737e8 0.00169912
\(267\) 1.49707e11 1.80278
\(268\) −3.03643e10 −0.359547
\(269\) 1.19242e11i 1.38849i 0.719740 + 0.694244i \(0.244261\pi\)
−0.719740 + 0.694244i \(0.755739\pi\)
\(270\) 3.46947e10 0.397306
\(271\) 5.02511e10i 0.565958i 0.959126 + 0.282979i \(0.0913226\pi\)
−0.959126 + 0.282979i \(0.908677\pi\)
\(272\) 1.24873e10i 0.138328i
\(273\) 1.36446e10i 0.148671i
\(274\) −4.12546e10 −0.442176
\(275\) 2.09018e10i 0.220387i
\(276\) 8.66035e9i 0.0898348i
\(277\) −6.86412e10 −0.700529 −0.350264 0.936651i \(-0.613908\pi\)
−0.350264 + 0.936651i \(0.613908\pi\)
\(278\) 6.57892e10i 0.660622i
\(279\) 7.14575e10i 0.706040i
\(280\) 3.55997e10i 0.346127i
\(281\) 6.20906e10 0.594084 0.297042 0.954864i \(-0.404000\pi\)
0.297042 + 0.954864i \(0.404000\pi\)
\(282\) 9.36750e9i 0.0882069i
\(283\) −5.62239e10 −0.521053 −0.260527 0.965467i \(-0.583896\pi\)
−0.260527 + 0.965467i \(0.583896\pi\)
\(284\) 1.48980e11 1.35893
\(285\) 3.09070e9 0.0277495
\(286\) 2.73278e9 0.0241523
\(287\) 4.69940e10i 0.408859i
\(288\) 5.49010e10i 0.470234i
\(289\) 1.10794e11 0.934277
\(290\) 4.24434e10 + 6.42482e10i 0.352387 + 0.533421i
\(291\) 3.47315e10 0.283926
\(292\) 1.27359e11i 1.02520i
\(293\) 1.00010e11i 0.792756i 0.918087 + 0.396378i \(0.129733\pi\)
−0.918087 + 0.396378i \(0.870267\pi\)
\(294\) −5.75405e10 −0.449170
\(295\) −4.80429e10 −0.369343
\(296\) 1.10146e11 0.833983
\(297\) −1.20905e10 −0.0901651
\(298\) 9.24299e10i 0.678953i
\(299\) 5.01586e9 0.0362932
\(300\) 2.18007e11i 1.55391i
\(301\) 6.82117e10i 0.478972i
\(302\) 7.54801e10i 0.522157i
\(303\) −8.88139e10 −0.605326
\(304\) 1.15046e9i 0.00772576i
\(305\) 3.16362e11i 2.09332i
\(306\) 7.77736e9 0.0507091
\(307\) 1.37949e11i 0.886330i 0.896440 + 0.443165i \(0.146144\pi\)
−0.896440 + 0.443165i \(0.853856\pi\)
\(308\) 5.65528e9i 0.0358076i
\(309\) 3.43990e11i 2.14651i
\(310\) 1.49463e11 0.919193
\(311\) 8.54107e9i 0.0517714i −0.999665 0.0258857i \(-0.991759\pi\)
0.999665 0.0258857i \(-0.00824060\pi\)
\(312\) 6.25265e10 0.373567
\(313\) −2.38313e11 −1.40346 −0.701728 0.712445i \(-0.747588\pi\)
−0.701728 + 0.712445i \(0.747588\pi\)
\(314\) −4.35748e10 −0.252960
\(315\) 4.01222e10 0.229608
\(316\) 1.62856e11i 0.918783i
\(317\) 1.22497e11i 0.681334i −0.940184 0.340667i \(-0.889347\pi\)
0.940184 0.340667i \(-0.110653\pi\)
\(318\) −8.52228e10 −0.467341
\(319\) −1.47908e10 2.23893e10i −0.0799709 0.121055i
\(320\) 4.58023e10 0.244181
\(321\) 4.70834e10i 0.247511i
\(322\) 2.01033e9i 0.0104212i
\(323\) −7.18063e8 −0.00367072
\(324\) −2.07706e11 −1.04712
\(325\) 1.26264e11 0.627777
\(326\) −7.00730e10 −0.343614
\(327\) 5.64987e10i 0.273259i
\(328\) −2.15351e11 −1.02734
\(329\) 1.12275e10i 0.0528324i
\(330\) 2.44001e10i 0.113261i
\(331\) 1.53413e11i 0.702484i −0.936285 0.351242i \(-0.885759\pi\)
0.936285 0.351242i \(-0.114241\pi\)
\(332\) 5.74576e10 0.259553
\(333\) 1.24139e11i 0.553235i
\(334\) 8.31678e9i 0.0365676i
\(335\) −1.57022e11 −0.681174
\(336\) 4.53485e10i 0.194105i
\(337\) 4.13594e11i 1.74678i 0.487018 + 0.873392i \(0.338085\pi\)
−0.487018 + 0.873392i \(0.661915\pi\)
\(338\) 8.01455e10i 0.334006i
\(339\) 1.37853e11 0.566915
\(340\) 8.39933e10i 0.340871i
\(341\) −5.20852e10 −0.208603
\(342\) 7.16531e8 0.00283216
\(343\) 1.44486e11 0.563639
\(344\) −3.12582e11 −1.20351
\(345\) 4.47850e10i 0.170195i
\(346\) 4.27597e10i 0.160395i
\(347\) −2.73280e11 −1.01187 −0.505936 0.862571i \(-0.668853\pi\)
−0.505936 + 0.862571i \(0.668853\pi\)
\(348\) −1.54268e11 2.33522e11i −0.563859 0.853535i
\(349\) −1.35603e11 −0.489278 −0.244639 0.969614i \(-0.578669\pi\)
−0.244639 + 0.969614i \(0.578669\pi\)
\(350\) 5.06061e10i 0.180259i
\(351\) 7.30364e10i 0.256837i
\(352\) 4.00172e10 0.138933
\(353\) −2.37707e11 −0.814808 −0.407404 0.913248i \(-0.633566\pi\)
−0.407404 + 0.913248i \(0.633566\pi\)
\(354\) −3.38197e10 −0.114460
\(355\) 7.70416e11 2.57453
\(356\) 3.74830e11i 1.23683i
