Properties

Label 1.52.a.a.1.4
Level $1$
Weight $52$
Character 1.1
Self dual yes
Analytic conductor $16.473$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 52 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(16.4731353414\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \(x^{4} - 2 x^{3} - 495735060514 x^{2} - 23954614981416598 x + 48979992255622025570313\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{23}\cdot 3^{10}\cdot 5^{3}\cdot 7^{2}\cdot 13\cdot 17 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(324949.\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+8.12369e7 q^{2} -2.41142e12 q^{3} +4.34763e15 q^{4} +2.42754e17 q^{5} -1.95896e20 q^{6} +2.85586e21 q^{7} +1.70259e23 q^{8} +3.66124e24 q^{9} +O(q^{10})\) \(q+8.12369e7 q^{2} -2.41142e12 q^{3} +4.34763e15 q^{4} +2.42754e17 q^{5} -1.95896e20 q^{6} +2.85586e21 q^{7} +1.70259e23 q^{8} +3.66124e24 q^{9} +1.97206e25 q^{10} +3.52088e26 q^{11} -1.04840e28 q^{12} +3.67432e28 q^{13} +2.32001e29 q^{14} -5.85381e29 q^{15} +4.04130e30 q^{16} -6.54277e30 q^{17} +2.97427e32 q^{18} +2.55736e32 q^{19} +1.05541e33 q^{20} -6.88666e33 q^{21} +2.86025e34 q^{22} -1.69990e34 q^{23} -4.10565e35 q^{24} -3.85160e35 q^{25} +2.98490e36 q^{26} -3.63531e36 q^{27} +1.24162e37 q^{28} +3.94490e36 q^{29} -4.75545e37 q^{30} +9.38800e37 q^{31} -5.50861e37 q^{32} -8.49031e38 q^{33} -5.31514e38 q^{34} +6.93270e38 q^{35} +1.59177e40 q^{36} -1.74413e40 q^{37} +2.07752e40 q^{38} -8.86032e40 q^{39} +4.13310e40 q^{40} +2.14671e41 q^{41} -5.59451e41 q^{42} -2.13159e41 q^{43} +1.53075e42 q^{44} +8.88780e41 q^{45} -1.38095e42 q^{46} +4.04105e42 q^{47} -9.74526e42 q^{48} -4.43335e42 q^{49} -3.12892e43 q^{50} +1.57773e43 q^{51} +1.59746e44 q^{52} -4.94974e42 q^{53} -2.95321e44 q^{54} +8.54708e43 q^{55} +4.86235e44 q^{56} -6.16687e44 q^{57} +3.20472e44 q^{58} -1.20757e45 q^{59} -2.54502e45 q^{60} +2.20569e45 q^{61} +7.62652e45 q^{62} +1.04560e46 q^{63} -1.35752e46 q^{64} +8.91957e45 q^{65} -6.89726e46 q^{66} +4.56801e46 q^{67} -2.84456e46 q^{68} +4.09917e46 q^{69} +5.63191e46 q^{70} -1.91444e47 q^{71} +6.23358e47 q^{72} -8.49448e46 q^{73} -1.41688e48 q^{74} +9.28780e47 q^{75} +1.11185e48 q^{76} +1.00551e48 q^{77} -7.19785e48 q^{78} +2.35655e48 q^{79} +9.81042e47 q^{80} +8.81070e47 q^{81} +1.74392e49 q^{82} +5.38960e48 q^{83} -2.99406e49 q^{84} -1.58828e48 q^{85} -1.73164e49 q^{86} -9.51281e48 q^{87} +5.99461e49 q^{88} -7.58432e49 q^{89} +7.22017e49 q^{90} +1.04933e50 q^{91} -7.39055e49 q^{92} -2.26384e50 q^{93} +3.28282e50 q^{94} +6.20810e49 q^{95} +1.32835e50 q^{96} -8.33376e50 q^{97} -3.60151e50 q^{98} +1.28908e51 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 32756040q^{2} + 403863773040q^{3} + 7978103470875712q^{4} + 1214113112967557880q^{5} - \)\(10\!\cdots\!92\)\(q^{6} + \)\(65\!\cdots\!00\)\(q^{7} - \)\(13\!\cdots\!20\)\(q^{8} + \)\(50\!\cdots\!28\)\(q^{9} + O(q^{10}) \) \( 4q + 32756040q^{2} + 403863773040q^{3} + 7978103470875712q^{4} + 1214113112967557880q^{5} - \)\(10\!\cdots\!92\)\(q^{6} + \)\(65\!\cdots\!00\)\(q^{7} - \)\(13\!\cdots\!20\)\(q^{8} + \)\(50\!\cdots\!28\)\(q^{9} - \)\(26\!\cdots\!20\)\(q^{10} + \)\(35\!\cdots\!48\)\(q^{11} - \)\(49\!\cdots\!20\)\(q^{12} + \)\(30\!\cdots\!80\)\(q^{13} + \)\(11\!\cdots\!24\)\(q^{14} + \)\(14\!\cdots\!60\)\(q^{15} + \)\(13\!\cdots\!44\)\(q^{16} + \)\(48\!\cdots\!20\)\(q^{17} + \)\(73\!\cdots\!40\)\(q^{18} + \)\(81\!\cdots\!80\)\(q^{19} + \)\(66\!\cdots\!40\)\(q^{20} + \)\(31\!\cdots\!48\)\(q^{21} - \)\(34\!\cdots\!20\)\(q^{22} - \)\(54\!\cdots\!80\)\(q^{23} - \)\(87\!\cdots\!60\)\(q^{24} - \)\(57\!\cdots\!00\)\(q^{25} + \)\(15\!\cdots\!48\)\(q^{26} + \)\(36\!\cdots\!20\)\(q^{27} + \)\(34\!\cdots\!80\)\(q^{28} + \)\(24\!\cdots\!20\)\(q^{29} - \)\(32\!\cdots\!40\)\(q^{30} - \)\(74\!\cdots\!72\)\(q^{31} - \)\(69\!\cdots\!60\)\(q^{32} - \)\(17\!\cdots\!20\)\(q^{33} + \)\(59\!\cdots\!64\)\(q^{34} + \)\(54\!\cdots\!80\)\(q^{35} + \)\(12\!\cdots\!84\)\(q^{36} + \)\(92\!\cdots\!60\)\(q^{37} + \)\(42\!\cdots\!20\)\(q^{38} - \)\(11\!\cdots\!04\)\(q^{39} - \)\(26\!\cdots\!00\)\(q^{40} + \)\(14\!\cdots\!68\)\(q^{41} - \)\(39\!\cdots\!80\)\(q^{42} - \)\(38\!\cdots\!00\)\(q^{43} + \)\(39\!\cdots\!44\)\(q^{44} + \)\(25\!\cdots\!60\)\(q^{45} - \)\(68\!\cdots\!12\)\(q^{46} + \)\(70\!\cdots\!80\)\(q^{47} - \)\(19\!\cdots\!80\)\(q^{48} - \)\(21\!\cdots\!28\)\(q^{49} - \)\(65\!\cdots\!00\)\(q^{50} + \)\(69\!\cdots\!28\)\(q^{51} + \)\(20\!\cdots\!00\)\(q^{52} - \)\(46\!\cdots\!60\)\(q^{53} + \)\(29\!\cdots\!80\)\(q^{54} + \)\(28\!\cdots\!60\)\(q^{55} - \)\(71\!\cdots\!80\)\(q^{56} - \)\(88\!\cdots\!60\)\(q^{57} - \)\(32\!\cdots\!20\)\(q^{58} + \)\(11\!\cdots\!40\)\(q^{59} + \)\(55\!\cdots\!80\)\(q^{60} + \)\(34\!\cdots\!48\)\(q^{61} + \)\(96\!\cdots\!80\)\(q^{62} + \)\(21\!\cdots\!60\)\(q^{63} - \)\(34\!\cdots\!28\)\(q^{64} + \)\(10\!\cdots\!60\)\(q^{65} - \)\(15\!\cdots\!04\)\(q^{66} + \)\(30\!\cdots\!20\)\(q^{67} - \)\(92\!\cdots\!60\)\(q^{68} + \)\(15\!\cdots\!76\)\(q^{69} - \)\(12\!\cdots\!20\)\(q^{70} + \)\(39\!\cdots\!88\)\(q^{71} + \)\(50\!\cdots\!60\)\(q^{72} + \)\(10\!\cdots\!20\)\(q^{73} - \)\(24\!\cdots\!56\)\(q^{74} + \)\(72\!\cdots\!00\)\(q^{75} - \)\(19\!\cdots\!60\)\(q^{76} + \)\(13\!\cdots\!00\)\(q^{77} - \)\(96\!\cdots\!00\)\(q^{78} + \)\(40\!\cdots\!20\)\(q^{79} + \)\(65\!\cdots\!80\)\(q^{80} + \)\(15\!\cdots\!44\)\(q^{81} + \)\(26\!\cdots\!80\)\(q^{82} + \)\(10\!\cdots\!60\)\(q^{83} - \)\(18\!\cdots\!56\)\(q^{84} - \)\(22\!\cdots\!20\)\(q^{85} - \)\(43\!\cdots\!32\)\(q^{86} - \)\(62\!\cdots\!40\)\(q^{87} - \)\(25\!\cdots\!40\)\(q^{88} - \)\(90\!\cdots\!40\)\(q^{89} + \)\(31\!\cdots\!60\)\(q^{90} + \)\(10\!\cdots\!88\)\(q^{91} + \)\(19\!\cdots\!20\)\(q^{92} - \)\(31\!\cdots\!20\)\(q^{93} + \)\(63\!\cdots\!84\)\(q^{94} - \)\(41\!\cdots\!00\)\(q^{95} - \)\(24\!\cdots\!32\)\(q^{96} - \)\(13\!\cdots\!20\)\(q^{97} - \)\(31\!\cdots\!80\)\(q^{98} - \)\(17\!\cdots\!64\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 8.12369e7 1.71194 0.855970 0.517026i \(-0.172961\pi\)
