Properties

Label 84.12.k.b.5.9
Level $84$
Weight $12$
Character 84.5
Analytic conductor $64.541$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [84,12,Mod(5,84)]
 
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, 3, 5]))
 
N = Newforms(chi, 12, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("84.5");
 
S:= CuspForms(chi, 12);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 84.k (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: \(64.5408271670\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(28\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 5.9
Character \(\chi\) \(=\) 84.5
Dual form 84.12.k.b.17.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-261.265 + 329.981i) q^{3} +(-3914.60 + 6780.29i) q^{5} +(-44460.5 - 768.569i) q^{7} +(-40628.4 - 172425. i) q^{9} +O(q^{10})\) \(q+(-261.265 + 329.981i) q^{3} +(-3914.60 + 6780.29i) q^{5} +(-44460.5 - 768.569i) q^{7} +(-40628.4 - 172425. i) q^{9} +(-650650. + 375653. i) q^{11} +1.53606e6i q^{13} +(-1.21462e6 - 3.06320e6i) q^{15} +(-1.13310e6 - 1.96259e6i) q^{17} +(-1.29343e7 - 7.46761e6i) q^{19} +(1.18696e7 - 1.44703e7i) q^{21} +(-4.98810e7 - 2.87988e7i) q^{23} +(-6.23417e6 - 1.07979e7i) q^{25} +(6.75118e7 + 3.16420e7i) q^{27} +1.09792e8i q^{29} +(-1.32191e8 + 7.63203e7i) q^{31} +(4.60334e7 - 3.12847e8i) q^{33} +(1.79256e8 - 2.98446e8i) q^{35} +(-3.09464e8 + 5.36007e8i) q^{37} +(-5.06872e8 - 4.01319e8i) q^{39} -5.72560e8 q^{41} +4.55328e8 q^{43} +(1.32814e9 + 3.99503e8i) q^{45} +(2.65090e8 - 4.59150e8i) q^{47} +(1.97615e9 + 6.83419e7i) q^{49} +(9.43656e8 + 1.38853e8i) q^{51} +(-3.33336e9 + 1.92452e9i) q^{53} -5.88213e9i q^{55} +(5.84344e9 - 2.31705e9i) q^{57} +(3.62559e9 + 6.27971e9i) q^{59} +(3.36594e9 + 1.94333e9i) q^{61} +(1.67384e9 + 7.69733e9i) q^{63} +(-1.04149e10 - 6.01307e9i) q^{65} +(3.95833e8 + 6.85604e8i) q^{67} +(2.25352e10 - 8.93569e9i) q^{69} +2.32309e10i q^{71} +(2.11716e10 - 1.22234e10i) q^{73} +(5.19187e9 + 7.63950e8i) q^{75} +(2.92169e10 - 1.62017e10i) q^{77} +(1.91219e10 - 3.31201e10i) q^{79} +(-2.80797e10 + 1.40107e10i) q^{81} -2.31403e10 q^{83} +1.77425e10 q^{85} +(-3.62292e10 - 2.86847e10i) q^{87} +(-5.17781e9 + 8.96823e9i) q^{89} +(1.18057e9 - 6.82941e10i) q^{91} +(9.35247e9 - 6.35602e10i) q^{93} +(1.01265e11 - 5.84655e10i) q^{95} -2.68038e10i q^{97} +(9.12069e10 + 9.69262e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q - 729 q^{3} - 27194 q^{7} - 172347 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q - 729 q^{3} - 27194 q^{7} - 172347 q^{9} - 4853058 q^{15} + 28700520 q^{19} - 11325429 q^{21} - 316601194 q^{25} - 1368416388 q^{31} + 40874949 q^{33} - 87435712 q^{37} + 1177474410 q^{39} - 3055078348 q^{43} + 4109921793 q^{45} - 742582522 q^{49} - 694793715 q^{51} + 14605100370 q^{57} + 72584834058 q^{61} - 7310837811 q^{63} + 6131679148 q^{67} - 74402605464 q^{73} - 161115157854 q^{75} + 52181713528 q^{79} + 44948282337 q^{81} + 4658488716 q^{85} + 243101263104 q^{87} - 85311757146 q^{91} - 256628211777 q^{93} + 157345775874 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(29\) \(43\) \(73\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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
\(3\) −261.265 + 329.981i −0.620746 + 0.784012i
\(4\) 0 0
\(5\) −3914.60 + 6780.29i −0.560212 + 0.970316i 0.437265 + 0.899333i \(0.355947\pi\)
−0.997477 + 0.0709836i \(0.977386\pi\)
\(6\) 0 0
\(7\) −44460.5 768.569i −0.999851 0.0172840i
\(8\) 0 0
\(9\) −40628.4 172425.i −0.229349 0.973344i
\(10\) 0 0
\(11\) −650650. + 375653.i −1.21811 + 0.703278i −0.964514 0.264031i \(-0.914948\pi\)
−0.253599 + 0.967309i \(0.581615\pi\)
\(12\) 0 0
\(13\) 1.53606e6i 1.14741i 0.819060 + 0.573707i \(0.194495\pi\)
−0.819060 + 0.573707i \(0.805505\pi\)
\(14\) 0 0
\(15\) −1.21462e6 3.06320e6i −0.412990 1.04153i
\(16\) 0 0
\(17\) −1.13310e6 1.96259e6i −0.193553 0.335243i 0.752872 0.658166i \(-0.228668\pi\)
−0.946425 + 0.322924i \(0.895334\pi\)
\(18\) 0 0
\(19\) −1.29343e7 7.46761e6i −1.19839 0.691890i −0.238192 0.971218i \(-0.576555\pi\)
−0.960196 + 0.279328i \(0.909888\pi\)
\(20\) 0 0
\(21\) 1.18696e7 1.44703e7i 0.634204 0.773166i
\(22\) 0 0
\(23\) −4.98810e7 2.87988e7i −1.61597 0.932978i −0.987949 0.154778i \(-0.950534\pi\)
−0.628016 0.778200i \(-0.716133\pi\)
\(24\) 0 0
\(25\) −6.23417e6 1.07979e7i −0.127676 0.221141i
\(26\) 0 0
\(27\) 6.75118e7 + 3.16420e7i 0.905481 + 0.424387i
\(28\) 0 0
\(29\) 1.09792e8i 0.993987i 0.867754 + 0.496993i \(0.165563\pi\)
−0.867754 + 0.496993i \(0.834437\pi\)
\(30\) 0 0
\(31\) −1.32191e8 + 7.63203e7i −0.829299 + 0.478796i −0.853613 0.520908i \(-0.825593\pi\)
0.0243135 + 0.999704i \(0.492260\pi\)
\(32\) 0 0
\(33\) 4.60334e7 3.12847e8i 0.204761 1.39157i
\(34\) 0 0
\(35\) 1.79256e8 2.98446e8i 0.576900 0.960489i
\(36\) 0 0
\(37\) −3.09464e8 + 5.36007e8i −0.733670 + 1.27075i 0.221635 + 0.975130i \(0.428861\pi\)
−0.955304 + 0.295624i \(0.904473\pi\)
\(38\) 0 0
\(39\) −5.06872e8 4.01319e8i −0.899586 0.712253i
\(40\) 0 0
\(41\) −5.72560e8 −0.771809 −0.385905 0.922539i \(-0.626111\pi\)
−0.385905 + 0.922539i \(0.626111\pi\)
\(42\) 0 0
\(43\) 4.55328e8 0.472333 0.236166 0.971713i \(-0.424109\pi\)
0.236166 + 0.971713i \(0.424109\pi\)
\(44\) 0 0
\(45\) 1.32814e9 + 3.99503e8i 1.07294 + 0.322739i
\(46\) 0 0
\(47\) 2.65090e8 4.59150e8i 0.168599 0.292022i −0.769328 0.638854i \(-0.779409\pi\)
0.937928 + 0.346831i \(0.112742\pi\)
\(48\) 0 0
\(49\) 1.97615e9 + 6.83419e7i 0.999403 + 0.0345628i
\(50\) 0 0
\(51\) 9.43656e8 + 1.38853e8i 0.382981 + 0.0563532i
\(52\) 0 0
\(53\) −3.33336e9 + 1.92452e9i −1.09488 + 0.632128i −0.934871 0.354988i \(-0.884485\pi\)
−0.160006 + 0.987116i \(0.551151\pi\)
\(54\) 0 0
\(55\) 5.88213e9i 1.57594i
\(56\) 0 0
\(57\) 5.84344e9 2.31705e9i 1.28634 0.510063i
\(58\) 0 0
