Properties

Label 1.94.a.a.1.5
Level 1
Weight 94
Character 1.1
Self dual yes
Analytic conductor 54.773
Analytic rank 1
Dimension 7
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 94 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(54.7725430605\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - x^{6} - 160477500301516091326739 x^{5} + 877016488484326647371325741724874 x^{4} + 7260529465737129707868752892581169765229378456 x^{3} - 20781038399188480098606854392326662967337072615105929280 x^{2} - 71309214652872234197294752847774640455181142633761719353245451878000 x - 1353216958878139720025204995487184336935523797943751976847532373756765247900000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: multiple of \( 2^{88}\cdot 3^{34}\cdot 5^{10}\cdot 7^{6}\cdot 13^{2}\cdot 19\cdot 23\cdot 31^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(1.30998e11\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+8.17029e13 q^{2} +3.94920e21 q^{3} -3.22816e27 q^{4} +2.56302e32 q^{5} +3.22661e35 q^{6} +2.42990e39 q^{7} -1.07290e42 q^{8} -2.20059e44 q^{9} +O(q^{10})\) \(q+8.17029e13 q^{2} +3.94920e21 q^{3} -3.22816e27 q^{4} +2.56302e32 q^{5} +3.22661e35 q^{6} +2.42990e39 q^{7} -1.07290e42 q^{8} -2.20059e44 q^{9} +2.09406e46 q^{10} -3.34519e48 q^{11} -1.27487e49 q^{12} -2.46539e51 q^{13} +1.98530e53 q^{14} +1.01219e54 q^{15} -5.56886e55 q^{16} +8.99207e56 q^{17} -1.79794e58 q^{18} +1.17863e58 q^{19} -8.27382e59 q^{20} +9.59616e60 q^{21} -2.73312e62 q^{22} +2.35938e63 q^{23} -4.23709e63 q^{24} -3.52837e64 q^{25} -2.01429e65 q^{26} -1.79971e66 q^{27} -7.84410e66 q^{28} -1.13023e68 q^{29} +8.26986e67 q^{30} -4.06811e69 q^{31} +6.07553e69 q^{32} -1.32109e70 q^{33} +7.34678e70 q^{34} +6.22787e71 q^{35} +7.10385e71 q^{36} -3.61681e72 q^{37} +9.62973e71 q^{38} -9.73633e72 q^{39} -2.74985e74 q^{40} -1.25412e74 q^{41} +7.84034e74 q^{42} +6.73029e75 q^{43} +1.07988e76 q^{44} -5.64014e76 q^{45} +1.92768e77 q^{46} -9.64475e77 q^{47} -2.19925e77 q^{48} +1.97689e78 q^{49} -2.88278e78 q^{50} +3.55115e78 q^{51} +7.95867e78 q^{52} -1.68714e80 q^{53} -1.47041e80 q^{54} -8.57379e80 q^{55} -2.60703e81 q^{56} +4.65464e79 q^{57} -9.23427e81 q^{58} -1.86287e82 q^{59} -3.26750e81 q^{60} -1.57323e83 q^{61} -3.32376e83 q^{62} -5.34720e83 q^{63} +1.04790e84 q^{64} -6.31883e83 q^{65} -1.07936e84 q^{66} +1.27961e85 q^{67} -2.90278e84 q^{68} +9.31767e84 q^{69} +5.08835e85 q^{70} +6.05042e84 q^{71} +2.36100e86 q^{72} +5.11356e86 q^{73} -2.95504e86 q^{74} -1.39342e86 q^{75} -3.80480e85 q^{76} -8.12848e87 q^{77} -7.95486e86 q^{78} -2.35972e88 q^{79} -1.42731e88 q^{80} +4.47506e88 q^{81} -1.02465e88 q^{82} -1.36739e88 q^{83} -3.09779e88 q^{84} +2.30468e89 q^{85} +5.49884e89 q^{86} -4.46349e89 q^{87} +3.58905e90 q^{88} +5.78854e90 q^{89} -4.60816e90 q^{90} -5.99064e90 q^{91} -7.61645e90 q^{92} -1.60658e91 q^{93} -7.88004e91 q^{94} +3.02084e90 q^{95} +2.39935e91 q^{96} -1.91326e92 q^{97} +1.61518e92 q^{98} +7.36140e92 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 43735426713792q^{2} - \)\(36\!\cdots\!84\)\(q^{3} + \)\(37\!\cdots\!44\)\(q^{4} - \)\(24\!\cdots\!50\)\(q^{5} - \)\(34\!\cdots\!56\)\(q^{6} - \)\(92\!\cdots\!08\)\(q^{7} + \)\(62\!\cdots\!60\)\(q^{8} + \)\(36\!\cdots\!11\)\(q^{9} + O(q^{10}) \) \( 7q + 43735426713792q^{2} - \)\(36\!\cdots\!84\)\(q^{3} + \)\(37\!\cdots\!44\)\(q^{4} - \)\(24\!\cdots\!50\)\(q^{5} - \)\(34\!\cdots\!56\)\(q^{6} - \)\(92\!\cdots\!08\)\(q^{7} + \)\(62\!\cdots\!60\)\(q^{8} + \)\(36\!\cdots\!11\)\(q^{9} + \)\(56\!\cdots\!00\)\(q^{10} + \)\(10\!\cdots\!24\)\(q^{11} - \)\(16\!\cdots\!48\)\(q^{12} + \)\(19\!\cdots\!26\)\(q^{13} - \)\(82\!\cdots\!32\)\(q^{14} - \)\(16\!\cdots\!00\)\(q^{15} - \)\(18\!\cdots\!48\)\(q^{16} + \)\(80\!\cdots\!42\)\(q^{17} + \)\(79\!\cdots\!36\)\(q^{18} - \)\(49\!\cdots\!00\)\(q^{19} - \)\(58\!\cdots\!00\)\(q^{20} + \)\(54\!\cdots\!84\)\(q^{21} + \)\(34\!\cdots\!44\)\(q^{22} - \)\(25\!\cdots\!64\)\(q^{23} - \)\(29\!\cdots\!00\)\(q^{24} + \)\(18\!\cdots\!25\)\(q^{25} + \)\(79\!\cdots\!64\)\(q^{26} - \)\(10\!\cdots\!40\)\(q^{27} + \)\(19\!\cdots\!24\)\(q^{28} + \)\(11\!\cdots\!50\)\(q^{29} - \)\(64\!\cdots\!00\)\(q^{30} - \)\(11\!\cdots\!56\)\(q^{31} - \)\(70\!\cdots\!88\)\(q^{32} + \)\(66\!\cdots\!12\)\(q^{33} + \)\(80\!\cdots\!28\)\(q^{34} - \)\(16\!\cdots\!00\)\(q^{35} + \)\(52\!\cdots\!12\)\(q^{36} + \)\(11\!\cdots\!42\)\(q^{37} - \)\(42\!\cdots\!60\)\(q^{38} - \)\(20\!\cdots\!68\)\(q^{39} + \)\(76\!\cdots\!00\)\(q^{40} - \)\(50\!\cdots\!46\)\(q^{41} - \)\(54\!\cdots\!76\)\(q^{42} - \)\(72\!\cdots\!44\)\(q^{43} + \)\(94\!\cdots\!08\)\(q^{44} + \)\(16\!\cdots\!50\)\(q^{45} - \)\(63\!\cdots\!16\)\(q^{46} - \)\(37\!\cdots\!08\)\(q^{47} - \)\(41\!\cdots\!64\)\(q^{48} + \)\(25\!\cdots\!99\)\(q^{49} - \)\(31\!\cdots\!00\)\(q^{50} - \)\(55\!\cdots\!36\)\(q^{51} - \)\(55\!\cdots\!28\)\(q^{52} - \)\(36\!\cdots\!34\)\(q^{53} - \)\(19\!\cdots\!00\)\(q^{54} - \)\(35\!\cdots\!00\)\(q^{55} - \)\(12\!\cdots\!00\)\(q^{56} - \)\(13\!\cdots\!80\)\(q^{57} - \)\(73\!\cdots\!40\)\(q^{58} - \)\(11\!\cdots\!00\)\(q^{59} - \)\(46\!\cdots\!00\)\(q^{60} - \)\(32\!\cdots\!26\)\(q^{61} - \)\(99\!\cdots\!36\)\(q^{62} - \)\(22\!\cdots\!64\)\(q^{63} - \)\(47\!\cdots\!16\)\(q^{64} + \)\(24\!\cdots\!00\)\(q^{65} + \)\(12\!\cdots\!08\)\(q^{66} + \)\(97\!\cdots\!92\)\(q^{67} + \)\(51\!\cdots\!24\)\(q^{68} + \)\(12\!\cdots\!92\)\(q^{69} + \)\(43\!\cdots\!00\)\(q^{70} + \)\(42\!\cdots\!84\)\(q^{71} + \)\(11\!\cdots\!80\)\(q^{72} + \)\(24\!\cdots\!86\)\(q^{73} + \)\(98\!\cdots\!48\)\(q^{74} + \)\(94\!\cdots\!00\)\(q^{75} - \)\(98\!\cdots\!00\)\(q^{76} - \)\(16\!\cdots\!56\)\(q^{77} - \)\(73\!\cdots\!28\)\(q^{78} - \)\(43\!\cdots\!00\)\(q^{79} - \)\(88\!\cdots\!00\)\(q^{80} - \)\(70\!\cdots\!53\)\(q^{81} - \)\(23\!\cdots\!76\)\(q^{82} - \)\(20\!\cdots\!04\)\(q^{83} + \)\(16\!\cdots\!28\)\(q^{84} + \)\(16\!\cdots\!00\)\(q^{85} + \)\(32\!\cdots\!24\)\(q^{86} + \)\(65\!\cdots\!80\)\(q^{87} + \)\(63\!\cdots\!20\)\(q^{88} + \)\(55\!\cdots\!50\)\(q^{89} + \)\(19\!\cdots\!00\)\(q^{90} - \)\(18\!\cdots\!96\)\(q^{91} - \)\(81\!\cdots\!08\)\(q^{92} - \)\(12\!\cdots\!28\)\(q^{93} - \)\(30\!\cdots\!92\)\(q^{94} - \)\(21\!\cdots\!00\)\(q^{95} - \)\(22\!\cdots\!16\)\(q^{96} + \)\(43\!\cdots\!42\)\(q^{97} - \)\(69\!\cdots\!56\)\(q^{98} + \)\(30\!\cdots\!52\)\(q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 8.17029e13 0.820999 0.410499 0.911861i \(-0.365354\pi\)