\(357\) −2.83043e10 −0.0922244
\(358\) 2.08389e11i 0.670505i
\(359\) 2.06080e11i 0.654803i −0.944885 0.327402i \(-0.893827\pi\)
0.944885 0.327402i \(-0.106173\pi\)
\(360\) 1.83861e11i 0.576937i
\(361\) 3.22622e11 0.999795
\(362\) 2.62895e10i 0.0804625i
\(363\) 3.95446e11i 1.19539i
\(364\) −3.41626e10 −0.101999
\(365\) 6.58610e11i 1.94227i
\(366\) 2.22702e11i 0.648723i
\(367\) 9.73391e10i 0.280085i 0.990145 + 0.140043i \(0.0447240\pi\)
−0.990145 + 0.140043i \(0.955276\pi\)
\(368\) 1.66705e10 0.0473842
\(369\) 2.42709e11i 0.681502i
\(370\) 2.59654e11 0.720257
\(371\) 1.02144e11 0.279919
\(372\) −5.43252e11 −1.47081
\(373\) 3.24735e11 0.868639 0.434319 0.900759i \(-0.356989\pi\)
0.434319 + 0.900759i \(0.356989\pi\)
\(374\) 5.66889e9i 0.0149822i
\(375\) 3.85203e11i 1.00589i
\(376\) 5.14502e10 0.132752
\(377\) −1.35250e11 + 8.93485e10i −0.344827 + 0.227799i
\(378\) −2.92726e10 −0.0737477
\(379\) 6.54191e11i 1.62865i 0.580408 + 0.814326i \(0.302893\pi\)
−0.580408 + 0.814326i \(0.697107\pi\)
\(380\) 7.73834e9i 0.0190380i
\(381\) 2.74990e11 0.668583
\(382\) 3.18996e11 0.766479
\(383\) 2.53312e11 0.601536 0.300768 0.953697i \(-0.402757\pi\)
0.300768 + 0.953697i \(0.402757\pi\)
\(384\) 5.30460e11 1.24498
\(385\) 2.92450e10i 0.0678387i
\(386\) 8.95053e10 0.205213
\(387\) 3.52292e11i 0.798368i
\(388\) 8.69590e10i 0.194792i
\(389\) 3.46642e11i 0.767551i −0.923426 0.383776i \(-0.874624\pi\)
0.923426 0.383776i \(-0.125376\pi\)
\(390\) 1.47397e11 0.322625
\(391\) 1.04049e10i 0.0225135i
\(392\) 3.16036e11i 0.676005i
\(393\) −7.96919e11 −1.68518
\(394\) 2.62314e11i 0.548389i
\(395\) 8.42174e11i 1.74066i
\(396\) 2.92077e10i 0.0596855i
\(397\) 4.37391e11 0.883717 0.441858 0.897085i \(-0.354319\pi\)
0.441858 + 0.897085i \(0.354319\pi\)
\(398\) 1.05480e11i 0.210715i
\(399\) −2.60769e9 −0.00515084
\(400\) 4.19647e11 0.819622
\(401\) −2.62577e11 −0.507115 −0.253557 0.967320i \(-0.581601\pi\)
−0.253557 + 0.967320i \(0.581601\pi\)
\(402\) −1.10535e11 −0.211098
\(403\) 3.14638e11i 0.594208i
\(404\) 2.22368e11i 0.415294i
\(405\) −1.07410e12 −1.98380
\(406\) −3.58104e10 5.42076e10i −0.0654097 0.0990131i
\(407\) −9.04847e10 −0.163456
\(408\) 1.29705e11i 0.231732i
\(409\) 4.14934e11i 0.733203i 0.930378 + 0.366601i \(0.119479\pi\)
−0.930378 + 0.366601i \(0.880521\pi\)
\(410\) −5.07659e11 −0.887247
\(411\) 7.75419e11 1.34044
\(412\) −8.61264e11 −1.47265
\(413\) 4.05348e10 0.0685572
\(414\) 1.03827e10i 0.0173704i
\(415\) 2.97129e11 0.491732
\(416\) 2.41737e11i 0.395752i
\(417\) 1.23657e12i 2.00266i
\(418\) 5.22277e8i 0.000836774i
\(419\) 5.99533e11 0.950277 0.475138 0.879911i \(-0.342398\pi\)
0.475138 + 0.879911i \(0.342398\pi\)
\(420\) 3.05027e11i 0.478317i
\(421\) 8.07295e11i 1.25246i −0.779639 0.626229i \(-0.784598\pi\)
0.779639 0.626229i \(-0.215402\pi\)
\(422\) 2.06293e11 0.316650
\(423\) 5.79863e10i 0.0880631i
\(424\) 4.68079e11i 0.703352i
\(425\) 2.61923e11i 0.389425i
\(426\) 5.42333e11 0.797853
\(427\) 2.66921e11i 0.388559i
\(428\) −1.17885e11 −0.169810
\(429\) −5.13652e10 −0.0732169
\(430\) −7.36866e11 −1.03940
\(431\) 4.29919e11 0.600121 0.300060 0.953920i \(-0.402993\pi\)
0.300060 + 0.953920i \(0.402993\pi\)
\(432\) 2.42741e11i 0.335325i
\(433\) 7.16813e11i 0.979965i 0.871732 + 0.489983i \(0.162997\pi\)
−0.871732 + 0.489983i \(0.837003\pi\)
\(434\) −1.26105e11 −0.170620
\(435\) −7.97764e11 1.20761e12i −1.06825 1.61705i
\(436\) 1.41459e11 0.187474
\(437\) 9.58609e8i 0.00125740i
\(438\) 4.63627e11i 0.601915i
\(439\) 6.17798e11 0.793882 0.396941 0.917844i \(-0.370072\pi\)
0.396941 + 0.917844i \(0.370072\pi\)
\(440\) 1.34016e11 0.170459
\(441\) 3.56185e11 0.448438
\(442\) −3.42448e10 −0.0426771
\(443\) 8.50599e11i 1.04932i −0.851312 0.524660i \(-0.824192\pi\)
0.851312 0.524660i \(-0.175808\pi\)
\(444\) −9.43761e11 −1.15249
\(445\) 1.93834e12i 2.34321i
\(446\) 2.87662e11i 0.344251i
\(447\) 1.73731e12i 2.05823i
