Properties

Label 5.34.a.a.1.4
Level 5
Weight 34
Character 5.1
Self dual Yes
Analytic conductor 34.491
Analytic rank 1
Dimension 5
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 34 \)
Character orbit: \([\chi]\) = 5.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(34.4914144405\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{21}\cdot 3^{5}\cdot 5^{4}\cdot 11 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-16460.4\)
Character \(\chi\) = 5.1

$q$-expansion

\(f(q)\) \(=\) \(q+71937.8 q^{2} +1.37573e8 q^{3} -3.41489e9 q^{4} -1.52588e11 q^{5} +9.89671e12 q^{6} -1.07684e14 q^{7} -8.63600e14 q^{8} +1.33673e16 q^{9} +O(q^{10})\) \(q+71937.8 q^{2} +1.37573e8 q^{3} -3.41489e9 q^{4} -1.52588e11 q^{5} +9.89671e12 q^{6} -1.07684e14 q^{7} -8.63600e14 q^{8} +1.33673e16 q^{9} -1.09768e16 q^{10} -2.33530e17 q^{11} -4.69797e17 q^{12} -2.28395e18 q^{13} -7.74658e18 q^{14} -2.09920e19 q^{15} -3.27918e19 q^{16} -2.09885e20 q^{17} +9.61615e20 q^{18} +6.01644e20 q^{19} +5.21071e20 q^{20} -1.48145e22 q^{21} -1.67997e22 q^{22} +4.84991e22 q^{23} -1.18808e23 q^{24} +2.32831e22 q^{25} -1.64302e23 q^{26} +1.07421e24 q^{27} +3.67730e23 q^{28} -8.15476e22 q^{29} -1.51012e24 q^{30} -1.49925e24 q^{31} +5.05930e24 q^{32} -3.21275e25 q^{33} -1.50986e25 q^{34} +1.64313e25 q^{35} -4.56479e25 q^{36} +1.78708e25 q^{37} +4.32809e25 q^{38} -3.14210e26 q^{39} +1.31775e26 q^{40} -1.94621e26 q^{41} -1.06572e27 q^{42} -9.48110e26 q^{43} +7.97481e26 q^{44} -2.03969e27 q^{45} +3.48891e27 q^{46} -6.29157e26 q^{47} -4.51128e27 q^{48} +3.86494e27 q^{49} +1.67493e27 q^{50} -2.88745e28 q^{51} +7.79943e27 q^{52} -8.56042e27 q^{53} +7.72760e28 q^{54} +3.56339e28 q^{55} +9.29963e28 q^{56} +8.27701e28 q^{57} -5.86635e27 q^{58} +5.43089e27 q^{59} +7.16853e28 q^{60} +1.79220e29 q^{61} -1.07853e29 q^{62} -1.43945e30 q^{63} +6.45635e29 q^{64} +3.48503e29 q^{65} -2.31118e30 q^{66} -3.33703e29 q^{67} +7.16732e29 q^{68} +6.67217e30 q^{69} +1.18203e30 q^{70} -3.44997e30 q^{71} -1.15440e31 q^{72} -7.11823e30 q^{73} +1.28559e30 q^{74} +3.20312e30 q^{75} -2.05455e30 q^{76} +2.51476e31 q^{77} -2.26036e31 q^{78} -1.57830e31 q^{79} +5.00364e30 q^{80} +7.34723e31 q^{81} -1.40006e31 q^{82} +3.45599e31 q^{83} +5.05898e31 q^{84} +3.20258e31 q^{85} -6.82049e31 q^{86} -1.12188e31 q^{87} +2.01677e32 q^{88} -2.35733e32 q^{89} -1.46731e32 q^{90} +2.45946e32 q^{91} -1.65619e32 q^{92} -2.06256e32 q^{93} -4.52602e31 q^{94} -9.18036e31 q^{95} +6.96024e32 q^{96} -3.55763e32 q^{97} +2.78035e32 q^{98} -3.12168e33 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q + 30472q^{2} - 14988714q^{3} + 1141311360q^{4} - 762939453125q^{5} + 12925063115760q^{6} - 65452561787158q^{7} + 155610638035200q^{8} + 14541250990408965q^{9} + O(q^{10}) \) \( 5q + 30472q^{2} - 14988714q^{3} + 1141311360q^{4} - 762939453125q^{5} + 12925063115760q^{6} - 65452561787158q^{7} + 155610638035200q^{8} + 14541250990408965q^{9} - 4649658203125000q^{10} - 287801801877976640q^{11} - 405379955363513088q^{12} + 2397201150889907466q^{13} + 11676449916272482320q^{14} + 2287096252441406250q^{15} - 89180089543245957120q^{16} - \)\(30\!\cdots\!18\)\(q^{17} + \)\(53\!\cdots\!56\)\(q^{18} + \)\(91\!\cdots\!00\)\(q^{19} - \)\(17\!\cdots\!00\)\(q^{20} - \)\(10\!\cdots\!40\)\(q^{21} - \)\(13\!\cdots\!96\)\(q^{22} + \)\(55\!\cdots\!46\)\(q^{23} - \)\(71\!\cdots\!00\)\(q^{24} + \)\(11\!\cdots\!25\)\(q^{25} - \)\(42\!\cdots\!40\)\(q^{26} + \)\(67\!\cdots\!00\)\(q^{27} - \)\(13\!\cdots\!36\)\(q^{28} - \)\(92\!\cdots\!50\)\(q^{29} - \)\(19\!\cdots\!00\)\(q^{30} - \)\(13\!\cdots\!40\)\(q^{31} - \)\(81\!\cdots\!08\)\(q^{32} - \)\(33\!\cdots\!48\)\(q^{33} - \)\(68\!\cdots\!80\)\(q^{34} + \)\(99\!\cdots\!50\)\(q^{35} - \)\(18\!\cdots\!20\)\(q^{36} - \)\(14\!\cdots\!38\)\(q^{37} - \)\(33\!\cdots\!00\)\(q^{38} - \)\(78\!\cdots\!20\)\(q^{39} - \)\(23\!\cdots\!00\)\(q^{40} - \)\(13\!\cdots\!90\)\(q^{41} - \)\(26\!\cdots\!36\)\(q^{42} - \)\(23\!\cdots\!94\)\(q^{43} - \)\(18\!\cdots\!80\)\(q^{44} - \)\(22\!\cdots\!25\)\(q^{45} - \)\(28\!\cdots\!40\)\(q^{46} - \)\(77\!\cdots\!98\)\(q^{47} - \)\(73\!\cdots\!04\)\(q^{48} + \)\(41\!\cdots\!85\)\(q^{49} + \)\(70\!\cdots\!00\)\(q^{50} + \)\(73\!\cdots\!60\)\(q^{51} + \)\(48\!\cdots\!72\)\(q^{52} + \)\(10\!\cdots\!86\)\(q^{53} + \)\(64\!\cdots\!00\)\(q^{54} + \)\(43\!\cdots\!00\)\(q^{55} + \)\(14\!\cdots\!00\)\(q^{56} + \)\(20\!\cdots\!00\)\(q^{57} + \)\(21\!\cdots\!00\)\(q^{58} + \)\(25\!\cdots\!00\)\(q^{59} + \)\(61\!\cdots\!00\)\(q^{60} + \)\(74\!\cdots\!10\)\(q^{61} + \)\(53\!\cdots\!24\)\(q^{62} - \)\(10\!\cdots\!34\)\(q^{63} - \)\(10\!\cdots\!40\)\(q^{64} - \)\(36\!\cdots\!50\)\(q^{65} - \)\(33\!\cdots\!80\)\(q^{66} - \)\(37\!\cdots\!18\)\(q^{67} + \)\(11\!\cdots\!44\)\(q^{68} - \)\(27\!\cdots\!20\)\(q^{69} - \)\(17\!\cdots\!00\)\(q^{70} - \)\(55\!\cdots\!40\)\(q^{71} - \)\(15\!\cdots\!00\)\(q^{72} - \)\(13\!\cdots\!54\)\(q^{73} - \)\(36\!\cdots\!80\)\(q^{74} - \)\(34\!\cdots\!50\)\(q^{75} + \)\(71\!\cdots\!00\)\(q^{76} + \)\(47\!\cdots\!44\)\(q^{77} + \)\(12\!\cdots\!72\)\(q^{78} - \)\(10\!\cdots\!00\)\(q^{79} + \)\(13\!\cdots\!00\)\(q^{80} + \)\(78\!\cdots\!05\)\(q^{81} + \)\(27\!\cdots\!84\)\(q^{82} + \)\(92\!\cdots\!26\)\(q^{83} + \)\(17\!\cdots\!20\)\(q^{84} + \)\(47\!\cdots\!50\)\(q^{85} + \)\(65\!\cdots\!60\)\(q^{86} + \)\(13\!\cdots\!00\)\(q^{87} + \)\(19\!\cdots\!00\)\(q^{88} - \)\(60\!\cdots\!50\)\(q^{89} - \)\(82\!\cdots\!00\)\(q^{90} - \)\(26\!\cdots\!40\)\(q^{91} - \)\(69\!\cdots\!68\)\(q^{92} - \)\(69\!\cdots\!88\)\(q^{93} - \)\(36\!\cdots\!80\)\(q^{94} - \)\(14\!\cdots\!00\)\(q^{95} - \)\(34\!\cdots\!40\)\(q^{96} - \)\(86\!\cdots\!98\)\(q^{97} - \)\(19\!\cdots\!96\)\(q^{98} - \)\(17\!\cdots\!20\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 71937.8 0.776180 0.388090 0.921622i \(-0.373135\pi\)
0.388090 + 0.921622i \(0.373135\pi\)
\(3\) 1.37573e8 1.84516 0.922578 0.385811i \(-0.126078\pi\)
