Properties

Label 1.38.a.a.1.1
Level $1$
Weight $38$
Character 1.1
Self dual yes
Analytic conductor $8.671$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 38 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(8.67140381246\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\mathbb{Q}[x]/(x^{2} - \cdots)\)
Defining polynomial: \(x^{2} - x - 15934380\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{5}\cdot 3 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3992.29\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-480412. q^{2} +3.45869e7 q^{3} +9.33565e10 q^{4} +1.38267e13 q^{5} -1.66160e13 q^{6} -5.42222e15 q^{7} +2.11777e16 q^{8} -4.49088e17 q^{9} +O(q^{10})\) \(q-480412. q^{2} +3.45869e7 q^{3} +9.33565e10 q^{4} +1.38267e13 q^{5} -1.66160e13 q^{6} -5.42222e15 q^{7} +2.11777e16 q^{8} -4.49088e17 q^{9} -6.64253e18 q^{10} -1.03285e18 q^{11} +3.22892e18 q^{12} -1.23244e19 q^{13} +2.60490e21 q^{14} +4.78225e20 q^{15} -2.30048e22 q^{16} -5.41594e22 q^{17} +2.15747e23 q^{18} -3.08845e23 q^{19} +1.29082e24 q^{20} -1.87538e23 q^{21} +4.96192e23 q^{22} -2.61592e25 q^{23} +7.32473e23 q^{24} +1.18419e26 q^{25} +5.92077e24 q^{26} -3.11065e25 q^{27} -5.06199e26 q^{28} +2.49238e26 q^{29} -2.29745e26 q^{30} -2.34643e27 q^{31} +8.14116e27 q^{32} -3.57230e25 q^{33} +2.60188e28 q^{34} -7.49716e28 q^{35} -4.19253e28 q^{36} +6.21792e28 q^{37} +1.48373e29 q^{38} -4.26262e26 q^{39} +2.92819e29 q^{40} -8.53404e29 q^{41} +9.00954e28 q^{42} +3.53994e29 q^{43} -9.64230e28 q^{44} -6.20942e30 q^{45} +1.25672e31 q^{46} +6.68978e29 q^{47} -7.95667e29 q^{48} +1.08383e31 q^{49} -5.68899e31 q^{50} -1.87321e30 q^{51} -1.15056e30 q^{52} +1.24128e32 q^{53} +1.49439e31 q^{54} -1.42809e31 q^{55} -1.14830e32 q^{56} -1.06820e31 q^{57} -1.19737e32 q^{58} +6.57033e31 q^{59} +4.46454e31 q^{60} -1.06034e33 q^{61} +1.12725e33 q^{62} +2.43505e33 q^{63} -7.49344e32 q^{64} -1.70406e32 q^{65} +1.71618e31 q^{66} -8.44869e33 q^{67} -5.05613e33 q^{68} -9.04768e32 q^{69} +3.60172e34 q^{70} -7.04837e33 q^{71} -9.51066e33 q^{72} +9.36735e33 q^{73} -2.98716e34 q^{74} +4.09575e33 q^{75} -2.88327e34 q^{76} +5.60032e33 q^{77} +2.04781e32 q^{78} +1.51854e35 q^{79} -3.18082e35 q^{80} +2.01141e35 q^{81} +4.09985e35 q^{82} -1.43761e35 q^{83} -1.75079e34 q^{84} -7.48847e35 q^{85} -1.70063e35 q^{86} +8.62039e33 q^{87} -2.18734e34 q^{88} +2.28283e35 q^{89} +2.98308e36 q^{90} +6.68253e34 q^{91} -2.44213e36 q^{92} -8.11557e34 q^{93} -3.21385e35 q^{94} -4.27032e36 q^{95} +2.81578e35 q^{96} +7.07361e36 q^{97} -5.20686e36 q^{98} +4.63839e35 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 194400q^{2} + 13991400q^{3} + 37720269824q^{4} + 5529584385900q^{5} - 22506543847296q^{6} - 3448443953486000q^{7} - 34044043043635200q^{8} - 898947378401769414q^{9} + O(q^{10}) \) \( 2q - 194400q^{2} + 13991400q^{3} + 37720269824q^{4} + 5529584385900q^{5} - 22506543847296q^{6} - 3448443953486000q^{7} - 34044043043635200q^{8} - 898947378401769414q^{9} - 9015609355013275200q^{10} - 26734036354848538056q^{11} + 4374774798370099200q^{12} + \)\(53\!\cdots\!00\)\(q^{13} + \)\(31\!\cdots\!48\)\(q^{14} + \)\(64\!\cdots\!00\)\(q^{15} - \)\(31\!\cdots\!08\)\(q^{16} - \)\(89\!\cdots\!00\)\(q^{17} + \)\(87\!\cdots\!00\)\(q^{18} + \)\(37\!\cdots\!20\)\(q^{19} + \)\(17\!\cdots\!00\)\(q^{20} - \)\(22\!\cdots\!56\)\(q^{21} - \)\(68\!\cdots\!00\)\(q^{22} - \)\(26\!\cdots\!00\)\(q^{23} + \)\(18\!\cdots\!60\)\(q^{24} + \)\(11\!\cdots\!50\)\(q^{25} + \)\(16\!\cdots\!44\)\(q^{26} - \)\(12\!\cdots\!00\)\(q^{27} - \)\(61\!\cdots\!00\)\(q^{28} - \)\(12\!\cdots\!20\)\(q^{29} - \)\(18\!\cdots\!00\)\(q^{30} + \)\(26\!\cdots\!24\)\(q^{31} + \)\(13\!\cdots\!00\)\(q^{32} + \)\(49\!\cdots\!00\)\(q^{33} + \)\(15\!\cdots\!08\)\(q^{34} - \)\(91\!\cdots\!00\)\(q^{35} - \)\(16\!\cdots\!68\)\(q^{36} - \)\(68\!\cdots\!00\)\(q^{37} + \)\(34\!\cdots\!00\)\(q^{38} - \)\(11\!\cdots\!68\)\(q^{39} + \)\(75\!\cdots\!00\)\(q^{40} - \)\(12\!\cdots\!36\)\(q^{41} + \)\(78\!\cdots\!00\)\(q^{42} - \)\(25\!\cdots\!00\)\(q^{43} + \)\(13\!\cdots\!28\)\(q^{44} - \)\(24\!\cdots\!00\)\(q^{45} + \)\(12\!\cdots\!84\)\(q^{46} + \)\(42\!\cdots\!00\)\(q^{47} - \)\(62\!\cdots\!00\)\(q^{48} - \)\(38\!\cdots\!86\)\(q^{49} - \)\(58\!\cdots\!00\)\(q^{50} - \)\(11\!\cdots\!76\)\(q^{51} - \)\(31\!\cdots\!00\)\(q^{52} + \)\(15\!\cdots\!00\)\(q^{53} + \)\(20\!\cdots\!20\)\(q^{54} + \)\(19\!\cdots\!00\)\(q^{55} - \)\(22\!\cdots\!80\)\(q^{56} - \)\(24\!\cdots\!00\)\(q^{57} - \)\(55\!\cdots\!00\)\(q^{58} - \)\(23\!\cdots\!40\)\(q^{59} + \)\(35\!\cdots\!00\)\(q^{60} + \)\(10\!\cdots\!44\)\(q^{61} + \)\(18\!\cdots\!00\)\(q^{62} + \)\(15\!\cdots\!00\)\(q^{63} + \)\(18\!\cdots\!64\)\(q^{64} - \)\(46\!\cdots\!00\)\(q^{65} + \)\(16\!\cdots\!88\)\(q^{66} - \)\(10\!\cdots\!00\)\(q^{67} - \)\(30\!\cdots\!00\)\(q^{68} - \)\(90\!\cdots\!48\)\(q^{69} + \)\(31\!\cdots\!00\)\(q^{70} - \)\(74\!\cdots\!16\)\(q^{71} + \)\(15\!\cdots\!00\)\(q^{72} + \)\(19\!\cdots\!00\)\(q^{73} - \)\(67\!\cdots\!72\)\(q^{74} + \)\(41\!\cdots\!00\)\(q^{75} - \)\(66\!\cdots\!60\)\(q^{76} - \)\(45\!\cdots\!00\)\(q^{77} - \)\(29\!\cdots\!00\)\(q^{78} + \)\(27\!\cdots\!80\)\(q^{79} - \)\(25\!\cdots\!00\)\(q^{80} + \)\(40\!\cdots\!42\)\(q^{81} + \)\(29\!\cdots\!00\)\(q^{82} - \)\(47\!\cdots\!00\)\(q^{83} - \)\(15\!\cdots\!72\)\(q^{84} - \)\(45\!\cdots\!00\)\(q^{85} - \)\(10\!\cdots\!36\)\(q^{86} + \)\(39\!\cdots\!00\)\(q^{87} + \)\(13\!\cdots\!00\)\(q^{88} - \)\(13\!\cdots\!60\)\(q^{89} + \)\(40\!\cdots\!00\)\(q^{90} + \)\(11\!\cdots\!84\)\(q^{91} - \)\(24\!\cdots\!00\)\(q^{92} - \)\(13\!\cdots\!00\)\(q^{93} + \)\(70\!\cdots\!88\)\(q^{94} - \)\(99\!\cdots\!00\)\(q^{95} + \)\(17\!\cdots\!64\)\(q^{96} + \)\(60\!\cdots\!00\)\(q^{97} - \)\(94\!\cdots\!00\)\(q^{98} + \)\(12\!\cdots\!92\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −480412. −1.29586 −0.647931 0.761699i \(-0.724365\pi\)
−0.647931 + 0.761699i \(0.724365\pi\)
\(3\) 3.45869e7 0.0515429 0.0257715 0.999668i \(-0.491796\pi\)
0.0257715 + 0.999668i \(0.491796\pi\)
