Properties

Label 2.50.a.b.1.2
Level 2
Weight 50
Character 2.1
Self dual Yes
Analytic conductor 30.413
Analytic rank 0
Dimension 3
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 50 \)
Character orbit: \([\chi]\) = 2.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(30.4132410198\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\mathbb{Q}[x]/(x^{3} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{22}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-3.42020e8\)
Character \(\chi\) = 2.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.67772e7 q^{2}\) \(-1.33407e11 q^{3}\) \(+2.81475e14 q^{4}\) \(+1.87739e17 q^{5}\) \(-2.23819e18 q^{6}\) \(+8.28497e20 q^{7}\) \(+4.72237e21 q^{8}\) \(-2.21502e23 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.67772e7 q^{2}\) \(-1.33407e11 q^{3}\) \(+2.81475e14 q^{4}\) \(+1.87739e17 q^{5}\) \(-2.23819e18 q^{6}\) \(+8.28497e20 q^{7}\) \(+4.72237e21 q^{8}\) \(-2.21502e23 q^{9}\) \(+3.14974e24 q^{10}\) \(-3.05508e25 q^{11}\) \(-3.75507e25 q^{12}\) \(-4.92824e25 q^{13}\) \(+1.38999e28 q^{14}\) \(-2.50456e28 q^{15}\) \(+7.92282e28 q^{16}\) \(+2.50818e30 q^{17}\) \(-3.71619e30 q^{18}\) \(+5.26388e30 q^{19}\) \(+5.28438e31 q^{20}\) \(-1.10527e32 q^{21}\) \(-5.12558e32 q^{22}\) \(-7.99827e32 q^{23}\) \(-6.29996e32 q^{24}\) \(+1.74823e34 q^{25}\) \(-8.26821e32 q^{26}\) \(+6.14740e34 q^{27}\) \(+2.33201e35 q^{28}\) \(-2.91459e35 q^{29}\) \(-4.20196e35 q^{30}\) \(+5.98168e36 q^{31}\) \(+1.32923e36 q^{32}\) \(+4.07569e36 q^{33}\) \(+4.20803e37 q^{34}\) \(+1.55541e38 q^{35}\) \(-6.23473e37 q^{36}\) \(+1.31540e38 q^{37}\) \(+8.83133e37 q^{38}\) \(+6.57461e36 q^{39}\) \(+8.86572e38 q^{40}\) \(-2.57335e39 q^{41}\) \(-1.85434e39 q^{42}\) \(+3.01162e39 q^{43}\) \(-8.59930e39 q^{44}\) \(-4.15845e40 q^{45}\) \(-1.34189e40 q^{46}\) \(-1.35707e41 q^{47}\) \(-1.05696e40 q^{48}\) \(+4.29484e41 q^{49}\) \(+2.93305e41 q^{50}\) \(-3.34609e41 q^{51}\) \(-1.38718e40 q^{52}\) \(+3.38284e42 q^{53}\) \(+1.03136e42 q^{54}\) \(-5.73558e42 q^{55}\) \(+3.91247e42 q^{56}\) \(-7.02238e41 q^{57}\) \(-4.88987e42 q^{58}\) \(-1.39260e42 q^{59}\) \(-7.04972e42 q^{60}\) \(-8.43699e43 q^{61}\) \(+1.00356e44 q^{62}\) \(-1.83514e44 q^{63}\) \(+2.23007e43 q^{64}\) \(-9.25222e42 q^{65}\) \(+6.83787e43 q^{66}\) \(+4.28654e44 q^{67}\) \(+7.05991e44 q^{68}\) \(+1.06702e44 q^{69}\) \(+2.60955e45 q^{70}\) \(-1.65460e45 q^{71}\) \(-1.04601e45 q^{72}\) \(-5.25815e45 q^{73}\) \(+2.20688e45 q^{74}\) \(-2.33226e45 q^{75}\) \(+1.48165e45 q^{76}\) \(-2.53113e46 q^{77}\) \(+1.10304e44 q^{78}\) \(+1.45663e46 q^{79}\) \(+1.48742e46 q^{80}\) \(+4.48042e46 q^{81}\) \(-4.31736e46 q^{82}\) \(-9.24216e46 q^{83}\) \(-3.11106e46 q^{84}\) \(+4.70884e47 q^{85}\) \(+5.05265e46 q^{86}\) \(+3.88826e46 q^{87}\) \(-1.44272e47 q^{88}\) \(+8.22598e46 q^{89}\) \(-6.97673e47 q^{90}\) \(-4.08303e46 q^{91}\) \(-2.25131e47 q^{92}\) \(-7.97996e47 q^{93}\) \(-2.27678e48 q^{94}\) \(+9.88236e47 q^{95}\) \(-1.77328e47 q^{96}\) \(-4.76751e48 q^{97}\) \(+7.20555e48 q^{98}\) \(+6.76707e48 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(3q \) \(\mathstrut +\mathstrut 50331648q^{2} \) \(\mathstrut -\mathstrut 16203614388q^{3} \) \(\mathstrut +\mathstrut 844424930131968q^{4} \) \(\mathstrut -\mathstrut 101813016401840430q^{5} \) \(\mathstrut -\mathstrut 271851538568183808q^{6} \) \(\mathstrut -\mathstrut 125479179230203797096q^{7} \) \(\mathstrut +\mathstrut 14167099448608935641088q^{8} \) \(\mathstrut +\mathstrut 389432931519696922052199q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut +\mathstrut 50331648q^{2} \) \(\mathstrut -\mathstrut 16203614388q^{3} \) \(\mathstrut +\mathstrut 844424930131968q^{4} \) \(\mathstrut -\mathstrut 101813016401840430q^{5} \) \(\mathstrut -\mathstrut 271851538568183808q^{6} \) \(\mathstrut -\mathstrut \)\(12\!\cdots\!96\)\(q^{7} \) \(\mathstrut +\mathstrut \)\(14\!\cdots\!88\)\(q^{8} \) \(\mathstrut +\mathstrut \)\(38\!\cdots\!99\)\(q^{9} \) \(\mathstrut -\mathstrut \)\(17\!\cdots\!80\)\(q^{10} \) \(\mathstrut -\mathstrut \)\(25\!\cdots\!04\)\(q^{11} \) \(\mathstrut -\mathstrut \)\(45\!\cdots\!28\)\(q^{12} \) \(\mathstrut +\mathstrut \)\(29\!\cdots\!42\)\(q^{13} \) \(\mathstrut -\mathstrut \)\(21\!\cdots\!36\)\(q^{14} \) \(\mathstrut +\mathstrut \)\(87\!\cdots\!80\)\(q^{15} \) \(\mathstrut +\mathstrut \)\(23\!\cdots\!08\)\(q^{16} \) \(\mathstrut +\mathstrut \)\(39\!\cdots\!54\)\(q^{17} \) \(\mathstrut +\mathstrut \)\(65\!\cdots\!84\)\(q^{18} \) \(\mathstrut +\mathstrut \)\(14\!\cdots\!80\)\(q^{19} \) \(\mathstrut -\mathstrut \)\(28\!\cdots\!80\)\(q^{20} \) \(\mathstrut -\mathstrut \)\(10\!\cdots\!84\)\(q^{21} \) \(\mathstrut -\mathstrut \)\(43\!\cdots\!64\)\(q^{22} \) \(\mathstrut -\mathstrut \)\(49\!\cdots\!08\)\(q^{23} \) \(\mathstrut -\mathstrut \)\(76\!\cdots\!48\)\(q^{24} \) \(\mathstrut +\mathstrut \)\(39\!\cdots\!25\)\(q^{25} \) \(\mathstrut +\mathstrut \)\(49\!\cdots\!72\)\(q^{26} \) \(\mathstrut +\mathstrut \)\(19\!\cdots\!00\)\(q^{27} \) \(\mathstrut -\mathstrut \)\(35\!\cdots\!76\)\(q^{28} \) \(\mathstrut +\mathstrut \)\(93\!\cdots\!30\)\(q^{29} \) \(\mathstrut +\mathstrut \)\(14\!\cdots\!80\)\(q^{30} \) \(\mathstrut +\mathstrut \)\(24\!\cdots\!56\)\(q^{31} \) \(\mathstrut +\mathstrut \)\(39\!\cdots\!28\)\(q^{32} \) \(\mathstrut +\mathstrut \)\(84\!\cdots\!84\)\(q^{33} \) \(\mathstrut +\mathstrut \)\(65\!\cdots\!64\)\(q^{34} \) \(\mathstrut +\mathstrut \)\(30\!\cdots\!60\)\(q^{35} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!44\)\(q^{36} \) \(\mathstrut +\mathstrut \)\(30\!\cdots\!74\)\(q^{37} \) \(\mathstrut +\mathstrut \)\(24\!\cdots\!80\)\(q^{38} \) \(\mathstrut +\mathstrut \)\(36\!\cdots\!68\)\(q^{39} \) \(\mathstrut -\mathstrut \)\(48\!\cdots\!80\)\(q^{40} \) \(\mathstrut -\mathstrut \)\(11\!\cdots\!54\)\(q^{41} \) \(\mathstrut -\mathstrut \)\(18\!\cdots\!44\)\(q^{42} \) \(\mathstrut -\mathstrut \)\(17\!\cdots\!48\)\(q^{43} \) \(\mathstrut -\mathstrut \)\(72\!\cdots\!24\)\(q^{44} \) \(\mathstrut -\mathstrut \)\(11\!\cdots\!90\)\(q^{45} \) \(\mathstrut -\mathstrut \)\(83\!\cdots\!28\)\(q^{46} \) \(\mathstrut -\mathstrut \)\(21\!\cdots\!56\)\(q^{47} \) \(\mathstrut -\mathstrut \)\(12\!\cdots\!68\)\(q^{48} \) \(\mathstrut +\mathstrut \)\(37\!\cdots\!51\)\(q^{49} \) \(\mathstrut +\mathstrut \)\(66\!\cdots\!00\)\(q^{50} \) \(\mathstrut +\mathstrut \)\(22\!