0.410499 + 0.911861i \(0.365354\pi\)
\(3\) 3.94920e21 0.257259 0.128630 0.991693i \(-0.458942\pi\)
0.128630 + 0.991693i \(0.458942\pi\)
\(4\) −3.22816e27 −0.325961
\(5\) 2.56302e32 0.806577 0.403289 0.915073i \(-0.367867\pi\)
0.403289 + 0.915073i \(0.367867\pi\)
\(6\) 3.22661e35 0.211210
\(7\) 2.42990e39 1.22611 0.613055 0.790041i \(-0.289941\pi\)
0.613055 + 0.790041i \(0.289941\pi\)
\(8\) −1.07290e42 −1.08861
\(9\) −2.20059e44 −0.933818
\(10\) 2.09406e46 0.662199
\(11\) −3.34519e48 −1.25794 −0.628972 0.777428i \(-0.716524\pi\)
−0.628972 + 0.777428i \(0.716524\pi\)
\(12\) −1.27487e49 −0.0838565
\(13\) −2.46539e51 −0.392211 −0.196105 0.980583i \(-0.562829\pi\)
−0.196105 + 0.980583i \(0.562829\pi\)
\(14\) 1.98530e53 1.00663
\(15\) 1.01219e54 0.207500
\(16\) −5.56886e55 −0.567789
\(17\) 8.99207e56 0.546997 0.273498 0.961872i \(-0.411819\pi\)
0.273498 + 0.961872i \(0.411819\pi\)
\(18\) −1.79794e58 −0.766663
\(19\) 1.17863e58 0.0406756 0.0203378 0.999793i \(-0.493526\pi\)
0.0203378 + 0.999793i \(0.493526\pi\)
\(20\) −8.27382e59 −0.262913
\(21\) 9.59616e60 0.315428
\(22\) −2.73312e62 −1.03277
\(23\) 2.35938e63 1.12837 0.564187 0.825647i \(-0.309190\pi\)
0.564187 + 0.825647i \(0.309190\pi\)
\(24\) −4.23709e63 −0.280056
\(25\) −3.52837e64 −0.349433
\(26\) −2.01429e65 −0.322005
\(27\) −1.79971e66 −0.497493
\(28\) −7.84410e66 −0.399664
\(29\) −1.13023e68 −1.12631 −0.563155 0.826351i \(-0.690413\pi\)
−0.563155 + 0.826351i \(0.690413\pi\)
\(30\) 8.26986e67 0.170357
\(31\) −4.06811e69 −1.82421 −0.912104 0.409960i \(-0.865543\pi\)
−0.912104 + 0.409960i \(0.865543\pi\)
\(32\) 6.07553e69 0.622458
\(33\) −1.32109e70 −0.323618
\(34\) 7.34678e70 0.449084
\(35\) 6.22787e71 0.988952
\(36\) 7.10385e71 0.304388
\(37\) −3.61681e72 −0.433456 −0.216728 0.976232i \(-0.569539\pi\)
−0.216728 + 0.976232i \(0.569539\pi\)
\(38\) 9.62973e71 0.0333946
\(39\) −9.73633e72 −0.100900
\(40\) −2.74985e74 −0.878050
\(41\) −1.25412e74 −0.127025 −0.0635127 0.997981i \(-0.520230\pi\)
−0.0635127 + 0.997981i \(0.520230\pi\)
\(42\) 7.84034e74 0.258966
\(43\) 6.73029e75 0.744305 0.372152 0.928172i \(-0.378620\pi\)
0.372152 + 0.928172i \(0.378620\pi\)
\(44\) 1.07988e76 0.410041
\(45\) −5.64014e76 −0.753196
\(46\) 1.92768e77 0.926395
\(47\) −9.64475e77 −1.70506 −0.852532 0.522676i \(-0.824934\pi\)
−0.852532 + 0.522676i \(0.824934\pi\)
\(48\) −2.19925e77 −0.146069
\(49\) 1.97689e78 0.503344
\(50\) −2.88278e78 −0.286884
\(51\) 3.55115e78 0.140720
\(52\) 7.95867e78 0.127845
\(53\) −1.68714e80 −1.11770 −0.558848 0.829270i \(-0.688756\pi\)
−0.558848 + 0.829270i \(0.688756\pi\)
\(54\) −1.47041e80 −0.408441
\(55\) −8.57379e80 −1.01463
\(56\) −2.60703e81 −1.33476
\(57\) 4.65464e79 0.0104642
\(58\) −9.23427e81 −0.924700
\(59\) −1.86287e82 −0.842490 −0.421245 0.906947i \(-0.638407\pi\)
−0.421245 + 0.906947i \(0.638407\pi\)
\(60\) −3.26750e81 −0.0676367
\(61\) −1.57323e83 −1.50993 −0.754963 0.655767i \(-0.772345\pi\)
−0.754963 + 0.655767i \(0.772345\pi\)
\(62\) −3.32376e83 −1.49767
\(63\) −5.34720e83 −1.14496
\(64\) 1.04790e84 1.07883
\(65\) −6.31883e83 −0.316348
\(66\) −1.07936e84 −0.265690
\(67\) 1.27961e85 1.56531 0.782653 0.622458i \(-0.213866\pi\)
0.782653 + 0.622458i \(0.213866\pi\)
\(68\) −2.90278e84 −0.178299
\(69\) 9.31767e84 0.290285
\(70\) 5.08835e85 0.811929
\(71\) 6.05042e84 0.0499197 0.0249599 0.999688i \(-0.492054\pi\)
0.0249599 + 0.999688i \(0.492054\pi\)
\(72\) 2.36100e86 1.01657
\(73\) 5.11356e86 1.15934 0.579670 0.814852i \(-0.303182\pi\)
0.579670 + 0.814852i \(0.303182\pi\)
\(74\) −2.95504e86 −0.355867
\(75\) −1.39342e86 −0.0898949
\(76\) −3.80480e85 −0.0132587
\(77\) −8.12848e87 −1.54238
\(78\) −7.95486e86 −0.0828387
\(79\) −2.35972e88 −1.35894 −0.679469 0.733704i \(-0.737790\pi\)
−0.679469 + 0.733704i \(0.737790\pi\)
\(80\) −1.42731e88 −0.457966
\(81\) 4.47506e88 0.805833
\(82\) −1.02465e88 −0.104288
\(83\) −1.36739e88 −0.0792066 −0.0396033 0.999215i \(-0.512609\pi\)
−0.0396033 + 0.999215i \(0.512609\pi\)
\(84\) −3.09779e88 −0.102817
\(85\) 2.30468e89 0.441195
\(86\) 5.49884e89 0.611073
\(87\) −4.46349e89 −0.289754
\(88\) 3.58905e90 1.36941
\(89\) 5.78854e90 1.30597 0.652986 0.757370i \(-0.273516\pi\)
0.652986 + 0.757370i \(0.273516\pi\)
\(90\) −4.60816e90 −0.618373
\(91\) −5.99064e90 −0.480893
\(92\) −7.61645e90 −0.367806
\(93\) −1.60658e91 −0.469294
\(94\) −7.88004e91 −1.39986
\(95\) 3.02084e90 0.0328080
\(96\) 2.39935e91 0.160133
\(97\) −1.91326e92 −0.788659 −0.394330 0.918969i \(-0.629023\pi\)
−0.394330 + 0.918969i \(0.629023\pi\)
\(98\) 1.61518e92 0.413245
\(99\) 7.36140e92 1.17469
\(100\) 1.13901e92 0.113901
\(101\) −7.76998e92 −0.489189 −0.244594 0.969626i \(-0.578655\pi\)
−0.244594 + 0.969626i \(0.578655\pi\)
\(102\) 2.90139e92 0.115531
\(103\) 4.59345e93 1.16200 0.581002 0.813902i \(-0.302661\pi\)
0.581002 + 0.813902i \(0.302661\pi\)
\(104\) 2.64511e93 0.426966
\(105\) 2.45951e93 0.254417
\(106\) −1.37844e94 −0.917627
\(107\) 9.88939e93 0.425426 0.212713 0.977115i \(-0.431770\pi\)
0.212713 + 0.977115i \(0.431770\pi\)
\(108\) 5.80974e93 0.162163
\(109\) −9.31242e94 −1.69329 −0.846643 0.532161i \(-0.821380\pi\)
−0.846643 + 0.532161i \(0.821380\pi\)
\(110\) −7.00503e94 −0.833010
\(111\) −1.42835e94 −0.111511
\(112\) −1.35318e95 −0.696171
\(113\) 4.19633e95 1.42798 0.713989 0.700157i \(-0.246887\pi\)
0.713989 + 0.700157i \(0.246887\pi\)
\(114\) 3.80298e93 0.00859109
\(115\) 6.04713e95 0.910122
\(116\) 3.64855e95 0.367133
\(117\) 5.42531e95 0.366253
\(118\) −1.52202e96 −0.691683
\(119\) 2.18498e96 0.670678
\(120\) −1.08597e96 −0.225887
\(121\) 4.11869e96 0.582425
\(122\) −1.28538e97 −1.23965
\(123\) −4.95278e95 −0.0326785
\(124\) 1.31325e97 0.594620
\(125\) −3.49231e97 −1.08842
\(126\) −4.36882e97 −0.940013
\(127\) 6.15633e96 0.0917168 0.0458584 0.998948i \(-0.485398\pi\)
0.0458584 + 0.998948i \(0.485398\pi\)
\(128\) 2.54474e97 0.263257