\(59\) 3.62559e9 + 6.27971e9i 0.660227 + 1.14355i 0.980556 + 0.196240i \(0.0628731\pi\)
−0.320329 + 0.947306i \(0.603794\pi\)
\(60\) 0 0
\(61\) 3.36594e9 + 1.94333e9i 0.510261 + 0.294599i 0.732941 0.680292i \(-0.238147\pi\)
−0.222680 + 0.974892i \(0.571480\pi\)
\(62\) 0 0
\(63\) 1.67384e9 + 7.69733e9i 0.212491 + 0.977163i
\(64\) 0 0
\(65\) −1.04149e10 6.01307e9i −1.11335 0.642796i
\(66\) 0 0
\(67\) 3.95833e8 + 6.85604e8i 0.0358180 + 0.0620386i 0.883379 0.468660i \(-0.155263\pi\)
−0.847561 + 0.530698i \(0.821930\pi\)
\(68\) 0 0
\(69\) 2.25352e10 8.93569e9i 1.73457 0.687794i
\(70\) 0 0
\(71\) 2.32309e10i 1.52808i 0.645171 + 0.764039i \(0.276786\pi\)
−0.645171 + 0.764039i \(0.723214\pi\)
\(72\) 0 0
\(73\) 2.11716e10 1.22234e10i 1.19530 0.690109i 0.235799 0.971802i \(-0.424229\pi\)
0.959504 + 0.281693i \(0.0908961\pi\)
\(74\) 0 0
\(75\) 5.19187e9 + 7.63950e8i 0.252631 + 0.0371730i
\(76\) 0 0
\(77\) 2.92169e10 1.62017e10i 1.23009 0.682119i
\(78\) 0 0
\(79\) 1.91219e10 3.31201e10i 0.699169 1.21100i −0.269586 0.962976i \(-0.586887\pi\)
0.968755 0.248020i \(-0.0797798\pi\)
\(80\) 0 0
\(81\) −2.80797e10 + 1.40107e10i −0.894798 + 0.446471i
\(82\) 0 0
\(83\) −2.31403e10 −0.644822 −0.322411 0.946600i \(-0.604493\pi\)
−0.322411 + 0.946600i \(0.604493\pi\)
\(84\) 0 0
\(85\) 1.77425e10 0.433722
\(86\) 0 0
\(87\) −3.62292e10 2.86847e10i −0.779297 0.617013i
\(88\) 0 0
\(89\) −5.17781e9 + 8.96823e9i −0.0982881 + 0.170240i −0.910976 0.412459i \(-0.864670\pi\)
0.812688 + 0.582699i \(0.198003\pi\)
\(90\) 0 0
\(91\) 1.18057e9 6.82941e10i 0.0198319 1.14724i
\(92\) 0 0
\(93\) 9.35247e9 6.35602e10i 0.139402 0.947391i
\(94\) 0 0
\(95\) 1.01265e11 5.84655e10i 1.34270 0.775210i
\(96\) 0 0
\(97\) 2.68038e10i 0.316922i −0.987365 0.158461i \(-0.949347\pi\)
0.987365 0.158461i \(-0.0506532\pi\)
\(98\) 0 0
\(99\) 9.12069e10 + 9.69262e10i 0.963905 + 1.02435i
\(100\) 0 0
\(101\) −9.56936e9 1.65746e10i −0.0905974 0.156919i 0.817165 0.576403i \(-0.195544\pi\)
−0.907763 + 0.419484i \(0.862211\pi\)
\(102\) 0 0
\(103\) 6.09296e10 + 3.51777e10i 0.517874 + 0.298994i 0.736064 0.676912i \(-0.236682\pi\)
−0.218191 + 0.975906i \(0.570015\pi\)
\(104\) 0 0
\(105\) 5.16484e10 + 1.37125e11i 0.394926 + 1.04852i
\(106\) 0 0
\(107\) 2.24209e11 + 1.29447e11i 1.54541 + 0.892241i 0.998483 + 0.0550581i \(0.0175344\pi\)
0.546923 + 0.837183i \(0.315799\pi\)
\(108\) 0 0
\(109\) 7.10453e10 + 1.23054e11i 0.442272 + 0.766038i 0.997858 0.0654214i \(-0.0208391\pi\)
−0.555585 + 0.831459i \(0.687506\pi\)
\(110\) 0 0
\(111\) −9.60204e10 2.42157e11i −0.540863 1.36402i
\(112\) 0 0
\(113\) 2.71376e11i 1.38561i 0.721126 + 0.692804i \(0.243625\pi\)
−0.721126 + 0.692804i \(0.756375\pi\)
\(114\) 0 0
\(115\) 3.90529e11 2.25472e11i 1.81057 1.04533i
\(116\) 0 0
\(117\) 2.64856e11 6.24078e10i 1.11683 0.263158i
\(118\) 0 0
\(119\) 4.88698e10 + 8.81284e10i 0.187729 + 0.338538i
\(120\) 0 0
\(121\) 1.39575e11 2.41750e11i 0.489200 0.847320i
\(122\) 0 0
\(123\) 1.49590e11 1.88934e11i 0.479098 0.605108i
\(124\) 0 0
\(125\) −2.84668e11 −0.834323
\(126\) 0 0
\(127\) −6.47094e11 −1.73799 −0.868994 0.494823i \(-0.835233\pi\)
−0.868994 + 0.494823i \(0.835233\pi\)
\(128\) 0 0
\(129\) −1.18961e11 + 1.50250e11i −0.293199 + 0.370314i
\(130\) 0 0
\(131\) 2.04238e11 3.53751e11i 0.462535 0.801135i −0.536551 0.843868i \(-0.680273\pi\)
0.999087 + 0.0427331i \(0.0136065\pi\)
\(132\) 0 0
\(133\) 5.69325e11 + 3.41955e11i 1.18625 + 0.712499i
\(134\) 0 0
\(135\) −4.78824e11 + 3.33884e11i −0.919052 + 0.640855i
\(136\) 0 0
\(137\) −5.62000e11 + 3.24471e11i −0.994885 + 0.574397i −0.906731 0.421710i \(-0.861430\pi\)
−0.0881541 + 0.996107i \(0.528097\pi\)
\(138\) 0 0
\(139\) 2.15022e11i 0.351480i −0.984437 0.175740i \(-0.943768\pi\)
0.984437 0.175740i \(-0.0562318\pi\)
\(140\) 0 0
\(141\) 8.22521e10 + 2.07434e11i 0.124292 + 0.313455i
\(142\) 0 0
\(143\) −5.77026e11 9.99439e11i −0.806952 1.39768i
\(144\) 0 0
\(145\) −7.44420e11 4.29791e11i −0.964481 0.556844i
\(146\) 0 0
\(147\) −5.38849e11 + 6.34236e11i −0.647473 + 0.762089i
\(148\) 0 0
\(149\) −1.06652e11 6.15753e10i −0.118972 0.0686882i 0.439333 0.898324i \(-0.355215\pi\)
−0.558305 + 0.829636i \(0.688548\pi\)
\(150\) 0 0
\(151\) −5.05755e10 8.75993e10i −0.0524284 0.0908087i 0.838620 0.544717i \(-0.183363\pi\)
−0.891049 + 0.453908i \(0.850029\pi\)
\(152\) 0 0
\(153\) −2.92363e11 + 2.75111e11i −0.281916 + 0.265281i
\(154\) 0 0
\(155\) 1.19505e12i 1.07291i
\(156\) 0 0
\(157\) −1.87323e12 + 1.08151e12i −1.56726 + 0.904861i −0.570778 + 0.821104i \(0.693358\pi\)
−0.996486 + 0.0837566i \(0.973308\pi\)
\(158\) 0 0
\(159\) 2.35835e11 1.60276e12i 0.184045 1.25079i
\(160\) 0 0
\(161\) 2.19560e12 + 1.31875e12i 1.59960 + 0.960769i
\(162\) 0 0
\(163\) 1.53517e11 2.65900e11i 0.104502 0.181003i −0.809032 0.587764i \(-0.800008\pi\)
0.913535 + 0.406761i \(0.133342\pi\)
\(164\) 0 0
\(165\) 1.94099e12 + 1.53679e12i 1.23556 + 0.978259i
\(166\) 0 0
\(167\) −1.44797e12 −0.862620 −0.431310 0.902204i \(-0.641948\pi\)
−0.431310 + 0.902204i \(0.641948\pi\)
\(168\) 0 0
\(169\) −5.67326e11 −0.316560
\(170\) 0 0
\(171\) −7.62103e11 + 2.53359e12i −0.398598 + 1.32513i
\(172\) 0 0
\(173\) −1.89441e11 + 3.28121e11i −0.0929436 + 0.160983i −0.908748 0.417344i \(-0.862961\pi\)
0.815805 + 0.578327i \(0.196294\pi\)
\(174\) 0 0
\(175\) 2.68875e11 + 4.84871e11i 0.123834 + 0.223315i
\(176\) 0 0
\(177\) −3.01943e12 4.44289e11i −1.30639 0.192226i
\(178\) 0 0
\(179\) −3.35250e12 + 1.93557e12i −1.36357 + 0.787258i −0.990097 0.140383i \(-0.955166\pi\)
−0.373473 + 0.927641i \(0.621833\pi\)
\(180\) 0 0
\(181\) 2.58201e11i 0.0987931i 0.998779 + 0.0493965i \(0.0157298\pi\)
−0.998779 + 0.0493965i \(0.984270\pi\)
\(182\) 0 0
\(183\) −1.52066e12 + 6.02975e11i −0.547712 + 0.217179i
\(184\) 0 0
\(185\) −2.42286e12 4.19651e12i −0.822022 1.42378i