\(4\) 9.33565e10 0.679258
\(5\) 1.38267e13 1.62097 0.810484 0.585760i \(-0.199204\pi\)
0.810484 + 0.585760i \(0.199204\pi\)
\(6\) −1.66160e13 −0.0667925
\(7\) −5.42222e15 −1.25853 −0.629264 0.777191i \(-0.716644\pi\)
−0.629264 + 0.777191i \(0.716644\pi\)
\(8\) 2.11777e16 0.415637
\(9\) −4.49088e17 −0.997343
\(10\) −6.64253e18 −2.10055
\(11\) −1.03285e18 −0.0560108 −0.0280054 0.999608i \(-0.508916\pi\)
−0.0280054 + 0.999608i \(0.508916\pi\)
\(12\) 3.22892e18 0.0350109
\(13\) −1.23244e19 −0.0303957 −0.0151979 0.999885i \(-0.504838\pi\)
−0.0151979 + 0.999885i \(0.504838\pi\)
\(14\) 2.60490e21 1.63088
\(15\) 4.78225e20 0.0835495
\(16\) −2.30048e22 −1.21787
\(17\) −5.41594e22 −0.934047 −0.467023 0.884245i \(-0.654674\pi\)
−0.467023 + 0.884245i \(0.654674\pi\)
\(18\) 2.15747e23 1.29242
\(19\) −3.08845e23 −0.680455 −0.340228 0.940343i \(-0.610504\pi\)
−0.340228 + 0.940343i \(0.610504\pi\)
\(20\) 1.29082e24 1.10106
\(21\) −1.87538e23 −0.0648682
\(22\) 4.96192e23 0.0725822
\(23\) −2.61592e25 −1.68136 −0.840678 0.541535i \(-0.817844\pi\)
−0.840678 + 0.541535i \(0.817844\pi\)
\(24\) 7.32473e23 0.0214232
\(25\) 1.18419e26 1.62754
\(26\) 5.92077e24 0.0393886
\(27\) −3.11065e25 −0.102949
\(28\) −5.06199e26 −0.854866
\(29\) 2.49238e26 0.219913 0.109957 0.993936i \(-0.464929\pi\)
0.109957 + 0.993936i \(0.464929\pi\)
\(30\) −2.29745e26 −0.108269
\(31\) −2.34643e27 −0.602859 −0.301429 0.953489i \(-0.597464\pi\)
−0.301429 + 0.953489i \(0.597464\pi\)
\(32\) 8.14116e27 1.16255
\(33\) −3.57230e25 −0.00288696
\(34\) 2.60188e28 1.21040
\(35\) −7.49716e28 −2.04004
\(36\) −4.19253e28 −0.677453
\(37\) 6.21792e28 0.605220 0.302610 0.953114i \(-0.402142\pi\)
0.302610 + 0.953114i \(0.402142\pi\)
\(38\) 1.48373e29 0.881776
\(39\) −4.26262e26 −0.00156668
\(40\) 2.92819e29 0.673735
\(41\) −8.53404e29 −1.24352 −0.621761 0.783207i \(-0.713582\pi\)
−0.621761 + 0.783207i \(0.713582\pi\)
\(42\) 9.00954e28 0.0840603
\(43\) 3.53994e29 0.213713 0.106856 0.994274i \(-0.465922\pi\)
0.106856 + 0.994274i \(0.465922\pi\)
\(44\) −9.64230e28 −0.0380457
\(45\) −6.20942e30 −1.61666
\(46\) 1.25672e31 2.17881
\(47\) 6.68978e29 0.0779115 0.0389557 0.999241i \(-0.487597\pi\)
0.0389557 + 0.999241i \(0.487597\pi\)
\(48\) −7.95667e29 −0.0627724
\(49\) 1.08383e31 0.583895
\(50\) −5.68899e31 −2.10907
\(51\) −1.87321e30 −0.0481435
\(52\) −1.15056e30 −0.0206465
\(53\) 1.24128e32 1.56591 0.782956 0.622077i \(-0.213711\pi\)
0.782956 + 0.622077i \(0.213711\pi\)
\(54\) 1.49439e31 0.133408
\(55\) −1.42809e31 −0.0907917
\(56\) −1.14830e32 −0.523092
\(57\) −1.06820e31 −0.0350726
\(58\) −1.19737e32 −0.284977
\(59\) 6.57033e31 0.113979 0.0569895 0.998375i \(-0.481850\pi\)
0.0569895 + 0.998375i \(0.481850\pi\)
\(60\) 4.46454e31 0.0567516
\(61\) −1.06034e33 −0.992758 −0.496379 0.868106i \(-0.665337\pi\)
−0.496379 + 0.868106i \(0.665337\pi\)
\(62\) 1.12725e33 0.781222
\(63\) 2.43505e33 1.25519
\(64\) −7.49344e32 −0.288637
\(65\) −1.70406e32 −0.0492705
\(66\) 1.71618e31 0.00374110
\(67\) −8.44869e33 −1.39446 −0.697229 0.716849i \(-0.745584\pi\)
−0.697229 + 0.716849i \(0.745584\pi\)
\(68\) −5.05613e33 −0.634459
\(69\) −9.04768e32 −0.0866620
\(70\) 3.60172e34 2.64360
\(71\) −7.04837e33 −0.397932 −0.198966 0.980006i \(-0.563758\pi\)
−0.198966 + 0.980006i \(0.563758\pi\)
\(72\) −9.51066e33 −0.414533
\(73\) 9.36735e33 0.316333 0.158166 0.987412i \(-0.449442\pi\)
0.158166 + 0.987412i \(0.449442\pi\)
\(74\) −2.98716e34 −0.784282
\(75\) 4.09575e33 0.0838881
\(76\) −2.88327e34 −0.462205
\(77\) 5.60032e33 0.0704911
\(78\) 2.04781e32 0.00203021
\(79\) 1.51854e35 1.18940 0.594698 0.803949i \(-0.297272\pi\)
0.594698 + 0.803949i \(0.297272\pi\)
\(80\) −3.18082e35 −1.97412
\(81\) 2.01141e35 0.992037
\(82\) 4.09985e35 1.61143
\(83\) −1.43761e35 −0.451541 −0.225771 0.974180i \(-0.572490\pi\)
−0.225771 + 0.974180i \(0.572490\pi\)
\(84\) −1.75079e34 −0.0440623
\(85\) −7.48847e35 −1.51406
\(86\) −1.70063e35 −0.276942
\(87\) 8.62039e33 0.0113350
\(88\) −2.18734e34 −0.0232802
\(89\) 2.28283e35 0.197133 0.0985664 0.995130i \(-0.468574\pi\)
0.0985664 + 0.995130i \(0.468574\pi\)
\(90\) 2.98308e36 2.09497
\(91\) 6.68253e34 0.0382539
\(92\) −2.44213e36 −1.14208
\(93\) −8.11557e34 −0.0310731
\(94\) −3.21385e35 −0.100962
\(95\) −4.27032e36 −1.10300
\(96\) 2.81578e35 0.0599212
\(97\) 7.07361e36 1.24269 0.621347 0.783535i \(-0.286586\pi\)
0.621347 + 0.783535i \(0.286586\pi\)
\(98\) −5.20686e36 −0.756647
\(99\) 4.63839e35 0.0558620
\(100\) 1.10552e37 1.10552
\(101\) −1.31355e37 −1.09270 −0.546350 0.837557i \(-0.683983\pi\)
−0.546350 + 0.837557i \(0.683983\pi\)
\(102\) 8.99911e35 0.0623873
\(103\) 2.33181e37 1.34960 0.674800 0.738000i \(-0.264230\pi\)
0.674800 + 0.738000i \(0.264230\pi\)
\(104\) −2.61002e35 −0.0126336
\(105\) −2.59304e36 −0.105149
\(106\) −5.96327e37 −2.02920
\(107\) 3.01693e36 0.0862909 0.0431454 0.999069i \(-0.486262\pi\)
0.0431454 + 0.999069i \(0.486262\pi\)
\(108\) −2.90400e36 −0.0699289
\(109\) 3.05531e37 0.620391 0.310195 0.950673i \(-0.399606\pi\)
0.310195 + 0.950673i \(0.399606\pi\)
\(110\) 6.86072e36 0.117653
\(111\) 2.15059e36 0.0311948
\(112\) 1.24737e38 1.53272
\(113\) 4.21983e37 0.439890 0.219945 0.975512i \(-0.429412\pi\)
0.219945 + 0.975512i \(0.429412\pi\)
\(114\) 5.13177e36 0.0454493
\(115\) −3.61697e38 −2.72543
\(116\) 2.32680e37 0.149378
\(117\) 5.53472e36 0.0303150
\(118\) −3.15646e37 −0.147701
\(119\) 2.93664e38 1.17552
\(120\) 1.01277e37 0.0347263
\(121\) −3.38973e38 −0.996863
\(122\) 5.09400e38 1.28648
\(123\) −2.95166e37 −0.0640947
\(124\) −2.19054e38 −0.409497
\(125\) 6.31322e38 1.01722
\(126\) −1.16983e39 −1.62655
\(127\) 1.09656e39 1.31724 0.658619 0.752476i \(-0.271141\pi\)
0.658619 + 0.752476i \(0.271141\pi\)
\(128\) −7.58918e38 −0.788516
\(129\) 1.22436e37 0.0110154
\(130\) 8.18649e37 0.0638477
\(131\) −2.36928e39 −1.60360 −0.801802 0.597590i \(-0.796125\pi\)
−0.801802 + 0.597590i \(0.796125\pi\)
\(132\) −3.33498e36 −0.00196099
\(133\) 1.67463e39 0.856373
\(134\) 4.05885e39 1.80702