0.922578 + 0.385811i \(0.126078\pi\)
\(4\) −3.41489e9 −0.397545
\(5\) −1.52588e11 −0.447214
\(6\) 9.89671e12 1.43217
\(7\) −1.07684e14 −1.22472 −0.612358 0.790581i \(-0.709779\pi\)
−0.612358 + 0.790581i \(0.709779\pi\)
\(8\) −8.63600e14 −1.08475
\(9\) 1.33673e16 2.40460
\(10\) −1.09768e16 −0.347118
\(11\) −2.33530e17 −1.53237 −0.766186 0.642619i \(-0.777848\pi\)
−0.766186 + 0.642619i \(0.777848\pi\)
\(12\) −4.69797e17 −0.733533
\(13\) −2.28395e18 −0.951965 −0.475983 0.879455i \(-0.657908\pi\)
−0.475983 + 0.879455i \(0.657908\pi\)
\(14\) −7.74658e18 −0.950599
\(15\) −2.09920e19 −0.825179
\(16\) −3.27918e19 −0.444412
\(17\) −2.09885e20 −1.04610 −0.523050 0.852302i \(-0.675206\pi\)
−0.523050 + 0.852302i \(0.675206\pi\)
\(18\) 9.61615e20 1.86640
\(19\) 6.01644e20 0.478526 0.239263 0.970955i \(-0.423094\pi\)
0.239263 + 0.970955i \(0.423094\pi\)
\(20\) 5.21071e20 0.177788
\(21\) −1.48145e22 −2.25979
\(22\) −1.67997e22 −1.18940
\(23\) 4.84991e22 1.64901 0.824506 0.565853i \(-0.191453\pi\)
0.824506 + 0.565853i \(0.191453\pi\)
\(24\) −1.18808e23 −2.00153
\(25\) 2.32831e22 0.200000
\(26\) −1.64302e23 −0.738896
\(27\) 1.07421e24 2.59171
\(28\) 3.67730e23 0.486880
\(29\) −8.15476e22 −0.0605124 −0.0302562 0.999542i \(-0.509632\pi\)
−0.0302562 + 0.999542i \(0.509632\pi\)
\(30\) −1.51012e24 −0.640487
\(31\) −1.49925e24 −0.370174 −0.185087 0.982722i \(-0.559257\pi\)
−0.185087 + 0.982722i \(0.559257\pi\)
\(32\) 5.05930e24 0.739802
\(33\) −3.21275e25 −2.82747
\(34\) −1.50986e25 −0.811961
\(35\) 1.64313e25 0.547709
\(36\) −4.56479e25 −0.955938
\(37\) 1.78708e25 0.238131 0.119066 0.992886i \(-0.462010\pi\)
0.119066 + 0.992886i \(0.462010\pi\)
\(38\) 4.32809e25 0.371422
\(39\) −3.14210e26 −1.75652
\(40\) 1.31775e26 0.485113
\(41\) −1.94621e26 −0.476712 −0.238356 0.971178i \(-0.576608\pi\)
−0.238356 + 0.971178i \(0.576608\pi\)
\(42\) −1.06572e27 −1.75400
\(43\) −9.48110e26 −1.05835 −0.529175 0.848513i \(-0.677498\pi\)
−0.529175 + 0.848513i \(0.677498\pi\)
\(44\) 7.97481e26 0.609187
\(45\) −2.03969e27 −1.07537
\(46\) 3.48891e27 1.27993
\(47\) −6.29157e26 −0.161862 −0.0809309 0.996720i \(-0.525789\pi\)
−0.0809309 + 0.996720i \(0.525789\pi\)
\(48\) −4.51128e27 −0.820010
\(49\) 3.86494e27 0.499927
\(50\) 1.67493e27 0.155236
\(51\) −2.88745e28 −1.93022
\(52\) 7.79943e27 0.378449
\(53\) −8.56042e27 −0.303350 −0.151675 0.988430i \(-0.548467\pi\)
−0.151675 + 0.988430i \(0.548467\pi\)
\(54\) 7.72760e28 2.01163
\(55\) 3.56339e28 0.685298
\(56\) 9.29963e28 1.32851
\(57\) 8.27701e28 0.882954
\(58\) −5.86635e27 −0.0469685
\(59\) 5.43089e27 0.0327954 0.0163977 0.999866i \(-0.494780\pi\)
0.0163977 + 0.999866i \(0.494780\pi\)
\(60\) 7.16853e28 0.328046
\(61\) 1.79220e29 0.624373 0.312186 0.950021i \(-0.398939\pi\)
0.312186 + 0.950021i \(0.398939\pi\)
\(62\) −1.07853e29 −0.287321
\(63\) −1.43945e30 −2.94495
\(64\) 6.45635e29 1.01863
\(65\) 3.48503e29 0.425732
\(66\) −2.31118e30 −2.19462
\(67\) −3.33703e29 −0.247244 −0.123622 0.992329i \(-0.539451\pi\)
−0.123622 + 0.992329i \(0.539451\pi\)
\(68\) 7.16732e29 0.415872
\(69\) 6.67217e30 3.04269
\(70\) 1.18203e30 0.425121
\(71\) −3.44997e30 −0.981866 −0.490933 0.871197i \(-0.663344\pi\)
−0.490933 + 0.871197i \(0.663344\pi\)
\(72\) −1.15440e31 −2.60838
\(73\) −7.11823e30 −1.28099 −0.640494 0.767963i \(-0.721270\pi\)
−0.640494 + 0.767963i \(0.721270\pi\)
\(74\) 1.28559e30 0.184833
\(75\) 3.20312e30 0.369031
\(76\) −2.05455e30 −0.190236
\(77\) 2.51476e31 1.87672
\(78\) −2.26036e31 −1.36338
\(79\) −1.57830e31 −0.771510 −0.385755 0.922601i \(-0.626059\pi\)
−0.385755 + 0.922601i \(0.626059\pi\)
\(80\) 5.00364e30 0.198747
\(81\) 7.34723e31 2.37750
\(82\) −1.40006e31 −0.370014
\(83\) 3.45599e31 0.747798 0.373899 0.927470i \(-0.378021\pi\)
0.373899 + 0.927470i \(0.378021\pi\)
\(84\) 5.05898e31 0.898369
\(85\) 3.20258e31 0.467830
\(86\) −6.82049e31 −0.821469
\(87\) −1.12188e31 −0.111655
\(88\) 2.01677e32 1.66223
\(89\) −2.35733e32 −1.61244 −0.806222 0.591613i \(-0.798491\pi\)
−0.806222 + 0.591613i \(0.798491\pi\)
\(90\) −1.46731e32 −0.834680
\(91\) 2.45946e32 1.16589
\(92\) −1.65619e32 −0.655557
\(93\) −2.06256e32 −0.683029
\(94\) −4.52602e31 −0.125634
\(95\) −9.18036e31 −0.214003
\(96\) 6.96024e32 1.36505
\(97\) −3.55763e32 −0.588067 −0.294033 0.955795i \(-0.594998\pi\)
−0.294033 + 0.955795i \(0.594998\pi\)
\(98\) 2.78035e32 0.388033
\(99\) −3.12168e33 −3.68474
\(100\) −7.95091e31 −0.0795091
\(101\) 9.03859e32 0.767004 0.383502 0.923540i \(-0.374718\pi\)
0.383502 + 0.923540i \(0.374718\pi\)
\(102\) −2.07717e33 −1.49820
\(103\) 2.36642e33 1.45304 0.726519 0.687146i \(-0.241137\pi\)
0.726519 + 0.687146i \(0.241137\pi\)
\(104\) 1.97242e33 1.03264
\(105\) 2.26051e33 1.01061
\(106\) −6.15818e32 −0.235454
\(107\) 2.84756e33 0.932482 0.466241 0.884658i \(-0.345608\pi\)
0.466241 + 0.884658i \(0.345608\pi\)
\(108\) −3.66830e33 −1.03032
\(109\) 3.46217e33 0.835241 0.417620 0.908622i \(-0.362864\pi\)
0.417620 + 0.908622i \(0.362864\pi\)
\(110\) 2.56343e33 0.531914
\(111\) 2.45855e33 0.439389
\(112\) 3.53117e33 0.544279
\(113\) −9.04247e33 −1.20363 −0.601815 0.798636i \(-0.705556\pi\)
−0.601815 + 0.798636i \(0.705556\pi\)
\(114\) 5.95430e33 0.685331
\(115\) −7.40037e33 −0.737461
\(116\) 2.78476e32 0.0240564
\(117\) −3.05303e34 −2.28910
\(118\) 3.90687e32 0.0254551
\(119\) 2.26013e34 1.28117
\(120\) 1.81287e34 0.895109
\(121\) 3.13113e34 1.34816
\(122\) 1.28927e34 0.484626
\(123\) −2.67746e34 −0.879608
\(124\) 5.11977e33 0.147161
\(125\) −3.55271e33 −0.0894427
\(126\) −1.03551e35 −2.28581
\(127\) −4.59458e33 −0.0890194 −0.0445097 0.999009i \(-0.514173\pi\)
−0.0445097 + 0.999009i \(0.514173\pi\)
\(128\) 2.98648e33 0.0508388
\(129\) −1.30434e35 −1.95282
\(130\) 2.50705e34 0.330444
\(131\) −2.50614e34 −0.291091 −0.145545 0.989352i \(-0.546494\pi\)
−0.145545 + 0.989352i \(0.546494\pi\)
\(132\) 1.09712e35 1.12405
\(133\) −6.47877e34 −0.586058