\(186\) 0 0
\(187\) 1.47450e12 + 8.51305e11i 0.471538 + 0.272243i
\(188\) 0 0
\(189\) −2.97729e12 1.45870e12i −0.898010 0.439974i
\(190\) 0 0
\(191\) 3.10868e12 + 1.79480e12i 0.884896 + 0.510895i 0.872269 0.489026i \(-0.162648\pi\)
0.0126261 + 0.999920i \(0.495981\pi\)
\(192\) 0 0
\(193\) 1.03325e10 + 1.78964e10i 0.00277742 + 0.00481063i 0.867411 0.497593i \(-0.165783\pi\)
−0.864633 + 0.502403i \(0.832449\pi\)
\(194\) 0 0
\(195\) 4.70526e12 1.86573e12i 1.19507 0.473870i
\(196\) 0 0
\(197\) 1.88985e12i 0.453799i 0.973918 + 0.226900i \(0.0728589\pi\)
−0.973918 + 0.226900i \(0.927141\pi\)
\(198\) 0 0
\(199\) −3.13197e12 + 1.80825e12i −0.711420 + 0.410739i −0.811587 0.584232i \(-0.801396\pi\)
0.100167 + 0.994971i \(0.468062\pi\)
\(200\) 0 0
\(201\) −3.29654e11 4.85064e10i −0.0708728 0.0104285i
\(202\) 0 0
\(203\) 8.43825e10 4.88139e12i 0.0171800 0.993838i
\(204\) 0 0
\(205\) 2.24135e12 3.88213e12i 0.432377 0.748899i
\(206\) 0 0
\(207\) −2.93905e12 + 9.77079e12i −0.537489 + 1.78687i
\(208\) 0 0
\(209\) 1.12209e13 1.94636
\(210\) 0 0
\(211\) −9.86782e11 −0.162431 −0.0812153 0.996697i \(-0.525880\pi\)
−0.0812153 + 0.996697i \(0.525880\pi\)
\(212\) 0 0
\(213\) −7.66577e12 6.06942e12i −1.19803 0.948548i
\(214\) 0 0
\(215\) −1.78243e12 + 3.08726e12i −0.264607 + 0.458312i
\(216\) 0 0
\(217\) 5.93592e12 3.29164e12i 0.837451 0.464391i
\(218\) 0 0
\(219\) −1.49789e12 + 1.01798e13i −0.200926 + 1.36551i
\(220\) 0 0
\(221\) 3.01465e12 1.74051e12i 0.384663 0.222085i
\(222\) 0 0
\(223\) 1.51241e13i 1.83651i −0.395995 0.918253i \(-0.629600\pi\)
0.395995 0.918253i \(-0.370400\pi\)
\(224\) 0 0
\(225\) −1.60854e12 + 1.51363e12i −0.185964 + 0.174991i
\(226\) 0 0
\(227\) 7.95720e11 + 1.37823e12i 0.0876230 + 0.151767i 0.906506 0.422193i \(-0.138740\pi\)
−0.818883 + 0.573961i \(0.805406\pi\)
\(228\) 0 0
\(229\) −1.17063e13 6.75866e12i −1.22836 0.709194i −0.261673 0.965156i \(-0.584274\pi\)
−0.966687 + 0.255962i \(0.917608\pi\)
\(230\) 0 0
\(231\) −2.28711e12 + 1.38740e13i −0.228782 + 1.38783i
\(232\) 0 0
\(233\) 1.15987e12 + 6.69654e11i 0.110651 + 0.0638841i 0.554304 0.832314i \(-0.312985\pi\)
−0.443653 + 0.896198i \(0.646318\pi\)
\(234\) 0 0
\(235\) 2.07545e12 + 3.59478e12i 0.188903 + 0.327189i
\(236\) 0 0
\(237\) 5.93314e12 + 1.49630e13i 0.515429 + 1.29988i
\(238\) 0 0
\(239\) 1.95527e13i 1.62187i −0.585133 0.810937i \(-0.698958\pi\)
0.585133 0.810937i \(-0.301042\pi\)
\(240\) 0 0
\(241\) 1.34554e13 7.76848e12i 1.06611 0.615520i 0.138996 0.990293i \(-0.455613\pi\)
0.927117 + 0.374773i \(0.122279\pi\)
\(242\) 0 0
\(243\) 2.71296e12 1.29263e13i 0.205404 0.978677i
\(244\) 0 0
\(245\) −8.19920e12 + 1.31313e13i −0.593414 + 0.950374i
\(246\) 0 0
\(247\) 1.14707e13 1.98679e13i 0.793884 1.37505i
\(248\) 0 0
\(249\) 6.04575e12 7.63588e12i 0.400271 0.505548i
\(250\) 0 0
\(251\) 7.50746e11 0.0475650 0.0237825 0.999717i \(-0.492429\pi\)
0.0237825 + 0.999717i \(0.492429\pi\)
\(252\) 0 0
\(253\) 4.32735e13 2.62457
\(254\) 0 0
\(255\) −4.63550e12 + 5.85471e12i −0.269231 + 0.340043i
\(256\) 0 0
\(257\) −8.73516e12 + 1.51297e13i −0.486003 + 0.841782i −0.999871 0.0160879i \(-0.994879\pi\)
0.513868 + 0.857869i \(0.328212\pi\)
\(258\) 0 0
\(259\) 1.41709e13 2.35933e13i 0.755524 1.25788i
\(260\) 0 0
\(261\) 1.89308e13 4.46067e12i 0.967491 0.227970i
\(262\) 0 0
\(263\) −3.34132e13 + 1.92911e13i −1.63742 + 0.945367i −0.655708 + 0.755014i \(0.727630\pi\)
−0.981716 + 0.190353i \(0.939037\pi\)
\(264\) 0 0
\(265\) 3.01349e13i 1.41650i
\(266\) 0 0
\(267\) −1.60657e12 4.05166e12i −0.0724582 0.182735i
\(268\) 0 0
\(269\) 1.63697e13 + 2.83532e13i 0.708604 + 1.22734i 0.965375 + 0.260866i \(0.0840082\pi\)
−0.256771 + 0.966472i \(0.582658\pi\)
\(270\) 0 0
\(271\) −6.95405e12 4.01492e12i −0.289006 0.166858i 0.348488 0.937313i \(-0.386695\pi\)
−0.637493 + 0.770456i \(0.720029\pi\)
\(272\) 0 0
\(273\) 2.22273e13 + 1.82324e13i 0.887141 + 0.727695i
\(274\) 0 0
\(275\) 8.11252e12 + 4.68377e12i 0.311047 + 0.179583i
\(276\) 0 0
\(277\) 1.06811e13 + 1.85002e13i 0.393529 + 0.681613i 0.992912 0.118850i \(-0.0379207\pi\)
−0.599383 + 0.800462i \(0.704587\pi\)
\(278\) 0 0
\(279\) 1.85302e13 + 1.96922e13i 0.656232 + 0.697382i
\(280\) 0 0
\(281\) 2.08162e13i 0.708789i −0.935096 0.354394i \(-0.884687\pi\)
0.935096 0.354394i \(-0.115313\pi\)
\(282\) 0 0
\(283\) 7.91344e12 4.56883e12i 0.259143 0.149617i −0.364800 0.931086i \(-0.618863\pi\)
0.623944 + 0.781469i \(0.285529\pi\)
\(284\) 0 0
\(285\) −7.16450e12 + 4.86906e13i −0.225704 + 1.53390i
\(286\) 0 0
\(287\) 2.54563e13 + 4.40052e11i 0.771694 + 0.0133399i
\(288\) 0 0
\(289\) 1.45681e13 2.52327e13i 0.425075 0.736251i
\(290\) 0 0
\(291\) 8.84476e12 + 7.00289e12i 0.248470 + 0.196728i
\(292\) 0 0
\(293\) 3.99193e12 0.107997 0.0539984 0.998541i \(-0.482803\pi\)
0.0539984 + 0.998541i \(0.482803\pi\)
\(294\) 0 0
\(295\) −5.67710e13 −1.47947
\(296\) 0 0
\(297\) −5.58130e13 + 4.77318e12i −1.40144 + 0.119853i
\(298\) 0 0
\(299\) 4.42368e13 7.66203e13i 1.07051 1.85418i
\(300\) 0 0
\(301\) −2.02441e13 3.49951e11i −0.472262 0.00816378i
\(302\) 0 0
\(303\) 7.96946e12 + 1.17265e12i 0.179264 + 0.0263776i
\(304\) 0 0
\(305\) −2.63526e13 + 1.52147e13i −0.571709 + 0.330076i
\(306\) 0 0
\(307\) 1.76589e13i 0.369575i −0.982779 0.184787i \(-0.940840\pi\)
0.982779 0.184787i \(-0.0591597\pi\)
\(308\) 0 0
\(309\) −2.75268e13 + 1.09149e13i −0.555883 + 0.220419i
\(310\) 0 0
\(311\) −6.93664e12 1.20146e13i −0.135197 0.234168i 0.790476 0.612493i \(-0.209833\pi\)
−0.925673 + 0.378325i \(0.876500\pi\)
\(312\) 0 0
\(313\) 3.92739e13 + 2.26748e13i 0.738941 + 0.426628i 0.821684 0.569943i \(-0.193035\pi\)
−0.0827432 + 0.996571i \(0.526368\pi\)
\(314\) 0 0
\(315\) −5.87425e13 1.87829e13i −1.06720 0.341235i
\(316\) 0 0
\(317\) −5.12138e13 2.95683e13i −0.898589 0.518801i −0.0218470 0.999761i \(-0.506955\pi\)