\(135\) −4.30102e38 −0.166877
\(136\) −1.14697e39 −0.388225
\(137\) 2.55274e39 0.754529 0.377265 0.926105i \(-0.376865\pi\)
0.377265 + 0.926105i \(0.376865\pi\)
\(138\) 4.34661e38 0.112302
\(139\) −6.38958e39 −1.44444 −0.722219 0.691665i \(-0.756878\pi\)
−0.722219 + 0.691665i \(0.756878\pi\)
\(140\) −6.99908e39 −1.38571
\(141\) 2.31379e37 0.00401578
\(142\) 3.38612e39 0.515665
\(143\) 1.27292e37 0.00170249
\(144\) 1.03312e40 1.21463
\(145\) 3.44615e39 0.356473
\(146\) −4.50019e39 −0.409923
\(147\) 3.74864e38 0.0300956
\(148\) 5.80483e39 0.411100
\(149\) −3.49035e39 −0.218234 −0.109117 0.994029i \(-0.534802\pi\)
−0.109117 + 0.994029i \(0.534802\pi\)
\(150\) −1.96765e39 −0.108707
\(151\) −1.43880e40 −0.702953 −0.351476 0.936197i \(-0.614320\pi\)
−0.351476 + 0.936197i \(0.614320\pi\)
\(152\) −6.54064e39 −0.282823
\(153\) 2.43223e40 0.931565
\(154\) −2.69046e39 −0.0913468
\(155\) −3.24434e40 −0.977215
\(156\) −3.97943e37 −0.00106418
\(157\) 3.81842e40 0.907277 0.453639 0.891186i \(-0.350126\pi\)
0.453639 + 0.891186i \(0.350126\pi\)
\(158\) −7.29527e40 −1.54129
\(159\) 4.29322e39 0.0807116
\(160\) 1.12566e41 1.88446
\(161\) 1.41841e41 2.11604
\(162\) −9.66305e40 −1.28554
\(163\) −7.49639e40 −0.889982 −0.444991 0.895535i \(-0.646793\pi\)
−0.444991 + 0.895535i \(0.646793\pi\)
\(164\) −7.96708e40 −0.844672
\(165\) −4.93933e38 −0.00467967
\(166\) 6.90646e40 0.585135
\(167\) −1.87857e41 −1.42421 −0.712104 0.702074i \(-0.752257\pi\)
−0.712104 + 0.702074i \(0.752257\pi\)
\(168\) −3.97163e39 −0.0269617
\(169\) −1.64249e41 −0.999076
\(170\) 3.59755e41 1.96201
\(171\) 1.38699e41 0.678648
\(172\) 3.30477e40 0.145166
\(173\) 2.98432e41 1.17759 0.588793 0.808284i \(-0.299603\pi\)
0.588793 + 0.808284i \(0.299603\pi\)
\(174\) −4.14134e39 −0.0146886
\(175\) −6.42094e41 −2.04830
\(176\) 2.37605e40 0.0682136
\(177\) 2.27248e39 0.00587481
\(178\) −1.09670e41 −0.255457
\(179\) 3.46258e41 0.727141 0.363570 0.931567i \(-0.381558\pi\)
0.363570 + 0.931567i \(0.381558\pi\)
\(180\) −5.79689e41 −1.09813
\(181\) 4.05668e41 0.693613 0.346806 0.937937i \(-0.387266\pi\)
0.346806 + 0.937937i \(0.387266\pi\)
\(182\) −3.21037e40 −0.0495717
\(183\) −3.66740e40 −0.0511697
\(184\) −5.53993e41 −0.698835
\(185\) 8.59735e41 0.981043
\(186\) 3.89882e40 0.0402664
\(187\) 5.59384e40 0.0523167
\(188\) 6.24534e40 0.0529220
\(189\) 1.68666e41 0.129564
\(190\) 2.05151e42 1.42933
\(191\) −1.41675e42 −0.895726 −0.447863 0.894102i \(-0.647815\pi\)
−0.447863 + 0.894102i \(0.647815\pi\)
\(192\) −2.59175e40 −0.0148772
\(193\) −1.28639e42 −0.670751 −0.335375 0.942085i \(-0.608863\pi\)
−0.335375 + 0.942085i \(0.608863\pi\)
\(194\) −3.39825e42 −1.61036
\(195\) −5.89381e39 −0.00253954
\(196\) 1.01183e42 0.396615
\(197\) 3.68135e41 0.131336 0.0656678 0.997842i \(-0.479082\pi\)
0.0656678 + 0.997842i \(0.479082\pi\)
\(198\) −2.22834e41 −0.0723894
\(199\) 3.12066e42 0.923557 0.461779 0.886995i \(-0.347211\pi\)
0.461779 + 0.886995i \(0.347211\pi\)
\(200\) 2.50785e42 0.676466
\(201\) −2.92214e41 −0.0718744
\(202\) 6.31044e42 1.41599
\(203\) −1.35142e42 −0.276767
\(204\) −1.74876e41 −0.0327019
\(205\) −1.17998e43 −2.01571
\(206\) −1.12023e43 −1.74890
\(207\) 1.17478e43 1.67689
\(208\) 2.83520e41 0.0370179
\(209\) 3.18990e41 0.0381128
\(210\) 1.24573e42 0.136259
\(211\) −7.58037e42 −0.759391 −0.379695 0.925112i \(-0.623971\pi\)
−0.379695 + 0.925112i \(0.623971\pi\)
\(212\) 1.15882e43 1.06366
\(213\) −2.43782e41 −0.0205106
\(214\) −1.44937e42 −0.111821
\(215\) 4.89459e42 0.346421
\(216\) −6.58765e41 −0.0427894
\(217\) 1.27228e43 0.758715
\(218\) −1.46781e43 −0.803941
\(219\) 3.23988e41 0.0163047
\(220\) −1.33322e42 −0.0616710
\(221\) 6.67479e41 0.0283910
\(222\) −1.03317e42 −0.0404242
\(223\) 4.00362e43 1.44149 0.720747 0.693198i \(-0.243799\pi\)
0.720747 + 0.693198i \(0.243799\pi\)
\(224\) −4.41431e43 −1.46310
\(225\) −5.31805e43 −1.62322
\(226\) −2.02726e43 −0.570037
\(227\) 3.89322e43 1.00886 0.504430 0.863453i \(-0.331703\pi\)
0.504430 + 0.863453i \(0.331703\pi\)
\(228\) −9.97236e41 −0.0238234
\(229\) −3.32118e43 −0.731704 −0.365852 0.930673i \(-0.619222\pi\)
−0.365852 + 0.930673i \(0.619222\pi\)
\(230\) 1.73763e44 3.53178
\(231\) 1.93698e41 0.00363332
\(232\) 5.27830e42 0.0914043
\(233\) −7.95672e43 −1.27248 −0.636238 0.771493i \(-0.719510\pi\)
−0.636238 + 0.771493i \(0.719510\pi\)
\(234\) −2.65894e42 −0.0392840
\(235\) 9.24978e42 0.126292
\(236\) 6.13383e42 0.0774211
\(237\) 5.25218e42 0.0613049
\(238\) −1.41080e44 −1.52332
\(239\) −1.42241e44 −1.42123 −0.710615 0.703581i \(-0.751583\pi\)
−0.710615 + 0.703581i \(0.751583\pi\)
\(240\) −1.10015e43 −0.101752
\(241\) 1.48641e44 1.27299 0.636494 0.771282i \(-0.280384\pi\)
0.636494 + 0.771282i \(0.280384\pi\)
\(242\) 1.62846e44 1.29180
\(243\) 2.09636e43 0.154081
\(244\) −9.89897e43 −0.674339
\(245\) 1.49859e44 0.946475
\(246\) 1.41801e43 0.0830579
\(247\) 3.80632e42 0.0206829
\(248\) −4.96920e43 −0.250571
\(249\) −4.97227e42 −0.0232738
\(250\) −3.03294e44 −1.31818
\(251\) 1.84398e44 0.744377 0.372189 0.928157i \(-0.378607\pi\)
0.372189 + 0.928157i \(0.378607\pi\)
\(252\) 2.27328e44 0.852595
\(253\) 2.70185e43 0.0941741
\(254\) −5.26801e44 −1.70696
\(255\) −2.59003e43 −0.0780391
\(256\) 4.67582e44 1.31044
\(257\) −2.92391e44 −0.762433 −0.381216 0.924486i \(-0.624495\pi\)
−0.381216 + 0.924486i \(0.624495\pi\)
\(258\) −5.88196e42 −0.0142744
\(259\) −3.37149e44 −0.761687
\(260\) −1.59085e43 −0.0334674
\(261\) −1.11930e44 −0.219329
\(262\) 1.13823e45 2.07805
\(263\) −4.07317e44 −0.693029 −0.346514 0.938045i \(-0.612635\pi\)
−0.346514 + 0.938045i \(0.612635\pi\)
\(264\) −7.56533e41 −0.00119993
\(265\) 1.71629e45 2.53829
\(266\) −8.04510e44 −1.10974
\(267\) 7.89562e42 0.0101608
\(268\) −7.88740e44 −0.947196
\(269\) −6.06370e44 −0.679705 −0.339853 0.940479i \(-0.610377\pi\)
−0.339853 + 0.940479i \(0.610377\pi\)
\(270\) 2.06626e44 0.216249
\(271\) −1.82672e45 −1.78542 −0.892711 0.450630i \(-0.851200\pi\)
−0.892711 + 0.450630i \(0.851200\pi\)
\(272\) 1.24593e45 1.13754