\(448\) −3.86444e10 −0.0453247
\(449\) 1.61972e12i 1.88075i 0.340145 + 0.940373i \(0.389524\pi\)
−0.340145 + 0.940373i \(0.610476\pi\)
\(450\) 2.61365e11i 0.300463i
\(451\) 1.76910e11 0.201353
\(452\) 3.45150e11i 0.388942i
\(453\) 1.41872e12i 1.58290i
\(454\) 4.94132e11i 0.545873i
\(455\) −1.76664e11 −0.193240
\(456\) 1.19498e10i 0.0129425i
\(457\) −1.04762e12 −1.12352 −0.561761 0.827300i \(-0.689876\pi\)
−0.561761 + 0.827300i \(0.689876\pi\)
\(458\) −3.62726e11 −0.385198
\(459\) 1.51507e11 0.159322
\(460\) 1.12131e11 0.116765
\(461\) 1.90900e12i 1.96857i 0.176582 + 0.984286i \(0.443496\pi\)
−0.176582 + 0.984286i \(0.556504\pi\)
\(462\) 2.05869e10i 0.0210234i
\(463\) −1.01902e12 −1.03055 −0.515273 0.857026i \(-0.672309\pi\)
−0.515273 + 0.857026i \(0.672309\pi\)
\(464\) −4.49511e11 + 2.96955e11i −0.450205 + 0.297412i
\(465\) −2.80930e12 −2.78651
\(466\) 5.44401e11i 0.534788i
\(467\) 1.04209e12i 1.01386i −0.861987 0.506931i \(-0.830780\pi\)
0.861987 0.506931i \(-0.169220\pi\)
\(468\) −1.76439e11 −0.170015
\(469\) 1.32483e11 0.126439
\(470\) 1.21286e11 0.114649
\(471\) 8.19029e11 0.766840
\(472\) 1.85752e11i 0.172264i
\(473\) 2.56785e11 0.235881
\(474\) 5.92847e11i 0.539436i
\(475\) 2.41311e10i 0.0217498i
\(476\) 7.08670e10i 0.0632721i
\(477\) 5.27543e11 0.466579
\(478\) 4.52668e11i 0.396601i
\(479\) 1.23856e12i 1.07500i −0.843264 0.537500i \(-0.819369\pi\)
0.843264 0.537500i \(-0.180631\pi\)
\(480\) 2.15839e12 1.85586
\(481\) 5.46603e11i 0.465606i
\(482\) 4.23859e11i 0.357693i
\(483\) 3.77861e10i 0.0315915i
\(484\) 9.90099e11 0.820115
\(485\) 4.49688e11i 0.369040i
\(486\) −4.48239e11 −0.364457
\(487\) 1.23184e12 0.992375 0.496187 0.868215i \(-0.334733\pi\)
0.496187 + 0.868215i \(0.334733\pi\)
\(488\) −1.22317e12 −0.976334
\(489\) 1.31709e12 1.04166
\(490\) 7.45010e11i 0.583821i
\(491\) 3.64942e11i 0.283372i 0.989912 + 0.141686i \(0.0452524\pi\)
−0.989912 + 0.141686i \(0.954748\pi\)
\(492\) 1.84518e12 1.41970
\(493\) 1.85345e11 + 2.80563e11i 0.141309 + 0.213904i
\(494\) −3.15499e9 −0.00238356
\(495\) 1.51041e11i 0.113076i
\(496\) 1.04572e12i 0.775794i
\(497\) −6.50017e11 −0.477882
\(498\) 2.09163e11 0.152389
\(499\) 2.07329e12 1.49695 0.748474 0.663164i \(-0.230787\pi\)
0.748474 + 0.663164i \(0.230787\pi\)
\(500\) 9.64453e11 0.690106
\(501\) 1.56322e11i 0.110854i
\(502\) 7.90152e11 0.555321
\(503\) 1.35056e11i 0.0940714i −0.998893 0.0470357i \(-0.985023\pi\)
0.998893 0.0470357i \(-0.0149774\pi\)
\(504\) 1.55127e11i 0.107091i
\(505\) 1.14992e12i 0.786788i
\(506\) 7.56794e9 0.00513216
\(507\) 1.50641e12i 1.01253i
\(508\) 6.88507e11i 0.458693i
\(509\) −3.38159e11 −0.223301 −0.111650 0.993748i \(-0.535614\pi\)
−0.111650 + 0.993748i \(0.535614\pi\)
\(510\) 3.05761e11i 0.200132i
\(511\) 5.55683e11i 0.360523i
\(512\) 1.42450e12i 0.916111i
\(513\) 1.39584e10 0.00889831
\(514\) 4.21410e11i 0.266300i
\(515\) −4.45383e12 −2.78998
\(516\) 2.67828e12 1.66315
\(517\) −4.22661e10 −0.0260186
\(518\) −2.19076e11 −0.133693
\(519\) 8.03709e11i 0.486234i
\(520\) 8.09566e11i 0.485554i
\(521\) 1.36366e12 0.810841 0.405421 0.914130i \(-0.367125\pi\)
0.405421 + 0.914130i \(0.367125\pi\)
\(522\) −1.84949e11 2.79965e11i −0.109027 0.165039i
\(523\) −2.72495e12 −1.59258 −0.796289 0.604917i \(-0.793206\pi\)
−0.796289 + 0.604917i \(0.793206\pi\)
\(524\) 1.99528e12i 1.15615i
\(525\) 9.51190e11i 0.546450i
\(526\) −5.45446e11 −0.310682
\(527\) 6.52686e11 0.368601
\(528\) −1.70715e11 −0.0955916
\(529\) −1.78726e12 −0.992288
\(530\) 1.10343e12i 0.607439i
\(531\) 2.09350e11 0.114274
\(532\) 6.52900e9i 0.00353382i
\(533\) 1.06868e12i 0.573556i
\(534\) 1.36449e12i 0.726166i
\(535\) −6.09616e11 −0.321710
\(536\) 6.07105e11i 0.317704i
\(537\) 3.91687e12i 2.03262i
\(538\) 1.08682e12 0.559289
\(539\) 2.59622e11i 0.132493i
\(540\) 1.63274e12i 0.826315i
\(541\) 2.67959e12i 1.34487i 0.740155 + 0.672436i \(0.234752\pi\)