−0.876742 + 0.480961i \(0.840288\pi\)
\(318\) 0 0
\(319\) −4.12436e13 7.14360e13i −0.699049 1.21079i
\(320\) 0 0
\(321\) −1.01293e14 + 4.01649e13i −1.65883 + 0.657762i
\(322\) 0 0
\(323\) 3.38462e13i 0.535668i
\(324\) 0 0
\(325\) 1.65862e13 9.57607e12i 0.253740 0.146497i
\(326\) 0 0
\(327\) −5.91672e13 8.70607e12i −0.875122 0.128768i
\(328\) 0 0
\(329\) −1.21389e13 + 2.02103e13i −0.173621 + 0.289065i
\(330\) 0 0
\(331\) −3.21737e13 + 5.57265e13i −0.445090 + 0.770918i −0.998058 0.0622840i \(-0.980162\pi\)
0.552969 + 0.833202i \(0.313495\pi\)
\(332\) 0 0
\(333\) 1.04994e14 + 3.15822e13i 1.40515 + 0.422668i
\(334\) 0 0
\(335\) −6.19812e12 −0.0802627
\(336\) 0 0
\(337\) 8.15966e13 1.02260 0.511302 0.859401i \(-0.329163\pi\)
0.511302 + 0.859401i \(0.329163\pi\)
\(338\) 0 0
\(339\) −8.95491e13 7.09010e13i −1.08633 0.860110i
\(340\) 0 0
\(341\) 5.73399e13 9.93156e13i 0.673454 1.16646i
\(342\) 0 0
\(343\) −8.78079e13 4.55732e12i −0.998656 0.0518313i
\(344\) 0 0
\(345\) −2.76299e13 + 1.87775e14i −0.304350 + 2.06839i
\(346\) 0 0
\(347\) 2.00571e13 1.15800e13i 0.214021 0.123565i −0.389158 0.921171i \(-0.627234\pi\)
0.603179 + 0.797606i \(0.293901\pi\)
\(348\) 0 0
\(349\) 3.68983e12i 0.0381475i −0.999818 0.0190738i \(-0.993928\pi\)
0.999818 0.0190738i \(-0.00607173\pi\)
\(350\) 0 0
\(351\) −4.86040e13 + 1.03702e14i −0.486948 + 1.03896i
\(352\) 0 0
\(353\) 2.76110e13 + 4.78237e13i 0.268115 + 0.464389i 0.968375 0.249499i \(-0.0802659\pi\)
−0.700260 + 0.713888i \(0.746933\pi\)
\(354\) 0 0
\(355\) −1.57512e14 9.09398e13i −1.48272 0.856048i
\(356\) 0 0
\(357\) −4.18487e13 6.89873e12i −0.381950 0.0629642i
\(358\) 0 0
\(359\) −8.88317e13 5.12870e13i −0.786228 0.453929i 0.0524051 0.998626i \(-0.483311\pi\)
−0.838633 + 0.544697i \(0.816645\pi\)
\(360\) 0 0
\(361\) 5.32853e13 + 9.22928e13i 0.457423 + 0.792279i
\(362\) 0 0
\(363\) 4.33072e13 + 1.09218e14i 0.360640 + 0.909509i
\(364\) 0 0
\(365\) 1.91400e14i 1.54643i
\(366\) 0 0
\(367\) 5.58521e13 3.22462e13i 0.437901 0.252822i −0.264806 0.964302i \(-0.585308\pi\)
0.702707 + 0.711480i \(0.251975\pi\)
\(368\) 0 0
\(369\) 2.32622e13 + 9.87237e13i 0.177013 + 0.751236i
\(370\) 0 0
\(371\) 1.49682e14 8.30031e13i 1.10564 0.613109i
\(372\) 0 0
\(373\) 1.05428e14 1.82606e14i 0.756060 1.30953i −0.188785 0.982018i \(-0.560455\pi\)
0.944845 0.327516i \(-0.106212\pi\)
\(374\) 0 0
\(375\) 7.43738e13 9.39352e13i 0.517902 0.654119i
\(376\) 0 0
\(377\) −1.68647e14 −1.14051
\(378\) 0 0
\(379\) −6.35546e13 −0.417476 −0.208738 0.977972i \(-0.566936\pi\)
−0.208738 + 0.977972i \(0.566936\pi\)
\(380\) 0 0
\(381\) 1.69063e14 2.13529e14i 1.07885 1.36260i
\(382\) 0 0
\(383\) −4.87687e13 + 8.44699e13i −0.302377 + 0.523732i −0.976674 0.214729i \(-0.931113\pi\)
0.674297 + 0.738460i \(0.264447\pi\)
\(384\) 0 0
\(385\) −4.52082e12 + 2.61522e14i −0.0272385 + 1.57571i
\(386\) 0 0
\(387\) −1.84993e13 7.85100e13i −0.108329 0.459742i
\(388\) 0 0
\(389\) 6.76559e13 3.90612e13i 0.385109 0.222343i −0.294930 0.955519i \(-0.595296\pi\)
0.680039 + 0.733176i \(0.261963\pi\)
\(390\) 0 0
\(391\) 1.30528e14i 0.722321i
\(392\) 0 0
\(393\) 6.33710e13 + 1.59817e14i 0.340982 + 0.859934i
\(394\) 0 0
\(395\) 1.49709e14 + 2.59304e14i 0.783366 + 1.35683i
\(396\) 0 0
\(397\) 7.05457e13 + 4.07296e13i 0.359023 + 0.207282i 0.668652 0.743575i \(-0.266871\pi\)
−0.309629 + 0.950857i \(0.600205\pi\)
\(398\) 0 0
\(399\) −2.61583e14 + 9.85261e13i −1.29497 + 0.487753i
\(400\) 0 0
\(401\) −1.30748e14 7.54872e13i −0.629709 0.363563i 0.150930 0.988544i \(-0.451773\pi\)
−0.780639 + 0.624982i \(0.785106\pi\)
\(402\) 0 0
\(403\) −1.17233e14 2.03053e14i −0.549378 0.951550i
\(404\) 0 0
\(405\) 1.49242e13 2.45235e14i 0.0680594 1.11836i
\(406\) 0 0
\(407\) 4.65004e14i 2.06390i
\(408\) 0 0
\(409\) 3.98507e13 2.30078e13i 0.172170 0.0994024i −0.411439 0.911437i \(-0.634974\pi\)
0.583609 + 0.812035i \(0.301640\pi\)
\(410\) 0 0
\(411\) 3.97614e13 2.70222e14i 0.167237 1.13656i
\(412\) 0 0
\(413\) −1.56369e14 2.81986e14i −0.640363 1.15479i
\(414\) 0 0
\(415\) 9.05852e13 1.56898e14i 0.361237 0.625682i
\(416\) 0 0
\(417\) 7.09531e13 + 5.61776e13i 0.275564 + 0.218180i
\(418\) 0 0
\(419\) −3.64676e14 −1.37953 −0.689763 0.724035i \(-0.742285\pi\)
−0.689763 + 0.724035i \(0.742285\pi\)
\(420\) 0 0
\(421\) 4.46037e13 0.164369 0.0821844 0.996617i \(-0.473810\pi\)
0.0821844 + 0.996617i \(0.473810\pi\)
\(422\) 0 0
\(423\) −8.99391e13 2.70536e13i −0.322906 0.0971301i
\(424\) 0 0
\(425\) −1.41279e13 + 2.44702e13i −0.0494239 + 0.0856048i
\(426\) 0 0
\(427\) −1.48158e14 8.89882e13i −0.505093 0.303375i
\(428\) 0 0
\(429\) 4.80553e14 + 7.07102e13i 1.59671 + 0.234946i
\(430\) 0 0
\(431\) −2.45964e14 + 1.42007e14i −0.796610 + 0.459923i −0.842284 0.539033i \(-0.818790\pi\)
0.0456743 + 0.998956i \(0.485456\pi\)
\(432\) 0 0
\(433\) 4.58726e14i 1.44834i 0.689623 + 0.724169i \(0.257776\pi\)
−0.689623 + 0.724169i \(0.742224\pi\)
\(434\) 0 0
\(435\) 3.36314e14 1.33355e14i 1.03527 0.410506i
\(436\) 0 0
\(437\) 4.30117e14 + 7.44984e14i 1.29104 + 2.23614i
\(438\) 0 0
\(439\) 1.20636e14 + 6.96493e13i 0.353120 + 0.203874i 0.666059 0.745899i \(-0.267980\pi\)
−0.312938 + 0.949773i \(0.601313\pi\)
\(440\) 0 0
\(441\) −6.85039e13 3.43514e14i −0.195570 0.980690i
\(442\) 0 0
\(443\) 5.37215e14 + 3.10161e14i 1.49599 + 0.863708i 0.999989 0.00461656i \(-0.00146950\pi\)
0.495997 + 0.868324i \(0.334803\pi\)
\(444\) 0 0
\(445\) −4.05381e13 7.02141e13i −0.110124 0.190741i
\(446\) 0 0
\(447\) 4.81830e13 1.91056e13i 0.127703 0.0506371i
\(448\) 0 0
\(449\) 2.84911e14i 0.736807i −0.929666 0.368404i \(-0.879904\pi\)
0.929666 0.368404i \(-0.120096\pi\)
\(450\) 0 0
\(451\) 3.72536e14 2.15084e14i 0.940151 0.542797i
\(452\) 0 0
\(453\) 4.21197e13 + 6.19764e12i 0.103740 + 0.0152646i
\(454\) 0 0