\(134\) −2.40059e34 −0.191906
\(135\) −1.63911e35 −1.15905
\(136\) 1.81256e35 1.13475
\(137\) 2.78859e35 1.54702 0.773510 0.633784i \(-0.218499\pi\)
0.773510 + 0.633784i \(0.218499\pi\)
\(138\) 4.79981e35 2.36167
\(139\) 1.40995e35 0.615827 0.307914 0.951414i \(-0.400369\pi\)
0.307914 + 0.951414i \(0.400369\pi\)
\(140\) −5.61112e34 −0.217739
\(141\) −8.65551e34 −0.298660
\(142\) −2.48183e35 −0.762104
\(143\) 5.33372e35 1.45877
\(144\) −4.38339e35 −1.06863
\(145\) 1.24432e34 0.0270620
\(146\) −5.12070e35 −0.994277
\(147\) 5.31711e35 0.922444
\(148\) −6.10269e34 −0.0946680
\(149\) −4.84716e35 −0.672844 −0.336422 0.941711i \(-0.609217\pi\)
−0.336422 + 0.941711i \(0.609217\pi\)
\(150\) 2.30426e35 0.286434
\(151\) −1.29129e35 −0.143848 −0.0719238 0.997410i \(-0.522914\pi\)
−0.0719238 + 0.997410i \(0.522914\pi\)
\(152\) −5.19580e35 −0.519079
\(153\) −2.80559e36 −2.51545
\(154\) 1.80906e36 1.45667
\(155\) 2.28767e35 0.165547
\(156\) 1.07299e36 0.698298
\(157\) 1.48727e36 0.871052 0.435526 0.900176i \(-0.356562\pi\)
0.435526 + 0.900176i \(0.356562\pi\)
\(158\) −1.13539e36 −0.598830
\(159\) −1.17768e36 −0.559727
\(160\) −7.71988e35 −0.330850
\(161\) −5.22259e36 −2.01957
\(162\) 5.28543e36 1.84537
\(163\) −5.65066e36 −1.78240 −0.891198 0.453615i \(-0.850134\pi\)
−0.891198 + 0.453615i \(0.850134\pi\)
\(164\) 6.64609e35 0.189515
\(165\) 4.90227e36 1.26448
\(166\) 2.48616e36 0.580425
\(167\) −8.79383e36 −1.85933 −0.929665 0.368407i \(-0.879903\pi\)
−0.929665 + 0.368407i \(0.879903\pi\)
\(168\) 1.27938e37 2.45130
\(169\) −5.39705e35 −0.0937617
\(170\) 2.30387e36 0.363120
\(171\) 8.04237e36 1.15066
\(172\) 3.23769e36 0.420742
\(173\) −5.34130e36 −0.630792 −0.315396 0.948960i \(-0.602137\pi\)
−0.315396 + 0.948960i \(0.602137\pi\)
\(174\) −8.07053e35 −0.0866641
\(175\) −2.50722e36 −0.244943
\(176\) 7.65790e36 0.681005
\(177\) 7.47145e35 0.0605127
\(178\) −1.69581e37 −1.25155
\(179\) −1.75097e37 −1.17816 −0.589080 0.808075i \(-0.700510\pi\)
−0.589080 + 0.808075i \(0.700510\pi\)
\(180\) 6.96532e36 0.427508
\(181\) 1.00404e37 0.562411 0.281205 0.959648i \(-0.409266\pi\)
0.281205 + 0.959648i \(0.409266\pi\)
\(182\) 1.76928e37 0.904937
\(183\) 2.46559e37 1.15207
\(184\) −4.18838e37 −1.78876
\(185\) −2.72687e36 −0.106496
\(186\) −1.48376e37 −0.530153
\(187\) 4.90144e37 1.60301
\(188\) 2.14850e36 0.0643474
\(189\) −1.15675e38 −3.17410
\(190\) −6.60415e36 −0.166105
\(191\) −1.96610e37 −0.453477 −0.226739 0.973956i \(-0.572806\pi\)
−0.226739 + 0.973956i \(0.572806\pi\)
\(192\) 8.88220e37 1.87953
\(193\) 3.92456e37 0.762246 0.381123 0.924524i \(-0.375537\pi\)
0.381123 + 0.924524i \(0.375537\pi\)
\(194\) −2.55928e37 −0.456446
\(195\) 4.79447e37 0.785542
\(196\) −1.31983e37 −0.198744
\(197\) −1.18069e38 −1.63471 −0.817357 0.576131i \(-0.804562\pi\)
−0.817357 + 0.576131i \(0.804562\pi\)
\(198\) −2.24566e38 −2.86002
\(199\) 1.43693e38 1.68407 0.842035 0.539423i \(-0.181358\pi\)
0.842035 + 0.539423i \(0.181358\pi\)
\(200\) −2.01073e37 −0.216949
\(201\) −4.59086e37 −0.456204
\(202\) 6.50216e37 0.595333
\(203\) 8.78140e36 0.0741104
\(204\) 9.86031e37 0.767349
\(205\) 2.96968e37 0.213192
\(206\) 1.70235e38 1.12782
\(207\) 6.48302e38 3.96522
\(208\) 7.48949e37 0.423065
\(209\) −1.40502e38 −0.733279
\(210\) 1.62616e38 0.784414
\(211\) −2.97825e38 −1.32831 −0.664157 0.747593i \(-0.731210\pi\)
−0.664157 + 0.747593i \(0.731210\pi\)
\(212\) 2.92329e37 0.120595
\(213\) −4.74623e38 −1.81170
\(214\) 2.04847e38 0.723773
\(215\) 1.44670e38 0.473308
\(216\) −9.27685e38 −2.81134
\(217\) 1.61446e38 0.453358
\(218\) 2.49061e38 0.648297
\(219\) −9.79278e38 −2.36362
\(220\) −1.21686e38 −0.272437
\(221\) 4.79366e38 0.995851
\(222\) 1.76863e38 0.341045
\(223\) −1.05983e38 −0.189761 −0.0948804 0.995489i \(-0.530247\pi\)
−0.0948804 + 0.995489i \(0.530247\pi\)
\(224\) −5.44808e38 −0.906047
\(225\) 3.11232e38 0.480920
\(226\) −6.50496e38 −0.934233
\(227\) 7.63192e38 1.01908 0.509538 0.860448i \(-0.329816\pi\)
0.509538 + 0.860448i \(0.329816\pi\)
\(228\) −2.82651e38 −0.351014
\(229\) 2.74424e38 0.317057 0.158528 0.987354i \(-0.449325\pi\)
0.158528 + 0.987354i \(0.449325\pi\)
\(230\) −5.32366e38 −0.572402
\(231\) 3.45963e39 3.46284
\(232\) 7.04245e37 0.0656406
\(233\) −7.50623e38 −0.651702 −0.325851 0.945421i \(-0.605651\pi\)
−0.325851 + 0.945421i \(0.605651\pi\)
\(234\) −2.19628e39 −1.77675
\(235\) 9.60017e37 0.0723868
\(236\) −1.85459e37 −0.0130377
\(237\) −2.17131e39 −1.42356
\(238\) 1.62589e39 0.994422
\(239\) −9.41651e38 −0.537434 −0.268717 0.963219i \(-0.586600\pi\)
−0.268717 + 0.963219i \(0.586600\pi\)
\(240\) 6.88366e38 0.366720
\(241\) −4.90507e38 −0.243985 −0.121993 0.992531i \(-0.538928\pi\)
−0.121993 + 0.992531i \(0.538928\pi\)
\(242\) 2.25247e39 1.04642
\(243\) 4.13623e39 1.79515
\(244\) −6.12016e38 −0.248217
\(245\) −5.89742e38 −0.223574
\(246\) −1.92611e39 −0.682734
\(247\) −1.37412e39 −0.455540
\(248\) 1.29475e39 0.401545
\(249\) 4.75452e39 1.37980
\(250\) −2.55574e38 −0.0694236
\(251\) 5.96650e39 1.51741 0.758705 0.651434i \(-0.225832\pi\)
0.758705 + 0.651434i \(0.225832\pi\)
\(252\) 4.91557e39 1.17075
\(253\) −1.13260e40 −2.52690
\(254\) −3.30524e38 −0.0690950
\(255\) 4.40590e39 0.863220
\(256\) −5.33112e39 −0.979172
\(257\) −8.25525e39 −1.42178 −0.710892 0.703301i \(-0.751709\pi\)
−0.710892 + 0.703301i \(0.751709\pi\)
\(258\) −9.38317e39 −1.51574
\(259\) −1.92441e39 −0.291643
\(260\) −1.19010e39 −0.169248
\(261\) −1.09007e39 −0.145508
\(262\) −1.80286e39 −0.225939
\(263\) 6.74712e39 0.794051 0.397026 0.917808i \(-0.370042\pi\)
0.397026 + 0.917808i \(0.370042\pi\)
\(264\) 2.77454e40 3.06708
\(265\) 1.30622e39 0.135662
\(266\) −4.66068e39 −0.454886
\(267\) −3.24305e40 −2.97521
\(268\) 1.13956e39 0.0982907
\(269\) −2.97390e39 −0.241220 −0.120610 0.992700i \(-0.538485\pi\)
−0.120610 + 0.992700i \(0.538485\pi\)
\(270\) −1.17914e40 −0.899628
\(271\) −7.89524e39 −0.566725 −0.283362 0.959013i \(-0.591450\pi\)