\(129\) 2.65793e97 0.191479
\(130\) −5.16267e97 −0.259722
\(131\) 4.93768e98 1.73943 0.869716 0.493553i \(-0.164302\pi\)
0.869716 + 0.493553i \(0.164302\pi\)
\(132\) 4.26467e97 0.105487
\(133\) 2.86395e97 0.0498728
\(134\) 1.04548e99 1.28512
\(135\) −4.61268e98 −0.401266
\(136\) −9.64755e98 −0.595467
\(137\) −4.08443e99 −1.79318 −0.896592 0.442858i \(-0.853965\pi\)
−0.896592 + 0.442858i \(0.853965\pi\)
\(138\) 7.61281e98 0.238324
\(139\) 9.82507e98 0.219861 0.109930 0.993939i \(-0.464937\pi\)
0.109930 + 0.993939i \(0.464937\pi\)
\(140\) −2.01045e99 −0.322360
\(141\) −3.80891e99 −0.438644
\(142\) 4.94337e98 0.0409840
\(143\) 8.24721e99 0.493380
\(144\) 1.22548e100 0.530211
\(145\) −2.89679e100 −0.908457
\(146\) 4.17793e100 0.951816
\(147\) 7.80714e99 0.129490
\(148\) 1.16756e100 0.141290
\(149\) 6.22850e100 0.551089 0.275545 0.961288i \(-0.411142\pi\)
0.275545 + 0.961288i \(0.411142\pi\)
\(150\) −1.13847e100 −0.0738036
\(151\) 1.42825e101 0.679794 0.339897 0.940463i \(-0.389608\pi\)
0.339897 + 0.940463i \(0.389608\pi\)
\(152\) −1.26455e100 −0.0442800
\(153\) −1.97878e101 −0.510795
\(154\) −6.64120e101 −1.26629
\(155\) −1.04266e102 −1.47136
\(156\) 3.14304e100 0.0328894
\(157\) 2.22191e102 1.72740 0.863698 0.504009i \(-0.168142\pi\)
0.863698 + 0.504009i \(0.168142\pi\)
\(158\) −1.92796e102 −1.11569
\(159\) −6.66287e101 −0.287538
\(160\) 1.55717e102 0.502061
\(161\) 5.73305e102 1.38351
\(162\) 3.65625e102 0.661588
\(163\) −6.84748e101 −0.0930694 −0.0465347 0.998917i \(-0.514818\pi\)
−0.0465347 + 0.998917i \(0.514818\pi\)
\(164\) 4.04851e101 0.0414053
\(165\) −3.38596e102 −0.261023
\(166\) −1.11720e102 −0.0650286
\(167\) −3.03324e102 −0.133534 −0.0667668 0.997769i \(-0.521268\pi\)
−0.0667668 + 0.997769i \(0.521268\pi\)
\(168\) −1.02957e103 −0.343379
\(169\) −3.34341e103 −0.846171
\(170\) 1.88299e103 0.362221
\(171\) −2.59367e102 −0.0379836
\(172\) −2.17265e103 −0.242614
\(173\) −6.79292e102 −0.0579313 −0.0289656 0.999580i \(-0.509221\pi\)
−0.0289656 + 0.999580i \(0.509221\pi\)
\(174\) −3.64680e103 −0.237888
\(175\) −8.57358e103 −0.428443
\(176\) 1.86289e104 0.714247
\(177\) −7.35686e103 −0.216738
\(178\) 4.72940e104 1.07220
\(179\) 7.58027e102 0.0132440 0.00662200 0.999978i \(-0.497892\pi\)
0.00662200 + 0.999978i \(0.497892\pi\)
\(180\) 1.82073e104 0.245512
\(181\) 1.46993e105 1.53194 0.765972 0.642874i \(-0.222258\pi\)
0.765972 + 0.642874i \(0.222258\pi\)
\(182\) −4.89453e104 −0.394813
\(183\) −6.21302e104 −0.388443
\(184\) −2.53137e105 −1.22836
\(185\) −9.26994e104 −0.349616
\(186\) −1.31262e105 −0.385290
\(187\) −3.00802e105 −0.688091
\(188\) 3.11348e105 0.555784
\(189\) −4.37310e105 −0.609980
\(190\) 2.46812e104 0.0269354
\(191\) 7.27780e105 0.622227 0.311113 0.950373i \(-0.399298\pi\)
0.311113 + 0.950373i \(0.399298\pi\)
\(192\) 4.13838e105 0.277538
\(193\) 3.26205e106 1.71821 0.859104 0.511801i \(-0.171021\pi\)
0.859104 + 0.511801i \(0.171021\pi\)
\(194\) −1.56319e106 −0.647488
\(195\) −2.49544e105 −0.0813836
\(196\) −6.38172e105 −0.164070
\(197\) −2.81792e105 −0.0571806 −0.0285903 0.999591i \(-0.509102\pi\)
−0.0285903 + 0.999591i \(0.509102\pi\)
\(198\) 6.01447e106 0.964420
\(199\) −9.39320e106 −1.19164 −0.595821 0.803117i \(-0.703173\pi\)
−0.595821 + 0.803117i \(0.703173\pi\)
\(200\) 3.78557e106 0.380397
\(201\) 5.05344e106 0.402690
\(202\) −6.34830e106 −0.401623
\(203\) −2.74633e107 −1.38098
\(204\) −1.14637e106 −0.0458692
\(205\) −3.21434e106 −0.102456
\(206\) 3.75298e107 0.954004
\(207\) −5.19202e107 −1.05370
\(208\) 1.37294e107 0.222693
\(209\) −3.94274e106 −0.0511677
\(210\) 2.00949e107 0.208876
\(211\) 1.56509e108 1.30438 0.652192 0.758053i \(-0.273849\pi\)
0.652192 + 0.758053i \(0.273849\pi\)
\(212\) 5.44636e107 0.364325
\(213\) 2.38943e106 0.0128423
\(214\) 8.07992e107 0.349274
\(215\) 1.72499e108 0.600340
\(216\) 1.93090e108 0.541577
\(217\) −9.88510e108 −2.23668
\(218\) −7.60852e108 −1.39019
\(219\) 2.01945e108 0.298251
\(220\) 2.76776e108 0.330730
\(221\) −2.21689e108 −0.214538
\(222\) −1.16700e108 −0.0915501
\(223\) −1.13170e109 −0.720371 −0.360186 0.932881i \(-0.617287\pi\)
−0.360186 + 0.932881i \(0.617287\pi\)
\(224\) 1.47629e109 0.763202
\(225\) 7.76449e108 0.326306
\(226\) 3.42852e109 1.17237
\(227\) 3.95198e108 0.110056 0.0550278 0.998485i \(-0.482475\pi\)
0.0550278 + 0.998485i \(0.482475\pi\)
\(228\) −1.50259e107 −0.00341091
\(229\) −5.55694e109 −1.02917 −0.514584 0.857440i \(-0.672054\pi\)
−0.514584 + 0.857440i \(0.672054\pi\)
\(230\) 4.94068e109 0.747209
\(231\) −3.21010e109 −0.396791
\(232\) 1.21261e110 1.22612
\(233\) −5.13478e109 −0.425081 −0.212540 0.977152i \(-0.568174\pi\)
−0.212540 + 0.977152i \(0.568174\pi\)
\(234\) 4.43263e109 0.300694
\(235\) −2.47196e110 −1.37527
\(236\) 6.01365e109 0.274619
\(237\) −9.31900e109 −0.349600
\(238\) 1.78519e110 0.550626
\(239\) −4.49294e110 −1.14032 −0.570162 0.821533i \(-0.693119\pi\)
−0.570162 + 0.821533i \(0.693119\pi\)
\(240\) −5.63672e109 −0.117816
\(241\) −5.09820e110 −0.878263 −0.439132 0.898423i \(-0.644714\pi\)
−0.439132 + 0.898423i \(0.644714\pi\)
\(242\) 3.36509e110 0.478170
\(243\) 6.00839e110 0.704801
\(244\) 5.07865e110 0.492177
\(245\) 5.06680e110 0.405986
\(246\) −4.04657e109 −0.0268290
\(247\) −2.90578e109 −0.0159534
\(248\) 4.36466e111 1.98585
\(249\) −5.40011e109 −0.0203766
\(250\) −2.85332e111 −0.893593
\(251\) −3.21902e111 −0.837329 −0.418665 0.908141i \(-0.637502\pi\)
−0.418665 + 0.908141i \(0.637502\pi\)
\(252\) 1.72616e111 0.373213
\(253\) −7.89258e111 −1.41943
\(254\) 5.02990e110 0.0752994
\(255\) 9.10165e110 0.113502
\(256\) −8.29879e111 −0.862693
\(257\) 4.14878e111 0.359775 0.179887 0.983687i \(-0.442427\pi\)
0.179887 + 0.983687i \(0.442427\pi\)
\(258\) 2.17161e111 0.157204
\(259\) −8.78847e111 −0.531465
\(260\) 2.03982e111 0.103117
\(261\) 2.48716e112 1.05177
\(262\) 4.03422e112 1.42807
\(263\) −2.13949e112 −0.634408 −0.317204 0.948357i \(-0.602744\pi\)
−0.317204 + 0.948357i \(0.602744\pi\)
\(264\) 1.41739e112 0.352295
\(265\) −4.32417e112 −0.901508
\(266\) 2.33993e111 0.0409455
\(267\) 2.28601e112 0.335973
\(268\) −4.13079e112 −0.510229
\(269\) 1.21860e113 1.26585 0.632924 0.774214i \(-0.281855\pi\)