\(455\) 4.58432e14 + 2.75349e14i 1.10208 + 0.661943i
\(456\) 0 0
\(457\) 1.73713e14 3.00879e14i 0.407654 0.706078i −0.586972 0.809607i \(-0.699680\pi\)
0.994626 + 0.103529i \(0.0330135\pi\)
\(458\) 0 0
\(459\) −1.43976e13 1.68351e14i −0.0329852 0.385697i
\(460\) 0 0
\(461\) 1.60458e14 0.358928 0.179464 0.983765i \(-0.442564\pi\)
0.179464 + 0.983765i \(0.442564\pi\)
\(462\) 0 0
\(463\) 4.22098e14 0.921972 0.460986 0.887408i \(-0.347496\pi\)
0.460986 + 0.887408i \(0.347496\pi\)
\(464\) 0 0
\(465\) 3.94346e14 + 3.12226e14i 0.841174 + 0.666005i
\(466\) 0 0
\(467\) −4.32028e13 + 7.48294e13i −0.0900055 + 0.155894i −0.907513 0.420024i \(-0.862022\pi\)
0.817508 + 0.575918i \(0.195355\pi\)
\(468\) 0 0
\(469\) −1.70720e13 3.07865e13i −0.0347404 0.0626484i
\(470\) 0 0
\(471\) 1.32531e14 9.00690e14i 0.263452 1.79044i
\(472\) 0 0
\(473\) −2.96259e14 + 1.71045e14i −0.575355 + 0.332181i
\(474\) 0 0
\(475\) 1.86217e14i 0.353350i
\(476\) 0 0
\(477\) 4.67264e14 + 4.96565e14i 0.866386 + 0.920715i
\(478\) 0 0
\(479\) −5.38068e14 9.31961e14i −0.974971 1.68870i −0.680031 0.733184i \(-0.738033\pi\)
−0.294941 0.955516i \(-0.595300\pi\)
\(480\) 0 0
\(481\) −8.23341e14 4.75356e14i −1.45808 0.841824i
\(482\) 0 0
\(483\) −1.00879e15 + 3.79965e14i −1.74620 + 0.657711i
\(484\) 0 0
\(485\) 1.81738e14 + 1.04926e14i 0.307514 + 0.177544i
\(486\) 0 0
\(487\) 5.41751e14 + 9.38341e14i 0.896171 + 1.55221i 0.832349 + 0.554252i \(0.186996\pi\)
0.0638218 + 0.997961i \(0.479671\pi\)
\(488\) 0 0
\(489\) 4.76333e13 + 1.20128e14i 0.0770393 + 0.194288i
\(490\) 0 0
\(491\) 4.73703e14i 0.749131i 0.927200 + 0.374565i \(0.122208\pi\)
−0.927200 + 0.374565i \(0.877792\pi\)
\(492\) 0 0
\(493\) 2.15476e14 1.24405e14i 0.333227 0.192389i
\(494\) 0 0
\(495\) −1.01423e15 + 2.38982e14i −1.53393 + 0.361440i
\(496\) 0 0
\(497\) 1.78545e13 1.03286e15i 0.0264112 1.52785i
\(498\) 0 0
\(499\) −2.91573e14 + 5.05019e14i −0.421885 + 0.730726i −0.996124 0.0879620i \(-0.971965\pi\)
0.574239 + 0.818688i \(0.305298\pi\)
\(500\) 0 0
\(501\) 3.78304e14 4.77804e14i 0.535468 0.676304i
\(502\) 0 0
\(503\) 1.37096e15 1.89845 0.949227 0.314592i \(-0.101868\pi\)
0.949227 + 0.314592i \(0.101868\pi\)
\(504\) 0 0
\(505\) 1.49841e14 0.203015
\(506\) 0 0
\(507\) 1.48222e14 1.87207e14i 0.196503 0.248187i
\(508\) 0 0
\(509\) −1.55389e14 + 2.69141e14i −0.201591 + 0.349166i −0.949041 0.315152i \(-0.897945\pi\)
0.747450 + 0.664318i \(0.231278\pi\)
\(510\) 0 0
\(511\) −9.50695e14 + 5.27188e14i −1.20705 + 0.669346i
\(512\) 0 0
\(513\) −6.36927e14 9.13418e14i −0.791488 1.13507i
\(514\) 0 0
\(515\) −4.77031e14 + 2.75414e14i −0.580238 + 0.335001i
\(516\) 0 0
\(517\) 3.98328e14i 0.474288i
\(518\) 0 0
\(519\) −5.87796e13 1.48238e14i −0.0685182 0.172798i
\(520\) 0 0
\(521\) 1.38465e14 + 2.39828e14i 0.158027 + 0.273711i 0.934157 0.356862i \(-0.116153\pi\)
−0.776130 + 0.630573i \(0.782820\pi\)
\(522\) 0 0
\(523\) −9.74025e14 5.62353e14i −1.08846 0.628420i −0.155291 0.987869i \(-0.549631\pi\)
−0.933165 + 0.359449i \(0.882965\pi\)
\(524\) 0 0
\(525\) −2.30246e14 3.79559e13i −0.251951 0.0415340i
\(526\) 0 0
\(527\) 2.99570e14 + 1.72957e14i 0.321026 + 0.185344i
\(528\) 0 0
\(529\) 1.18234e15 + 2.04787e15i 1.24090 + 2.14930i
\(530\) 0 0
\(531\) 9.35477e14 8.80278e14i 0.961642 0.904899i
\(532\) 0 0
\(533\) 8.79488e14i 0.885585i
\(534\) 0 0
\(535\) −1.75538e15 + 1.01347e15i −1.73151 + 0.999689i
\(536\) 0 0
\(537\) 2.37189e14 1.61196e15i 0.229212 1.55774i
\(538\) 0 0
\(539\) −1.31145e15 + 6.97878e14i −1.24169 + 0.660757i
\(540\) 0 0
\(541\) −3.40956e14 + 5.90554e14i −0.316311 + 0.547866i −0.979715 0.200395i \(-0.935778\pi\)
0.663405 + 0.748261i \(0.269111\pi\)
\(542\) 0 0
\(543\) −8.52017e13 6.74589e13i −0.0774549 0.0613254i
\(544\) 0 0
\(545\) −1.11246e15 −0.991066
\(546\) 0 0
\(547\) −1.13043e15 −0.986992 −0.493496 0.869748i \(-0.664281\pi\)
−0.493496 + 0.869748i \(0.664281\pi\)
\(548\) 0 0
\(549\) 1.98325e14 6.59327e14i 0.169719 0.564226i
\(550\) 0 0
\(551\) 8.19882e14 1.42008e15i 0.687729 1.19118i
\(552\) 0 0
\(553\) −8.75624e14 + 1.45784e15i −0.719995 + 1.19873i
\(554\) 0 0
\(555\) 2.01778e15 + 2.96903e14i 1.62653 + 0.239333i
\(556\) 0 0
\(557\) −1.14154e15 + 6.59067e14i −0.902167 + 0.520866i −0.877903 0.478839i \(-0.841058\pi\)
−0.0242644 + 0.999706i \(0.507724\pi\)
\(558\) 0 0
\(559\) 6.99412e14i 0.541961i
\(560\) 0 0
\(561\) −6.66150e14 + 2.64143e14i −0.506147 + 0.200698i
\(562\) 0 0
\(563\) −1.07279e15 1.85812e15i −0.799313 1.38445i −0.920064 0.391767i \(-0.871864\pi\)
0.120752 0.992683i \(-0.461469\pi\)
\(564\) 0 0
\(565\) −1.84001e15 1.06233e15i −1.34448 0.776235i
\(566\) 0 0
\(567\) 1.25921e15 6.01342e14i 0.902381 0.430938i
\(568\) 0 0
\(569\) 1.09271e14 + 6.30877e13i 0.0768047 + 0.0443432i 0.537911 0.843002i \(-0.319214\pi\)
−0.461106 + 0.887345i \(0.652547\pi\)
\(570\) 0 0
\(571\) 8.35236e14 + 1.44667e15i 0.575851 + 0.997404i 0.995949 + 0.0899247i \(0.0286626\pi\)
−0.420097 + 0.907479i \(0.638004\pi\)
\(572\) 0 0
\(573\) −1.40444e15 + 5.56889e14i −0.949843 + 0.376633i
\(574\) 0 0
\(575\) 7.18147e14i 0.476475i
\(576\) 0 0
\(577\) −2.56393e15 + 1.48029e15i −1.66893 + 0.963560i −0.700720 + 0.713436i \(0.747138\pi\)
−0.968214 + 0.250124i \(0.919529\pi\)
\(578\) 0 0
\(579\) −8.60502e12 1.26617e12i −0.00549566 0.000808650i
\(580\) 0 0
\(581\) 1.02883e15 + 1.77849e13i 0.644726 + 0.0111451i
\(582\) 0 0
\(583\) 1.44590e15 2.50438e15i 0.889123 1.54001i
\(584\) 0 0
\(585\) −6.13661e14 + 2.04010e15i −0.370315 + 1.23110i
\(586\) 0 0
\(587\) −1.56255e15 −0.925386 −0.462693 0.886519i \(-0.653117\pi\)
−0.462693 + 0.886519i \(0.653117\pi\)
\(588\) 0 0
\(589\) 2.27972e15 1.32510
\(590\) 0 0
\(591\) −6.23616e14 4.93752e14i −0.355784 0.281694i
\(592\) 0 0
\(593\) 3.24512e14 5.62072e14i 0.181731 0.314768i −0.760739 0.649058i \(-0.775163\pi\)