0.855970 + 0.517026i \(0.172961\pi\)
\(3\) −2.41142e12 −1.64316 −0.821581 0.570092i \(-0.806907\pi\)
−0.821581 + 0.570092i \(0.806907\pi\)
\(4\) 4.34763e15 1.93074
\(5\) 2.42754e17 0.364277 0.182138 0.983273i \(-0.441698\pi\)
0.182138 + 0.983273i \(0.441698\pi\)
\(6\) −1.95896e20 −2.81299
\(7\) 2.85586e21 0.804889 0.402445 0.915444i \(-0.368161\pi\)
0.402445 + 0.915444i \(0.368161\pi\)
\(8\) 1.70259e23 1.59336
\(9\) 3.66124e24 1.69998
\(10\) 1.97206e25 0.623620
\(11\) 3.52088e26 0.979801 0.489900 0.871778i \(-0.337033\pi\)
0.489900 + 0.871778i \(0.337033\pi\)
\(12\) −1.04840e28 −3.17251
\(13\) 3.67432e28 1.44418 0.722091 0.691798i \(-0.243181\pi\)
0.722091 + 0.691798i \(0.243181\pi\)
\(14\) 2.32001e29 1.37792
\(15\) −5.85381e29 −0.598565
\(16\) 4.04130e30 0.797006
\(17\) −6.54277e30 −0.274988 −0.137494 0.990503i \(-0.543905\pi\)
−0.137494 + 0.990503i \(0.543905\pi\)
\(18\) 2.97427e32 2.91026
\(19\) 2.55736e32 0.630341 0.315170 0.949035i \(-0.397938\pi\)
0.315170 + 0.949035i \(0.397938\pi\)
\(20\) 1.05541e33 0.703322
\(21\) −6.88666e33 −1.32256
\(22\) 2.86025e34 1.67736
\(23\) −1.69990e34 −0.320896 −0.160448 0.987044i \(-0.551294\pi\)
−0.160448 + 0.987044i \(0.551294\pi\)
\(24\) −4.10565e35 −2.61815
\(25\) −3.85160e35 −0.867302
\(26\) 2.98490e36 2.47235
\(27\) −3.63531e36 −1.15018
\(28\) 1.24162e37 1.55403
\(29\) 3.94490e36 0.201784 0.100892 0.994897i \(-0.467830\pi\)
0.100892 + 0.994897i \(0.467830\pi\)
\(30\) −4.75545e37 −1.02471
\(31\) 9.38800e37 0.876698 0.438349 0.898805i \(-0.355563\pi\)
0.438349 + 0.898805i \(0.355563\pi\)
\(32\) −5.50861e37 −0.228938
\(33\) −8.49031e38 −1.60997
\(34\) −5.31514e38 −0.470763
\(35\) 6.93270e38 0.293202
\(36\) 1.59177e40 3.28221
\(37\) −1.74413e40 −1.78828 −0.894140 0.447787i \(-0.852212\pi\)
−0.894140 + 0.447787i \(0.852212\pi\)
\(38\) 2.07752e40 1.07911
\(39\) −8.86032e40 −2.37302
\(40\) 4.13310e40 0.580425
\(41\) 2.14671e41 1.60615 0.803074 0.595880i \(-0.203197\pi\)
0.803074 + 0.595880i \(0.203197\pi\)
\(42\) −5.59451e41 −2.26415
\(43\) −2.13159e41 −0.473432 −0.236716 0.971579i \(-0.576071\pi\)
−0.236716 + 0.971579i \(0.576071\pi\)
\(44\) 1.53075e42 1.89174
\(45\) 8.88780e41 0.619263
\(46\) −1.38095e42 −0.549354
\(47\) 4.04105e42 0.928963 0.464481 0.885583i \(-0.346241\pi\)
0.464481 + 0.885583i \(0.346241\pi\)
\(48\) −9.74526e42 −1.30961
\(49\) −4.43335e42 −0.352153
\(50\) −3.12892e43 −1.48477
\(51\) 1.57773e43 0.451850
\(52\) 1.59746e44 2.78833
\(53\) −4.94974e42 −0.0531555 −0.0265777 0.999647i \(-0.508461\pi\)
−0.0265777 + 0.999647i \(0.508461\pi\)
\(54\) −2.95321e44 −1.96904
\(55\) 8.54708e43 0.356919
\(56\) 4.86235e44 1.28248
\(57\) −6.16687e44 −1.03575
\(58\) 3.20472e44 0.345443
\(59\) −1.20757e45 −0.841752 −0.420876 0.907118i \(-0.638277\pi\)
−0.420876 + 0.907118i \(0.638277\pi\)
\(60\) −2.54502e45 −1.15567
\(61\) 2.20569e45 0.657104 0.328552 0.944486i \(-0.393439\pi\)
0.328552 + 0.944486i \(0.393439\pi\)
\(62\) 7.62652e45 1.50085
\(63\) 1.04560e46 1.36830
\(64\) −1.35752e46 −1.18893
\(65\) 8.91957e45 0.526082
\(66\) −6.89726e46 −2.75617
\(67\) 4.56801e46 1.24400 0.621999 0.783018i \(-0.286321\pi\)
0.621999 + 0.783018i \(0.286321\pi\)
\(68\) −2.84456e46 −0.530930
\(69\) 4.09917e46 0.527284
\(70\) 5.63191e46 0.501945
\(71\) −1.91444e47 −1.18838 −0.594189 0.804326i \(-0.702527\pi\)
−0.594189 + 0.804326i \(0.702527\pi\)
\(72\) 6.23358e47 2.70869
\(73\) −8.49448e46 −0.259659 −0.129830 0.991536i \(-0.541443\pi\)
−0.129830 + 0.991536i \(0.541443\pi\)
\(74\) −1.41688e48 −3.06143
\(75\) 9.28780e47 1.42512
\(76\) 1.11185e48 1.21702
\(77\) 1.00551e48 0.788631
\(78\) −7.19785e48 −4.06247
\(79\) 2.35655e48 0.961139 0.480570 0.876957i \(-0.340430\pi\)
0.480570 + 0.876957i \(0.340430\pi\)
\(80\) 9.81042e47 0.290331
\(81\) 8.81070e47 0.189951
\(82\) 1.74392e49 2.74963
\(83\) 5.38960e48 0.623828 0.311914 0.950110i \(-0.399030\pi\)
0.311914 + 0.950110i \(0.399030\pi\)
\(84\) −2.99406e49 −2.55352
\(85\) −1.58828e48 −0.100172
\(86\) −1.73164e49 −0.810487
\(87\) −9.51281e48 −0.331564
\(88\) 5.99461e49 1.56118
\(89\) −7.58432e49 −1.48071 −0.740357 0.672213i \(-0.765344\pi\)
−0.740357 + 0.672213i \(0.765344\pi\)
\(90\) 7.22017e49 1.06014
\(91\) 1.04933e50 1.16241
\(92\) −7.39055e49 −0.619565
\(93\) −2.26384e50 −1.44056
\(94\) 3.28282e50 1.59033
\(95\) 6.20810e49 0.229619
\(96\) 1.32835e50 0.376182
\(97\) −8.33376e50 −1.81201 −0.906007 0.423263i \(-0.860885\pi\)
−0.906007 + 0.423263i \(0.860885\pi\)
\(98\) −3.60151e50 −0.602865
\(99\) 1.28908e51 1.66564
\(100\) −1.67453e51 −1.67453
\(101\) 3.60874e50 0.280001 0.140001 0.990151i \(-0.455290\pi\)
0.140001 + 0.990151i \(0.455290\pi\)
\(102\) 1.28170e51 0.773540
\(103\) −5.92261e50 −0.278717 −0.139359 0.990242i \(-0.544504\pi\)
−0.139359 + 0.990242i \(0.544504\pi\)
\(104\) 6.25586e51 2.30111
\(105\) −1.67176e51 −0.481779
\(106\) −4.02102e50 −0.0909989
\(107\) −2.68636e51 −0.478495 −0.239247 0.970959i \(-0.576901\pi\)
−0.239247 + 0.970959i \(0.576901\pi\)
\(108\) −1.58050e52 −2.22069
\(109\) −1.08273e52 −1.20267 −0.601335 0.798997i \(-0.705364\pi\)
−0.601335 + 0.798997i \(0.705364\pi\)
\(110\) 6.94338e51 0.611023
\(111\) 4.20583e52 2.93843
\(112\) 1.15414e52 0.641502
\(113\) −1.18691e52 −0.525915 −0.262958 0.964807i \(-0.584698\pi\)
−0.262958 + 0.964807i \(0.584698\pi\)
\(114\) −5.00977e52 −1.77314
\(115\) −4.12658e51 −0.116895
\(116\) 1.71510e52 0.389592
\(117\) 1.34526e53 2.45508
\(118\) −9.80988e52 −1.44103
\(119\) −1.86852e52 −0.221335
\(120\) −9.96663e52 −0.953733
\(121\) −5.16394e51 −0.0399903
\(122\) 1.79184e53 1.12492
\(123\) −5.17662e53 −2.63916
\(124\) 4.08156e53 1.69267
\(125\) −2.01304e53 −0.680215
\(126\) 8.49410e53 2.34244
\(127\) 2.91976e53 0.658190 0.329095 0.944297i \(-0.393256\pi\)
0.329095 + 0.944297i \(0.393256\pi\)
\(128\) −9.78766e53 −1.80644
\(129\) 5.14015e53 0.777925
\(130\) 7.24598e53 0.900620