\cdots\!16\)\(q^{51} \) \(\mathstrut +\mathstrut \)\(82\!\cdots\!52\)\(q^{52} \) \(\mathstrut +\mathstrut \)\(74\!\cdots\!02\)\(q^{53} \) \(\mathstrut +\mathstrut \)\(32\!\cdots\!00\)\(q^{54} \) \(\mathstrut +\mathstrut \)\(32\!\cdots\!40\)\(q^{55} \) \(\mathstrut -\mathstrut \)\(59\!\cdots\!16\)\(q^{56} \) \(\mathstrut -\mathstrut \)\(20\!\cdots\!80\)\(q^{57} \) \(\mathstrut +\mathstrut \)\(15\!\cdots\!80\)\(q^{58} \) \(\mathstrut -\mathstrut \)\(53\!\cdots\!40\)\(q^{59} \) \(\mathstrut +\mathstrut \)\(24\!\cdots\!80\)\(q^{60} \) \(\mathstrut -\mathstrut \)\(12\!\cdots\!94\)\(q^{61} \) \(\mathstrut +\mathstrut \)\(40\!\cdots\!96\)\(q^{62} \) \(\mathstrut -\mathstrut \)\(46\!\cdots\!68\)\(q^{63} \) \(\mathstrut +\mathstrut \)\(66\!\cdots\!48\)\(q^{64} \) \(\mathstrut -\mathstrut \)\(42\!\cdots\!20\)\(q^{65} \) \(\mathstrut +\mathstrut \)\(14\!\cdots\!44\)\(q^{66} \) \(\mathstrut +\mathstrut \)\(11\!\cdots\!24\)\(q^{67} \) \(\mathstrut +\mathstrut \)\(11\!\cdots\!24\)\(q^{68} \) \(\mathstrut +\mathstrut \)\(77\!\cdots\!68\)\(q^{69} \) \(\mathstrut +\mathstrut \)\(50\!\cdots\!60\)\(q^{70} \) \(\mathstrut -\mathstrut \)\(40\!\cdots\!24\)\(q^{71} \) \(\mathstrut +\mathstrut \)\(18\!\cdots\!04\)\(q^{72} \) \(\mathstrut -\mathstrut \)\(10\!\cdots\!18\)\(q^{73} \) \(\mathstrut +\mathstrut \)\(51\!\cdots\!84\)\(q^{74} \) \(\mathstrut -\mathstrut \)\(38\!\cdots\!00\)\(q^{75} \) \(\mathstrut +\mathstrut \)\(41\!\cdots\!80\)\(q^{76} \) \(\mathstrut -\mathstrut \)\(23\!\cdots\!72\)\(q^{77} \) \(\mathstrut +\mathstrut \)\(60\!\cdots\!88\)\(q^{78} \) \(\mathstrut +\mathstrut \)\(36\!\cdots\!60\)\(q^{79} \) \(\mathstrut -\mathstrut \)\(80\!\cdots\!80\)\(q^{80} \) \(\mathstrut -\mathstrut \)\(14\!\cdots\!17\)\(q^{81} \) \(\mathstrut -\mathstrut \)\(19\!\cdots\!64\)\(q^{82} \) \(\mathstrut +\mathstrut \)\(15\!\cdots\!92\)\(q^{83} \) \(\mathstrut -\mathstrut \)\(30\!\cdots\!04\)\(q^{84} \) \(\mathstrut +\mathstrut \)\(56\!\cdots\!60\)\(q^{85} \) \(\mathstrut -\mathstrut \)\(29\!\cdots\!68\)\(q^{86} \) \(\mathstrut +\mathstrut \)\(10\!\cdots\!20\)\(q^{87} \) \(\mathstrut -\mathstrut \)\(12\!\cdots\!84\)\(q^{88} \) \(\mathstrut +\mathstrut \)\(54\!\cdots\!70\)\(q^{89} \) \(\mathstrut -\mathstrut \)\(19\!\cdots\!40\)\(q^{90} \) \(\mathstrut -\mathstrut \)\(14\!\cdots\!44\)\(q^{91} \) \(\mathstrut -\mathstrut \)\(13\!\cdots\!48\)\(q^{92} \) \(\mathstrut -\mathstrut \)\(23\!\cdots\!76\)\(q^{93} \) \(\mathstrut -\mathstrut \)\(36\!\cdots\!96\)\(q^{94} \) \(\mathstrut -\mathstrut \)\(28\!\cdots\!00\)\(q^{95} \) \(\mathstrut -\mathstrut \)\(21\!\cdots\!88\)\(q^{96} \) \(\mathstrut +\mathstrut \)\(43\!\cdots\!14\)\(q^{97} \) \(\mathstrut +\mathstrut \)\(62\!\cdots\!16\)\(q^{98} \) \(\mathstrut +\mathstrut \)\(17\!\cdots\!68\)\(q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.67772e7 0.707107
\(3\) −1.33407e11 −0.272714 −0.136357 0.990660i \(-0.543539\pi\)
−0.136357 + 0.990660i \(0.543539\pi\)
\(4\) 2.81475e14 0.500000
\(5\) 1.87739e17 1.40860 0.704302 0.709900i \(-0.251260\pi\)
0.704302 + 0.709900i \(0.251260\pi\)
\(6\) −2.23819e18 −0.192838
\(7\) 8.28497e20 1.63452 0.817258 0.576272i \(-0.195493\pi\)
0.817258 + 0.576272i \(0.195493\pi\)
\(8\) 4.72237e21 0.353553
\(9\) −2.21502e23 −0.925627
\(10\) 3.14974e24 0.996034
\(11\) −3.05508e25 −0.935195 −0.467598 0.883941i \(-0.654880\pi\)
−0.467598 + 0.883941i \(0.654880\pi\)
\(12\) −3.75507e25 −0.136357
\(13\) −4.92824e25 −0.0251814 −0.0125907 0.999921i \(-0.504008\pi\)
−0.0125907 + 0.999921i \(0.504008\pi\)
\(14\) 1.38999e28 1.15578
\(15\) −2.50456e28 −0.384146
\(16\) 7.92282e28 0.250000
\(17\) 2.50818e30 1.79209 0.896047 0.443959i \(-0.146427\pi\)
0.896047 + 0.443959i \(0.146427\pi\)
\(18\) −3.71619e30 −0.654517
\(19\) 5.26388e30 0.246515 0.123257 0.992375i \(-0.460666\pi\)
0.123257 + 0.992375i \(0.460666\pi\)
\(20\) 5.28438e31 0.704302
\(21\) −1.10527e32 −0.445755
\(22\) −5.12558e32 −0.661283
\(23\) −7.99827e32 −0.347268 −0.173634 0.984810i \(-0.555551\pi\)
−0.173634 + 0.984810i \(0.555551\pi\)
\(24\) −6.29996e32 −0.0964189
\(25\) 1.74823e34 0.984168
\(26\) −8.26821e32 −0.0178059
\(27\) 6.14740e34 0.525145
\(28\) 2.33201e35 0.817258
\(29\) −2.91459e35 −0.432341 −0.216171 0.976356i \(-0.569357\pi\)
−0.216171 + 0.976356i \(0.569357\pi\)
\(30\) −4.20196e35 −0.271632
\(31\) 5.98168e36 1.73166 0.865828 0.500342i \(-0.166792\pi\)
0.865828 + 0.500342i \(0.166792\pi\)
\(32\) 1.32923e36 0.176777
\(33\) 4.07569e36 0.255041
\(34\) 4.20803e37 1.26720
\(35\) 1.55541e38 2.30239
\(36\) −6.23473e37 −0.462814
\(37\) 1.31540e38 0.499018 0.249509 0.968372i \(-0.419731\pi\)
0.249509 + 0.968372i \(0.419731\pi\)
\(38\) 8.83133e37 0.174312
\(39\) 6.57461e36 0.00686731
\(40\) 8.86572e38 0.498017
\(41\) −2.57335e39 −0.789394 −0.394697 0.918811i \(-0.629150\pi\)
−0.394697 + 0.918811i \(0.629150\pi\)
\(42\) −1.85434e39 −0.315196
\(43\) 3.01162e39 0.287622 0.143811 0.989605i \(-0.454064\pi\)
0.143811 + 0.989605i \(0.454064\pi\)
\(44\) −8.59930e39 −0.467598
\(45\) −4.15845e40 −1.30384
\(46\) −1.34189e40 −0.245555
\(47\) −1.35707e41 −1.46624 −0.733118 0.680102i \(-0.761936\pi\)
−0.733118 + 0.680102i \(0.761936\pi\)
\(48\) −1.05696e40 −0.0681784
\(49\) 4.29484e41 1.67164
\(50\) 2.93305e41 0.695912
\(51\) −3.34609e41 −0.488729
\(52\) −1.38718e40 −0.0125907
\(53\) 3.38284e42 1.92541 0.962704 0.270557i \(-0.0872079\pi\)
0.962704 + 0.270557i \(0.0872079\pi\)
\(54\) 1.03136e42 0.371334
\(55\) −5.73558e42 −1.31732
\(56\) 3.91247e42 0.577889
\(57\) −7.02238e41 −0.0672280
\(58\) −4.88987e42 −0.305711
\(59\) −1.39260e42 −0.0572732 −0.0286366 0.999590i \(-0.509117\pi\)
−0.0286366 + 0.999590i \(0.509117\pi\)
\(60\) −7.04972e42 −0.192073
\(61\) −8.43699e43 −1.53323 −0.766614 0.642108i \(-0.778060\pi\)
−0.766614 + 0.642108i \(0.778060\pi\)
\(62\) 1.00356e44 1.22447
\(63\) −1.83514e44 −1.51295
\(64\) 2.23007e43 0.125000
\(65\) −9.25222e42 −0.0354706
\(66\) 6.83787e43 0.180341
\(67\) 4.28654e44 0.782121 0.391060 0.920365i \(-0.372108\pi\)
0.391060 + 0.920365i \(0.372108\pi\)
\(68\) 7.05991e44 0.896047
\(69\) 1.06702e44 0.0947046
\(70\) 2.60955e45 1.62803
\(71\) −1.65460e45 −0.729228 −0.364614 0.931159i \(-0.618799\pi\)
−0.364614 + 0.931159i \(0.618799\pi\)
\(72\) −1.04601e45 −0.327259
\(73\) −5.25815e45 −1.17334 −0.586669 0.809827i \(-0.699561\pi\)
−0.586669 + 0.809827i \(0.699561\pi\)
\(74\) 2.20688e45 0.352859
