Properties

Label 1.76.a.a.1.5
Level $1$
Weight $76$
Character 1.1
Self dual yes
Analytic conductor $35.623$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 76 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(35.6228392822\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
Defining polynomial: \(x^{6} - 3 x^{5} - 38457853073924058692 x^{4} - 10276556354621685339901678086 x^{3} + 371187556674475060057870954681799784505 x^{2} + 52686123927652036687598761277591247931691204025 x - 675344021115865838575279495800656435684060652010336995750\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: multiple of \( 2^{58}\cdot 3^{26}\cdot 5^{7}\cdot 7^{3}\cdot 11\cdot 13\cdot 19 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(3.19848e9\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.20777e11 q^{2} +1.08881e18 q^{3} +1.09637e22 q^{4} -2.30711e25 q^{5} +2.40385e29 q^{6} +1.96027e31 q^{7} -5.92020e33 q^{8} +5.77242e35 q^{9} +O(q^{10})\) \(q+2.20777e11 q^{2} +1.08881e18 q^{3} +1.09637e22 q^{4} -2.30711e25 q^{5} +2.40385e29 q^{6} +1.96027e31 q^{7} -5.92020e33 q^{8} +5.77242e35 q^{9} -5.09358e36 q^{10} +9.40509e38 q^{11} +1.19374e40 q^{12} +1.14147e42 q^{13} +4.32784e42 q^{14} -2.51201e43 q^{15} -1.72124e45 q^{16} +1.79040e46 q^{17} +1.27442e47 q^{18} +1.43901e48 q^{19} -2.52945e47 q^{20} +2.13436e49 q^{21} +2.07643e50 q^{22} -1.23136e51 q^{23} -6.44597e51 q^{24} -2.59375e52 q^{25} +2.52010e53 q^{26} -3.37806e52 q^{27} +2.14918e53 q^{28} -2.48097e54 q^{29} -5.54594e54 q^{30} +1.95055e55 q^{31} -1.56352e56 q^{32} +1.02404e57 q^{33} +3.95280e57 q^{34} -4.52257e56 q^{35} +6.32870e57 q^{36} -2.65296e58 q^{37} +3.17702e59 q^{38} +1.24284e60 q^{39} +1.36586e59 q^{40} +3.61594e59 q^{41} +4.71219e60 q^{42} +8.98859e59 q^{43} +1.03115e61 q^{44} -1.33176e61 q^{45} -2.71857e62 q^{46} +2.48355e62 q^{47} -1.87411e63 q^{48} -2.02760e63 q^{49} -5.72641e63 q^{50} +1.94941e64 q^{51} +1.25147e64 q^{52} +3.59994e64 q^{53} -7.45799e63 q^{54} -2.16986e64 q^{55} -1.16052e65 q^{56} +1.56681e66 q^{57} -5.47742e65 q^{58} -4.00811e66 q^{59} -2.75409e65 q^{60} -1.59203e67 q^{61} +4.30637e66 q^{62} +1.13155e67 q^{63} +3.05076e67 q^{64} -2.63349e67 q^{65} +2.26084e68 q^{66} +1.61324e68 q^{67} +1.96294e68 q^{68} -1.34072e69 q^{69} -9.98480e67 q^{70} +2.63303e69 q^{71} -3.41738e69 q^{72} -2.52652e69 q^{73} -5.85713e69 q^{74} -2.82410e70 q^{75} +1.57769e70 q^{76} +1.84365e70 q^{77} +2.74391e71 q^{78} -9.29901e70 q^{79} +3.97110e70 q^{80} -3.87898e71 q^{81} +7.98318e70 q^{82} -7.84087e71 q^{83} +2.34005e71 q^{84} -4.13066e71 q^{85} +1.98448e71 q^{86} -2.70130e72 q^{87} -5.56800e72 q^{88} +2.05618e73 q^{89} -2.94023e72 q^{90} +2.23759e73 q^{91} -1.35003e73 q^{92} +2.12378e73 q^{93} +5.48312e73 q^{94} -3.31997e73 q^{95} -1.70238e74 q^{96} -4.10454e74 q^{97} -4.47648e74 q^{98} +5.42901e74 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 57080822040q^{2} - 785092363818710040q^{3} + \)\(17\!\cdots\!28\)\(q^{4} - \)\(38\!\cdots\!40\)\(q^{5} + \)\(31\!\cdots\!92\)\(q^{6} + \)\(19\!\cdots\!00\)\(q^{7} + \)\(44\!\cdots\!20\)\(q^{8} + \)\(21\!\cdots\!82\)\(q^{9} + O(q^{10}) \) \( 6q - 57080822040q^{2} - 785092363818710040q^{3} + \)\(17\!\cdots\!28\)\(q^{4} - \)\(38\!\cdots\!40\)\(q^{5} + \)\(31\!\cdots\!92\)\(q^{6} + \)\(19\!\cdots\!00\)\(q^{7} + \)\(44\!\cdots\!20\)\(q^{8} + \)\(21\!\cdots\!82\)\(q^{9} + \)\(13\!\cdots\!60\)\(q^{10} - \)\(94\!\cdots\!88\)\(q^{11} - \)\(11\!\cdots\!80\)\(q^{12} + \)\(53\!\cdots\!20\)\(q^{13} + \)\(82\!\cdots\!76\)\(q^{14} - \)\(30\!\cdots\!80\)\(q^{15} + \)\(26\!\cdots\!16\)\(q^{16} + \)\(18\!\cdots\!80\)\(q^{17} - \)\(43\!\cdots\!40\)\(q^{18} + \)\(10\!\cdots\!80\)\(q^{19} + \)\(92\!\cdots\!80\)\(q^{20} - \)\(10\!\cdots\!28\)\(q^{21} + \)\(15\!\cdots\!20\)\(q^{22} + \)\(15\!\cdots\!80\)\(q^{23} - \)\(76\!\cdots\!60\)\(q^{24} + \)\(19\!\cdots\!50\)\(q^{25} + \)\(11\!\cdots\!52\)\(q^{26} - \)\(10\!\cdots\!20\)\(q^{27} + \)\(14\!\cdots\!20\)\(q^{28} + \)\(14\!\cdots\!20\)\(q^{29} - \)\(25\!\cdots\!80\)\(q^{30} - \)\(41\!\cdots\!88\)\(q^{31} + \)\(11\!\cdots\!60\)\(q^{32} + \)\(59\!\cdots\!20\)\(q^{33} + \)\(30\!\cdots\!56\)\(q^{34} + \)\(27\!\cdots\!60\)\(q^{35} + \)\(17\!\cdots\!16\)\(q^{36} + \)\(98\!\cdots\!40\)\(q^{37} + \)\(12\!\cdots\!80\)\(q^{38} + \)\(24\!\cdots\!44\)\(q^{39} + \)\(88\!\cdots\!00\)\(q^{40} + \)\(50\!\cdots\!12\)\(q^{41} + \)\(43\!\cdots\!80\)\(q^{42} + \)\(27\!\cdots\!00\)\(q^{43} - \)\(86\!\cdots\!44\)\(q^{44} - \)\(23\!\cdots\!80\)\(q^{45} - \)\(82\!\cdots\!88\)\(q^{46} - \)\(13\!\cdots\!80\)\(q^{47} - \)\(82\!\cdots\!20\)\(q^{48} - \)\(57\!\cdots\!42\)\(q^{49} + \)\(31\!\cdots\!00\)\(q^{50} + \)\(28\!\cdots\!32\)\(q^{51} + \)\(41\!\cdots\!00\)\(q^{52} + \)\(64\!\cdots\!60\)\(q^{53} + \)\(78\!\cdots\!80\)\(q^{54} + \)\(43\!\cdots\!20\)\(q^{55} + \)\(28\!\cdots\!20\)\(q^{56} - \)\(67\!\cdots\!40\)\(q^{57} - \)\(17\!\cdots\!80\)\(q^{58} - \)\(24\!\cdots\!60\)\(q^{59} - \)\(31\!\cdots\!40\)\(q^{60} - \)\(25\!\cdots\!88\)\(q^{61} - \)\(29\!\cdots\!80\)\(q^{62} + \)\(42\!\cdots\!40\)\(q^{63} + \)\(47\!\cdots\!48\)\(q^{64} + \)\(12\!\cdots\!20\)\(q^{65} + \)\(93\!\cdots\!84\)\(q^{66} + \)\(95\!\cdots\!80\)\(q^{67} + \)\(12\!\cdots\!60\)\(q^{68} - \)\(14\!\cdots\!36\)\(q^{69} - \)\(34\!\cdots\!40\)\(q^{70} - \)\(25\!\cdots\!88\)\(q^{71} - \)\(21\!\cdots\!60\)\(q^{72} - \)\(30\!\cdots\!20\)\(q^{73} - \)\(24\!\cdots\!84\)\(q^{74} + \)\(19\!\cdots\!00\)\(q^{75} + \)\(10\!\cdots\!40\)\(q^{76} + \)\(15\!\cdots\!00\)\(q^{77} + \)\(13\!\cdots\!00\)\(q^{78} + \)\(11\!\cdots\!20\)\(q^{79} + \)\(12\!\cdots\!60\)\(q^{80} + \)\(29\!\cdots\!86\)\(q^{81} - \)\(25\!\cdots\!80\)\(q^{82} - \)\(79\!\cdots\!60\)\(q^{83} - \)\(91\!\cdots\!64\)\(q^{84} - \)\(36\!\cdots\!40\)\(q^{85} + \)\(72\!\cdots\!32\)\(q^{86} - \)\(14\!\cdots\!60\)\(q^{87} - \)\(48\!\cdots\!60\)\(q^{88} + \)\(53\!\cdots\!60\)\(q^{89} + \)\(85\!\cdots\!20\)\(q^{90} + \)\(34\!\cdots\!32\)\(q^{91} + \)\(18\!\cdots\!80\)\(q^{92} - \)\(16\!\cdots\!80\)\(q^{93} - \)\(29\!\cdots\!04\)\(q^{94} + \)\(19\!\cdots\!00\)\(q^{95} - \)\(89\!\cdots\!08\)\(q^{96} - \)\(74\!\cdots\!80\)\(q^{97} - \)\(16\!\cdots\!20\)\(q^{98} - \)\(18\!\cdots\!36\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.20777e11 1.13587 0.567936 0.823072i \(-0.307742\pi\)
