Properties

Label 84.12.k.b.5.20
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 5.20
Character \(\chi\) \(=\) 84.5
Dual form 84.12.k.b.17.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(204.376 - 367.937i) q^{3} +(1631.25 - 2825.41i) q^{5} +(25977.5 - 36090.1i) q^{7} +(-93607.5 - 150395. i) q^{9} +O(q^{10})\) \(q+(204.376 - 367.937i) q^{3} +(1631.25 - 2825.41i) q^{5} +(25977.5 - 36090.1i) q^{7} +(-93607.5 - 150395. i) q^{9} +(-759895. + 438726. i) q^{11} +2.65981e6i q^{13} +(-706181. - 1.17764e6i) q^{15} +(5.28810e6 + 9.15925e6i) q^{17} +(-45948.9 - 26528.6i) q^{19} +(-7.96969e6 - 1.69340e7i) q^{21} +(-2.42309e6 - 1.39897e6i) q^{23} +(1.90921e7 + 3.30685e7i) q^{25} +(-7.44670e7 + 3.70442e6i) q^{27} +9.08750e7i q^{29} +(-6.33162e7 + 3.65556e7i) q^{31} +(6.11853e6 + 3.69258e8i) q^{33} +(-5.95935e7 - 1.32269e8i) q^{35} +(2.19975e8 - 3.81008e8i) q^{37} +(9.78641e8 + 5.43602e8i) q^{39} -8.27550e8 q^{41} -4.38417e8 q^{43} +(-5.77624e8 + 1.91475e7i) q^{45} +(-8.36570e8 + 1.44898e9i) q^{47} +(-6.27667e8 - 1.87506e9i) q^{49} +(4.45078e9 - 7.37485e7i) q^{51} +(3.20646e9 - 1.85125e9i) q^{53} +2.86268e9i q^{55} +(-1.91517e7 + 1.14845e7i) q^{57} +(-3.94646e9 - 6.83546e9i) q^{59} +(6.69398e9 + 3.86477e9i) q^{61} +(-7.85947e9 - 5.28578e8i) q^{63} +(7.51504e9 + 4.33881e9i) q^{65} +(4.55459e9 + 7.88877e9i) q^{67} +(-1.00995e9 + 6.05626e8i) q^{69} +6.04217e9i q^{71} +(2.57592e10 - 1.48721e10i) q^{73} +(1.60691e10 - 2.66261e8i) q^{75} +(-3.90650e9 + 3.88217e10i) q^{77} +(-6.45666e9 + 1.11833e10i) q^{79} +(-1.38563e10 + 2.81562e10i) q^{81} -4.05047e10 q^{83} +3.45048e10 q^{85} +(3.34362e10 + 1.85727e10i) q^{87} +(-2.20949e10 + 3.82694e10i) q^{89} +(9.59928e10 + 6.90951e10i) q^{91} +(5.09810e8 + 3.07675e10i) q^{93} +(-1.49908e8 + 8.65496e7i) q^{95} -3.96326e8i q^{97} +(1.37114e11 + 7.32164e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q - 729 q^{3} - 27194 q^{7} - 172347 q^{9}+O(q^{10}) \) 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
\(3\) 204.376 367.937i 0.485583 0.874190i
\(4\) 0 0
\(5\) 1631.25 2825.41i 0.233445 0.404339i −0.725374 0.688355i \(-0.758333\pi\)
0.958820 + 0.284015i \(0.0916667\pi\)
\(6\) 0 0
\(7\) 25977.5 36090.1i 0.584195 0.811613i
\(8\) 0 0
\(9\) −93607.5 150395.i −0.528417 0.848985i
\(10\) 0 0
\(11\) −759895. + 438726.i −1.42264 + 0.821359i −0.996524 0.0833111i \(-0.973450\pi\)
−0.426112 + 0.904670i \(0.640117\pi\)
\(12\) 0 0
\(13\) 2.65981e6i 1.98684i 0.114545 + 0.993418i \(0.463459\pi\)
−0.114545 + 0.993418i \(0.536541\pi\)
\(14\) 0 0
\(15\) −706181. 1.17764e6i −0.240112 0.400416i
\(16\) 0 0
\(17\) 5.28810e6 + 9.15925e6i 0.903296 + 1.56455i 0.823188 + 0.567769i \(0.192193\pi\)
0.0801082 + 0.996786i \(0.474473\pi\)
\(18\) 0 0
\(19\) −45948.9 26528.6i −0.00425726 0.00245793i 0.497870 0.867252i \(-0.334116\pi\)
−0.502127 + 0.864794i \(0.667449\pi\)
\(20\) 0 0
\(21\) −7.96969e6 1.69340e7i −0.425829 0.904804i
\(22\) 0 0
\(23\) −2.42309e6 1.39897e6i −0.0784994 0.0453216i 0.460237 0.887796i \(-0.347765\pi\)
−0.538736 + 0.842475i \(0.681098\pi\)
\(24\) 0 0
\(25\) 1.90921e7 + 3.30685e7i 0.391007 + 0.677243i
\(26\) 0 0
\(27\) −7.44670e7 + 3.70442e6i −0.998765 + 0.0496843i
\(28\) 0 0
\(29\) 9.08750e7i 0.822726i 0.911472 + 0.411363i \(0.134947\pi\)
−0.911472 + 0.411363i \(0.865053\pi\)
\(30\) 0 0
\(31\) −6.33162e7 + 3.65556e7i −0.397215 + 0.229332i −0.685282 0.728278i \(-0.740321\pi\)
0.288067 + 0.957610i \(0.406988\pi\)
\(32\) 0 0
\(33\) 6.11853e6 + 3.69258e8i 0.0272158 + 1.64249i
\(34\) 0 0
\(35\) −5.95935e7 1.32269e8i −0.191789 0.425680i
\(36\) 0 0
\(37\) 2.19975e8 3.81008e8i 0.521511 0.903284i −0.478176 0.878264i \(-0.658702\pi\)
0.999687 0.0250199i \(-0.00796490\pi\)
\(38\) 0 0
\(39\) 9.78641e8 + 5.43602e8i 1.73687 + 0.964775i
\(40\) 0 0
\(41\) −8.27550e8 −1.11554 −0.557768 0.829997i \(-0.688342\pi\)
−0.557768 + 0.829997i \(0.688342\pi\)
\(42\) 0 0
\(43\) −4.38417e8 −0.454790 −0.227395 0.973803i \(-0.573021\pi\)
−0.227395 + 0.973803i \(0.573021\pi\)
\(44\) 0 0
\(45\) −5.77624e8 + 1.91475e7i −0.466634 + 0.0154683i
\(46\) 0 0
\(47\) −8.36570e8 + 1.44898e9i −0.532064 + 0.921562i 0.467235 + 0.884133i \(0.345250\pi\)
−0.999299 + 0.0374289i \(0.988083\pi\)
\(48\) 0 0
\(49\) −6.27667e8 1.87506e9i −0.317432 0.948281i
\(50\) 0 0
\(51\) 4.45078e9 7.37485e7i 1.80634 0.0299307i
\(52\) 0 0
\(53\) 3.20646e9 1.85125e9i 1.05319 0.608062i 0.129652 0.991560i \(-0.458614\pi\)
0.923542 + 0.383497i \(0.125281\pi\)
\(54\) 0 0
\(55\) 2.86268e9i 0.766970i
\(56\) 0 0
\(57\) −1.91517e7 + 1.14845e7i −0.00421596 + 0.00252813i
\(58\) 0 0
\(59\) −3.94646e9 6.83546e9i −0.718656 1.24475i −0.961532 0.274692i \(-0.911424\pi\)
0.242876 0.970057i \(-0.421909\pi\)
\(60\) 0 0
\(61\) 6.69398e9 + 3.86477e9i 1.01478 + 0.585882i 0.912587 0.408883i \(-0.134082\pi\)
0.102190 + 0.994765i \(0.467415\pi\)
\(62\) 0 0
\(63\) −7.85947e9 5.28578e8i −0.997746 0.0671021i
\(64\) 0 0
\(65\) 7.51504e9 + 4.33881e9i 0.803356 + 0.463818i
\(66\) 0 0
\(67\) 4.55459e9 + 7.88877e9i 0.412133 + 0.713835i 0.995123 0.0986441i \(-0.0314506\pi\)
−0.582990 + 0.812480i \(0.698117\pi\)
\(68\) 0 0
\(69\) −1.00995e9 + 6.05626e8i −0.0777377 + 0.0466160i
\(70\) 0 0
\(71\) 6.04217e9i 0.397440i 0.980056 + 0.198720i \(0.0636784\pi\)
−0.980056 + 0.198720i \(0.936322\pi\)
\(72\) 0 0
\(73\) 2.57592e10 1.48721e10i 1.45431 0.839646i 0.455588 0.890191i \(-0.349429\pi\)
0.998722 + 0.0505448i \(0.0160958\pi\)
\(74\) 0 0
\(75\) 1.60691e10 2.66261e8i 0.781906 0.0129560i
\(76\) 0 0
\(77\) −3.90650e9 + 3.88217e10i −0.164471 + 1.63446i
\(78\) 0 0
\(79\) −6.45666e9 + 1.11833e10i −0.236080 + 0.408902i −0.959586 0.281416i \(-0.909196\pi\)
0.723506 + 0.690318i \(0.242529\pi\)