\(273\) 2.31128e42 0.00197172
\(274\) −1.22637e45 −0.977766
\(275\) −1.22309e44 −0.0911597
\(276\) −8.44659e43 −0.0588659
\(277\) 2.33400e45 1.52134 0.760668 0.649141i \(-0.224872\pi\)
0.760668 + 0.649141i \(0.224872\pi\)
\(278\) 3.06963e45 1.87179
\(279\) 1.05375e45 0.601257
\(280\) −1.58773e45 −0.847915
\(281\) −1.00137e45 −0.500643 −0.250322 0.968163i \(-0.580536\pi\)
−0.250322 + 0.968163i \(0.580536\pi\)
\(282\) −1.11157e43 −0.00520390
\(283\) −2.73703e45 −1.20014 −0.600069 0.799948i \(-0.704860\pi\)
−0.600069 + 0.799948i \(0.704860\pi\)
\(284\) −6.58011e44 −0.270299
\(285\) −1.47697e44 −0.0568517
\(286\) −6.11525e42 −0.00220619
\(287\) 4.62734e45 1.56501
\(288\) −3.65609e45 −1.15946
\(289\) −4.28857e44 −0.127557
\(290\) −1.65557e45 −0.461940
\(291\) 2.44655e44 0.0640521
\(292\) 8.74503e44 0.214871
\(293\) 1.07452e45 0.247836 0.123918 0.992292i \(-0.460454\pi\)
0.123918 + 0.992292i \(0.460454\pi\)
\(294\) −1.80089e44 −0.0389998
\(295\) 9.08462e44 0.184756
\(296\) 1.31681e45 0.251552
\(297\) 3.21283e43 0.00576625
\(298\) 1.67680e45 0.282801
\(299\) 3.22396e44 0.0511060
\(300\) 3.82365e44 0.0569817
\(301\) −1.91943e45 −0.268963
\(302\) 6.91215e45 0.910930
\(303\) −4.54316e44 −0.0563209
\(304\) 7.10494e45 0.828704
\(305\) −1.46611e46 −1.60923
\(306\) −1.16847e46 −1.20718
\(307\) −1.41267e46 −1.37398 −0.686989 0.726668i \(-0.741068\pi\)
−0.686989 + 0.726668i \(0.741068\pi\)
\(308\) 5.22826e44 0.0478817
\(309\) 8.06503e44 0.0695624
\(310\) 1.55862e46 1.26634
\(311\) 1.21153e46 0.927399 0.463700 0.885992i \(-0.346522\pi\)
0.463700 + 0.885992i \(0.346522\pi\)
\(312\) −9.02726e42 −0.000651172 0
\(313\) 8.67864e45 0.590040 0.295020 0.955491i \(-0.404674\pi\)
0.295020 + 0.955491i \(0.404674\pi\)
\(314\) −1.83441e46 −1.17571
\(315\) 3.36688e46 2.03462
\(316\) 1.41766e46 0.807906
\(317\) −2.34417e46 −1.26006 −0.630031 0.776570i \(-0.716958\pi\)
−0.630031 + 0.776570i \(0.716958\pi\)
\(318\) −2.06251e45 −0.104591
\(319\) −2.57425e44 −0.0123175
\(320\) −1.03610e46 −0.467871
\(321\) 1.04346e44 0.00444768
\(322\) −6.81421e46 −2.74209
\(323\) 1.67269e46 0.635577
\(324\) 1.87778e46 0.673849
\(325\) −1.45944e45 −0.0494702
\(326\) 3.60135e46 1.15329
\(327\) 1.05674e45 0.0319768
\(328\) −1.80732e46 −0.516854
\(329\) −3.62734e45 −0.0980538
\(330\) 2.37291e44 0.00606420
\(331\) 5.11187e46 1.23527 0.617635 0.786465i \(-0.288091\pi\)
0.617635 + 0.786465i \(0.288091\pi\)
\(332\) −1.34211e46 −0.306713
\(333\) −2.79239e46 −0.603612
\(334\) 9.02488e46 1.84558
\(335\) −1.16818e47 −2.26037
\(336\) 4.31428e45 0.0790009
\(337\) 2.29819e46 0.398320 0.199160 0.979967i \(-0.436179\pi\)
0.199160 + 0.979967i \(0.436179\pi\)
\(338\) 7.89071e46 1.29466
\(339\) 1.45951e45 0.0226732
\(340\) −6.99098e46 −1.02844
\(341\) 2.42350e45 0.0337666
\(342\) −6.66325e46 −0.879433
\(343\) 4.18801e46 0.523680
\(344\) 7.49680e45 0.0888269
\(345\) −1.25100e46 −0.140476
\(346\) −1.43370e47 −1.52599
\(347\) −8.38076e46 −0.845645 −0.422822 0.906213i \(-0.638961\pi\)
−0.422822 + 0.906213i \(0.638961\pi\)
\(348\) 8.04770e44 0.00769938
\(349\) 1.33845e47 1.21432 0.607158 0.794581i \(-0.292310\pi\)
0.607158 + 0.794581i \(0.292310\pi\)
\(350\) 3.08469e47 2.65432
\(351\) 3.83368e44 0.00312920
\(352\) −8.40857e45 −0.0651153
\(353\) 1.44127e46 0.105904 0.0529520 0.998597i \(-0.483137\pi\)
0.0529520 + 0.998597i \(0.483137\pi\)
\(354\) −1.09172e45 −0.00761294
\(355\) −9.74560e46 −0.645036
\(356\) 2.13117e46 0.133904
\(357\) 1.01569e46 0.0605900
\(358\) −1.66346e47 −0.942274
\(359\) 6.57303e46 0.353605 0.176802 0.984246i \(-0.443425\pi\)
0.176802 + 0.984246i \(0.443425\pi\)
\(360\) −1.31501e47 −0.671945
\(361\) −1.10622e47 −0.536981
\(362\) −1.94888e47 −0.898826
\(363\) −1.17240e46 −0.0513812
\(364\) 6.23858e45 0.0259842
\(365\) 1.29520e47 0.512765
\(366\) 1.76186e46 0.0663088
\(367\) 2.16797e47 0.775768 0.387884 0.921708i \(-0.373206\pi\)
0.387884 + 0.921708i \(0.373206\pi\)
\(368\) 6.01789e47 2.04767
\(369\) 3.83253e47 1.24022
\(370\) −4.13027e47 −1.27130
\(371\) −6.73051e47 −1.97074
\(372\) −7.57641e45 −0.0211066
\(373\) 2.47528e47 0.656163 0.328081 0.944649i \(-0.393598\pi\)
0.328081 + 0.944649i \(0.393598\pi\)
\(374\) −2.68734e46 −0.0677952
\(375\) 2.18355e46 0.0524305
\(376\) 1.41674e46 0.0323829
\(377\) −3.07170e45 −0.00668442
\(378\) −8.10293e46 −0.167897
\(379\) 1.02737e47 0.202722 0.101361 0.994850i \(-0.467680\pi\)
0.101361 + 0.994850i \(0.467680\pi\)
\(380\) −3.98663e47 −0.749219
\(381\) 3.79267e46 0.0678943
\(382\) 6.80622e47 1.16074
\(383\) −1.22188e48 −1.98541 −0.992706 0.120559i \(-0.961531\pi\)
−0.992706 + 0.120559i \(0.961531\pi\)
\(384\) −2.62487e46 −0.0406424
\(385\) 7.74342e46 0.114264
\(386\) 6.17995e47 0.869200
\(387\) −1.58975e47 −0.213145
\(388\) 6.60368e47 0.844110
\(389\) −1.16416e48 −1.41888 −0.709440 0.704766i \(-0.751052\pi\)
−0.709440 + 0.704766i \(0.751052\pi\)
\(390\) 2.83146e45 0.00329090
\(391\) 1.41677e48 1.57047
\(392\) 2.29531e47 0.242688
\(393\) −8.19461e46 −0.0826544
\(394\) −1.76857e47 −0.170193
\(395\) 2.09965e48 1.92797
\(396\) 4.33024e46 0.0379447
\(397\) −1.33628e48 −1.11756 −0.558781 0.829315i \(-0.688731\pi\)
−0.558781 + 0.829315i \(0.688731\pi\)
\(398\) −1.49920e48 −1.19680
\(399\) 5.79202e46 0.0441399
\(400\) −2.72421e48 −1.98213
\(401\) 2.54007e47 0.176472 0.0882358 0.996100i \(-0.471877\pi\)
0.0882358 + 0.996100i \(0.471877\pi\)
\(402\) 1.40383e47 0.0931393
\(403\) 2.89182e46 0.0183243
\(404\) −1.22628e48 −0.742225
\(405\) 2.78112e48 1.60806
\(406\) 6.49240e47 0.358652
\(407\) −6.42216e46 −0.0338988
\(408\) −3.96703e46 −0.0200102
\(409\) −1.33788e48 −0.644967 −0.322484 0.946575i \(-0.604518\pi\)
−0.322484 + 0.946575i \(0.604518\pi\)
\(410\) 5.66876e48 2.61208
\(411\) 8.82915e46 0.0388906
\(412\) 2.17690e48 0.916727
\(413\) −3.56257e47 −0.143446
\(414\) −5.64377e48 −2.17302
\(415\) −1.98775e48 −0.731934
\(416\) −1.00334e47 −0.0353365
\(417\) −2.20996e47 −0.0744505
\(418\) −1.53247e47 −0.0493889
\(419\) 2.08239e48 0.642101 0.321050 0.947062i \(-0.395964\pi\)