\(131\) −1.12031e54 −1.14530 −0.572651 0.819799i \(-0.694085\pi\)
−0.572651 + 0.819799i \(0.694085\pi\)
\(132\) −3.69127e54 −3.10843
\(133\) 7.30346e53 0.507355
\(134\) 3.71091e54 2.12965
\(135\) −8.82487e53 −0.418984
\(136\) −1.11396e54 −0.438156
\(137\) 3.16309e54 1.03214 0.516068 0.856548i \(-0.327395\pi\)
0.516068 + 0.856548i \(0.327395\pi\)
\(138\) 3.33004e54 0.902678
\(139\) −8.65660e53 −0.195196 −0.0975978 0.995226i \(-0.531116\pi\)
−0.0975978 + 0.995226i \(0.531116\pi\)
\(140\) 3.01408e54 0.566097
\(141\) −9.74464e54 −1.52644
\(142\) −1.55523e55 −2.03443
\(143\) 1.29368e55 1.41501
\(144\) 1.47962e55 1.35489
\(145\) 9.57641e53 0.0735053
\(146\) −6.90065e54 −0.444521
\(147\) 1.06906e55 0.578645
\(148\) −7.58285e55 −3.45270
\(149\) −6.45813e54 −0.247661 −0.123830 0.992303i \(-0.539518\pi\)
−0.123830 + 0.992303i \(0.539518\pi\)
\(150\) 7.54512e55 2.43972
\(151\) 2.64453e55 0.721832 0.360916 0.932598i \(-0.382464\pi\)
0.360916 + 0.932598i \(0.382464\pi\)
\(152\) 4.35414e55 1.00436
\(153\) −2.39546e55 −0.467474
\(154\) 8.16847e55 1.35009
\(155\) 2.27898e55 0.319361
\(156\) −3.85214e56 −4.58168
\(157\) −1.74550e55 −0.176392 −0.0881962 0.996103i \(-0.528110\pi\)
−0.0881962 + 0.996103i \(0.528110\pi\)
\(158\) 1.91439e56 1.64541
\(159\) 1.19359e55 0.0873430
\(160\) −1.33724e55 −0.0833967
\(161\) −4.85467e55 −0.258286
\(162\) 7.15754e55 0.325185
\(163\) −2.44447e56 −0.949296 −0.474648 0.880176i \(-0.657425\pi\)
−0.474648 + 0.880176i \(0.657425\pi\)
\(164\) 9.33311e56 3.10105
\(165\) −2.06106e56 −0.586475
\(166\) 4.37834e56 1.06796
\(167\) −7.65512e56 −1.60207 −0.801036 0.598616i \(-0.795718\pi\)
−0.801036 + 0.598616i \(0.795718\pi\)
\(168\) −1.17251e57 −2.10732
\(169\) 7.02756e56 1.08566
\(170\) −1.29027e56 −0.171488
\(171\) 9.36311e56 1.07157
\(172\) −9.26736e56 −0.914073
\(173\) 6.79321e56 0.577963 0.288981 0.957335i \(-0.406683\pi\)
0.288981 + 0.957335i \(0.406683\pi\)
\(174\) −7.72791e56 −0.567618
\(175\) −1.09996e57 −0.698082
\(176\) 1.42289e57 0.780907
\(177\) 2.91194e57 1.38313
\(178\) −6.16126e57 −2.53489
\(179\) 2.98876e57 1.06596 0.532978 0.846129i \(-0.321073\pi\)
0.532978 + 0.846129i \(0.321073\pi\)
\(180\) 3.86409e57 1.19563
\(181\) −1.29245e57 −0.347223 −0.173611 0.984814i \(-0.555544\pi\)
−0.173611 + 0.984814i \(0.555544\pi\)
\(182\) 8.52446e57 1.98997
\(183\) −5.31885e57 −1.07973
\(184\) −2.89423e57 −0.511304
\(185\) −4.23395e57 −0.651429
\(186\) −1.83907e58 −2.46614
\(187\) −2.30363e57 −0.269434
\(188\) 1.75690e58 1.79358
\(189\) −1.03819e58 −0.925767
\(190\) 5.04327e57 0.393093
\(191\) 2.79327e58 1.90442 0.952209 0.305446i \(-0.0988057\pi\)
0.952209 + 0.305446i \(0.0988057\pi\)
\(192\) 3.27355e58 1.95361
\(193\) 1.88817e58 0.987027 0.493514 0.869738i \(-0.335712\pi\)
0.493514 + 0.869738i \(0.335712\pi\)
\(194\) −6.77008e58 −3.10206
\(195\) −2.15088e58 −0.864437
\(196\) −1.92746e58 −0.679915
\(197\) −3.18961e58 −0.988209 −0.494104 0.869403i \(-0.664504\pi\)
−0.494104 + 0.869403i \(0.664504\pi\)
\(198\) 1.04721e59 2.85148
\(199\) 4.26943e58 1.02239 0.511195 0.859465i \(-0.329203\pi\)
0.511195 + 0.859465i \(0.329203\pi\)
\(200\) −6.55768e58 −1.38193
\(201\) −1.10154e59 −2.04409
\(202\) 2.93163e58 0.479346
\(203\) 1.12661e58 0.162414
\(204\) 6.85941e58 0.872403
\(205\) 5.21123e58 0.585082
\(206\) −4.81134e58 −0.477147
\(207\) −6.22374e58 −0.545517
\(208\) 1.48490e59 1.15102
\(209\) 9.00417e58 0.617609
\(210\) −1.35809e59 −0.824776
\(211\) −1.08128e59 −0.581748 −0.290874 0.956761i \(-0.593946\pi\)
−0.290874 + 0.956761i \(0.593946\pi\)
\(212\) −2.15197e58 −0.102629
\(213\) 4.61652e59 1.95270
\(214\) −2.18231e59 −0.819154
\(215\) −5.17452e58 −0.172460
\(216\) −6.18944e59 −1.83266
\(217\) 2.68108e59 0.705645
\(218\) −8.79580e59 −2.05890
\(219\) 2.04837e59 0.426662
\(220\) 3.71596e59 0.689116
\(221\) −2.40402e59 −0.397133
\(222\) 3.41669e60 5.03042
\(223\) −6.98254e59 −0.916726 −0.458363 0.888765i \(-0.651564\pi\)
−0.458363 + 0.888765i \(0.651564\pi\)
\(224\) −1.57318e59 −0.184270
\(225\) −1.41016e60 −1.47440
\(226\) −9.64205e59 −0.900335
\(227\) 1.84393e60 1.53846 0.769228 0.638975i \(-0.220641\pi\)
0.769228 + 0.638975i \(0.220641\pi\)
\(228\) −2.68113e60 −1.99976
\(229\) 3.39685e59 0.226606 0.113303 0.993560i \(-0.463857\pi\)
0.113303 + 0.993560i \(0.463857\pi\)
\(230\) −3.35231e59 −0.200117
\(231\) −2.42471e60 −1.29585
\(232\) 6.71655e59 0.321516
\(233\) −1.17691e60 −0.504854 −0.252427 0.967616i \(-0.581229\pi\)
−0.252427 + 0.967616i \(0.581229\pi\)
\(234\) 1.09284e61 4.20295
\(235\) 9.80980e59 0.338400
\(236\) −5.25005e60 −1.62520
\(237\) −5.68263e60 −1.57931
\(238\) −1.51793e60 −0.378912
\(239\) 5.07807e60 1.13907 0.569537 0.821966i \(-0.307122\pi\)
0.569537 + 0.821966i \(0.307122\pi\)
\(240\) −2.36570e60 −0.477060
\(241\) 4.94984e60 0.897752 0.448876 0.893594i \(-0.351824\pi\)
0.448876 + 0.893594i \(0.351824\pi\)
\(242\) −4.19503e59 −0.0684609
\(243\) 5.70472e60 0.838059
\(244\) 9.58954e60 1.26870
\(245\) −1.07621e60 −0.128281
\(246\) −4.20532e61 −4.51808
\(247\) 9.39657e60 0.910327
\(248\) 1.59839e61 1.39690
\(249\) −1.29966e61 −1.02505
\(250\) −1.63533e61 −1.16449
\(251\) −1.18124e60 −0.0759731 −0.0379866 0.999278i \(-0.512094\pi\)
−0.0379866 + 0.999278i \(0.512094\pi\)
\(252\) 4.54587e61 2.64182
\(253\) −5.98515e60 −0.314414
\(254\) 2.37192e61 1.12678
\(255\) 3.83001e60 0.164598
\(256\) −4.89432e61 −1.90359
\(257\) 2.72008e61 0.957827 0.478914 0.877862i \(-0.341031\pi\)
0.478914 + 0.877862i \(0.341031\pi\)
\(258\) 4.17570e61 1.33176
\(259\) −4.98099e61 −1.43937
\(260\) 3.87790e61 1.01572
\(261\) 1.44432e61 0.343029
\(262\) −9.10105e61 −1.96069
\(263\) −2.48007e61 −0.484834 −0.242417 0.970172i \(-0.577940\pi\)
−0.242417 + 0.970172i \(0.577940\pi\)
\(264\) −1.44555e62 −2.56527
\(265\) −1.20157e60 −0.0193633
\(266\) 5.93310e61 0.868560
\(267\) 1.82890e62 2.43305
\(268\) 1.98600e62 2.40183
\(269\) −6.54289e61 −0.719592 −0.359796 0.933031i \(-0.617154\pi\)