\(80\) 0 0
\(81\) −1.38563e10 + 2.81562e10i −0.441550 + 0.897237i
\(82\) 0 0
\(83\) −4.05047e10 −1.12869 −0.564346 0.825538i \(-0.690872\pi\)
−0.564346 + 0.825538i \(0.690872\pi\)
\(84\) 0 0
\(85\) 3.45048e10 0.843481
\(86\) 0 0
\(87\) 3.34362e10 + 1.85727e10i 0.719219 + 0.399502i
\(88\) 0 0
\(89\) −2.20949e10 + 3.82694e10i −0.419417 + 0.726452i −0.995881 0.0906709i \(-0.971099\pi\)
0.576464 + 0.817123i \(0.304432\pi\)
\(90\) 0 0
\(91\) 9.59928e10 + 6.90951e10i 1.61254 + 1.16070i
\(92\) 0 0
\(93\) 5.09810e8 + 3.07675e10i 0.00759893 + 0.458601i
\(94\) 0 0
\(95\) −1.49908e8 + 8.65496e7i −0.00198768 + 0.00114759i
\(96\) 0 0
\(97\) 3.96326e8i 0.00468606i −0.999997 0.00234303i \(-0.999254\pi\)
0.999997 0.00234303i \(-0.000745810\pi\)
\(98\) 0 0
\(99\) 1.37114e11 + 7.32164e10i 1.44907 + 0.773776i
\(100\) 0 0
\(101\) 6.42870e10 + 1.11348e11i 0.608633 + 1.05418i 0.991466 + 0.130366i \(0.0416153\pi\)
−0.382832 + 0.923818i \(0.625051\pi\)
\(102\) 0 0
\(103\) 1.70529e10 + 9.84548e9i 0.144941 + 0.0836820i 0.570717 0.821147i \(-0.306665\pi\)
−0.425776 + 0.904829i \(0.639999\pi\)
\(104\) 0 0
\(105\) −6.08461e10 5.10602e9i −0.465255 0.0390428i
\(106\) 0 0
\(107\) −1.25780e11 7.26194e10i −0.866967 0.500543i −0.000627646 1.00000i \(-0.500200\pi\)
−0.866339 + 0.499456i \(0.833533\pi\)
\(108\) 0 0
\(109\) 2.79034e10 + 4.83301e10i 0.173705 + 0.300865i 0.939712 0.341966i \(-0.111093\pi\)
−0.766008 + 0.642831i \(0.777760\pi\)
\(110\) 0 0
\(111\) −9.52290e10 1.58806e11i −0.536405 0.894520i
\(112\) 0 0
\(113\) 2.81459e10i 0.143709i −0.997415 0.0718545i \(-0.977108\pi\)
0.997415 0.0718545i \(-0.0228917\pi\)
\(114\) 0 0
\(115\) −7.90532e9 + 4.56414e9i −0.0366506 + 0.0211602i
\(116\) 0 0
\(117\) 4.00022e11 2.48978e11i 1.68679 1.04988i
\(118\) 0 0
\(119\) 4.67930e11 + 4.70862e10i 1.79751 + 0.180878i
\(120\) 0 0
\(121\) 2.42304e11 4.19683e11i 0.849262 1.47096i
\(122\) 0 0
\(123\) −1.69132e11 + 3.04486e11i −0.541685 + 0.975190i
\(124\) 0 0
\(125\) 2.83878e11 0.832005
\(126\) 0 0
\(127\) −4.16856e11 −1.11961 −0.559803 0.828626i \(-0.689123\pi\)
−0.559803 + 0.828626i \(0.689123\pi\)
\(128\) 0 0
\(129\) −8.96021e10 + 1.61310e11i −0.220838 + 0.397573i
\(130\) 0 0
\(131\) −3.70325e11 + 6.41422e11i −0.838670 + 1.45262i 0.0523376 + 0.998629i \(0.483333\pi\)
−0.891007 + 0.453989i \(0.850001\pi\)
\(132\) 0 0
\(133\) −2.15106e9 + 9.69156e8i −0.00448196 + 0.00201934i
\(134\) 0 0
\(135\) −1.11008e11 + 2.16442e11i −0.213068 + 0.415438i
\(136\) 0 0
\(137\) −3.57867e11 + 2.06615e11i −0.633517 + 0.365761i −0.782113 0.623137i \(-0.785858\pi\)
0.148596 + 0.988898i \(0.452525\pi\)
\(138\) 0 0
\(139\) 9.15488e11i 1.49648i 0.663427 + 0.748241i \(0.269101\pi\)
−0.663427 + 0.748241i \(0.730899\pi\)
\(140\) 0 0
\(141\) 3.62158e11 + 6.03942e11i 0.547259 + 0.912620i
\(142\) 0 0
\(143\) −1.16693e12 2.02118e12i −1.63191 2.82654i
\(144\) 0 0
\(145\) 2.56759e11 + 1.48240e11i 0.332660 + 0.192062i
\(146\) 0 0
\(147\) −8.18184e11 1.52277e11i −0.983118 0.182973i
\(148\) 0 0
\(149\) 6.77109e11 + 3.90929e11i 0.755326 + 0.436088i 0.827615 0.561296i \(-0.189697\pi\)
−0.0722892 + 0.997384i \(0.523030\pi\)
\(150\) 0 0
\(151\) −2.78532e11 4.82432e11i −0.288737 0.500107i 0.684772 0.728758i \(-0.259902\pi\)
−0.973508 + 0.228651i \(0.926569\pi\)
\(152\) 0 0
\(153\) 8.82501e11 1.65268e12i 0.850966 1.59362i
\(154\) 0 0
\(155\) 2.38525e11i 0.214146i
\(156\) 0 0
\(157\) −5.73937e11 + 3.31363e11i −0.480193 + 0.277240i −0.720497 0.693458i \(-0.756086\pi\)
0.240304 + 0.970698i \(0.422753\pi\)
\(158\) 0 0
\(159\) −2.58178e10 1.55813e12i −0.0201482 1.21596i
\(160\) 0 0
\(161\) −1.13435e11 + 5.11078e10i −0.0826426 + 0.0372345i
\(162\) 0 0
\(163\) −3.01748e10 + 5.22643e10i −0.0205406 + 0.0355773i −0.876113 0.482106i \(-0.839872\pi\)
0.855572 + 0.517683i \(0.173205\pi\)
\(164\) 0 0
\(165\) 1.05329e12 + 5.85065e11i 0.670478 + 0.372428i
\(166\) 0 0
\(167\) −3.58050e11 −0.213306 −0.106653 0.994296i \(-0.534013\pi\)
−0.106653 + 0.994296i \(0.534013\pi\)
\(168\) 0 0
\(169\) −5.28242e12 −2.94752
\(170\) 0 0
\(171\) 3.11391e8 + 9.39377e9i 0.000162865 + 0.00491317i
\(172\) 0 0
\(173\) 1.20251e12 2.08281e12i 0.589979 1.02187i −0.404256 0.914646i \(-0.632469\pi\)
0.994235 0.107227i \(-0.0341972\pi\)
\(174\) 0 0
\(175\) 1.68941e12 + 1.70000e11i 0.778084 + 0.0782960i
\(176\) 0 0
\(177\) −3.32158e12 + 5.50378e10i −1.43712 + 0.0238127i
\(178\) 0 0
\(179\) 1.32135e12 7.62882e11i 0.537435 0.310288i −0.206604 0.978425i \(-0.566241\pi\)
0.744039 + 0.668136i \(0.232908\pi\)
\(180\) 0 0
\(181\) 2.19711e12i 0.840660i −0.907371 0.420330i \(-0.861914\pi\)
0.907371 0.420330i \(-0.138086\pi\)
\(182\) 0 0
\(183\) 2.79008e12 1.67309e12i 1.00493 0.602614i
\(184\) 0 0
\(185\) −7.17668e11 1.24304e12i −0.243489 0.421735i
\(186\) 0 0
\(187\) −8.03679e12 4.64004e12i −2.57012 1.48386i
\(188\) 0 0
\(189\) −1.80077e12 + 2.78376e12i −0.543149 + 0.839636i
\(190\) 0 0
\(191\) 4.47282e12 + 2.58238e12i 1.27320 + 0.735084i 0.975590 0.219602i \(-0.0704759\pi\)
0.297614 + 0.954686i \(0.403809\pi\)
\(192\) 0 0
\(193\) −2.50501e11 4.33881e11i −0.0673357 0.116629i 0.830392 0.557180i \(-0.188117\pi\)
−0.897728 + 0.440551i \(0.854783\pi\)
\(194\) 0 0
\(195\) 3.13230e12 1.87831e12i 0.795561 0.477064i
\(196\) 0 0
\(197\) 5.68212e12i 1.36441i −0.731159 0.682207i \(-0.761020\pi\)
0.731159 0.682207i \(-0.238980\pi\)
\(198\) 0 0
\(199\) −4.60888e12 + 2.66094e12i −1.04690 + 0.604426i −0.921779 0.387716i \(-0.873264\pi\)
−0.125118 + 0.992142i \(0.539931\pi\)
\(200\) 0 0
\(201\) 3.83342e12 6.35189e10i 0.824153 0.0136560i
\(202\) 0 0
\(203\) 3.27969e12 + 2.36070e12i 0.667735 + 0.480632i
\(204\) 0 0
\(205\) −1.34994e12 + 2.33817e12i −0.260416 + 0.451055i