0.632924 + 0.774214i \(0.281855\pi\)
\(270\) −3.76869e112 −0.329439
\(271\) −1.36731e112 −0.100645 −0.0503227 0.998733i \(-0.516025\pi\)
−0.0503227 + 0.998733i \(0.516025\pi\)
\(272\) −5.00755e112 −0.310579
\(273\) −2.36583e112 −0.123714
\(274\) −3.33710e113 −1.47220
\(275\) 1.18031e113 0.439567
\(276\) −3.00789e112 −0.0946215
\(277\) −4.24731e113 −1.12929 −0.564643 0.825335i \(-0.690986\pi\)
−0.564643 + 0.825335i \(0.690986\pi\)
\(278\) 8.02737e112 0.180505
\(279\) 8.95224e113 1.70348
\(280\) −6.68185e113 −1.07659
\(281\) 8.59813e113 1.17371 0.586854 0.809692i \(-0.300366\pi\)
0.586854 + 0.809692i \(0.300366\pi\)
\(282\) −3.11199e113 −0.360126
\(283\) 1.59719e114 1.56779 0.783893 0.620896i \(-0.213231\pi\)
0.783893 + 0.620896i \(0.213231\pi\)
\(284\) −1.95317e112 −0.0162719
\(285\) 1.19299e112 0.00844018
\(286\) 6.73821e113 0.405064
\(287\) −3.04739e113 −0.155747
\(288\) −1.33697e114 −0.581263
\(289\) −1.89383e114 −0.700795
\(290\) −2.36676e114 −0.745842
\(291\) −7.55587e113 −0.202890
\(292\) −1.65074e114 −0.377899
\(293\) 1.18964e114 0.232312 0.116156 0.993231i \(-0.462943\pi\)
0.116156 + 0.993231i \(0.462943\pi\)
\(294\) 6.37866e113 0.106311
\(295\) −4.77457e114 −0.679533
\(296\) 3.88046e114 0.471866
\(297\) 6.02037e114 0.625818
\(298\) 5.08886e114 0.452443
\(299\) −5.81679e114 −0.442561
\(300\) 4.49820e113 0.0293022
\(301\) 1.63539e115 0.912599
\(302\) 1.16692e115 0.558110
\(303\) −3.06853e114 −0.125848
\(304\) −6.56361e113 −0.0230952
\(305\) −4.03222e115 −1.21787
\(306\) −1.61672e115 −0.419362
\(307\) 6.18500e115 1.37849 0.689247 0.724526i \(-0.257941\pi\)
0.689247 + 0.724526i \(0.257941\pi\)
\(308\) 2.62400e115 0.502755
\(309\) 1.81405e115 0.298936
\(310\) −8.51886e115 −1.20799
\(311\) −1.07902e116 −1.31727 −0.658633 0.752465i \(-0.728865\pi\)
−0.658633 + 0.752465i \(0.728865\pi\)
\(312\) 1.04461e115 0.109841
\(313\) −5.97065e115 −0.541016 −0.270508 0.962718i \(-0.587192\pi\)
−0.270508 + 0.962718i \(0.587192\pi\)
\(314\) 1.81536e116 1.41819
\(315\) −1.37050e116 −0.923501
\(316\) 7.61754e115 0.442961
\(317\) −2.55009e116 −1.28027 −0.640133 0.768264i \(-0.721121\pi\)
−0.640133 + 0.768264i \(0.721121\pi\)
\(318\) −5.44375e115 −0.236068
\(319\) 3.78082e116 1.41684
\(320\) 2.68579e116 0.870157
\(321\) 3.90552e115 0.109445
\(322\) 4.68407e116 1.13586
\(323\) 1.05983e115 0.0222494
\(324\) −1.44462e116 −0.262670
\(325\) 8.69880e115 0.137051
\(326\) −5.59459e115 −0.0764099
\(327\) −3.67766e116 −0.435614
\(328\) 1.34554e116 0.138281
\(329\) −2.34358e117 −2.09059
\(330\) −2.76643e116 −0.214300
\(331\) −3.38538e116 −0.227827 −0.113914 0.993491i \(-0.536339\pi\)
−0.113914 + 0.993491i \(0.536339\pi\)
\(332\) 4.41416e115 0.0258183
\(333\) 7.95910e116 0.404769
\(334\) −2.47824e116 −0.109631
\(335\) 3.27966e117 1.26254
\(336\) −5.34396e116 −0.179097
\(337\) −4.10228e116 −0.119739 −0.0598694 0.998206i \(-0.519068\pi\)
−0.0598694 + 0.998206i \(0.519068\pi\)
\(338\) −2.73166e117 −0.694705
\(339\) 1.65721e117 0.367361
\(340\) −7.43988e116 −0.143812
\(341\) 1.36086e118 2.29475
\(342\) −2.11911e116 −0.0311845
\(343\) −4.73982e117 −0.608955
\(344\) −7.22091e117 −0.810259
\(345\) 2.38813e117 0.234137
\(346\) −5.55001e116 −0.0475615
\(347\) −1.44206e117 −0.108060 −0.0540298 0.998539i \(-0.517207\pi\)
−0.0540298 + 0.998539i \(0.517207\pi\)
\(348\) 1.44089e117 0.0944484
\(349\) 2.46411e117 0.141344 0.0706722 0.997500i \(-0.477486\pi\)
0.0706722 + 0.997500i \(0.477486\pi\)
\(350\) −7.00486e117 −0.351751
\(351\) 4.43698e117 0.195122
\(352\) −2.03238e118 −0.783018
\(353\) −1.33642e118 −0.451253 −0.225627 0.974214i \(-0.572443\pi\)
−0.225627 + 0.974214i \(0.572443\pi\)
\(354\) −6.01077e117 −0.177942
\(355\) 1.55073e117 0.0402641
\(356\) −1.86863e118 −0.425695
\(357\) 8.62893e117 0.172538
\(358\) 6.19330e116 0.0108733
\(359\) 6.50020e118 1.00239 0.501193 0.865335i \(-0.332895\pi\)
0.501193 + 0.865335i \(0.332895\pi\)
\(360\) 6.05129e118 0.819939
\(361\) −8.38235e118 −0.998345
\(362\) 1.20097e119 1.25772
\(363\) 1.62656e118 0.149834
\(364\) 1.93388e118 0.156752
\(365\) 1.31061e119 0.935097
\(366\) −5.07622e118 −0.318911
\(367\) −1.27243e119 −0.704144 −0.352072 0.935973i \(-0.614523\pi\)
−0.352072 + 0.935973i \(0.614523\pi\)
\(368\) −1.31390e119 −0.640679
\(369\) 2.75981e118 0.118619
\(370\) −7.57380e118 −0.287034
\(371\) −4.09958e119 −1.37042
\(372\) 5.18630e118 0.152972
\(373\) −1.61115e119 −0.419444 −0.209722 0.977761i \(-0.567256\pi\)
−0.209722 + 0.977761i \(0.567256\pi\)
\(374\) −2.45764e119 −0.564922
\(375\) −1.37918e119 −0.280007
\(376\) 1.03478e120 1.85615
\(377\) 2.78645e119 0.441751
\(378\) −3.57295e119 −0.500793
\(379\) 5.32525e119 0.660111 0.330056 0.943961i \(-0.392932\pi\)
0.330056 + 0.943961i \(0.392932\pi\)
\(380\) −9.75176e117 −0.0106941
\(381\) 2.43126e118 0.0235950
\(382\) 5.94617e119 0.510847
\(383\) 3.01520e119 0.229389 0.114694 0.993401i \(-0.463411\pi\)
0.114694 + 0.993401i \(0.463411\pi\)
\(384\) 1.00497e119 0.0677253
\(385\) −2.08334e120 −1.24405
\(386\) 2.66519e120 1.41065
\(387\) −1.48106e120 −0.695045
\(388\) 6.17632e119 0.257072
\(389\) −2.34405e120 −0.865585 −0.432793 0.901493i \(-0.642472\pi\)
−0.432793 + 0.901493i \(0.642472\pi\)
\(390\) −2.03884e119 −0.0668159
\(391\) 2.12157e120 0.617217
\(392\) −2.12100e120 −0.547946
\(393\) 1.94999e120 0.447485
\(394\) −2.30232e119 −0.0469452
\(395\) −6.04799e120 −1.09609
\(396\) −2.37638e120 −0.382903
\(397\) 3.15657e120 0.452332 0.226166 0.974089i \(-0.427381\pi\)
0.226166 + 0.974089i \(0.427381\pi\)
\(398\) −7.67452e120 −0.978337
\(399\) 1.13103e119 0.0128302
\(400\) 1.96490e120 0.198404
\(401\) 1.29870e121 1.16761 0.583803 0.811895i \(-0.301564\pi\)
0.583803 + 0.811895i \(0.301564\pi\)
\(402\) 4.12881e120 0.330608
\(403\) 1.00295e121 0.715474
\(404\) 2.50827e120 0.159456
\(405\) 1.14696e121 0.649967
\(406\) −2.24383e121 −1.13378
\(407\) 1.20989e121 0.545264
\(408\) −3.81002e120 −0.153190
\(409\) 2.34486e121 0.841363 0.420682 0.907208i \(-0.361791\pi\)
0.420682 + 0.907208i \(0.361791\pi\)
\(410\) −2.62620e120 −0.0841161
\(411\) −1.61302e121 −0.461313
\(412\) −1.48284e121 −0.378768
\(413\) −4.52659e121 −1.03298