−0.359796 + 0.933031i \(0.617154\pi\)
\(270\) −7.16905e61 −0.717275
\(271\) −6.85359e60 −0.0624024 −0.0312012 0.999513i \(-0.509933\pi\)
−0.0312012 + 0.999513i \(0.509933\pi\)
\(272\) −2.64413e61 −0.219167
\(273\) −2.53038e62 −1.91002
\(274\) 2.56959e62 1.76695
\(275\) −1.35610e62 −0.849784
\(276\) 1.78217e62 1.01805
\(277\) −2.43203e62 −1.26688 −0.633438 0.773793i \(-0.718357\pi\)
−0.633438 + 0.773793i \(0.718357\pi\)
\(278\) −7.03235e61 −0.334163
\(279\) 3.43717e62 1.49037
\(280\) 1.18035e62 0.467178
\(281\) 2.21655e62 0.801062 0.400531 0.916283i \(-0.368826\pi\)
0.400531 + 0.916283i \(0.368826\pi\)
\(282\) −7.91624e62 −2.61317
\(283\) 1.63167e62 0.492127 0.246063 0.969254i \(-0.420863\pi\)
0.246063 + 0.969254i \(0.420863\pi\)
\(284\) −8.32329e62 −2.29444
\(285\) −1.49703e62 −0.377300
\(286\) 1.05095e63 2.42241
\(287\) 6.13070e62 1.29277
\(288\) −2.01683e62 −0.389190
\(289\) −5.23295e62 −0.924381
\(290\) 7.77958e61 0.125837
\(291\) 2.00962e63 2.97743
\(292\) −3.69309e62 −0.501334
\(293\) −7.35742e62 −0.915380 −0.457690 0.889112i \(-0.651323\pi\)
−0.457690 + 0.889112i \(0.651323\pi\)
\(294\) 8.68475e62 0.990605
\(295\) −2.93141e62 −0.306631
\(296\) −2.96954e63 −2.84938
\(297\) −1.27995e63 −1.12695
\(298\) −5.24638e62 −0.423980
\(299\) −6.24599e62 −0.463432
\(300\) 4.03800e63 2.75153
\(301\) −6.08751e62 −0.381060
\(302\) 2.14833e63 1.23573
\(303\) −8.70217e62 −0.460088
\(304\) 1.03351e63 0.502386
\(305\) 5.35441e62 0.239368
\(306\) −1.94600e63 −0.800288
\(307\) −2.33959e63 −0.885341 −0.442671 0.896684i \(-0.645969\pi\)
−0.442671 + 0.896684i \(0.645969\pi\)
\(308\) 4.37160e63 1.52264
\(309\) 1.42819e63 0.457977
\(310\) 1.85137e63 0.546726
\(311\) 5.85752e63 1.59340 0.796698 0.604378i \(-0.206578\pi\)
0.796698 + 0.604378i \(0.206578\pi\)
\(312\) −1.50855e64 −3.78109
\(313\) −5.58306e63 −1.28971 −0.644855 0.764305i \(-0.723082\pi\)
−0.644855 + 0.764305i \(0.723082\pi\)
\(314\) −1.41799e63 −0.301973
\(315\) 2.53823e63 0.498438
\(316\) 1.02454e64 1.85571
\(317\) −2.94076e63 −0.491414 −0.245707 0.969344i \(-0.579020\pi\)
−0.245707 + 0.969344i \(0.579020\pi\)
\(318\) 9.69634e62 0.149526
\(319\) 1.38895e63 0.197708
\(320\) −3.29544e63 −0.433101
\(321\) 6.47792e63 0.786244
\(322\) −3.94379e63 −0.442169
\(323\) −1.67322e63 −0.173336
\(324\) 3.83057e63 0.366746
\(325\) −1.41520e64 −1.25254
\(326\) −1.98582e64 −1.62514
\(327\) 2.61092e64 1.97618
\(328\) 3.65497e64 2.55918
\(329\) 1.15406e64 0.747712
\(330\) −1.67434e64 −1.00401
\(331\) 8.27822e63 0.459540 0.229770 0.973245i \(-0.426203\pi\)
0.229770 + 0.973245i \(0.426203\pi\)
\(332\) 2.34320e64 1.20445
\(333\) −6.38568e64 −3.04004
\(334\) −6.21878e64 −2.74265
\(335\) 1.10890e64 0.453159
\(336\) −2.78311e64 −1.05409
\(337\) 2.46670e63 0.0866070 0.0433035 0.999062i \(-0.486212\pi\)
0.0433035 + 0.999062i \(0.486212\pi\)
\(338\) 5.70897e64 1.85858
\(339\) 2.86212e64 0.864164
\(340\) −6.90527e63 −0.193405
\(341\) 3.30540e64 0.858989
\(342\) 7.60630e64 1.83446
\(343\) −4.86141e64 −1.08833
\(344\) −3.62922e64 −0.754350
\(345\) 9.95091e63 0.192077
\(346\) 5.51860e64 0.989437
\(347\) 1.55920e64 0.259717 0.129858 0.991533i \(-0.458548\pi\)
0.129858 + 0.991533i \(0.458548\pi\)
\(348\) −4.13582e64 −0.640163
\(349\) −5.23164e64 −0.752644 −0.376322 0.926489i \(-0.622811\pi\)
−0.376322 + 0.926489i \(0.622811\pi\)
\(350\) −8.93573e64 −1.19507
\(351\) −1.33573e65 −1.66107
\(352\) −1.93951e64 −0.224313
\(353\) 1.78259e65 1.91777 0.958885 0.283795i \(-0.0915934\pi\)
0.958885 + 0.283795i \(0.0915934\pi\)
\(354\) 2.36557e65 2.36784
\(355\) −4.64739e64 −0.432898
\(356\) −3.29738e65 −2.85887
\(357\) 4.50578e64 0.363689
\(358\) 2.42798e65 1.82485
\(359\) −1.48533e65 −1.03972 −0.519858 0.854253i \(-0.674015\pi\)
−0.519858 + 0.854253i \(0.674015\pi\)
\(360\) 1.51323e65 0.986711
\(361\) −9.92004e64 −0.602670
\(362\) −1.04994e65 −0.594425
\(363\) 1.24524e64 0.0657105
\(364\) 4.56211e65 2.24430
\(365\) −2.06207e64 −0.0945879
\(366\) −4.32086e65 −1.84843
\(367\) 8.05130e64 0.321278 0.160639 0.987013i \(-0.448644\pi\)
0.160639 + 0.987013i \(0.448644\pi\)
\(368\) −6.86982e64 −0.255756
\(369\) 7.85962e65 2.73042
\(370\) −3.43953e65 −1.11521
\(371\) −1.41357e64 −0.0427843
\(372\) −9.84233e65 −2.78133
\(373\) 2.25234e64 0.0594372 0.0297186 0.999558i \(-0.490539\pi\)
0.0297186 + 0.999558i \(0.490539\pi\)
\(374\) −1.87140e65 −0.461254
\(375\) 4.85427e65 1.11770
\(376\) 6.88024e65 1.48018
\(377\) 1.44948e65 0.291413
\(378\) −8.43395e65 −1.58486
\(379\) −1.01382e66 −1.78098 −0.890491 0.455001i \(-0.849639\pi\)
−0.890491 + 0.455001i \(0.849639\pi\)
\(380\) 2.69905e65 0.443333
\(381\) −7.04075e65 −1.08151
\(382\) 2.26917e66 3.26025
\(383\) −3.69389e65 −0.496496 −0.248248 0.968697i \(-0.579855\pi\)
−0.248248 + 0.968697i \(0.579855\pi\)
\(384\) 2.36021e66 2.96828
\(385\) 2.44092e65 0.287280
\(386\) 1.53389e66 1.68973
\(387\) −7.80425e65 −0.804825
\(388\) −3.62321e66 −3.49852
\(389\) −1.20048e66 −1.08552 −0.542762 0.839887i \(-0.682621\pi\)
−0.542762 + 0.839887i \(0.682621\pi\)
\(390\) −1.74731e66 −1.47986
\(391\) 1.11221e65 0.0882426
\(392\) −7.54816e65 −0.561108
\(393\) 2.70153e66 1.88192
\(394\) −2.59114e66 −1.69175
\(395\) 5.72063e65 0.350121
\(396\) 5.60443e66 3.21591
\(397\) −2.17708e66 −1.17143 −0.585714 0.810518i \(-0.699186\pi\)
−0.585714 + 0.810518i \(0.699186\pi\)
\(398\) 3.46835e66 1.75027
\(399\) −1.76117e66 −0.833666
\(400\) −1.55655e66 −0.691245
\(401\) 4.28565e66 1.78581 0.892905 0.450245i \(-0.148663\pi\)
0.892905 + 0.450245i \(0.148663\pi\)
\(402\) −8.94854e66 −3.49935
\(403\) 3.44945e66 1.26611
\(404\) 1.56895e66 0.540609
\(405\) 2.13883e65 0.0691949
\(406\) 9.15221e65 0.278043
\(407\) −6.14088e66 −1.75216
\(408\) 2.68623e66 0.719962
\(409\) 7.61605e66 1.91772 0.958860 0.283878i \(-0.0916211\pi\)
0.958860 + 0.283878i \(0.0916211\pi\)
\(410\) 4.23344e66 1.00162
\(411\) −7.62752e66 −1.69597
\(412\) −2.57493e66 −0.538129
\(413\) −3.44863e66 −0.677517