\(206\) 0 0
\(207\) 1.64210e10 + 4.95375e11i 0.00300305 + 0.0905935i
\(208\) 0 0
\(209\) 4.65551e10 0.00807538
\(210\) 0 0
\(211\) 3.35994e12 0.553067 0.276534 0.961004i \(-0.410814\pi\)
0.276534 + 0.961004i \(0.410814\pi\)
\(212\) 0 0
\(213\) 2.22313e12 + 1.23488e12i 0.347438 + 0.192990i
\(214\) 0 0
\(215\) −7.15167e11 + 1.23871e12i −0.106169 + 0.183889i
\(216\) 0 0
\(217\) −3.25499e11 + 3.23471e12i −0.0459220 + 0.456360i
\(218\) 0 0
\(219\) −2.07408e11 1.25173e13i −0.0278217 1.67906i
\(220\) 0 0
\(221\) −2.43619e13 + 1.40653e13i −3.10851 + 1.79470i
\(222\) 0 0
\(223\) 3.63453e12i 0.441338i 0.975349 + 0.220669i \(0.0708240\pi\)
−0.975349 + 0.220669i \(0.929176\pi\)
\(224\) 0 0
\(225\) 3.18618e12 5.96682e12i 0.368354 0.689826i
\(226\) 0 0
\(227\) −5.30101e12 9.18162e12i −0.583736 1.01106i −0.995032 0.0995583i \(-0.968257\pi\)
0.411296 0.911502i \(-0.365076\pi\)
\(228\) 0 0
\(229\) 1.22823e13 + 7.09120e12i 1.28880 + 0.744088i 0.978440 0.206531i \(-0.0662175\pi\)
0.310359 + 0.950620i \(0.399551\pi\)
\(230\) 0 0
\(231\) 1.34855e13 + 9.37158e12i 1.34897 + 0.937448i
\(232\) 0 0
\(233\) 1.32964e13 + 7.67668e12i 1.26846 + 0.732345i 0.974696 0.223533i \(-0.0717590\pi\)
0.293763 + 0.955878i \(0.405092\pi\)
\(234\) 0 0
\(235\) 2.72931e12 + 4.72730e12i 0.248416 + 0.430269i
\(236\) 0 0
\(237\) 2.79514e12 + 4.66123e12i 0.242822 + 0.404935i
\(238\) 0 0
\(239\) 5.82714e12i 0.483356i 0.970356 + 0.241678i \(0.0776978\pi\)
−0.970356 + 0.241678i \(0.922302\pi\)
\(240\) 0 0
\(241\) −1.36416e13 + 7.87599e12i −1.08087 + 0.624039i −0.931130 0.364687i \(-0.881176\pi\)
−0.149736 + 0.988726i \(0.547843\pi\)
\(242\) 0 0
\(243\) 7.52780e12 + 1.08527e13i 0.569946 + 0.821682i
\(244\) 0 0
\(245\) −6.32169e12 1.28528e12i −0.457530 0.0930214i
\(246\) 0 0
\(247\) 7.05611e10 1.22215e11i 0.00488351 0.00845849i
\(248\) 0 0
\(249\) −8.27820e12 + 1.49031e13i −0.548074 + 0.986692i
\(250\) 0 0
\(251\) 2.58946e13 1.64061 0.820303 0.571930i \(-0.193805\pi\)
0.820303 + 0.571930i \(0.193805\pi\)
\(252\) 0 0
\(253\) 2.45506e12 0.148901
\(254\) 0 0
\(255\) 7.05197e12 1.26956e13i 0.409581 0.737363i
\(256\) 0 0
\(257\) −5.04076e12 + 8.73086e12i −0.280456 + 0.485763i −0.971497 0.237052i \(-0.923819\pi\)
0.691041 + 0.722815i \(0.257152\pi\)
\(258\) 0 0
\(259\) −8.03622e12 1.78365e13i −0.428453 0.950960i
\(260\) 0 0
\(261\) 1.36671e13 8.50658e12i 0.698482 0.434743i
\(262\) 0 0
\(263\) 1.95406e13 1.12818e13i 0.957593 0.552866i 0.0621613 0.998066i \(-0.480201\pi\)
0.895431 + 0.445200i \(0.146867\pi\)
\(264\) 0 0
\(265\) 1.20794e13i 0.567797i
\(266\) 0 0
\(267\) 9.56505e12 + 1.59509e13i 0.431395 + 0.719403i
\(268\) 0 0
\(269\) −2.22091e12 3.84672e12i −0.0961375 0.166515i 0.813945 0.580942i \(-0.197316\pi\)
−0.910083 + 0.414426i \(0.863982\pi\)
\(270\) 0 0
\(271\) −1.91238e13 1.10411e13i −0.794771 0.458861i 0.0468683 0.998901i \(-0.485076\pi\)
−0.841640 + 0.540040i \(0.818409\pi\)
\(272\) 0 0
\(273\) 4.50413e13 2.11979e13i 1.79770 0.846052i
\(274\) 0 0
\(275\) −2.90160e13 1.67524e13i −1.11252 0.642314i
\(276\) 0 0
\(277\) 1.42979e13 + 2.47647e13i 0.526786 + 0.912420i 0.999513 + 0.0312111i \(0.00993640\pi\)
−0.472727 + 0.881209i \(0.656730\pi\)
\(278\) 0 0
\(279\) 1.14247e13 + 6.10057e12i 0.404595 + 0.216046i
\(280\) 0 0
\(281\) 1.38668e13i 0.472163i 0.971733 + 0.236082i \(0.0758633\pi\)
−0.971733 + 0.236082i \(0.924137\pi\)
\(282\) 0 0
\(283\) −7.23338e12 + 4.17620e12i −0.236873 + 0.136759i −0.613739 0.789509i \(-0.710335\pi\)
0.376866 + 0.926268i \(0.377002\pi\)
\(284\) 0 0
\(285\) 1.20703e9 + 7.28454e10i 3.80253e−5 + 0.00229486i
\(286\) 0 0
\(287\) −2.14977e13 + 2.98664e13i −0.651690 + 0.905383i
\(288\) 0 0
\(289\) −3.87920e13 + 6.71896e13i −1.13189 + 1.96049i
\(290\) 0 0
\(291\) −1.45823e11 8.09997e10i −0.00409651 0.00227547i
\(292\) 0 0
\(293\) −8.14544e11 −0.0220365 −0.0110182 0.999939i \(-0.503507\pi\)
−0.0110182 + 0.999939i \(0.503507\pi\)
\(294\) 0 0
\(295\) −2.57506e13 −0.671068
\(296\) 0 0
\(297\) 5.49619e13 3.54856e13i 1.38007 0.891028i
\(298\) 0 0
\(299\) 3.72100e12 6.44495e12i 0.0900467 0.155965i
\(300\) 0 0
\(301\) −1.13890e13 + 1.58225e13i −0.265686 + 0.369114i
\(302\) 0 0
\(303\) 5.41079e13 8.96556e11i 1.21710 0.0201671i
\(304\) 0 0
\(305\) 2.18391e13 1.26088e13i 0.473790 0.273543i
\(306\) 0 0
\(307\) 5.50636e13i 1.15240i −0.817308 0.576201i \(-0.804535\pi\)
0.817308 0.576201i \(-0.195465\pi\)
\(308\) 0 0
\(309\) 7.10772e12 4.26219e12i 0.143535 0.0860718i
\(310\) 0 0
\(311\) −7.23497e12 1.25313e13i −0.141011 0.244239i 0.786866 0.617123i \(-0.211702\pi\)
−0.927878 + 0.372884i \(0.878369\pi\)
\(312\) 0 0
\(313\) −2.34098e13 1.35156e13i −0.440457 0.254298i 0.263335 0.964705i \(-0.415178\pi\)
−0.703791 + 0.710407i \(0.748511\pi\)
\(314\) 0 0
\(315\) −1.43142e13 + 2.13439e13i −0.260051 + 0.387763i
\(316\) 0 0
\(317\) −5.72992e13 3.30817e13i −1.00536 0.580446i −0.0955321 0.995426i \(-0.530455\pi\)
−0.909831 + 0.414980i \(0.863789\pi\)
\(318\) 0 0
\(319\) −3.98692e13 6.90554e13i −0.675754 1.17044i
\(320\) 0 0
\(321\) −5.24259e13 + 3.14375e13i −0.858555 + 0.514838i
\(322\) 0 0
\(323\) 5.61144e11i 0.00888096i
\(324\) 0 0
\(325\) −8.79559e13 + 5.07814e13i −1.34557 + 0.776866i
\(326\) 0 0
\(327\) 2.34852e13 3.89145e11i 0.347361 0.00575571i
\(328\) 0 0
\(329\) 3.05619e13 + 6.78328e13i 0.437123 + 0.970202i
\(330\) 0 0
\(331\) −3.38852e12 + 5.86909e12i −0.0468766 + 0.0811927i −0.888512 0.458854i \(-0.848260\pi\)
0.841635 + 0.540047i \(0.181593\pi\)
\(332\) 0 0
\(333\) −7.78930e13 + 2.58205e12i −1.04245 + 0.0345558i
\(334\) 0 0
\(335\) 2.97187e13 0.384842
\(336\) 0 0
\(337\) −5.68257e13 −0.712165 −0.356082 0.934455i \(-0.615888\pi\)
