Properties

Label 5.18.b.a.4.1
Level 5
Weight 18
Character 5.4
Analytic conductor 9.161
Analytic rank 0
Dimension 8
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 18 \)
Character orbit: \([\chi]\) = 5.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(9.16110436723\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{21}\cdot 3^{8}\cdot 5^{12}\cdot 11 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 4.1
Root \(-330.281i\)
Character \(\chi\) = 5.4
Dual form 5.18.b.a.4.8

$q$-expansion

\(f(q)\) \(=\) \(q-660.562i q^{2} -11309.3i q^{3} -305271. q^{4} +(-21187.7 + 873207. i) q^{5} -7.47047e6 q^{6} -2.37065e7i q^{7} +1.15069e8i q^{8} +1.24087e6 q^{9} +O(q^{10})\) \(q-660.562i q^{2} -11309.3i q^{3} -305271. q^{4} +(-21187.7 + 873207. i) q^{5} -7.47047e6 q^{6} -2.37065e7i q^{7} +1.15069e8i q^{8} +1.24087e6 q^{9} +(5.76808e8 + 1.39958e7i) q^{10} -3.40136e8 q^{11} +3.45238e9i q^{12} +6.20461e8i q^{13} -1.56596e10 q^{14} +(9.87532e9 + 2.39618e8i) q^{15} +3.59979e10 q^{16} -9.78165e9i q^{17} -8.19675e8i q^{18} -3.92941e10 q^{19} +(6.46800e9 - 2.66565e11i) q^{20} -2.68102e11 q^{21} +2.24681e11i q^{22} +2.44514e11i q^{23} +1.30135e12 q^{24} +(-7.62042e11 - 3.70026e10i) q^{25} +4.09853e11 q^{26} -1.47451e12i q^{27} +7.23689e12i q^{28} -3.98521e12 q^{29} +(1.58282e11 - 6.52327e12i) q^{30} +2.84863e12 q^{31} -8.69651e12i q^{32} +3.84668e12i q^{33} -6.46139e12 q^{34} +(2.07006e13 + 5.02286e11i) q^{35} -3.78802e11 q^{36} -2.87331e13i q^{37} +2.59562e13i q^{38} +7.01695e12 q^{39} +(-1.00479e14 - 2.43806e12i) q^{40} +2.58650e13 q^{41} +1.77098e14i q^{42} -7.92427e13i q^{43} +1.03833e14 q^{44} +(-2.62913e10 + 1.08354e12i) q^{45} +1.61517e14 q^{46} -3.42344e13i q^{47} -4.07109e14i q^{48} -3.29366e14 q^{49} +(-2.44425e13 + 5.03376e14i) q^{50} -1.10623e14 q^{51} -1.89408e14i q^{52} -6.28298e14i q^{53} -9.74008e14 q^{54} +(7.20671e12 - 2.97009e14i) q^{55} +2.72788e15 q^{56} +4.44388e14i q^{57} +2.63248e15i q^{58} +1.43672e15 q^{59} +(-3.01465e15 - 7.31483e13i) q^{60} -1.41408e15 q^{61} -1.88170e15i q^{62} -2.94167e13i q^{63} -1.02627e15 q^{64} +(-5.41791e14 - 1.31462e13i) q^{65} +2.54097e15 q^{66} +3.52003e14i q^{67} +2.98605e15i q^{68} +2.76527e15 q^{69} +(3.31792e14 - 1.36741e16i) q^{70} +5.76817e15 q^{71} +1.42786e14i q^{72} +1.24525e15i q^{73} -1.89800e16 q^{74} +(-4.18472e14 + 8.61812e15i) q^{75} +1.19953e16 q^{76} +8.06341e15i q^{77} -4.63513e15i q^{78} -8.16669e15 q^{79} +(-7.62714e14 + 3.14336e16i) q^{80} -1.65154e16 q^{81} -1.70854e16i q^{82} -2.09840e16i q^{83} +8.18438e16 q^{84} +(8.54140e15 + 2.07251e14i) q^{85} -5.23447e16 q^{86} +4.50697e16i q^{87} -3.91391e16i q^{88} -2.91132e16 q^{89} +(7.15746e14 + 1.73671e13i) q^{90} +1.47089e16 q^{91} -7.46430e16i q^{92} -3.22159e16i q^{93} -2.26140e16 q^{94} +(8.32554e14 - 3.43119e16i) q^{95} -9.83511e16 q^{96} +4.58585e16i q^{97} +2.17567e17i q^{98} -4.22065e14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 579096q^{4} + 379200q^{5} + 357816q^{6} - 234916344q^{9} + O(q^{10}) \) \( 8q - 579096q^{4} + 379200q^{5} + 357816q^{6} - 234916344q^{9} + 329570200q^{10} + 463296576q^{11} - 29937907992q^{14} + 30646226400q^{15} + 30848001568q^{16} - 20615713280q^{19} - 47558579400q^{20} - 75039699024q^{21} + 1768741136160q^{24} - 1789249435000q^{25} - 838901194224q^{26} - 4079017824720q^{29} + 2416984007400q^{30} + 11329328658496q^{31} - 36406243632832q^{34} + 4019663899200q^{35} + 59729752432728q^{36} + 40318460422272q^{39} - 209747532172000q^{40} + 97217252847456q^{41} - 116357853210912q^{44} - 366841998003600q^{45} + 1081224261700136q^{46} - 856574357621656q^{49} - 1283266301910000q^{50} + 2468309514424896q^{51} - 3408409774777680q^{54} - 2042713226757600q^{55} + 8363016326678880q^{56} - 1091409512240640q^{59} - 11479379108104800q^{60} + 8064731010774976q^{61} - 3616160324265856q^{64} - 11989509557901600q^{65} + 27318846906958752q^{66} - 12078989597365008q^{69} - 13190931213697800q^{70} + 25241492058140736q^{71} - 29902523510328912q^{74} + 3839235716880000q^{75} + 20767634734678560q^{76} + 3229852337730880q^{79} + 1263407265391200q^{80} - 49353541005202632q^{81} + 101439947332382688q^{84} + 25693702369787200q^{85} - 165112838769552744q^{86} + 92963987535626640q^{89} + 206315814421823400q^{90} - 225591670236809664q^{91} + 162612564681867848q^{94} + 204319715505252000q^{95} - 654303222993538944q^{96} - 56327331239952768q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 660.562i 1.82456i −0.409564 0.912282i \(-0.634319\pi\)
0.409564 0.912282i \(-0.365681\pi\)
\(3\) 11309.3i 0.995184i −0.867411 0.497592i \(-0.834218\pi\)
0.867411 0.497592i \(-0.165782\pi\)
\(4\) −305271. −2.32903
\(5\) −21187.7 + 873207.i −0.0242571 + 0.999706i
\(6\) −7.47047e6 −1.81578
\(7\) 2.37065e7i 1.55429i −0.629319 0.777147i \(-0.716666\pi\)
0.629319 0.777147i \(-0.283334\pi\)
\(8\) 1.15069e8i 2.42490i
\(9\) 1.24087e6 0.00960874
\(10\) 5.76808e8 + 1.39958e7i 1.82403 + 0.0442587i
\(11\) −3.40136e8 −0.478425 −0.239213 0.970967i \(-0.576889\pi\)
−0.239213 + 0.970967i \(0.576889\pi\)
\(12\) 3.45238e9i 2.31781i
\(13\) 6.20461e8i 0.210958i 0.994422 + 0.105479i \(0.0336376\pi\)
