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lfunc_lfunctions • Show schema
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{'Lhash': '2174870326760934725472387930707', 'a10': -1084098960, 'a2': -456, 'a3': 0, 'a4': -316352, 'a5': 2377410, 'a6': 0, 'a7': -16917544, 'a8': 383331840, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.593502690074267, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '9.5', 'prec': 10}, 'bad_lfactors': [[3, [1]]], 'bad_primes': [3], 'central_character': '9.1', 'coefficient_field': '1.1.1.1', 'conductor': 9, 'conductor_radical': 3, 'degree': 2, 'euler_factors': [[1, 456, 524288], [1], [1, -2377410, 19073486328125], [1, 16917544, 11398895185373143], [1, -16212108, 61159090448414546291], [1, -50421615062, 1461920290375446110677], [1, 225070099506, 239072435685151324847153], [1, 1710278572660, 1978419655660313589123979], [1, 14036534788872, 74615470927590710561908487], [1, 1137835269510, 6103261246589991489578849669], [1, 104626880141728, 21670662219970396194714277471], [1, 169392327370594, 624931990990842127748277129373], [1, -3309984750560838, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-3e2-1.1-c19-0-5', 'load_key': 'CMFs-workshop', 'motivic_weight': 19, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [19], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/9/20/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [0.0, 0.3831245609944733, 0.7320037408792325, 1.0148651538772167, 1.2047201593142067, 1.2813595820049277, 1.232900100519328, 1.05677362630866, 0.7600854810352642, 0.359305858908872, -0.12069905728994686, -0.6482471299155721, -1.1869409153753396, -1.6981610577420896, -2.1437936879511574, -2.4890109686527215, -2.704912497182403, -2.770836001670181, -2.6761594590777347, -2.421443484723567, -2.0188017832017957, -1.4914368871305494, -0.8723357088945126, -0.20218112110546257, 0.4734022929846141, 1.107092633829965, 1.653381153936498, 2.0720900826831086, 2.331622169544287, 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'16.04739768922484444483668698118815'], 'prelabel': '2-3e2-1.1-c19-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.5380064665086435, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c19-0', 'trace_hash': 1631656103524504976, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.71567017470694870363590472201', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.09516699712993796838853653258', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.06842387795516792449446418651', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 20.593502690074267, 'bad_primes': [3], 'central_character': '1.1', 'conductor': 9, 'conductor_radical': 3, 'degree': 2, 'dirichlet_coefficients': [1, -456, 0, -316352, 2377410, 0, -16917544, 383331840, 0, -1084098960, 16212108, 0, 50421615062, 7714400064, 0, -8939761664, -225070099506, 0, -1710278572660, -752098408320, 0, -7392721248, -14036534788872, 0, -13421408020025, -22992256468272, 0, 5351898879488, -1137835269510, 0, -104626880141728, -196899752411136, 0, 102631965374736, -40219938281040, 0, -169392327370594, 779887029132960, 0, 911336949734400, 3309984750560838, 0, 1127913532193492, -5128732790016, 0, 6400659863725632, -3498693987674256, 0, -11112691890381207, 6120162057131400, 0, -15950978768093824, -29956294112980302, 0, 38542827680280, -6485033269800960, 0, 518852882896560, -58391397642732420, 0, 23373685132672742, 47709857344627968, 0, 94473296862773248, 119872851864549420, 0, -205102524257382244, 71201376118922112, 0, 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'nu_real_doubled': [19], 'order_of_vanishing': 1, 'prelabel': '2-3e2-1.1-c19-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.5380064665086435, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c19-0', 'trace_hash': 1631656103524504976, 'z1': {'__RealLiteral__': 0, 'data': '1.71567017470694870363590472201', 'prec': 103}}
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lfunc_instances • Show schema
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id: 17105873
{'Lhash': '2174870326760934725472387930707', 'Lhash_array': ['2174870326760934725472387930707'], 'label': '2-3e2-1.1-c19-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9/20/a/a'}
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id: 24557857
{'Lhash': '2174870326760934725472387930707', 'Lhash_array': ['2174870326760934725472387930707'], 'label': '2-3e2-1.1-c19-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9/20/a/a/1/1'}