0.321050 + 0.947062i \(0.395964\pi\)
\(420\) −2.42077e47 −0.0714236
\(421\) −4.42178e48 −1.24847 −0.624236 0.781236i \(-0.714590\pi\)
−0.624236 + 0.781236i \(0.714590\pi\)
\(422\) 3.64170e48 0.984065
\(423\) −3.00430e47 −0.0777045
\(424\) 2.62876e48 0.650851
\(425\) −6.41350e48 −1.52020
\(426\) 1.17116e47 0.0265789
\(427\) 5.74940e48 1.24941
\(428\) 2.81650e47 0.0586138
\(429\) 4.40263e44 8.77511e−5 0
\(430\) −2.35142e48 −0.448914
\(431\) 3.37175e48 0.616631 0.308315 0.951284i \(-0.400235\pi\)
0.308315 + 0.951284i \(0.400235\pi\)
\(432\) 7.15601e47 0.125378
\(433\) 2.37577e48 0.398822 0.199411 0.979916i \(-0.436097\pi\)
0.199411 + 0.979916i \(0.436097\pi\)
\(434\) −6.11220e48 −0.983190
\(435\) 1.19192e47 0.0183736
\(436\) 2.85233e48 0.421405
\(437\) 8.07916e48 1.14409
\(438\) −1.55648e47 −0.0211286
\(439\) −2.31976e48 −0.301890 −0.150945 0.988542i \(-0.548232\pi\)
−0.150945 + 0.988542i \(0.548232\pi\)
\(440\) −3.02437e47 −0.0377364
\(441\) −4.86736e48 −0.582344
\(442\) −3.20665e47 −0.0367908
\(443\) −1.52174e49 −1.67444 −0.837222 0.546864i \(-0.815822\pi\)
−0.837222 + 0.546864i \(0.815822\pi\)
\(444\) 2.00771e47 0.0211893
\(445\) 3.15641e48 0.319546
\(446\) −1.92339e49 −1.86798
\(447\) −1.20720e47 −0.0112484
\(448\) 4.06311e48 0.363258
\(449\) 1.92781e49 1.65390 0.826948 0.562279i \(-0.190075\pi\)
0.826948 + 0.562279i \(0.190075\pi\)
\(450\) 2.55486e49 2.10346
\(451\) 8.81436e47 0.0696506
\(452\) 3.93949e48 0.298799
\(453\) −4.97636e47 −0.0362322
\(454\) −1.87035e49 −1.30734
\(455\) 9.23976e47 0.0620083
\(456\) −2.26221e47 −0.0145775
\(457\) 1.19646e49 0.740367 0.370183 0.928959i \(-0.379295\pi\)
0.370183 + 0.928959i \(0.379295\pi\)
\(458\) 1.59553e49 0.948187
\(459\) 1.68471e48 0.0961591
\(460\) −3.37667e49 −1.85127
\(461\) −2.78549e49 −1.46702 −0.733508 0.679680i \(-0.762119\pi\)
−0.733508 + 0.679680i \(0.762119\pi\)
\(462\) −9.30548e46 −0.00470828
\(463\) −1.11920e49 −0.544075 −0.272038 0.962287i \(-0.587697\pi\)
−0.272038 + 0.962287i \(0.587697\pi\)
\(464\) −5.73369e48 −0.267825
\(465\) −1.12212e48 −0.0503685
\(466\) 3.82250e49 1.64895
\(467\) −1.63248e49 −0.676840 −0.338420 0.940995i \(-0.609892\pi\)
−0.338420 + 0.940995i \(0.609892\pi\)
\(468\) 5.16702e47 0.0205917
\(469\) 4.58106e49 1.75497
\(470\) −4.44370e48 −0.163657
\(471\) 1.32067e48 0.0467637
\(472\) 1.39145e48 0.0473739
\(473\) −3.65622e47 −0.0119702
\(474\) −2.52321e48 −0.0794427
\(475\) −3.65732e49 −1.10747
\(476\) 2.74154e49 0.798485
\(477\) −5.57445e49 −1.56175
\(478\) 6.83344e49 1.84172
\(479\) 2.63654e49 0.683639 0.341820 0.939766i \(-0.388957\pi\)
0.341820 + 0.939766i \(0.388957\pi\)
\(480\) 3.89330e48 0.0971304
\(481\) −7.66319e47 −0.0183961
\(482\) −7.14090e49 −1.64962
\(483\) 4.90585e48 0.109067
\(484\) −3.16453e49 −0.677127
\(485\) 9.78050e49 2.01437
\(486\) −1.00712e49 −0.199668
\(487\) −7.78447e49 −1.48574 −0.742871 0.669435i \(-0.766536\pi\)
−0.742871 + 0.669435i \(0.766536\pi\)
\(488\) −2.24556e49 −0.412628
\(489\) −2.59277e48 −0.0458723
\(490\) −7.19938e49 −1.22650
\(491\) 9.85282e49 1.61642 0.808208 0.588897i \(-0.200438\pi\)
0.808208 + 0.588897i \(0.200438\pi\)
\(492\) −2.75557e48 −0.0435368
\(493\) −1.34986e49 −0.205409
\(494\) −1.82860e48 −0.0268022
\(495\) 6.41338e48 0.0905505
\(496\) 5.39792e49 0.734201
\(497\) 3.82178e49 0.500809
\(498\) 2.38874e48 0.0301596
\(499\) 1.25338e50 1.52483 0.762415 0.647088i \(-0.224013\pi\)
0.762415 + 0.647088i \(0.224013\pi\)
\(500\) 5.89380e49 0.690955
\(501\) −6.49741e48 −0.0734078
\(502\) −8.85871e49 −0.964610
\(503\) −1.11020e50 −1.16518 −0.582589 0.812767i \(-0.697960\pi\)
−0.582589 + 0.812767i \(0.697960\pi\)
\(504\) 5.15688e49 0.521702
\(505\) −1.81621e50 −1.77123
\(506\) −1.29800e49 −0.122037
\(507\) −5.68087e48 −0.0514953
\(508\) 1.02371e50 0.894745
\(509\) −1.38813e50 −1.16991 −0.584955 0.811066i \(-0.698888\pi\)
−0.584955 + 0.811066i \(0.698888\pi\)
\(510\) 1.24428e49 0.101128
\(511\) −5.07918e49 −0.398114
\(512\) −1.20327e50 −0.909639
\(513\) 9.60711e48 0.0700521
\(514\) 1.40468e50 0.988007
\(515\) 3.22414e50 2.18766
\(516\) 1.14302e48 0.00748228
\(517\) −6.90952e47 −0.00436388
\(518\) 1.61970e50 0.987041
\(519\) 1.03219e49 0.0606962
\(520\) −3.60880e48 −0.0204787
\(521\) −2.33871e50 −1.28079 −0.640396 0.768045i \(-0.721230\pi\)
−0.640396 + 0.768045i \(0.721230\pi\)
\(522\) 5.37724e49 0.284220
\(523\) −1.30285e50 −0.664679 −0.332340 0.943160i \(-0.607838\pi\)
−0.332340 + 0.943160i \(0.607838\pi\)
\(524\) −2.21188e50 −1.08926
\(525\) −2.22081e49 −0.105576
\(526\) 1.95680e50 0.898070
\(527\) 1.27081e50 0.563098
\(528\) 8.21803e47 0.00351593
\(529\) 4.42241e50 1.82696
\(530\) −8.24525e50 −3.28928
\(531\) −2.95065e49 −0.113676
\(532\) 1.56337e50 0.581698
\(533\) 1.05177e49 0.0377977
\(534\) −3.79315e48 −0.0131670
\(535\) 4.17143e49 0.139875
\(536\) −1.78924e50 −0.579589
\(537\) 1.19760e49 0.0374789
\(538\) 2.91307e50 0.880804
\(539\) −1.11943e49 −0.0327044
\(540\) −4.01528e49 −0.113352
\(541\) −5.31273e50 −1.44933 −0.724667 0.689099i \(-0.758007\pi\)
−0.724667 + 0.689099i \(0.758007\pi\)
\(542\) 8.77579e50 2.31366
\(543\) 1.40308e49 0.0357508
\(544\) −4.40920e50 −1.08588
\(545\) 4.22450e50 1.00563
\(546\) −1.11037e48 −0.00255507
\(547\) −7.47732e49 −0.166334 −0.0831669 0.996536i \(-0.526503\pi\)
−0.0831669 + 0.996536i \(0.526503\pi\)
\(548\) 2.38315e50 0.512520
\(549\) 4.76186e50 0.990121
\(550\) 5.87586e49 0.118130
\(551\) −7.69761e49 −0.149641
\(552\) −1.91609e49 −0.0360200
\(553\) −8.23388e50 −1.49689
\(554\) −1.12128e51 −1.97144
\(555\) 2.97356e49 0.0505658
\(556\) −5.96509e50 −0.981146
\(557\) 3.60496e50 0.573560 0.286780 0.957996i \(-0.407415\pi\)
0.286780 + 0.957996i \(0.407415\pi\)
\(558\) −5.06234e50 −0.779146
\(559\) −4.36275e48 −0.00649594
\(560\) 1.72471e51 2.48449
\(561\) 1.93474e48 0.00269655
\(562\) 4.81071e50 0.648764
\(563\) −3.94055e50 −0.514223 −0.257112 0.966382i \(-0.582771\pi\)
−0.257112 + 0.966382i \(0.582771\pi\)
\(564\) 2.16007e48 0.00272775
\(565\) 5.83465e50 0.713048
\(566\) 1.31490e51 1.55521
\(567\) −1.09063e51 −1.24851