−0.994422 + 0.105479i \(0.966362\pi\)
\(14\) −1.56596e10 −2.83591
\(15\) 9.87532e9 + 2.39618e8i 0.994891 + 0.0241403i
\(16\) 3.59979e10 2.09535
\(17\) 9.78165e9i 0.340092i −0.985436 0.170046i \(-0.945608\pi\)
0.985436 0.170046i \(-0.0543916\pi\)
\(18\) 8.19675e8i 0.0175317i
\(19\) −3.92941e10 −0.530789 −0.265395 0.964140i \(-0.585502\pi\)
−0.265395 + 0.964140i \(0.585502\pi\)
\(20\) 6.46800e9 2.66565e11i 0.0564956 2.32835i
\(21\) −2.68102e11 −1.54681
\(22\) 2.24681e11i 0.872917i
\(23\) 2.44514e11i 0.651055i 0.945533 + 0.325527i \(0.105542\pi\)
−0.945533 + 0.325527i \(0.894458\pi\)
\(24\) 1.30135e12 2.41322
\(25\) −7.62042e11 3.70026e10i −0.998823 0.0485000i
\(26\) 4.09853e11 0.384906
\(27\) 1.47451e12i 1.00475i
\(28\) 7.23689e12i 3.62000i
\(29\) −3.98521e12 −1.47934 −0.739670 0.672970i \(-0.765018\pi\)
−0.739670 + 0.672970i \(0.765018\pi\)
\(30\) 1.58282e11 6.52327e12i 0.0440455 1.81524i
\(31\) 2.84863e12 0.599877 0.299939 0.953959i \(-0.403034\pi\)
0.299939 + 0.953959i \(0.403034\pi\)
\(32\) 8.69651e12i 1.39820i
\(33\) 3.84668e12i 0.476121i
\(34\) −6.46139e12 −0.620519
\(35\) 2.07006e13 + 5.02286e11i 1.55384 + 0.0377028i
\(36\) −3.78802e11 −0.0223790
\(37\) 2.87331e13i 1.34483i −0.740173 0.672417i \(-0.765256\pi\)
0.740173 0.672417i \(-0.234744\pi\)
\(38\) 2.59562e13i 0.968459i
\(39\) 7.01695e12 0.209942
\(40\) −1.00479e14 2.43806e12i −2.42419 0.0588212i
\(41\) 2.58650e13 0.505882 0.252941 0.967482i \(-0.418602\pi\)
0.252941 + 0.967482i \(0.418602\pi\)
\(42\) 1.77098e14i 2.82225i
\(43\) 7.92427e13i 1.03390i −0.856016 0.516949i \(-0.827068\pi\)
0.856016 0.516949i \(-0.172932\pi\)
\(44\) 1.03833e14 1.11427
\(45\) −2.62913e10 + 1.08354e12i −0.000233081 + 0.00960591i
\(46\) 1.61517e14 1.18789
\(47\) 3.42344e13i 0.209716i −0.994487 0.104858i \(-0.966561\pi\)
0.994487 0.104858i \(-0.0334388\pi\)
\(48\) 4.07109e14i 2.08526i
\(49\) −3.29366e14 −1.41583
\(50\) −2.44425e13 + 5.03376e14i −0.0884913 + 1.82242i
\(51\) −1.10623e14 −0.338454
\(52\) 1.89408e14i 0.491327i
\(53\) 6.28298e14i 1.38618i −0.720850 0.693091i \(-0.756248\pi\)
0.720850 0.693091i \(-0.243752\pi\)
\(54\) −9.74008e14 −1.83322
\(55\) 7.20671e12 2.97009e14i 0.0116052 0.478285i
\(56\) 2.72788e15 3.76901
\(57\) 4.44388e14i 0.528233i
\(58\) 2.63248e15i 2.69915i
\(59\) 1.43672e15 1.27389 0.636943 0.770911i \(-0.280199\pi\)
0.636943 + 0.770911i \(0.280199\pi\)
\(60\) −3.01465e15 7.31483e13i −2.31713 0.0562236i
\(61\) −1.41408e15 −0.944428 −0.472214 0.881484i \(-0.656545\pi\)
−0.472214 + 0.881484i \(0.656545\pi\)
\(62\) 1.88170e15i 1.09451i
\(63\) 2.94167e13i 0.0149348i
\(64\) −1.02627e15 −0.455757
\(65\) −5.41791e14 1.31462e13i −0.210896 0.00511724i
\(66\) 2.54097e15 0.868713
\(67\) 3.52003e14i 0.105904i 0.998597 + 0.0529518i \(0.0168630\pi\)
−0.998597 + 0.0529518i \(0.983137\pi\)
\(68\) 2.98605e15i 0.792084i
\(69\) 2.76527e15 0.647919
\(70\) 3.31792e14 1.36741e16i 0.0687910 2.83507i
\(71\) 5.76817e15 1.06009 0.530044 0.847970i \(-0.322175\pi\)
0.530044 + 0.847970i \(0.322175\pi\)
\(72\) 1.42786e14i 0.0233002i
\(73\) 1.24525e15i 0.180723i 0.995909 + 0.0903613i \(0.0288022\pi\)
−0.995909 + 0.0903613i \(0.971198\pi\)
\(74\) −1.89800e16 −2.45373
\(75\) −4.18472e14 + 8.61812e15i −0.0482664 + 0.994013i
\(76\) 1.19953e16 1.23622
\(77\) 8.06341e15i 0.743614i
\(78\) 4.63513e15i 0.383052i
\(79\) −8.16669e15 −0.605642 −0.302821 0.953048i \(-0.597928\pi\)
−0.302821 + 0.953048i \(0.597928\pi\)
\(80\) −7.62714e14 + 3.14336e16i −0.0508273 + 2.09474i
\(81\) −1.65154e16 −0.990299
\(82\) 1.70854e16i 0.923013i
\(83\) 2.09840e16i 1.02264i −0.859389 0.511322i \(-0.829156\pi\)
0.859389 0.511322i \(-0.170844\pi\)
\(84\) 8.18438e16 3.60257
\(85\) 8.54140e15 + 2.07251e14i 0.339992 + 0.00824966i
\(86\) −5.23447e16 −1.88641
\(87\) 4.50697e16i 1.47222i
\(88\) 3.91391e16i 1.16013i
\(89\) −2.91132e16 −0.783926 −0.391963 0.919981i \(-0.628204\pi\)
−0.391963 + 0.919981i \(0.628204\pi\)
\(90\) 7.15746e14 + 1.73671e13i 0.0175266 + 0.000425270i
\(91\) 1.47089e16 0.327891
\(92\) 7.46430e16i 1.51633i
\(93\) 3.22159e16i 0.596988i
\(94\) −2.26140e16 −0.382640
\(95\) 8.32554e14 3.43119e16i 0.0128754 0.530633i
\(96\) −9.83511e16 −1.39147
\(97\) 4.58585e16i 0.594100i 0.954862 + 0.297050i \(0.0960029\pi\)
−0.954862 + 0.297050i \(0.903997\pi\)
\(98\) 2.17567e17i 2.58327i
\(99\) −4.22065e14 −0.00459706
\(100\) 2.32629e17 + 1.12958e16i 2.32629 + 0.112958i
\(101\) 1.53390e17 1.40950 0.704752 0.709454i \(-0.251058\pi\)
0.704752 + 0.709454i \(0.251058\pi\)
\(102\) 7.30735e16i 0.617531i
\(103\) 1.35527e17i 1.05416i −0.849815 0.527082i \(-0.823286\pi\)
0.849815 0.527082i \(-0.176714\pi\)
\(104\) −7.13958e16 −0.511552
\(105\) 5.68049e15 2.34109e17i 0.0375212 1.54635i
\(106\) −4.15030e17 −2.52918
\(107\) 1.40345e17i 0.789649i 0.918757 + 0.394824i \(0.129195\pi\)
−0.918757 + 0.394824i \(0.870805\pi\)
\(108\) 4.50125e17i 2.34009i
\(109\) 2.67560e17 1.28616 0.643081 0.765798i \(-0.277656\pi\)
0.643081 + 0.765798i \(0.277656\pi\)
\(110\) −1.96193e17 4.76048e15i −0.872660 0.0211745i
\(111\) −3.24950e17 −1.33836
\(112\) 8.53382e17i 3.25680i
\(113\) 9.95662e16i 0.352326i 0.984361 + 0.176163i \(0.0563687\pi\)