−0.740155 + 0.672436i \(0.765248\pi\)
\(542\) 4.58009e11 0.227970
\(543\) 4.94136e11i 0.243920i
\(544\) −5.01460e11 −0.245494
\(545\) 7.31521e11 0.355175
\(546\) −1.24362e11 −0.0598855
\(547\) 2.42147e12 1.15647 0.578237 0.815869i \(-0.303741\pi\)
0.578237 + 0.815869i \(0.303741\pi\)
\(548\) 1.94146e12i 0.919634i
\(549\) 1.37856e12i 0.647666i
\(550\) 1.90508e11 0.0887730
\(551\) 1.70759e10 + 2.58484e10i 0.00789225 + 0.0119468i
\(552\) 1.73156e11 0.0793799
\(553\) 7.10561e11i 0.323101i
\(554\) 6.25625e11i 0.282176i
\(555\) −4.88044e12 −2.18344
\(556\) −3.09606e12 −1.37396
\(557\) 3.83260e12 1.68712 0.843558 0.537038i \(-0.180457\pi\)
0.843558 + 0.537038i \(0.180457\pi\)
\(558\) −6.51294e11 −0.284396
\(559\) 1.55119e12i 0.671912i
\(560\) −5.87152e11 −0.252293
\(561\) 1.06552e11i 0.0454182i
\(562\) 5.65920e11i 0.239299i
\(563\) 3.03957e12i 1.27504i −0.770434 0.637520i \(-0.779960\pi\)
0.770434 0.637520i \(-0.220040\pi\)
\(564\) −4.40838e11 −0.183452
\(565\) 1.78486e12i 0.736863i
\(566\) 5.12448e11i 0.209882i
\(567\) 9.06244e11 0.368232
\(568\) 2.97872e12i 1.20078i
\(569\) 2.64705e12i 1.05866i −0.848416 0.529330i \(-0.822443\pi\)
0.848416 0.529330i \(-0.177557\pi\)
\(570\) 2.81699e10i 0.0111776i
\(571\) 1.38445e12 0.545021 0.272511 0.962153i \(-0.412146\pi\)
0.272511 + 0.962153i \(0.412146\pi\)
\(572\) 1.28606e11i 0.0502317i
\(573\) −5.99584e12 −2.32356
\(574\) 4.28322e11 0.164690
\(575\) 3.49666e11 0.133398
\(576\) −1.99586e11 −0.0755489
\(577\) 3.30623e12i 1.24177i −0.783900 0.620887i \(-0.786773\pi\)
0.783900 0.620887i \(-0.213227\pi\)
\(578\) 1.00982e12i 0.376330i
\(579\) −1.68234e12 −0.622099
\(580\) −3.02354e12 + 1.99740e12i −1.10940 + 0.732891i
\(581\) −2.50694e11 −0.0912748
\(582\) 3.16557e11i 0.114366i
\(583\) 3.84525e11i 0.137853i
\(584\) −2.54643e12 −0.905887
\(585\) −9.12413e11 −0.322099
\(586\) 9.11534e11 0.319325
\(587\) 1.19393e12 0.415055 0.207528 0.978229i \(-0.433458\pi\)
0.207528 + 0.978229i \(0.433458\pi\)
\(588\) 2.70788e12i 0.934181i
\(589\) 6.01322e10 0.0205868
\(590\) 4.37883e11i 0.148773i
\(591\) 4.93045e12i 1.66243i
\(592\) 1.81666e12i 0.607893i
\(593\) 2.01482e12 0.669100 0.334550 0.942378i \(-0.391416\pi\)
0.334550 + 0.942378i \(0.391416\pi\)
\(594\) 1.10197e11i 0.0363189i
\(595\) 3.66472e11i 0.119871i
\(596\) 4.34978e12 1.41208
\(597\) 1.98260e12i 0.638778i
\(598\) 4.57166e10i 0.0146190i
\(599\) 1.27106e12i 0.403410i 0.979446 + 0.201705i \(0.0646482\pi\)
−0.979446 + 0.201705i \(0.935352\pi\)
\(600\) 4.35885e12 1.37307
\(601\) 8.21053e11i 0.256706i −0.991729 0.128353i \(-0.959031\pi\)
0.991729 0.128353i \(-0.0409691\pi\)
\(602\) 6.21710e11 0.192932
\(603\) 6.84231e11 0.210753
\(604\) −3.55212e12 −1.08598
\(605\) 5.12007e12 1.55373
\(606\) 8.09486e11i 0.243828i
\(607\) 3.90308e12i 1.16697i −0.812125 0.583484i \(-0.801689\pi\)
0.812125 0.583484i \(-0.198311\pi\)
\(608\) −4.61997e10 −0.0137111
\(609\) 6.73091e11 + 1.01888e12i 0.198288 + 0.300156i
\(610\) −2.88345e12 −0.843196
\(611\) 2.55322e11i 0.0741145i
\(612\) 3.66005e11i 0.105464i
\(613\) −3.39594e12 −0.971376 −0.485688 0.874132i \(-0.661431\pi\)
−0.485688 + 0.874132i \(0.661431\pi\)
\(614\) 1.25732e12 0.357017
\(615\) 9.54192e12 2.68966
\(616\) −1.13072e11 −0.0316404
\(617\) 4.07289e12i 1.13141i 0.824609 + 0.565704i \(0.191395\pi\)
−0.824609 + 0.565704i \(0.808605\pi\)
\(618\) −3.13526e12 −0.864621
\(619\) 7.71794e11i 0.211297i 0.994404 + 0.105649i \(0.0336919\pi\)
−0.994404 + 0.105649i \(0.966308\pi\)
\(620\) 7.03379e12i 1.91173i
\(621\) 2.02261e11i 0.0545757i
\(622\) −7.78468e10 −0.0208537
\(623\) 1.63542e12i 0.434945i
\(624\) 1.03126e12i 0.272294i
\(625\) −8.07164e11 −0.211593
\(626\) 2.17208e12i 0.565317i
\(627\) 9.81670e9i 0.00253666i
\(628\) 2.05064e12i 0.526104i
\(629\) 1.13387e12 0.288827
\(630\) 3.65690e11i 0.0924871i
\(631\) 5.11916e11 0.128548 0.0642742 0.997932i \(-0.479527\pi\)
0.0642742 + 0.997932i \(0.479527\pi\)