−0.283362 + 0.959013i \(0.591450\pi\)
\(272\) 6.88250e39 0.464900
\(273\) 3.38355e40 2.15124
\(274\) 2.00605e40 1.20076
\(275\) −5.43731e39 −0.306474
\(276\) −2.27847e40 −1.20961
\(277\) 2.12171e40 1.06113 0.530566 0.847644i \(-0.321980\pi\)
0.530566 + 0.847644i \(0.321980\pi\)
\(278\) 1.01429e40 0.477993
\(279\) −2.00409e40 −0.890120
\(280\) −1.41901e40 −0.594126
\(281\) 4.91397e40 1.93989 0.969947 0.243317i \(-0.0782355\pi\)
0.969947 + 0.243317i \(0.0782355\pi\)
\(282\) −6.22658e39 −0.231814
\(283\) −4.22019e40 −1.48203 −0.741013 0.671491i \(-0.765654\pi\)
−0.741013 + 0.671491i \(0.765654\pi\)
\(284\) 1.17813e40 0.390336
\(285\) −1.26297e40 −0.394869
\(286\) 3.83696e40 1.13226
\(287\) 2.09576e40 0.583836
\(288\) 6.76292e40 1.77893
\(289\) 3.79702e39 0.0943253
\(290\) 8.95135e38 0.0210049
\(291\) −4.89434e40 −1.08508
\(292\) 2.43080e40 0.509251
\(293\) 2.96004e40 0.586115 0.293057 0.956095i \(-0.405327\pi\)
0.293057 + 0.956095i \(0.405327\pi\)
\(294\) 3.82502e40 0.715982
\(295\) −8.28689e38 −0.0146666
\(296\) −1.54333e40 −0.258312
\(297\) −2.50860e41 −3.97146
\(298\) −3.48694e40 −0.522248
\(299\) −1.10769e41 −1.56980
\(300\) −1.09383e40 −0.146707
\(301\) 1.02097e41 1.29618
\(302\) −9.28922e39 −0.111652
\(303\) 1.24347e41 1.41524
\(304\) −1.97290e40 −0.212663
\(305\) −2.73468e40 −0.279228
\(306\) −2.01828e41 −1.95244
\(307\) −1.70501e41 −1.56295 −0.781474 0.623938i \(-0.785532\pi\)
−0.781474 + 0.623938i \(0.785532\pi\)
\(308\) −8.58762e40 −0.746081
\(309\) 3.25556e41 2.68108
\(310\) 1.64570e40 0.128494
\(311\) 1.09238e41 0.808774 0.404387 0.914588i \(-0.367485\pi\)
0.404387 + 0.914588i \(0.367485\pi\)
\(312\) 2.71352e41 1.90538
\(313\) −2.55151e41 −1.69948 −0.849738 0.527205i \(-0.823240\pi\)
−0.849738 + 0.527205i \(0.823240\pi\)
\(314\) 1.06991e41 0.676093
\(315\) 2.19643e41 1.31702
\(316\) 5.38971e40 0.306710
\(317\) 1.40033e41 0.756400 0.378200 0.925724i \(-0.376543\pi\)
0.378200 + 0.925724i \(0.376543\pi\)
\(318\) −8.47200e40 −0.434449
\(319\) 1.90438e40 0.0927275
\(320\) −9.85160e40 −0.455546
\(321\) 3.91748e41 1.72057
\(322\) −3.75702e41 −1.56755
\(323\) −1.26276e41 −0.500586
\(324\) −2.50900e41 −0.945164
\(325\) −5.31773e40 −0.190393
\(326\) −4.06496e41 −1.38346
\(327\) 4.76302e41 1.54115
\(328\) 1.68075e41 0.517111
\(329\) 6.77504e40 0.198235
\(330\) 3.52659e41 0.981464
\(331\) −2.36103e41 −0.625086 −0.312543 0.949904i \(-0.601181\pi\)
−0.312543 + 0.949904i \(0.601181\pi\)
\(332\) −1.18018e41 −0.297283
\(333\) 2.38885e41 0.572611
\(334\) −6.32609e41 −1.44317
\(335\) 5.09190e40 0.110571
\(336\) 4.85794e41 1.00428
\(337\) 5.72695e41 1.12728 0.563638 0.826022i \(-0.309401\pi\)
0.563638 + 0.826022i \(0.309401\pi\)
\(338\) −3.88252e40 −0.0727759
\(339\) −1.24400e42 −2.22088
\(340\) −1.09365e41 −0.185984
\(341\) 3.50120e41 0.567244
\(342\) 5.78550e41 0.893121
\(343\) 4.16314e41 0.612446
\(344\) 8.18788e41 1.14804
\(345\) −1.01809e42 −1.36073
\(346\) −3.84241e41 −0.489608
\(347\) 7.23409e41 0.878917 0.439458 0.898263i \(-0.355170\pi\)
0.439458 + 0.898263i \(0.355170\pi\)
\(348\) 3.83108e40 0.0443878
\(349\) −1.72145e42 −1.90228 −0.951140 0.308761i \(-0.900086\pi\)
−0.951140 + 0.308761i \(0.900086\pi\)
\(350\) −1.80364e41 −0.190120
\(351\) −2.45343e42 −2.46721
\(352\) −1.18150e42 −1.13365
\(353\) −1.10466e42 −1.01145 −0.505725 0.862695i \(-0.668775\pi\)
−0.505725 + 0.862695i \(0.668775\pi\)
\(354\) 5.37480e40 0.0469687
\(355\) 5.26423e41 0.439104
\(356\) 8.05001e41 0.641020
\(357\) 3.10933e42 2.36397
\(358\) −1.25961e42 −0.914464
\(359\) 1.24115e42 0.860528 0.430264 0.902703i \(-0.358420\pi\)
0.430264 + 0.902703i \(0.358420\pi\)
\(360\) 1.76148e42 1.16650
\(361\) −1.21880e42 −0.771013
\(362\) 7.22283e41 0.436532
\(363\) 4.30760e42 2.48757
\(364\) −8.39877e41 −0.463493
\(365\) 1.08616e42 0.572875
\(366\) 1.77369e42 0.894210
\(367\) 7.83869e41 0.377792 0.188896 0.981997i \(-0.439509\pi\)
0.188896 + 0.981997i \(0.439509\pi\)
\(368\) −1.59037e42 −0.732842
\(369\) −2.60156e42 −1.14630
\(370\) −1.96165e41 −0.0826597
\(371\) 9.21824e41 0.371517
\(372\) 7.04343e41 0.271535
\(373\) −4.48131e42 −1.65276 −0.826378 0.563116i \(-0.809603\pi\)
−0.826378 + 0.563116i \(0.809603\pi\)
\(374\) 3.52599e42 1.24423
\(375\) −4.88758e41 −0.165036
\(376\) 5.43340e41 0.175579
\(377\) 1.86251e41 0.0576057
\(378\) −8.32142e42 −2.46367
\(379\) 5.32753e42 1.51001 0.755003 0.655721i \(-0.227635\pi\)
0.755003 + 0.655721i \(0.227635\pi\)
\(380\) 3.13499e41 0.0850760
\(381\) −6.32091e41 −0.164255
\(382\) −1.41437e42 −0.351980
\(383\) 7.66000e42 1.82578 0.912891 0.408203i \(-0.133844\pi\)
0.912891 + 0.408203i \(0.133844\pi\)
\(384\) 4.10860e41 0.0938055
\(385\) −3.83722e42 −0.839295
\(386\) 2.82324e42 0.591640
\(387\) −1.26737e43 −2.54491
\(388\) 1.21489e42 0.233783
\(389\) 2.42415e42 0.447085 0.223543 0.974694i \(-0.428238\pi\)
0.223543 + 0.974694i \(0.428238\pi\)
\(390\) 3.44903e42 0.609721
\(391\) −1.01792e43 −1.72503
\(392\) −3.33776e42 −0.542294
\(393\) −3.44777e42 −0.537108
\(394\) −8.49360e42 −1.26883
\(395\) 2.40829e42 0.345030
\(396\) 1.06602e43 1.46485
\(397\) 4.43937e42 0.585164 0.292582 0.956240i \(-0.405486\pi\)
0.292582 + 0.956240i \(0.405486\pi\)
\(398\) 1.03370e43 1.30714
\(399\) −8.91304e42 −1.08137
\(400\) −7.63495e41 −0.0888825
\(401\) 6.39786e41 0.0714747 0.0357374 0.999361i \(-0.488622\pi\)
0.0357374 + 0.999361i \(0.488622\pi\)
\(402\) −3.30256e42 −0.354096
\(403\) 3.42421e42 0.352393
\(404\) −3.08658e42 −0.304919
\(405\) −1.12110e43 −1.06325
\(406\) 6.31715e41 0.0575230
\(407\) −4.17339e42 −0.364906
\(408\) 2.49360e43 2.09380
\(409\) −1.16096e43 −0.936227 −0.468114 0.883668i \(-0.655066\pi\)
−0.468114 + 0.883668i \(0.655066\pi\)
\(410\) 2.13632e42 0.165475
\(411\) 3.83636e43 2.85449
\(412\) −8.08105e42 −0.577649
\(413\) −5.84823e41 −0.0401650
\(414\) 4.66374e43 3.07772
\(415\) −5.27342e42 −0.334425
\(416\) −1.15552e43 −0.704266