−0.984361 + 0.176163i \(0.943631\pi\)
\(114\) 2.93546e17 0.963795
\(115\) −2.13512e17 5.18070e15i −0.650863 0.0157927i
\(116\) 1.21657e18 3.44543
\(117\) 7.69913e14i 0.00202704i
\(118\) 9.49044e17i 2.32428i
\(119\) −2.31888e17 −0.528603
\(120\) −2.75726e16 + 1.13634e18i −0.0585379 + 2.41251i
\(121\) −3.89755e17 −0.771109
\(122\) 9.34085e17i 1.72317i
\(123\) 2.92513e17i 0.503445i
\(124\) −8.69605e17 −1.39713
\(125\) 4.84569e16 6.64636e17i 0.0727143 0.997353i
\(126\) −1.94316e16 −0.0272495
\(127\) 1.33130e18i 1.74559i 0.488084 + 0.872797i \(0.337696\pi\)
−0.488084 + 0.872797i \(0.662304\pi\)
\(128\) 4.61951e17i 0.566645i
\(129\) −8.96176e17 −1.02892
\(130\) −8.68386e15 + 3.57886e17i −0.00933672 + 0.384793i
\(131\) 1.65183e18 1.66402 0.832010 0.554760i \(-0.187190\pi\)
0.832010 + 0.554760i \(0.187190\pi\)
\(132\) 1.17428e18i 1.10890i
\(133\) 9.31525e17i 0.825003i
\(134\) 2.32520e17 0.193228
\(135\) 1.28755e18 + 3.12416e16i 1.00445 + 0.0243723i
\(136\) 1.12557e18 0.824689
\(137\) 8.57280e17i 0.590198i 0.955467 + 0.295099i \(0.0953527\pi\)
−0.955467 + 0.295099i \(0.904647\pi\)
\(138\) 1.82664e18i 1.18217i
\(139\) 1.70531e18 1.03795 0.518976 0.854789i \(-0.326313\pi\)
0.518976 + 0.854789i \(0.326313\pi\)
\(140\) −6.31930e18 1.53333e17i −3.61893 0.0878109i
\(141\) −3.87166e17 −0.208706
\(142\) 3.81024e18i 1.93420i
\(143\) 2.11041e17i 0.100928i
\(144\) 4.46688e16 0.0201337
\(145\) 8.44376e16 3.47991e18i 0.0358846 1.47890i
\(146\) 8.22566e17 0.329740
\(147\) 3.72488e18i 1.40901i
\(148\) 8.77139e18i 3.13216i
\(149\) −1.88380e18 −0.635259 −0.317629 0.948215i \(-0.602887\pi\)
−0.317629 + 0.948215i \(0.602887\pi\)
\(150\) 5.69281e18 + 2.76427e17i 1.81364 + 0.0880652i
\(151\) −3.21839e18 −0.969024 −0.484512 0.874785i \(-0.661003\pi\)
−0.484512 + 0.874785i \(0.661003\pi\)
\(152\) 4.52154e18i 1.28711i
\(153\) 1.21378e16i 0.00326785i
\(154\) 5.32638e18 1.35677
\(155\) −6.03561e16 + 2.48745e18i −0.0145513 + 0.599701i
\(156\) −2.14207e18 −0.488961
\(157\) 5.70488e18i 1.23339i −0.787204 0.616693i \(-0.788472\pi\)
0.787204 0.616693i \(-0.211528\pi\)
\(158\) 5.39461e18i 1.10503i
\(159\) −7.10558e18 −1.37951
\(160\) 7.59386e18 + 1.84259e17i 1.39779 + 0.0339164i
\(161\) 5.79657e18 1.01193
\(162\) 1.09094e19i 1.80686i
\(163\) 2.76799e18i 0.435080i −0.976051 0.217540i \(-0.930197\pi\)
0.976051 0.217540i \(-0.0698033\pi\)
\(164\) −7.89581e18 −1.17821
\(165\) −3.35895e18 8.15025e16i −0.475981 0.0115493i
\(166\) −1.38613e19 −1.86588
\(167\) 2.96598e18i 0.379384i −0.981844 0.189692i \(-0.939251\pi\)
0.981844 0.189692i \(-0.0607489\pi\)
\(168\) 3.08503e19i 3.75086i
\(169\) 8.26544e18 0.955497
\(170\) 1.36902e17 5.64213e18i 0.0150520 0.620336i
\(171\) −4.87591e16 −0.00510021
\(172\) 2.41905e19i 2.40798i
\(173\) 1.22679e19i 1.16246i −0.813740 0.581228i \(-0.802572\pi\)
0.813740 0.581228i \(-0.197428\pi\)
\(174\) 2.97714e19 2.68615
\(175\) −8.77200e17 + 1.80653e19i −0.0753833 + 1.55247i
\(176\) −1.22442e19 −1.00247
\(177\) 1.62482e19i 1.26775i
\(178\) 1.92311e19i 1.43032i
\(179\) 1.05059e19 0.745048 0.372524 0.928023i \(-0.378492\pi\)
0.372524 + 0.928023i \(0.378492\pi\)
\(180\) 8.02597e15 3.30773e17i 0.000542852 0.0223725i
\(181\) −6.36140e18 −0.410473 −0.205236 0.978712i \(-0.565796\pi\)
−0.205236 + 0.978712i \(0.565796\pi\)
\(182\) 9.71616e18i 0.598257i
\(183\) 1.59921e19i 0.939880i
\(184\) −2.81360e19 −1.57874
\(185\) 2.50900e19 + 6.08791e17i 1.34444 + 0.0326218i
\(186\) −2.12806e19 −1.08924
\(187\) 3.32709e18i 0.162709i
\(188\) 1.04508e19i 0.488435i
\(189\) −3.49555e19 −1.56167
\(190\) −2.26652e19 5.49954e17i −0.968174 0.0234920i
\(191\) 2.68237e19 1.09581 0.547905 0.836541i \(-0.315426\pi\)
0.547905 + 0.836541i \(0.315426\pi\)
\(192\) 1.16064e19i 0.453562i
\(193\) 1.22468e19i 0.457916i −0.973436 0.228958i \(-0.926468\pi\)
0.973436 0.228958i \(-0.0735319\pi\)
\(194\) 3.02924e19 1.08397
\(195\) −1.48673e17 + 6.12725e18i −0.00509259 + 0.209880i
\(196\) 1.00546e20 3.29751
\(197\) 1.20855e19i 0.379580i −0.981825 0.189790i \(-0.939219\pi\)
0.981825 0.189790i \(-0.0607807\pi\)
\(198\) 2.78800e17i 0.00838763i
\(199\) −6.55776e19 −1.89018 −0.945092 0.326804i \(-0.894028\pi\)
−0.945092 + 0.326804i \(0.894028\pi\)
\(200\) 4.25785e18 8.76874e19i 0.117608 2.42205i
\(201\) 3.98090e18 0.105394
\(202\) 1.01324e20i 2.57173i
\(203\) 9.44751e19i 2.29933i
\(204\) 3.37700e19 0.788270
\(205\) −5.48020e17 + 2.25855e19i −0.0122712 + 0.505733i
\(206\) −8.95237e19 −1.92339
\(207\) 3.03411e17i 0.00625581i
\(208\) 2.23353e19i 0.442031i
\(209\) 1.33653e19 0.253943
\(210\) −1.54644e20 3.75232e18i −2.82142 0.0684598i
\(211\) −2.90167e19 −0.508449 −0.254224 0.967145i \(-0.581820\pi\)
−0.254224 + 0.967145i \(0.581820\pi\)
\(212\) 1.91801e20i 3.22846i
\(213\) 6.52337e19i 1.05498i
\(214\) 9.27065e19 1.44076
\(215\) 6.91953e19 + 1.67897e18i 1.03359 + 0.0250794i
\(216\) 1.69671e20 2.43641
\(217\) 6.75310e19i 0.932386i
\(218\) 1.76740e20i 2.34668i
\(219\) 1.40829e19 0.179852
\(220\) −2.20000e18 + 9.06681e19i −0.0270289 + 1.11394i
\(221\) 6.06913e18 0.0717450
\(222\) 2.14650e20i 2.44192i
\(223\) 1.00403e20i 1.09940i 0.835363 + 0.549699i \(0.185258\pi\)