\(414\) −5.05598e66 −0.933891
\(415\) 1.30835e66 0.227246
\(416\) −2.02404e66 −0.330628
\(417\) 2.08747e66 0.320738
\(418\) 7.31471e66 1.05731
\(419\) 3.51155e66 0.477574 0.238787 0.971072i \(-0.423250\pi\)
0.238787 + 0.971072i \(0.423250\pi\)
\(420\) −7.26821e66 −0.930188
\(421\) −3.18883e66 −0.384094 −0.192047 0.981386i \(-0.561513\pi\)
−0.192047 + 0.981386i \(0.561513\pi\)
\(422\) −8.78397e66 −0.995917
\(423\) 1.47952e67 1.57922
\(424\) −8.42737e65 −0.0846960
\(425\) 2.52001e66 0.238498
\(426\) 3.75031e67 3.34290
\(427\) 6.29914e66 0.528896
\(428\) −1.16793e67 −0.923847
\(429\) −3.11961e67 −2.32509
\(430\) −4.20362e66 −0.295242
\(431\) −2.27664e66 −0.150704 −0.0753519 0.997157i \(-0.524008\pi\)
−0.0753519 + 0.997157i \(0.524008\pi\)
\(432\) −1.46914e67 −0.916700
\(433\) −2.96559e66 −0.174449 −0.0872247 0.996189i \(-0.527800\pi\)
−0.0872247 + 0.996189i \(0.527800\pi\)
\(434\) 2.17802e67 1.20802
\(435\) −2.30927e66 −0.120781
\(436\) −4.70733e67 −2.32204
\(437\) −4.34727e66 −0.202274
\(438\) 1.66404e67 0.730420
\(439\) 3.03815e67 1.25824 0.629121 0.777307i \(-0.283415\pi\)
0.629121 + 0.777307i \(0.283415\pi\)
\(440\) 1.45522e67 0.568701
\(441\) −1.62315e67 −0.598653
\(442\) −1.95295e67 −0.679867
\(443\) −1.74549e67 −0.573619 −0.286810 0.957988i \(-0.592595\pi\)
−0.286810 + 0.957988i \(0.592595\pi\)
\(444\) 1.82854e68 5.67334
\(445\) −1.84112e67 −0.539390
\(446\) −5.67240e67 −1.56938
\(447\) 1.55732e67 0.406946
\(448\) −3.87689e67 −0.956960
\(449\) −2.54711e67 −0.593972 −0.296986 0.954882i \(-0.595981\pi\)
−0.296986 + 0.954882i \(0.595981\pi\)
\(450\) −1.14557e68 −2.52408
\(451\) 7.55832e67 1.57370
\(452\) −5.16023e67 −1.01540
\(453\) −6.37706e67 −1.18609
\(454\) 1.49795e68 2.63374
\(455\) 2.54730e67 0.423437
\(456\) −1.04996e68 −1.65033
\(457\) 8.96015e67 1.33184 0.665920 0.746023i \(-0.268039\pi\)
0.665920 + 0.746023i \(0.268039\pi\)
\(458\) 2.75949e67 0.387935
\(459\) 2.37850e67 0.316286
\(460\) −1.79409e67 −0.225693
\(461\) 8.19688e67 0.975607 0.487804 0.872953i \(-0.337798\pi\)
0.487804 + 0.872953i \(0.337798\pi\)
\(462\) −1.96976e68 −2.21841
\(463\) −1.13766e68 −1.21254 −0.606269 0.795259i \(-0.707335\pi\)
−0.606269 + 0.795259i \(0.707335\pi\)
\(464\) 1.59425e67 0.160823
\(465\) −5.49556e67 −0.524761
\(466\) −9.56082e67 −0.864280
\(467\) 2.22344e67 0.190303 0.0951516 0.995463i \(-0.469666\pi\)
0.0951516 + 0.995463i \(0.469666\pi\)
\(468\) 5.84868e68 4.74011
\(469\) 1.30456e68 1.00128
\(470\) 7.96918e67 0.579319
\(471\) 4.20914e67 0.289841
\(472\) −2.05599e68 −1.34122
\(473\) −7.50507e67 −0.463869
\(474\) −4.61639e68 −2.70368
\(475\) −9.84993e67 −0.546696
\(476\) −8.12364e67 −0.427340
\(477\) −1.81222e67 −0.0903632
\(478\) 4.12527e68 1.95003
\(479\) −1.15577e68 −0.517983 −0.258992 0.965880i \(-0.583390\pi\)
−0.258992 + 0.965880i \(0.583390\pi\)
\(480\) 3.22464e67 0.137034
\(481\) −6.40851e68 −2.58260
\(482\) 4.02110e68 1.53690
\(483\) 1.17066e68 0.424405
\(484\) −2.24509e67 −0.0772107
\(485\) −2.02305e68 −0.660074
\(486\) 4.63434e68 1.43471
\(487\) 2.20619e66 0.00648118 0.00324059 0.999995i \(-0.498968\pi\)
0.00324059 + 0.999995i \(0.498968\pi\)
\(488\) 3.75539e68 1.04701
\(489\) 5.89465e68 1.55985
\(490\) −8.74282e67 −0.219610
\(491\) 7.91071e68 1.88642 0.943208 0.332202i \(-0.107792\pi\)
0.943208 + 0.332202i \(0.107792\pi\)
\(492\) −2.25060e69 −5.09552
\(493\) −2.58106e67 −0.0554883
\(494\) 7.63348e68 1.55842
\(495\) 3.12929e68 0.606754
\(496\) 3.79397e68 0.698734
\(497\) −5.46737e68 −0.956512
\(498\) −1.05580e69 −1.75482
\(499\) −9.62285e68 −1.51964 −0.759819 0.650135i \(-0.774712\pi\)
−0.759819 + 0.650135i \(0.774712\pi\)
\(500\) −8.75194e68 −1.31332
\(501\) 1.84597e69 2.63246
\(502\) −9.59607e67 −0.130061
\(503\) 5.82620e67 0.0750588 0.0375294 0.999296i \(-0.488051\pi\)
0.0375294 + 0.999296i \(0.488051\pi\)
\(504\) 1.78022e69 2.18019
\(505\) 8.76036e67 0.101998
\(506\) −4.86215e68 −0.538258
\(507\) −1.69464e69 −1.78391
\(508\) 1.26940e69 1.27079
\(509\) 5.13252e68 0.488683 0.244342 0.969689i \(-0.421428\pi\)
0.244342 + 0.969689i \(0.421428\pi\)
\(510\) 3.11138e68 0.281783
\(511\) −2.42590e68 −0.208997
\(512\) −1.77201e69 −1.45239
\(513\) −9.29681e68 −0.725005
\(514\) 2.20971e69 1.63974
\(515\) −1.43774e68 −0.101530
\(516\) 2.23475e69 1.50197
\(517\) 1.42280e69 0.910199
\(518\) −4.04640e69 −2.46411
\(519\) −1.63813e69 −0.949686
\(520\) 1.51863e69 0.838240
\(521\) 1.75529e69 0.922545 0.461272 0.887259i \(-0.347393\pi\)
0.461272 + 0.887259i \(0.347393\pi\)
\(522\) 1.17332e69 0.587245
\(523\) 3.31068e68 0.157806 0.0789032 0.996882i \(-0.474858\pi\)
0.0789032 + 0.996882i \(0.474858\pi\)
\(524\) −4.87069e69 −2.21128
\(525\) 2.65246e69 1.14706
\(526\) −2.01473e69 −0.830006
\(527\) −6.14235e68 −0.241082
\(528\) −3.43119e69 −1.28316
\(529\) −2.51724e69 −0.897026
\(530\) −9.76118e67 −0.0331488
\(531\) −4.42118e69 −1.43096
\(532\) 3.17527e69 0.979568
\(533\) 7.88771e69 2.31957
\(534\) 1.48574e70 4.16524
\(535\) −6.52124e68 −0.174304
\(536\) 7.77744e69 1.98214
\(537\) −7.20716e69 −1.75154
\(538\) −5.31524e69 −1.23190
\(539\) −1.56093e69 −0.345040
\(540\) −3.83673e69 −0.808947
\(541\) −8.41369e69 −1.69222 −0.846109 0.533009i \(-0.821061\pi\)
−0.846109 + 0.533009i \(0.821061\pi\)
\(542\) −5.56764e68 −0.106829
\(543\) 3.11662e69 0.570543
\(544\) 3.60415e68 0.0629552
\(545\) −2.62838e69 −0.438104
\(546\) −2.05560e70 −3.26984
\(547\) 1.11230e70 1.68867 0.844334 0.535817i \(-0.179996\pi\)
0.844334 + 0.535817i \(0.179996\pi\)
\(548\) 1.37519e70 1.99278
\(549\) 8.07556e69 1.11706
\(550\) −1.10165e70 −1.45478
\(551\) 1.00885e69 0.127193
\(552\) 6.97920e69 0.840155
\(553\) 6.72997e69 0.773611
\(554\) −1.97570e70 −2.16882
\(555\) 1.02098e70 1.07040
\(556\) −3.76357e69 −0.376871
\(557\) −1.12523e70 −1.07630 −0.538152 0.842848i \(-0.680877\pi\)
−0.538152 + 0.842848i \(0.680877\pi\)
\(558\) 2.79225e70 2.55142
\(559\) −7.83214e69 −0.683722
\(560\) 2.80171e69 0.233684
\(561\) 5.55501e69 0.442723