\(75\) −2.33226e45 −0.268396
\(76\) 1.48165e45 0.123257
\(77\) −2.53113e46 −1.52859
\(78\) 1.10304e44 0.00485592
\(79\) 1.45663e46 0.469338 0.234669 0.972075i \(-0.424599\pi\)
0.234669 + 0.972075i \(0.424599\pi\)
\(80\) 1.48742e46 0.352151
\(81\) 4.48042e46 0.782413
\(82\) −4.31736e46 −0.558186
\(83\) −9.24216e46 −0.887892 −0.443946 0.896054i \(-0.646422\pi\)
−0.443946 + 0.896054i \(0.646422\pi\)
\(84\) −3.11106e46 −0.222877
\(85\) 4.70884e47 2.52435
\(86\) 5.05265e46 0.203380
\(87\) 3.88826e46 0.117905
\(88\) −1.44272e47 −0.330641
\(89\) 8.22598e46 0.142933 0.0714665 0.997443i \(-0.477232\pi\)
0.0714665 + 0.997443i \(0.477232\pi\)
\(90\) −6.97673e47 −0.921956
\(91\) −4.08303e46 −0.0411594
\(92\) −2.25131e47 −0.173634
\(93\) −7.97996e47 −0.472246
\(94\) −2.27678e48 −1.03678
\(95\) 9.88236e47 0.347242
\(96\) −1.77328e47 −0.0482094
\(97\) −4.76751e48 −1.00551 −0.502753 0.864430i \(-0.667679\pi\)
−0.502753 + 0.864430i \(0.667679\pi\)
\(98\) 7.20555e48 1.18203
\(99\) 6.76707e48 0.865642
\(100\) 4.92084e48 0.492084
\(101\) 1.44113e49 1.12935 0.564674 0.825314i \(-0.309002\pi\)
0.564674 + 0.825314i \(0.309002\pi\)
\(102\) −5.61380e48 −0.345583
\(103\) −1.10349e49 −0.534879 −0.267440 0.963575i \(-0.586178\pi\)
−0.267440 + 0.963575i \(0.586178\pi\)
\(104\) −2.32730e47 −0.00890297
\(105\) −2.07502e49 −0.627893
\(106\) 5.67547e49 1.36147
\(107\) −7.92403e49 −1.51023 −0.755116 0.655591i \(-0.772419\pi\)
−0.755116 + 0.655591i \(0.772419\pi\)
\(108\) 1.73034e49 0.262573
\(109\) −1.47552e48 −0.0178647 −0.00893236 0.999960i \(-0.502843\pi\)
−0.00893236 + 0.999960i \(0.502843\pi\)
\(110\) −9.62271e49 −0.931486
\(111\) −1.75484e49 −0.136089
\(112\) 6.56403e49 0.408629
\(113\) 2.29547e49 0.114935 0.0574673 0.998347i \(-0.481698\pi\)
0.0574673 + 0.998347i \(0.481698\pi\)
\(114\) −1.17816e49 −0.0475374
\(115\) −1.50159e50 −0.489163
\(116\) −8.20384e49 −0.216171
\(117\) 1.09161e49 0.0233086
\(118\) −2.33639e49 −0.0404982
\(119\) 2.07802e51 2.92921
\(120\) −1.18275e50 −0.135816
\(121\) −1.33836e50 −0.125410
\(122\) −1.41549e51 −1.08416
\(123\) 3.43302e50 0.215279
\(124\) 1.68369e51 0.865828
\(125\) −5.27986e49 −0.0223011
\(126\) −3.07885e51 −1.06982
\(127\) −5.51820e51 −1.57981 −0.789907 0.613227i \(-0.789871\pi\)
−0.789907 + 0.613227i \(0.789871\pi\)
\(128\) 3.74144e50 0.0883883
\(129\) −4.01770e50 −0.0784385
\(130\) −1.55227e50 −0.0250815
\(131\) −1.30117e51 −0.174256 −0.0871282 0.996197i \(-0.527769\pi\)
−0.0871282 + 0.996197i \(0.527769\pi\)
\(132\) 1.14720e51 0.127520
\(133\) 4.36111e51 0.402932
\(134\) 7.19162e51 0.553043
\(135\) 1.15411e52 0.739722
\(136\) 1.18446e52 0.633601
\(137\) −1.00417e52 −0.448902 −0.224451 0.974485i \(-0.572059\pi\)
−0.224451 + 0.974485i \(0.572059\pi\)
\(138\) 1.79017e51 0.0669663
\(139\) −3.07477e52 −0.963719 −0.481860 0.876248i \(-0.660038\pi\)
−0.481860 + 0.876248i \(0.660038\pi\)
\(140\) 4.37809e52 1.15119
\(141\) 1.81042e52 0.399863
\(142\) −2.77596e52 −0.515642
\(143\) 1.50562e51 0.0235495
\(144\) −1.75492e52 −0.231407
\(145\) −5.47182e52 −0.608998
\(146\) −8.82172e52 −0.829675
\(147\) −5.72961e52 −0.455880
\(148\) 3.70253e52 0.249509
\(149\) 1.89224e53 1.08122 0.540608 0.841275i \(-0.318194\pi\)
0.540608 + 0.841275i \(0.318194\pi\)
\(150\) −3.91289e52 −0.189785
\(151\) 2.34497e52 0.0966500 0.0483250 0.998832i \(-0.484612\pi\)
0.0483250 + 0.998832i \(0.484612\pi\)
\(152\) 2.48580e52 0.0871562
\(153\) −5.55568e53 −1.65881
\(154\) −4.24653e53 −1.08088
\(155\) 1.12299e54 2.43922
\(156\) 1.85059e51 0.00343366
\(157\) 1.13167e54 1.79546 0.897732 0.440542i \(-0.145214\pi\)
0.897732 + 0.440542i \(0.145214\pi\)
\(158\) 2.44382e53 0.331872
\(159\) −4.51294e53 −0.525085
\(160\) 2.49548e53 0.249009
\(161\) −6.62655e53 −0.567614
\(162\) 7.51690e53 0.553249
\(163\) −2.02699e54 −1.28308 −0.641542 0.767088i \(-0.721705\pi\)
−0.641542 + 0.767088i \(0.721705\pi\)
\(164\) −7.24333e53 −0.394697
\(165\) 7.65165e53 0.359252
\(166\) −1.55058e54 −0.627834
\(167\) −2.35877e54 −0.824389 −0.412194 0.911096i \(-0.635238\pi\)
−0.412194 + 0.911096i \(0.635238\pi\)
\(168\) −5.21950e53 −0.157598
\(169\) −3.82780e54 −0.999366
\(170\) 7.90012e54 1.78499
\(171\) −1.16596e54 −0.228181
\(172\) 8.47695e53 0.143811
\(173\) 6.16168e53 0.0906921 0.0453461 0.998971i \(-0.485561\pi\)
0.0453461 + 0.998971i \(0.485561\pi\)
\(174\) 6.52342e53 0.0833717
\(175\) 1.44841e55 1.60864
\(176\) −2.42049e54 −0.233799
\(177\) 1.85782e53 0.0156192
\(178\) 1.38009e54 0.101069
\(179\) 3.10481e54 0.198215 0.0991073 0.995077i \(-0.468401\pi\)
0.0991073 + 0.995077i \(0.468401\pi\)
\(180\) −1.17050e55 −0.651922
\(181\) −8.59693e54 −0.418041 −0.209020 0.977911i \(-0.567027\pi\)
−0.209020 + 0.977911i \(0.567027\pi\)
\(182\) −6.85019e53 −0.0291041
\(183\) 1.12555e55 0.418132
\(184\) −3.77708e54 −0.122778
\(185\) 2.46952e55 0.702920
\(186\) −1.33882e55 −0.333929
\(187\) −7.66271e55 −1.67596
\(188\) −3.81980e55 −0.733118
\(189\) 5.09310e55 0.858358
\(190\) 1.65798e55 0.245537
\(191\) −2.27680e55 −0.296488 −0.148244 0.988951i \(-0.547362\pi\)
−0.148244 + 0.988951i \(0.547362\pi\)
\(192\) −2.97507e54 −0.0340892
\(193\) 6.99559e55 0.705782 0.352891 0.935664i \(-0.385199\pi\)
0.352891 + 0.935664i \(0.385199\pi\)
\(194\) −7.99856e55 −0.710999
\(195\) 1.23431e54 0.00967333
\(196\) 1.20889e56 0.835821
\(197\) −1.40903e56 −0.860000 −0.430000 0.902829i \(-0.641486\pi\)
−0.430000 + 0.902829i \(0.641486\pi\)
\(198\) 1.13533e56 0.612101
\(199\) 3.14321e56 1.49786 0.748932 0.662647i \(-0.230567\pi\)
0.748932 + 0.662647i \(0.230567\pi\)
\(200\) 8.25580e55 0.347956
\(201\) −5.71853e55 −0.213295
\(202\) 2.41781e56 0.798570
\(203\) −2.41473e56 −0.706668
\(204\) −9.41840e55 −0.244364
\(205\) −4.83117e56 −1.11194
\(206\) −1.85135e56 −0.378217
\(207\) 1.77163e56 0.321440
\(208\) −3.90455e54 −0.00629535
\(209\) −1.60816e56 −0.230539
\(210\) −3.48131e56 −0.443987
\(211\) −1.36710e57 −1.55196 −0.775978 0.630760i \(-0.782743\pi\)
−0.775978 + 0.630760i \(0.782743\pi\)
\(212\) 9.52185e56 0.962704
\(213\) 2.20735e56 0.198870
\(214\) −1.32943e57 −1.06790
\(215\) 5.65398e56 0.405146
\(216\) 2.90303e56 0.185667
\(217\) 4.95580e57 2.83042
\(218\) −2.47551e55 −0.0126323
\(219\) 7.01473e56 0.319985
\(220\) −1.61442e57 −0.658660
\(221\) −1.23609e56 −0.0451274
\(222\) −2.94413e56 −0.0962296
\(223\) 1.75293e56 0.0513210 0.0256605 0.999671i \(-0.491831\pi\)
0.0256605 + 0.999671i \(0.491831\pi\)