0.942470 + 0.334290i \(0.108496\pi\)
\(594\) 0 0
\(595\) −7.88842e14 1.36364e13i −0.433657 0.00749644i
\(596\) 0 0
\(597\) 2.21587e14 1.50592e15i 0.119587 0.812726i
\(598\) 0 0
\(599\) −1.60010e15 + 9.23818e14i −0.847812 + 0.489485i −0.859912 0.510442i \(-0.829482\pi\)
0.0120998 + 0.999927i \(0.496148\pi\)
\(600\) 0 0
\(601\) 9.66604e14i 0.502851i −0.967877 0.251425i \(-0.919101\pi\)
0.967877 0.251425i \(-0.0808993\pi\)
\(602\) 0 0
\(603\) 1.02133e14 9.61066e13i 0.0521701 0.0490917i
\(604\) 0 0
\(605\) 1.09276e15 + 1.89271e15i 0.548112 + 0.949358i
\(606\) 0 0
\(607\) 1.62928e15 + 9.40663e14i 0.802522 + 0.463336i 0.844352 0.535788i \(-0.179986\pi\)
−0.0418303 + 0.999125i \(0.513319\pi\)
\(608\) 0 0
\(609\) 1.58872e15 + 1.30318e15i 0.768516 + 0.630390i
\(610\) 0 0
\(611\) 7.05282e14 + 4.07195e14i 0.335071 + 0.193453i
\(612\) 0 0
\(613\) −1.18489e14 2.05229e14i −0.0552898 0.0957647i 0.837056 0.547118i \(-0.184275\pi\)
−0.892346 + 0.451353i \(0.850942\pi\)
\(614\) 0 0
\(615\) 6.95444e14 + 1.75387e15i 0.318749 + 0.803865i
\(616\) 0 0
\(617\) 1.98091e15i 0.891859i 0.895068 + 0.445929i \(0.147127\pi\)
−0.895068 + 0.445929i \(0.852873\pi\)
\(618\) 0 0
\(619\) 2.51866e15 1.45415e15i 1.11396 0.643146i 0.174109 0.984726i \(-0.444295\pi\)
0.939853 + 0.341580i \(0.110962\pi\)
\(620\) 0 0
\(621\) −2.45631e15 3.52259e15i −1.06728 1.53059i
\(622\) 0 0
\(623\) 2.37101e14 3.94752e14i 0.101216 0.168516i
\(624\) 0 0
\(625\) 1.41877e15 2.45737e15i 0.595074 1.03070i
\(626\) 0 0
\(627\) −2.93163e15 + 3.70270e15i −1.20820 + 1.52597i
\(628\) 0 0
\(629\) 1.40261e15 0.568015
\(630\) 0 0
\(631\) 1.45914e15 0.580678 0.290339 0.956924i \(-0.406232\pi\)
0.290339 + 0.956924i \(0.406232\pi\)
\(632\) 0 0
\(633\) 2.57811e14 3.25620e14i 0.100828 0.127348i
\(634\) 0 0
\(635\) 2.53311e15 4.38748e15i 0.973642 1.68640i
\(636\) 0 0
\(637\) −1.04977e14 + 3.03548e15i −0.0396578 + 1.14673i
\(638\) 0 0
\(639\) 4.00559e15 9.43836e14i 1.48735 0.350463i
\(640\) 0 0
\(641\) 4.05736e15 2.34252e15i 1.48090 0.854995i 0.481130 0.876649i \(-0.340227\pi\)
0.999766 + 0.0216541i \(0.00689326\pi\)
\(642\) 0 0
\(643\) 1.55663e14i 0.0558503i 0.999610 + 0.0279252i \(0.00889001\pi\)
−0.999610 + 0.0279252i \(0.991110\pi\)
\(644\) 0 0
\(645\) −5.53052e14 1.39476e15i −0.195069 0.491950i
\(646\) 0 0
\(647\) 5.82203e14 + 1.00841e15i 0.201884 + 0.349673i 0.949135 0.314868i \(-0.101960\pi\)
−0.747252 + 0.664541i \(0.768627\pi\)
\(648\) 0 0
\(649\) −4.71799e15 2.72393e15i −1.60846 0.928646i
\(650\) 0 0
\(651\) −4.64666e14 + 2.81873e15i −0.155756 + 0.944840i
\(652\) 0 0
\(653\) 1.02620e15 + 5.92478e14i 0.338229 + 0.195276i 0.659488 0.751715i \(-0.270773\pi\)
−0.321260 + 0.946991i \(0.604106\pi\)
\(654\) 0 0
\(655\) 1.59902e15 + 2.76959e15i 0.518236 + 0.897611i
\(656\) 0 0
\(657\) −2.96779e15 3.15390e15i −0.945854 1.00517i
\(658\) 0 0
\(659\) 3.09117e15i 0.968843i 0.874835 + 0.484422i \(0.160970\pi\)
−0.874835 + 0.484422i \(0.839030\pi\)
\(660\) 0 0
\(661\) 1.36474e15 7.87932e14i 0.420670 0.242874i −0.274694 0.961532i \(-0.588577\pi\)
0.695364 + 0.718658i \(0.255243\pi\)
\(662\) 0 0
\(663\) −2.13286e14 + 1.44951e15i −0.0646605 + 0.439438i
\(664\) 0 0
\(665\) −4.54723e15 + 2.52157e15i −1.35590 + 0.751887i
\(666\) 0 0
\(667\) 3.16187e15 5.47652e15i 0.927368 1.60625i
\(668\) 0 0
\(669\) 4.99066e15 + 3.95139e15i 1.43984 + 1.14000i
\(670\) 0 0
\(671\) −2.92007e15 −0.828741
\(672\) 0 0
\(673\) −2.57612e15 −0.719256 −0.359628 0.933096i \(-0.617096\pi\)
−0.359628 + 0.933096i \(0.617096\pi\)
\(674\) 0 0
\(675\) −7.92136e13 9.26247e14i −0.0217585 0.254423i
\(676\) 0 0
\(677\) −3.50799e14 + 6.07601e14i −0.0948026 + 0.164203i −0.909526 0.415647i \(-0.863555\pi\)
0.814724 + 0.579849i \(0.196889\pi\)
\(678\) 0 0
\(679\) −2.06006e13 + 1.19171e15i −0.00547767 + 0.316874i
\(680\) 0 0
\(681\) −6.62683e14 9.75094e13i −0.173379 0.0255116i
\(682\) 0 0
\(683\) 1.03080e15 5.95135e14i 0.265377 0.153215i −0.361408 0.932408i \(-0.617704\pi\)
0.626785 + 0.779193i \(0.284371\pi\)
\(684\) 0 0
\(685\) 5.08069e15i 1.28714i
\(686\) 0 0
\(687\) 5.28868e15 2.09707e15i 1.31852 0.522819i
\(688\) 0 0
\(689\) −2.95618e15 5.12025e15i −0.725312 1.25628i
\(690\) 0 0
\(691\) −4.26662e15 2.46334e15i −1.03028 0.594832i −0.113215 0.993571i \(-0.536115\pi\)
−0.917065 + 0.398738i \(0.869448\pi\)
\(692\) 0 0
\(693\) −3.98061e15 4.37948e15i −0.946056 1.04086i
\(694\) 0 0
\(695\) 1.45791e15 + 8.41724e14i 0.341047 + 0.196903i
\(696\) 0 0
\(697\) 6.48768e14 + 1.12370e15i 0.149386 + 0.258744i
\(698\) 0 0
\(699\) −5.24008e14 + 2.07780e14i −0.118772 + 0.0470955i
\(700\) 0 0
\(701\) 1.31638e15i 0.293719i 0.989157 + 0.146860i \(0.0469166\pi\)
−0.989157 + 0.146860i \(0.953083\pi\)
\(702\) 0 0
\(703\) 8.00539e15 4.62191e15i 1.75844 1.01524i
\(704\) 0 0
\(705\) −1.72845e15 2.54330e14i −0.373781 0.0549994i
\(706\) 0 0
\(707\) 4.12720e14 + 7.44271e14i 0.0878716 + 0.158462i
\(708\) 0 0
\(709\) 2.86327e15 4.95932e15i 0.600216 1.03960i −0.392572 0.919721i \(-0.628415\pi\)
0.992788 0.119883i \(-0.0382520\pi\)
\(710\) 0 0
\(711\) −6.48763e15 1.95148e15i −1.33907 0.402792i
\(712\) 0 0
\(713\) 8.79173e15 1.78683
\(714\) 0 0
\(715\) 9.03532e15 1.80826
\(716\) 0 0
\(717\) 6.45201e15 + 5.10842e15i 1.27157 + 1.00677i
\(718\) 0 0
\(719\) −3.94175e14 + 6.82732e14i −0.0765034 + 0.132508i −0.901739 0.432281i \(-0.857709\pi\)
0.825236 + 0.564789i \(0.191042\pi\)
\(720\) 0 0
\(721\) −2.68193e15 1.61085e15i −0.512628 0.307901i
\(722\) 0 0
\(723\) −9.51969e14 + 6.46966e15i −0.179210 + 1.21793i
\(724\) 0 0
\(725\) 1.18552e15 6.84460e14i 0.219811 0.126908i
\(726\) 0 0
\(727\) 1.07902e16i 1.97056i 0.170952 + 0.985279i \(0.445316\pi\)
−0.170952 + 0.985279i \(0.554684\pi\)
\(728\) 0 0
\(729\) 3.55663e15 + 4.27241e15i 0.639791 + 0.768549i
\(730\) 0 0