\(562\) 1.80065e70 1.37137
\(563\) −2.06561e68 −0.0150344 −0.00751718 0.999972i \(-0.502393\pi\)
−0.00751718 + 0.999972i \(0.502393\pi\)
\(564\) −4.23661e70 −2.94715
\(565\) −2.88126e69 −0.191579
\(566\) 1.32551e70 0.842491
\(567\) 2.51621e69 0.152890
\(568\) −3.25951e70 −1.89352
\(569\) 1.15170e70 0.639698 0.319849 0.947469i \(-0.396368\pi\)
0.319849 + 0.947469i \(0.396368\pi\)
\(570\) −1.21614e70 −0.645915
\(571\) 2.10280e70 1.06801 0.534007 0.845480i \(-0.320686\pi\)
0.534007 + 0.845480i \(0.320686\pi\)
\(572\) 5.62447e70 2.73201
\(573\) −6.73574e70 −3.12927
\(574\) 4.98039e70 2.21315
\(575\) 6.54734e69 0.278314
\(576\) −4.97021e70 −2.02116
\(577\) 5.78798e68 0.0225187 0.0112594 0.999937i \(-0.496416\pi\)
0.0112594 + 0.999937i \(0.496416\pi\)
\(578\) −4.25108e70 −1.58248
\(579\) −4.55316e70 −1.62185
\(580\) 4.16347e69 0.141919
\(581\) 1.53919e70 0.502113
\(582\) 1.63255e71 5.09718
\(583\) −1.74274e69 −0.0520818
\(584\) −1.44626e70 −0.413732
\(585\) 3.26566e70 0.894328
\(586\) −5.97694e70 −1.56707
\(587\) −3.63201e70 −0.911748 −0.455874 0.890044i \(-0.650673\pi\)
−0.455874 + 0.890044i \(0.650673\pi\)
\(588\) 4.64790e70 1.11721
\(589\) 2.40085e70 0.552619
\(590\) −2.38139e70 −0.524933
\(591\) 7.69148e70 1.62379
\(592\) −7.04857e70 −1.42527
\(593\) −2.80060e70 −0.542447 −0.271223 0.962516i \(-0.587428\pi\)
−0.271223 + 0.962516i \(0.587428\pi\)
\(594\) −1.03979e71 −1.92927
\(595\) −4.53591e69 −0.0806272
\(596\) −2.80776e70 −0.478167
\(597\) −1.02954e71 −1.67995
\(598\) −5.07405e70 −0.793367
\(599\) 4.36080e70 0.653404 0.326702 0.945127i \(-0.394063\pi\)
0.326702 + 0.945127i \(0.394063\pi\)
\(600\) 1.58133e71 2.27073
\(601\) 3.82831e70 0.526875 0.263437 0.964676i \(-0.415144\pi\)
0.263437 + 0.964676i \(0.415144\pi\)
\(602\) −4.94530e70 −0.652352
\(603\) 1.67246e71 2.11477
\(604\) 1.14974e71 1.39367
\(605\) −1.25357e69 −0.0145675
\(606\) −7.06937e70 −0.787642
\(607\) −2.49833e70 −0.266894 −0.133447 0.991056i \(-0.542605\pi\)
−0.133447 + 0.991056i \(0.542605\pi\)
\(608\) −1.40875e70 −0.144309
\(609\) −2.71672e70 −0.266872
\(610\) 4.34976e70 0.409783
\(611\) 1.48481e71 1.34159
\(612\) −1.04146e71 −0.902570
\(613\) −1.99012e71 −1.65439 −0.827193 0.561919i \(-0.810063\pi\)
−0.827193 + 0.561919i \(0.810063\pi\)
\(614\) −1.90061e71 −1.51565
\(615\) −1.25664e71 −0.961384
\(616\) 1.71197e71 1.25658
\(617\) 5.04536e70 0.355321 0.177660 0.984092i \(-0.443147\pi\)
0.177660 + 0.984092i \(0.443147\pi\)
\(618\) 1.16021e71 0.784029
\(619\) −8.80938e70 −0.571260 −0.285630 0.958340i \(-0.592203\pi\)
−0.285630 + 0.958340i \(0.592203\pi\)
\(620\) 9.90814e70 0.616601
\(621\) 6.17968e70 0.369088
\(622\) 4.75846e71 2.72780
\(623\) −2.16597e71 −1.19181
\(624\) −3.58072e71 −1.89131
\(625\) 1.22178e71 0.619516
\(626\) −4.53551e71 −2.20790
\(627\) −2.17128e71 −1.01483
\(628\) −7.58881e70 −0.340567
\(629\) 1.14115e71 0.491756
\(630\) 2.06198e71 0.853296
\(631\) 3.58339e71 1.42411 0.712057 0.702121i \(-0.247764\pi\)
0.712057 + 0.702121i \(0.247764\pi\)
\(632\) 4.01224e71 1.53144
\(633\) 2.60741e71 0.955906
\(634\) −2.38898e71 −0.841271
\(635\) 7.08782e70 0.239763
\(636\) 5.18928e70 0.168636
\(637\) −1.62895e71 −0.508573
\(638\) 1.12834e71 0.338465
\(639\) −7.00922e71 −2.02022
\(640\) −2.37599e71 −0.658046
\(641\) 6.07769e71 1.61755 0.808777 0.588116i \(-0.200130\pi\)
0.808777 + 0.588116i \(0.200130\pi\)
\(642\) 5.26246e71 1.34600
\(643\) −7.85977e71 −1.93210 −0.966050 0.258353i \(-0.916820\pi\)
−0.966050 + 0.258353i \(0.916820\pi\)
\(644\) −2.11063e71 −0.498681
\(645\) 1.24779e71 0.283380
\(646\) −1.35927e71 −0.296741
\(647\) 5.80462e71 1.21819 0.609095 0.793098i \(-0.291533\pi\)
0.609095 + 0.793098i \(0.291533\pi\)
\(648\) 1.50010e71 0.302662
\(649\) −4.25169e71 −0.824750
\(650\) −1.14966e72 −2.14428
\(651\) −6.46519e71 −1.15949
\(652\) −1.06277e72 −1.83284
\(653\) 9.50695e71 1.57672 0.788361 0.615213i \(-0.210930\pi\)
0.788361 + 0.615213i \(0.210930\pi\)
\(654\) 2.12103e72 3.38310
\(655\) −2.71960e71 −0.417207
\(656\) 8.67551e71 1.28011
\(657\) −3.11003e71 −0.441416
\(658\) 9.37526e71 1.28004
\(659\) 5.24300e71 0.688655 0.344327 0.938850i \(-0.388107\pi\)
0.344327 + 0.938850i \(0.388107\pi\)
\(660\) −8.96072e71 −1.13233
\(661\) 1.48904e71 0.181038 0.0905189 0.995895i \(-0.471147\pi\)
0.0905189 + 0.995895i \(0.471147\pi\)
\(662\) 6.72497e71 0.786704
\(663\) 5.79710e71 0.652553
\(664\) 9.17627e71 0.993986
\(665\) 1.77294e71 0.184817
\(666\) −5.18753e72 −5.20437
\(667\) −6.70595e70 −0.0647518
\(668\) −3.32817e72 −3.09318
\(669\) 1.68378e72 1.50633
\(670\) 9.00838e71 0.775781
\(671\) 7.76598e71 0.643831
\(672\) 3.79359e71 0.302785
\(673\) −5.12793e70 −0.0394056 −0.0197028 0.999806i \(-0.506272\pi\)
−0.0197028 + 0.999806i \(0.506272\pi\)
\(674\) 2.00387e71 0.148266
\(675\) 1.40018e72 0.997554
\(676\) 3.05533e72 2.09612
\(677\) −2.88331e72 −1.90494 −0.952468 0.304639i \(-0.901464\pi\)
−0.952468 + 0.304639i \(0.901464\pi\)
\(678\) 2.32510e72 1.47940
\(679\) −2.38000e72 −1.45847
\(680\) −2.70419e71 −0.159610
\(681\) −4.44648e72 −2.52793
\(682\) 2.68521e72 1.47054
\(683\) 1.21910e72 0.643150 0.321575 0.946884i \(-0.395788\pi\)
0.321575 + 0.946884i \(0.395788\pi\)
\(684\) 4.07073e72 2.06891
\(685\) 7.67852e71 0.375983
\(686\) −3.94926e72 −1.86316
\(687\) −8.19121e71 −0.372350
\(688\) −8.61439e71 −0.377328
\(689\) −1.81869e71 −0.0767661
\(690\) 8.08381e71 0.328824
\(691\) −1.39481e72 −0.546794 −0.273397 0.961901i \(-0.588147\pi\)
−0.273397 + 0.961901i \(0.588147\pi\)
\(692\) 2.95344e72 1.11589
\(693\) 3.68142e72 1.34066
\(694\) 1.26665e72 0.444619
\(695\) −2.10143e71 −0.0711052
\(696\) −1.61964e72 −0.528302
\(697\) −1.40454e72 −0.441672
\(698\) −4.25002e72 −1.28848
\(699\) 2.83801e72 0.829557
\(700\) −4.78222e72 −1.34781
\(701\) 5.63382e72 1.53106 0.765532 0.643397i \(-0.222476\pi\)
0.765532 + 0.643397i \(0.222476\pi\)
\(702\) −1.08511e73 −2.84365
\(703\) −4.46038e72 −1.12723
\(704\) −4.77967e72 −1.16492
\(705\) −2.36555e72 −0.556045