−0.835363 + 0.549699i \(0.814742\pi\)
\(224\) −2.06163e20 −2.17322
\(225\) −9.45597e17 4.59155e16i −0.00959743 0.000466024i
\(226\) 6.57697e19 0.642842
\(227\) 7.25392e19i 0.682894i −0.939901 0.341447i \(-0.889083\pi\)
0.939901 0.341447i \(-0.110917\pi\)
\(228\) 1.35658e20i 1.23027i
\(229\) −1.05419e20 −0.921124 −0.460562 0.887628i \(-0.652352\pi\)
−0.460562 + 0.887628i \(0.652352\pi\)
\(230\) −3.42218e18 + 1.41038e20i −0.0288148 + 1.18754i
\(231\) 9.11912e19 0.740033
\(232\) 4.58574e20i 3.58725i
\(233\) 1.19870e20i 0.904037i −0.892008 0.452019i \(-0.850704\pi\)
0.892008 0.452019i \(-0.149296\pi\)
\(234\) 5.08576e17 0.00369846
\(235\) 2.98937e19 + 7.25350e17i 0.209654 + 0.00508711i
\(236\) −4.38589e20 −2.96692
\(237\) 9.23592e19i 0.602725i
\(238\) 1.53177e20i 0.964469i
\(239\) 8.27461e19 0.502766 0.251383 0.967888i \(-0.419115\pi\)
0.251383 + 0.967888i \(0.419115\pi\)
\(240\) 3.55491e20 + 8.62573e18i 2.08465 + 0.0505825i
\(241\) 8.99963e19 0.509425 0.254712 0.967017i \(-0.418019\pi\)
0.254712 + 0.967017i \(0.418019\pi\)
\(242\) 2.57457e20i 1.40694i
\(243\) 3.64195e18i 0.0192168i
\(244\) 4.31676e20 2.19960
\(245\) 6.97851e18 2.87604e20i 0.0343440 1.41541i
\(246\) −1.93223e20 −0.918568
\(247\) 2.43805e19i 0.111974i
\(248\) 3.27790e20i 1.45464i
\(249\) −2.37314e20 −1.01772
\(250\) −4.39034e20 3.20088e19i −1.81973 0.132672i
\(251\) −5.05233e19 −0.202425 −0.101213 0.994865i \(-0.532272\pi\)
−0.101213 + 0.994865i \(0.532272\pi\)
\(252\) 8.98006e18i 0.0347836i
\(253\) 8.31680e19i 0.311481i
\(254\) 8.79404e20 3.18495
\(255\) 2.34386e18 9.65969e19i 0.00820993 0.338354i
\(256\) −4.39663e20 −1.48964
\(257\) 5.06773e20i 1.66105i 0.556984 + 0.830524i \(0.311959\pi\)
−0.556984 + 0.830524i \(0.688041\pi\)
\(258\) 5.91980e20i 1.87733i
\(259\) −6.81161e20 −2.09027
\(260\) 1.65393e20 + 4.01314e18i 0.491183 + 0.0119182i
\(261\) −4.94514e18 −0.0142146
\(262\) 1.09114e21i 3.03611i
\(263\) 5.09531e19i 0.137261i −0.997642 0.0686305i \(-0.978137\pi\)
0.997642 0.0686305i \(-0.0218629\pi\)
\(264\) −4.42634e20 −1.15455
\(265\) 5.48634e20 + 1.33122e19i 1.38577 + 0.0336248i
\(266\) 6.15330e20 1.50527
\(267\) 3.29249e20i 0.780151i
\(268\) 1.07456e20i 0.246653i
\(269\) −9.13493e19 −0.203147 −0.101574 0.994828i \(-0.532388\pi\)
−0.101574 + 0.994828i \(0.532388\pi\)
\(270\) 2.06370e19 8.50510e20i 0.0444688 1.83268i
\(271\) 3.85248e19 0.0804455 0.0402227 0.999191i \(-0.487193\pi\)
0.0402227 + 0.999191i \(0.487193\pi\)
\(272\) 3.52119e20i 0.712612i
\(273\) 1.66347e20i 0.326312i
\(274\) 5.66287e20 1.07685
\(275\) 2.59197e20 + 1.25859e19i 0.477862 + 0.0232036i
\(276\) −8.44157e20 −1.50902
\(277\) 8.52898e20i 1.47849i 0.673435 + 0.739246i \(0.264818\pi\)
−0.673435 + 0.739246i \(0.735182\pi\)
\(278\) 1.12646e21i 1.89381i
\(279\) 3.53480e18 0.00576406
\(280\) −5.77976e19 + 2.38200e21i −0.0914254 + 3.76790i
\(281\) 7.66403e20 1.17612 0.588062 0.808816i \(-0.299891\pi\)
0.588062 + 0.808816i \(0.299891\pi\)
\(282\) 2.55747e20i 0.380797i
\(283\) 6.44868e20i 0.931721i −0.884858 0.465860i \(-0.845745\pi\)
0.884858 0.465860i \(-0.154255\pi\)
\(284\) −1.76085e21 −2.46898
\(285\) −3.88042e20 9.41557e18i −0.528078 0.0128134i
\(286\) −1.39406e20 −0.184149
\(287\) 6.13167e20i 0.786289i
\(288\) 1.07913e19i 0.0134350i
\(289\) 7.31560e20 0.884338
\(290\) −2.29870e21 5.57763e19i −2.69835 0.0654737i
\(291\) 5.18625e20 0.591239
\(292\) 3.80139e20i 0.420908i
\(293\) 1.05852e21i 1.13847i 0.822173 + 0.569237i \(0.192761\pi\)
−0.822173 + 0.569237i \(0.807239\pi\)
\(294\) 2.46052e21 2.57083
\(295\) −3.04409e19 + 1.25455e21i −0.0309008 + 1.27351i
\(296\) 3.30630e21 3.26109
\(297\) 5.01534e20i 0.480696i
\(298\) 1.24436e21i 1.15907i
\(299\) −1.51711e20 −0.137345
\(300\) 1.27747e20 2.63086e21i 0.112414 2.31509i
\(301\) −1.87856e21 −1.60698
\(302\) 2.12595e21i 1.76805i
\(303\) 1.73473e21i 1.40272i
\(304\) −1.41451e21 −1.11219
\(305\) 2.99611e19 1.23478e21i 0.0229091 0.944150i
\(306\) −8.01777e18 −0.00596240
\(307\) 2.20525e21i 1.59508i −0.603268 0.797538i \(-0.706135\pi\)
0.603268 0.797538i \(-0.293865\pi\)
\(308\) 2.46152e21i 1.73190i
\(309\) −1.53270e21 −1.04909
\(310\) 1.64311e21 + 3.98690e19i 1.09419 + 0.0265498i
\(311\) −1.67631e21 −1.08615 −0.543077 0.839683i \(-0.682741\pi\)
−0.543077 + 0.839683i \(0.682741\pi\)
\(312\) 8.07434e20i 0.509088i
\(313\) 1.91815e21i 1.17695i 0.808517 + 0.588473i \(0.200271\pi\)
−0.808517 + 0.588473i \(0.799729\pi\)
\(314\) −3.76843e21 −2.25039
\(315\) 2.56869e19 + 6.23274e17i 0.0149304 + 0.000362276i
\(316\) 2.49305e21 1.41056
\(317\) 2.94101e20i 0.161992i 0.996714 + 0.0809959i \(0.0258101\pi\)
−0.996714 + 0.0809959i \(0.974190\pi\)
\(318\) 4.69368e21i 2.51700i
\(319\) 1.35551e21 0.707754
\(320\) 2.17444e19 8.96150e20i 0.0110554 0.455623i
\(321\) 1.58719e21 0.785846
\(322\) 3.82899e21i 1.84633i
\(323\) 3.84361e20i 0.180517i
\(324\) 5.04167e21 2.30644
\(325\) 2.29586e19 4.72817e20i 0.0102315 0.210710i
\(326\) −1.82843e21 −0.793831
\(327\) 3.02590e21i 1.27997i
\(328\) 2.97626e21i 1.22671i
\(329\) −8.11577e20 −0.325960
\(330\) −5.38375e19 + 2.21879e21i −0.0210725 + 0.868458i
\(331\) 3.51653e21 1.34145 0.670727 0.741704i \(-0.265982\pi\)