\(224\) 1.10126e57 0.288944
\(225\) −3.87237e57 −0.910973
\(226\) 3.85117e56 0.0812710
\(227\) −4.13704e57 −0.783531 −0.391765 0.920065i \(-0.628135\pi\)
−0.391765 + 0.920065i \(0.628135\pi\)
\(228\) −1.97662e56 −0.0336140
\(229\) 6.25222e57 0.955136 0.477568 0.878595i \(-0.341518\pi\)
0.477568 + 0.878595i \(0.341518\pi\)
\(230\) −2.51924e57 −0.345890
\(231\) 3.37670e57 0.416868
\(232\) −1.37638e57 −0.152856
\(233\) −5.79416e57 −0.579123 −0.289561 0.957159i \(-0.593509\pi\)
−0.289561 + 0.957159i \(0.593509\pi\)
\(234\) 1.83143e56 0.0164817
\(235\) −2.54774e58 −2.06535
\(236\) −3.91981e56 −0.0286366
\(237\) −1.94324e57 −0.127995
\(238\) 3.48634e58 2.07126
\(239\) 1.99860e58 1.07146 0.535732 0.844388i \(-0.320036\pi\)
0.535732 + 0.844388i \(0.320036\pi\)
\(240\) −1.98432e57 −0.0960365
\(241\) −8.71374e57 −0.380879 −0.190440 0.981699i \(-0.560991\pi\)
−0.190440 + 0.981699i \(0.560991\pi\)
\(242\) −2.24540e57 −0.0886782
\(243\) −2.06879e58 −0.738520
\(244\) −2.37480e58 −0.766614
\(245\) 8.06309e58 2.35468
\(246\) 5.75965e57 0.152225
\(247\) −2.59417e56 −0.00620759
\(248\) 2.82477e58 0.612233
\(249\) 1.23297e58 0.242140
\(250\) −8.85813e56 −0.0157693
\(251\) −7.09795e58 −1.14585 −0.572924 0.819609i \(-0.694191\pi\)
−0.572924 + 0.819609i \(0.694191\pi\)
\(252\) −5.16545e58 −0.756476
\(253\) 2.44354e58 0.324763
\(254\) −9.25800e58 −1.11710
\(255\) −6.28191e58 −0.688426
\(256\) 6.27710e57 0.0625000
\(257\) −3.39451e58 −0.307196 −0.153598 0.988133i \(-0.549086\pi\)
−0.153598 + 0.988133i \(0.549086\pi\)
\(258\) −6.74058e57 −0.0554644
\(259\) 1.08981e59 0.815653
\(260\) −2.60427e57 −0.0177353
\(261\) 6.45587e58 0.400187
\(262\) −2.18301e58 −0.123218
\(263\) −2.34522e59 −1.20578 −0.602890 0.797825i \(-0.705984\pi\)
−0.602890 + 0.797825i \(0.705984\pi\)
\(264\) 1.92469e58 0.0901705
\(265\) 6.35091e59 2.71214
\(266\) 7.31673e58 0.284916
\(267\) −1.09740e58 −0.0389798
\(268\) 1.20655e59 0.391060
\(269\) −2.15592e59 −0.637826 −0.318913 0.947784i \(-0.603318\pi\)
−0.318913 + 0.947784i \(0.603318\pi\)
\(270\) 1.93627e59 0.523062
\(271\) −3.52922e59 −0.870825 −0.435413 0.900231i \(-0.643398\pi\)
−0.435413 + 0.900231i \(0.643398\pi\)
\(272\) 1.98719e59 0.448023
\(273\) 5.44704e57 0.0112247
\(274\) −1.68471e59 −0.317421
\(275\) −5.34100e59 −0.920389
\(276\) 3.00340e58 0.0473523
\(277\) 2.94410e59 0.424813 0.212406 0.977181i \(-0.431870\pi\)
0.212406 + 0.977181i \(0.431870\pi\)
\(278\) −5.15861e59 −0.681452
\(279\) −1.32495e60 −1.60287
\(280\) 7.34522e59 0.814017
\(281\) 4.56150e59 0.463237 0.231618 0.972807i \(-0.425598\pi\)
0.231618 + 0.972807i \(0.425598\pi\)
\(282\) 3.03738e59 0.282746
\(283\) 5.39564e59 0.460548 0.230274 0.973126i \(-0.426038\pi\)
0.230274 + 0.973126i \(0.426038\pi\)
\(284\) −4.65728e59 −0.364614
\(285\) −1.31837e59 −0.0946977
\(286\) 2.52601e58 0.0166520
\(287\) −2.13201e60 −1.29028
\(288\) −2.94427e59 −0.163629
\(289\) 4.33215e60 2.21160
\(290\) −9.18019e59 −0.430626
\(291\) 6.36018e59 0.274215
\(292\) −1.48004e60 −0.586669
\(293\) 3.90821e60 1.42469 0.712346 0.701828i \(-0.247632\pi\)
0.712346 + 0.701828i \(0.247632\pi\)
\(294\) −9.61269e59 −0.322356
\(295\) −2.61445e59 −0.0806753
\(296\) 6.21181e59 0.176430
\(297\) −1.87808e60 −0.491113
\(298\) 3.17465e60 0.764535
\(299\) 3.94174e58 0.00874468
\(300\) −6.56473e59 −0.134198
\(301\) 2.49512e60 0.470123
\(302\) 3.93421e59 0.0683419
\(303\) −1.92256e60 −0.307989
\(304\) 4.17048e59 0.0616287
\(305\) −1.58395e61 −2.15971
\(306\) −9.32088e60 −1.17296
\(307\) 2.34251e59 0.0272140 0.0136070 0.999907i \(-0.495669\pi\)
0.0136070 + 0.999907i \(0.495669\pi\)
\(308\) −7.12449e60 −0.764296
\(309\) 1.47213e60 0.145869
\(310\) 1.88407e61 1.72479
\(311\) −4.35273e60 −0.368241 −0.184120 0.982904i \(-0.558944\pi\)
−0.184120 + 0.982904i \(0.558944\pi\)
\(312\) 3.10477e58 0.00242796
\(313\) 1.93545e61 1.39941 0.699706 0.714431i \(-0.253314\pi\)
0.699706 + 0.714431i \(0.253314\pi\)
\(314\) 1.89862e61 1.26958
\(315\) −3.44527e61 −2.13115
\(316\) 4.10005e60 0.234669
\(317\) 2.36551e61 1.25306 0.626530 0.779397i \(-0.284475\pi\)
0.626530 + 0.779397i \(0.284475\pi\)
\(318\) −7.57145e60 −0.371291
\(319\) 8.90431e60 0.404323
\(320\) 4.18672e60 0.176076
\(321\) 1.05712e61 0.411861
\(322\) −1.11175e61 −0.401364
\(323\) 1.32028e61 0.441778
\(324\) 1.26113e61 0.391206
\(325\) −8.61571e59 −0.0247827
\(326\) −3.40072e61 −0.907277
\(327\) 1.96844e59 0.00487196
\(328\) −1.21523e61 −0.279093
\(329\) −1.12433e62 −2.39658
\(330\) 1.28373e61 0.254029
\(331\) 6.39438e61 1.17493 0.587466 0.809249i \(-0.300126\pi\)
0.587466 + 0.809249i \(0.300126\pi\)
\(332\) −2.60144e61 −0.443946
\(333\) −2.91364e61 −0.461905
\(334\) −3.95736e61 −0.582931
\(335\) 8.04750e61 1.10170
\(336\) −8.75686e60 −0.111439
\(337\) 9.36305e61 1.10786 0.553930 0.832563i \(-0.313128\pi\)
0.553930 + 0.832563i \(0.313128\pi\)
\(338\) −6.42198e61 −0.706658
\(339\) −3.06232e60 −0.0313442
\(340\) 1.32542e62 1.26218
\(341\) −1.82745e62 −1.61944
\(342\) −1.95616e61 −0.161348
\(343\) 1.42966e62 1.09781
\(344\) 1.42220e61 0.101690
\(345\) 2.00322e61 0.133401
\(346\) 1.03376e61 0.0641290
\(347\) −9.31722e61 −0.538535 −0.269268 0.963065i \(-0.586782\pi\)
−0.269268 + 0.963065i \(0.586782\pi\)
\(348\) 1.09445e61 0.0589527
\(349\) 2.03454e62 1.02151 0.510755 0.859726i \(-0.329366\pi\)
0.510755 + 0.859726i \(0.329366\pi\)
\(350\) 2.43002e62 1.13748
\(351\) −3.02959e60 −0.0132239
\(352\) −4.06090e61 −0.165321
\(353\) −2.78134e62 −1.05627 −0.528133 0.849161i \(-0.677108\pi\)
−0.528133 + 0.849161i \(0.677108\pi\)
\(354\) 3.11690e60 0.0110444
\(355\) −3.10633e62 −1.02719
\(356\) 2.31541e61 0.0714665
\(357\) −2.77222e62 −0.798835
\(358\) 5.20900e61 0.140159
\(359\) 7.25567e62 1.82332 0.911662 0.410942i \(-0.134800\pi\)
0.911662 + 0.410942i \(0.134800\pi\)
\(360\) −1.96377e62 −0.460978
\(361\) −4.28251e62 −0.939230
\(362\) −1.44233e62 −0.295599
\(363\) 1.78546e61 0.0342010
\(364\) −1.14927e61 −0.0205797
\(365\) −9.87160e62 −1.65277
\(366\) 1.88836e62 0.295664
\(367\) −3.66239e62 −0.536347 −0.268174 0.963371i \(-0.586420\pi\)
−0.268174 + 0.963371i \(0.586420\pi\)
\(368\) −6.33688e61 −0.0868169
\(369\) 5.70001e62 0.730685
\(370\) 4.14317e62 0.497039
\(371\) 2.80267e63 3.14711
\(372\) −2.24616e62 −0.236123
\(373\) 1.01303e63 0.997140 0.498570 0.866850i \(-0.333859\pi\)
0.498570 + 0.866850i \(0.333859\pi\)
\(374\) −1.28559e63 −1.18508