\(414\) −4.24203e121 −0.865084
\(415\) −3.50465e120 −0.0638863
\(416\) −1.49786e121 −0.244135
\(417\) 3.88012e120 0.0565612
\(418\) −3.22133e120 −0.0420086
\(419\) 6.83542e121 0.797651 0.398826 0.917027i \(-0.369418\pi\)
0.398826 + 0.917027i \(0.369418\pi\)
\(420\) −7.93970e120 −0.0829300
\(421\) −1.26027e122 −1.17855 −0.589273 0.807934i \(-0.700586\pi\)
−0.589273 + 0.807934i \(0.700586\pi\)
\(422\) 1.27873e122 1.07090
\(423\) 2.12241e122 1.59222
\(424\) 1.81013e122 1.21674
\(425\) −3.17273e121 −0.191139
\(426\) 1.95224e120 0.0105435
\(427\) −3.82280e122 −1.85134
\(428\) −3.19245e121 −0.138672
\(429\) 3.25699e121 0.126927
\(430\) 1.40936e122 0.492878
\(431\) 3.14662e122 0.987760 0.493880 0.869530i \(-0.335578\pi\)
0.493880 + 0.869530i \(0.335578\pi\)
\(432\) 1.00223e122 0.282471
\(433\) −2.51232e122 −0.635898 −0.317949 0.948108i \(-0.602994\pi\)
−0.317949 + 0.948108i \(0.602994\pi\)
\(434\) −8.07641e122 −1.83631
\(435\) −1.14400e122 −0.233709
\(436\) 3.00620e122 0.551945
\(437\) 2.78083e121 0.0458974
\(438\) 1.64995e122 0.244864
\(439\) −5.27593e122 −0.704204 −0.352102 0.935962i \(-0.614533\pi\)
−0.352102 + 0.935962i \(0.614533\pi\)
\(440\) 9.19878e122 1.10454
\(441\) −4.35032e122 −0.470031
\(442\) −1.81127e122 −0.176135
\(443\) −1.20330e123 −1.05342 −0.526710 0.850045i \(-0.676575\pi\)
−0.526710 + 0.850045i \(0.676575\pi\)
\(444\) 4.61095e121 0.0363481
\(445\) 1.48361e123 1.05337
\(446\) −9.24634e122 −0.591424
\(447\) 2.45976e122 0.141773
\(448\) 2.54629e123 1.32276
\(449\) 1.57788e123 0.738957 0.369479 0.929239i \(-0.379536\pi\)
0.369479 + 0.929239i \(0.379536\pi\)
\(450\) 6.34381e122 0.267897
\(451\) 4.19528e122 0.159791
\(452\) −1.35464e123 −0.465465
\(453\) 5.64047e122 0.174883
\(454\) 3.22888e122 0.0903556
\(455\) −1.53541e123 −0.387878
\(456\) −4.99395e121 −0.0113914
\(457\) −3.61599e123 −0.744944 −0.372472 0.928043i \(-0.621490\pi\)
−0.372472 + 0.928043i \(0.621490\pi\)
\(458\) −4.54018e123 −0.844946
\(459\) −1.61831e123 −0.272127
\(460\) −1.95211e123 −0.296664
\(461\) −4.18169e123 −0.574458 −0.287229 0.957862i \(-0.592734\pi\)
−0.287229 + 0.957862i \(0.592734\pi\)
\(462\) −2.62275e123 −0.325765
\(463\) 6.81222e123 0.765196 0.382598 0.923915i \(-0.375030\pi\)
0.382598 + 0.923915i \(0.375030\pi\)
\(464\) 6.29406e123 0.639507
\(465\) −4.11769e123 −0.378522
\(466\) −4.19526e123 −0.348991
\(467\) 1.53529e124 1.15600 0.577998 0.816038i \(-0.303834\pi\)
0.577998 + 0.816038i \(0.303834\pi\)
\(468\) −1.75138e123 −0.119384
\(469\) 3.10932e124 1.91924
\(470\) −2.01967e124 −1.12909
\(471\) 8.77476e123 0.444389
\(472\) 1.99867e124 0.917145
\(473\) −2.25141e124 −0.936294
\(474\) −7.61389e123 −0.287021
\(475\) −4.15863e122 −0.0142134
\(476\) −7.05346e123 −0.218615
\(477\) 3.71270e124 1.04372
\(478\) −3.67086e124 −0.936204
\(479\) −3.65719e124 −0.846344 −0.423172 0.906049i \(-0.639083\pi\)
−0.423172 + 0.906049i \(0.639083\pi\)
\(480\) 6.14958e123 0.129160
\(481\) 8.91684e123 0.170006
\(482\) −4.16538e124 −0.721053
\(483\) 2.26410e124 0.355921
\(484\) −1.32958e124 −0.189848
\(485\) −4.90373e124 −0.636115
\(486\) 4.90903e124 0.578641
\(487\) −8.75398e124 −0.937797 −0.468899 0.883252i \(-0.655349\pi\)
−0.468899 + 0.883252i \(0.655349\pi\)
\(488\) 1.68792e125 1.64372
\(489\) −2.70421e123 −0.0239430
\(490\) 4.13972e124 0.333314
\(491\) −9.36249e124 −0.685649 −0.342825 0.939399i \(-0.611384\pi\)
−0.342825 + 0.939399i \(0.611384\pi\)
\(492\) 1.59884e123 0.0106519
\(493\) −1.01631e125 −0.616088
\(494\) −2.37410e123 −0.0130977
\(495\) 1.88674e125 0.947479
\(496\) 2.26547e125 1.03576
\(497\) 1.47019e124 0.0612070
\(498\) −4.41204e123 −0.0167292
\(499\) 1.65067e125 0.570144 0.285072 0.958506i \(-0.407982\pi\)
0.285072 + 0.958506i \(0.407982\pi\)
\(500\) 1.12737e125 0.354783
\(501\) −1.19789e124 −0.0343528
\(502\) −2.63004e125 −0.687446
\(503\) −8.31350e125 −1.98095 −0.990473 0.137706i \(-0.956027\pi\)
−0.990473 + 0.137706i \(0.956027\pi\)
\(504\) 5.73699e125 1.24642
\(505\) −1.99146e125 −0.394568
\(506\) −6.44847e125 −1.16535
\(507\) −1.32038e125 −0.217685
\(508\) −1.98736e124 −0.0298961
\(509\) −4.64595e125 −0.637819 −0.318909 0.947785i \(-0.603317\pi\)
−0.318909 + 0.947785i \(0.603317\pi\)
\(510\) 7.43631e124 0.0931847
\(511\) 1.24254e126 1.42148
\(512\) −9.30054e125 −0.971527
\(513\) −2.12118e124 −0.0202358
\(514\) 3.38968e125 0.295375
\(515\) 1.17731e126 0.937246
\(516\) −8.58022e124 −0.0624148
\(517\) 3.22636e126 2.14488
\(518\) −7.18044e125 −0.436332
\(519\) −2.68266e124 −0.0149034
\(520\) 6.77945e125 0.344381
\(521\) −3.08051e126 −1.43110 −0.715548 0.698564i \(-0.753823\pi\)
−0.715548 + 0.698564i \(0.753823\pi\)
\(522\) 2.03208e126 0.863501
\(523\) 4.47820e124 0.0174090 0.00870452 0.999962i \(-0.497229\pi\)
0.00870452 + 0.999962i \(0.497229\pi\)
\(524\) −1.59396e126 −0.566986
\(525\) −3.38588e125 −0.110221
\(526\) −1.74803e126 −0.520848
\(527\) −3.65807e126 −0.997835
\(528\) 7.35693e125 0.183747
\(529\) 1.19458e126 0.273230
\(530\) −3.53297e126 −0.740137
\(531\) 4.09941e126 0.786732
\(532\) −9.24527e124 −0.0162566
\(533\) 3.09190e125 0.0498207
\(534\) 1.86774e126 0.275834
\(535\) 2.53467e126 0.343139
\(536\) −1.37289e127 −1.70401
\(537\) 2.99360e124 0.00340714
\(538\) 9.95634e126 1.03926
\(539\) −6.61308e126 −0.633179
\(540\) 1.48905e126 0.130797
\(541\) 2.32405e127 1.87315 0.936574 0.350469i \(-0.113978\pi\)
0.936574 + 0.350469i \(0.113978\pi\)
\(542\) −1.11713e126 −0.0826298
\(543\) 5.80505e126 0.394107
\(544\) 5.46316e126 0.340483
\(545\) −2.38679e127 −1.36577
\(546\) −1.93295e126 −0.101569
\(547\) −1.13550e127 −0.547993 −0.273997 0.961731i \(-0.588346\pi\)
−0.273997 + 0.961731i \(0.588346\pi\)
\(548\) 1.31852e127 0.584508
\(549\) 3.46204e127 1.41000
\(550\) 9.64346e126 0.360884
\(551\) −1.33212e126 −0.0458134
\(552\) −9.99689e126 −0.316008
\(553\) −5.73387e127 −1.66621
\(554\) −3.47017e127 −0.927143
\(555\) −3.66089e126 −0.0899420
\(556\) −3.17169e126 −0.0716660
\(557\) −3.44821e127 −0.716682 −0.358341 0.933591i \(-0.616657\pi\)
−0.358341 + 0.933591i \(0.616657\pi\)
\(558\) 7.31424e127 1.39855
\(559\) −1.65928e127 −0.291924
\(560\) −3.46821e127 −0.561516
\(561\) −1.18793e127 −0.177018