\(731\) −5.15932e14 8.93621e14i −0.0914212 0.158346i
\(732\) 0 0
\(733\) −5.87209e15 3.39025e15i −1.02499 0.591779i −0.109446 0.993993i \(-0.534908\pi\)
−0.915546 + 0.402213i \(0.868241\pi\)
\(734\) 0 0
\(735\) −2.19093e15 6.13633e15i −0.376745 1.05518i
\(736\) 0 0
\(737\) −5.15098e14 2.97392e14i −0.0872607 0.0503800i
\(738\) 0 0
\(739\) 4.13087e15 + 7.15488e15i 0.689441 + 1.19415i 0.972019 + 0.234903i \(0.0754771\pi\)
−0.282578 + 0.959244i \(0.591190\pi\)
\(740\) 0 0
\(741\) 3.55913e15 + 8.97589e15i 0.585253 + 1.47597i
\(742\) 0 0
\(743\) 1.13253e16i 1.83489i 0.397861 + 0.917446i \(0.369753\pi\)
−0.397861 + 0.917446i \(0.630247\pi\)
\(744\) 0 0
\(745\) 8.34997e14 4.82086e14i 0.133299 0.0769600i
\(746\) 0 0
\(747\) 9.40156e14 + 3.98997e15i 0.147889 + 0.627634i
\(748\) 0 0
\(749\) −9.86897e15 5.92761e15i −1.52975 0.918818i
\(750\) 0 0
\(751\) 5.24618e15 9.08665e15i 0.801353 1.38798i −0.117373 0.993088i \(-0.537447\pi\)
0.918726 0.394896i \(-0.129219\pi\)
\(752\) 0 0
\(753\) −1.96144e14 + 2.47732e14i −0.0295258 + 0.0372915i
\(754\) 0 0
\(755\) 7.91932e14 0.117484
\(756\) 0 0
\(757\) −1.94582e15 −0.284495 −0.142248 0.989831i \(-0.545433\pi\)
−0.142248 + 0.989831i \(0.545433\pi\)
\(758\) 0 0
\(759\) −1.13058e16 + 1.42794e16i −1.62919 + 2.05770i
\(760\) 0 0
\(761\) 1.28327e15 2.22269e15i 0.182265 0.315692i −0.760386 0.649471i \(-0.774990\pi\)
0.942652 + 0.333779i \(0.108324\pi\)
\(762\) 0 0
\(763\) −3.06413e15 5.52565e15i −0.428966 0.773568i
\(764\) 0 0
\(765\) −7.20852e14 3.05926e15i −0.0994736 0.422161i
\(766\) 0 0
\(767\) −9.64603e15 + 5.56914e15i −1.31212 + 0.757554i
\(768\) 0 0
\(769\) 9.14883e14i 0.122679i −0.998117 0.0613396i \(-0.980463\pi\)
0.998117 0.0613396i \(-0.0195373\pi\)
\(770\) 0 0
\(771\) −2.71034e15 6.83531e15i −0.358282 0.903564i
\(772\) 0 0
\(773\) 1.12136e15 + 1.94225e15i 0.146136 + 0.253115i 0.929796 0.368075i \(-0.119983\pi\)
−0.783660 + 0.621190i \(0.786650\pi\)
\(774\) 0 0
\(775\) 1.64820e15 + 9.51587e14i 0.211763 + 0.122261i
\(776\) 0 0
\(777\) 4.08300e15 + 1.08402e16i 0.517207 + 1.37317i
\(778\) 0 0
\(779\) 7.40566e15 + 4.27566e15i 0.924927 + 0.534007i
\(780\) 0 0
\(781\) −8.72676e15 1.51152e16i −1.07466 1.86137i
\(782\) 0 0
\(783\) −3.47402e15 + 7.41224e15i −0.421836 + 0.900036i
\(784\) 0 0
\(785\) 1.69347e16i 2.02766i
\(786\) 0 0
\(787\) 2.84798e15 1.64428e15i 0.336260 0.194140i −0.322357 0.946618i \(-0.604475\pi\)
0.658617 + 0.752478i \(0.271142\pi\)
\(788\) 0 0
\(789\) 2.36398e15 1.60658e16i 0.275246 1.87059i
\(790\) 0 0
\(791\) 2.08571e14 1.20655e16i 0.0239488 1.38540i
\(792\) 0 0
\(793\) −2.98507e15 + 5.17029e15i −0.338028 + 0.585481i
\(794\) 0 0
\(795\) 9.94396e15 + 7.87319e15i 1.11055 + 0.879288i
\(796\) 0 0
\(797\) −9.63390e15 −1.06116 −0.530580 0.847635i \(-0.678026\pi\)
−0.530580 + 0.847635i \(0.678026\pi\)
\(798\) 0 0
\(799\) −1.20149e15 −0.130531
\(800\) 0 0
\(801\) 1.75671e15 + 5.28419e14i 0.188244 + 0.0566239i
\(802\) 0 0
\(803\) −9.18354e15 + 1.59064e16i −0.970677 + 1.68126i
\(804\) 0 0
\(805\) −1.75364e16 + 9.72444e15i −1.82836 + 1.01388i
\(806\) 0 0
\(807\) −1.36329e16 2.00599e15i −1.40211 0.206312i
\(808\) 0 0
\(809\) −2.02037e14 + 1.16646e14i −0.0204981 + 0.0118346i −0.510214 0.860047i \(-0.670434\pi\)
0.489716 + 0.871882i \(0.337100\pi\)
\(810\) 0 0
\(811\) 2.17182e15i 0.217375i −0.994076 0.108688i \(-0.965335\pi\)
0.994076 0.108688i \(-0.0346648\pi\)
\(812\) 0 0
\(813\) 3.14170e15 1.24575e15i 0.310218 0.123008i
\(814\) 0 0
\(815\) 1.20192e15 + 2.08179e15i 0.117087 + 0.202801i
\(816\) 0 0
\(817\) −5.88934e15 3.40021e15i −0.566038 0.326802i
\(818\) 0 0
\(819\) −1.18236e16 + 2.57112e15i −1.12121 + 0.243816i
\(820\) 0 0
\(821\) 1.15578e15 + 6.67291e14i 0.108141 + 0.0624350i 0.553095 0.833118i \(-0.313447\pi\)
−0.444954 + 0.895553i \(0.646780\pi\)
\(822\) 0 0
\(823\) 4.66232e15 + 8.07538e15i 0.430431 + 0.745528i 0.996910 0.0785478i \(-0.0250283\pi\)
−0.566480 + 0.824076i \(0.691695\pi\)
\(824\) 0 0
\(825\) −3.66507e15 + 1.45328e15i −0.333877 + 0.132389i
\(826\) 0 0
\(827\) 1.85920e16i 1.67127i −0.549286 0.835634i \(-0.685100\pi\)
0.549286 0.835634i \(-0.314900\pi\)
\(828\) 0 0
\(829\) 2.07899e14 1.20030e14i 0.0184417 0.0106473i −0.490751 0.871300i \(-0.663277\pi\)
0.509193 + 0.860653i \(0.329944\pi\)
\(830\) 0 0
\(831\) −8.89531e15 1.30889e15i −0.778674 0.114577i
\(832\) 0 0
\(833\) −2.10504e15 3.95579e15i −0.181850 0.341732i
\(834\) 0 0
\(835\) 5.66824e15 9.81767e15i 0.483250 0.837014i
\(836\) 0 0
\(837\) −1.13394e16 + 9.69753e14i −0.954109 + 0.0815964i
\(838\) 0 0
\(839\) −1.34331e16 −1.11554 −0.557770 0.829996i \(-0.688343\pi\)
−0.557770 + 0.829996i \(0.688343\pi\)
\(840\) 0 0
\(841\) 1.46290e14 0.0119905
\(842\) 0 0
\(843\) 6.86896e15 + 5.43854e15i 0.555699 + 0.439978i
\(844\) 0 0
\(845\) 2.22086e15 3.84664e15i 0.177341 0.307163i
\(846\) 0 0
\(847\) −6.39136e15 + 1.06411e16i −0.503772 + 0.838738i
\(848\) 0 0
\(849\) −5.59875e14 + 3.80496e15i −0.0435611 + 0.296045i
\(850\) 0 0
\(851\) 3.08728e16 1.78244e16i 2.37117 1.36900i
\(852\) 0 0
\(853\) 2.09188e16i 1.58605i 0.609190 + 0.793025i \(0.291495\pi\)
−0.609190 + 0.793025i \(0.708505\pi\)
\(854\) 0 0
\(855\) −1.41952e16 1.50853e16i −1.06249 1.12912i
\(856\) 0 0
\(857\) 6.09388e15 + 1.05549e16i 0.450297 + 0.779938i 0.998404 0.0564703i \(-0.0179846\pi\)
−0.548107 + 0.836408i \(0.684651\pi\)
\(858\) 0 0
\(859\) −7.03889e15 4.06391e15i −0.513502 0.296470i 0.220770 0.975326i \(-0.429143\pi\)
−0.734272 + 0.678856i \(0.762476\pi\)
\(860\) 0 0
\(861\) −6.79605e15 + 8.28514e15i −0.489485 + 0.596736i
\(862\) 0 0
\(863\) 6.06283e15 + 3.50038e15i 0.431138 + 0.248917i 0.699831 0.714308i \(-0.253259\pi\)
−0.268694 + 0.963226i \(0.586592\pi\)
\(864\) 0 0
\(865\) −1.48317e15 2.56892e15i −0.104136 0.180369i
\(866\) 0 0
\(867\) 4.52019e15 + 1.13996e16i 0.313366 + 0.790289i