\(632\) 3.25616e12 0.811856
\(633\) −3.87747e12 −0.959914
\(634\) −1.11649e12 −0.274444
\(635\) 3.56046e12i 0.869009i
\(636\) 4.01062e12i 0.971973i
\(637\) −1.56833e12 −0.377408
\(638\) −2.04066e11 + 1.34809e11i −0.0487615 + 0.0322126i
\(639\) −3.35713e12 −0.796552
\(640\) 6.86817e12i 1.61820i
\(641\) 8.56776e11i 0.200450i 0.994965 + 0.100225i \(0.0319563\pi\)
−0.994965 + 0.100225i \(0.968044\pi\)
\(642\) −4.29138e11 −0.0996986
\(643\) −2.78211e12 −0.641837 −0.320919 0.947107i \(-0.603992\pi\)
−0.320919 + 0.947107i \(0.603992\pi\)
\(644\) −9.46069e10 −0.0216739
\(645\) 1.38501e13 3.15090
\(646\) 6.54472e9i 0.00147858i
\(647\) −1.48557e12 −0.333292 −0.166646 0.986017i \(-0.553294\pi\)
−0.166646 + 0.986017i \(0.553294\pi\)
\(648\) 4.15288e12i 0.925257i
\(649\) 1.52594e11i 0.0337627i
\(650\) 1.15083e12i 0.252871i
\(651\) 2.37027e12 0.517229
\(652\) 3.29766e12i 0.714647i
\(653\) 5.01554e12i 1.07946i −0.841837 0.539732i \(-0.818525\pi\)
0.841837 0.539732i \(-0.181475\pi\)
\(654\) 5.14953e11 0.110070
\(655\) 1.03182e13i 2.19036i
\(656\) 3.55182e12i 0.748832i
\(657\) 2.86993e12i 0.600934i
\(658\) −1.02332e11 −0.0212811
\(659\) 5.38425e12i 1.11209i 0.831151 + 0.556046i \(0.187682\pi\)
−0.831151 + 0.556046i \(0.812318\pi\)
\(660\) −1.14828e12 −0.235559
\(661\) 3.49051e12 0.711184 0.355592 0.934641i \(-0.384279\pi\)
0.355592 + 0.934641i \(0.384279\pi\)
\(662\) −1.39827e12 −0.282963
\(663\) 6.43664e11 0.129374
\(664\) 1.14881e12i 0.229346i
\(665\) 3.37632e10i 0.00669494i
\(666\) −1.13146e12 −0.222845
\(667\) −3.74550e11 + 2.47434e11i −0.0732730 + 0.0484053i
\(668\) 3.91391e11 0.0760530
\(669\) 5.40687e12i 1.04359i
\(670\) 1.43116e12i 0.274380i
\(671\) 1.00483e12 0.191356
\(672\) −1.82108e12 −0.344483
\(673\) 5.18202e12 0.973714 0.486857 0.873482i \(-0.338143\pi\)
0.486857 + 0.873482i \(0.338143\pi\)
\(674\) 3.76966e12 0.703611
\(675\) 5.09152e12i 0.944018i
\(676\) −3.77168e12 −0.694663
\(677\) 1.97020e11i 0.0360463i 0.999838 + 0.0180232i \(0.00573726\pi\)
−0.999838 + 0.0180232i \(0.994263\pi\)
\(678\) 1.25645e12i 0.228355i
\(679\) 3.79412e11i 0.0685010i
\(680\) −1.67937e12 −0.301200
\(681\) 9.28768e12i 1.65480i
\(682\) 4.74726e11i 0.0840259i
\(683\) −9.85344e12 −1.73259 −0.866293 0.499536i \(-0.833504\pi\)
−0.866293 + 0.499536i \(0.833504\pi\)
\(684\) 3.37202e10i 0.00589031i
\(685\) 1.00398e13i 1.74228i
\(686\) 1.31690e12i 0.227036i
\(687\) 6.81778e12 1.16772
\(688\) 5.15547e12i 0.877245i
\(689\) −2.32285e12 −0.392676
\(690\) 4.08189e11 0.0685552
\(691\) −6.94442e12 −1.15874 −0.579369 0.815066i \(-0.696701\pi\)
−0.579369 + 0.815066i \(0.696701\pi\)
\(692\) −2.01229e12 −0.333589
\(693\) 1.27436e11i 0.0209891i
\(694\) 2.49079e12i 0.407586i
\(695\) −1.60106e13 −2.60301
\(696\) −4.66905e12 + 3.08445e12i −0.754201 + 0.498238i
\(697\) −2.21688e12 −0.355790
\(698\) 1.23594e12i 0.197083i
\(699\) 1.02325e13i 1.62120i
\(700\) −2.38154e12 −0.374901
\(701\) 5.73691e12 0.897319 0.448660 0.893703i \(-0.351902\pi\)
0.448660 + 0.893703i \(0.351902\pi\)
\(702\) 6.65684e11 0.103455
\(703\) 1.04464e11 0.0161313
\(704\) 1.45477e11i 0.0223213i
\(705\) −2.27969e12 −0.347556
\(706\) 2.16656e12i 0.328208i
\(707\) 9.70215e11i 0.146043i
\(708\) 1.59157e12i 0.238054i
\(709\) 8.11851e12 1.20661 0.603307 0.797509i \(-0.293849\pi\)
0.603307 + 0.797509i \(0.293849\pi\)
\(710\) 7.02189e12i 1.03703i
\(711\) 3.66982e12i 0.538557i
\(712\) −7.49437e12 −1.09289
\(713\) 8.71331e11i 0.126264i
\(714\) 2.57977e11i 0.0371483i
\(715\) 6.65055e11i 0.0951657i
\(716\) 9.80688e12 1.39451
\(717\) 8.50831e12i 1.20228i
\(718\) −1.87830e12 −0.263757
\(719\) 3.82838e12 0.534238 0.267119 0.963663i \(-0.413928\pi\)
0.267119 + 0.963663i \(0.413928\pi\)
\(720\) −3.03245e12 −0.420531
\(721\) 3.75779e12 0.517874
\(722\) 2.94051e12i 0.402721i
\(723\) 7.96684e12i 1.08434i
\(724\) 1.23719e12 0.167345
\(725\) −9.42856e12 + 6.22866e12i −1.26743 + 0.837286i