\(562\) 7.02492e127 0.963614
\(563\) −9.14565e127 −1.15498 −0.577489 0.816398i \(-0.695968\pi\)
−0.577489 + 0.816398i \(0.695968\pi\)
\(564\) 1.22958e127 0.142981
\(565\) 1.07553e128 1.15178
\(566\) 1.30495e128 1.28715
\(567\) 1.08739e128 0.988039
\(568\) −6.49147e126 −0.0543432
\(569\) −2.43339e127 −0.187712 −0.0938560 0.995586i \(-0.529919\pi\)
−0.0938560 + 0.995586i \(0.529919\pi\)
\(570\) 9.74709e125 0.00692938
\(571\) −3.60430e127 −0.236180 −0.118090 0.993003i \(-0.537677\pi\)
−0.118090 + 0.993003i \(0.537677\pi\)
\(572\) −2.66233e127 −0.160822
\(573\) 2.87415e127 0.160074
\(574\) −2.48980e127 −0.127868
\(575\) −8.32476e127 −0.394291
\(576\) −2.30600e128 −1.00743
\(577\) −2.26961e128 −0.914695 −0.457347 0.889288i \(-0.651200\pi\)
−0.457347 + 0.889288i \(0.651200\pi\)
\(578\) −1.54731e128 −0.575352
\(579\) 1.28825e128 0.442025
\(580\) 9.35129e127 0.296121
\(581\) −3.32262e127 −0.0971160
\(582\) −6.17337e127 −0.166572
\(583\) 5.64382e128 1.40600
\(584\) −5.48632e128 −1.26207
\(585\) 1.39051e128 0.295412
\(586\) 9.71971e127 0.190728
\(587\) 3.79672e128 0.688236 0.344118 0.938926i \(-0.388178\pi\)
0.344118 + 0.938926i \(0.388178\pi\)
\(588\) −2.52027e127 −0.0422086
\(589\) −4.79479e127 −0.0742008
\(590\) −3.90096e128 −0.557896
\(591\) −1.11285e127 −0.0147102
\(592\) 2.01415e128 0.246112
\(593\) 6.59860e128 0.745433 0.372716 0.927945i \(-0.378426\pi\)
0.372716 + 0.927945i \(0.378426\pi\)
\(594\) 4.91882e128 0.513796
\(595\) 5.60014e128 0.540953
\(596\) −2.01066e128 −0.179633
\(597\) −3.70957e128 −0.306561
\(598\) −4.75248e128 −0.363342
\(599\) −1.08803e129 −0.769652 −0.384826 0.922989i \(-0.625739\pi\)
−0.384826 + 0.922989i \(0.625739\pi\)
\(600\) 1.49500e128 0.0978606
\(601\) 1.43607e129 0.869986 0.434993 0.900434i \(-0.356751\pi\)
0.434993 + 0.900434i \(0.356751\pi\)
\(602\) 1.33616e129 0.749243
\(603\) −2.81590e129 −1.46171
\(604\) −4.61063e128 −0.221586
\(605\) 1.05563e129 0.469771
\(606\) −2.50707e128 −0.103321
\(607\) −3.14623e129 −1.20093 −0.600464 0.799652i \(-0.705017\pi\)
−0.600464 + 0.799652i \(0.705017\pi\)
\(608\) 7.16079e127 0.0253189
\(609\) −1.08458e129 −0.355270
\(610\) −3.29444e129 −0.999872
\(611\) 2.37781e129 0.668744
\(612\) 6.38783e128 0.166499
\(613\) −2.38828e129 −0.576997 −0.288499 0.957480i \(-0.593156\pi\)
−0.288499 + 0.957480i \(0.593156\pi\)
\(614\) 5.05332e129 1.13174
\(615\) −1.26941e128 −0.0263577
\(616\) 8.72102e129 1.67905
\(617\) −1.21225e129 −0.216437 −0.108218 0.994127i \(-0.534515\pi\)
−0.108218 + 0.994127i \(0.534515\pi\)
\(618\) 1.48213e129 0.245427
\(619\) 3.23232e129 0.496477 0.248238 0.968699i \(-0.420148\pi\)
0.248238 + 0.968699i \(0.420148\pi\)
\(620\) 3.36588e129 0.479607
\(621\) −4.24619e129 −0.561358
\(622\) −8.81594e129 −1.08147
\(623\) 1.40656e130 1.60126
\(624\) 5.42202e128 0.0572898
\(625\) −5.38811e129 −0.528464
\(626\) −4.87819e129 −0.444173
\(627\) −1.55707e128 −0.0131634
\(628\) −7.17267e129 −0.563064
\(629\) −3.25226e129 −0.237099
\(630\) −1.11974e130 −0.758193
\(631\) −2.62414e130 −1.65052 −0.825262 0.564750i \(-0.808973\pi\)
−0.825262 + 0.564750i \(0.808973\pi\)
\(632\) 2.53173e130 1.47936
\(633\) 6.18087e129 0.335565
\(634\) −2.08350e130 −1.05110
\(635\) 1.57788e129 0.0739767
\(636\) 2.15088e129 0.0937260
\(637\) −4.87380e129 −0.197417
\(638\) 3.08904e130 1.16322
\(639\) −1.33145e129 −0.0466159
\(640\) 6.52221e129 0.212337
\(641\) 4.38203e130 1.32671 0.663356 0.748304i \(-0.269131\pi\)
0.663356 + 0.748304i \(0.269131\pi\)
\(642\) 3.19093e129 0.0898541
\(643\) −3.72458e129 −0.0975589 −0.0487795 0.998810i \(-0.515533\pi\)
−0.0487795 + 0.998810i \(0.515533\pi\)
\(644\) −1.85072e130 −0.450970
\(645\) 6.81232e129 0.154443
\(646\) 8.65912e128 0.0182668
\(647\) −5.42339e129 −0.106469 −0.0532343 0.998582i \(-0.516953\pi\)
−0.0532343 + 0.998582i \(0.516953\pi\)
\(648\) −4.80127e130 −0.877240
\(649\) 6.23167e130 1.05981
\(650\) 7.10717e129 0.112519
\(651\) −3.90383e130 −0.575406
\(652\) 2.21047e129 0.0303370
\(653\) −8.13013e129 −0.103905 −0.0519523 0.998650i \(-0.516544\pi\)
−0.0519523 + 0.998650i \(0.516544\pi\)
\(654\) −3.00476e130 −0.357638
\(655\) 1.26553e131 1.40299
\(656\) 6.98403e129 0.0721236
\(657\) −1.12528e131 −1.08261
\(658\) −1.91477e131 −1.71638
\(659\) 7.29337e130 0.609196 0.304598 0.952481i \(-0.401478\pi\)
0.304598 + 0.952481i \(0.401478\pi\)
\(660\) 1.09304e130 0.0850833
\(661\) 5.42034e129 0.0393241 0.0196621 0.999807i \(-0.493741\pi\)
0.0196621 + 0.999807i \(0.493741\pi\)
\(662\) −2.76595e130 −0.187046
\(663\) −8.75497e129 −0.0551919
\(664\) 1.46707e130 0.0862253
\(665\) 7.34034e129 0.0402262
\(666\) 6.50282e130 0.332315
\(667\) −2.66663e131 −1.27090
\(668\) 9.79178e129 0.0435267
\(669\) −4.46932e130 −0.185322
\(670\) 2.67958e131 1.03654
\(671\) 5.26277e131 1.89940
\(672\) 5.83018e130 0.196341
\(673\) 2.85131e131 0.896075 0.448037 0.894015i \(-0.352123\pi\)
0.448037 + 0.894015i \(0.352123\pi\)
\(674\) −3.35168e130 −0.0983054
\(675\) 6.35003e130 0.173840
\(676\) 1.07931e131 0.275818
\(677\) −6.99964e131 −1.66995 −0.834973 0.550291i \(-0.814517\pi\)
−0.834973 + 0.550291i \(0.814517\pi\)
\(678\) 1.35399e131 0.301603
\(679\) −4.64904e131 −0.966983
\(680\) −2.47268e131 −0.480290
\(681\) 1.56072e130 0.0283128
\(682\) 1.11186e132 1.88399
\(683\) −7.86376e131 −1.24471 −0.622354 0.782736i \(-0.713824\pi\)
−0.622354 + 0.782736i \(0.713824\pi\)
\(684\) 8.37280e129 0.0123812
\(685\) −1.04685e132 −1.44634
\(686\) −3.87257e131 −0.499951
\(687\) −2.19455e131 −0.264763
\(688\) −3.74800e131 −0.422608
\(689\) 4.15946e131 0.438372
\(690\) 1.95117e131 0.192227
\(691\) 4.34229e131 0.399935 0.199968 0.979803i \(-0.435916\pi\)
0.199968 + 0.979803i \(0.435916\pi\)
\(692\) 2.19286e130 0.0188833
\(693\) 1.78874e132 1.44030
\(694\) −1.17821e131 −0.0887169
\(695\) 2.51818e131 0.177335
\(696\) 4.78886e131 0.315430
\(697\) −1.12771e131 −0.0694825
\(698\) 2.01325e131 0.116044
\(699\) −2.02783e131 −0.109356
\(700\) 2.76769e131 0.139656
\(701\) 2.09353e132 0.988534 0.494267 0.869310i \(-0.335437\pi\)
0.494267 + 0.869310i \(0.335437\pi\)
\(702\) 3.62514e131 0.160195
\(703\) −4.26287e130 −0.0176311
\(704\) −3.50543e132 −1.35710