\(417\) 1.93971e43 1.13630
\(418\) −1.01074e43 −0.569156
\(419\) −7.07188e42 −0.382828 −0.191414 0.981509i \(-0.561307\pi\)
−0.191414 + 0.981509i \(0.561307\pi\)
\(420\) −7.71939e42 −0.401763
\(421\) −2.32219e43 −1.16210 −0.581050 0.813868i \(-0.697358\pi\)
−0.581050 + 0.813868i \(0.697358\pi\)
\(422\) −2.14249e43 −1.03101
\(423\) −8.41014e42 −0.389213
\(424\) 7.39279e42 0.329057
\(425\) −4.88676e42 −0.209220
\(426\) −3.41433e43 −1.40620
\(427\) −1.92992e43 −0.764679
\(428\) −9.72410e42 −0.370704
\(429\) 7.33777e43 2.69165
\(430\) 1.04072e43 0.367372
\(431\) −3.01488e43 −1.02422 −0.512112 0.858919i \(-0.671137\pi\)
−0.512112 + 0.858919i \(0.671137\pi\)
\(432\) −3.52252e43 −1.15179
\(433\) 3.63888e43 1.14530 0.572648 0.819802i \(-0.305916\pi\)
0.572648 + 0.819802i \(0.305916\pi\)
\(434\) 1.16141e43 0.351887
\(435\) 1.71185e42 0.0499335
\(436\) −1.18229e43 −0.332046
\(437\) 2.91792e43 0.789095
\(438\) −7.04471e43 −1.83460
\(439\) −3.62391e42 −0.0908893 −0.0454446 0.998967i \(-0.514470\pi\)
−0.0454446 + 0.998967i \(0.514470\pi\)
\(440\) −3.07735e43 −0.743374
\(441\) 5.16638e43 1.20213
\(442\) 3.44845e43 0.772959
\(443\) 2.84653e43 0.614686 0.307343 0.951599i \(-0.400560\pi\)
0.307343 + 0.951599i \(0.400560\pi\)
\(444\) −8.39567e42 −0.174677
\(445\) 3.59699e43 0.721107
\(446\) −7.62419e42 −0.147288
\(447\) −6.66840e43 −1.24150
\(448\) −6.95248e43 −1.24753
\(449\) −3.05597e43 −0.528548 −0.264274 0.964448i \(-0.585132\pi\)
−0.264274 + 0.964448i \(0.585132\pi\)
\(450\) 2.23893e43 0.373280
\(451\) 4.54499e43 0.730500
\(452\) 3.08790e43 0.478497
\(453\) −1.77646e43 −0.265421
\(454\) 5.49023e43 0.790987
\(455\) −3.75283e43 −0.521400
\(456\) −7.14803e43 −0.957781
\(457\) −8.70256e42 −0.112468 −0.0562341 0.998418i \(-0.517909\pi\)
−0.0562341 + 0.998418i \(0.517909\pi\)
\(458\) 1.97415e43 0.246093
\(459\) −2.25459e44 −2.71118
\(460\) 2.52714e43 0.293174
\(461\) 7.28964e43 0.815907 0.407954 0.913003i \(-0.366243\pi\)
0.407954 + 0.913003i \(0.366243\pi\)
\(462\) 2.48878e44 2.68779
\(463\) 1.54940e44 1.61465 0.807324 0.590108i \(-0.200915\pi\)
0.807324 + 0.590108i \(0.200915\pi\)
\(464\) 2.67410e42 0.0268924
\(465\) 3.14722e43 0.305460
\(466\) −5.39982e43 −0.505838
\(467\) −9.15725e43 −0.828011 −0.414006 0.910274i \(-0.635871\pi\)
−0.414006 + 0.910274i \(0.635871\pi\)
\(468\) 1.04257e44 0.910020
\(469\) 3.59346e43 0.302804
\(470\) 6.90615e42 0.0561852
\(471\) 2.04608e44 1.60723
\(472\) −4.69012e42 −0.0355747
\(473\) 2.21413e44 1.62179
\(474\) −1.56199e44 −1.10494
\(475\) 1.40081e43 0.0957051
\(476\) −7.71809e43 −0.509325
\(477\) −1.14430e44 −0.729434
\(478\) −6.77403e43 −0.417145
\(479\) 3.67745e43 0.218782 0.109391 0.993999i \(-0.465110\pi\)
0.109391 + 0.993999i \(0.465110\pi\)
\(480\) −1.06205e44 −0.610469
\(481\) −4.08161e43 −0.226693
\(482\) −3.52860e43 −0.189376
\(483\) −7.18488e44 −3.72642
\(484\) −1.06925e44 −0.535957
\(485\) 5.42851e43 0.262992
\(486\) 2.97552e44 1.39336
\(487\) 2.46290e44 1.11485 0.557427 0.830226i \(-0.311789\pi\)
0.557427 + 0.830226i \(0.311789\pi\)
\(488\) −1.54774e44 −0.677286
\(489\) −7.77380e44 −3.28880
\(490\) −4.24248e43 −0.173534
\(491\) 1.21128e44 0.479071 0.239535 0.970888i \(-0.423005\pi\)
0.239535 + 0.970888i \(0.423005\pi\)
\(492\) 9.14324e43 0.349684
\(493\) 1.71156e43 0.0633020
\(494\) −9.88515e43 −0.353581
\(495\) 4.76330e44 1.64787
\(496\) 4.91632e43 0.164510
\(497\) 3.71508e44 1.20251
\(498\) 3.42029e44 1.07097
\(499\) 4.07835e44 1.23545 0.617726 0.786393i \(-0.288054\pi\)
0.617726 + 0.786393i \(0.288054\pi\)
\(500\) 1.21321e43 0.0355575
\(501\) −1.20980e45 −3.43075
\(502\) 4.29217e44 1.17778
\(503\) −5.88791e44 −1.56347 −0.781734 0.623612i \(-0.785665\pi\)
−0.781734 + 0.623612i \(0.785665\pi\)
\(504\) 1.24311e45 3.19452
\(505\) −1.37918e44 −0.343015
\(506\) −8.14768e44 −1.96133
\(507\) −7.42489e43 −0.173005
\(508\) 1.56900e43 0.0353892
\(509\) 7.13633e44 1.55823 0.779115 0.626881i \(-0.215669\pi\)
0.779115 + 0.626881i \(0.215669\pi\)
\(510\) 3.16950e44 0.670013
\(511\) 7.66523e44 1.56885
\(512\) −4.09163e44 −0.810852
\(513\) 6.46290e44 1.24020
\(514\) −5.93864e44 −1.10356
\(515\) −3.61087e44 −0.649819
\(516\) 4.45419e44 0.776335
\(517\) 1.46927e44 0.248033
\(518\) −1.38438e44 −0.226367
\(519\) −7.34820e44 −1.16391
\(520\) −3.00967e44 −0.461811
\(521\) −1.39893e44 −0.207957 −0.103978 0.994580i \(-0.533157\pi\)
−0.103978 + 0.994580i \(0.533157\pi\)
\(522\) −7.84174e43 −0.112940
\(523\) −4.12677e44 −0.575880 −0.287940 0.957648i \(-0.592970\pi\)
−0.287940 + 0.957648i \(0.592970\pi\)
\(524\) 8.55818e43 0.115722
\(525\) −3.44927e44 −0.451958
\(526\) 4.85373e44 0.616326
\(527\) 3.14669e44 0.387239
\(528\) 1.05352e45 1.25656
\(529\) 1.48715e45 1.71924
\(530\) 9.39664e43 0.105298
\(531\) 7.25965e43 0.0788599
\(532\) 2.21243e44 0.232984
\(533\) 4.44504e44 0.453813
\(534\) −2.33298e45 −2.30930
\(535\) −4.34503e44 −0.417019
\(536\) 2.88186e44 0.268197
\(537\) −2.40887e45 −2.17389
\(538\) −2.13936e44 −0.187230
\(539\) −9.02580e44 −0.766075
\(540\) 5.59737e44 0.460773
\(541\) −2.35683e45 −1.88180 −0.940899 0.338687i \(-0.890017\pi\)
−0.940899 + 0.338687i \(0.890017\pi\)
\(542\) −5.67966e44 −0.439880
\(543\) 1.38129e45 1.03774
\(544\) −1.06187e45 −0.773907
\(545\) −5.28286e44 −0.373531
\(546\) 2.43405e45 1.66975
\(547\) 2.11321e45 1.40654 0.703270 0.710923i \(-0.251723\pi\)
0.703270 + 0.710923i \(0.251723\pi\)
\(548\) −9.52274e44 −0.615010
\(549\) 2.39569e45 1.50137
\(550\) −3.91148e44 −0.237879
\(551\) −4.90626e43 −0.0289567
\(552\) −5.76209e45 −3.30054
\(553\) 1.69958e45 0.944880
\(554\) 1.52631e45 0.823628
\(555\) −3.75145e44 −0.196501
\(556\) −4.81482e44 −0.244819
\(557\) 2.27438e45 1.12267 0.561335 0.827589i \(-0.310288\pi\)
0.561335 + 0.827589i \(0.310288\pi\)
\(558\) −1.44170e45 −0.690893
\(559\) 2.16544e45 1.00751
\(560\) −5.38814e44 −0.243409
\(561\) 6.74307e45 2.95781
\(562\) 3.53500e45 1.50571