0.567936 + 0.823072i \(0.307742\pi\)
\(3\) 1.08881e18 1.39606 0.698032 0.716067i \(-0.254059\pi\)
0.698032 + 0.716067i \(0.254059\pi\)
\(4\) 1.09637e22 0.290207
\(5\) −2.30711e25 −0.141806 −0.0709028 0.997483i \(-0.522588\pi\)
−0.0709028 + 0.997483i \(0.522588\pi\)
\(6\) 2.40385e29 1.58575
\(7\) 1.96027e31 0.399153 0.199577 0.979882i \(-0.436043\pi\)
0.199577 + 0.979882i \(0.436043\pi\)
\(8\) −5.92020e33 −0.806235
\(9\) 5.77242e35 0.948994
\(10\) −5.09358e36 −0.161073
\(11\) 9.40509e38 0.833945 0.416972 0.908919i \(-0.363091\pi\)
0.416972 + 0.908919i \(0.363091\pi\)
\(12\) 1.19374e40 0.405147
\(13\) 1.14147e42 1.92570 0.962848 0.270042i \(-0.0870377\pi\)
0.962848 + 0.270042i \(0.0870377\pi\)
\(14\) 4.32784e42 0.453387
\(15\) −2.51201e43 −0.197970
\(16\) −1.72124e45 −1.20599
\(17\) 1.79040e46 1.29156 0.645782 0.763522i \(-0.276531\pi\)
0.645782 + 0.763522i \(0.276531\pi\)
\(18\) 1.27442e47 1.07794
\(19\) 1.43901e48 1.60253 0.801263 0.598312i \(-0.204162\pi\)
0.801263 + 0.598312i \(0.204162\pi\)
\(20\) −2.52945e47 −0.0411529
\(21\) 2.13436e49 0.557244
\(22\) 2.07643e50 0.947255
\(23\) −1.23136e51 −1.06070 −0.530349 0.847779i \(-0.677939\pi\)
−0.530349 + 0.847779i \(0.677939\pi\)
\(24\) −6.44597e51 −1.12556
\(25\) −2.59375e52 −0.979891
\(26\) 2.52010e53 2.18735
\(27\) −3.37806e52 −0.0712075
\(28\) 2.14918e53 0.115837
\(29\) −2.48097e54 −0.358671 −0.179336 0.983788i \(-0.557395\pi\)
−0.179336 + 0.983788i \(0.557395\pi\)
\(30\) −5.54594e54 −0.224868
\(31\) 1.95055e55 0.231256 0.115628 0.993293i \(-0.463112\pi\)
0.115628 + 0.993293i \(0.463112\pi\)
\(32\) −1.56352e56 −0.563613
\(33\) 1.02404e57 1.16424
\(34\) 3.95280e57 1.46705
\(35\) −4.52257e56 −0.0566022
\(36\) 6.32870e57 0.275404
\(37\) −2.65296e58 −0.413205 −0.206603 0.978425i \(-0.566241\pi\)
−0.206603 + 0.978425i \(0.566241\pi\)
\(38\) 3.17702e59 1.82027
\(39\) 1.24284e60 2.68840
\(40\) 1.36586e59 0.114329
\(41\) 3.61594e59 0.119902 0.0599511 0.998201i \(-0.480906\pi\)
0.0599511 + 0.998201i \(0.480906\pi\)
\(42\) 4.71219e60 0.632958
\(43\) 8.98859e59 0.0499603 0.0249801 0.999688i \(-0.492048\pi\)
0.0249801 + 0.999688i \(0.492048\pi\)
\(44\) 1.03115e61 0.242016
\(45\) −1.33176e61 −0.134573
\(46\) −2.71857e62 −1.20482
\(47\) 2.48355e62 0.491364 0.245682 0.969350i \(-0.420988\pi\)
0.245682 + 0.969350i \(0.420988\pi\)
\(48\) −1.87411e63 −1.68363
\(49\) −2.02760e63 −0.840677
\(50\) −5.72641e63 −1.11303
\(51\) 1.94941e64 1.80311
\(52\) 1.25147e64 0.558850
\(53\) 3.59994e64 0.786955 0.393477 0.919334i \(-0.371272\pi\)
0.393477 + 0.919334i \(0.371272\pi\)
\(54\) −7.45799e63 −0.0808827
\(55\) −2.16986e64 −0.118258
\(56\) −1.16052e65 −0.321811
\(57\) 1.56681e66 2.23723
\(58\) −5.47742e65 −0.407405
\(59\) −4.00811e66 −1.57032 −0.785162 0.619291i \(-0.787420\pi\)
−0.785162 + 0.619291i \(0.787420\pi\)
\(60\) −2.75409e65 −0.0574521
\(61\) −1.59203e67 −1.78683 −0.893413 0.449237i \(-0.851696\pi\)
−0.893413 + 0.449237i \(0.851696\pi\)
\(62\) 4.30637e66 0.262678
\(63\) 1.13155e67 0.378794
\(64\) 3.05076e67 0.565795
\(65\) −2.63349e67 −0.273075
\(66\) 2.26084e68 1.32243
\(67\) 1.61324e68 0.536900 0.268450 0.963294i \(-0.413489\pi\)
0.268450 + 0.963294i \(0.413489\pi\)
\(68\) 1.96294e68 0.374821
\(69\) −1.34072e69 −1.48080
\(70\) −9.98480e67 −0.0642929
\(71\) 2.63303e69 0.996020 0.498010 0.867171i \(-0.334064\pi\)
0.498010 + 0.867171i \(0.334064\pi\)
\(72\) −3.41738e69 −0.765112
\(73\) −2.52652e69 −0.337221 −0.168611 0.985683i \(-0.553928\pi\)
−0.168611 + 0.985683i \(0.553928\pi\)
\(74\) −5.85713e69 −0.469348
\(75\) −2.82410e70 −1.36799
\(76\) 1.57769e70 0.465064
\(77\) 1.84365e70 0.332872
\(78\) 2.74391e71 3.05368
\(79\) −9.29901e70 −0.641831 −0.320916 0.947108i \(-0.603991\pi\)
−0.320916 + 0.947108i \(0.603991\pi\)
\(80\) 3.97110e70 0.171016
\(81\) −3.87898e71 −1.04840
\(82\) 7.98318e70 0.136194
\(83\) −7.84087e71 −0.849055 −0.424528 0.905415i \(-0.639560\pi\)
−0.424528 + 0.905415i \(0.639560\pi\)
\(84\) 2.34005e71 0.161716
\(85\) −4.13066e71 −0.183151
\(86\) 1.98448e71 0.0567485
\(87\) −2.70130e72 −0.500728
\(88\) −5.56800e72 −0.672355
\(89\) 2.05618e73 1.62531 0.812656 0.582744i \(-0.198021\pi\)
0.812656 + 0.582744i \(0.198021\pi\)
\(90\) −2.94023e72 −0.152857
\(91\) 2.23759e73 0.768648
\(92\) −1.35003e73 −0.307822
\(93\) 2.12378e73 0.322848
\(94\) 5.48312e73 0.558127
\(95\) −3.31997e73 −0.227247
\(96\) −1.70238e74 −0.786839
\(97\) −4.10454e74 −1.28625 −0.643123 0.765763i \(-0.722362\pi\)
−0.643123 + 0.765763i \(0.722362\pi\)
\(98\) −4.47648e74 −0.954902
\(99\) 5.42901e74 0.791409
\(100\) −2.84371e74 −0.284371
\(101\) 1.81290e75 1.24831 0.624154 0.781302i \(-0.285444\pi\)
0.624154 + 0.781302i \(0.285444\pi\)
\(102\) 4.30385e75 2.04810
\(103\) −1.54416e75 −0.509677 −0.254839 0.966984i \(-0.582022\pi\)
−0.254839 + 0.966984i \(0.582022\pi\)
\(104\) −6.75771e75 −1.55256
\(105\) −4.92422e74 −0.0790203
\(106\) 7.94784e75 0.893880
\(107\) −4.90777e73 −0.00388144 −0.00194072 0.999998i \(-0.500618\pi\)
−0.00194072 + 0.999998i \(0.500618\pi\)
\(108\) −3.70360e74 −0.0206649
\(109\) −1.45643e76 −0.575171 −0.287586 0.957755i \(-0.592853\pi\)
−0.287586 + 0.957755i \(0.592853\pi\)
\(110\) −4.79056e75 −0.134326
\(111\) −2.88857e76 −0.576861
\(112\) −3.37410e76 −0.481374
\(113\) −1.13049e77 −1.15564 −0.577822 0.816163i \(-0.696097\pi\)
−0.577822 + 0.816163i \(0.696097\pi\)
\(114\) 3.45917e77 2.54121
\(115\) 2.84089e76 0.150413
\(116\) −2.72006e76 −0.104089
\(117\) 6.58903e77 1.82747
\(118\) −8.84899e77 −1.78369
\(119\) 3.50968e77 0.515532
\(120\) 1.48716e77 0.159610
\(121\) −3.87338e77 −0.304536
\(122\) −3.51484e78 −2.02961
\(123\) 3.93708e77 0.167391
\(124\) 2.13852e77 0.0671121
\(125\) 1.20909e78 0.280760
\(126\) 2.49821e78 0.430262
\(127\) 1.39623e78 0.178779 0.0893894 0.995997i \(-0.471508\pi\)
0.0893894 + 0.995997i \(0.471508\pi\)
\(128\) 1.26422e79 1.20628