\(726\) 3.60426e12 0.481506
\(727\) 1.18895e13i 1.57855i 0.614040 + 0.789275i \(0.289543\pi\)
−0.614040 + 0.789275i \(0.710457\pi\)
\(728\) 6.83049e11i 0.0901281i
\(729\) −1.10632e12 −0.145080
\(730\) −6.00284e12 −0.782355
\(731\) −3.21780e12 −0.416803
\(732\) 1.04804e13 1.34921
\(733\) 1.35618e13i 1.73520i 0.497264 + 0.867599i \(0.334338\pi\)
−0.497264 + 0.867599i \(0.665662\pi\)
\(734\) 8.87189e11 0.112819
\(735\) 1.40032e13i 1.76984i
\(736\) 6.69446e11i 0.0840940i
\(737\) 4.98734e11i 0.0622680i
\(738\) 2.21215e12 0.274512
\(739\) 5.92021e12i 0.730192i −0.930970 0.365096i \(-0.881036\pi\)
0.930970 0.365096i \(-0.118964\pi\)
\(740\) 1.22194e13i 1.49798i
\(741\) 5.93010e10 0.00722570
\(742\) 9.30986e11i 0.112752i
\(743\) 1.83434e12i 0.220816i −0.993886 0.110408i \(-0.964784\pi\)
0.993886 0.110408i \(-0.0352158\pi\)
\(744\) 1.08618e13i 1.29964i
\(745\) 2.24939e13 2.67523
\(746\) 2.95977e12i 0.349891i
\(747\) −1.29475e12 −0.152140
\(748\) 2.66780e11 0.0311599
\(749\) 5.14346e11 0.0597155
\(750\) 3.51090e12 0.405175
\(751\) 1.39891e13i 1.60476i −0.596816 0.802378i \(-0.703568\pi\)
0.596816 0.802378i \(-0.296432\pi\)
\(752\) 8.48577e11i 0.0967634i
\(753\) −1.48516e13 −1.68344
\(754\) 8.14359e11 + 1.23273e12i 0.0917582 + 0.138898i
\(755\) −1.83690e13 −2.05742
\(756\) 1.37758e12i 0.153380i
\(757\) 5.92603e12i 0.655892i 0.944696 + 0.327946i \(0.106356\pi\)
−0.944696 + 0.327946i \(0.893644\pi\)
\(758\) 5.96257e12 0.656028
\(759\) −1.42246e11 −0.0155580
\(760\) −1.54721e11 −0.0168224
\(761\) 1.26129e13 1.36327 0.681637 0.731690i \(-0.261268\pi\)
0.681637 + 0.731690i \(0.261268\pi\)
\(762\) 2.50638e12i 0.269308i
\(763\) −6.17200e11 −0.0659273
\(764\) 1.50121e13i 1.59412i
\(765\) 1.89271e12i 0.199806i
\(766\) 2.30879e12i 0.242301i
\(767\) −9.21796e11 −0.0961736
\(768\) 3.02362e12i 0.313619i
\(769\) 2.22074e12i 0.228997i −0.993423 0.114498i \(-0.963474\pi\)
0.993423 0.114498i \(-0.0365261\pi\)
\(770\) −2.66551e11 −0.0273257
\(771\) 7.92080e12i 0.807280i
\(772\) 4.21215e12i 0.426802i
\(773\) 4.19155e12i 0.422247i 0.977459 + 0.211124i \(0.0677123\pi\)
−0.977459 + 0.211124i \(0.932288\pi\)
\(774\) 3.21093e12 0.321586
\(775\) 2.19340e13i 2.18404i
\(776\) −1.73866e12 −0.172123
\(777\) 4.11773e12 0.405288
\(778\) −3.15943e12 −0.309173
\(779\) −2.04242e11 −0.0198713
\(780\) 6.93656e12i 0.670994i
\(781\) 2.44700e12i 0.235345i
\(782\) −9.48347e10 −0.00906853
\(783\) −3.60291e12 5.45386e12i −0.342551 0.518533i
\(784\) −5.21245e12 −0.492742
\(785\) 1.06044e13i 0.996722i
\(786\) 7.26344e12i 0.678799i
\(787\) 3.47697e12 0.323083 0.161542 0.986866i \(-0.448353\pi\)
0.161542 + 0.986866i \(0.448353\pi\)
\(788\) 1.23446e13 1.14054
\(789\) 1.02522e13 0.941822
\(790\) 7.67593e12 0.701147
\(791\) 1.50593e12i 0.136776i
\(792\) −5.83980e11 −0.0527394
\(793\) 6.07001e12i 0.545080i
\(794\) 3.98657e12i 0.355965i
\(795\) 2.07400e13i 1.84143i
\(796\) 4.96393e12 0.438245
\(797\) 1.52083e13i 1.33512i 0.744558 + 0.667558i \(0.232660\pi\)
−0.744558 + 0.667558i \(0.767340\pi\)
\(798\) 2.37675e10i 0.00207478i
\(799\) 5.29641e11 0.0459749
\(800\) 1.68520e13i 1.45461i
\(801\) 8.44644e12i 0.724982i
\(802\) 2.39323e12i 0.204268i
\(803\) 2.09188e12 0.177548
\(804\) 5.20182e12i 0.439039i
\(805\) −4.89238e11 −0.0410619
\(806\) 2.86774e12 0.239349
\(807\) −2.04277e13 −1.69547
\(808\) 4.44604e12 0.366963
\(809\) 6.02802e12i 0.494773i 0.968917 + 0.247387i \(0.0795718\pi\)
−0.968917 + 0.247387i \(0.920428\pi\)
\(810\) 9.78982e12i 0.799083i
\(811\) 1.28327e13 1.04166 0.520830 0.853661i \(-0.325623\pi\)
0.520830 + 0.853661i \(0.325623\pi\)
\(812\) 2.55103e12 1.68525e12i 0.205927 0.136039i
\(813\) −8.60872e12 −0.691085
\(814\) 8.24715e11i 0.0658406i
\(815\) 1.70531e13i 1.35392i
\(816\) 2.13925e12 0.168910
\(817\) −2.96457e11 −0.0232789
\(818\) 3.78188e12 0.295337
\(819\) 7.69822e11 0.0597878
\(820\) 2.38906e13i 1.84529i