0.670727 + 0.741704i \(0.265982\pi\)
\(332\) 6.40581e21i 2.38177i
\(333\) 3.56542e19i 0.0129221i
\(334\) −1.95922e21 −0.692210
\(335\) −3.07372e20 7.45816e18i −0.105873 0.00256892i
\(336\) −9.65112e21 −3.24111
\(337\) 1.06259e21i 0.347947i 0.984750 + 0.173973i \(0.0556607\pi\)
−0.984750 + 0.173973i \(0.944339\pi\)
\(338\) 5.45984e21i 1.74336i
\(339\) 1.12602e21 0.350630
\(340\) −2.60744e21 6.32677e19i −0.791851 0.0192137i
\(341\) −9.68922e20 −0.286996
\(342\) 3.22084e19i 0.00930566i
\(343\) 2.29325e21i 0.646325i
\(344\) 9.11838e21 2.50710
\(345\) −5.85899e19 + 2.41466e21i −0.0157167 + 0.647729i
\(346\) −8.10369e21 −2.12098
\(347\) 6.26207e21i 1.59925i −0.600498 0.799626i \(-0.705031\pi\)
0.600498 0.799626i \(-0.294969\pi\)
\(348\) 1.37585e22i 3.42883i
\(349\) 4.92952e21 1.19891 0.599457 0.800407i \(-0.295383\pi\)
0.599457 + 0.800407i \(0.295383\pi\)
\(350\) 1.19333e22 + 5.79445e20i 2.83257 + 0.137542i
\(351\) 9.14877e20 0.211959
\(352\) 2.95799e21i 0.668936i
\(353\) 1.65310e21i 0.364934i 0.983212 + 0.182467i \(0.0584083\pi\)
−0.983212 + 0.182467i \(0.941592\pi\)
\(354\) −1.07330e22 −2.31309
\(355\) −1.22215e20 + 5.03681e21i −0.0257147 + 1.05978i
\(356\) 8.88742e21 1.82579
\(357\) 2.62248e21i 0.526057i
\(358\) 6.93983e21i 1.35939i
\(359\) −5.64380e21 −1.07961 −0.539807 0.841789i \(-0.681503\pi\)
−0.539807 + 0.841789i \(0.681503\pi\)
\(360\) −1.24682e20 3.02532e18i −0.0232934 0.000565197i
\(361\) −3.93636e21 −0.718263
\(362\) 4.20210e21i 0.748934i
\(363\) 4.40784e21i 0.767396i
\(364\) −4.49020e21 −0.763667
\(365\) −1.08736e21 2.63841e19i −0.180669 0.00438381i
\(366\) 1.05638e22 1.71487
\(367\) 7.92023e20i 0.125625i 0.998025 + 0.0628125i \(0.0200070\pi\)
−0.998025 + 0.0628125i \(0.979993\pi\)
\(368\) 8.80199e21i 1.36419i
\(369\) 3.20952e19 0.00486088
\(370\) 4.02144e20 1.65735e22i 0.0595206 2.45301i
\(371\) −1.48947e22 −2.15454
\(372\) 9.83458e21i 1.39040i
\(373\) 5.60332e21i 0.774320i −0.922012 0.387160i \(-0.873456\pi\)
0.922012 0.387160i \(-0.126544\pi\)
\(374\) 2.19775e21 0.296872
\(375\) −7.51654e21 5.48011e20i −0.992550 0.0723642i
\(376\) 3.93932e21 0.508540
\(377\) 2.47266e21i 0.312078i
\(378\) 2.30903e22i 2.84937i
\(379\) 1.12046e22 1.35195 0.675977 0.736923i \(-0.263722\pi\)
0.675977 + 0.736923i \(0.263722\pi\)
\(380\) −2.54154e20 + 1.04744e22i −0.0299873 + 1.23586i
\(381\) 1.50560e22 1.73719
\(382\) 1.77187e22i 1.99937i
\(383\) 7.07404e21i 0.780689i 0.920669 + 0.390344i \(0.127644\pi\)
−0.920669 + 0.390344i \(0.872356\pi\)
\(384\) −5.22432e21 −0.563916
\(385\) −7.04103e21 1.70845e20i −0.743395 0.0180380i
\(386\) −8.08979e21 −0.835497
\(387\) 9.83302e19i 0.00993444i
\(388\) 1.39992e22i 1.38368i
\(389\) 1.85301e22 1.79187 0.895937 0.444182i \(-0.146506\pi\)
0.895937 + 0.444182i \(0.146506\pi\)
\(390\) 4.04743e21 + 9.82080e19i 0.382939 + 0.00929175i
\(391\) 2.39175e21 0.221418
\(392\) 3.78998e22i 3.43325i
\(393\) 1.86809e22i 1.65601i
\(394\) −7.98326e21 −0.692568
\(395\) 1.73034e20 7.13121e21i 0.0146911 0.605463i
\(396\) 1.28844e20 0.0107067
\(397\) 2.32134e22i 1.88807i 0.329840 + 0.944037i \(0.393005\pi\)
−0.329840 + 0.944037i \(0.606995\pi\)
\(398\) 4.33181e22i 3.44876i
\(399\) 1.05349e22 0.821030
\(400\) −2.74319e22 1.33201e21i −2.09289 0.101625i
\(401\) −1.49395e22 −1.11586 −0.557928 0.829890i \(-0.688403\pi\)
−0.557928 + 0.829890i \(0.688403\pi\)
\(402\) 2.62963e21i 0.192297i
\(403\) 1.76747e21i 0.126549i
\(404\) −4.68256e22 −3.28278
\(405\) 3.49924e20 1.44214e22i 0.0240218 0.990008i
\(406\) 6.24067e22 4.19527
\(407\) 9.77316e21i 0.643402i
\(408\) 1.27293e22i 0.820717i
\(409\) −2.14032e22 −1.35155 −0.675774 0.737109i \(-0.736190\pi\)
−0.675774 + 0.737109i \(0.736190\pi\)
\(410\) 1.49191e22 + 3.62002e20i 0.922742 + 0.0223897i
\(411\) 9.69520e21 0.587356
\(412\) 4.13723e22i 2.45518i
\(413\) 3.40596e22i 1.97999i
\(414\) 2.00422e20 0.0114141
\(415\) 1.83234e22 + 4.44604e20i 1.02234 + 0.0248064i
\(416\) 5.39584e21 0.294962
\(417\) 1.92858e22i 1.03295i
\(418\) 8.82864e21i 0.463335i
\(419\) −4.94779e20 −0.0254444 −0.0127222 0.999919i \(-0.504050\pi\)
−0.0127222 + 0.999919i \(0.504050\pi\)
\(420\) −1.73409e21 + 7.14666e22i −0.0873880 + 3.60151i
\(421\) −2.45451e22 −1.21218 −0.606091 0.795395i \(-0.707263\pi\)
−0.606091 + 0.795395i \(0.707263\pi\)
\(422\) 1.91673e22i 0.927696i
\(423\) 4.24806e19i 0.00201510i
\(424\) 7.22976e22 3.36135
\(425\) −3.61946e20 + 7.45402e21i −0.0164945 + 0.339692i
\(426\) −4.30910e22 −1.92488
\(427\) 3.35227e22i 1.46792i
\(428\) 4.28431e22i 1.83912i
\(429\) −2.38671e21 −0.100442
\(430\) 1.10907e21 4.57078e22i 0.0457589 1.88586i
\(431\) 2.21018e22 0.894067 0.447033 0.894517i \(-0.352480\pi\)
0.447033 + 0.894517i \(0.352480\pi\)
\(432\) 5.30793e22i 2.10530i
\(433\) 2.47754e22i 0.963549i 0.876295 + 0.481774i \(0.160008\pi\)
−0.876295 + 0.481774i \(0.839992\pi\)
\(434\) −4.46085e22 −1.70120
\(435\) −3.93552e22 9.54926e20i −1.47178 0.0357117i
\(436\) −8.16781e22 −2.99551
\(437\) 9.60798e21i 0.345573i
\(438\) 9.30261e21i 0.328152i
\(439\) −7.72167e21 −0.267155 −0.133577 0.991038i \(-0.542646\pi\)
−0.133577 + 0.991038i \(0.542646\pi\)
\(440\) 3.41765e22 + 8.29269e20i 1.15979 + 0.0281415i