\(129\) 9.78688e77 0.0697477
\(130\) −5.81416e78 −0.310178
\(131\) −3.06227e79 −1.22566 −0.612830 0.790215i \(-0.709969\pi\)
−0.612830 + 0.790215i \(0.709969\pi\)
\(132\) 1.12272e79 0.337870
\(133\) 2.82086e79 0.639654
\(134\) 3.56167e79 0.609850
\(135\) 7.79356e77 0.0100976
\(136\) −1.05995e80 −1.04130
\(137\) −1.01580e80 −0.758207 −0.379103 0.925354i \(-0.623768\pi\)
−0.379103 + 0.925354i \(0.623768\pi\)
\(138\) −2.96001e80 −1.68200
\(139\) 2.74853e80 1.19137 0.595684 0.803219i \(-0.296881\pi\)
0.595684 + 0.803219i \(0.296881\pi\)
\(140\) −4.95840e78 −0.0164263
\(141\) 2.70412e80 0.685976
\(142\) 5.81314e80 1.13135
\(143\) 1.07356e81 1.60592
\(144\) −9.93572e80 −1.14447
\(145\) 5.72387e79 0.0508616
\(146\) −5.57798e80 −0.383041
\(147\) −2.20767e81 −1.17364
\(148\) −2.90862e80 −0.119915
\(149\) 3.12728e81 1.00157 0.500786 0.865571i \(-0.333045\pi\)
0.500786 + 0.865571i \(0.333045\pi\)
\(150\) −6.23498e81 −1.55386
\(151\) 3.88189e81 0.754062 0.377031 0.926201i \(-0.376945\pi\)
0.377031 + 0.926201i \(0.376945\pi\)
\(152\) −8.51925e81 −1.29201
\(153\) 1.03349e82 1.22569
\(154\) 4.07037e81 0.378100
\(155\) −4.50014e80 −0.0327934
\(156\) 1.36261e82 0.780190
\(157\) −3.39510e81 −0.152973 −0.0764867 0.997071i \(-0.524370\pi\)
−0.0764867 + 0.997071i \(0.524370\pi\)
\(158\) −2.05301e82 −0.729039
\(159\) 3.91965e82 1.09864
\(160\) 3.60723e81 0.0799234
\(161\) −2.41380e82 −0.423381
\(162\) −8.56390e82 −1.19085
\(163\) 8.90306e82 0.982888 0.491444 0.870909i \(-0.336469\pi\)
0.491444 + 0.870909i \(0.336469\pi\)
\(164\) 3.96441e81 0.0347964
\(165\) −2.36257e82 −0.165096
\(166\) −1.73109e83 −0.964419
\(167\) −3.38631e83 −1.50612 −0.753059 0.657952i \(-0.771423\pi\)
−0.753059 + 0.657952i \(0.771423\pi\)
\(168\) −1.26359e83 −0.449269
\(169\) 9.51589e83 2.70831
\(170\) −9.11956e82 −0.208036
\(171\) 8.30659e83 1.52079
\(172\) 9.85482e81 0.0144988
\(173\) 4.90633e83 0.580801 0.290401 0.956905i \(-0.406211\pi\)
0.290401 + 0.956905i \(0.406211\pi\)
\(174\) −5.96387e83 −0.568763
\(175\) −5.08446e83 −0.391127
\(176\) −1.61884e84 −1.00573
\(177\) −4.36407e84 −2.19227
\(178\) 4.53959e84 1.84615
\(179\) −1.46434e84 −0.482674 −0.241337 0.970441i \(-0.577586\pi\)
−0.241337 + 0.970441i \(0.577586\pi\)
\(180\) −1.46010e83 −0.0390539
\(181\) 5.14219e84 1.11738 0.558691 0.829376i \(-0.311304\pi\)
0.558691 + 0.829376i \(0.311304\pi\)
\(182\) 4.94009e84 0.873087
\(183\) −1.73342e85 −2.49452
\(184\) 7.28990e84 0.855172
\(185\) 6.12067e83 0.0585948
\(186\) 4.68882e84 0.366715
\(187\) 1.68389e85 1.07709
\(188\) 2.72289e84 0.142597
\(189\) −6.62191e83 −0.0284227
\(190\) −7.32973e84 −0.258124
\(191\) −3.57215e85 −1.03318 −0.516592 0.856231i \(-0.672800\pi\)
−0.516592 + 0.856231i \(0.672800\pi\)
\(192\) 3.32170e85 0.789886
\(193\) 9.29438e84 0.181895 0.0909476 0.995856i \(-0.471010\pi\)
0.0909476 + 0.995856i \(0.471010\pi\)
\(194\) −9.06189e85 −1.46101
\(195\) −2.86738e85 −0.381230
\(196\) −2.22300e85 −0.243970
\(197\) 5.56745e85 0.504862 0.252431 0.967615i \(-0.418770\pi\)
0.252431 + 0.967615i \(0.418770\pi\)
\(198\) 1.19860e86 0.898939
\(199\) −2.63184e86 −1.63407 −0.817033 0.576591i \(-0.804382\pi\)
−0.817033 + 0.576591i \(0.804382\pi\)
\(200\) 1.53555e86 0.790022
\(201\) 1.75651e86 0.749547
\(202\) 4.00247e86 1.41792
\(203\) −4.86337e85 −0.143165
\(204\) 2.13727e86 0.523273
\(205\) −8.34238e84 −0.0170028
\(206\) −3.40915e86 −0.578928
\(207\) −7.10793e86 −1.00660
\(208\) −1.96474e87 −2.32237
\(209\) 1.35341e87 1.33642
\(210\) −1.08716e86 −0.0897570
\(211\) −5.62170e86 −0.388397 −0.194199 0.980962i \(-0.562211\pi\)
−0.194199 + 0.980962i \(0.562211\pi\)
\(212\) 3.94686e86 0.228379
\(213\) 2.86687e87 1.39051
\(214\) −1.08353e85 −0.00440882
\(215\) −2.07377e85 −0.00708465
\(216\) 1.99988e86 0.0574100
\(217\) 3.82361e86 0.0923067
\(218\) −3.21548e87 −0.653321
\(219\) −2.75090e87 −0.470783
\(220\) −2.37897e86 −0.0343193
\(221\) 2.04369e88 2.48716
\(222\) −6.37730e87 −0.655240
\(223\) 2.95997e87 0.256954 0.128477 0.991712i \(-0.458991\pi\)
0.128477 + 0.991712i \(0.458991\pi\)
\(224\) −3.06493e87 −0.224968
\(225\) −1.49722e88 −0.929911
\(226\) −2.49586e88 −1.31266
\(227\) −1.99529e88 −0.889275 −0.444638 0.895711i \(-0.646668\pi\)
−0.444638 + 0.895711i \(0.646668\pi\)
\(228\) 1.71781e88 0.649259
\(229\) 6.29641e87 0.201959 0.100979 0.994889i \(-0.467802\pi\)
0.100979 + 0.994889i \(0.467802\pi\)
\(230\) 6.27204e87 0.170850
\(231\) 2.00739e88 0.464710
\(232\) 1.46878e88 0.289173
\(233\) −9.92233e87 −0.166252 −0.0831260 0.996539i \(-0.526490\pi\)
−0.0831260 + 0.996539i \(0.526490\pi\)
\(234\) 1.45471e89 2.07578
\(235\) −5.72983e87 −0.0696783
\(236\) −4.39437e88 −0.455718
\(237\) −1.01249e89 −0.896038
\(238\) 7.74857e88 0.585579
\(239\) −1.09445e89 −0.706764 −0.353382 0.935479i \(-0.614968\pi\)
−0.353382 + 0.935479i \(0.614968\pi\)
\(240\) 4.32377e88 0.238749
\(241\) −3.43159e88 −0.162127 −0.0810636 0.996709i \(-0.525832\pi\)
−0.0810636 + 0.996709i \(0.525832\pi\)
\(242\) −8.55155e88 −0.345914
\(243\) −4.01799e89 −1.39243
\(244\) −1.74545e89 −0.518549
\(245\) 4.67790e88 0.119213
\(246\) 8.69217e88 0.190135
\(247\) 1.64259e90 3.08598
\(248\) −1.15476e89 −0.186447
\(249\) −8.53723e89 −1.18534
\(250\) 2.66941e89 0.318907
\(251\) 3.39159e89 0.348851 0.174425 0.984670i \(-0.444193\pi\)
0.174425 + 0.984670i \(0.444193\pi\)
\(252\) 1.24060e89 0.109929
\(253\) −1.15811e90 −0.884564
\(254\) 3.08255e89 0.203070
\(255\) −4.49750e89 −0.255691
\(256\) 1.63857e90 0.804389
\(257\) −4.75773e89 −0.201794 −0.100897 0.994897i \(-0.532171\pi\)
−0.100897 + 0.994897i \(0.532171\pi\)
\(258\) 2.16072e89 0.0792245
\(259\) −5.20052e89 −0.164932
\(260\) −2.88728e89 −0.0792481
\(261\) −1.43212e90 −0.340377
\(262\) −6.76080e90 −1.39219
\(263\) 2.04074e90 0.364289 0.182145 0.983272i \(-0.441696\pi\)
0.182145 + 0.983272i \(0.441696\pi\)
\(264\) −6.06249e90 −0.938651
\(265\) −8.30546e89 −0.111595
\(266\) 6.22782e90 0.726565
\(267\) 2.23879e91 2.26904
\(268\) 1.76871e90 0.155812
\(269\) 1.37778e91 1.05553 0.527764 0.849391i \(-0.323031\pi\)
0.527764 + 0.849391i \(0.323031\pi\)