−0.356082 + 0.934455i \(0.615888\pi\)
\(338\) 0 0
\(339\) −1.03559e13 5.75236e12i −0.125629 0.0697827i
\(340\) 0 0
\(341\) 3.20758e13 5.55569e13i 0.376728 0.652512i
\(342\) 0 0
\(343\) −8.39764e13 2.60568e13i −0.955080 0.296349i
\(344\) 0 0
\(345\) 6.36522e10 + 3.84146e12i 0.000701145 + 0.0423147i
\(346\) 0 0
\(347\) 9.78016e13 5.64658e13i 1.04360 0.602522i 0.122749 0.992438i \(-0.460829\pi\)
0.920851 + 0.389915i \(0.127496\pi\)
\(348\) 0 0
\(349\) 1.15743e14i 1.19661i 0.801268 + 0.598306i \(0.204159\pi\)
−0.801268 + 0.598306i \(0.795841\pi\)
\(350\) 0 0
\(351\) −9.85305e12 1.98068e14i −0.0987147 1.98438i
\(352\) 0 0
\(353\) 4.59576e13 + 7.96010e13i 0.446269 + 0.772961i 0.998140 0.0609690i \(-0.0194191\pi\)
−0.551870 + 0.833930i \(0.686086\pi\)
\(354\) 0 0
\(355\) 1.70716e13 + 9.85628e12i 0.160701 + 0.0927805i
\(356\) 0 0
\(357\) 1.12959e14 1.62545e14i 1.03097 1.48354i
\(358\) 0 0
\(359\) 8.24544e10 + 4.76051e10i 0.000729784 + 0.000421341i 0.500365 0.865815i \(-0.333199\pi\)
−0.499635 + 0.866236i \(0.666533\pi\)
\(360\) 0 0
\(361\) −5.82437e13 1.00881e14i −0.499988 0.866004i
\(362\) 0 0
\(363\) −1.04896e14 1.74926e14i −0.873515 1.45669i
\(364\) 0 0
\(365\) 9.70403e13i 0.784046i
\(366\) 0 0
\(367\) 1.12170e13 6.47613e12i 0.0879454 0.0507753i −0.455382 0.890296i \(-0.650497\pi\)
0.543328 + 0.839521i \(0.317164\pi\)
\(368\) 0 0
\(369\) 7.74650e13 + 1.24460e14i 0.589468 + 0.947072i
\(370\) 0 0
\(371\) 1.64839e13 1.63812e14i 0.121760 1.21001i
\(372\) 0 0
\(373\) 8.87774e11 1.53767e12i 0.00636655 0.0110272i −0.862825 0.505503i \(-0.831307\pi\)
0.869191 + 0.494476i \(0.164640\pi\)
\(374\) 0 0
\(375\) 5.80179e13 1.04449e14i 0.404008 0.727331i
\(376\) 0 0
\(377\) −2.41710e14 −1.63462
\(378\) 0 0
\(379\) −2.73701e14 −1.79788 −0.898942 0.438068i \(-0.855663\pi\)
−0.898942 + 0.438068i \(0.855663\pi\)
\(380\) 0 0
\(381\) −8.51955e13 + 1.53376e14i −0.543662 + 0.978749i
\(382\) 0 0
\(383\) −2.61001e13 + 4.52066e13i −0.161826 + 0.280291i −0.935524 0.353264i \(-0.885072\pi\)
0.773698 + 0.633555i \(0.218405\pi\)
\(384\) 0 0
\(385\) 1.03315e14 + 7.43653e13i 0.622483 + 0.448060i
\(386\) 0 0
\(387\) 4.10391e13 + 6.59358e13i 0.240319 + 0.386110i
\(388\) 0 0
\(389\) 2.17356e14 1.25490e14i 1.23722 0.714312i 0.268699 0.963224i \(-0.413406\pi\)
0.968526 + 0.248912i \(0.0800731\pi\)
\(390\) 0 0
\(391\) 2.95916e13i 0.163755i
\(392\) 0 0
\(393\) 1.60317e14 + 2.67348e14i 0.862621 + 1.43852i
\(394\) 0 0
\(395\) 2.10648e13 + 3.64854e13i 0.110223 + 0.190913i
\(396\) 0 0
\(397\) 9.84470e13 + 5.68384e13i 0.501020 + 0.289264i 0.729134 0.684370i \(-0.239923\pi\)
−0.228115 + 0.973634i \(0.573256\pi\)
\(398\) 0 0
\(399\) −8.30380e10 + 9.89526e11i −0.000411080 + 0.00489865i
\(400\) 0 0
\(401\) −1.35237e14 7.80794e13i −0.651333 0.376047i 0.137634 0.990483i \(-0.456050\pi\)
−0.788967 + 0.614436i \(0.789384\pi\)
\(402\) 0 0
\(403\) −9.72310e13 1.68409e14i −0.455646 0.789201i
\(404\) 0 0
\(405\) 5.69497e13 + 8.50795e13i 0.259710 + 0.387992i
\(406\) 0 0
\(407\) 3.86034e14i 1.71339i
\(408\) 0 0
\(409\) 2.13142e14 1.23057e14i 0.920853 0.531655i 0.0369461 0.999317i \(-0.488237\pi\)
0.883907 + 0.467662i \(0.154904\pi\)
\(410\) 0 0
\(411\) 2.88148e12 + 1.73899e14i 0.0121195 + 0.731422i
\(412\) 0 0
\(413\) −3.49212e14 3.51400e13i −1.43009 0.143905i
\(414\) 0 0
\(415\) −6.60732e13 + 1.14442e14i −0.263488 + 0.456375i
\(416\) 0 0
\(417\) 3.36842e14 + 1.87104e14i 1.30821 + 0.726667i
\(418\) 0 0
\(419\) 1.70620e14 0.645436 0.322718 0.946495i \(-0.395404\pi\)
0.322718 + 0.946495i \(0.395404\pi\)
\(420\) 0 0
\(421\) 2.48151e14 0.914459 0.457230 0.889349i \(-0.348842\pi\)
0.457230 + 0.889349i \(0.348842\pi\)
\(422\) 0 0
\(423\) 2.96229e14 9.81960e12i 1.06354 0.0352551i
\(424\) 0 0
\(425\) −2.01922e14 + 3.49739e14i −0.706389 + 1.22350i
\(426\) 0 0
\(427\) 3.13373e14 1.41190e14i 1.06834 0.481337i
\(428\) 0 0
\(429\) −9.82156e14 + 1.62741e13i −3.26336 + 0.0540732i
\(430\) 0 0
\(431\) −1.28149e14 + 7.39868e13i −0.415040 + 0.239624i −0.692953 0.720983i \(-0.743691\pi\)
0.277913 + 0.960606i \(0.410357\pi\)
\(432\) 0 0
\(433\) 3.44844e14i 1.08878i 0.838833 + 0.544388i \(0.183238\pi\)
−0.838833 + 0.544388i \(0.816762\pi\)
\(434\) 0 0
\(435\) 1.07018e14 6.41742e13i 0.329433 0.197547i
\(436\) 0 0
\(437\) 7.42255e10 + 1.28562e11i 0.000222795 + 0.000385892i
\(438\) 0 0
\(439\) 2.65935e14 + 1.53538e14i 0.778433 + 0.449428i 0.835875 0.548920i \(-0.184961\pi\)
−0.0574417 + 0.998349i \(0.518294\pi\)
\(440\) 0 0
\(441\) −2.23246e14 + 2.69918e14i −0.637339 + 0.770583i
\(442\) 0 0
\(443\) 3.35932e14 + 1.93951e14i 0.935473 + 0.540095i 0.888538 0.458803i \(-0.151721\pi\)
0.0469344 + 0.998898i \(0.485055\pi\)
\(444\) 0 0
\(445\) 7.20844e13 + 1.24854e14i 0.195822 + 0.339174i
\(446\) 0 0
\(447\) 2.82222e14 1.69237e14i 0.747997 0.448542i
\(448\) 0 0
\(449\) 8.54077e13i 0.220873i 0.993883 + 0.110436i \(0.0352248\pi\)
−0.993883 + 0.110436i \(0.964775\pi\)
\(450\) 0 0
\(451\) 6.28851e14 3.63067e14i 1.58700 0.916255i
\(452\) 0 0
\(453\) −2.34430e14 + 3.88445e12i −0.577394 + 0.00956730i
\(454\) 0 0
\(455\) 3.51810e14 1.58507e14i 0.845757 0.381054i
\(456\) 0 0
\(457\) −1.59878e13 + 2.76916e13i −0.0375188 + 0.0649844i −0.884175 0.467156i \(-0.845279\pi\)
0.846656 + 0.532140i \(0.178612\pi\)
\(458\) 0 0
\(459\) −4.27718e14 6.62473e14i −0.979915 1.51774i
\(460\) 0 0
\(461\) −1.97115e13 −0.0440924 −0.0220462 0.999757i \(-0.507018\pi\)
−0.0220462 + 0.999757i \(0.507018\pi\)
\(462\) 0 0
\(463\) 1.41121e14 0.308246 0.154123 0.988052i \(-0.450745\pi\)
0.154123 + 0.988052i \(0.450745\pi\)
\(464\) 0 0
\(465\) 8.77622e13 + 4.87490e13i 0.187205 + 0.103986i
\(466\) 0 0