\(705\) −9.76229e131 −0.353800
\(706\) −1.09190e132 −0.370478
\(707\) −1.88803e132 −0.599799
\(708\) 2.37491e131 0.0706482
\(709\) 4.97568e132 1.38612 0.693062 0.720878i \(-0.256261\pi\)
0.693062 + 0.720878i \(0.256261\pi\)
\(710\) 1.26699e131 0.0330568
\(711\) 5.19276e132 1.26900
\(712\) −6.21050e132 −1.42170
\(713\) −9.59822e132 −2.05839
\(714\) 7.05009e131 0.141654
\(715\) 2.11377e132 0.397949
\(716\) −2.44703e130 −0.00431702
\(717\) −1.77435e132 −0.293359
\(718\) 5.31085e132 0.822958
\(719\) −4.88173e132 −0.709055 −0.354528 0.935045i \(-0.615358\pi\)
−0.354528 + 0.935045i \(0.615358\pi\)
\(720\) 3.14091e132 0.427656
\(721\) 1.11616e133 1.42474
\(722\) −6.84862e132 −0.819641
\(723\) −2.01338e132 −0.225941
\(724\) −4.74517e132 −0.499353
\(725\) 3.98785e132 0.393570
\(726\) 1.32894e132 0.123014
\(727\) 7.26876e132 0.631117 0.315559 0.948906i \(-0.397808\pi\)
0.315559 + 0.948906i \(0.397808\pi\)
\(728\) 6.42734e132 0.523506
\(729\) −8.17286e132 −0.624516
\(730\) 1.07081e133 0.767713
\(731\) 6.05192e132 0.407132
\(732\) 2.00566e132 0.126617
\(733\) 1.29322e133 0.766190 0.383095 0.923709i \(-0.374858\pi\)
0.383095 + 0.923709i \(0.374858\pi\)
\(734\) −1.03961e133 −0.578102
\(735\) 2.00098e132 0.104444
\(736\) 1.43345e133 0.702366
\(737\) −4.28055e133 −1.96907
\(738\) 2.25484e132 0.0973857
\(739\) −4.10724e133 −1.66565 −0.832824 0.553537i \(-0.813278\pi\)
−0.832824 + 0.553537i \(0.813278\pi\)
\(740\) 2.99248e132 0.113961
\(741\) −1.14755e131 −0.00410417
\(742\) −3.34948e133 −1.12511
\(743\) −1.21328e132 −0.0382809 −0.0191405 0.999817i \(-0.506093\pi\)
−0.0191405 + 0.999817i \(0.506093\pi\)
\(744\) 1.72369e133 0.510880
\(745\) 1.59637e133 0.444496
\(746\) −1.31635e133 −0.344363
\(747\) 3.00907e132 0.0739646
\(748\) 9.71037e132 0.224291
\(749\) 2.40302e133 0.521619
\(750\) −1.12683e133 −0.229885
\(751\) 5.11984e133 0.981746 0.490873 0.871231i \(-0.336678\pi\)
0.490873 + 0.871231i \(0.336678\pi\)
\(752\) 5.37102e133 0.968116
\(753\) −1.27126e133 −0.215411
\(754\) 2.27661e133 0.362677
\(755\) 3.66064e133 0.548307
\(756\) 1.41171e133 0.198830
\(757\) −1.03853e134 −1.37550 −0.687748 0.725950i \(-0.741400\pi\)
−0.687748 + 0.725950i \(0.741400\pi\)
\(758\) 4.35089e133 0.541951
\(759\) −3.11694e133 −0.365162
\(760\) −3.24105e132 −0.0357152
\(761\) 1.18377e134 1.22710 0.613552 0.789655i \(-0.289740\pi\)
0.613552 + 0.789655i \(0.289740\pi\)
\(762\) 1.98641e132 0.0193715
\(763\) −2.26282e134 −2.07615
\(764\) −2.34939e133 −0.202822
\(765\) −5.07165e133 −0.411996
\(766\) 2.46350e133 0.188328
\(767\) 4.59271e133 0.330434
\(768\) −3.27736e133 −0.221936
\(769\) 1.09883e134 0.700418 0.350209 0.936672i \(-0.386111\pi\)
0.350209 + 0.936672i \(0.386111\pi\)
\(770\) −1.70215e134 −1.02136
\(771\) 1.63844e133 0.0925554
\(772\) −1.05304e134 −0.560069
\(773\) 9.95234e133 0.498401 0.249200 0.968452i \(-0.419832\pi\)
0.249200 + 0.968452i \(0.419832\pi\)
\(774\) −1.21007e134 −0.570631
\(775\) 1.43538e134 0.637438
\(776\) 2.05273e134 0.858544
\(777\) −3.47075e133 −0.136724
\(778\) −1.91515e134 −0.710645
\(779\) −1.47814e132 −0.00516684
\(780\) 8.05566e132 0.0265279
\(781\) −2.02398e133 −0.0627962
\(782\) 1.73338e134 0.506735
\(783\) 2.03407e134 0.560331
\(784\) −1.10090e134 −0.285793
\(785\) 5.69478e134 1.39328
\(786\) 1.59320e134 0.367385
\(787\) −4.25421e134 −0.924685 −0.462343 0.886701i \(-0.652991\pi\)
−0.462343 + 0.886701i \(0.652991\pi\)
\(788\) 9.09668e132 0.0186386
\(789\) −8.44929e133 −0.163207
\(790\) −4.94138e134 −0.899888
\(791\) 1.01966e135 1.75086
\(792\) −7.89801e134 −1.27878
\(793\) 3.87863e134 0.592210
\(794\) 2.57901e134 0.371364
\(795\) −1.70770e134 −0.231921
\(796\) 3.03228e134 0.388429
\(797\) −1.05793e135 −1.27834 −0.639168 0.769067i \(-0.720721\pi\)
−0.639168 + 0.769067i \(0.720721\pi\)
\(798\) 9.24084e132 0.0105336
\(799\) −8.67262e134 −0.932664
\(800\) −2.14367e134 −0.217507
\(801\) −1.27382e135 −1.21954
\(802\) 1.06108e135 0.958603
\(803\) −1.71059e135 −1.45838
\(804\) −1.63133e134 −0.131261
\(805\) 1.46939e135 1.11591
\(806\) 8.19437e134 0.587403
\(807\) 4.81251e134 0.325651
\(808\) 8.33639e134 0.532537
\(809\) 5.72597e134 0.345337 0.172668 0.984980i \(-0.444761\pi\)
0.172668 + 0.984980i \(0.444761\pi\)
\(810\) 9.37102e134 0.533622
\(811\) −4.39300e134 −0.236207 −0.118103 0.993001i \(-0.537681\pi\)
−0.118103 + 0.993001i \(0.537681\pi\)
\(812\) 8.86560e134 0.450145
\(813\) −5.39977e133 −0.0258920
\(814\) 9.88517e134 0.447661
\(815\) −1.75502e134 −0.0750677
\(816\) −1.97758e134 −0.0798992
\(817\) 7.93251e133 0.0302751
\(818\) 1.91582e135 0.690758
\(819\) 1.31829e135 0.449067
\(820\) 1.03764e134 0.0333966
\(821\) −2.16864e135 −0.659523 −0.329762 0.944064i \(-0.606968\pi\)
−0.329762 + 0.944064i \(0.606968\pi\)
\(822\) −1.31789e135 −0.378738
\(823\) −4.99161e135 −1.35565 −0.677826 0.735222i \(-0.737078\pi\)
−0.677826 + 0.735222i \(0.737078\pi\)
\(824\) −4.92829e135 −1.26497
\(825\) 4.66128e134 0.113083
\(826\) −3.69835e135 −0.848079
\(827\) 1.61582e135 0.350257 0.175129 0.984546i \(-0.443966\pi\)
0.175129 + 0.984546i \(0.443966\pi\)
\(828\) 1.67607e135 0.343464
\(829\) 5.76678e135 1.11724 0.558622 0.829422i \(-0.311330\pi\)
0.558622 + 0.829422i \(0.311330\pi\)
\(830\) −2.86340e134 −0.0524506
\(831\) −1.67735e135 −0.290520
\(832\) −2.58348e135 −0.423127
\(833\) 1.77763e135 0.275327
\(834\) 3.17017e134 0.0464367
\(835\) −7.77424e134 −0.107705
\(836\) 1.27278e134 0.0166787
\(837\) 7.32141e135 0.907530
\(838\) 5.58473e135 0.654871
\(839\) −1.05736e134 −0.0117298 −0.00586489 0.999983i \(-0.501867\pi\)
−0.00586489 + 0.999983i \(0.501867\pi\)
\(840\) −2.63880e135 −0.276962
\(841\) 2.70446e135 0.268576
\(842\) −1.02968e136 −0.967584
\(843\) 3.39558e135 0.301948
\(844\) −5.05237e135 −0.425178
\(845\) −8.56921e135 −0.682502
\(846\) 1.73407e136 1.30721
\(847\) 1.00080e136 0.714116
\(848\) 9.39545e135 0.634615
\(849\) 6.30762e135 0.403328
\(850\) −2.59221e135 −0.156925
\(851\) −8.53342e135 −0.489101
\(852\) −7.71347e133 −0.00418609
\(853\) −5.38353e134 −0.0276654 −0.0138327 0.999904i \(-0.504403\pi\)
−0.0138327 + 0.999904i \(0.504403\pi\)
\(854\) −3.12334e136 −1.51994
\(855\) −6.64763e134 −0.0306367