\(270\) 1.72064e89 0.0114696
\(271\) −7.60957e90 −0.441582 −0.220791 0.975321i \(-0.570864\pi\)
−0.220791 + 0.975321i \(0.570864\pi\)
\(272\) −3.08172e91 −1.55761
\(273\) 2.43631e91 1.07308
\(274\) −2.24266e91 −0.861226
\(275\) −2.43945e91 −0.817175
\(276\) −1.46992e91 −0.429739
\(277\) −4.78450e91 −1.22136 −0.610682 0.791876i \(-0.709105\pi\)
−0.610682 + 0.791876i \(0.709105\pi\)
\(278\) 6.06814e91 1.35324
\(279\) 1.12594e91 0.219461
\(280\) 2.67745e90 0.0456347
\(281\) 1.67133e91 0.249215 0.124608 0.992206i \(-0.460233\pi\)
0.124608 + 0.992206i \(0.460233\pi\)
\(282\) 5.97008e91 0.779182
\(283\) −1.00325e92 −1.14662 −0.573310 0.819339i \(-0.694341\pi\)
−0.573310 + 0.819339i \(0.694341\pi\)
\(284\) 2.88678e91 0.289052
\(285\) −3.61482e91 −0.317252
\(286\) 2.37018e92 1.82413
\(287\) 7.08823e90 0.0478593
\(288\) −9.02532e91 −0.534865
\(289\) 1.28391e92 0.668138
\(290\) 1.26370e91 0.0577723
\(291\) −4.46906e92 −1.79568
\(292\) −2.77000e91 −0.0978639
\(293\) 3.51636e92 1.09284 0.546421 0.837511i \(-0.315990\pi\)
0.546421 + 0.837511i \(0.315990\pi\)
\(294\) −4.87404e92 −1.33310
\(295\) 9.24715e91 0.222681
\(296\) 1.57060e92 0.333140
\(297\) −3.17709e91 −0.0593832
\(298\) 6.90433e92 1.13766
\(299\) −1.40556e93 −2.04258
\(300\) −3.09626e92 −0.397000
\(301\) 1.76201e91 0.0199418
\(302\) 8.57032e92 0.856519
\(303\) 1.97390e93 1.74272
\(304\) −2.47689e93 −1.93263
\(305\) 3.67299e92 0.253382
\(306\) 2.28172e93 1.39222
\(307\) 2.83130e93 1.52861 0.764305 0.644855i \(-0.223082\pi\)
0.764305 + 0.644855i \(0.223082\pi\)
\(308\) 2.02133e92 0.0966016
\(309\) −1.68129e93 −0.711542
\(310\) −9.93528e91 −0.0372492
\(311\) −1.00581e93 −0.334196 −0.167098 0.985940i \(-0.553440\pi\)
−0.167098 + 0.985940i \(0.553440\pi\)
\(312\) −7.35787e93 −2.16748
\(313\) −3.95730e93 −1.03392 −0.516959 0.856010i \(-0.672936\pi\)
−0.516959 + 0.856010i \(0.672936\pi\)
\(314\) −7.49562e92 −0.173758
\(315\) −2.61061e92 −0.0537151
\(316\) −1.01952e93 −0.186264
\(317\) 1.02388e94 1.66161 0.830804 0.556565i \(-0.187881\pi\)
0.830804 + 0.556565i \(0.187881\pi\)
\(318\) 8.65369e93 1.24791
\(319\) −2.33337e93 −0.299112
\(320\) −7.03844e92 −0.0802329
\(321\) −5.34364e91 −0.00541874
\(322\) −5.32913e93 −0.480907
\(323\) 2.57641e94 2.06977
\(324\) −4.25279e93 −0.304254
\(325\) −2.96068e94 −1.88697
\(326\) 1.96559e94 1.11644
\(327\) −1.58578e94 −0.802976
\(328\) −2.14071e93 −0.0966693
\(329\) 4.86844e93 0.196130
\(330\) −5.21601e93 −0.187528
\(331\) 4.19453e94 1.34627 0.673137 0.739518i \(-0.264947\pi\)
0.673137 + 0.739518i \(0.264947\pi\)
\(332\) −8.59650e93 −0.246402
\(333\) −1.53140e94 −0.392129
\(334\) −7.47621e94 −1.71076
\(335\) −3.72192e93 −0.0761355
\(336\) −3.67376e94 −0.672028
\(337\) −1.23784e94 −0.202554 −0.101277 0.994858i \(-0.532293\pi\)
−0.101277 + 0.994858i \(0.532293\pi\)
\(338\) 2.10089e95 3.07629
\(339\) −1.23089e95 −1.61335
\(340\) −4.52873e93 −0.0531517
\(341\) 1.83451e94 0.192855
\(342\) 1.83391e95 1.72742
\(343\) −8.70256e94 −0.734712
\(344\) −5.32142e93 −0.0402797
\(345\) 3.09319e94 0.209986
\(346\) 1.08321e95 0.659716
\(347\) −7.20855e93 −0.0393996 −0.0196998 0.999806i \(-0.506271\pi\)
−0.0196998 + 0.999806i \(0.506271\pi\)
\(348\) −2.96163e94 −0.145315
\(349\) −1.02804e95 −0.452958 −0.226479 0.974016i \(-0.572721\pi\)
−0.226479 + 0.974016i \(0.572721\pi\)
\(350\) −1.12253e95 −0.444270
\(351\) −3.85595e94 −0.137124
\(352\) −1.47051e95 −0.470022
\(353\) 2.67413e95 0.768477 0.384239 0.923234i \(-0.374464\pi\)
0.384239 + 0.923234i \(0.374464\pi\)
\(354\) −9.63488e95 −2.49014
\(355\) −6.07470e94 −0.141241
\(356\) 2.25434e95 0.471676
\(357\) 3.82137e95 0.719716
\(358\) −3.23294e95 −0.548257
\(359\) 7.10202e95 1.08478 0.542388 0.840128i \(-0.317520\pi\)
0.542388 + 0.840128i \(0.317520\pi\)
\(360\) 7.88428e94 0.108497
\(361\) 1.26442e96 1.56809
\(362\) 1.13528e96 1.26920
\(363\) −4.21738e95 −0.425152
\(364\) 2.45322e95 0.223067
\(365\) 5.82896e94 0.0478199
\(366\) −3.82699e96 −2.83346
\(367\) −1.75912e96 −1.17576 −0.587878 0.808950i \(-0.700036\pi\)
−0.587878 + 0.808950i \(0.700036\pi\)
\(368\) 2.11947e96 1.27919
\(369\) 2.08727e95 0.113786
\(370\) 1.35130e95 0.0665562
\(371\) 7.05685e95 0.314116
\(372\) 2.32845e95 0.0936928
\(373\) −3.67079e96 −1.33561 −0.667803 0.744338i \(-0.732765\pi\)
−0.667803 + 0.744338i \(0.732765\pi\)
\(374\) 3.71765e96 1.22344
\(375\) 1.31647e96 0.391958
\(376\) −1.47031e96 −0.396155
\(377\) −2.83195e96 −0.690692
\(378\) −1.46197e95 −0.0322846
\(379\) −4.49109e95 −0.0898217 −0.0449108 0.998991i \(-0.514300\pi\)
−0.0449108 + 0.998991i \(0.514300\pi\)
\(380\) −3.63991e95 −0.0659487
\(381\) 1.52022e96 0.249587
\(382\) −7.88649e96 −1.17357
\(383\) 1.26028e97 1.70025 0.850123 0.526583i \(-0.176527\pi\)
0.850123 + 0.526583i \(0.176527\pi\)
\(384\) 1.37650e97 1.68405
\(385\) −4.25351e95 −0.0472031
\(386\) 2.05199e96 0.206610
\(387\) 5.18859e95 0.0474120
\(388\) −4.50009e96 −0.373277
\(389\) −5.15319e96 −0.388120 −0.194060 0.980990i \(-0.562166\pi\)
−0.194060 + 0.980990i \(0.562166\pi\)
\(390\) −6.33052e96 −0.433028
\(391\) −2.20463e97 −1.36996
\(392\) 1.20038e97 0.677783
\(393\) −3.33423e97 −1.71110
\(394\) 1.22917e97 0.573459
\(395\) 2.14539e96 0.0910153
\(396\) 5.95220e96 0.229672
\(397\) 1.73194e97 0.607979 0.303989 0.952675i \(-0.401681\pi\)
0.303989 + 0.952675i \(0.401681\pi\)
\(398\) −5.81051e97 −1.85609
\(399\) 3.07138e97 0.892997
\(400\) 4.46447e97 1.18174
\(401\) −8.61687e96 −0.207700 −0.103850 0.994593i \(-0.533116\pi\)
−0.103850 + 0.994593i \(0.533116\pi\)
\(402\) 3.87798e97 0.851390
\(403\) 2.22649e97 0.445329
\(404\) 1.98761e97 0.362267
\(405\) 8.94923e96 0.148670
\(406\) −1.07372e97 −0.162617
\(407\) −2.49513e97 −0.344590
\(408\) −1.15409e98 −1.45373
\(409\) 1.42017e98 1.63198 0.815990 0.578065i \(-0.196192\pi\)
0.815990 + 0.578065i \(0.196192\pi\)
\(410\) −1.84181e96 −0.0193130
\(411\) −1.10602e98 −1.05850
\(412\) −1.69297e97 −0.147912
\(413\) −7.85698e97 −0.626800
\(414\) −1.56927e98 −1.14337
\(415\) 1.80898e97 0.120401
\(416\) −1.78471e98 −1.08535
\(417\) 2.99263e98 1.66323
\(418\) 2.98801e98 1.51800