\(568\) −1.49268e50 −0.165396
\(569\) −1.14686e50 −0.123008 −0.0615040 0.998107i \(-0.519590\pi\)
−0.0615040 + 0.998107i \(0.519590\pi\)
\(570\) 7.09556e49 0.0736719
\(571\) 1.48184e51 1.48948 0.744739 0.667356i \(-0.232574\pi\)
0.744739 + 0.667356i \(0.232574\pi\)
\(572\) 1.18835e48 0.00115643
\(573\) −4.90010e49 −0.0461683
\(574\) −2.22303e51 −2.02803
\(575\) −3.09775e51 −2.73647
\(576\) 3.36521e50 0.287870
\(577\) 1.51306e51 1.25344 0.626722 0.779243i \(-0.284396\pi\)
0.626722 + 0.779243i \(0.284396\pi\)
\(578\) 2.06028e50 0.165296
\(579\) −4.44922e49 −0.0345725
\(580\) 3.21721e50 0.242137
\(581\) 7.79505e50 0.568278
\(582\) −1.17535e50 −0.0830027
\(583\) −1.28206e50 −0.0877079
\(584\) 1.98379e50 0.131480
\(585\) 7.65271e49 0.0491396
\(586\) −5.16213e50 −0.321161
\(587\) 8.72797e50 0.526148 0.263074 0.964776i \(-0.415264\pi\)
0.263074 + 0.964776i \(0.415264\pi\)
\(588\) 3.49960e49 0.0204427
\(589\) 7.24683e50 0.410218
\(590\) −4.36436e50 −0.239419
\(591\) 1.27327e49 0.00676942
\(592\) −1.43042e51 −0.737077
\(593\) 4.58679e49 0.0229085 0.0114543 0.999934i \(-0.496354\pi\)
0.0114543 + 0.999934i \(0.496354\pi\)
\(594\) −1.54348e49 −0.00747226
\(595\) 4.06041e51 1.90549
\(596\) −3.25846e50 −0.148237
\(597\) 1.07934e50 0.0476028
\(598\) −1.54883e50 −0.0662263
\(599\) −2.10919e51 −0.874420 −0.437210 0.899360i \(-0.644033\pi\)
−0.437210 + 0.899360i \(0.644033\pi\)
\(600\) 8.67388e49 0.0348670
\(601\) −2.46594e51 −0.961179 −0.480589 0.876946i \(-0.659577\pi\)
−0.480589 + 0.876946i \(0.659577\pi\)
\(602\) 9.22119e50 0.348539
\(603\) 3.79420e51 1.39075
\(604\) −1.34321e51 −0.477486
\(605\) −4.68689e51 −1.61588
\(606\) 2.18259e50 0.0729841
\(607\) −4.33541e51 −1.40618 −0.703088 0.711103i \(-0.748196\pi\)
−0.703088 + 0.711103i \(0.748196\pi\)
\(608\) −2.51436e51 −0.791063
\(609\) −4.67416e49 −0.0142654
\(610\) 7.04334e51 2.08534
\(611\) −8.24472e48 −0.00236817
\(612\) 2.27065e51 0.632773
\(613\) −1.36136e51 −0.368091 −0.184046 0.982918i \(-0.558919\pi\)
−0.184046 + 0.982918i \(0.558919\pi\)
\(614\) 6.78662e51 1.78049
\(615\) −4.08119e50 −0.103896
\(616\) 1.18602e50 0.0292988
\(617\) 3.77980e51 0.906136 0.453068 0.891476i \(-0.350329\pi\)
0.453068 + 0.891476i \(0.350329\pi\)
\(618\) −3.87454e50 −0.0901432
\(619\) 6.56261e50 0.148183 0.0740917 0.997251i \(-0.476394\pi\)
0.0740917 + 0.997251i \(0.476394\pi\)
\(620\) −3.02880e51 −0.663781
\(621\) 8.13722e50 0.173094
\(622\) −5.82033e51 −1.20178
\(623\) −1.23780e51 −0.248097
\(624\) 9.80609e48 0.00190801
\(625\) 1.12996e50 0.0213443
\(626\) −4.16932e51 −0.764610
\(627\) 1.10329e49 0.00196445
\(628\) 3.56474e51 0.616275
\(629\) −3.36759e51 −0.565304
\(630\) −1.61749e52 −2.63658
\(631\) 3.19436e51 0.505640 0.252820 0.967513i \(-0.418642\pi\)
0.252820 + 0.967513i \(0.418642\pi\)
\(632\) 3.21593e51 0.494357
\(633\) −2.62182e50 −0.0391412
\(634\) 1.12617e52 1.63287
\(635\) 1.51619e52 2.13520
\(636\) 4.00800e50 0.0548240
\(637\) −1.33575e50 −0.0177479
\(638\) 1.23670e50 0.0159618
\(639\) 3.16534e51 0.396875
\(640\) −1.04934e52 −1.27816
\(641\) −1.48064e52 −1.75217 −0.876085 0.482157i \(-0.839853\pi\)
−0.876085 + 0.482157i \(0.839853\pi\)
\(642\) −5.01292e49 −0.00576358
\(643\) 6.82003e51 0.761874 0.380937 0.924601i \(-0.375601\pi\)
0.380937 + 0.924601i \(0.375601\pi\)
\(644\) 1.32418e52 1.43733
\(645\) 1.69289e50 0.0178556
\(646\) −8.03579e51 −0.823620
\(647\) −2.43296e51 −0.242329 −0.121165 0.992632i \(-0.538663\pi\)
−0.121165 + 0.992632i \(0.538663\pi\)
\(648\) 4.25971e51 0.412328
\(649\) −6.78614e49 −0.00638405
\(650\) 7.01131e50 0.0641065
\(651\) 4.40044e50 0.0391064
\(652\) −6.99837e51 −0.604528
\(653\) 5.92349e51 0.497375 0.248687 0.968584i \(-0.420001\pi\)
0.248687 + 0.968584i \(0.420001\pi\)
\(654\) −5.07670e50 −0.0414375
\(655\) −3.27594e52 −2.59939
\(656\) 1.96324e52 1.51444
\(657\) −4.20676e51 −0.315492
\(658\) 1.74262e51 0.127064
\(659\) 2.77432e51 0.196687 0.0983437 0.995153i \(-0.468646\pi\)
0.0983437 + 0.995153i \(0.468646\pi\)
\(660\) −4.61118e49 −0.00317870
\(661\) 1.53847e52 1.03124 0.515622 0.856816i \(-0.327561\pi\)
0.515622 + 0.856816i \(0.327561\pi\)
\(662\) −2.45580e52 −1.60074
\(663\) 2.30861e49 0.00146336
\(664\) −3.04454e51 −0.187677
\(665\) 2.31546e52 1.38815
\(666\) 1.34150e52 0.782198
\(667\) −6.51988e51 −0.369753
\(668\) −1.75377e52 −0.967404
\(669\) 1.38473e51 0.0742988
\(670\) 5.61206e52 2.92913
\(671\) 1.09517e51 0.0556051
\(672\) −1.52678e51 −0.0754125
\(673\) −8.54768e50 −0.0410742 −0.0205371 0.999789i \(-0.506538\pi\)
−0.0205371 + 0.999789i \(0.506538\pi\)
\(674\) −1.10408e52 −0.516168
\(675\) −3.68360e51 −0.167553
\(676\) −1.53337e52 −0.678630
\(677\) −3.33629e52 −1.43673 −0.718363 0.695669i \(-0.755108\pi\)
−0.718363 + 0.695669i \(0.755108\pi\)
\(678\) −7.01167e50 −0.0293814
\(679\) −3.83547e52 −1.56397
\(680\) −1.58589e52 −0.629300
\(681\) 1.34655e51 0.0519996
\(682\) −1.16428e51 −0.0437568
\(683\) 3.41377e52 1.24868 0.624340 0.781153i \(-0.285368\pi\)
0.624340 + 0.781153i \(0.285368\pi\)
\(684\) 1.29484e52 0.460977
\(685\) 3.52961e52 1.22307
\(686\) −2.01197e52 −0.678618
\(687\) −1.14869e51 −0.0377142
\(688\) −8.14359e51 −0.260273
\(689\) −1.52980e51 −0.0475970
\(690\) 6.00994e51 0.182038
\(691\) 5.92716e52 1.74784 0.873922 0.486066i \(-0.161569\pi\)
0.873922 + 0.486066i \(0.161569\pi\)
\(692\) 2.78606e52 0.799884
\(693\) −2.51504e51 −0.0703039
\(694\) 4.02621e52 1.09584
\(695\) −8.83471e52 −2.34139
\(696\) 1.82560e50 0.00471124
\(697\) 4.62198e52 1.16151
\(698\) −6.43007e52 −1.57359
\(699\) −2.75199e51 −0.0655871
\(700\) −5.99436e52 −1.39133
\(701\) 4.09077e52 0.924744 0.462372 0.886686i \(-0.346998\pi\)
0.462372 + 0.886686i \(0.346998\pi\)
\(702\) −1.84174e50 −0.00405502
\(703\) −1.92038e52 −0.411825
\(704\) 7.73958e50 0.0161668
\(705\) 3.19922e50 0.00650946
\(706\) −6.92401e51 −0.137237
\(707\) 7.12235e52 1.37519
\(708\) 2.12150e50 0.00399051
\(709\) −8.44115e52 −1.54684 −0.773422 0.633891i \(-0.781457\pi\)
−0.773422 + 0.633891i \(0.781457\pi\)