\(563\) −1.75752e45 −0.726962 −0.363481 0.931602i \(-0.618412\pi\)
−0.363481 + 0.931602i \(0.618412\pi\)
\(564\) 2.95576e44 0.118731
\(565\) 1.37977e45 0.538280
\(566\) −3.03591e45 −1.15032
\(567\) −7.91182e45 −2.91176
\(568\) 2.97939e45 1.06508
\(569\) 9.61177e44 0.333773 0.166886 0.985976i \(-0.446629\pi\)
0.166886 + 0.985976i \(0.446629\pi\)
\(570\) −9.08553e44 −0.306489
\(571\) −5.28842e45 −1.73313 −0.866563 0.499067i \(-0.833676\pi\)
−0.866563 + 0.499067i \(0.833676\pi\)
\(572\) −1.82141e45 −0.579925
\(573\) −2.70483e45 −0.836737
\(574\) 1.50765e45 0.453162
\(575\) 1.12921e45 0.329803
\(576\) 8.63040e45 2.44940
\(577\) −1.11538e45 −0.307626 −0.153813 0.988100i \(-0.549155\pi\)
−0.153813 + 0.988100i \(0.549155\pi\)
\(578\) 2.73149e44 0.0732134
\(579\) 5.39914e45 1.40646
\(580\) −4.24921e43 −0.0107584
\(581\) −3.72156e45 −0.915839
\(582\) −3.52088e45 −0.842213
\(583\) 1.99912e45 0.464845
\(584\) 6.14731e45 1.38955
\(585\) 4.65855e45 1.02371
\(586\) 2.12939e45 0.454930
\(587\) 3.02679e45 0.628714 0.314357 0.949305i \(-0.398211\pi\)
0.314357 + 0.949305i \(0.398211\pi\)
\(588\) −1.81574e45 −0.366713
\(589\) −9.02014e44 −0.177138
\(590\) −5.96140e43 −0.0113839
\(591\) −1.62431e46 −3.01630
\(592\) −5.86018e44 −0.105829
\(593\) 2.02049e45 0.354857 0.177428 0.984134i \(-0.443222\pi\)
0.177428 + 0.984134i \(0.443222\pi\)
\(594\) −1.80463e46 −3.08256
\(595\) −3.44868e45 −0.572959
\(596\) 1.65525e45 0.267486
\(597\) 1.97683e46 3.10737
\(598\) −7.96851e45 −1.21845
\(599\) −7.17593e45 −1.06742 −0.533710 0.845667i \(-0.679203\pi\)
−0.533710 + 0.845667i \(0.679203\pi\)
\(600\) −2.76622e45 −0.400305
\(601\) −8.79572e44 −0.123835 −0.0619174 0.998081i \(-0.519722\pi\)
−0.0619174 + 0.998081i \(0.519722\pi\)
\(602\) 7.34461e45 1.00607
\(603\) −4.46071e45 −0.594523
\(604\) 4.40960e44 0.0571859
\(605\) −4.77773e45 −0.602918
\(606\) 8.94523e45 1.09848
\(607\) −1.35040e46 −1.61380 −0.806902 0.590686i \(-0.798857\pi\)
−0.806902 + 0.590686i \(0.798857\pi\)
\(608\) 3.04390e45 0.354014
\(609\) 1.20809e45 0.136745
\(610\) −1.96727e45 −0.216731
\(611\) 1.43696e45 0.154087
\(612\) 9.58079e45 1.00001
\(613\) −1.09063e45 −0.110810 −0.0554052 0.998464i \(-0.517645\pi\)
−0.0554052 + 0.998464i \(0.517645\pi\)
\(614\) −1.22655e46 −1.21313
\(615\) 4.08548e45 0.393373
\(616\) −2.17175e46 −2.03576
\(617\) 1.20780e46 1.10227 0.551137 0.834415i \(-0.314194\pi\)
0.551137 + 0.834415i \(0.314194\pi\)
\(618\) 2.34197e46 2.08100
\(619\) −3.00533e45 −0.260014 −0.130007 0.991513i \(-0.541500\pi\)
−0.130007 + 0.991513i \(0.541500\pi\)
\(620\) −7.81215e44 −0.0658124
\(621\) 5.20980e46 4.27376
\(622\) 7.85834e45 0.627754
\(623\) 2.53847e46 1.97478
\(624\) 1.03035e46 0.780621
\(625\) 5.42101e44 0.0400000
\(626\) −1.83550e46 −1.31910
\(627\) −1.93293e46 −1.35301
\(628\) −5.07885e45 −0.346283
\(629\) −3.75081e45 −0.249109
\(630\) 1.58006e46 1.02225
\(631\) −2.08614e46 −1.31480 −0.657400 0.753542i \(-0.728344\pi\)
−0.657400 + 0.753542i \(0.728344\pi\)
\(632\) 1.36302e46 0.836892
\(633\) −4.09728e46 −2.45095
\(634\) 1.00736e46 0.587102
\(635\) 7.01077e44 0.0398107
\(636\) 4.02166e45 0.222517
\(637\) −8.82732e45 −0.475914
\(638\) 1.36997e45 0.0719732
\(639\) −4.61168e46 −2.36099
\(640\) −4.55701e44 −0.0227358
\(641\) −1.91329e46 −0.930299 −0.465149 0.885232i \(-0.653999\pi\)
−0.465149 + 0.885232i \(0.653999\pi\)
\(642\) 2.81815e46 1.33547
\(643\) −3.18460e46 −1.47087 −0.735434 0.677597i \(-0.763022\pi\)
−0.735434 + 0.677597i \(0.763022\pi\)
\(644\) 1.78346e46 0.802871
\(645\) 1.99027e46 0.873328
\(646\) −9.08400e45 −0.388544
\(647\) 3.25342e46 1.35650 0.678250 0.734831i \(-0.262739\pi\)
0.678250 + 0.734831i \(0.262739\pi\)
\(648\) −6.34507e46 −2.57898
\(649\) −1.26828e45 −0.0502548
\(650\) −3.82546e45 −0.147779
\(651\) 2.22106e46 0.836516
\(652\) 1.92964e46 0.708583
\(653\) 1.98304e46 0.710009 0.355005 0.934865i \(-0.384479\pi\)
0.355005 + 0.934865i \(0.384479\pi\)
\(654\) 3.42641e46 1.19621
\(655\) 3.82406e45 0.130180
\(656\) 6.38198e45 0.211857
\(657\) −9.51517e46 −3.08026
\(658\) 4.87381e45 0.153866
\(659\) 2.96542e45 0.0913011 0.0456506 0.998957i \(-0.485464\pi\)
0.0456506 + 0.998957i \(0.485464\pi\)
\(660\) −1.67407e46 −0.502689
\(661\) 1.20833e46 0.353886 0.176943 0.984221i \(-0.443379\pi\)
0.176943 + 0.984221i \(0.443379\pi\)
\(662\) −1.69847e46 −0.485179
\(663\) 6.59479e46 1.83750
\(664\) −2.98460e46 −0.811170
\(665\) 9.88581e45 0.262093
\(666\) 1.71849e46 0.444449
\(667\) −3.95498e45 −0.0997857
\(668\) 3.00300e46 0.739168
\(669\) −1.45804e46 −0.350138
\(670\) 3.66300e45 0.0858229
\(671\) −4.18533e46 −0.956772
\(672\) −7.49509e46 −1.67180
\(673\) 2.52503e46 0.549565 0.274782 0.961506i \(-0.411394\pi\)
0.274782 + 0.961506i \(0.411394\pi\)
\(674\) 4.11984e46 0.874968
\(675\) 2.50108e46 0.518341
\(676\) 1.84303e45 0.0372745
\(677\) 3.98633e46 0.786793 0.393396 0.919369i \(-0.371300\pi\)
0.393396 + 0.919369i \(0.371300\pi\)
\(678\) −8.94908e46 −1.72381
\(679\) 3.83101e46 0.720215
\(680\) −2.76575e46 −0.507477
\(681\) 1.04995e47 1.88036
\(682\) 2.51869e46 0.440284
\(683\) −3.89128e46 −0.663973 −0.331986 0.943284i \(-0.607719\pi\)
−0.331986 + 0.943284i \(0.607719\pi\)
\(684\) −2.74638e46 −0.457441
\(685\) −4.25506e46 −0.691848
\(686\) 2.99487e46 0.475368
\(687\) 3.77534e46 0.585019
\(688\) 3.10903e46 0.470344
\(689\) 1.95516e46 0.288778
\(690\) −7.32393e46 −1.05617
\(691\) −3.16293e46 −0.445350 −0.222675 0.974893i \(-0.571479\pi\)
−0.222675 + 0.974893i \(0.571479\pi\)
\(692\) 1.82399e46 0.250769
\(693\) 3.36156e47 4.51276
\(694\) 5.20405e46 0.682197
\(695\) −2.15141e46 −0.275406
\(696\) 9.68853e45 0.121117
\(697\) 4.08479e46 0.498688
\(698\) −1.23837e47 −1.47651
\(699\) −1.03266e47 −1.20249
\(700\) 8.56189e45 0.0973760
\(701\) −5.26072e46 −0.584384 −0.292192 0.956360i \(-0.594385\pi\)
−0.292192 + 0.956360i \(0.594385\pi\)
\(702\) −1.76495e47 −1.91500
\(703\) 1.07519e46 0.113952