\(419\) 5.15399e97 0.239396 0.119698 0.992810i \(-0.461807\pi\)
0.119698 + 0.992810i \(0.461807\pi\)
\(420\) −5.39876e96 −0.0229322
\(421\) −2.32868e97 −0.0904757 −0.0452378 0.998976i \(-0.514405\pi\)
−0.0452378 + 0.998976i \(0.514405\pi\)
\(422\) −1.24114e98 −0.441170
\(423\) 1.43361e98 0.466302
\(424\) −2.13123e98 −0.634470
\(425\) −4.64386e98 −1.26559
\(426\) 6.32941e98 1.57944
\(427\) −3.12081e98 −0.713217
\(428\) −5.38074e95 −0.00112642
\(429\) 1.16890e99 2.24197
\(430\) −4.57841e96 −0.00804726
\(431\) −6.03815e98 −0.972762 −0.486381 0.873747i \(-0.661683\pi\)
−0.486381 + 0.873747i \(0.661683\pi\)
\(432\) 5.81446e97 0.0858754
\(433\) −1.62785e98 −0.220455 −0.110227 0.993906i \(-0.535158\pi\)
−0.110227 + 0.993906i \(0.535158\pi\)
\(434\) 8.44166e97 0.104849
\(435\) 6.23221e97 0.0710060
\(436\) −1.59679e98 −0.166919
\(437\) −1.77195e99 −1.69980
\(438\) −6.07336e98 −0.534749
\(439\) −1.67222e99 −1.35168 −0.675840 0.737048i \(-0.736219\pi\)
−0.675840 + 0.737048i \(0.736219\pi\)
\(440\) 1.28460e98 0.0953438
\(441\) −1.17041e99 −0.797797
\(442\) 4.51200e99 2.82510
\(443\) 2.94738e99 1.69549 0.847747 0.530401i \(-0.177959\pi\)
0.847747 + 0.530401i \(0.177959\pi\)
\(444\) −3.16694e98 −0.167409
\(445\) −4.74385e98 −0.230478
\(446\) 6.53495e98 0.291867
\(447\) 3.40502e99 1.39826
\(448\) 5.98032e98 0.225839
\(449\) −2.98962e99 −1.03843 −0.519216 0.854643i \(-0.673776\pi\)
−0.519216 + 0.854643i \(0.673776\pi\)
\(450\) −3.30552e99 −1.05626
\(451\) 3.40083e98 0.0999917
\(452\) −1.23943e99 −0.335376
\(453\) 4.22664e99 1.05272
\(454\) −4.40515e99 −1.01010
\(455\) −5.16236e98 −0.108999
\(456\) −9.27585e99 −1.80373
\(457\) 5.57415e99 0.998438 0.499219 0.866476i \(-0.333620\pi\)
0.499219 + 0.866476i \(0.333620\pi\)
\(458\) 1.39010e99 0.229399
\(459\) −6.04808e98 −0.0919691
\(460\) 3.11467e98 0.0436508
\(461\) −7.38632e99 −0.954209 −0.477104 0.878847i \(-0.658314\pi\)
−0.477104 + 0.878847i \(0.658314\pi\)
\(462\) 4.43186e99 0.527852
\(463\) 5.44068e99 0.597539 0.298769 0.954325i \(-0.403424\pi\)
0.298769 + 0.954325i \(0.403424\pi\)
\(464\) 4.27035e99 0.432553
\(465\) −4.89979e98 −0.0457817
\(466\) −2.19063e99 −0.188841
\(467\) 2.61476e99 0.207993 0.103996 0.994578i \(-0.466837\pi\)
0.103996 + 0.994578i \(0.466837\pi\)
\(468\) 7.22401e99 0.530345
\(469\) 3.16239e99 0.214306
\(470\) −1.26502e99 −0.0791456
\(471\) −3.69663e99 −0.213561
\(472\) 2.37288e100 1.26605
\(473\) 8.45385e98 0.0416641
\(474\) −2.23534e100 −1.01778
\(475\) −3.73244e100 −1.57030
\(476\) 3.84790e99 0.149611
\(477\) 2.07803e100 0.746815
\(478\) −2.41630e100 −0.802794
\(479\) 4.90702e100 1.50743 0.753713 0.657204i \(-0.228261\pi\)
0.753713 + 0.657204i \(0.228261\pi\)
\(480\) 3.92759e99 0.111578
\(481\) −3.02827e100 −0.795708
\(482\) −7.57616e99 −0.184156
\(483\) −2.62818e100 −0.591067
\(484\) −4.24666e99 −0.0883784
\(485\) 9.46963e99 0.182397
\(486\) −8.87082e100 −1.58163
\(487\) −2.18940e100 −0.361402 −0.180701 0.983538i \(-0.557837\pi\)
−0.180701 + 0.983538i \(0.557837\pi\)
\(488\) 9.42512e100 1.44060
\(489\) 9.69374e100 1.37217
\(490\) 1.03277e100 0.135410
\(491\) −5.47812e100 −0.665389 −0.332694 0.943035i \(-0.607958\pi\)
−0.332694 + 0.943035i \(0.607958\pi\)
\(492\) 4.31649e99 0.0485780
\(493\) −4.44193e100 −0.463247
\(494\) 3.62646e101 3.50528
\(495\) −1.25253e100 −0.112226
\(496\) −3.35737e100 −0.278892
\(497\) 5.16146e100 0.397565
\(498\) −1.88483e101 −1.34639
\(499\) −1.49760e101 −0.992257 −0.496128 0.868249i \(-0.665246\pi\)
−0.496128 + 0.868249i \(0.665246\pi\)
\(500\) 1.32561e100 0.0814783
\(501\) −3.68705e101 −2.10264
\(502\) 7.48787e100 0.396250
\(503\) −1.80374e101 −0.885879 −0.442939 0.896552i \(-0.646064\pi\)
−0.442939 + 0.896552i \(0.646064\pi\)
\(504\) −6.69900e100 −0.305397
\(505\) −4.18256e100 −0.177017
\(506\) −2.55684e101 −1.00475
\(507\) 1.03610e102 3.78097
\(508\) 1.53078e100 0.0518828
\(509\) 2.40040e101 0.755729 0.377865 0.925861i \(-0.376658\pi\)
0.377865 + 0.925861i \(0.376658\pi\)
\(510\) −9.92947e100 −0.290432
\(511\) −4.95266e100 −0.134603
\(512\) −1.15850e101 −0.292599
\(513\) −4.86108e100 −0.114112
\(514\) −1.05040e101 −0.229212
\(515\) 3.56254e100 0.0722751
\(516\) 1.07300e100 0.0202412
\(517\) 2.33580e101 0.409771
\(518\) −1.14816e101 −0.187342
\(519\) 5.34206e101 0.810836
\(520\) 1.55908e101 0.220162
\(521\) −1.00783e102 −1.32425 −0.662126 0.749392i \(-0.730346\pi\)
−0.662126 + 0.749392i \(0.730346\pi\)
\(522\) −3.16179e101 −0.386625
\(523\) 9.80597e101 1.11603 0.558017 0.829830i \(-0.311562\pi\)
0.558017 + 0.829830i \(0.311562\pi\)
\(524\) −3.35738e101 −0.355695
\(525\) −5.53601e101 −0.546038
\(526\) 4.50548e101 0.413786
\(527\) 3.49227e101 0.298682
\(528\) −1.76261e102 −1.40406
\(529\) 1.68569e101 0.125081
\(530\) −1.83366e101 −0.126757
\(531\) −2.31365e102 −1.49023
\(532\) 3.09271e101 0.185632
\(533\) 4.12748e101 0.230895
\(534\) 4.94275e102 2.57734
\(535\) 1.13228e99 0.000550410 0
\(536\) −9.55069e101 −0.432868
\(537\) −1.59439e102 −0.673844
\(538\) 3.04183e102 1.19894
\(539\) −1.90697e102 −0.701078
\(540\) 8.54462e99 0.00293040
\(541\) 1.90764e102 0.610378 0.305189 0.952292i \(-0.401280\pi\)
0.305189 + 0.952292i \(0.401280\pi\)
\(542\) −1.68002e102 −0.501581
\(543\) 5.59887e102 1.55994
\(544\) −2.79934e102 −0.727942
\(545\) 3.36016e101 0.0815625
\(546\) 5.37882e102 1.21888
\(547\) −3.72021e102 −0.787123 −0.393562 0.919298i \(-0.628757\pi\)
−0.393562 + 0.919298i \(0.628757\pi\)
\(548\) −1.11369e102 −0.220037
\(549\) −9.18985e102 −1.69569
\(550\) −5.38574e102 −0.928207
\(551\) −3.57015e102 −0.574780
\(552\) 7.93732e102 1.19387
\(553\) −1.82286e102 −0.256189
\(554\) −1.05631e103 −1.38731
\(555\) 6.66425e101 0.0818021
\(556\) 3.01341e102 0.345743
\(557\) 9.39626e102 1.00782 0.503912 0.863755i \(-0.331893\pi\)
0.503912 + 0.863755i \(0.331893\pi\)
\(558\) 2.48582e102 0.249279
\(559\) 1.02602e102 0.0962083
\(560\) 7.78443e101 0.0682615
\(561\) 1.83344e103 1.50369
\(562\) 3.68991e102 0.283077
\(563\) 1.45593e103 1.04490 0.522450 0.852670i \(-0.325018\pi\)
0.522450 + 0.852670i \(0.325018\pi\)
\(564\) 2.96471e102 0.199075