\(856\) −1.06103e136 −0.463124
\(857\) −4.16850e135 −0.172334 −0.0861672 0.996281i \(-0.527462\pi\)
−0.0861672 + 0.996281i \(0.527462\pi\)
\(858\) 2.66105e135 0.104207
\(859\) 1.20248e136 0.446061 0.223030 0.974811i \(-0.428405\pi\)
0.223030 + 0.974811i \(0.428405\pi\)
\(860\) −5.56853e135 −0.195687
\(861\) −1.20348e135 −0.0400674
\(862\) 2.57088e136 0.810950
\(863\) −5.13038e136 −1.53337 −0.766686 0.642022i \(-0.778096\pi\)
−0.766686 + 0.642022i \(0.778096\pi\)
\(864\) −1.09342e136 −0.309669
\(865\) −1.74104e135 −0.0467260
\(866\) −2.05264e136 −0.522072
\(867\) −7.47911e135 −0.180286
\(868\) 3.19107e136 0.729069
\(869\) 7.89371e136 1.70947
\(870\) −9.34681e135 −0.191875
\(871\) −3.15474e136 −0.613930
\(872\) 9.99126e136 1.84333
\(873\) 4.21031e136 0.736464
\(874\) 2.27202e135 0.0376817
\(875\) −8.48596e136 −1.33452
\(876\) −6.51911e135 −0.0972181
\(877\) 1.17795e137 1.66588 0.832942 0.553360i \(-0.186655\pi\)
0.832942 + 0.553360i \(0.186655\pi\)
\(878\) −4.31059e136 −0.578151
\(879\) 4.69814e135 0.0597644
\(880\) 4.77462e136 0.576095
\(881\) −6.33850e136 −0.725449 −0.362724 0.931896i \(-0.618153\pi\)
−0.362724 + 0.931896i \(0.618153\pi\)
\(882\) −3.55434e136 −0.385895
\(883\) −6.81818e136 −0.702257 −0.351128 0.936327i \(-0.614202\pi\)
−0.351128 + 0.936327i \(0.614202\pi\)
\(884\) 7.15649e135 0.0699310
\(885\) −1.88558e136 −0.174816
\(886\) −9.83132e136 −0.864856
\(887\) −1.40305e137 −1.17118 −0.585591 0.810606i \(-0.699138\pi\)
−0.585591 + 0.810606i \(0.699138\pi\)
\(888\) 1.53247e136 0.121392
\(889\) 1.49593e136 0.112455
\(890\) 1.21215e137 0.864813
\(891\) −1.49699e137 −1.01369
\(892\) 3.65332e136 0.234813
\(893\) −1.13676e136 −0.0693545
\(894\) 2.00970e136 0.116395
\(895\) 1.94284e135 0.0106823
\(896\) 6.18346e136 0.322782
\(897\) −2.29717e136 −0.113853
\(898\) 1.28917e137 0.606683
\(899\) 4.59788e137 2.05462
\(900\) −2.50650e136 −0.106363
\(901\) −1.51709e137 −0.611376
\(902\) 3.42767e136 0.131188
\(903\) 6.45850e136 0.234775
\(904\) −4.50222e137 −1.55452
\(905\) 3.76745e137 1.23563
\(906\) 4.60842e136 0.143579
\(907\) −7.49838e136 −0.221936 −0.110968 0.993824i \(-0.535395\pi\)
−0.110968 + 0.993824i \(0.535395\pi\)
\(908\) −1.27576e136 −0.0358738
\(909\) 1.70985e137 0.456813
\(910\) −1.25448e137 −0.318447
\(911\) −2.34388e137 −0.565368 −0.282684 0.959213i \(-0.591225\pi\)
−0.282684 + 0.959213i \(0.591225\pi\)
\(912\) −2.59210e135 −0.00594145
\(913\) 4.57419e136 0.0996376
\(914\) −2.95437e137 −0.611598
\(915\) −1.59241e137 −0.313309
\(916\) 1.79387e137 0.335468
\(917\) 1.19980e138 2.13273
\(918\) −1.32220e137 −0.223416
\(919\) −1.12468e138 −1.80658 −0.903291 0.429028i \(-0.858856\pi\)
−0.903291 + 0.429028i \(0.858856\pi\)
\(920\) −6.48794e137 −0.990770
\(921\) 2.44258e137 0.354631
\(922\) −3.41656e137 −0.471630
\(923\) −1.49166e136 −0.0195791
\(924\) 1.03627e137 0.129338
\(925\) 1.27614e137 0.151464
\(926\) 5.56578e137 0.628225
\(927\) −1.01083e138 −1.08510
\(928\) −6.86672e137 −0.701082
\(929\) 1.90398e138 1.84898 0.924491 0.381203i \(-0.124490\pi\)
0.924491 + 0.381203i \(0.124490\pi\)
\(930\) −3.36427e137 −0.310766
\(931\) 2.33002e136 0.0204738
\(932\) 1.65759e137 0.138560
\(933\) −4.26129e137 −0.338879
\(934\) 1.25438e138 0.949071
\(935\) −7.70961e137 −0.554999
\(936\) −5.82079e137 −0.398708
\(937\) 2.21638e138 1.44462 0.722309 0.691570i \(-0.243081\pi\)
0.722309 + 0.691570i \(0.243081\pi\)
\(938\) 2.54041e138 1.57569
\(939\) −2.35793e137 −0.139181
\(940\) 7.97990e137 0.448283
\(941\) −1.76168e138 −0.941911 −0.470955 0.882157i \(-0.656091\pi\)
−0.470955 + 0.882157i \(0.656091\pi\)
\(942\) 7.16923e137 0.364843
\(943\) −2.95895e137 −0.143332
\(944\) 1.03741e138 0.478356
\(945\) −1.12083e138 −0.491996
\(946\) −1.83947e138 −0.768697
\(947\) −4.99662e138 −1.98793 −0.993967 0.109675i \(-0.965019\pi\)
−0.993967 + 0.109675i \(0.965019\pi\)
\(948\) 3.00832e137 0.113956
\(949\) −1.26069e138 −0.454705
\(950\) −3.39772e136 −0.0116692
\(951\) −1.00708e138 −0.329361
\(952\) −2.34426e138 −0.730108
\(953\) 1.22547e138 0.363483 0.181741 0.983346i \(-0.441827\pi\)
0.181741 + 0.983346i \(0.441827\pi\)
\(954\) 3.03339e138 0.856896
\(955\) 1.86531e138 0.501874
\(956\) 1.45039e138 0.371701
\(957\) 1.49312e138 0.364494
\(958\) −2.98803e138 −0.694847
\(959\) −9.92474e138 −2.19864
\(960\) 1.06067e138 0.223856
\(961\) 1.15763e139 2.32773
\(962\) 7.28531e137 0.139575
\(963\) −2.17625e138 −0.397270
\(964\) 1.64578e138 0.286279
\(965\) 8.36069e138 1.38587
\(966\) 1.84983e138 0.292211
\(967\) 4.82909e138 0.727000 0.363500 0.931594i \(-0.381582\pi\)
0.363500 + 0.931594i \(0.381582\pi\)
\(968\) −4.41893e138 −0.634035
\(969\) 4.18548e136 0.00572387
\(970\) −4.00649e138 −0.522250
\(971\) 6.25878e137 0.0777670 0.0388835 0.999244i \(-0.487620\pi\)
0.0388835 + 0.999244i \(0.487620\pi\)
\(972\) −1.93960e138 −0.229737
\(973\) 2.38739e138 0.269573
\(974\) −7.15226e138 −0.769930
\(975\) 3.43533e137 0.0352577
\(976\) 8.76111e138 0.857319
\(977\) −1.15470e139 −1.07739 −0.538695 0.842501i \(-0.681082\pi\)
−0.538695 + 0.842501i \(0.681082\pi\)
\(978\) −2.20942e137 −0.0196572
\(979\) −1.93638e139 −1.64284
\(980\) −1.63564e138 −0.132335
\(981\) 2.04928e139 1.58122
\(982\) −7.64942e138 −0.562917
\(983\) 3.61265e138 0.253564 0.126782 0.991931i \(-0.459535\pi\)
0.126782 + 0.991931i \(0.459535\pi\)
\(984\) 5.31382e137 0.0355742
\(985\) −7.22236e137 −0.0461205
\(986\) −8.30351e138 −0.505808
\(987\) −9.25526e138 −0.537825
\(988\) 9.38031e136 0.00520019
\(989\) 1.58793e139 0.839855
\(990\) 1.54152e139 0.777879
\(991\) 4.76355e138 0.229354 0.114677 0.993403i \(-0.463417\pi\)
0.114677 + 0.993403i \(0.463417\pi\)
\(992\) −2.47159e139 −1.13549
\(993\) −1.33696e138 −0.0586107
\(994\) 1.20119e138 0.0502509
\(995\) −2.40749e139 −0.961151
\(996\) 1.74324e137 0.00664199
\(997\) 2.29424e139 0.834283 0.417142 0.908842i \(-0.363032\pi\)
0.417142 + 0.908842i \(0.363032\pi\)
\(998\) 1.34864e139 0.468088
\(999\) 6.50919e138 0.215641
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 1.94.a.a.1.5 7
3.2 odd 2 9.94.a.b.1.3 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.94.a.a.1.5 7 1.1 even 1 trivial
9.94.a.b.1.3 7 3.2 odd 2