\(706\) 1.44812e73 3.28311
\(707\) 1.03060e72 0.225370
\(708\) 1.26601e73 2.67047
\(709\) 3.78104e72 0.769365 0.384682 0.923049i \(-0.374311\pi\)
0.384682 + 0.923049i \(0.374311\pi\)
\(710\) −3.77539e72 −0.741095
\(711\) 8.62789e72 1.63392
\(712\) −1.29130e73 −2.35932
\(713\) −1.59587e72 −0.281329
\(714\) 3.66036e72 0.622614
\(715\) 3.14047e72 0.515455
\(716\) 1.29940e73 2.05808
\(717\) −1.22453e73 −1.87168
\(718\) −1.20664e73 −1.77993
\(719\) 6.26463e72 0.891885 0.445943 0.895062i \(-0.352869\pi\)
0.445943 + 0.895062i \(0.352869\pi\)
\(720\) 3.59183e72 0.493556
\(721\) −1.69141e72 −0.224336
\(722\) −8.05873e72 −1.03173
\(723\) −1.19361e73 −1.47515
\(724\) −5.61907e72 −0.670396
\(725\) −1.51942e72 −0.175008
\(726\) 1.01160e72 0.112492
\(727\) 1.48516e73 1.59457 0.797287 0.603600i \(-0.206267\pi\)
0.797287 + 0.603600i \(0.206267\pi\)
\(728\) 1.78658e73 1.85214
\(729\) −1.56540e73 −1.56702
\(730\) −1.67516e72 −0.161929
\(731\) 1.39465e72 0.130188
\(732\) −2.31244e73 −2.08467
\(733\) 5.93373e72 0.516627 0.258313 0.966061i \(-0.416833\pi\)
0.258313 + 0.966061i \(0.416833\pi\)
\(734\) 6.54063e72 0.550009
\(735\) 2.59520e72 0.210787
\(736\) 9.36409e71 0.0734652
\(737\) 1.60834e73 1.21887
\(738\) 6.38491e73 4.67431
\(739\) 1.50074e72 0.106138 0.0530692 0.998591i \(-0.483100\pi\)
0.0530692 + 0.998591i \(0.483100\pi\)
\(740\) −1.84077e73 −1.25774
\(741\) −2.26591e73 −1.49581
\(742\) −1.14834e72 −0.0732441
\(743\) −2.89489e73 −1.78409 −0.892047 0.451943i \(-0.850731\pi\)
−0.892047 + 0.451943i \(0.850731\pi\)
\(744\) −3.85438e73 −2.29533
\(745\) −1.56774e72 −0.0902170
\(746\) 1.82973e72 0.101753
\(747\) 1.97326e73 1.06050
\(748\) −1.00153e73 −0.520205
\(749\) −7.67184e72 −0.385135
\(750\) 3.94346e73 1.91344
\(751\) 1.40821e73 0.660462 0.330231 0.943900i \(-0.392873\pi\)
0.330231 + 0.943900i \(0.392873\pi\)
\(752\) 1.63311e73 0.740389
\(753\) 2.84847e72 0.124836
\(754\) 1.17752e73 0.498882
\(755\) 6.41970e72 0.262946
\(756\) −4.51368e73 −1.78741
\(757\) −9.83514e72 −0.376561 −0.188281 0.982115i \(-0.560291\pi\)
−0.188281 + 0.982115i \(0.560291\pi\)
\(758\) −8.23593e73 −3.04893
\(759\) 1.44327e73 0.516633
\(760\) 1.05698e73 0.365866
\(761\) 4.56710e73 1.52873 0.764367 0.644782i \(-0.223052\pi\)
0.764367 + 0.644782i \(0.223052\pi\)
\(762\) −5.71968e73 −1.85148
\(763\) −3.09213e73 −0.968016
\(764\) 1.21441e74 3.67693
\(765\) −5.81508e72 −0.170290
\(766\) −3.00081e73 −0.849971
\(767\) −4.43698e73 −1.21564
\(768\) 1.18022e74 3.12791
\(769\) 3.75294e73 0.962167 0.481083 0.876675i \(-0.340243\pi\)
0.481083 + 0.876675i \(0.340243\pi\)
\(770\) 1.98293e73 0.491806
\(771\) −6.55925e73 −1.57386
\(772\) 8.20906e73 1.90569
\(773\) 3.47460e73 0.780419 0.390210 0.920726i \(-0.372403\pi\)
0.390210 + 0.920726i \(0.372403\pi\)
\(774\) −6.33993e73 −1.37781
\(775\) −3.61588e73 −0.760362
\(776\) −1.41890e74 −2.88720
\(777\) 1.20112e74 2.36511
\(778\) −9.75230e73 −1.85835
\(779\) 5.48992e73 1.01242
\(780\) −9.35123e73 −1.66900
\(781\) −6.74052e73 −1.16437
\(782\) 9.03522e72 0.151066
\(783\) −1.43410e73 −0.232088
\(784\) −1.79165e73 −0.280668
\(785\) −4.23728e72 −0.0642556
\(786\) 2.19464e74 3.22173
\(787\) −5.13224e72 −0.0729376 −0.0364688 0.999335i \(-0.511611\pi\)
−0.0364688 + 0.999335i \(0.511611\pi\)
\(788\) −1.38672e74 −1.90797
\(789\) 5.98049e73 0.796660
\(790\) 4.64726e73 0.599385
\(791\) −3.38963e73 −0.423304
\(792\) 2.19477e74 2.65397
\(793\) 8.10443e73 0.948978
\(794\) −1.76859e74 −2.00541
\(795\) 2.89749e72 0.0318170
\(796\) 1.85619e74 1.97397
\(797\) −5.49546e73 −0.566001 −0.283000 0.959120i \(-0.591330\pi\)
−0.283000 + 0.959120i \(0.591330\pi\)
\(798\) −1.43072e74 −1.42719
\(799\) −2.64396e73 −0.255454
\(800\) 2.12169e73 0.198558
\(801\) −2.77680e74 −2.51719
\(802\) 3.48153e74 3.05720
\(803\) −2.99081e73 −0.254414
\(804\) −4.78908e74 −3.94659
\(805\) −1.17849e73 −0.0940874
\(806\) 2.80223e74 2.16750
\(807\) 1.57776e74 1.18241
\(808\) 6.14420e73 0.446144
\(809\) 2.78397e73 0.195874 0.0979372 0.995193i \(-0.468776\pi\)
0.0979372 + 0.995193i \(0.468776\pi\)
\(810\) 1.73752e73 0.118457
\(811\) −2.13458e74 −1.41020 −0.705099 0.709109i \(-0.749098\pi\)
−0.705099 + 0.709109i \(0.749098\pi\)
\(812\) 4.89807e73 0.313579
\(813\) 1.65269e73 0.102537
\(814\) −4.98866e74 −2.99959
\(815\) −5.93406e73 −0.345806
\(816\) 6.37610e73 0.360127
\(817\) −5.45124e73 −0.298424
\(818\) 6.18704e74 3.28302
\(819\) 3.84186e74 1.97607
\(820\) 2.26565e74 1.12964
\(821\) −1.21993e74 −0.589639 −0.294819 0.955553i \(-0.595259\pi\)
−0.294819 + 0.955553i \(0.595259\pi\)
\(822\) −6.19636e74 −2.90339
\(823\) −9.32706e72 −0.0423691 −0.0211845 0.999776i \(-0.506744\pi\)
−0.0211845 + 0.999776i \(0.506744\pi\)
\(824\) −1.00838e74 −0.444098
\(825\) 3.27012e74 1.39633
\(826\) −2.80156e74 −1.15987
\(827\) 2.77630e73 0.111449 0.0557244 0.998446i \(-0.482253\pi\)
0.0557244 + 0.998446i \(0.482253\pi\)
\(828\) −2.70585e74 −1.05325
\(829\) 3.61616e74 1.36492 0.682461 0.730922i \(-0.260910\pi\)
0.682461 + 0.730922i \(0.260910\pi\)
\(830\) 1.06286e74 0.389032
\(831\) 5.86463e74 2.08168
\(832\) −4.98797e74 −1.71704
\(833\) 2.90064e73 0.0968380
\(834\) 1.69579e74 0.549084
\(835\) −1.85831e74 −0.583598
\(836\) 3.91468e74 1.19244
\(837\) −3.41283e74 −1.00836
\(838\) 2.85267e74 0.817578
\(839\) −4.79920e74 −1.33425 −0.667127 0.744944i \(-0.732476\pi\)
−0.667127 + 0.744944i \(0.732476\pi\)
\(840\) −2.84633e74 −0.767649
\(841\) −3.66644e74 −0.959283
\(842\) −2.59050e74 −0.657546
\(843\) −5.34502e74 −1.31627
\(844\) −4.70100e74 −1.12320
\(845\) 1.70597e74 0.395481
\(846\) 1.20192e75 2.70353
\(847\) −1.47475e73 −0.0321877
\(848\) −2.00034e73 −0.0423652
\(849\) −3.93463e74 −0.808644
\(850\) 2.04718e74 0.408294
\(851\) 2.96486e74 0.573852
\(852\) 2.00709e75 3.77014
\(853\) 6.60846e74 1.20476 0.602379 0.798210i \(-0.294220\pi\)
0.602379 + 0.798210i \(0.294220\pi\)
\(854\) 5.11723e74 0.905438
\(855\) 2.27293e74 0.390347
\(856\) −4.57376e74 −0.762416