\(467\) −8.74550e13 + 1.51476e14i −0.182197 + 0.315575i −0.942628 0.333844i \(-0.891654\pi\)
0.760431 + 0.649418i \(0.224988\pi\)
\(468\) 0 0
\(469\) 4.03023e14 + 4.05549e13i 0.820124 + 0.0825264i
\(470\) 0 0
\(471\) 4.62123e12 + 2.78895e14i 0.00918634 + 0.554403i
\(472\) 0 0
\(473\) 3.33151e14 1.92345e14i 0.647000 0.373546i
\(474\) 0 0
\(475\) 2.02595e12i 0.00384427i
\(476\) 0 0
\(477\) −5.78568e14 3.08945e14i −1.07276 0.572835i
\(478\) 0 0
\(479\) −2.69560e14 4.66892e14i −0.488439 0.846001i 0.511473 0.859300i \(-0.329100\pi\)
−0.999912 + 0.0132984i \(0.995767\pi\)
\(480\) 0 0
\(481\) 1.01341e15 + 5.85091e14i 1.79468 + 1.03616i
\(482\) 0 0
\(483\) −4.37896e12 + 5.21820e13i −0.00757987 + 0.0903258i
\(484\) 0 0
\(485\) −1.11978e12 6.46506e11i −0.00189476 0.00109394i
\(486\) 0 0
\(487\) −1.61066e14 2.78974e14i −0.266437 0.461482i 0.701502 0.712667i \(-0.252513\pi\)
−0.967939 + 0.251185i \(0.919180\pi\)
\(488\) 0 0
\(489\) 1.30629e13 + 2.17840e13i 0.0211272 + 0.0352321i
\(490\) 0 0
\(491\) 3.22865e14i 0.510590i −0.966863 0.255295i \(-0.917827\pi\)
0.966863 0.255295i \(-0.0821726\pi\)
\(492\) 0 0
\(493\) −8.32346e14 + 4.80555e14i −1.28720 + 0.743165i
\(494\) 0 0
\(495\) 4.30533e14 2.67969e14i 0.651146 0.405280i
\(496\) 0 0
\(497\) 2.18062e14 + 1.56960e14i 0.322568 + 0.232183i
\(498\) 0 0
\(499\) 2.45306e13 4.24882e13i 0.0354940 0.0614774i −0.847733 0.530424i \(-0.822033\pi\)
0.883227 + 0.468946i \(0.155366\pi\)
\(500\) 0 0
\(501\) −7.31771e13 + 1.31740e14i −0.103578 + 0.186470i
\(502\) 0 0
\(503\) −1.47454e14 −0.204189 −0.102095 0.994775i \(-0.532554\pi\)
−0.102095 + 0.994775i \(0.532554\pi\)
\(504\) 0 0
\(505\) 4.19473e14 0.568331
\(506\) 0 0
\(507\) −1.07960e15 + 1.94360e15i −1.43127 + 2.57669i
\(508\) 0 0
\(509\) −7.25926e14 + 1.25734e15i −0.941769 + 1.63119i −0.179675 + 0.983726i \(0.557505\pi\)
−0.762094 + 0.647466i \(0.775829\pi\)
\(510\) 0 0
\(511\) 1.32424e14 1.31599e15i 0.168133 1.67085i
\(512\) 0 0
\(513\) 3.51995e12 + 1.80529e12i 0.00437413 + 0.00224338i
\(514\) 0 0
\(515\) 5.56349e13 3.21209e13i 0.0676718 0.0390704i
\(516\) 0 0
\(517\) 1.46810e15i 1.74806i
\(518\) 0 0
\(519\) −5.20578e14 8.68127e14i −0.606828 1.01196i
\(520\) 0 0
\(521\) 1.76153e14 + 3.05106e14i 0.201040 + 0.348212i 0.948864 0.315686i \(-0.102234\pi\)
−0.747824 + 0.663897i \(0.768901\pi\)
\(522\) 0 0
\(523\) 6.80071e14 + 3.92639e14i 0.759968 + 0.438768i 0.829284 0.558827i \(-0.188748\pi\)
−0.0693165 + 0.997595i \(0.522082\pi\)
\(524\) 0 0
\(525\) 4.07825e14 5.86852e14i 0.446270 0.642174i
\(526\) 0 0
\(527\) −6.69644e14 3.86619e14i −0.717606 0.414310i
\(528\) 0 0
\(529\) −4.72491e14 8.18378e14i −0.495892 0.858910i
\(530\) 0 0
\(531\) −6.58602e14 + 1.23338e15i −0.677023 + 1.26788i
\(532\) 0 0
\(533\) 2.20113e15i 2.21639i
\(534\) 0 0
\(535\) −4.10359e14 + 2.36921e14i −0.404779 + 0.233699i
\(536\) 0 0
\(537\) −1.06393e13 6.42088e14i −0.0102814 0.620492i
\(538\) 0 0
\(539\) 1.29960e15 + 1.14948e15i 1.23047 + 1.08833i
\(540\) 0 0
\(541\) −5.72954e14 + 9.92386e14i −0.531539 + 0.920652i 0.467783 + 0.883843i \(0.345053\pi\)
−0.999322 + 0.0368093i \(0.988281\pi\)
\(542\) 0 0
\(543\) −8.08399e14 4.49038e14i −0.734897 0.408211i
\(544\) 0 0
\(545\) 1.82070e14 0.162202
\(546\) 0 0
\(547\) −1.25038e14 −0.109172 −0.0545860 0.998509i \(-0.517384\pi\)
−0.0545860 + 0.998509i \(0.517384\pi\)
\(548\) 0 0
\(549\) −4.53644e13 1.36851e15i −0.0388211 1.17112i
\(550\) 0 0
\(551\) 2.41079e12 4.17561e12i 0.00202220 0.00350256i
\(552\) 0 0
\(553\) 2.35877e14 + 5.23534e14i 0.193954 + 0.430484i
\(554\) 0 0
\(555\) −6.04033e14 + 1.00087e13i −0.486911 + 0.00806801i
\(556\) 0 0
\(557\) 6.97890e14 4.02927e14i 0.551548 0.318437i −0.198198 0.980162i \(-0.563509\pi\)
0.749746 + 0.661725i \(0.230176\pi\)
\(558\) 0 0
\(559\) 1.16611e15i 0.903593i
\(560\) 0 0
\(561\) −3.34977e15 + 2.00871e15i −2.54519 + 1.52624i
\(562\) 0 0
\(563\) −1.08538e15 1.87993e15i −0.808696 1.40070i −0.913767 0.406238i \(-0.866840\pi\)
0.105071 0.994465i \(-0.466493\pi\)
\(564\) 0 0
\(565\) −7.95237e13 4.59130e13i −0.0581072 0.0335482i
\(566\) 0 0
\(567\) 6.56210e14 + 1.23150e15i 0.470258 + 0.882529i
\(568\) 0 0
\(569\) 4.83451e13 + 2.79121e13i 0.0339809 + 0.0196189i 0.516894 0.856049i \(-0.327088\pi\)
−0.482913 + 0.875668i \(0.660421\pi\)
\(570\) 0 0
\(571\) 2.45388e14 + 4.25025e14i 0.169182 + 0.293032i 0.938133 0.346276i \(-0.112554\pi\)
−0.768950 + 0.639309i \(0.779221\pi\)
\(572\) 0 0
\(573\) 1.86429e15 1.11794e15i 1.26085 0.756077i
\(574\) 0 0
\(575\) 1.06837e14i 0.0708842i
\(576\) 0 0
\(577\) 7.36955e14 4.25481e14i 0.479705 0.276958i −0.240589 0.970627i \(-0.577340\pi\)
0.720293 + 0.693670i \(0.244007\pi\)
\(578\) 0 0
\(579\) −2.10837e14 + 3.49353e12i −0.134653 + 0.00223117i
\(580\) 0 0
\(581\) −1.05221e15 + 1.46182e15i −0.659376 + 0.916062i
\(582\) 0 0
\(583\) −1.62438e15 + 2.81351e15i −0.998875 + 1.73010i
\(584\) 0 0
\(585\) −5.09287e13 1.53637e15i −0.0307330 0.927126i
\(586\) 0 0
\(587\) 2.10431e15 1.24624 0.623119 0.782127i \(-0.285865\pi\)
0.623119 + 0.782127i \(0.285865\pi\)
\(588\) 0 0
\(589\) 3.87908e12 0.00225473
\(590\) 0 0
\(591\) −2.09066e15 1.16129e15i −1.19276 0.662537i
\(592\) 0 0
\(593\) 6.75597e14 1.17017e15i 0.378344 0.655311i −0.612478 0.790488i \(-0.709827\pi\)
0.990821 + 0.135177i \(0.0431603\pi\)
\(594\) 0 0
\(595\) 8.96348e14 1.24528e15i 0.492758 0.684581i
\(596\) 0 0
\(597\) 3.71099e13 + 2.23961e15i 0.0200277 + 1.20869i
\(598\) 0 0
\(599\) −3.17424e14 + 1.83265e14i −0.168187 + 0.0971029i −0.581731 0.813381i \(-0.697624\pi\)
0.413544 + 0.910484i \(0.364291\pi\)
\(600\) 0 0
\(601\) 2.62688e15i 1.36657i −0.730153 0.683284i \(-0.760551\pi\)
0.730153 0.683284i \(-0.239449\pi\)
\(602\) 0 0