\(710\) 4.68190e52 0.835877
\(711\) −6.81960e52 −1.18624
\(712\) 4.83452e51 0.0819357
\(713\) 6.13807e52 1.01362
\(714\) −4.87951e51 −0.0785162
\(715\) 1.76003e50 0.00275968
\(716\) 3.23254e52 0.493916
\(717\) −4.91969e51 −0.0732544
\(718\) −3.15776e52 −0.458223
\(719\) −2.81946e52 −0.398733 −0.199367 0.979925i \(-0.563888\pi\)
−0.199367 + 0.979925i \(0.563888\pi\)
\(720\) 1.42847e53 1.96888
\(721\) −1.26436e53 −1.69851
\(722\) 5.31442e52 0.695853
\(723\) 5.14105e51 0.0656135
\(724\) 3.78717e52 0.471142
\(725\) 2.95146e52 0.357918
\(726\) 5.63236e51 0.0665830
\(727\) 6.98427e52 0.804886 0.402443 0.915445i \(-0.368161\pi\)
0.402443 + 0.915445i \(0.368161\pi\)
\(728\) 1.41521e51 0.0158997
\(729\) −8.98455e52 −0.984095
\(730\) −6.22229e52 −0.664473
\(731\) −1.91721e52 −0.199618
\(732\) −3.42375e51 −0.0347574
\(733\) 3.54513e52 0.350921 0.175460 0.984487i \(-0.443859\pi\)
0.175460 + 0.984487i \(0.443859\pi\)
\(734\) −1.04152e53 −1.00529
\(735\) 5.18315e51 0.0487841
\(736\) −2.12966e53 −1.95466
\(737\) 8.72620e51 0.0781046
\(738\) −1.84119e53 −1.60715
\(739\) 1.51689e53 1.29131 0.645655 0.763629i \(-0.276584\pi\)
0.645655 + 0.763629i \(0.276584\pi\)
\(740\) 8.02619e52 0.666381
\(741\) 1.31649e50 0.00106606
\(742\) 3.23341e53 2.55381
\(743\) 1.52901e53 1.17793 0.588964 0.808159i \(-0.299536\pi\)
0.588964 + 0.808159i \(0.299536\pi\)
\(744\) −1.71869e51 −0.0129151
\(745\) −4.82601e52 −0.353750
\(746\) −1.18916e53 −0.850296
\(747\) 6.45615e52 0.450342
\(748\) 5.22221e51 0.0355365
\(749\) −1.63584e52 −0.108600
\(750\) −1.04900e52 −0.0679427
\(751\) 1.42568e53 0.900916 0.450458 0.892798i \(-0.351261\pi\)
0.450458 + 0.892798i \(0.351261\pi\)
\(752\) −1.53897e52 −0.0948858
\(753\) 6.37778e51 0.0383674
\(754\) 1.47568e51 0.00866209
\(755\) −1.98939e53 −1.13946
\(756\) 1.57461e52 0.0880075
\(757\) −2.82784e53 −1.54234 −0.771171 0.636628i \(-0.780329\pi\)
−0.771171 + 0.636628i \(0.780329\pi\)
\(758\) −4.93559e52 −0.262699
\(759\) 9.34487e50 0.00485401
\(760\) −9.04358e52 −0.458447
\(761\) 3.71288e52 0.183694 0.0918470 0.995773i \(-0.470723\pi\)
0.0918470 + 0.995773i \(0.470723\pi\)
\(762\) −1.82204e52 −0.0879817
\(763\) −1.65666e53 −0.780780
\(764\) −1.32263e53 −0.608429
\(765\) 3.36298e53 1.51004
\(766\) 5.87005e53 2.57282
\(767\) −8.09750e50 −0.00346447
\(768\) 1.61722e52 0.0675441
\(769\) −6.15158e52 −0.250813 −0.125406 0.992105i \(-0.540023\pi\)
−0.125406 + 0.992105i \(0.540023\pi\)
\(770\) −3.72003e52 −0.148070
\(771\) −1.01129e52 −0.0392980
\(772\) −1.20093e53 −0.455613
\(773\) −2.28656e53 −0.846960 −0.423480 0.905905i \(-0.639192\pi\)
−0.423480 + 0.905905i \(0.639192\pi\)
\(774\) 7.63732e52 0.276206
\(775\) −2.77862e53 −0.981176
\(776\) 1.49803e53 0.516510
\(777\) −1.16610e52 −0.0392596
\(778\) 5.59277e53 1.83867
\(779\) 2.63570e53 0.846161
\(780\) −5.50225e50 −0.00172501
\(781\) 7.27989e51 0.0222885
\(782\) −6.80632e53 −2.03511
\(783\) −7.75294e51 −0.0226399
\(784\) −2.49334e53 −0.711106
\(785\) 5.27963e53 1.47067
\(786\) 3.93679e52 0.107109
\(787\) 7.05791e52 0.187561 0.0937807 0.995593i \(-0.470105\pi\)
0.0937807 + 0.995593i \(0.470105\pi\)
\(788\) 3.43678e52 0.0892108
\(789\) −1.40879e52 −0.0357207
\(790\) −1.00870e54 −2.49839
\(791\) −2.28809e53 −0.553614
\(792\) 9.82306e51 0.0232183
\(793\) 1.30680e52 0.0301756
\(794\) 6.41963e53 1.44821
\(795\) 5.93612e52 0.130831
\(796\) 2.91333e53 0.627334
\(797\) −8.88567e53 −1.86944 −0.934719 0.355387i \(-0.884349\pi\)
−0.934719 + 0.355387i \(0.884349\pi\)
\(798\) −2.78256e52 −0.0571993
\(799\) −3.62314e52 −0.0727729
\(800\) 9.64068e53 1.89209
\(801\) −1.02519e53 −0.196609
\(802\) −1.22028e53 −0.228683
\(803\) −9.67504e51 −0.0177180
\(804\) −2.72801e52 −0.0488213
\(805\) 1.96120e54 3.43003
\(806\) −1.38926e52 −0.0237458
\(807\) −2.09725e52 −0.0350340
\(808\) −2.78180e53 −0.454167
\(809\) 3.72232e53 0.593972 0.296986 0.954882i \(-0.404019\pi\)
0.296986 + 0.954882i \(0.404019\pi\)
\(810\) −1.33608e54 −2.08382
\(811\) −5.96718e53 −0.909668 −0.454834 0.890576i \(-0.650301\pi\)
−0.454834 + 0.890576i \(0.650301\pi\)
\(812\) −1.26164e53 −0.187996
\(813\) −6.31808e52 −0.0920259
\(814\) 3.08528e52 0.0439282
\(815\) −1.03651e54 −1.44263
\(816\) 4.30929e52 0.0586324
\(817\) −1.09330e53 −0.145422
\(818\) 6.42736e53 0.835788
\(819\) −3.00104e52 −0.0381522
\(820\) −1.10159e54 −1.36919
\(821\) 8.74697e52 0.106294 0.0531471 0.998587i \(-0.483075\pi\)
0.0531471 + 0.998587i \(0.483075\pi\)
\(822\) −4.24163e52 −0.0503969
\(823\) 1.05135e54 1.22138 0.610692 0.791869i \(-0.290892\pi\)
0.610692 + 0.791869i \(0.290892\pi\)
\(824\) 4.93825e53 0.560945
\(825\) −4.23029e51 −0.00469864
\(826\) 1.71150e53 0.185886
\(827\) −1.54483e53 −0.164069 −0.0820347 0.996629i \(-0.526142\pi\)
−0.0820347 + 0.996629i \(0.526142\pi\)
\(828\) 1.09673e54 1.13904
\(829\) 2.69934e53 0.274156 0.137078 0.990560i \(-0.456229\pi\)
0.137078 + 0.990560i \(0.456229\pi\)
\(830\) 9.54939e53 0.948486
\(831\) 8.07259e52 0.0784141
\(832\) 9.23518e51 0.00877332
\(833\) −5.86997e53 −0.545385
\(834\) 1.06169e53 0.0964776
\(835\) −2.59745e54 −2.30860
\(836\) 2.97798e52 0.0258884
\(837\) 7.29891e52 0.0620636
\(838\) −1.00041e54 −0.832074
\(839\) 2.43290e54 1.97937 0.989686 0.143252i \(-0.0457561\pi\)
0.989686 + 0.143252i \(0.0457561\pi\)
\(840\) −5.49146e52 −0.0437040
\(841\) −1.22236e54 −0.951638
\(842\) 2.12428e54 1.61785
\(843\) −3.46344e52 −0.0258046
\(844\) −7.07677e53 −0.515822
\(845\) −2.27103e54 −1.61947
\(846\) 1.44330e53 0.100694
\(847\) 1.83798e54 1.25458
\(848\) −2.85555e54 −1.90707
\(849\) −9.46656e52 −0.0618586
\(850\) 3.08112e54 1.96997
\(851\) −1.62656e54 −1.01759
\(852\) −2.27586e52 −0.0139320
\(853\) 9.59321e53 0.574654 0.287327 0.957832i \(-0.407233\pi\)
0.287327 + 0.957832i \(0.407233\pi\)
\(854\) −2.76208e54 −1.61907
\(855\) 1.91775e54 1.10007
\(856\) 6.38917e52 0.0358657
\(857\) 3.59352e52 0.0197413 0.00987063 0.999951i \(-0.496858\pi\)
0.00987063 + 0.999951i \(0.496858\pi\)
\(858\) −2.11508e50 −0.000113713 0
\(859\) 8.55580e53 0.450181 0.225091 0.974338i \(-0.427732\pi\)