\(821\) 7.11839e11 0.0546812 0.0273406 0.999626i \(-0.491296\pi\)
0.0273406 + 0.999626i \(0.491296\pi\)
\(822\) 7.06749e12i 0.539936i
\(823\) 1.13470e12i 0.0862146i −0.999070 0.0431073i \(-0.986274\pi\)
0.999070 0.0431073i \(-0.0137257\pi\)
\(824\) 1.72202e13i 1.30126i
\(825\) −3.58077e12 −0.269113
\(826\) 3.69451e11i 0.0276151i
\(827\) 2.22368e12i 0.165310i −0.996578 0.0826548i \(-0.973660\pi\)
0.996578 0.0826548i \(-0.0263399\pi\)
\(828\) −4.88615e11 −0.0361268
\(829\) 1.53409e12i 0.112812i −0.998408 0.0564062i \(-0.982036\pi\)
0.998408 0.0564062i \(-0.0179642\pi\)
\(830\) 2.70815e12i 0.198071i
\(831\) 1.17592e13i 0.855408i
\(832\) 8.78805e11 0.0635825
\(833\) 3.25336e12i 0.234115i
\(834\) −1.12706e13 −0.806677
\(835\) 2.02399e12 0.144085
\(836\) 2.45786e10 0.00174032
\(837\) −1.26875e13 −0.893537
\(838\) 5.46439e12i 0.382775i
\(839\) 4.49145e12i 0.312938i −0.987683 0.156469i \(-0.949989\pi\)
0.987683 0.156469i \(-0.0500111\pi\)
\(840\) −6.09872e12 −0.422651
\(841\) 5.69197e12 1.33439e13i 0.392356 0.919813i
\(842\) −7.35802e12 −0.504495
\(843\) 1.06370e13i 0.725429i
\(844\) 9.70823e12i 0.658566i
\(845\) −1.95044e13 −1.31606
\(846\) −5.28511e11 −0.0354722
\(847\) −4.31991e12 −0.288403
\(848\) −7.72012e12 −0.512675
\(849\) 9.63194e12i 0.636252i
\(850\) −2.38728e12 −0.156862
\(851\) 1.51372e12i 0.0989375i
\(852\) 2.55224e13i 1.65937i
\(853\) 3.03833e13i 1.96501i 0.186248 + 0.982503i \(0.440367\pi\)
−0.186248 + 0.982503i \(0.559633\pi\)
\(854\) 2.43283e12 0.156513
\(855\) 1.74376e11i 0.0111594i
\(856\) 2.35700e12i 0.150047i
\(857\) 1.70562e13 1.08011 0.540055 0.841630i \(-0.318403\pi\)
0.540055 + 0.841630i \(0.318403\pi\)
\(858\) 4.68164e11i 0.0294921i
\(859\) 6.48723e12i 0.406528i 0.979124 + 0.203264i \(0.0651549\pi\)
−0.979124 + 0.203264i \(0.934845\pi\)
\(860\) 3.46772e13i 2.16173i
\(861\) −8.05072e12 −0.499253
\(862\) 3.91846e12i 0.241731i
\(863\) −1.74624e13 −1.07166 −0.535828 0.844327i \(-0.680001\pi\)
−0.535828 + 0.844327i \(0.680001\pi\)
\(864\) 9.74786e12 0.595110
\(865\) −1.04061e13 −0.631996
\(866\) 6.53333e12 0.394734
\(867\) 1.89805e13i 1.14083i
\(868\) 5.93456e12i 0.354854i
\(869\) −2.67492e12 −0.159119
\(870\) −1.10066e13 + 7.27115e12i −0.651354 + 0.430295i
\(871\) −3.01277e12 −0.177371
\(872\) 2.82833e12i 0.165656i
\(873\) 1.95954e12i 0.114180i
\(874\) −8.73716e9 −0.000506488
\(875\) −4.20802e12 −0.242684
\(876\) 2.18184e13 1.25186
\(877\) −1.33654e13 −0.762931 −0.381466 0.924383i \(-0.624581\pi\)
−0.381466 + 0.924383i \(0.624581\pi\)
\(878\) 5.63086e12i 0.319779i
\(879\) −1.71331e13 −0.968026
\(880\) 2.21035e12i 0.124248i
\(881\) 1.79363e13i 1.00310i −0.865130 0.501548i \(-0.832764\pi\)
0.865130 0.501548i \(-0.167236\pi\)
\(882\) 3.24642e12i 0.180633i
\(883\) 8.77653e12 0.485847 0.242924 0.970045i \(-0.421894\pi\)
0.242924 + 0.970045i \(0.421894\pi\)
\(884\) 1.61157e12i 0.0887595i
\(885\) 8.23042e12i 0.451001i
\(886\) −7.75271e12 −0.422670
\(887\) 8.66694e12i 0.470121i −0.971981 0.235060i \(-0.924471\pi\)
0.971981 0.235060i \(-0.0755288\pi\)
\(888\) 1.88696e13i 1.01837i
\(889\) 3.00403e12i 0.161305i
\(890\) −1.76669e13 −0.943854
\(891\) 3.41157e12i 0.181345i
\(892\) −1.35375e13 −0.715970
\(893\) 4.87960e10 0.00256775
\(894\) 1.58345e13 0.829061
\(895\) 5.07140e13 2.64195
\(896\) 5.79482e12i 0.300368i
\(897\) 8.59287e11i 0.0443172i
\(898\) 1.47628e13 0.757572
\(899\) −1.55212e13 2.34950e13i −0.792513 1.19966i
\(900\) −1.22999e13 −0.624900
\(901\) 4.81852e12i 0.243586i
\(902\) 1.61243e12i 0.0811056i
\(903\) −1.16856e13 −0.584867
\(904\) −6.90094e12 −0.343677
\(905\) 6.39786e12 0.317041
\(906\) −1.29308e13 −0.637600
\(907\) 1.23089e13i 0.603928i −0.953319 0.301964i \(-0.902358\pi\)
0.953319 0.301964i \(-0.0976423\pi\)
\(908\) 2.32540e13 1.13530
\(909\) 5.01085e12i 0.243430i
\(910\) 1.61019e12i 0.0778377i
\(911\) 1.40935e12i 0.0677932i 0.999425 + 0.0338966i \(0.0107917\pi\)