\(603\) 7.60089e14 1.42344e15i 0.388257 0.727098i
\(604\) 0 0
\(605\) −7.90517e14 1.36922e15i −0.396512 0.686780i
\(606\) 0 0
\(607\) 6.72128e14 + 3.88053e14i 0.331066 + 0.191141i 0.656314 0.754488i \(-0.272115\pi\)
−0.325248 + 0.945629i \(0.605448\pi\)
\(608\) 0 0
\(609\) 1.53888e15 7.24245e14i 0.744405 0.350341i
\(610\) 0 0
\(611\) −3.85401e15 2.22512e15i −1.83099 1.05712i
\(612\) 0 0
\(613\) −8.82208e14 1.52803e15i −0.411660 0.713015i 0.583412 0.812177i \(-0.301717\pi\)
−0.995071 + 0.0991611i \(0.968384\pi\)
\(614\) 0 0
\(615\) 5.84401e14 + 9.74559e14i 0.267854 + 0.446678i
\(616\) 0 0
\(617\) 1.98087e15i 0.891841i 0.895073 + 0.445920i \(0.147124\pi\)
−0.895073 + 0.445920i \(0.852876\pi\)
\(618\) 0 0
\(619\) 6.46694e14 3.73369e14i 0.286022 0.165135i −0.350124 0.936703i \(-0.613861\pi\)
0.636147 + 0.771568i \(0.280527\pi\)
\(620\) 0 0
\(621\) 1.85623e14 + 9.52011e13i 0.0806542 + 0.0413655i
\(622\) 0 0
\(623\) 8.07179e14 + 1.79155e15i 0.344577 + 0.764794i
\(624\) 0 0
\(625\) −4.69157e14 + 8.12604e14i −0.196779 + 0.340831i
\(626\) 0 0
\(627\) 9.51477e12 1.71293e13i 0.00392127 0.00705942i
\(628\) 0 0
\(629\) 4.65299e15 1.88432
\(630\) 0 0
\(631\) −2.48659e15 −0.989561 −0.494780 0.869018i \(-0.664751\pi\)
−0.494780 + 0.869018i \(0.664751\pi\)
\(632\) 0 0
\(633\) 6.86693e14 1.23624e15i 0.268560 0.483486i
\(634\) 0 0
\(635\) −6.79995e14 + 1.17779e15i −0.261367 + 0.452701i
\(636\) 0 0
\(637\) 4.98730e15 1.66948e15i 1.88408 0.630686i
\(638\) 0 0
\(639\) 9.08712e14 5.65592e14i 0.337421 0.210014i
\(640\) 0 0
\(641\) 7.75339e14 4.47642e14i 0.282991 0.163385i −0.351786 0.936081i \(-0.614425\pi\)
0.634777 + 0.772696i \(0.281092\pi\)
\(642\) 0 0
\(643\) 1.33450e15i 0.478806i 0.970920 + 0.239403i \(0.0769518\pi\)
−0.970920 + 0.239403i \(0.923048\pi\)
\(644\) 0 0
\(645\) 3.09602e14 + 5.16298e14i 0.109201 + 0.182105i
\(646\) 0 0
\(647\) 5.26317e14 + 9.11608e14i 0.182505 + 0.316108i 0.942733 0.333549i \(-0.108246\pi\)
−0.760228 + 0.649656i \(0.774913\pi\)
\(648\) 0 0
\(649\) 5.99778e15 + 3.46282e15i 2.04477 + 1.18055i
\(650\) 0 0
\(651\) 1.12365e15 + 7.80862e14i 0.376646 + 0.261745i
\(652\) 0 0
\(653\) −1.22024e15 7.04504e14i −0.402181 0.232199i 0.285244 0.958455i \(-0.407925\pi\)
−0.687425 + 0.726256i \(0.741259\pi\)
\(654\) 0 0
\(655\) 1.20818e15 + 2.09264e15i 0.391567 + 0.678214i
\(656\) 0 0
\(657\) −4.64795e15 2.48192e15i −1.48133 0.791003i
\(658\) 0 0
\(659\) 3.56604e15i 1.11768i 0.829276 + 0.558839i \(0.188753\pi\)
−0.829276 + 0.558839i \(0.811247\pi\)
\(660\) 0 0
\(661\) −4.80721e15 + 2.77545e15i −1.48179 + 0.855509i −0.999787 0.0206627i \(-0.993422\pi\)
−0.481999 + 0.876172i \(0.660089\pi\)
\(662\) 0 0
\(663\) 1.96157e14 + 1.18382e16i 0.0594675 + 3.58891i
\(664\) 0 0
\(665\) −7.70654e11 + 7.65855e12i −0.000229795 + 0.00228364i
\(666\) 0 0
\(667\) 1.27131e14 2.20198e14i 0.0372873 0.0645835i
\(668\) 0 0
\(669\) 1.33727e15 + 7.42811e14i 0.385813 + 0.214306i
\(670\) 0 0
\(671\) −6.78230e15 −1.92488
\(672\) 0 0
\(673\) −1.15970e15 −0.323790 −0.161895 0.986808i \(-0.551761\pi\)
−0.161895 + 0.986808i \(0.551761\pi\)
\(674\) 0 0
\(675\) −1.54423e15 2.39179e15i −0.424172 0.656980i
\(676\) 0 0
\(677\) 1.90351e14 3.29697e14i 0.0514419 0.0891000i −0.839158 0.543888i \(-0.816952\pi\)
0.890600 + 0.454788i \(0.150285\pi\)
\(678\) 0 0
\(679\) −1.43034e13 1.02955e13i −0.00380327 0.00273757i
\(680\) 0 0
\(681\) −4.46165e15 + 7.39286e13i −1.16731 + 0.0193421i
\(682\) 0 0
\(683\) −2.96367e15 + 1.71108e15i −0.762985 + 0.440509i −0.830366 0.557218i \(-0.811869\pi\)
0.0673816 + 0.997727i \(0.478536\pi\)
\(684\) 0 0
\(685\) 1.34816e15i 0.341541i
\(686\) 0 0
\(687\) 5.11933e15 3.06984e15i 1.27629 0.765338i
\(688\) 0 0
\(689\) 4.92397e15 + 8.52857e15i 1.20812 + 2.09252i
\(690\) 0 0
\(691\) 6.71666e15 + 3.87787e15i 1.62190 + 0.936405i 0.986411 + 0.164296i \(0.0525351\pi\)
0.635490 + 0.772109i \(0.280798\pi\)
\(692\) 0 0
\(693\) 6.20427e15 3.04648e15i 1.47454 0.724046i
\(694\) 0 0
\(695\) 2.58663e15 + 1.49339e15i 0.605086 + 0.349347i
\(696\) 0 0
\(697\) −4.37617e15 7.57974e15i −1.00766 1.74532i
\(698\) 0 0
\(699\) 5.54200e15 3.32330e15i 1.25615 0.753260i
\(700\) 0 0
\(701\) 4.96728e15i 1.10833i −0.832407 0.554165i \(-0.813038\pi\)
0.832407 0.554165i \(-0.186962\pi\)
\(702\) 0 0
\(703\) −2.02152e13 + 1.16713e13i −0.00444042 + 0.00256368i
\(704\) 0 0
\(705\) 2.29715e15 3.80633e13i 0.496763 0.00823126i
\(706\) 0 0
\(707\) 5.68859e15 + 5.72424e14i 1.21115 + 0.121874i
\(708\) 0 0
\(709\) −6.86753e14 + 1.18949e15i −0.143961 + 0.249348i −0.928985 0.370117i \(-0.879317\pi\)
0.785024 + 0.619466i \(0.212651\pi\)
\(710\) 0 0
\(711\) 2.28630e15 7.57878e13i 0.471900 0.0156429i
\(712\) 0 0
\(713\) 2.04561e14 0.0415748
\(714\) 0 0
\(715\) −7.61419e15 −1.52384
\(716\) 0 0
\(717\) 2.14402e15 + 1.19093e15i 0.422545 + 0.234710i
\(718\) 0 0
\(719\) −9.33514e14 + 1.61689e15i −0.181181 + 0.313814i −0.942283 0.334818i \(-0.891325\pi\)
0.761102 + 0.648632i \(0.224659\pi\)
\(720\) 0 0
\(721\) 7.98315e14 3.59679e14i 0.152592 0.0687498i
\(722\) 0 0
\(723\) 1.09840e14 + 6.62891e15i 0.0206775 + 1.24791i
\(724\) 0 0
\(725\) −3.00510e15 + 1.73500e15i −0.557186 + 0.321691i
\(726\) 0 0
\(727\) 3.47515e15i 0.634649i 0.948317 + 0.317325i \(0.102784\pi\)
−0.948317 + 0.317325i \(0.897216\pi\)
\(728\) 0 0
\(729\) 5.53162e15 5.51714e14i 0.995063 0.0992460i
\(730\) 0 0
\(731\) −2.31839e15 4.01557e15i −0.410810 0.711544i
\(732\) 0 0
\(733\) −6.25145e15 3.60928e15i −1.09121 0.630011i −0.157313 0.987549i \(-0.550283\pi\)
−0.933899 + 0.357537i \(0.883616\pi\)
\(734\) 0 0
\(735\) −1.76490e15 + 2.06330e15i −0.303488 + 0.354799i
\(736\) 0 0
\(737\) −6.92201e15 3.99643e15i −1.17263 0.677019i