\(441\) −4.08701e20 −0.0136044
\(442\) 4.00904e21i 0.130903i
\(443\) 3.47364e21i 0.111264i −0.998451 0.0556318i \(-0.982283\pi\)
0.998451 0.0556318i \(-0.0177173\pi\)
\(444\) 9.91979e22 3.11707
\(445\) 6.16844e20 2.54219e22i 0.0190158 0.783696i
\(446\) 6.63224e22 2.00592
\(447\) 2.13043e22i 0.632199i
\(448\) 2.43293e22i 0.708381i
\(449\) 3.35625e22 0.958871 0.479435 0.877577i \(-0.340841\pi\)
0.479435 + 0.877577i \(0.340841\pi\)
\(450\) −3.03301e19 + 6.24626e20i −0.000850290 + 0.0175111i
\(451\) −8.79759e21 −0.242027
\(452\) 3.03946e22i 0.820579i
\(453\) 3.63976e22i 0.964357i
\(454\) −4.79167e22 −1.24598
\(455\) −3.11649e20 + 1.28439e22i −0.00795369 + 0.327794i
\(456\) −5.11353e22 −1.28091
\(457\) 3.47799e22i 0.855146i −0.903981 0.427573i \(-0.859369\pi\)
0.903981 0.427573i \(-0.140631\pi\)
\(458\) 6.96359e22i 1.68065i
\(459\) −1.44232e22 −0.341706
\(460\) 6.51788e22 + 1.58152e21i 1.51588 + 0.0367818i
\(461\) 4.25534e22 0.971574 0.485787 0.874077i \(-0.338533\pi\)
0.485787 + 0.874077i \(0.338533\pi\)
\(462\) 6.02375e22i 1.35024i
\(463\) 4.02870e22i 0.886597i 0.896374 + 0.443299i \(0.146192\pi\)
−0.896374 + 0.443299i \(0.853808\pi\)
\(464\) −1.43459e23 −3.09974
\(465\) 2.81312e22 + 6.82583e20i 0.596813 + 0.0144812i
\(466\) −7.91818e22 −1.64947
\(467\) 1.32049e21i 0.0270110i 0.999909 + 0.0135055i \(0.00429907\pi\)
−0.999909 + 0.0135055i \(0.995701\pi\)
\(468\) 2.35032e20i 0.00472103i
\(469\) 8.34476e21 0.164606
\(470\) 4.79139e20 1.97467e22i 0.00928175 0.382527i
\(471\) −6.45179e22 −1.22745
\(472\) 1.65322e23i 3.08904i
\(473\) 2.69533e22i 0.494643i
\(474\) 6.10090e22 1.09971
\(475\) 2.99438e22 + 1.45398e21i 0.530165 + 0.0257433i
\(476\) 7.07887e22 1.23113
\(477\) 7.79638e20i 0.0133195i
\(478\) 5.46590e22i 0.917328i
\(479\) 4.98795e22 0.822375 0.411188 0.911551i \(-0.365114\pi\)
0.411188 + 0.911551i \(0.365114\pi\)
\(480\) 2.08384e21 8.58809e22i 0.0337531 1.39106i
\(481\) 1.78278e22 0.283703
\(482\) 5.94482e22i 0.929477i
\(483\) 6.55548e22i 1.00706i
\(484\) 1.18981e23 1.79594
\(485\) −4.00439e22 9.71638e20i −0.593926 0.0144112i
\(486\) −2.40574e21 −0.0350623
\(487\) 1.58494e22i 0.226996i 0.993538 + 0.113498i \(0.0362055\pi\)
−0.993538 + 0.113498i \(0.963794\pi\)
\(488\) 1.62716e23i 2.29014i
\(489\) −3.13039e22 −0.432985
\(490\) −1.89981e23 4.60974e21i −2.58251 0.0626629i
\(491\) 6.29353e22 0.840817 0.420409 0.907335i \(-0.361887\pi\)
0.420409 + 0.907335i \(0.361887\pi\)
\(492\) 8.92958e22i 1.17254i
\(493\) 3.89819e22i 0.503111i
\(494\) −1.61048e22 −0.204304
\(495\) 8.94261e18 3.68550e20i 0.000111512 0.00459571i
\(496\) 1.02545e23 1.25695
\(497\) 1.36743e23i 1.64769i
\(498\) 1.56760e23i 1.85689i
\(499\) −1.06080e23 −1.23532 −0.617660 0.786445i \(-0.711919\pi\)
−0.617660 + 0.786445i \(0.711919\pi\)
\(500\) −1.47925e22 + 2.02894e23i −0.169354 + 2.32287i
\(501\) −3.35431e22 −0.377557
\(502\) 3.33738e22i 0.369338i
\(503\) 9.88915e22i 1.07605i −0.842930 0.538024i \(-0.819171\pi\)
0.842930 0.538024i \(-0.180829\pi\)
\(504\) 3.38496e21 0.0362154
\(505\) −3.24999e21 + 1.33941e23i −0.0341905 + 1.40909i
\(506\) −5.49376e22 −0.568317
\(507\) 9.34760e22i 0.950895i
\(508\) 4.06406e23i 4.06554i
\(509\) −1.44169e23 −1.41831 −0.709156 0.705051i \(-0.750924\pi\)
−0.709156 + 0.705051i \(0.750924\pi\)
\(510\) −6.38083e22 1.54826e21i −0.617349 0.0149795i
\(511\) 2.95205e22 0.280896
\(512\) 2.29876e23i 2.15129i
\(513\) 5.79397e22i 0.533309i
\(514\) 3.34755e23 3.03069
\(515\) 1.18343e23 + 2.87150e21i 1.05385 + 0.0255710i
\(516\) 2.73576e23 2.39638
\(517\) 1.16443e22i 0.100333i
\(518\) 4.49949e23i 3.81382i
\(519\) −1.38740e23 −1.15686
\(520\) 1.51272e21 6.23433e22i 0.0124088 0.511401i
\(521\) −2.14130e22 −0.172805 −0.0864025 0.996260i \(-0.527537\pi\)
−0.0864025 + 0.996260i \(0.527537\pi\)
\(522\) 3.26657e21i 0.0259354i
\(523\) 8.29652e22i 0.648084i −0.946043 0.324042i \(-0.894958\pi\)
0.946043 0.324042i \(-0.105042\pi\)
\(524\) −5.04255e23 −3.87556
\(525\) 2.04305e23 + 9.92048e21i 1.54499 + 0.0750203i
\(526\) −3.36577e22 −0.250441
\(527\) 2.78643e22i 0.204013i
\(528\) 1.38472e23i 0.997642i
\(529\) 8.12628e22 0.576128
\(530\) 8.79355e21 3.62407e23i 0.0613506 2.52843i
\(531\) 1.78279e21 0.0122404
\(532\) 2.84367e23i 1.92146i
\(533\) 1.60482e22i 0.106720i
\(534\) 2.17490e23 1.42343
\(535\) −1.22550e23 2.97359e21i −0.789417 0.0191546i
\(536\) −4.05047e22 −0.256806
\(537\) 1.18814e23i 0.741460i
\(538\) 6.03419e22i 0.370655i
\(539\) 1.12029e23 0.677370
\(540\) −3.93053e23 9.53714e21i −2.33940 0.0567638i
\(541\) 4.66901e22 0.273557 0.136779 0.990602i \(-0.456325\pi\)
0.136779 + 0.990602i \(0.456325\pi\)
\(542\) 2.54480e22i 0.146778i
\(543\) 7.19427e22i 0.408496i
\(544\) −8.50662e22 −0.475517
\(545\) −5.66899e21 + 2.33635e23i −0.0311986 + 1.28578i
\(546\) −1.09883e23 −0.595376
\(547\) 2.17735e22i 0.116155i −0.998312 0.0580773i \(-0.981503\pi\)
0.998312 0.0580773i \(-0.0184970\pi\)
\(548\) 2.61702e23i 1.37459i
\(549\) −1.75469e21 −0.00907476
\(550\) 8.31377e21 1.71216e23i 0.0423365 0.871890i
\(551\) 1.56595e23 0.785218
\(552\) 3.18198e23i 1.57114i
\(553\) 1.93603e23i 0.941345i
\(554\) 5.63392e23 2.69760