\(565\) 2.60816e102 0.163877
\(566\) −2.21496e103 −1.30241
\(567\) −7.60385e102 −0.418474
\(568\) −1.55881e103 −0.803026
\(569\) −3.42122e103 −1.64995 −0.824976 0.565168i \(-0.808811\pi\)
−0.824976 + 0.565168i \(0.808811\pi\)
\(570\) −7.98069e102 −0.360357
\(571\) 4.10130e103 1.73407 0.867036 0.498245i \(-0.166022\pi\)
0.867036 + 0.498245i \(0.166022\pi\)
\(572\) 1.17702e103 0.466050
\(573\) −3.88939e103 −1.44239
\(574\) 1.56492e102 0.0543621
\(575\) 3.19385e103 1.03937
\(576\) 1.76102e103 0.536936
\(577\) −4.20900e103 −1.20250 −0.601251 0.799060i \(-0.705331\pi\)
−0.601251 + 0.799060i \(0.705331\pi\)
\(578\) 2.83459e103 0.758920
\(579\) 1.01198e103 0.253937
\(580\) 6.27548e101 0.0147604
\(581\) −1.53702e103 −0.338903
\(582\) −9.86668e103 −2.03967
\(583\) 3.38577e103 0.656277
\(584\) 1.49575e103 0.271880
\(585\) −1.52016e103 −0.259146
\(586\) 7.76332e103 1.24133
\(587\) 1.81185e103 0.271764 0.135882 0.990725i \(-0.456613\pi\)
0.135882 + 0.990725i \(0.456613\pi\)
\(588\) −2.42042e103 −0.340598
\(589\) 2.80687e103 0.370594
\(590\) 2.04156e103 0.252937
\(591\) 6.06189e103 0.704819
\(592\) 4.56638e103 0.498320
\(593\) 5.45632e103 0.558919 0.279459 0.960158i \(-0.409845\pi\)
0.279459 + 0.960158i \(0.409845\pi\)
\(594\) −7.01431e102 −0.0674517
\(595\) −8.09721e102 −0.0731054
\(596\) 3.42866e103 0.290663
\(597\) −2.86558e104 −2.28126
\(598\) −3.10316e104 −2.32011
\(599\) 1.50324e104 1.05565 0.527826 0.849352i \(-0.323007\pi\)
0.527826 + 0.849352i \(0.323007\pi\)
\(600\) 1.67192e104 1.10292
\(601\) −3.00993e104 −1.86536 −0.932682 0.360699i \(-0.882538\pi\)
−0.932682 + 0.360699i \(0.882538\pi\)
\(602\) 3.89012e102 0.0226514
\(603\) 9.31228e103 0.509515
\(604\) 4.25598e103 0.218834
\(605\) 8.93632e102 0.0431849
\(606\) 4.35793e104 1.97950
\(607\) −2.70698e104 −1.15587 −0.577936 0.816082i \(-0.696142\pi\)
−0.577936 + 0.816082i \(0.696142\pi\)
\(608\) −2.24993e104 −0.903204
\(609\) −5.29529e103 −0.199867
\(610\) 8.10912e103 0.287810
\(611\) 2.83490e104 0.946219
\(612\) 1.13309e104 0.355702
\(613\) 1.37369e104 0.405621 0.202810 0.979218i \(-0.434993\pi\)
0.202810 + 0.979218i \(0.434993\pi\)
\(614\) 6.25086e104 1.73631
\(615\) −9.08327e102 −0.0237370
\(616\) −1.09148e104 −0.268373
\(617\) −1.04793e104 −0.242459 −0.121229 0.992625i \(-0.538684\pi\)
−0.121229 + 0.992625i \(0.538684\pi\)
\(618\) −3.71191e104 −0.808221
\(619\) −1.99374e104 −0.408573 −0.204286 0.978911i \(-0.565487\pi\)
−0.204286 + 0.978911i \(0.565487\pi\)
\(620\) −4.93381e102 −0.00951687
\(621\) 4.15961e103 0.0755297
\(622\) −2.22060e104 −0.379604
\(623\) 4.03068e104 0.648749
\(624\) −2.13923e105 −3.24217
\(625\) 6.58665e104 0.940078
\(626\) −8.73682e104 −1.17440
\(627\) 1.47360e105 1.86573
\(628\) −3.72229e103 −0.0443939
\(629\) −4.74986e104 −0.533681
\(630\) −5.76364e103 −0.0610136
\(631\) 7.56039e104 0.754125 0.377062 0.926188i \(-0.376934\pi\)
0.377062 + 0.926188i \(0.376934\pi\)
\(632\) 5.50520e104 0.517467
\(633\) −6.12097e104 −0.542227
\(634\) 2.26050e105 1.88738
\(635\) −3.22125e103 −0.0253518
\(636\) 4.29738e104 0.318832
\(637\) −2.31444e105 −1.61889
\(638\) −5.15156e104 −0.339753
\(639\) 1.51990e105 0.945217
\(640\) −2.91670e104 −0.171058
\(641\) −2.20699e105 −1.22074 −0.610371 0.792116i \(-0.708980\pi\)
−0.610371 + 0.792116i \(0.708980\pi\)
\(642\) −1.17975e103 −0.00615500
\(643\) 1.66481e105 0.819317 0.409659 0.912239i \(-0.365648\pi\)
0.409659 + 0.912239i \(0.365648\pi\)
\(644\) −2.64642e104 −0.122868
\(645\) −2.25794e103 −0.00989062
\(646\) 5.68814e105 2.35099
\(647\) −2.95788e104 −0.115364 −0.0576819 0.998335i \(-0.518371\pi\)
−0.0576819 + 0.998335i \(0.518371\pi\)
\(648\) 2.29643e105 0.845260
\(649\) −3.76966e105 −1.30956
\(650\) −6.53652e105 −2.14336
\(651\) 4.16318e104 0.128866
\(652\) 9.76104e104 0.285241
\(653\) −1.46213e105 −0.403406 −0.201703 0.979447i \(-0.564648\pi\)
−0.201703 + 0.979447i \(0.564648\pi\)
\(654\) −3.50104e105 −0.912078
\(655\) 7.06500e104 0.173805
\(656\) −6.22391e104 −0.144600
\(657\) −1.45841e105 −0.320021
\(658\) 1.07484e105 0.222778
\(659\) −1.49655e105 −0.293013 −0.146507 0.989210i \(-0.546803\pi\)
−0.146507 + 0.989210i \(0.546803\pi\)
\(660\) −2.59025e104 −0.0479119
\(661\) −8.31783e105 −1.45363 −0.726817 0.686831i \(-0.759001\pi\)
−0.726817 + 0.686831i \(0.759001\pi\)
\(662\) 9.26056e105 1.52919
\(663\) 2.22519e106 3.47224
\(664\) 4.64195e105 0.684538
\(665\) −6.50804e104 −0.0907065
\(666\) −3.38098e105 −0.445409
\(667\) 3.05497e105 0.380442
\(668\) −3.71265e105 −0.437086
\(669\) 3.22285e105 0.358724
\(670\) −8.21716e104 −0.0864802
\(671\) −1.49732e106 −1.49011
\(672\) −3.33713e105 −0.314069
\(673\) −1.42322e106 −1.26680 −0.633400 0.773824i \(-0.718341\pi\)
−0.633400 + 0.773824i \(0.718341\pi\)
\(674\) −2.73286e105 −0.230076
\(675\) 8.76184e104 0.0697756
\(676\) 1.04329e106 0.785969
\(677\) 2.39084e106 1.70402 0.852012 0.523523i \(-0.175382\pi\)
0.852012 + 0.523523i \(0.175382\pi\)
\(678\) −2.71752e106 −1.83256
\(679\) −8.04601e105 −0.513410
\(680\) 2.44543e105 0.147663
\(681\) −2.17249e106 −1.24149
\(682\) 4.05018e105 0.219059
\(683\) 2.42848e106 1.24325 0.621624 0.783316i \(-0.286473\pi\)
0.621624 + 0.783316i \(0.286473\pi\)
\(684\) 9.10709e105 0.441343
\(685\) 2.34357e105 0.107518
\(686\) −1.92133e106 −0.834540
\(687\) 6.85560e105 0.281947
\(688\) −1.54715e105 −0.0602514
\(689\) 4.10921e106 1.51544
\(690\) 6.82906e105 0.238517
\(691\) −1.62806e106 −0.538573 −0.269287 0.963060i \(-0.586788\pi\)
−0.269287 + 0.963060i \(0.586788\pi\)
\(692\) 5.37915e105 0.168552
\(693\) 1.06423e106 0.315893
\(694\) −1.59148e105 −0.0447530
\(695\) −6.34118e105 −0.168943
\(696\) 1.59923e106 0.403704
\(697\) 6.47399e105 0.154861
\(698\) −2.26968e106 −0.514502
\(699\) −1.08035e106 −0.232098
\(700\) −5.57444e105 −0.113508
\(701\) −4.65996e106 −0.899408 −0.449704 0.893178i \(-0.648470\pi\)
−0.449704 + 0.893178i \(0.648470\pi\)
\(702\) −8.51305e105 −0.155756
\(703\) −3.81764e106 −0.662172
\(704\) 2.86927e106 0.471842
\(705\) −6.23870e105 −0.0972753
\(706\) 5.90387e106 0.872892
\(707\) 3.55377e106 0.498266
\(708\) −4.78464e106 −0.636212