\(738\) 0 0
\(739\) −4.60280e15 7.97229e15i −0.768206 1.33057i −0.938535 0.345185i \(-0.887816\pi\)
0.170328 0.985387i \(-0.445517\pi\)
\(740\) 0 0
\(741\) −3.05465e13 5.09399e13i −0.00502297 0.00837642i
\(742\) 0 0
\(743\) 1.13612e16i 1.84072i −0.391074 0.920359i \(-0.627896\pi\)
0.391074 0.920359i \(-0.372104\pi\)
\(744\) 0 0
\(745\) 2.20907e15 1.27541e15i 0.352655 0.203605i
\(746\) 0 0
\(747\) 3.79154e15 + 6.09170e15i 0.596421 + 0.958242i
\(748\) 0 0
\(749\) −5.88830e15 + 2.65296e15i −0.912725 + 0.411227i
\(750\) 0 0
\(751\) −4.44479e15 + 7.69860e15i −0.678940 + 1.17596i 0.296360 + 0.955076i \(0.404227\pi\)
−0.975300 + 0.220883i \(0.929106\pi\)
\(752\) 0 0
\(753\) 5.29225e15 9.52758e15i 0.796651 1.43420i
\(754\) 0 0
\(755\) −1.81742e15 −0.269617
\(756\) 0 0
\(757\) −1.93247e15 −0.282543 −0.141272 0.989971i \(-0.545119\pi\)
−0.141272 + 0.989971i \(0.545119\pi\)
\(758\) 0 0
\(759\) 5.01756e14 9.03305e14i 0.0723040 0.130168i
\(760\) 0 0
\(761\) 1.80383e15 3.12432e15i 0.256200 0.443751i −0.709021 0.705188i \(-0.750863\pi\)
0.965221 + 0.261436i \(0.0841961\pi\)
\(762\) 0 0
\(763\) 2.46910e15 + 2.48457e14i 0.345664 + 0.0347830i
\(764\) 0 0
\(765\) −3.22991e15 5.18935e15i −0.445710 0.716103i
\(766\) 0 0
\(767\) 1.81810e16 1.04968e16i 2.47311 1.42785i
\(768\) 0 0
\(769\) 1.94760e15i 0.261159i 0.991438 + 0.130579i \(0.0416838\pi\)
−0.991438 + 0.130579i \(0.958316\pi\)
\(770\) 0 0
\(771\) 2.18219e15 + 3.63906e15i 0.288465 + 0.481050i
\(772\) 0 0
\(773\) 1.28222e15 + 2.22087e15i 0.167100 + 0.289425i 0.937399 0.348257i \(-0.113226\pi\)
−0.770299 + 0.637683i \(0.779893\pi\)
\(774\) 0 0
\(775\) −2.41768e15 1.39585e15i −0.310627 0.179341i
\(776\) 0 0
\(777\) −8.20513e15 6.88550e14i −1.03937 0.0872208i
\(778\) 0 0
\(779\) 3.80251e13 + 2.19538e13i 0.00474913 + 0.00274191i
\(780\) 0 0
\(781\) −2.65085e15 4.59141e15i −0.326441 0.565413i
\(782\) 0 0
\(783\) −3.36639e14 6.76719e15i −0.0408766 0.821710i
\(784\) 0 0
\(785\) 2.16214e15i 0.258881i
\(786\) 0 0
\(787\) −1.52454e15 + 8.80192e14i −0.180002 + 0.103924i −0.587294 0.809374i \(-0.699807\pi\)
0.407292 + 0.913298i \(0.366473\pi\)
\(788\) 0 0
\(789\) −1.57337e14 9.49542e15i −0.0183192 1.10558i
\(790\) 0 0
\(791\) −1.01579e15 7.31160e14i −0.116636 0.0839541i
\(792\) 0 0
\(793\) −1.02796e16 + 1.78047e16i −1.16405 + 2.01620i
\(794\) 0 0
\(795\) −4.44445e15 2.46874e15i −0.496363 0.275713i
\(796\) 0 0
\(797\) 1.15235e16 1.26930 0.634648 0.772801i \(-0.281145\pi\)
0.634648 + 0.772801i \(0.281145\pi\)
\(798\) 0 0
\(799\) −1.76954e16 −1.92245
\(800\) 0 0
\(801\) 7.82378e15 2.59348e14i 0.838374 0.0277910i
\(802\) 0 0
\(803\) −1.30495e16 + 2.26024e16i −1.37930 + 2.38902i
\(804\) 0 0
\(805\) −4.06400e13 + 4.03869e14i −0.00423717 + 0.0421078i
\(806\) 0 0
\(807\) −1.86925e15 + 3.09731e13i −0.192249 + 0.00318552i
\(808\) 0 0
\(809\) 7.67377e15 4.43045e15i 0.778560 0.449502i −0.0573597 0.998354i \(-0.518268\pi\)
0.835920 + 0.548852i \(0.184935\pi\)
\(810\) 0 0
\(811\) 4.08074e15i 0.408436i −0.978925 0.204218i \(-0.934535\pi\)
0.978925 0.204218i \(-0.0654652\pi\)
\(812\) 0 0
\(813\) −7.97087e15 + 4.77979e15i −0.787060 + 0.471966i
\(814\) 0 0
\(815\) 9.84453e13 + 1.70512e14i 0.00959021 + 0.0166107i
\(816\) 0 0
\(817\) 2.01448e13 + 1.16306e13i 0.00193616 + 0.00111784i
\(818\) 0 0
\(819\) 1.40592e15 2.09047e16i 0.133321 1.98236i
\(820\) 0 0
\(821\) −1.27365e16 7.35343e15i −1.19169 0.688023i −0.233001 0.972477i \(-0.574854\pi\)
−0.958690 + 0.284454i \(0.908188\pi\)
\(822\) 0 0
\(823\) 4.84910e14 + 8.39889e14i 0.0447674 + 0.0775395i 0.887541 0.460729i \(-0.152412\pi\)
−0.842773 + 0.538268i \(0.819079\pi\)
\(824\) 0 0
\(825\) −1.20940e16 + 7.25225e15i −1.10173 + 0.660657i
\(826\) 0 0
\(827\) 4.82412e15i 0.433648i 0.976211 + 0.216824i \(0.0695699\pi\)
−0.976211 + 0.216824i \(0.930430\pi\)
\(828\) 0 0
\(829\) −5.28967e15 + 3.05399e15i −0.469223 + 0.270906i −0.715914 0.698188i \(-0.753990\pi\)
0.246692 + 0.969094i \(0.420657\pi\)
\(830\) 0 0
\(831\) 1.20340e16 1.99401e14i 1.05343 0.0174551i
\(832\) 0 0
\(833\) 1.38550e16 1.56645e16i 1.19690 1.35322i
\(834\) 0 0
\(835\) −5.84069e14 + 1.01164e15i −0.0497954 + 0.0862481i
\(836\) 0 0
\(837\) 4.57955e15 2.95674e15i 0.385330 0.248784i
\(838\) 0 0
\(839\) −1.68190e16 −1.39672 −0.698360 0.715747i \(-0.746087\pi\)
−0.698360 + 0.715747i \(0.746087\pi\)
\(840\) 0 0
\(841\) 3.94225e15 0.323122
\(842\) 0 0
\(843\) 5.10211e15 + 2.83405e15i 0.412761 + 0.229275i
\(844\) 0 0
\(845\) −8.61695e15 + 1.49250e16i −0.688084 + 1.19180i
\(846\) 0 0
\(847\) −8.85197e15 1.96471e16i −0.697720 1.54860i
\(848\) 0 0
\(849\) 5.82418e13 + 3.51494e15i 0.00453151 + 0.273480i
\(850\) 0 0
\(851\) −1.06604e15 + 6.15477e14i −0.0818766 + 0.0472715i
\(852\) 0 0
\(853\) 1.38889e16i 1.05305i −0.850159 0.526526i \(-0.823494\pi\)
0.850159 0.526526i \(-0.176506\pi\)
\(854\) 0 0
\(855\) 2.70492e13 + 1.44438e13i 0.00202461 + 0.00108110i
\(856\) 0 0
\(857\) −3.57068e15 6.18459e15i −0.263849 0.457000i 0.703412 0.710782i \(-0.251659\pi\)
−0.967262 + 0.253782i \(0.918326\pi\)
\(858\) 0 0
\(859\) 6.23330e15 + 3.59880e15i 0.454732 + 0.262540i 0.709827 0.704376i \(-0.248773\pi\)
−0.255094 + 0.966916i \(0.582107\pi\)
\(860\) 0 0
\(861\) 6.59532e15 + 1.40138e16i 0.475027 + 1.00934i
\(862\) 0 0
\(863\) 1.29698e16 + 7.48810e15i 0.922302 + 0.532491i 0.884369 0.466789i \(-0.154589\pi\)
0.0379333 + 0.999280i \(0.487923\pi\)
\(864\) 0 0
\(865\) −3.92320e15 6.79518e15i −0.275456 0.477103i
\(866\) 0 0
\(867\) 1.67934e16 + 2.80050e16i 1.16421 + 1.94147i
\(868\) 0 0
\(869\) 1.13308e16i 0.775625i
\(870\) 0 0
\(871\) −2.09826e16 + 1.21143e16i −1.41827 + 0.818841i
\(872\) 0 0