\(704\) −1.50775e47 −1.56092
\(705\) 1.32073e46 0.133565
\(706\) −7.94665e46 −0.785066
\(707\) −9.73315e46 −0.939362
\(708\) −2.55142e45 −0.0240565
\(709\) 1.31306e47 1.20954 0.604771 0.796399i \(-0.293265\pi\)
0.604771 + 0.796399i \(0.293265\pi\)
\(710\) 3.78697e46 0.340823
\(711\) −2.10976e47 −1.85517
\(712\) 2.03579e47 1.74909
\(713\) −7.27122e46 −0.610422
\(714\) 2.23678e47 1.83486
\(715\) −8.13861e46 −0.652380
\(716\) 5.97938e46 0.468372
\(717\) −1.29546e47 −0.991649
\(718\) 8.92855e46 0.667925
\(719\) 1.58298e47 1.15731 0.578653 0.815574i \(-0.303579\pi\)
0.578653 + 0.815574i \(0.303579\pi\)
\(720\) 6.68852e46 0.477908
\(721\) −2.54826e47 −1.77956
\(722\) −8.76774e46 −0.598445
\(723\) −6.74806e46 −0.450191
\(724\) −3.42868e46 −0.223584
\(725\) −1.89868e45 −0.0121025
\(726\) 3.09879e47 1.93080
\(727\) −2.56013e47 −1.55935 −0.779676 0.626184i \(-0.784616\pi\)
−0.779676 + 0.626184i \(0.784616\pi\)
\(728\) −2.12399e47 −1.26469
\(729\) 1.60598e47 0.934838
\(730\) 7.81357e46 0.444654
\(731\) 1.98994e47 1.10714
\(732\) −8.41970e46 −0.457998
\(733\) −5.58232e46 −0.296893 −0.148446 0.988920i \(-0.547427\pi\)
−0.148446 + 0.988920i \(0.547427\pi\)
\(734\) 5.63898e46 0.293235
\(735\) −8.11327e46 −0.412529
\(736\) 2.45371e47 1.21994
\(737\) 7.79298e46 0.378870
\(738\) −1.87150e47 −0.889736
\(739\) 1.40164e47 0.651634 0.325817 0.945433i \(-0.394361\pi\)
0.325817 + 0.945433i \(0.394361\pi\)
\(740\) 9.31197e45 0.0423368
\(741\) −1.89043e47 −0.840542
\(742\) 6.63140e46 0.288364
\(743\) 3.74285e46 0.159180 0.0795898 0.996828i \(-0.474639\pi\)
0.0795898 + 0.996828i \(0.474639\pi\)
\(744\) 1.78123e47 0.740913
\(745\) 7.39618e46 0.300905
\(746\) −3.22375e47 −1.28284
\(747\) 4.61973e47 1.79815
\(748\) −1.67379e47 −0.637271
\(749\) −3.06638e47 −1.14202
\(750\) −3.51602e46 −0.128097
\(751\) 2.45331e47 0.874365 0.437182 0.899373i \(-0.355976\pi\)
0.437182 + 0.899373i \(0.355976\pi\)
\(752\) 2.06312e46 0.0719334
\(753\) 8.20830e47 2.79986
\(754\) 1.33985e46 0.0447124
\(755\) 1.97035e46 0.0643306
\(756\) 3.95018e47 1.26185
\(757\) 3.89117e47 1.21618 0.608090 0.793868i \(-0.291936\pi\)
0.608090 + 0.793868i \(0.291936\pi\)
\(758\) 3.83251e47 1.17204
\(759\) −1.55815e48 −4.66253
\(760\) 7.92816e46 0.232139
\(761\) −2.57108e47 −0.736662 −0.368331 0.929695i \(-0.620071\pi\)
−0.368331 + 0.929695i \(0.620071\pi\)
\(762\) −4.54712e46 −0.127491
\(763\) −3.72822e47 −1.02293
\(764\) 6.71402e46 0.180278
\(765\) 4.28100e47 1.12494
\(766\) 5.51044e47 1.41714
\(767\) −1.24039e46 −0.0312201
\(768\) −7.33419e47 −1.80672
\(769\) 1.74753e47 0.421348 0.210674 0.977556i \(-0.432434\pi\)
0.210674 + 0.977556i \(0.432434\pi\)
\(770\) −2.76041e47 −0.651443
\(771\) −1.13570e48 −2.62341
\(772\) −1.34019e47 −0.303027
\(773\) 1.07838e47 0.238676 0.119338 0.992854i \(-0.461923\pi\)
0.119338 + 0.992854i \(0.461923\pi\)
\(774\) −9.11717e47 −1.97531
\(775\) −3.49071e46 −0.0740348
\(776\) 3.07237e47 0.637903
\(777\) −2.64747e47 −0.538127
\(778\) 1.74388e47 0.347019
\(779\) −1.17093e47 −0.228119
\(780\) −1.63726e47 −0.312288
\(781\) 8.05672e47 1.50458
\(782\) −7.32269e47 −1.33893
\(783\) −8.75990e46 −0.156830
\(784\) −1.26738e47 −0.222174
\(785\) −2.26939e47 −0.389546
\(786\) −2.48025e47 −0.416892
\(787\) −2.21953e47 −0.365324 −0.182662 0.983176i \(-0.558471\pi\)
−0.182662 + 0.983176i \(0.558471\pi\)
\(788\) 4.03191e47 0.649873
\(789\) 9.28223e47 1.46515
\(790\) 1.73247e47 0.267805
\(791\) 9.73733e47 1.47410
\(792\) 2.69588e48 3.99701
\(793\) −4.09329e47 −0.594382
\(794\) 3.19358e47 0.454192
\(795\) 1.79700e47 0.250318
\(796\) −4.90696e47 −0.669494
\(797\) 9.77934e47 1.30691 0.653457 0.756963i \(-0.273318\pi\)
0.653457 + 0.756963i \(0.273318\pi\)
\(798\) −6.41185e47 −0.839335
\(799\) 1.32050e47 0.169324
\(800\) 1.17796e47 0.147960
\(801\) −3.15111e48 −3.87728
\(802\) 4.60248e46 0.0554772
\(803\) 1.66232e48 1.96295
\(804\) 1.56773e47 0.181362
\(805\) 7.96904e47 0.903180
\(806\) 2.46330e47 0.273520
\(807\) −4.09129e47 −0.445089
\(808\) −7.80573e47 −0.832005
\(809\) −6.43989e47 −0.672555 −0.336278 0.941763i \(-0.609168\pi\)
−0.336278 + 0.941763i \(0.609168\pi\)
\(810\) −8.06493e47 −0.825273
\(811\) −3.92035e47 −0.393080 −0.196540 0.980496i \(-0.562971\pi\)
−0.196540 + 0.980496i \(0.562971\pi\)
\(812\) −2.99875e46 −0.0294623
\(813\) −1.08617e48 −1.04570
\(814\) −3.00224e47 −0.283232
\(815\) 8.62223e47 0.797111
\(816\) 9.46847e47 0.857813
\(817\) −5.70425e47 −0.506447
\(818\) −8.35166e47 −0.726680
\(819\) 3.28763e48 2.80349
\(820\) −1.01411e47 −0.0847535
\(821\) −3.66301e47 −0.300038 −0.150019 0.988683i \(-0.547934\pi\)
−0.150019 + 0.988683i \(0.547934\pi\)
\(822\) 2.75979e48 2.21560
\(823\) 6.74278e47 0.530569 0.265284 0.964170i \(-0.414534\pi\)
0.265284 + 0.964170i \(0.414534\pi\)
\(824\) −2.04364e48 −1.57618
\(825\) −7.48027e47 −0.565493
\(826\) −4.20708e46 −0.0311753
\(827\) −1.83329e48 −1.33165 −0.665827 0.746106i \(-0.731921\pi\)
−0.665827 + 0.746106i \(0.731921\pi\)
\(828\) −2.21388e48 −1.57635
\(829\) 1.99989e48 1.39591 0.697954 0.716142i \(-0.254094\pi\)
0.697954 + 0.716142i \(0.254094\pi\)
\(830\) −3.79358e47 −0.259574
\(831\) 2.91890e48 1.95795
\(832\) −1.47460e48 −0.969702
\(833\) −8.11190e47 −0.522974
\(834\) 1.39539e48 0.881971
\(835\) 1.34183e48 0.831517
\(836\) 4.79799e47 0.291512
\(837\) −1.61050e48 −0.959382
\(838\) −5.08735e47 −0.297143
\(839\) −7.68878e47 −0.440337 −0.220168 0.975462i \(-0.570661\pi\)
−0.220168 + 0.975462i \(0.570661\pi\)
\(840\) −1.95218e48 −1.09625
\(841\) −1.80943e48 −0.996338
\(842\) −1.67053e48 −0.901998
\(843\) 6.76030e48 3.57941
\(844\) 1.01704e48 0.528065
\(845\) 8.23524e46 0.0419315
\(846\) −6.05007e47 −0.302099
\(847\) −3.37174e48 −1.65112
\(848\) 2.80712e47 0.134812
\(849\) −5.80585e48 −2.73457
\(850\) −3.51542e47 −0.162392
\(851\) 8.66719e47 0.392682
\(852\) 1.62078e48 0.720231
\(853\) 1.63399e47 0.0712180 0.0356090 0.999366i \(-0.488663\pi\)