\(709\) 5.38281e106 0.678853 0.339426 0.940633i \(-0.389767\pi\)
0.339426 + 0.940633i \(0.389767\pi\)
\(710\) −1.34116e106 −0.160432
\(711\) −5.36778e106 −0.609094
\(712\) −1.21730e107 −1.31038
\(713\) −2.40183e106 −0.245293
\(714\) 8.43672e106 0.817506
\(715\) −2.47682e106 −0.227729
\(716\) −1.60546e106 −0.140075
\(717\) −1.19165e107 −0.986688
\(718\) 1.56796e107 1.23217
\(719\) 2.39201e107 1.78414 0.892071 0.451895i \(-0.149252\pi\)
0.892071 + 0.451895i \(0.149252\pi\)
\(720\) 2.29228e106 0.162293
\(721\) −3.02697e106 −0.203439
\(722\) 2.79155e107 1.78115
\(723\) −3.73635e106 −0.226340
\(724\) 5.63774e106 0.324272
\(725\) 6.43501e106 0.351459
\(726\) −9.31101e106 −0.482918
\(727\) −2.28277e107 −1.12440 −0.562202 0.827000i \(-0.690046\pi\)
−0.562202 + 0.827000i \(0.690046\pi\)
\(728\) −1.32470e107 −0.619711
\(729\) −2.01538e107 −0.895519
\(730\) 1.28690e106 0.0543173
\(731\) 1.60932e106 0.0645269
\(732\) −1.90047e107 −0.723927
\(733\) −1.58880e107 −0.575004 −0.287502 0.957780i \(-0.592825\pi\)
−0.287502 + 0.957780i \(0.592825\pi\)
\(734\) −3.88373e107 −1.33551
\(735\) 5.09334e106 0.166428
\(736\) 1.92527e107 0.597823
\(737\) 1.51727e107 0.447745
\(738\) 4.60822e106 0.129247
\(739\) −5.34509e107 −1.42491 −0.712457 0.701715i \(-0.752418\pi\)
−0.712457 + 0.701715i \(0.752418\pi\)
\(740\) 6.71052e105 0.0170046
\(741\) 1.78847e108 4.30822
\(742\) 1.55799e107 0.356795
\(743\) 2.60517e107 0.567226 0.283613 0.958939i \(-0.408467\pi\)
0.283613 + 0.958939i \(0.408467\pi\)
\(744\) −1.25732e107 −0.260292
\(745\) −7.21499e106 −0.142028
\(746\) −8.10428e107 −1.51708
\(747\) −4.52608e107 −0.805748
\(748\) 1.84617e107 0.312580
\(749\) −9.62057e104 −0.00154929
\(750\) 2.90648e107 0.445215
\(751\) 3.70994e107 0.540592 0.270296 0.962777i \(-0.412879\pi\)
0.270296 + 0.962777i \(0.412879\pi\)
\(752\) −4.27480e107 −0.592579
\(753\) 3.69280e107 0.487018
\(754\) −6.25229e107 −0.784538
\(755\) −8.95595e106 −0.106930
\(756\) −7.26007e105 −0.00824847
\(757\) 8.77971e107 0.949259 0.474629 0.880186i \(-0.342582\pi\)
0.474629 + 0.880186i \(0.342582\pi\)
\(758\) −9.91530e106 −0.102026
\(759\) −1.26096e108 −1.23491
\(760\) 1.96549e107 0.183215
\(761\) −5.45469e107 −0.484000 −0.242000 0.970276i \(-0.577803\pi\)
−0.242000 + 0.970276i \(0.577803\pi\)
\(762\) 3.35631e107 0.283499
\(763\) −2.85501e107 −0.229582
\(764\) −3.91639e107 −0.299837
\(765\) −2.38439e107 −0.173809
\(766\) 2.78241e108 1.93126
\(767\) −4.57513e108 −3.02397
\(768\) 1.78409e108 1.12298
\(769\) 5.31194e107 0.318431 0.159215 0.987244i \(-0.449104\pi\)
0.159215 + 0.987244i \(0.449104\pi\)
\(770\) −9.39080e106 −0.0536167
\(771\) −5.18027e107 −0.281717
\(772\) 1.01901e107 0.0527872
\(773\) 3.36099e108 1.65858 0.829290 0.558818i \(-0.188745\pi\)
0.829290 + 0.558818i \(0.188745\pi\)
\(774\) 1.14552e107 0.0538540
\(775\) −5.05924e107 −0.226606
\(776\) 2.42997e108 1.03702
\(777\) −5.66238e107 −0.230256
\(778\) −1.13771e108 −0.440855
\(779\) 5.20339e107 0.192146
\(780\) −3.14370e107 −0.110635
\(781\) 2.47639e108 0.830626
\(782\) −4.86733e108 −1.55610
\(783\) 8.38086e106 0.0255401
\(784\) 3.48999e108 1.01384
\(785\) 7.83289e106 0.0216925
\(786\) −7.36123e108 −1.94359
\(787\) 3.71560e108 0.935356 0.467678 0.883899i \(-0.345091\pi\)
0.467678 + 0.883899i \(0.345091\pi\)
\(788\) 6.10398e107 0.146514
\(789\) 2.22198e108 0.508571
\(790\) 4.73653e107 0.103382
\(791\) −2.21606e108 −0.461279
\(792\) −3.21408e108 −0.638061
\(793\) −1.81725e109 −3.44088
\(794\) 3.82373e108 0.690586
\(795\) −9.04307e107 −0.155793
\(796\) −2.88547e108 −0.474217
\(797\) 8.59521e108 1.34763 0.673813 0.738901i \(-0.264655\pi\)
0.673813 + 0.738901i \(0.264655\pi\)
\(798\) 6.78091e108 1.01433
\(799\) 4.44656e108 0.634629
\(800\) 4.05539e108 0.552279
\(801\) 1.18691e109 1.54241
\(802\) −1.90241e108 −0.235920
\(803\) −2.37621e108 −0.281224
\(804\) 1.92579e108 0.217524
\(805\) 5.56892e107 0.0600379
\(806\) 4.91558e108 0.505837
\(807\) 1.50014e109 1.47358
\(808\) −1.07327e109 −1.00643
\(809\) −7.94957e108 −0.711663 −0.355831 0.934550i \(-0.615802\pi\)
−0.355831 + 0.934550i \(0.615802\pi\)
\(810\) 1.97579e108 0.168870
\(811\) −1.89106e109 −1.54320 −0.771602 0.636106i \(-0.780544\pi\)
−0.771602 + 0.636106i \(0.780544\pi\)
\(812\) −5.33206e107 −0.0415474
\(813\) −8.28538e108 −0.616477
\(814\) −5.50868e108 −0.391411
\(815\) −2.05404e108 −0.139379
\(816\) −3.35540e109 −2.17452
\(817\) 1.29347e108 0.0800626
\(818\) 3.13540e109 1.85372
\(819\) 1.29163e109 0.729443
\(820\) −9.14633e106 −0.00493432
\(821\) 2.82901e109 1.45803 0.729015 0.684497i \(-0.239978\pi\)
0.729015 + 0.684497i \(0.239978\pi\)
\(822\) −2.44183e109 −1.20233
\(823\) 2.24716e109 1.05716 0.528579 0.848884i \(-0.322725\pi\)
0.528579 + 0.848884i \(0.322725\pi\)
\(824\) 9.14170e108 0.410919
\(825\) −2.65609e109 −1.14083
\(826\) −1.73464e109 −0.711965
\(827\) −1.40884e109 −0.552591 −0.276296 0.961073i \(-0.589107\pi\)
−0.276296 + 0.961073i \(0.589107\pi\)
\(828\) −7.79292e108 −0.292121
\(829\) 4.51132e109 1.61625 0.808125 0.589011i \(-0.200483\pi\)
0.808125 + 0.589011i \(0.200483\pi\)
\(830\) 3.99381e108 0.136760
\(831\) −5.20941e109 −1.70510
\(832\) 3.48234e109 1.08955
\(833\) −3.63022e109 −1.08579
\(834\) 6.60706e109 1.88921
\(835\) 7.81260e108 0.213576
\(836\) 1.48383e109 0.387837
\(837\) −6.58907e107 −0.0164672
\(838\) 1.13788e109 0.271924
\(839\) 1.09964e109 0.251290 0.125645 0.992075i \(-0.459900\pi\)
0.125645 + 0.992075i \(0.459900\pi\)
\(840\) 2.91523e108 0.0637089
\(841\) −4.16913e109 −0.871355
\(842\) −5.14120e108 −0.102769
\(843\) 1.81976e109 0.347920
\(844\) −6.16347e108 −0.112715
\(845\) −2.19542e109 −0.384053
\(846\) 3.16509e109 0.529660
\(847\) −7.59288e108 −0.121557
\(848\) −6.19636e109 −0.949057
\(849\) −1.09235e110 −1.60075
\(850\) −1.02526e110 −1.43755
\(851\) 3.26675e109 0.438286
\(852\) 3.14315e109 0.403535
\(853\) 1.44601e110 1.77657 0.888287 0.459289i \(-0.151896\pi\)
0.888287 + 0.459289i \(0.151896\pi\)
\(854\) −6.89004e109 −0.810124
\(855\) −1.91642e109 −0.215656
\(856\) 2.90550e107 0.00312935