\(375\) 7.04369e60 0.00608183
\(376\) −6.40857e62 −0.518392
\(377\) 1.43638e61 0.0108869
\(378\) 8.54481e62 0.606951
\(379\) −4.10768e62 −0.273486 −0.136743 0.990607i \(-0.543664\pi\)
−0.136743 + 0.990607i \(0.543664\pi\)
\(380\) 2.78164e62 0.173621
\(381\) 7.36165e62 0.430837
\(382\) −3.81984e62 −0.209649
\(383\) −1.90644e63 −0.981415 −0.490708 0.871324i \(-0.663262\pi\)
−0.490708 + 0.871324i \(0.663262\pi\)
\(384\) −4.99134e61 −0.0241047
\(385\) −4.75191e63 −2.15318
\(386\) 1.17367e63 0.499063
\(387\) −6.67079e62 −0.266231
\(388\) −1.34194e63 −0.502753
\(389\) 3.21862e63 1.13215 0.566076 0.824353i \(-0.308461\pi\)
0.566076 + 0.824353i \(0.308461\pi\)
\(390\) 2.07083e61 0.00684008
\(391\) −2.00611e63 −0.622336
\(392\) 2.02818e63 0.591015
\(393\) 1.73586e62 0.0475221
\(394\) −2.36396e63 −0.608112
\(395\) 2.73466e63 0.661111
\(396\) 1.90476e63 0.432821
\(397\) −1.66988e63 −0.356713 −0.178356 0.983966i \(-0.557078\pi\)
−0.178356 + 0.983966i \(0.557078\pi\)
\(398\) 5.27343e63 1.05915
\(399\) −5.81802e62 −0.109885
\(400\) 1.38509e63 0.246042
\(401\) −3.21505e63 −0.537218 −0.268609 0.963249i \(-0.586564\pi\)
−0.268609 + 0.963249i \(0.586564\pi\)
\(402\) −9.59410e62 −0.150822
\(403\) −2.94791e62 −0.0436055
\(404\) 4.05641e63 0.564674
\(405\) 8.41150e63 1.10211
\(406\) −4.05124e63 −0.499690
\(407\) −4.01867e63 −0.466680
\(408\) −1.58014e63 −0.172792
\(409\) 1.21477e64 1.25104 0.625522 0.780207i \(-0.284886\pi\)
0.625522 + 0.780207i \(0.284886\pi\)
\(410\) −8.10537e63 −0.786263
\(411\) 1.33962e63 0.122422
\(412\) −3.10604e63 −0.267440
\(413\) −1.15376e63 −0.0936139
\(414\) 2.97231e63 0.227293
\(415\) −1.73511e64 −1.25069
\(416\) −6.55075e61 −0.00445148
\(417\) 4.10196e63 0.262820
\(418\) −2.69805e63 −0.163016
\(419\) −9.43742e63 −0.537786 −0.268893 0.963170i \(-0.586658\pi\)
−0.268893 + 0.963170i \(0.586658\pi\)
\(420\) −5.84067e63 −0.313946
\(421\) −7.07535e63 −0.358787 −0.179394 0.983777i \(-0.557414\pi\)
−0.179394 + 0.983777i \(0.557414\pi\)
\(422\) −2.29361e64 −1.09740
\(423\) 3.00593e64 1.35719
\(424\) 1.59750e64 0.680734
\(425\) 4.38489e64 1.76372
\(426\) 3.70331e63 0.140623
\(427\) −6.99002e64 −2.50608
\(428\) −2.23042e64 −0.755116
\(429\) −2.00860e62 −0.00642228
\(430\) 9.48580e63 0.286482
\(431\) 1.47866e64 0.421867 0.210933 0.977500i \(-0.432350\pi\)
0.210933 + 0.977500i \(0.432350\pi\)
\(432\) 4.87047e63 0.131286
\(433\) 5.40840e64 1.37757 0.688787 0.724963i \(-0.258143\pi\)
0.688787 + 0.724963i \(0.258143\pi\)
\(434\) 8.31446e64 2.00141
\(435\) 7.29978e63 0.166082
\(436\) −4.15322e62 −0.00893236
\(437\) −4.21020e63 −0.0856066
\(438\) 1.17688e64 0.226264
\(439\) −3.69191e63 −0.0671229 −0.0335614 0.999437i \(-0.510685\pi\)
−0.0335614 + 0.999437i \(0.510685\pi\)
\(440\) −2.70855e64 −0.465743
\(441\) −9.51316e64 −1.54732
\(442\) −2.07382e63 −0.0319099
\(443\) −7.49563e64 −1.09123 −0.545616 0.838036i \(-0.683704\pi\)
−0.545616 + 0.838036i \(0.683704\pi\)
\(444\) −4.93942e63 −0.0680446
\(445\) 1.54434e64 0.201336
\(446\) 2.94092e63 0.0362894
\(447\) −2.52437e64 −0.294862
\(448\) 1.84761e64 0.204314
\(449\) −5.65052e64 −0.591634 −0.295817 0.955245i \(-0.595592\pi\)
−0.295817 + 0.955245i \(0.595592\pi\)
\(450\) −6.49676e64 −0.644155
\(451\) 7.86179e64 0.738238
\(452\) 6.46118e63 0.0574673
\(453\) −3.12835e63 −0.0263578
\(454\) −6.94080e64 −0.554040
\(455\) −7.66544e63 −0.0579773
\(456\) −3.31622e63 −0.0237687
\(457\) 5.93488e64 0.403148 0.201574 0.979473i \(-0.435394\pi\)
0.201574 + 0.979473i \(0.435394\pi\)
\(458\) 1.04895e65 0.675383
\(459\) 1.54188e65 0.941109
\(460\) −4.22659e64 −0.244581
\(461\) 1.06042e65 0.581840 0.290920 0.956747i \(-0.406039\pi\)
0.290920 + 0.956747i \(0.406039\pi\)
\(462\) 5.66516e64 0.294770
\(463\) 1.86764e65 0.921637 0.460818 0.887495i \(-0.347556\pi\)
0.460818 + 0.887495i \(0.347556\pi\)
\(464\) −2.30918e64 −0.108085
\(465\) −1.49815e65 −0.665209
\(466\) −9.72099e64 −0.409502
\(467\) −2.28278e64 −0.0912432 −0.0456216 0.998959i \(-0.514527\pi\)
−0.0456216 + 0.998959i \(0.514527\pi\)
\(468\) 3.07262e63 0.0116543
\(469\) 3.55138e65 1.27839
\(470\) −4.27440e65 −1.46042
\(471\) −1.50972e65 −0.489648
\(472\) −6.57635e63 −0.0202491
\(473\) −9.20074e64 −0.268983
\(474\) −3.26022e64 −0.0905060
\(475\) 9.20250e64 0.242612
\(476\) 5.84912e65 1.46460
\(477\) −7.49306e65 −1.78221
\(478\) 3.35309e65 0.757639
\(479\) −1.07480e65 −0.230732 −0.115366 0.993323i \(-0.536804\pi\)
−0.115366 + 0.993323i \(0.536804\pi\)
\(480\) −3.32914e64 −0.0679081
\(481\) −6.48262e63 −0.0125660
\(482\) −1.46192e65 −0.269322
\(483\) 8.84026e64 0.154796
\(484\) −3.76715e64 −0.0627049
\(485\) −8.95047e65 −1.41636
\(486\) −3.47085e65 −0.522212
\(487\) 9.52950e64 0.136336 0.0681680 0.997674i \(-0.478285\pi\)
0.0681680 + 0.997674i \(0.478285\pi\)
\(488\) −3.98426e65 −0.542078
\(489\) 2.70414e65 0.349915
\(490\) 1.35276e66 1.66501
\(491\) 7.75386e65 0.907865 0.453933 0.891036i \(-0.350021\pi\)
0.453933 + 0.891036i \(0.350021\pi\)
\(492\) 9.66309e64 0.107639
\(493\) −7.31033e65 −0.774796
\(494\) −4.35229e63 −0.00438943
\(495\) 1.27044e66 1.21935
\(496\) 4.73917e65 0.432914
\(497\) −1.37083e66 −1.19193
\(498\) 2.06857e65 0.171219
\(499\) 1.56740e66 1.23514 0.617569 0.786517i \(-0.288118\pi\)
0.617569 + 0.786517i \(0.288118\pi\)
\(500\) −1.48615e64 −0.0111506
\(501\) 3.14676e65 0.224822
\(502\) −1.19084e66 −0.810237
\(503\) −5.11802e65 −0.331655 −0.165827 0.986155i \(-0.553029\pi\)
−0.165827 + 0.986155i \(0.553029\pi\)
\(504\) −8.66619e65 −0.534909
\(505\) 2.70555e66 1.59081
\(506\) 4.09958e65 0.229642
\(507\) 5.10654e65 0.272541
\(508\) −1.55323e66 −0.789907
\(509\) −1.63079e66 −0.790335 −0.395167 0.918609i \(-0.629313\pi\)
−0.395167 + 0.918609i \(0.629313\pi\)
\(510\) −1.05393e66 −0.486790
\(511\) −4.35636e66 −1.91784
\(512\) 1.05312e65 0.0441942
\(513\) 3.23592e65 0.129456
\(514\) −5.69504e65 −0.217220
\(515\) −2.07168e66 −0.753434
\(516\) −1.13088e65 −0.0392193
\(517\) 4.14595e66 1.37122
\(518\) 1.82839e66 0.576754
\(519\) −8.22010e64 −0.0247330
\(520\) −4.36924e64 −0.0125408
\(521\) 3.56843e65 0.0977133 0.0488566 0.998806i \(-0.484442\pi\)
0.0488566 + 0.998806i \(0.484442\pi\)
\(522\) 1.08312e66 0.282975
\(523\) −7.86554e65 −0.196082 −0.0980408 0.995182i \(-0.531258\pi\)
−0.0980408 + 0.995182i \(0.531258\pi\)
\(524\) −3.66248e65 −0.0871282
\(525\) −1.93227e66 −0.438698
\(526\) −3.93463e66 −0.852615