0.225091 + 0.974338i \(0.427732\pi\)
\(860\) 4.56942e53 0.235309
\(861\) 1.60046e53 0.0806651
\(862\) −1.61983e54 −0.799068
\(863\) 1.56057e54 0.753502 0.376751 0.926315i \(-0.377041\pi\)
0.376751 + 0.926315i \(0.377041\pi\)
\(864\) −2.53243e53 −0.119683
\(865\) 4.12634e54 1.90883
\(866\) −1.14135e54 −0.516818
\(867\) −1.48329e52 −0.00657464
\(868\) 1.18776e54 0.515363
\(869\) −1.56842e53 −0.0666190
\(870\) −5.72612e52 −0.0238097
\(871\) 1.04125e53 0.0423855
\(872\) 6.47046e53 0.257858
\(873\) −3.17667e54 −1.23939
\(874\) −3.88132e54 −1.48258
\(875\) −3.42316e54 −1.28020
\(876\) 3.02464e52 0.0110751
\(877\) −3.37270e54 −1.20916 −0.604581 0.796544i \(-0.706659\pi\)
−0.604581 + 0.796544i \(0.706659\pi\)
\(878\) 1.11444e54 0.391208
\(879\) 3.71644e52 0.0127742
\(880\) 3.28530e53 0.110572
\(881\) 1.67513e54 0.552069 0.276034 0.961148i \(-0.410980\pi\)
0.276034 + 0.961148i \(0.410980\pi\)
\(882\) 2.33834e54 0.754637
\(883\) 1.42002e54 0.448767 0.224383 0.974501i \(-0.427963\pi\)
0.224383 + 0.974501i \(0.427963\pi\)
\(884\) 6.23135e52 0.0192848
\(885\) 3.14209e52 0.00952288
\(886\) 7.31060e54 2.16985
\(887\) 1.98874e54 0.578085 0.289042 0.957316i \(-0.406663\pi\)
0.289042 + 0.957316i \(0.406663\pi\)
\(888\) 4.55446e52 0.0129657
\(889\) −5.94580e54 −1.65778
\(890\) −1.51638e54 −0.414087
\(891\) −2.07748e53 −0.0555647
\(892\) 3.73764e54 0.979147
\(893\) −2.06611e53 −0.0530153
\(894\) 5.79955e52 0.0145764
\(895\) 4.78761e54 1.17867
\(896\) 4.11502e54 0.992370
\(897\) 1.11507e52 0.00263415
\(898\) −9.26145e54 −2.14322
\(899\) −5.84819e53 −0.132577
\(900\) −4.96475e54 −1.10258
\(901\) −6.72271e54 −1.46263
\(902\) −4.23452e53 −0.0902575
\(903\) −6.63874e52 −0.0138632
\(904\) 8.93665e53 0.182835
\(905\) 5.60906e54 1.12432
\(906\) 2.39070e53 0.0469520
\(907\) −6.36503e54 −1.22480 −0.612401 0.790547i \(-0.709796\pi\)
−0.612401 + 0.790547i \(0.709796\pi\)
\(908\) 3.63458e54 0.685276
\(909\) 5.89899e54 1.08980
\(910\) −4.43889e53 −0.0803542
\(911\) 2.93922e54 0.521365 0.260683 0.965425i \(-0.416052\pi\)
0.260683 + 0.965425i \(0.416052\pi\)
\(912\) 2.45738e53 0.0427138
\(913\) 1.48484e53 0.0252912
\(914\) −5.74791e54 −0.959413
\(915\) −5.07081e53 −0.0829444
\(916\) −3.10053e54 −0.497016
\(917\) 1.28467e55 2.01818
\(918\) −8.09354e53 −0.124609
\(919\) −7.57823e54 −1.14349 −0.571743 0.820433i \(-0.693733\pi\)
−0.571743 + 0.820433i \(0.693733\pi\)
\(920\) −7.65991e54 −1.13279
\(921\) −4.88598e53 −0.0708189
\(922\) 1.33818e55 1.90105
\(923\) 8.68666e52 0.0120954
\(924\) 1.80830e52 0.00246796
\(925\) 7.36320e54 0.985019
\(926\) 5.37676e54 0.705046
\(927\) −1.04719e55 −1.34602
\(928\) 2.02909e54 0.255660
\(929\) 6.55047e53 0.0809062 0.0404531 0.999181i \(-0.487120\pi\)
0.0404531 + 0.999181i \(0.487120\pi\)
\(930\) 5.39079e53 0.0652706
\(931\) −3.34737e54 −0.397314
\(932\) −7.42812e54 −0.864340
\(933\) 4.19031e53 0.0478009
\(934\) 7.84263e54 0.877091
\(935\) 7.73445e53 0.0848037
\(936\) 1.17213e53 0.0126000
\(937\) −3.87596e54 −0.408505 −0.204253 0.978918i \(-0.565476\pi\)
−0.204253 + 0.978918i \(0.565476\pi\)
\(938\) −2.20080e55 −2.27419
\(939\) 3.00168e53 0.0304124
\(940\) 8.63527e53 0.0857849
\(941\) −1.38620e55 −1.35027 −0.675133 0.737696i \(-0.735914\pi\)
−0.675133 + 0.737696i \(0.735914\pi\)
\(942\) −6.34468e53 −0.0605993
\(943\) 2.23244e55 2.09080
\(944\) −1.51149e54 −0.138811
\(945\) 2.33210e54 0.210019
\(946\) 1.75649e53 0.0155117
\(947\) −8.86598e53 −0.0767807 −0.0383903 0.999263i \(-0.512223\pi\)
−0.0383903 + 0.999263i \(0.512223\pi\)
\(948\) 4.90325e53 0.0416419
\(949\) −1.15447e53 −0.00961515
\(950\) 1.75702e55 1.43512
\(951\) −8.10776e53 −0.0649473
\(952\) 6.21913e54 0.488592
\(953\) 1.94425e55 1.49807 0.749036 0.662530i \(-0.230517\pi\)
0.749036 + 0.662530i \(0.230517\pi\)
\(954\) 2.67803e55 2.02381
\(955\) −1.95890e55 −1.45194
\(956\) −1.32791e55 −0.965382
\(957\) −8.90355e51 −0.000634881 0
\(958\) −1.26662e55 −0.885902
\(959\) −1.38415e55 −0.949597
\(960\) −3.58355e53 −0.0241155
\(961\) −9.64324e54 −0.636561
\(962\) 3.68148e53 0.0238388
\(963\) −1.35486e54 −0.0860616
\(964\) 1.38766e55 0.864687
\(965\) −1.77865e55 −1.08727
\(966\) −2.35683e54 −0.141335
\(967\) 6.67380e54 0.392630 0.196315 0.980541i \(-0.437103\pi\)
0.196315 + 0.980541i \(0.437103\pi\)
\(968\) −7.17867e54 −0.414333
\(969\) 5.78532e53 0.0327595
\(970\) −4.69867e55 −2.61034
\(971\) −3.90466e52 −0.00212827 −0.00106414 0.999999i \(-0.500339\pi\)
−0.00106414 + 0.999999i \(0.500339\pi\)
\(972\) 1.95709e54 0.104661
\(973\) 3.46457e55 1.81787
\(974\) 3.73975e55 1.92532
\(975\) −5.04775e52 −0.00254984
\(976\) 2.43930e55 1.20905
\(977\) −6.49911e54 −0.316085 −0.158043 0.987432i \(-0.550518\pi\)
−0.158043 + 0.987432i \(0.550518\pi\)
\(978\) 1.24560e54 0.0594441
\(979\) −2.35782e53 −0.0110416
\(980\) 1.39903e55 0.642901
\(981\) −1.37210e55 −0.618743
\(982\) −4.73341e55 −2.09465
\(983\) 1.39076e55 0.603967 0.301984 0.953313i \(-0.402351\pi\)
0.301984 + 0.953313i \(0.402351\pi\)
\(984\) −6.25095e53 −0.0266402
\(985\) 5.09011e54 0.212891
\(986\) 6.48488e54 0.266182
\(987\) −1.25459e53 −0.00505398
\(988\) 3.55345e53 0.0140490
\(989\) −9.26022e54 −0.359327
\(990\) −3.08106e54 −0.117341
\(991\) 4.28319e55 1.60105 0.800525 0.599300i \(-0.204554\pi\)
0.800525 + 0.599300i \(0.204554\pi\)
\(992\) −1.91026e55 −0.700853
\(993\) 1.76804e54 0.0636695
\(994\) −1.83603e55 −0.648980
\(995\) 4.31485e55 1.49706
\(996\) −4.64193e53 −0.0158089
\(997\) −3.24811e55 −1.08585 −0.542925 0.839781i \(-0.682683\pi\)
−0.542925 + 0.839781i \(0.682683\pi\)
\(998\) −6.02137e55 −1.97597
\(999\) −1.93418e54 −0.0623067
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 1.38.a.a.1.1 2
3.2 odd 2 9.38.a.a.1.2 2
4.3 odd 2 16.38.a.b.1.1 2
5.2 odd 4 25.38.b.a.24.1 4
5.3 odd 4 25.38.b.a.24.4 4
5.4 even 2 25.38.a.a.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.38.a.a.1.1 2 1.1 even 1 trivial
9.38.a.a.1.2 2 3.2 odd 2
16.38.a.b.1.1 2 4.3 odd 2
25.38.a.a.1.2 2 5.4 even 2
25.38.b.a.24.1 4 5.2 odd 4
25.38.b.a.24.4 4 5.3 odd 4