\(857\) −9.49435e109 −0.978778 −0.489389 0.872066i \(-0.662780\pi\)
−0.489389 + 0.872066i \(0.662780\pi\)
\(858\) 2.58068e110 2.54660
\(859\) 9.18306e109 0.867449 0.433724 0.901046i \(-0.357199\pi\)
0.433724 + 0.901046i \(0.357199\pi\)
\(860\) −2.27362e107 −0.00205601
\(861\) 7.71774e108 0.0668147
\(862\) −1.33309e110 −1.10493
\(863\) 1.19495e110 0.948299 0.474150 0.880444i \(-0.342756\pi\)
0.474150 + 0.880444i \(0.342756\pi\)
\(864\) 5.28168e108 0.0401335
\(865\) −1.13194e109 −0.0823609
\(866\) −3.59393e109 −0.250408
\(867\) 1.39794e110 0.932764
\(868\) 4.19209e108 0.0267880
\(869\) −8.74581e109 −0.535252
\(870\) 1.37593e109 0.0806538
\(871\) 1.84146e110 1.03391
\(872\) 8.62238e109 0.463723
\(873\) −2.36931e110 −1.22064
\(874\) −3.91206e110 −1.93075
\(875\) 2.37015e109 0.112066
\(876\) −3.01600e109 −0.136624
\(877\) −1.79278e110 −0.778112 −0.389056 0.921214i \(-0.627199\pi\)
−0.389056 + 0.921214i \(0.627199\pi\)
\(878\) −3.69188e110 −1.53534
\(879\) 3.82864e110 1.52568
\(880\) 3.73485e109 0.142618
\(881\) −1.61512e110 −0.591030 −0.295515 0.955338i \(-0.595491\pi\)
−0.295515 + 0.955338i \(0.595491\pi\)
\(882\) −2.58401e110 −0.906196
\(883\) 2.02977e110 0.682214 0.341107 0.940024i \(-0.389198\pi\)
0.341107 + 0.940024i \(0.389198\pi\)
\(884\) 2.24064e110 0.721791
\(885\) 1.00684e110 0.310876
\(886\) 6.50714e110 1.92586
\(887\) −1.52176e110 −0.431729 −0.215865 0.976423i \(-0.569257\pi\)
−0.215865 + 0.976423i \(0.569257\pi\)
\(888\) 1.71009e110 0.465085
\(889\) 2.73698e109 0.0713601
\(890\) −1.04733e110 −0.261794
\(891\) −3.64821e110 −0.874311
\(892\) 3.24523e109 0.0745698
\(893\) 3.57387e110 0.787424
\(894\) 7.51750e110 1.58824
\(895\) 3.37840e109 0.0684459
\(896\) 2.47822e110 0.481492
\(897\) −1.53039e111 −2.85158
\(898\) −6.60040e110 −1.17953
\(899\) −4.83925e109 −0.0829449
\(900\) −1.64151e110 −0.269866
\(901\) 6.44533e110 1.01640
\(902\) 7.50825e109 0.113578
\(903\) 1.91849e109 0.0278400
\(904\) 6.69271e110 0.931720
\(905\) −1.18636e110 −0.158451
\(906\) 9.33146e110 1.19575
\(907\) −4.71321e110 −0.579486 −0.289743 0.957104i \(-0.593570\pi\)
−0.289743 + 0.957104i \(0.593570\pi\)
\(908\) −2.18757e110 −0.258074
\(909\) 1.04648e111 1.18464
\(910\) −1.13973e110 −0.123809
\(911\) −1.43595e111 −1.49693 −0.748465 0.663174i \(-0.769209\pi\)
−0.748465 + 0.663174i \(0.769209\pi\)
\(912\) −2.69687e111 −2.69807
\(913\) −7.37441e110 −0.708065
\(914\) 1.23065e111 1.13410
\(915\) 3.99919e110 0.353737
\(916\) 6.90319e109 0.0586097
\(917\) −6.00288e110 −0.489226
\(918\) −1.33528e110 −0.104465
\(919\) 4.57653e110 0.343720 0.171860 0.985121i \(-0.445022\pi\)
0.171860 + 0.985121i \(0.445022\pi\)
\(920\) −1.68186e110 −0.121268
\(921\) 3.08275e111 2.13404
\(922\) −1.63073e111 −1.08386
\(923\) 3.00552e111 1.91803
\(924\) 2.20084e110 0.134862
\(925\) 6.88111e110 0.404896
\(926\) 1.20118e111 0.678728
\(927\) −8.91351e110 −0.483681
\(928\) 3.87906e110 0.202152
\(929\) 1.05558e111 0.528325 0.264163 0.964478i \(-0.414904\pi\)
0.264163 + 0.964478i \(0.414904\pi\)
\(930\) −1.08176e110 −0.0520022
\(931\) −2.91774e111 −1.34721
\(932\) −1.08785e110 −0.0482474
\(933\) −1.09514e111 −0.466559
\(934\) 5.77279e110 0.236253
\(935\) −3.88492e110 −0.152738
\(936\) −3.90083e111 −1.47337
\(937\) −8.13002e110 −0.295024 −0.147512 0.989060i \(-0.547126\pi\)
−0.147512 + 0.989060i \(0.547126\pi\)
\(938\) 6.98183e110 0.243424
\(939\) −4.30875e111 −1.44342
\(940\) −6.28202e109 −0.0202211
\(941\) 1.60666e111 0.496950 0.248475 0.968638i \(-0.420071\pi\)
0.248475 + 0.968638i \(0.420071\pi\)
\(942\) −8.16131e110 −0.242578
\(943\) −4.45253e110 −0.127180
\(944\) 6.89892e111 1.89379
\(945\) 1.52775e109 0.00403050
\(946\) 1.86642e110 0.0473251
\(947\) 1.93183e111 0.470809 0.235404 0.971898i \(-0.424359\pi\)
0.235404 + 0.971898i \(0.424359\pi\)
\(948\) −1.11006e111 −0.260036
\(949\) −2.88394e111 −0.649386
\(950\) −8.24039e111 −1.78366
\(951\) 1.11482e112 2.31971
\(952\) −2.07780e111 −0.415640
\(953\) 4.48955e111 0.863414 0.431707 0.902014i \(-0.357912\pi\)
0.431707 + 0.902014i \(0.357912\pi\)
\(954\) 4.58783e111 0.848287
\(955\) 8.24134e110 0.146511
\(956\) −1.19992e111 −0.205108
\(957\) −2.54060e111 −0.417579
\(958\) 1.08336e112 1.71224
\(959\) −1.99125e111 −0.302641
\(960\) −7.66353e110 −0.112010
\(961\) −6.73375e111 −0.946521
\(962\) −6.68572e111 −0.903823
\(963\) −2.83297e109 −0.00368346
\(964\) −3.76229e110 −0.0470504
\(965\) −2.14432e110 −0.0257938
\(966\) −5.80242e111 −0.671377
\(967\) −1.19520e112 −1.33030 −0.665148 0.746712i \(-0.731631\pi\)
−0.665148 + 0.746712i \(0.731631\pi\)
\(968\) 2.29312e111 0.245528
\(969\) 2.80523e112 2.88952
\(970\) 2.09068e111 0.207180
\(971\) −2.02515e112 −1.93079 −0.965395 0.260790i \(-0.916017\pi\)
−0.965395 + 0.260790i \(0.916017\pi\)
\(972\) −4.40521e111 −0.404093
\(973\) 5.38788e111 0.475539
\(974\) −4.83371e111 −0.410506
\(975\) −3.22362e112 −2.63434
\(976\) 2.74027e112 2.15489
\(977\) −4.99871e111 −0.378279 −0.189140 0.981950i \(-0.560570\pi\)
−0.189140 + 0.981950i \(0.560570\pi\)
\(978\) 2.14016e112 1.55862
\(979\) 1.93386e112 1.35542
\(980\) 5.12870e110 0.0345963
\(981\) −8.40714e111 −0.545834
\(982\) −1.20944e112 −0.755797
\(983\) −5.82663e111 −0.350478 −0.175239 0.984526i \(-0.556070\pi\)
−0.175239 + 0.984526i \(0.556070\pi\)
\(984\) −2.33083e111 −0.134956
\(985\) −1.28447e111 −0.0715922
\(986\) −9.80678e111 −0.526189
\(987\) 5.30081e111 0.273810
\(988\) 1.80088e112 0.895572
\(989\) −1.10682e111 −0.0529928
\(990\) −2.76531e111 −0.127475
\(991\) 5.49657e111 0.243966 0.121983 0.992532i \(-0.461075\pi\)
0.121983 + 0.992532i \(0.461075\pi\)
\(992\) −3.04973e111 −0.130339
\(993\) 4.56704e112 1.87948
\(994\) 1.13953e112 0.451583
\(995\) 6.07195e111 0.231720
\(996\) −9.35996e111 −0.343992
\(997\) 1.26397e112 0.447372 0.223686 0.974661i \(-0.428191\pi\)
0.223686 + 0.974661i \(0.428191\pi\)
\(998\) −3.30635e112 −1.12708
\(999\) 8.96185e110 0.0294233
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1.76.a.a.1.5 6
3.2 odd 2 9.76.a.c.1.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.76.a.a.1.5 6 1.1 even 1 trivial
9.76.a.c.1.2 6 3.2 odd 2