\(868\) 0 0
\(869\) 2.87328e16i 1.96684i
\(870\) 0 0
\(871\) −1.05313e15 + 6.08025e14i −0.0711839 + 0.0410981i
\(872\) 0 0
\(873\) −4.62165e15 + 1.08900e15i −0.308474 + 0.0726856i
\(874\) 0 0
\(875\) 1.26565e16 + 2.18787e14i 0.834198 + 0.0144204i
\(876\) 0 0
\(877\) −5.35218e15 + 9.27025e15i −0.348364 + 0.603384i −0.985959 0.166988i \(-0.946596\pi\)
0.637595 + 0.770372i \(0.279929\pi\)
\(878\) 0 0
\(879\) −1.04295e15 + 1.31726e15i −0.0670386 + 0.0846708i
\(880\) 0 0
\(881\) 1.55605e16 0.987772 0.493886 0.869527i \(-0.335576\pi\)
0.493886 + 0.869527i \(0.335576\pi\)
\(882\) 0 0
\(883\) 1.61350e16 1.01155 0.505773 0.862667i \(-0.331208\pi\)
0.505773 + 0.862667i \(0.331208\pi\)
\(884\) 0 0
\(885\) 1.48323e16 1.87334e16i 0.918374 1.15992i
\(886\) 0 0
\(887\) 5.60498e15 9.70811e15i 0.342763 0.593683i −0.642182 0.766552i \(-0.721971\pi\)
0.984945 + 0.172869i \(0.0553039\pi\)
\(888\) 0 0
\(889\) 2.87701e16 + 4.97336e14i 1.73773 + 0.0300393i
\(890\) 0 0
\(891\) 1.30069e16 1.96643e16i 0.775973 1.17314i
\(892\) 0 0
\(893\) −6.85750e15 + 3.95918e15i −0.404094 + 0.233304i
\(894\) 0 0
\(895\) 3.03079e16i 1.76413i
\(896\) 0 0
\(897\) 1.37258e16 + 3.46155e16i 0.789184 + 1.99027i
\(898\) 0 0
\(899\) −8.37933e15 1.45134e16i −0.475917 0.824312i
\(900\) 0 0
\(901\) 7.55406e15 + 4.36134e15i 0.423833 + 0.244700i
\(902\) 0 0
\(903\) 5.40455e15 6.58875e15i 0.299555 0.365191i
\(904\) 0 0
\(905\) −1.75068e15 1.01076e15i −0.0958605 0.0553451i
\(906\) 0 0
\(907\) −4.28904e15 7.42884e15i −0.232017 0.401866i 0.726384 0.687289i \(-0.241199\pi\)
−0.958402 + 0.285423i \(0.907866\pi\)
\(908\) 0 0
\(909\) −2.46909e15 + 2.32340e15i −0.131958 + 0.124172i
\(910\) 0 0
\(911\) 2.86298e16i 1.51171i 0.654741 + 0.755854i \(0.272778\pi\)
−0.654741 + 0.755854i \(0.727222\pi\)
\(912\) 0 0
\(913\) 1.50563e16 8.69274e15i 0.785467 0.453489i
\(914\) 0 0
\(915\) 1.86445e15 1.26709e16i 0.0961024 0.653120i
\(916\) 0 0
\(917\) −9.35241e15 + 1.55710e16i −0.476313 + 0.793020i
\(918\) 0 0
\(919\) 2.45902e15 4.25915e15i 0.123745 0.214332i −0.797497 0.603323i \(-0.793843\pi\)
0.921242 + 0.388991i \(0.127176\pi\)
\(920\) 0 0
\(921\) 5.82711e15 + 4.61365e15i 0.289751 + 0.229412i
\(922\) 0 0
\(923\) −3.56841e16 −1.75334
\(924\) 0 0
\(925\) 7.71700e15 0.374687
\(926\) 0 0
\(927\) 3.59005e15 1.19350e16i 0.172251 0.572643i
\(928\) 0 0
\(929\) 2.72223e15 4.71505e15i 0.129074 0.223563i −0.794244 0.607599i \(-0.792133\pi\)
0.923318 + 0.384036i \(0.125466\pi\)
\(930\) 0 0
\(931\) −2.50497e16 1.56410e16i −1.17376 0.732896i
\(932\) 0 0
\(933\) 5.77690e15 + 8.50033e14i 0.267514 + 0.0393629i
\(934\) 0 0
\(935\) −1.15442e16 + 6.66504e15i −0.528323 + 0.305027i
\(936\) 0 0
\(937\) 2.60283e16i 1.17728i −0.808397 0.588638i \(-0.799664\pi\)
0.808397 0.588638i \(-0.200336\pi\)
\(938\) 0 0
\(939\) −1.77431e16 + 7.03552e15i −0.793176 + 0.314511i
\(940\) 0 0
\(941\) −5.09386e15 8.82283e15i −0.225063 0.389821i 0.731275 0.682082i \(-0.238925\pi\)
−0.956338 + 0.292262i \(0.905592\pi\)
\(942\) 0 0
\(943\) 2.85599e16 + 1.64891e16i 1.24722 + 0.720081i
\(944\) 0 0
\(945\) 2.15454e16 1.44766e16i 0.929991 0.624875i
\(946\) 0 0
\(947\) 1.34755e16 + 7.78009e15i 0.574937 + 0.331940i 0.759119 0.650952i \(-0.225630\pi\)
−0.184182 + 0.982892i \(0.558963\pi\)
\(948\) 0 0
\(949\) 1.87759e16 + 3.25209e16i 0.791841 + 1.37151i
\(950\) 0 0
\(951\) 2.31374e16 9.17445e15i 0.964541 0.382461i
\(952\) 0 0
\(953\) 1.14850e16i 0.473281i −0.971597 0.236641i \(-0.923954\pi\)
0.971597 0.236641i \(-0.0760464\pi\)
\(954\) 0 0
\(955\) −2.43385e16 + 1.40518e16i −0.991459 + 0.572419i
\(956\) 0 0
\(957\) 3.43480e16 + 5.05409e15i 1.38320 + 0.203530i
\(958\) 0 0
\(959\) 2.52362e16 1.39942e16i 1.00466 0.557116i
\(960\) 0 0
\(961\) −1.05467e15 + 1.82675e15i −0.0415087 + 0.0718951i
\(962\) 0 0
\(963\) 1.32107e16 4.39185e16i 0.514020 1.70885i
\(964\) 0 0
\(965\) −1.61791e14 −0.00622377
\(966\) 0 0
\(967\) −2.18286e16 −0.830194 −0.415097 0.909777i \(-0.636252\pi\)
−0.415097 + 0.909777i \(0.636252\pi\)
\(968\) 0 0
\(969\) −1.11686e16 8.84281e15i −0.419970 0.332514i
\(970\) 0 0
\(971\) −6.93013e15 + 1.20033e16i −0.257653 + 0.446268i −0.965613 0.259985i \(-0.916283\pi\)
0.707960 + 0.706253i \(0.249616\pi\)
\(972\) 0 0
\(973\) −1.65259e14 + 9.55997e15i −0.00607497 + 0.351428i
\(974\) 0 0
\(975\) −1.17347e15 + 7.97504e15i −0.0426529 + 0.289873i
\(976\) 0 0
\(977\) −2.38113e16 + 1.37474e16i −0.855781 + 0.494085i −0.862597 0.505891i \(-0.831164\pi\)
0.00681620 + 0.999977i \(0.497830\pi\)
\(978\) 0 0
\(979\) 7.78024e15i 0.276496i
\(980\) 0 0
\(981\) 1.83311e16 1.72495e16i 0.644184 0.606173i
\(982\) 0 0
\(983\) 2.23017e15 + 3.86277e15i 0.0774987 + 0.134232i 0.902170 0.431380i \(-0.141973\pi\)
−0.824671 + 0.565612i \(0.808640\pi\)
\(984\) 0 0
\(985\) −1.28138e16 7.39802e15i −0.440329 0.254224i
\(986\) 0 0
\(987\) −3.49754e15 9.28586e15i −0.118855 0.315557i
\(988\) 0 0
\(989\) −2.27122e16 1.31129e16i −0.763273 0.440676i
\(990\) 0 0
\(991\) 4.26211e15 + 7.38220e15i 0.141651 + 0.245347i 0.928119 0.372285i \(-0.121426\pi\)
−0.786467 + 0.617632i \(0.788092\pi\)
\(992\) 0 0
\(993\) −9.98286e15 2.51761e16i −0.328121 0.827500i
\(994\) 0 0
\(995\) 2.83142e16i 0.920403i
\(996\) 0 0
\(997\) 1.07346e15 6.19763e14i 0.0345114 0.0199252i −0.482645 0.875816i \(-0.660324\pi\)
0.517156 + 0.855891i \(0.326991\pi\)
\(998\) 0 0
\(999\) −3.78528e16 + 2.63948e16i −1.20362 + 0.839282i
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 84.12.k.b.5.9 yes 56
3.2 odd 2 inner 84.12.k.b.5.2 56
7.3 odd 6 inner 84.12.k.b.17.2 yes 56
21.17 even 6 inner 84.12.k.b.17.9 yes 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.12.k.b.5.2 56 3.2 odd 2 inner
84.12.k.b.5.9 yes 56 1.1 even 1 trivial
84.12.k.b.17.2 yes 56 7.3 odd 6 inner
84.12.k.b.17.9 yes 56 21.17 even 6 inner