−0.999425 + 0.0338966i \(0.989208\pi\)
\(912\) 1.97090e11 0.00943384
\(913\) 9.43742e11i 0.0449505i
\(914\) 9.54845e12i 0.452559i
\(915\) 5.41972e13 2.55612
\(916\) 1.70700e13i 0.801133i
\(917\) 8.70565e12i 0.406574i
\(918\) 1.38090e12i 0.0641755i
\(919\) 2.93611e13 1.35785 0.678926 0.734206i \(-0.262446\pi\)
0.678926 + 0.734206i \(0.262446\pi\)
\(920\) 2.24194e12i 0.103176i
\(921\) −2.36326e13 −1.08229
\(922\) 1.73994e13 0.792949
\(923\) 1.47819e13 0.670383
\(924\) 9.68828e11 0.0437243
\(925\) 3.81048e13i 1.71136i
\(926\) 9.28775e12i 0.415108i
\(927\) 1.94078e13 0.863211
\(928\) 1.19250e13 + 1.80513e13i 0.527826 + 0.798991i
\(929\) 3.19310e13 1.40651 0.703253 0.710940i \(-0.251730\pi\)
0.703253 + 0.710940i \(0.251730\pi\)
\(930\) 2.56051e13i 1.12242i
\(931\) 2.99733e11i 0.0130756i
\(932\) −2.56197e13 −1.11225
\(933\) 1.46320e12 0.0632175
\(934\) −9.49802e12 −0.408387
\(935\) 1.37959e12 0.0590335
\(936\) 3.52773e12i 0.150229i
\(937\) 8.05622e12 0.341431 0.170716 0.985320i \(-0.445392\pi\)
0.170716 + 0.985320i \(0.445392\pi\)
\(938\) 1.20750e12i 0.0509301i
\(939\) 4.08264e13i 1.71374i
\(940\) 5.70777e12i 0.238447i
\(941\) −6.01825e12 −0.250217 −0.125109 0.992143i \(-0.539928\pi\)
−0.125109 + 0.992143i \(0.539928\pi\)
\(942\) 7.46497e12i 0.308886i
\(943\) 2.95952e12i 0.121876i
\(944\) −3.06364e12 −0.125564
\(945\) 7.12384e12i 0.290583i
\(946\) 2.34044e12i 0.0950140i
\(947\) 3.33563e13i 1.34773i 0.738855 + 0.673865i \(0.235367\pi\)
−0.738855 + 0.673865i \(0.764633\pi\)
\(948\) −2.78996e13 −1.12192
\(949\) 1.26367e13i 0.505750i
\(950\) −2.19941e11 −0.00876091
\(951\) 2.09855e13 0.831969
\(952\) 1.41692e12 0.0559086
\(953\) −2.09184e12 −0.0821505 −0.0410753 0.999156i \(-0.513078\pi\)
−0.0410753 + 0.999156i \(0.513078\pi\)
\(954\) 4.80825e12i 0.187940i
\(955\) 7.76315e13i 3.02011i
\(956\) −2.13027e13 −0.824848
\(957\) 3.83560e12 2.53386e12i 0.147819 0.0976516i
\(958\) −1.12888e13 −0.433014
\(959\) 8.47079e12i 0.323400i
\(960\) 7.84657e12i 0.298167i
\(961\) −2.82178e13 −1.06725
\(962\) 4.98196e12 0.187548
\(963\) 2.65643e12 0.0995361
\(964\) −1.99470e13 −0.743927
\(965\) 2.17822e13i 0.808590i
\(966\) −3.44398e11 −0.0127252
\(967\) 2.03974e11i 0.00750164i −0.999993 0.00375082i \(-0.998806\pi\)
0.999993 0.00375082i \(-0.00119393\pi\)
\(968\) 1.97961e13i 0.724670i
\(969\) 1.23014e11i 0.00448227i
\(970\) −4.09865e12 −0.148651
\(971\) 1.90929e12i 0.0689264i 0.999406 + 0.0344632i \(0.0109721\pi\)
−0.999406 + 0.0344632i \(0.989028\pi\)
\(972\) 2.10943e13i 0.757995i
\(973\) 1.35085e13 0.483168
\(974\) 1.12275e13i 0.399732i
\(975\) 2.16309e13i 0.766572i
\(976\) 2.01740e13i 0.711653i
\(977\) −4.87823e13 −1.71292 −0.856460 0.516213i \(-0.827341\pi\)
−0.856460 + 0.516213i \(0.827341\pi\)
\(978\) 1.20045e13i 0.419584i
\(979\) 6.15658e12 0.214199
\(980\) −3.50604e13 −1.21423
\(981\) −3.18764e12 −0.109890
\(982\) 3.32623e12 0.114143
\(983\) 3.61858e13i 1.23608i 0.786146 + 0.618041i \(0.212073\pi\)
−0.786146 + 0.618041i \(0.787927\pi\)
\(984\) 3.68926e13i 1.25447i
\(985\) 6.38373e13 2.16078
\(986\) 2.55717e12 1.68931e12i 0.0861616 0.0569197i
\(987\) 1.92342e12 0.0645131
\(988\) 1.48475e11i 0.00495732i
\(989\) 4.29574e12i 0.142776i
\(990\) −1.37665e12 −0.0455475
\(991\) −1.83077e13 −0.602979 −0.301489 0.953470i \(-0.597484\pi\)
−0.301489 + 0.953470i \(0.597484\pi\)
\(992\) 4.19934e13 1.37682
\(993\) 2.62818e13 0.857795
\(994\) 5.92452e12i 0.192493i
\(995\) 2.56698e13 0.830269
\(996\) 9.84329e12i 0.316937i
\(997\) 5.07766e13i 1.62755i −0.581178 0.813777i \(-0.697408\pi\)
0.581178 0.813777i \(-0.302592\pi\)
\(998\) 1.88968e13i 0.602977i
\(999\) −2.20413e13 −0.700154
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 29.10.b.a.28.10 22
29.28 even 2 inner 29.10.b.a.28.13 yes 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.10.b.a.28.10 22 1.1 even 1 trivial
29.10.b.a.28.13 yes 22 29.28 even 2 inner