\(555\) 6.88497e21 2.83749e23i 0.0324647 1.33796i
\(556\) −5.20581e23 −2.41742
\(557\) 3.95082e23i 1.80683i 0.428763 + 0.903417i \(0.358949\pi\)
−0.428763 + 0.903417i \(0.641051\pi\)
\(558\) 2.33495e21i 0.0105169i
\(559\) 4.91670e22 0.218109
\(560\) 7.45179e23 + 1.80812e22i 3.25584 + 0.0790006i
\(561\) 3.76269e22 0.161925
\(562\) 5.06257e23i 2.14591i
\(563\) 1.57683e23i 0.658359i −0.944267 0.329180i \(-0.893228\pi\)
0.944267 0.329180i \(-0.106772\pi\)
\(564\) 1.18190e23 0.486082
\(565\) −8.69419e22 2.10958e21i −0.352223 0.00854643i
\(566\) −4.25975e23 −1.69998
\(567\) 3.91522e23i 1.53922i
\(568\) 6.63738e23i 2.57061i
\(569\) −2.40022e23 −0.915791 −0.457896 0.889006i \(-0.651397\pi\)
−0.457896 + 0.889006i \(0.651397\pi\)
\(570\) −6.21957e21 + 2.56326e23i −0.0233789 + 0.963511i
\(571\) 1.03536e23 0.383428 0.191714 0.981451i \(-0.438595\pi\)
0.191714 + 0.981451i \(0.438595\pi\)
\(572\) 6.44245e22i 0.235063i
\(573\) 3.03356e23i 1.09053i
\(574\) −4.05035e23 −1.43463
\(575\) 9.04766e21 1.86330e23i 0.0315762 0.650289i
\(576\) −1.27348e21 −0.00437925
\(577\) 5.37249e22i 0.182046i −0.995849 0.0910229i \(-0.970986\pi\)
0.995849 0.0910229i \(-0.0290137\pi\)
\(578\) 4.83241e23i 1.61353i
\(579\) −1.38502e23 −0.455711
\(580\) −2.57763e22 + 1.06231e24i −0.0835762 + 3.44441i
\(581\) −4.97457e23 −1.58949
\(582\) 3.42584e23i 1.07875i
\(583\) 2.13706e23i 0.663185i
\(584\) −1.43290e23 −0.438234
\(585\) −6.72294e20 1.63127e19i −0.00202644 4.91702e-5i
\(586\) 6.99217e23 2.07722
\(587\) 7.97439e22i 0.233493i −0.993162 0.116746i \(-0.962753\pi\)
0.993162 0.116746i \(-0.0372465\pi\)
\(588\) 1.13710e24i 3.28163i
\(589\) −1.11935e23 −0.318408
\(590\) 8.28712e23 + 2.01081e22i 2.32360 + 0.0563805i
\(591\) −1.36679e23 −0.377752
\(592\) 1.03433e24i 2.81790i
\(593\) 2.92994e22i 0.0786854i 0.999226 + 0.0393427i \(0.0125264\pi\)
−0.999226 + 0.0393427i \(0.987474\pi\)
\(594\) 3.31295e23 0.877061
\(595\) 4.91319e21 2.02486e23i 0.0128224 0.528447i
\(596\) 5.75068e23 1.47954
\(597\) 7.41634e23i 1.88108i
\(598\) 1.00215e23i 0.250595i
\(599\) −2.14554e23 −0.528942 −0.264471 0.964394i \(-0.585197\pi\)
−0.264471 + 0.964394i \(0.585197\pi\)
\(600\) −9.91680e23 4.81532e22i −2.41038 0.117041i
\(601\) 3.54004e23 0.848351 0.424175 0.905580i \(-0.360564\pi\)
0.424175 + 0.905580i \(0.360564\pi\)
\(602\) 1.24091e24i 2.93204i
\(603\) 4.36792e20i 0.00101760i
\(604\) 9.82480e23 2.25689
\(605\) 8.25803e21 3.40337e23i 0.0187049 0.770882i
\(606\) −1.14590e24 −2.55934
\(607\) 2.65810e23i 0.585419i −0.956201 0.292710i \(-0.905443\pi\)
0.956201 0.292710i \(-0.0945569\pi\)
\(608\) 3.41722e23i 0.742151i
\(609\) 1.06844e24 2.28826
\(610\) −8.15650e23 1.97912e22i −1.72266 0.0417992i
\(611\) 2.12411e22 0.0442412
\(612\) 3.70531e21i 0.00761093i
\(613\) 6.38443e23i 1.29333i −0.762776 0.646663i \(-0.776164\pi\)
0.762776 0.646663i \(-0.223836\pi\)
\(614\) −1.45670e24 −2.91032
\(615\) 2.55425e23 + 6.19770e21i 0.503297 + 0.0122122i
\(616\) −9.27849e23 −1.80319
\(617\) 8.39922e23i 1.60996i −0.593301 0.804980i \(-0.702176\pi\)
0.593301 0.804980i \(-0.297824\pi\)
\(618\) 1.01245e24i 1.91412i
\(619\) −1.78611e23 −0.333072 −0.166536 0.986035i \(-0.553258\pi\)
−0.166536 + 0.986035i \(0.553258\pi\)
\(620\) 1.84250e22 7.59345e23i 0.0338904 1.39672i
\(621\) 3.60539e23 0.654145
\(622\) 1.10731e24i 1.98175i
\(623\) 6.90172e23i 1.21845i
\(624\) 2.52595e23 0.439902
\(625\) 5.79338e23 + 5.63950e22i 0.995295 + 0.0968859i
\(626\) 1.26706e24 2.14741
\(627\) 1.51152e23i 0.252720i
\(628\) 1.74153e24i 2.87260i
\(629\) −2.81057e23 −0.457367
\(630\) 4.11711e20 1.69678e22i 0.000660995 0.0272415i
\(631\) 4.46452e23 0.707173 0.353586 0.935402i \(-0.384962\pi\)
0.353586 + 0.935402i \(0.384962\pi\)
\(632\) 9.39733e23i 1.46862i
\(633\) 3.28157e23i 0.506000i
\(634\) 1.94272e23 0.295564
\(635\) −1.16250e24 2.82072e22i −1.74508 0.0423431i
\(636\) 2.16912e24 3.21291
\(637\) 2.04358e23i 0.298681i
\(638\) 8.95399e23i 1.29134i
\(639\) 7.15757e21 0.0101861
\(640\) 4.03379e23 + 9.78770e21i 0.566479 + 0.0137452i
\(641\) −5.46949e23 −0.757973 −0.378987 0.925402i \(-0.623727\pi\)
−0.378987 + 0.925402i \(0.623727\pi\)
\(642\) 1.04844e24i 1.43383i
\(643\) 7.19921e23i 0.971609i −0.874067 0.485805i \(-0.838527\pi\)
0.874067 0.485805i \(-0.161473\pi\)
\(644\) −1.76952e24 −2.35682
\(645\) 1.89879e22 7.82547e23i 0.0249586 1.02862i
\(646\) 2.53895e23 0.329365
\(647\) 1.25975e24i 1.61287i 0.591324 + 0.806434i \(0.298605\pi\)
−0.591324 + 0.806434i \(0.701395\pi\)
\(648\) 1.90041e24i 2.40138i
\(649\) −4.88680e23 −0.609459
\(650\) −3.12325e23 1.51656e22i −0.384453 0.0186679i
\(651\) −7.63726e23 −0.927895
\(652\) 8.44985e23i 1.01332i
\(653\) 5.58543e23i 0.661142i 0.943781 + 0.330571i \(0.107241\pi\)
−0.943781 + 0.330571i \(0.892759\pi\)
\(654\) −1.99880e24 −2.33538
\(655\) −3.49985e22 + 1.44239e24i −0.0403644 + 1.66353i
\(656\) 9.31084e23 1.06000
\(657\) 1.54520e21i 0.00173652i
\(658\) 5.36097e23i 0.594735i
\(659\) 1.40175e24 1.53513 0.767563 0.640973i \(-0.221469\pi\)
0.767563 + 0.640973i \(0.221469\pi\)
\(660\) 1.02539e24 + 2.48803e22i 1.10857 + 0.0268988i
\(661\) −1.56535e24 −1.67070 −0.835349 0.549720i \(-0.814734\pi\)