0.0356090 + 0.999366i \(0.488663\pi\)
\(854\) −1.38834e48 −0.593528
\(855\) −1.22717e48 −0.514592
\(856\) −2.45915e48 −1.01151
\(857\) −5.35960e47 −0.216247 −0.108123 0.994137i \(-0.534484\pi\)
−0.108123 + 0.994137i \(0.534484\pi\)
\(858\) 5.27863e48 2.08920
\(859\) −3.45793e48 −1.34255 −0.671273 0.741210i \(-0.734252\pi\)
−0.671273 + 0.741210i \(0.734252\pi\)
\(860\) −4.94032e47 −0.188162
\(861\) 2.88321e48 1.07727
\(862\) −2.16884e48 −0.794982
\(863\) 1.95932e48 0.704574 0.352287 0.935892i \(-0.385404\pi\)
0.352287 + 0.935892i \(0.385404\pi\)
\(864\) 5.43473e48 1.91735
\(865\) 8.15018e47 0.282099
\(866\) 2.61773e48 0.888955
\(867\) 5.22368e47 0.174045
\(868\) −5.51319e47 −0.180230
\(869\) 3.68580e48 1.18224
\(870\) 1.23146e47 0.0387574
\(871\) 7.62161e47 0.235368
\(872\) −2.98994e48 −0.906024
\(873\) −4.75559e48 −1.41407
\(874\) 2.09908e48 0.612479
\(875\) 3.82572e47 0.109542
\(876\) 3.34413e48 0.939647
\(877\) 1.31812e48 0.363464 0.181732 0.983348i \(-0.441830\pi\)
0.181732 + 0.983348i \(0.441830\pi\)
\(878\) −2.60696e47 −0.0705464
\(879\) 4.07223e48 1.08147
\(880\) −1.16850e48 −0.304555
\(881\) 6.02351e48 1.54080 0.770401 0.637559i \(-0.220056\pi\)
0.770401 + 0.637559i \(0.220056\pi\)
\(882\) 3.71658e48 0.933065
\(883\) −5.51914e48 −1.35994 −0.679970 0.733240i \(-0.738007\pi\)
−0.679970 + 0.733240i \(0.738007\pi\)
\(884\) −1.63698e48 −0.395896
\(885\) −1.14005e47 −0.0270621
\(886\) 2.04773e48 0.477107
\(887\) 2.46908e48 0.564672 0.282336 0.959316i \(-0.408891\pi\)
0.282336 + 0.959316i \(0.408891\pi\)
\(888\) −2.12320e48 −0.476626
\(889\) 4.94765e47 0.109023
\(890\) 2.58760e48 0.559708
\(891\) −1.71580e49 −3.64322
\(892\) 3.61921e47 0.0754385
\(893\) −3.78528e47 −0.0774550
\(894\) −4.79710e48 −0.963628
\(895\) 2.67177e48 0.526889
\(896\) −3.21597e47 −0.0622631
\(897\) −1.52389e49 −2.89653
\(898\) −2.19840e48 −0.410248
\(899\) 1.22260e47 0.0224001
\(900\) −1.06282e48 −0.191188
\(901\) 1.79670e48 0.317334
\(902\) 3.26957e48 0.566999
\(903\) 1.40458e49 2.39165
\(904\) 7.80909e48 1.30563
\(905\) −1.53204e48 −0.251518
\(906\) −1.27795e48 −0.206015
\(907\) 1.76568e48 0.279507 0.139753 0.990186i \(-0.455369\pi\)
0.139753 + 0.990186i \(0.455369\pi\)
\(908\) −2.60621e48 −0.405129
\(909\) 1.20822e49 1.84434
\(910\) −2.69971e48 −0.404700
\(911\) −4.90626e48 −0.722266 −0.361133 0.932514i \(-0.617610\pi\)
−0.361133 + 0.932514i \(0.617610\pi\)
\(912\) −2.71418e48 −0.392396
\(913\) −8.07079e48 −1.14590
\(914\) −6.26043e47 −0.0872955
\(915\) −3.76219e48 −0.515219
\(916\) −9.37128e47 −0.126044
\(917\) 2.69872e48 0.356503
\(918\) −1.62190e49 −2.10437
\(919\) −7.03091e48 −0.895994 −0.447997 0.894035i \(-0.647863\pi\)
−0.447997 + 0.894035i \(0.647863\pi\)
\(920\) 6.39096e48 0.799958
\(921\) −2.34564e49 −2.88388
\(922\) 5.24400e48 0.633290
\(923\) 7.87955e48 0.934702
\(924\) −1.18143e49 −1.37664
\(925\) 4.16088e47 0.0476263
\(926\) 1.11461e49 1.25326
\(927\) 3.16327e49 3.49398
\(928\) −4.12574e47 −0.0447672
\(929\) 3.42900e48 0.365517 0.182759 0.983158i \(-0.441497\pi\)
0.182759 + 0.983158i \(0.441497\pi\)
\(930\) 2.26404e48 0.237092
\(931\) 2.32532e48 0.239228
\(932\) 2.56329e48 0.259081
\(933\) 1.50282e49 1.49231
\(934\) −6.58752e48 −0.642686
\(935\) −7.47901e48 −0.716890
\(936\) 2.63660e49 2.48309
\(937\) −2.88611e48 −0.267060 −0.133530 0.991045i \(-0.542631\pi\)
−0.133530 + 0.991045i \(0.542631\pi\)
\(938\) 2.58506e48 0.235030
\(939\) −3.51019e49 −3.13580
\(940\) −3.27835e47 −0.0287770
\(941\) −1.90690e49 −1.64475 −0.822373 0.568949i \(-0.807350\pi\)
−0.822373 + 0.568949i \(0.807350\pi\)
\(942\) 1.47190e49 1.24750
\(943\) −9.43893e48 −0.786104
\(944\) −1.78089e47 −0.0145747
\(945\) 1.76506e49 1.41950
\(946\) 1.59279e49 1.25880
\(947\) 7.16410e48 0.556400 0.278200 0.960523i \(-0.410262\pi\)
0.278200 + 0.960523i \(0.410262\pi\)
\(948\) 7.41479e48 0.565928
\(949\) 1.62577e49 1.21946
\(950\) 1.00771e48 0.0742843
\(951\) 1.92647e49 1.39568
\(952\) −1.95185e49 −1.38975
\(953\) 3.01662e48 0.211100 0.105550 0.994414i \(-0.466340\pi\)
0.105550 + 0.994414i \(0.466340\pi\)
\(954\) −8.23183e48 −0.566172
\(955\) 3.00004e48 0.202801
\(956\) 3.21563e48 0.213654
\(957\) 2.61992e48 0.171097
\(958\) 2.64548e48 0.169814
\(959\) −3.00288e49 −1.89466
\(960\) −1.35532e49 −0.840553
\(961\) −1.41557e49 −0.862971
\(962\) −2.93622e48 −0.175954
\(963\) 3.80642e49 2.24225
\(964\) 1.67503e48 0.0969952
\(965\) −5.98840e48 −0.340887
\(966\) −5.16865e49 −2.89237
\(967\) −9.56534e48 −0.526216 −0.263108 0.964766i \(-0.584748\pi\)
−0.263108 + 0.964766i \(0.584748\pi\)
\(968\) −2.70405e49 −1.46242
\(969\) −1.73722e49 −0.923658
\(970\) 3.90515e48 0.204129
\(971\) 3.02376e49 1.55392 0.776961 0.629548i \(-0.216760\pi\)
0.776961 + 0.629548i \(0.216760\pi\)
\(972\) −1.41248e49 −0.713655
\(973\) −1.51829e49 −0.754213
\(974\) 1.77175e49 0.865327
\(975\) −7.31578e48 −0.351305
\(976\) −5.87695e48 −0.277479
\(977\) 5.10941e48 0.237198 0.118599 0.992942i \(-0.462160\pi\)
0.118599 + 0.992942i \(0.462160\pi\)
\(978\) −5.59230e49 −2.55270
\(979\) 5.50508e49 2.47086
\(980\) 2.01390e48 0.0888809
\(981\) 4.62800e49 2.00842
\(982\) 8.71368e48 0.371845
\(983\) −1.15145e49 −0.483183 −0.241591 0.970378i \(-0.577669\pi\)
−0.241591 + 0.970378i \(0.577669\pi\)
\(984\) 2.31226e49 0.954151
\(985\) 1.80159e49 0.731067
\(986\) 1.23126e48 0.0491337
\(987\) 9.32064e48 0.365774
\(988\) 4.69248e48 0.181098
\(989\) −4.59824e49 −1.74523
\(990\) 3.42661e49 1.27904
\(991\) 6.06784e48 0.222751 0.111375 0.993778i \(-0.464474\pi\)
0.111375 + 0.993778i \(0.464474\pi\)
\(992\) −7.58515e48 −0.273856
\(993\) −3.24815e49 −1.15338
\(994\) 2.67254e49 0.933361
\(995\) −2.19258e49 −0.753139
\(996\) −1.62361e49 −0.548534
\(997\) 3.14175e49 1.04400 0.522000 0.852945i \(-0.325186\pi\)
0.522000 + 0.852945i \(0.325186\pi\)
\(998\) 2.93388e49 0.958932
\(999\) 1.91970e49 0.617166
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 \(a_p\))