\(873\) −5.96055e13 + 3.70991e13i −0.00397839 + 0.00247620i
\(874\) 0 0
\(875\) 7.37443e15 1.02452e16i 0.486053 0.675267i
\(876\) 0 0
\(877\) 4.71763e15 8.17118e15i 0.307062 0.531847i −0.670656 0.741768i \(-0.733987\pi\)
0.977718 + 0.209921i \(0.0673207\pi\)
\(878\) 0 0
\(879\) −1.66474e14 + 2.99700e14i −0.0107006 + 0.0192641i
\(880\) 0 0
\(881\) 9.15600e15 0.581217 0.290608 0.956842i \(-0.406142\pi\)
0.290608 + 0.956842i \(0.406142\pi\)
\(882\) 0 0
\(883\) 5.66081e15 0.354891 0.177445 0.984131i \(-0.443217\pi\)
0.177445 + 0.984131i \(0.443217\pi\)
\(884\) 0 0
\(885\) −5.26282e15 + 9.47459e15i −0.325859 + 0.586641i
\(886\) 0 0
\(887\) 6.33808e15 1.09779e16i 0.387595 0.671334i −0.604531 0.796582i \(-0.706639\pi\)
0.992125 + 0.125248i \(0.0399726\pi\)
\(888\) 0 0
\(889\) −1.08289e16 + 1.50444e16i −0.654068 + 0.908687i
\(890\) 0 0
\(891\) −1.82352e15 2.74749e16i −0.108788 1.63911i
\(892\) 0 0
\(893\) 7.68790e13 4.43861e13i 0.00453027 0.00261555i
\(894\) 0 0
\(895\) 4.97780e15i 0.289742i
\(896\) 0 0
\(897\) −1.61085e15 2.68629e15i −0.0926183 0.154452i
\(898\) 0 0
\(899\) −3.32199e15 5.75386e15i −0.188678 0.326799i
\(900\) 0 0
\(901\) 3.39121e16 + 1.95792e16i 1.90269 + 1.09852i
\(902\) 0 0
\(903\) 3.49405e15 + 7.42417e15i 0.193663 + 0.411496i
\(904\) 0 0
\(905\) −6.20774e15 3.58404e15i −0.339912 0.196248i
\(906\) 0 0
\(907\) −8.59053e15 1.48792e16i −0.464708 0.804897i 0.534481 0.845181i \(-0.320507\pi\)
−0.999188 + 0.0402836i \(0.987174\pi\)
\(908\) 0 0
\(909\) 1.07285e16 2.00915e16i 0.573374 1.07377i
\(910\) 0 0
\(911\) 1.11490e16i 0.588685i 0.955700 + 0.294343i \(0.0951007\pi\)
−0.955700 + 0.294343i \(0.904899\pi\)
\(912\) 0 0
\(913\) 3.07793e16 1.77704e16i 1.60572 0.927062i
\(914\) 0 0
\(915\) −1.75844e14 1.06124e16i −0.00906385 0.547010i
\(916\) 0 0
\(917\) 1.35289e16 + 3.00276e16i 0.689018 + 1.52929i
\(918\) 0 0
\(919\) 3.00179e14 5.19925e14i 0.0151058 0.0261641i −0.858374 0.513025i \(-0.828525\pi\)
0.873480 + 0.486861i \(0.161858\pi\)
\(920\) 0 0
\(921\) −2.02599e16 1.12537e16i −1.00742 0.559587i
\(922\) 0 0
\(923\) −1.60710e16 −0.789648
\(924\) 0 0
\(925\) 1.67991e16 0.815657
\(926\) 0 0
\(927\) −1.15566e14 3.48628e15i −0.00554485 0.167272i
\(928\) 0 0
\(929\) −3.11234e14 + 5.39074e14i −0.0147571 + 0.0255601i −0.873310 0.487166i \(-0.838031\pi\)
0.858553 + 0.512726i \(0.171364\pi\)
\(930\) 0 0
\(931\) −2.09021e13 + 1.02808e14i −0.000979417 + 0.00481731i
\(932\) 0 0
\(933\) −6.08939e15 + 1.00900e14i −0.281984 + 0.00467242i
\(934\) 0 0
\(935\) −2.62200e16 + 1.51381e16i −1.19997 + 0.692801i
\(936\) 0 0
\(937\) 1.09590e16i 0.495681i 0.968801 + 0.247841i \(0.0797209\pi\)
−0.968801 + 0.247841i \(0.920279\pi\)
\(938\) 0 0
\(939\) −9.75730e15 + 5.85103e15i −0.436183 + 0.261560i
\(940\) 0 0
\(941\) 1.25535e16 + 2.17433e16i 0.554653 + 0.960687i 0.997930 + 0.0643028i \(0.0204824\pi\)
−0.443277 + 0.896385i \(0.646184\pi\)
\(942\) 0 0
\(943\) 2.00523e15 + 1.15772e15i 0.0875688 + 0.0505579i
\(944\) 0 0
\(945\) 4.92773e15 + 9.62891e15i 0.212702 + 0.415626i
\(946\) 0 0
\(947\) 1.72938e16 + 9.98456e15i 0.737844 + 0.425994i 0.821285 0.570518i \(-0.193258\pi\)
−0.0834409 + 0.996513i \(0.526591\pi\)
\(948\) 0 0
\(949\) 3.95569e16 + 6.85146e16i 1.66824 + 2.88947i
\(950\) 0 0
\(951\) −2.38826e16 + 1.43214e16i −0.995608 + 0.597023i
\(952\) 0 0
\(953\) 3.48840e15i 0.143752i −0.997414 0.0718762i \(-0.977101\pi\)
0.997414 0.0718762i \(-0.0228987\pi\)
\(954\) 0 0
\(955\) 1.45926e16 8.42502e15i 0.594447 0.343204i
\(956\) 0 0
\(957\) −3.35563e16 + 5.56021e14i −1.35132 + 0.0223911i
\(958\) 0 0
\(959\) −1.83974e15 + 1.82828e16i −0.0732409 + 0.727847i
\(960\) 0 0
\(961\) −1.00316e16 + 1.73753e16i −0.394813 + 0.683837i
\(962\) 0 0
\(963\) 8.52401e14 + 2.57145e16i 0.0331665 + 1.00054i
\(964\) 0 0
\(965\) −1.63452e15 −0.0628768
\(966\) 0 0
\(967\) 4.99693e16 1.90045 0.950227 0.311559i \(-0.100851\pi\)
0.950227 + 0.311559i \(0.100851\pi\)
\(968\) 0 0
\(969\) −2.06465e14 1.14685e14i −0.00776365 0.00431245i
\(970\) 0 0
\(971\) 1.78361e16 3.08930e16i 0.663121 1.14856i −0.316670 0.948536i \(-0.602565\pi\)
0.979791 0.200024i \(-0.0641020\pi\)
\(972\) 0 0
\(973\) 3.30401e16 + 2.37821e16i 1.21456 + 0.874237i
\(974\) 0 0
\(975\) 7.08205e14 + 4.27407e16i 0.0257415 + 1.55352i
\(976\) 0 0
\(977\) −1.83993e16 + 1.06229e16i −0.661274 + 0.381787i −0.792762 0.609531i \(-0.791358\pi\)
0.131488 + 0.991318i \(0.458025\pi\)
\(978\) 0 0
\(979\) 3.87743e16i 1.37797i
\(980\) 0 0
\(981\) 4.65664e15 8.72060e15i 0.163641 0.306455i
\(982\) 0 0
\(983\) −9.16801e15 1.58795e16i −0.318589 0.551812i 0.661605 0.749853i \(-0.269876\pi\)
−0.980194 + 0.198040i \(0.936542\pi\)
\(984\) 0 0
\(985\) −1.60543e16 9.26896e15i −0.551686 0.318516i
\(986\) 0 0
\(987\) 3.12043e16 + 2.61857e15i 1.06040 + 0.0889856i
\(988\) 0 0
\(989\) 1.06232e15 + 6.13332e14i 0.0357007 + 0.0206118i
\(990\) 0 0
\(991\) −7.26417e15 1.25819e16i −0.241424 0.418159i 0.719696 0.694289i \(-0.244281\pi\)
−0.961120 + 0.276130i \(0.910948\pi\)
\(992\) 0 0
\(993\) 1.46692e15 + 2.44626e15i 0.0482153 + 0.0804049i
\(994\) 0 0
\(995\) 1.73626e16i 0.564402i
\(996\) 0 0
\(997\) 1.81880e16 1.05009e16i 0.584739 0.337599i −0.178275 0.983981i \(-0.557052\pi\)
0.763015 + 0.646381i \(0.223718\pi\)
\(998\) 0 0
\(999\) −1.49695e16 + 2.91874e16i −0.475988 + 0.928079i
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.5.20 56
3.2 odd 2 inner 84.12.k.b.5.28 yes 56
7.3 odd 6 inner 84.12.k.b.17.28 yes 56
21.17 even 6 inner 84.12.k.b.17.20 yes 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.12.k.b.5.20 56 1.1 even 1 trivial
84.12.k.b.5.28 yes 56 3.2 odd 2 inner
84.12.k.b.17.20 yes 56 21.17 even 6 inner
84.12.k.b.17.28 yes 56 7.3 odd 6 inner