\(857\) −2.87199e74 −0.464699 −0.232349 0.972632i \(-0.574641\pi\)
−0.232349 + 0.972632i \(0.574641\pi\)
\(858\) −2.53428e75 −3.98041
\(859\) 7.69360e74 1.17302 0.586508 0.809944i \(-0.300502\pi\)
0.586508 + 0.809944i \(0.300502\pi\)
\(860\) −2.24969e74 −0.332975
\(861\) −1.47837e75 −2.12423
\(862\) −1.84947e74 −0.257996
\(863\) −8.71585e74 −1.18041 −0.590207 0.807252i \(-0.700954\pi\)
−0.590207 + 0.807252i \(0.700954\pi\)
\(864\) 2.00255e74 0.263320
\(865\) 1.64908e74 0.210538
\(866\) −2.40915e74 −0.298647
\(867\) 1.26188e75 1.51891
\(868\) 1.16563e75 1.36241
\(869\) 8.29714e74 0.941725
\(870\) −1.87598e74 −0.206770
\(871\) 1.67843e75 1.79656
\(872\) −1.84345e75 −1.91629
\(873\) −3.05118e75 −3.08039
\(874\) −3.53158e74 −0.346280
\(875\) −5.74894e74 −0.547498
\(876\) 8.90557e74 0.823772
\(877\) 1.44865e75 1.30159 0.650797 0.759252i \(-0.274435\pi\)
0.650797 + 0.759252i \(0.274435\pi\)
\(878\) 2.46810e75 2.15403
\(879\) 1.77418e75 1.50412
\(880\) 3.45413e74 0.284466
\(881\) −1.16519e75 −0.932207 −0.466103 0.884730i \(-0.654343\pi\)
−0.466103 + 0.884730i \(0.654343\pi\)
\(882\) −1.31860e75 −1.02486
\(883\) −1.52991e75 −1.15523 −0.577615 0.816309i \(-0.696016\pi\)
−0.577615 + 0.816309i \(0.696016\pi\)
\(884\) −1.04518e75 −0.766759
\(885\) 7.06886e74 0.503844
\(886\) −1.41799e75 −0.982001
\(887\) −2.18618e75 −1.47107 −0.735535 0.677487i \(-0.763069\pi\)
−0.735535 + 0.677487i \(0.763069\pi\)
\(888\) 7.16080e75 4.68199
\(889\) 8.33840e74 0.529770
\(890\) −1.49567e75 −0.923403
\(891\) 3.10214e74 0.186115
\(892\) −3.03575e75 −1.76996
\(893\) 1.03344e75 0.585563
\(894\) 1.26512e75 0.696667
\(895\) 7.25535e74 0.388303
\(896\) −2.79521e75 −1.45399
\(897\) 1.50617e75 0.761493
\(898\) −2.06919e75 −1.01684
\(899\) 3.70348e74 0.176904
\(900\) −6.13086e75 −2.84667
\(901\) 3.23850e73 0.0146171
\(902\) 6.14014e75 2.69409
\(903\) 1.46795e75 0.626144
\(904\) −2.02081e75 −0.837975
\(905\) −3.13746e74 −0.126485
\(906\) −5.18052e75 −2.03051
\(907\) −3.40042e75 −1.29583 −0.647914 0.761714i \(-0.724358\pi\)
−0.647914 + 0.761714i \(0.724358\pi\)
\(908\) 8.01672e75 2.97035
\(909\) 1.32124e75 0.475997
\(910\) 2.06935e75 0.724899
\(911\) −4.11484e74 −0.140163 −0.0700817 0.997541i \(-0.522326\pi\)
−0.0700817 + 0.997541i \(0.522326\pi\)
\(912\) −2.49222e75 −0.825501
\(913\) 1.89761e75 0.611228
\(914\) 7.27895e75 2.28003
\(915\) −1.29117e75 −0.393320
\(916\) 1.47682e75 0.437516
\(917\) −3.19944e75 −0.921841
\(918\) 1.93222e75 0.541462
\(919\) −4.75576e75 −1.29621 −0.648104 0.761552i \(-0.724438\pi\)
−0.648104 + 0.761552i \(0.724438\pi\)
\(920\) −7.02587e74 −0.186256
\(921\) 5.64172e75 1.45476
\(922\) 6.65889e75 1.67018
\(923\) −7.03428e75 −1.71623
\(924\) −1.05417e76 −2.50194
\(925\) 6.71770e75 1.55098
\(926\) −9.24196e75 −2.07579
\(927\) −2.16841e75 −0.473814
\(928\) −2.17309e74 −0.0461960
\(929\) 7.98781e75 1.65207 0.826033 0.563622i \(-0.190593\pi\)
0.826033 + 0.563622i \(0.190593\pi\)
\(930\) −4.46442e75 −0.898359
\(931\) −1.13377e75 −0.221977
\(932\) −5.11675e75 −0.974740
\(933\) −1.41249e76 −2.61821
\(934\) 1.80626e75 0.325787
\(935\) −5.59216e74 −0.0981484
\(936\) 2.29042e76 3.91183
\(937\) −3.77230e75 −0.626970 −0.313485 0.949593i \(-0.601497\pi\)
−0.313485 + 0.949593i \(0.601497\pi\)
\(938\) 1.05978e76 1.71413
\(939\) 1.34631e76 2.11920
\(940\) 4.26494e75 0.653360
\(941\) −1.08168e75 −0.161274 −0.0806371 0.996744i \(-0.525695\pi\)
−0.0806371 + 0.996744i \(0.525695\pi\)
\(942\) 3.41937e75 0.496191
\(943\) −3.64920e75 −0.515406
\(944\) −4.88014e75 −0.670882
\(945\) −2.52025e75 −0.337235
\(946\) −6.09688e75 −0.794116
\(947\) 2.23798e75 0.283747 0.141873 0.989885i \(-0.454687\pi\)
0.141873 + 0.989885i \(0.454687\pi\)
\(948\) −2.47060e76 −3.04922
\(949\) −3.12115e75 −0.374995
\(950\) −8.00178e75 −0.935911
\(951\) 7.09139e75 0.807473
\(952\) −3.18132e75 −0.352667
\(953\) 1.63024e76 1.75947 0.879737 0.475461i \(-0.157719\pi\)
0.879737 + 0.475461i \(0.157719\pi\)
\(954\) −1.47219e75 −0.154696
\(955\) 6.78078e75 0.693735
\(956\) 2.20776e76 2.19925
\(957\) −3.34935e75 −0.324867
\(958\) −9.38912e75 −0.886756
\(959\) 9.03332e75 0.830755
\(960\) 7.94668e75 0.711655
\(961\) −2.65345e75 −0.231401
\(962\) −5.20607e76 −4.42126
\(963\) −9.83538e75 −0.813431
\(964\) 2.15201e76 1.73332
\(965\) 4.58360e75 0.359551
\(966\) 9.51011e75 0.726556
\(967\) −1.19422e76 −0.888609 −0.444305 0.895876i \(-0.646549\pi\)
−0.444305 + 0.895876i \(0.646549\pi\)
\(968\) −8.79207e74 −0.0637191
\(969\) 4.03484e75 0.284820
\(970\) −1.64347e76 −1.13001
\(971\) −9.57238e75 −0.641106 −0.320553 0.947231i \(-0.603869\pi\)
−0.320553 + 0.947231i \(0.603869\pi\)
\(972\) 2.48020e76 1.61807
\(973\) −2.47220e75 −0.157111
\(974\) 1.79224e74 0.0110954
\(975\) 3.41264e76 2.05813
\(976\) 8.91387e75 0.523716
\(977\) −3.03295e75 −0.173602 −0.0868008 0.996226i \(-0.527664\pi\)
−0.0868008 + 0.996226i \(0.527664\pi\)
\(978\) 4.78863e76 2.67036
\(979\) −2.67035e76 −1.45081
\(980\) −4.67898e75 −0.247677
\(981\) −3.96415e76 −2.04451
\(982\) 6.42642e76 3.22943
\(983\) 7.25776e75 0.355376 0.177688 0.984087i \(-0.443138\pi\)
0.177688 + 0.984087i \(0.443138\pi\)
\(984\) −8.81365e76 −4.20514
\(985\) −7.74291e75 −0.359981
\(986\) −2.09677e75 −0.0949926
\(987\) −2.78293e76 −1.22861
\(988\) 4.08528e76 1.75760
\(989\) 3.62349e75 0.151922
\(990\) 2.54214e76 1.03873
\(991\) −1.83886e74 −0.00732268 −0.00366134 0.999993i \(-0.501165\pi\)
−0.00366134 + 0.999993i \(0.501165\pi\)
\(992\) −5.17148e75 −0.200709
\(993\) −1.99622e76 −0.755098
\(994\) −4.44152e76 −1.63749
\(995\) 1.03642e76 0.372433
\(996\) −5.65043e76 −1.97910
\(997\) 4.30923e76 1.47120 0.735602 0.677414i \(-0.236900\pi\)
0.735602 + 0.677414i \(0.236900\pi\)
\(998\) −7.81731e76 −2.60153
\(999\) 6.34047e76 2.05684
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 1.52.a.a.1.4 4
3.2 odd 2 9.52.a.b.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.52.a.a.1.4 4 1.1 even 1 trivial
9.52.a.b.1.1 4 3.2 odd 2