\(527\) 1.50031e67 3.10329
\(528\) 3.22909e65 0.0637602
\(529\) −4.66501e66 −0.879405
\(530\) 1.06551e67 1.91777
\(531\) 3.08463e65 0.0530136
\(532\) 1.22754e66 0.201466
\(533\) 1.26821e65 0.0198780
\(534\) −1.84113e65 −0.0275629
\(535\) −1.48765e67 −2.12732
\(536\) 2.02426e66 0.276522
\(537\) −4.14202e65 −0.0540558
\(538\) −3.61704e66 −0.451011
\(539\) −1.31211e67 −1.56331
\(540\) 3.24852e66 0.369861
\(541\) 9.49189e66 1.03281 0.516404 0.856345i \(-0.327270\pi\)
0.516404 + 0.856345i \(0.327270\pi\)
\(542\) −5.92105e66 −0.615766
\(543\) 1.14689e66 0.114005
\(544\) 3.33395e66 0.316800
\(545\) −2.77013e65 −0.0251643
\(546\) 9.13862e64 0.00793708
\(547\) −1.44217e67 −1.19764 −0.598819 0.800884i \(-0.704363\pi\)
−0.598819 + 0.800884i \(0.704363\pi\)
\(548\) −2.82647e66 −0.224451
\(549\) 1.86881e67 1.41920
\(550\) −8.96071e66 −0.650813
\(551\) −1.53421e66 −0.106578
\(552\) 5.03888e65 0.0334831
\(553\) 1.20681e67 0.767140
\(554\) 4.93937e66 0.300388
\(555\) −3.29451e66 −0.191696
\(556\) −8.65472e66 −0.481860
\(557\) 7.89683e65 0.0420727 0.0210364 0.999779i \(-0.493303\pi\)
0.0210364 + 0.999779i \(0.493303\pi\)
\(558\) −2.22290e67 −1.13340
\(559\) −1.48420e65 −0.00724273
\(560\) 1.23232e67 0.575597
\(561\) 1.02226e67 0.457057
\(562\) 7.65293e66 0.327558
\(563\) 2.05636e67 0.842643 0.421321 0.906911i \(-0.361566\pi\)
0.421321 + 0.906911i \(0.361566\pi\)
\(564\) 5.09588e66 0.199931
\(565\) 4.30950e66 0.161897
\(566\) 9.05238e66 0.325657
\(567\) 3.71202e67 1.27887
\(568\) −7.81362e66 −0.257821
\(569\) −2.99189e67 −0.945573 −0.472787 0.881177i \(-0.656752\pi\)
−0.472787 + 0.881177i \(0.656752\pi\)
\(570\) −2.21186e66 −0.0669614
\(571\) −1.50438e67 −0.436289 −0.218144 0.975917i \(-0.570000\pi\)
−0.218144 + 0.975917i \(0.570000\pi\)
\(572\) 4.23794e65 0.0117748
\(573\) 3.03741e66 0.0808564
\(574\) −3.57692e67 −0.912364
\(575\) −1.39828e67 −0.341770
\(576\) −4.93966e66 −0.115703
\(577\) 1.42499e67 0.319893 0.159947 0.987126i \(-0.448868\pi\)
0.159947 + 0.987126i \(0.448868\pi\)
\(578\) 7.26815e67 1.56384
\(579\) −9.33259e66 −0.192476
\(580\) −1.54018e67 −0.304499
\(581\) −7.65710e67 −1.45127
\(582\) 1.06706e67 0.193899
\(583\) −1.03349e68 −1.80063
\(584\) −2.48309e67 −0.414838
\(585\) 2.04939e66 0.0328326
\(586\) 6.55689e67 1.00741
\(587\) −4.53396e67 −0.668104 −0.334052 0.942555i \(-0.608416\pi\)
−0.334052 + 0.942555i \(0.608416\pi\)
\(588\) −1.61274e67 −0.227940
\(589\) 3.14869e67 0.426879
\(590\) −4.38631e66 −0.0570460
\(591\) 1.87974e67 0.234534
\(592\) 1.04217e67 0.124755
\(593\) 5.39408e67 0.619552 0.309776 0.950810i \(-0.399746\pi\)
0.309776 + 0.950810i \(0.399746\pi\)
\(594\) −3.15090e67 −0.347269
\(595\) 3.90126e68 4.12609
\(596\) 5.32618e67 0.540608
\(597\) −4.19325e67 −0.408488
\(598\) 6.61314e65 0.00618342
\(599\) −1.84268e68 −1.65383 −0.826917 0.562323i \(-0.809908\pi\)
−0.826917 + 0.562323i \(0.809908\pi\)
\(600\) −1.10138e67 −0.0948924
\(601\) −6.15406e67 −0.509023 −0.254511 0.967070i \(-0.581915\pi\)
−0.254511 + 0.967070i \(0.581915\pi\)
\(602\) 4.18611e67 0.332427
\(603\) −9.49476e67 −0.723952
\(604\) 6.60050e66 0.0483250
\(605\) −2.51262e67 −0.176653
\(606\) −3.22552e67 −0.217781
\(607\) 2.91666e68 1.89131 0.945654 0.325175i \(-0.105423\pi\)
0.945654 + 0.325175i \(0.105423\pi\)
\(608\) 6.99690e66 0.0435781
\(609\) 3.22141e67 0.192718
\(610\) −2.65743e68 −1.52715
\(611\) 6.68795e66 0.0369218
\(612\) −1.56378e68 −0.829405
\(613\) −1.34057e68 −0.683139 −0.341569 0.939857i \(-0.610958\pi\)
−0.341569 + 0.939857i \(0.610958\pi\)
\(614\) 3.93008e66 0.0192432
\(615\) 6.44511e67 0.303243
\(616\) −1.19529e68 −0.540439
\(617\) −2.63476e68 −1.14487 −0.572433 0.819951i \(-0.694000\pi\)
−0.572433 + 0.819951i \(0.694000\pi\)
\(618\) 2.46982e67 0.103145
\(619\) 1.18534e68 0.475799 0.237899 0.971290i \(-0.423541\pi\)
0.237899 + 0.971290i \(0.423541\pi\)
\(620\) 3.16095e68 1.21961
\(621\) −4.91686e67 −0.182366
\(622\) −7.30267e67 −0.260386
\(623\) 6.81520e67 0.233626
\(624\) 5.20894e65 0.00171683
\(625\) −3.20461e68 −1.01558
\(626\) 3.24715e68 0.989534
\(627\) 2.14539e67 0.0628713
\(628\) 3.18536e68 0.897732
\(629\) 3.29927e68 0.894288
\(630\) −5.78020e68 −1.50695
\(631\) 4.68843e68 1.17573 0.587866 0.808959i \(-0.299968\pi\)
0.587866 + 0.808959i \(0.299968\pi\)
\(632\) 6.87874e67 0.165936
\(633\) 1.82380e68 0.423240
\(634\) 3.96866e68 0.886048
\(635\) −1.03598e69 −2.22533
\(636\) −1.27028e68 −0.262543
\(637\) −2.11660e67 −0.0420943
\(638\) 1.49390e68 0.285900
\(639\) 3.66497e68 0.674993
\(640\) 7.02415e67 0.124504
\(641\) −2.45988e68 −0.419654 −0.209827 0.977738i \(-0.567290\pi\)
−0.209827 + 0.977738i \(0.567290\pi\)
\(642\) 1.77355e68 0.291230
\(643\) 6.14694e68 0.971605 0.485803 0.874069i \(-0.338527\pi\)
0.485803 + 0.874069i \(0.338527\pi\)
\(644\) −1.86521e68 −0.283807
\(645\) −7.54279e67 −0.110489
\(646\) 2.21506e68 0.312384
\(647\) −9.77317e68 −1.32703 −0.663515 0.748163i \(-0.730936\pi\)
−0.663515 + 0.748163i \(0.730936\pi\)
\(648\) 2.11582e68 0.276625
\(649\) 4.25450e67 0.0535616
\(650\) −1.44548e67 −0.0175240
\(651\) −6.61138e68 −0.771894
\(652\) −5.70547e68 −0.641542
\(653\) 8.35256e67 0.0904580 0.0452290 0.998977i \(-0.485598\pi\)
0.0452290 + 0.998977i \(0.485598\pi\)
\(654\) 3.30250e66 0.00344499
\(655\) −2.44281e68 −0.245459
\(656\) −2.03882e68 −0.197349
\(657\) 1.16469e69 1.08607
\(658\) −1.88631e69 −1.69464
\(659\) −3.35474e68 −0.290380 −0.145190 0.989404i \(-0.546379\pi\)
−0.145190 + 0.989404i \(0.546379\pi\)
\(660\) 2.15375e68 0.179626
\(661\) 2.63520e68 0.211776 0.105888 0.994378i \(-0.466231\pi\)
0.105888 + 0.994378i \(0.466231\pi\)
\(662\) 1.07280e69 0.830802
\(663\) 1.64903e67 0.0123069
\(664\) −4.36449e68 −0.313917
\(665\) 8.18751e68 0.567572
\(666\) −4.88828e68 −0.326616
\(667\) 2.33117e68 0.150138
\(668\) −6.63935e68 −0.412194
\(669\) −2.33852e67 −0.0139959
\(670\) 1.35015e69 0.779019
\(671\) 2.57757e69 1.43387
\(672\) −1.46916e68 −0.0787991
\(673\) 3.25131e69 1.68147 0.840735 0.541447i \(-0.182123\pi\)
0.840735 + 0.541447i \(0.182123\pi\)
\(674\) 1.57086e69 0.783375
\(675\) 1.07471e69 0.516831
\(676\) −1.07743e69 −0.499683
\(677\) −2.82926e69 −1.26547 −0.632733 0.774370i \(-0.718067\pi\)
−0.632733 + 0.774370i \(0.718067\pi\)
\(678\) −5.13772e67 −0.0221637
\(679\) −3.94987e69 −1.64351
\(680\) 2.22369e69 0.892493
\(681\) 5.51909e68 0.213680
\(682\) −3.06596e69 −1.14511