−0.835349 + 0.549720i \(0.814734\pi\)
\(662\) 2.32288e24i 2.44757i
\(663\) 6.86373e22i 0.0713995i
\(664\) 2.41461e24 2.47981
\(665\) −8.13414e23 1.97369e22i −0.824760 0.0200122i
\(666\) −2.35518e22 −0.0235773
\(667\) 9.74440e23i 0.963131i
\(668\) 9.05428e23i 0.883596i
\(669\) 1.13548e24 1.09410
\(670\) −4.92658e21 + 2.03038e23i −0.00468716 + 0.193171i
\(671\) 4.80977e23 0.451838
\(672\) 2.33156e24i 2.16275i
\(673\) 1.06512e24i 0.975593i −0.872957 0.487797i \(-0.837801\pi\)
0.872957 0.487797i \(-0.162199\pi\)
\(674\) 7.01909e23 0.634851
\(675\) −5.45608e22 + 1.12364e24i −0.0487302 + 1.00356i
\(676\) −2.52320e24 −2.22538
\(677\) 1.35343e23i 0.117878i −0.998262 0.0589389i \(-0.981228\pi\)
0.998262 0.0589389i \(-0.0187717\pi\)
\(678\) 7.43806e23i 0.639746i
\(679\) 1.08714e24 0.923407
\(680\) −2.38482e22 + 9.82852e23i −0.0200046 + 0.824446i
\(681\) −8.20365e23 −0.679605
\(682\) 6.40033e23i 0.523643i
\(683\) 6.70521e23i 0.541797i 0.962608 + 0.270898i \(0.0873207\pi\)
−0.962608 + 0.270898i \(0.912679\pi\)
\(684\) 1.48847e22 0.0118786
\(685\) −7.48583e23 1.81638e22i −0.590024 0.0143165i
\(686\) 1.51483e24 1.17926
\(687\) 1.19221e24i 0.916687i
\(688\) 2.85257e24i 2.16638i
\(689\) 3.89834e23 0.292426
\(690\) 1.59503e24 + 3.87023e22i 1.18182 + 0.0286761i
\(691\) 1.91000e24 1.39788 0.698941 0.715179i \(-0.253655\pi\)
0.698941 + 0.715179i \(0.253655\pi\)
\(692\) 3.74502e24i 2.70740i
\(693\) 1.00057e22i 0.00714519i
\(694\) −4.13649e24 −2.91794
\(695\) −3.61317e22 + 1.48909e24i −0.0251778 + 1.03765i
\(696\) −5.18613e24 −3.56998
\(697\) 2.53002e23i 0.172046i
\(698\) 3.25625e24i 2.18750i
\(699\) −1.35564e24 −0.899684
\(700\) 2.67783e23 5.51481e24i 0.175570 3.61574i
\(701\) 2.38901e24 1.54745 0.773723 0.633524i \(-0.218392\pi\)
0.773723 + 0.633524i \(0.218392\pi\)
\(702\) 6.04333e23i 0.386733i
\(703\) 1.12904e24i 0.713823i
\(704\) 3.49072e23 0.218046
\(705\) 8.20317e21 3.38076e23i 0.00506261 0.208644i
\(706\) 1.09198e24 0.665845
\(707\) 3.63634e24i 2.19078i
\(708\) 4.96011e24i 2.95263i
\(709\) 1.18830e24 0.698926 0.349463 0.936950i \(-0.386364\pi\)
0.349463 + 0.936950i \(0.386364\pi\)
\(710\) 3.32713e24 + 8.07304e22i 1.93363 + 0.0469182i
\(711\) −1.01338e22 −0.00581945
\(712\) 3.35003e24i 1.90094i
\(713\) 6.96532e23i 0.390553i
\(714\) 1.73231e24 0.959824
\(715\) 1.84282e23 + 4.47148e21i 0.100898 + 0.00244822i
\(716\) −3.20716e24 −1.73524
\(717\) 9.35797e23i 0.500344i
\(718\) 3.72808e24i 1.96983i
\(719\) −7.00134e23 −0.365583 −0.182791 0.983152i \(-0.558513\pi\)
−0.182791 + 0.983152i \(0.558513\pi\)
\(720\) −9.46432e20 + 3.90051e22i −0.000488386 + 0.0201278i
\(721\) −3.21285e24 −1.63848
\(722\) 2.60021e24i 1.31052i
\(723\) 1.01779e24i 0.506971i
\(724\) 1.94195e24 0.956004
\(725\) 3.03689e24 + 1.47463e23i 1.47760 + 0.0717480i
\(726\) 2.91165e24 1.40016
\(727\) 6.64217e23i 0.315695i −0.987464 0.157847i \(-0.949545\pi\)
0.987464 0.157847i \(-0.0504554\pi\)
\(728\) 1.69254e24i 0.795102i
\(729\) −2.17399e24 −1.00942
\(730\) −1.74283e22 + 7.18270e23i −0.00799855 + 0.329643i
\(731\) −7.75124e23 −0.351620
\(732\) 4.88193e24i 2.18901i
\(733\) 1.04024e24i 0.461054i −0.973066 0.230527i \(-0.925955\pi\)
0.973066 0.230527i \(-0.0740450\pi\)
\(734\) 5.23181e23 0.229211
\(735\) −3.25259e24 7.89218e22i −1.40860 0.0341786i
\(736\) 2.12642e24 0.910307
\(737\) 1.19729e23i 0.0506670i
\(738\) 2.12008e22i 0.00886899i
\(739\) −7.14037e23 −0.295286 −0.147643 0.989041i \(-0.547169\pi\)
−0.147643 + 0.989041i \(0.547169\pi\)
\(740\) −7.65924e24 1.85846e23i −3.13124 0.0759772i
\(741\) −2.75725e23 −0.111435
\(742\) 9.83889e24i 3.93109i
\(743\) 3.15273e24i 1.24532i 0.782492 + 0.622661i \(0.213948\pi\)
−0.782492 + 0.622661i \(0.786052\pi\)
\(744\) 3.70706e24 1.44764
\(745\) 3.99134e22 1.64494e24i 0.0154096 0.635072i
\(746\) −3.70134e24 −1.41280
\(747\) 2.60385e22i 0.00982632i
\(748\) 1.01566e24i 0.378953i
\(749\) 3.32708e24 1.22735
\(750\) −3.61995e23 + 4.96514e24i −0.132033 + 1.81097i
\(751\) −9.62214e21 −0.00347002 −0.00173501 0.999998i \(-0.500552\pi\)
−0.00173501 + 0.999998i \(0.500552\pi\)
\(752\) 1.23237e24i 0.439429i
\(753\) 5.71381e23i 0.201451i
\(754\) −1.63335e24 −0.569407
\(755\) 6.81904e22 2.81032e24i 0.0235058 0.968739i
\(756\) 1.06709e25 3.63718
\(757\) 2.06888e24i 0.697302i 0.937253 + 0.348651i \(0.113360\pi\)
−0.937253 + 0.348651i \(0.886640\pi\)
\(758\) 7.40132e24i 2.46672i
\(759\) −9.40568e23 −0.309981
\(760\) 3.94824e24 + 9.58013e22i 1.28673 + 0.0312216i
\(761\) −1.54775e24 −0.498807 −0.249404 0.968400i \(-0.580235\pi\)
−0.249404 + 0.968400i \(0.580235\pi\)
\(762\) 9.94541e24i 3.16961i
\(763\) 6.34289e24i 1.99907i
\(764\) −8.18849e24 −2.55218
\(765\) 1.05988e22 + 2.57172e20i 0.00326689 + 7.92688e-5i
\(766\) 4.67284e24 1.42442
\(767\) 8.91429e23i 0.268736i
\(768\) 4.97227e24i 1.48246i
\(769\) 1.41912e24 0.418451 0.209226 0.977867i \(-0.432906\pi\)
0.209226 + 0.977867i \(0.432906\pi\)
\(770\) −1.12854e23 + 4.65104e24i −0.0329114 + 1.35637i
\(771\) 5.73123e24 1.65305
\(772\) 3.73859e24i 1.06650i
\(773\) 7.68448e23i 0.216815i −0.994107 0.108407i \(-0.965425\pi\)
0.994107 0.108407i \(-0.0345751\pi\)
\(774\) −6.49532e22 −0.0181260