\(683\) −2.71804e69 −0.979374 −0.489687 0.871898i \(-0.662889\pi\)
−0.489687 + 0.871898i \(0.662889\pi\)
\(684\) −3.28189e68 −0.114090
\(685\) −1.88521e69 −0.632325
\(686\) 2.39857e69 0.776268
\(687\) −8.34089e68 −0.260479
\(688\) 2.38605e68 0.0719056
\(689\) −1.66715e68 −0.0484845
\(690\) 3.36084e68 0.0943291
\(691\) −2.43872e69 −0.660618 −0.330309 0.943873i \(-0.607153\pi\)
−0.330309 + 0.943873i \(0.607153\pi\)
\(692\) 1.73436e68 0.0453461
\(693\) 5.60650e69 1.41491
\(694\) −1.56317e69 −0.380802
\(695\) −5.77255e69 −1.35750
\(696\) 1.83618e68 0.0416858
\(697\) −6.45443e69 −1.41467
\(698\) 3.41339e69 0.722317
\(699\) 7.72980e68 0.157935
\(700\) 4.07690e69 0.804319
\(701\) 7.63989e69 1.45544 0.727722 0.685872i \(-0.240579\pi\)
0.727722 + 0.685872i \(0.240579\pi\)
\(702\) −5.08280e67 −0.00935070
\(703\) 6.92413e68 0.123015
\(704\) −6.81306e68 −0.116899
\(705\) 3.39886e69 0.563248
\(706\) −4.66631e69 −0.746893
\(707\) 1.19397e70 1.84594
\(708\) 5.22929e67 0.00780959
\(709\) 2.36736e69 0.341533 0.170766 0.985312i \(-0.445376\pi\)
0.170766 + 0.985312i \(0.445376\pi\)
\(710\) −5.21155e69 −0.726336
\(711\) −3.22646e69 −0.434432
\(712\) 3.88461e68 0.0505344
\(713\) −4.78431e69 −0.601348
\(714\) −4.65102e69 −0.564861
\(715\) 2.82663e68 0.0331720
\(716\) 8.73926e68 0.0991073
\(717\) −2.66627e69 −0.292203
\(718\) 1.21730e70 1.28928
\(719\) 9.01007e69 0.922296 0.461148 0.887323i \(-0.347438\pi\)
0.461148 + 0.887323i \(0.347438\pi\)
\(720\) −3.29467e69 −0.325961
\(721\) −9.14237e69 −0.874269
\(722\) −7.18486e69 −0.664136
\(723\) 1.16247e69 0.103871
\(724\) −2.41982e69 −0.209020
\(725\) −5.09538e69 −0.425496
\(726\) 2.99551e68 0.0241838
\(727\) 1.12644e70 0.879257 0.439628 0.898180i \(-0.355110\pi\)
0.439628 + 0.898180i \(0.355110\pi\)
\(728\) −1.92816e68 −0.0145520
\(729\) −7.96172e69 −0.581008
\(730\) −1.65618e70 −1.16868
\(731\) 7.55369e69 0.515446
\(732\) 3.16815e69 0.209066
\(733\) 4.32996e69 0.276335 0.138168 0.990409i \(-0.455879\pi\)
0.138168 + 0.990409i \(0.455879\pi\)
\(734\) −6.14447e69 −0.379255
\(735\) −1.07567e70 −0.642154
\(736\) −1.06315e69 −0.0613888
\(737\) −1.30957e70 −0.731436
\(738\) 9.56304e69 0.516672
\(739\) −2.10376e70 −1.09953 −0.549766 0.835319i \(-0.685283\pi\)
−0.549766 + 0.835319i \(0.685283\pi\)
\(740\) 6.95109e69 0.351460
\(741\) 3.46080e67 0.00169289
\(742\) 4.70211e70 2.22534
\(743\) 3.09494e69 0.141718 0.0708592 0.997486i \(-0.477426\pi\)
0.0708592 + 0.997486i \(0.477426\pi\)
\(744\) −3.76843e69 −0.166964
\(745\) 3.55247e70 1.52301
\(746\) 1.69958e70 0.705084
\(747\) 2.04716e70 0.821857
\(748\) −2.15686e70 −0.837979
\(749\) −6.56504e70 −2.46850
\(750\) 1.18173e68 0.00430050
\(751\) 2.36292e70 0.832281 0.416140 0.909300i \(-0.363383\pi\)
0.416140 + 0.909300i \(0.363383\pi\)
\(752\) −1.07518e70 −0.366559
\(753\) 9.46915e69 0.312488
\(754\) 2.40985e68 0.00769824
\(755\) 4.40242e69 0.136142
\(756\) 1.43358e70 0.429179
\(757\) 4.84445e70 1.40409 0.702045 0.712132i \(-0.252270\pi\)
0.702045 + 0.712132i \(0.252270\pi\)
\(758\) −6.89154e69 −0.193384
\(759\) −3.25985e69 −0.0885673
\(760\) 4.66681e69 0.122769
\(761\) −1.48623e70 −0.378584 −0.189292 0.981921i \(-0.560619\pi\)
−0.189292 + 0.981921i \(0.560619\pi\)
\(762\) 1.23508e70 0.304648
\(763\) −1.22247e69 −0.0292002
\(764\) −6.40862e69 −0.148244
\(765\) −1.04302e71 −2.33661
\(766\) −3.19847e70 −0.693965
\(767\) 6.86305e67 0.00144222
\(768\) −8.37408e68 −0.0170446
\(769\) −6.67570e70 −1.31614 −0.658069 0.752957i \(-0.728627\pi\)
−0.658069 + 0.752957i \(0.728627\pi\)
\(770\) −7.97239e70 −1.52253
\(771\) 4.52850e69 0.0837765
\(772\) 1.96908e70 0.352891
\(773\) 8.33587e70 1.44728 0.723642 0.690176i \(-0.242467\pi\)
0.723642 + 0.690176i \(0.242467\pi\)
\(774\) −1.11917e70 −0.188254
\(775\) 1.04574e71 1.70424
\(776\) −2.25139e70 −0.355500
\(777\) −1.45388e70 −0.222440
\(778\) 5.39995e70 0.800553
\(779\) −1.35458e70 −0.194597
\(780\) 3.47427e68 0.00483667
\(781\) 5.05494e70 0.681970
\(782\) −3.36570e70 −0.440058
\(783\) −1.79172e70 −0.227042
\(784\) 3.40272e70 0.417910
\(785\) 2.12458e71 2.52910
\(786\) 2.91228e69 0.0336032
\(787\) −1.52479e71 −1.70541 −0.852706 0.522390i \(-0.825040\pi\)
−0.852706 + 0.522390i \(0.825040\pi\)
\(788\) −3.96607e70 −0.430000
\(789\) 3.12868e70 0.328833
\(790\) 4.58800e70 0.467476
\(791\) 1.90179e70 0.187862
\(792\) 3.19566e70 0.306051
\(793\) 4.15795e69 0.0386088
\(794\) −2.80160e70 −0.252234
\(795\) −8.47254e70 −0.739638
\(796\) 8.84734e70 0.748932
\(797\) 8.15352e70 0.669293 0.334647 0.942344i \(-0.391383\pi\)
0.334647 + 0.942344i \(0.391383\pi\)
\(798\) −9.76102e69 −0.0777006
\(799\) −3.40377e71 −2.62763
\(800\) 2.32380e70 0.173978
\(801\) −1.82207e70 −0.132303
\(802\) −5.39396e70 −0.379871
\(803\) 1.60641e71 1.09730
\(804\) −1.60962e70 −0.106648
\(805\) −1.24406e71 −0.799544
\(806\) −4.94578e69 −0.0308337
\(807\) 2.87615e70 0.173944
\(808\) 6.80552e70 0.399285
\(809\) −2.92840e71 −1.66683 −0.833416 0.552646i \(-0.813618\pi\)
−0.833416 + 0.552646i \(0.813618\pi\)
\(810\) 1.41121e71 0.779310
\(811\) 2.95951e71 1.58565 0.792827 0.609446i \(-0.208608\pi\)
0.792827 + 0.609446i \(0.208608\pi\)
\(812\) −6.79686e70 −0.353334
\(813\) 4.70822e70 0.237486
\(814\) −6.74220e70 −0.329992
\(815\) −3.80545e71 −1.80736
\(816\) −2.65104e70 −0.122182
\(817\) 1.58528e70 0.0709031
\(818\) 2.03804e71 0.884621
\(819\) 9.04400e69 0.0380982
\(820\) −1.35985e71 −0.555972
\(821\) 2.31367e71 0.918107 0.459053 0.888409i \(-0.348189\pi\)
0.459053 + 0.888409i \(0.348189\pi\)
\(822\) 2.24752e70 0.0865652
\(823\) 1.40957e70 0.0526976 0.0263488 0.999653i \(-0.491612\pi\)
0.0263488 + 0.999653i \(0.491612\pi\)
\(824\) −5.21108e70 −0.189108
\(825\) 7.12525e70 0.251003
\(826\) −1.93569e70 −0.0661950
\(827\) 3.13935e71 1.04221 0.521105 0.853493i \(-0.325520\pi\)
0.521105 + 0.853493i \(0.325520\pi\)
\(828\) 4.98670e70 0.160720
\(829\) −1.00068e71 −0.313118 −0.156559 0.987669i \(-0.550040\pi\)
−0.156559 + 0.987669i \(0.550040\pi\)
\(830\) −2.91104e71 −0.884371
\(831\) −3.92762e70 −0.115852
\(832\) −1.09903e69 −0.00314767
\(833\) 1.07722e72 2.99574
\(834\) 6.88194e70 0.185841
\(835\) −4.42833e71 −1.16124
\(836\) −4.52657e70 −0.115270
\(837\) 3.67718e71 0.909370
\(838\) −1.58334e71 −0.380272
\(839\) 7.28357e70 0.169893 0.0849466 0.996386i \(-0.472928\pi\)
0.0849466 + 0.996386i \(0.472928\pi\)
\(840\) −9.79903e70 −0.221994
\(841\) −3.69518e71 −0.813081
\(842\) −1.18705e71 −0.253701
\(843\) −6.08535e70 −0.126331
\(844\) −3.84804e71 −0.775978
\(845\) −7.18626e71 −1.40771
\(846\) 5.04311e71 0.959676
\(847\) −1.10883e71 −0.204984
\(848\) 2.68016e71 0.481352
\(849\) −7.19814e70 −0.125598
\(850\) 7.35663e71 1.24714
\(851\) −1.05209e71 −0.173293
\(852\) 6.21313e70 0.0994352
\(853\) −3.12687e71 −0.486249 −0.243125 0.969995i \(-0.578172\pi\)
−0.243125 + 0.969995i \(0.578172\pi\)
\(854\) −1.17273e72 −1.77207
\(855\) −2.18896e71 −0.321417
\(856\) −3.74202e71 −0.533948
\(857\) −1.07117e72 −1.48535 −0.742675 0.669652i \(-0.766443\pi\)
−0.742675 + 0.669652i \(0.766443\pi\)
\(858\) −3.36987e69 −0.00454124
\(859\) 6.94017e71 0.908945 0.454473 0.890761i \(-0.349828\pi\)
0.454473 + 0.890761i \(0.349828\pi\)
\(860\) 1.59145e71 0.202573
\(861\) 2.84425e71 0.351876
\(862\) 2.48078e71 0.298305
\(863\) 1.51616e72 1.77207 0.886037 0.463614i \(-0.153448\pi\)
0.886037 + 0.463614i \(0.153448\pi\)
\(864\) 8.17130e70 0.0928334
\(865\) 1.15679e71 0.127749
\(866\) 9.07379e71 0.974092
\(867\) −5.77938e71 −0.603134
\(868\) 1.39493e72 1.41521
\(869\) −4.45012e71 −0.438922
\(870\) 1.22470e71 0.117438
\(871\) −2.11251e70 −0.0196949
\(872\) −6.96795e69 −0.00631613
\(873\) 1.05601e72 0.930723
\(874\) −7.06354e70 −0.0605330
\(875\) −4.37435e70 −0.0364516
\(876\) 1.97447e71 0.159993
\(877\) −1.82968e72 −1.44173 −0.720867 0.693073i \(-0.756256\pi\)
−0.720867 + 0.693073i \(0.756256\pi\)
\(878\) −6.19400e70 −0.0474630
\(879\) −5.21382e71 −0.388533
\(880\) −4.54420e71 −0.329330
\(881\) 8.23192e71 0.580218 0.290109 0.956994i \(-0.406308\pi\)
0.290109 + 0.956994i \(0.406308\pi\)
\(882\) −1.59604e72 −1.09412
\(883\) 2.32646e72 1.55116 0.775582 0.631247i \(-0.217456\pi\)
0.775582 + 0.631247i \(0.217456\pi\)
\(884\) −3.47929e70 −0.0225637
\(885\) 3.48785e70 0.0220013
\(886\) −1.25756e72 −0.771617
\(887\) 2.02329e72 1.20762 0.603809 0.797129i \(-0.293649\pi\)
0.603809 + 0.797129i \(0.293649\pi\)
\(888\) −8.28698e70 −0.0481148
\(889\) −4.57181e72 −2.58223
\(890\) 2.59097e71 0.142366
\(891\) −1.36881e72 −0.731709
\(892\) 4.93405e70 0.0256605
\(893\) −7.14344e71 −0.361449
\(894\) −4.23520e71 −0.208499
\(895\) 5.82893e71 0.279206
\(896\) 3.09978e71 0.144472
\(897\) −5.25855e69 −0.00238479
\(898\) −9.48000e71 −0.418349
\(899\) −1.74341e72 −0.748666
\(900\) −1.08998e72 −0.455486
\(901\) 8.48479e72 3.45051
\(902\) 1.31899e72 0.522013
\(903\) −3.32865e71 −0.128209
\(904\) 1.08401e71 0.0406355
\(905\) −1.61398e72 −0.588854
\(906\) −5.24850e70 −0.0186378
\(907\) 5.38576e72 1.86152 0.930762 0.365627i \(-0.119145\pi\)
0.930762 + 0.365627i \(0.119145\pi\)
\(908\) −1.16447e72 −0.391765
\(909\) −3.19212e72 −1.04536
\(910\) −1.28605e71 −0.0409961
\(911\) −4.00433e72 −1.24260 −0.621298 0.783574i \(-0.713394\pi\)
−0.621298 + 0.783574i \(0.713394\pi\)
\(912\) −5.56370e70 −0.0168070
\(913\) 2.82356e72 0.830352
\(914\) 9.95707e71 0.285069
\(915\) 2.11310e72 0.588983
\(916\) 1.75984e72 0.477568
\(917\) −1.07802e72 −0.284825
\(918\) 2.58685e72 0.665465
\(919\) −6.26307e72 −1.56876 −0.784381 0.620279i \(-0.787019\pi\)
−0.784381 + 0.620279i \(0.787019\pi\)
\(920\) −7.09104e71 −0.172945
\(921\) −3.12507e70 −0.00742162
\(922\) 1.77908e72 0.411423
\(923\) 8.15426e70 0.0183630
\(924\) 9.50455e71 0.208434
\(925\) 2.29963e72 0.491118
\(926\) 3.13339e72 0.651695
\(927\) 2.44425e72 0.495099
\(928\) −3.87415e71 −0.0764278
\(929\) −3.00047e72 −0.576508 −0.288254 0.957554i \(-0.593075\pi\)
−0.288254 + 0.957554i \(0.593075\pi\)
\(930\) −2.51348e72 −0.470373
\(931\) 2.26075e72 0.412084
\(932\) −1.63091e72 −0.289561
\(933\) 5.80684e71 0.100424
\(934\) −3.82987e71 −0.0645187
\(935\) −1.43859e73 −2.36076
\(936\) 5.15501e70 0.00824083
\(937\) −3.72864e72 −0.580671 −0.290336 0.956925i \(-0.593767\pi\)
−0.290336 + 0.956925i \(0.593767\pi\)
\(938\) 5.95823e72 0.903957
\(939\) −2.58202e72 −0.381639
\(940\) −7.17126e72 −1.03267
\(941\) −2.09160e72 −0.293449 −0.146724 0.989177i \(-0.546873\pi\)
−0.146724 + 0.989177i \(0.546873\pi\)
\(942\) −2.53289e72 −0.346233
\(943\) 2.05823e72 0.274131
\(944\) −1.10333e71 −0.0143183
\(945\) 9.56174e72 1.20909
\(946\) −1.54363e72 −0.190200
\(947\) 8.20140e72 0.984721 0.492361 0.870391i \(-0.336134\pi\)
0.492361 + 0.870391i \(0.336134\pi\)
\(948\) −5.46974e71 −0.0639974
\(949\) 2.59134e71 0.0295463
\(950\) 1.54392e72 0.171553
\(951\) −3.15574e72 −0.341727
\(952\) 9.81319e72 1.03563
\(953\) 1.17749e73 1.21110 0.605549 0.795808i \(-0.292953\pi\)
0.605549 + 0.795808i \(0.292953\pi\)
\(954\) −1.25713e73 −1.26021
\(955\) −4.27444e72 −0.417635
\(956\) 5.62556e72 0.535732
\(957\) −1.18790e72 −0.110265
\(958\) −1.80321e72 −0.163152
\(959\) −8.31948e72 −0.733737
\(960\) −5.58536e71 −0.0480182
\(961\) 2.38482e73 1.99863
\(962\) −1.08760e71 −0.00888549
\(963\) 1.75519e73 1.39791
\(964\) −2.45270e72 −0.190440
\(965\) 1.31334e73 0.994168
\(966\) 1.48315e72 0.109457
\(967\) −3.48982e72 −0.251105 −0.125552 0.992087i \(-0.540070\pi\)
−0.125552 + 0.992087i \(0.540070\pi\)
\(968\) −6.32023e71 −0.0443391
\(969\) −1.76134e72 −0.120479
\(970\) −1.50164e73 −1.00152
\(971\) −2.02593e73 −1.31751 −0.658753 0.752359i \(-0.728916\pi\)
−0.658753 + 0.752359i \(0.728916\pi\)
\(972\) −5.82312e72 −0.369260
\(973\) −2.54744e73 −1.57521
\(974\) 1.59879e72 0.0964041
\(975\) 1.14939e71 0.00675859
\(976\) −6.68447e72 −0.383307
\(977\) −1.10677e73 −0.618926 −0.309463 0.950911i \(-0.600149\pi\)
−0.309463 + 0.950911i \(0.600149\pi\)
\(978\) 4.53679e72 0.247427
\(979\) −2.51311e72 −0.133670
\(980\) 2.26956e73 1.17734
\(981\) 3.26831e71 0.0165361
\(982\) 1.30088e73 0.641958
\(983\) −6.73348e72 −0.324100 −0.162050 0.986783i \(-0.551811\pi\)
−0.162050 + 0.986783i \(0.551811\pi\)
\(984\) 1.62120e72 0.0761125
\(985\) −2.64530e73 −1.21140
\(986\) −1.22647e73 −0.547863
\(987\) 1.49993e73 0.653582
\(988\) −7.30193e70 −0.00310379
\(989\) −2.40877e72 −0.0998819
\(990\) 2.13145e73 0.862209
\(991\) −2.62295e73 −1.03511 −0.517554 0.855650i \(-0.673157\pi\)
−0.517554 + 0.855650i \(0.673157\pi\)
\(992\) 7.95101e72 0.306116
\(993\) −8.53053e72 −0.320420
\(994\) −2.29987e73 −0.842824
\(995\) 5.90102e73 2.10990
\(996\) 3.47049e72 0.121070
\(997\) 2.54966e73 0.867864 0.433932 0.900946i \(-0.357126\pi\)
0.433932 + 0.900946i \(0.357126\pi\)
\(998\) 2.62966e73 0.873375
\(999\) 8.08631e72 0.262057
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 \(a_p\))