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lfunc_lfunctions • Show schema
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{'Lhash': '74661130432970046925939252966', 'a10': [0.0, 0.0], 'a2': [0.0, -2.4892885718100786], 'a3': [0.0, 1.0], 'a4': [-4.196557593744262, 0.0], 'a5': [0.0, 0.0], 'a6': [2.4892885718100786, 0.0], 'a7': [0.0, -1.1965575937442616], 'a8': [0.0, 5.467865715430237], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.785414197074841, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, -1.0]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [3, 5, 13], 'central_character': '975.274', 'coefficient_field': 'CDF', 'conductor': 975, 'conductor_radical': 195, 'conjugate': '2088461349119966435909242211860', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.4892885718100786], [-2.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.1965575937442616], [-7.0, 0]], [[1.0, 0], [1.1965575937442616, 0], [11.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, -6.175134737364419], [-17.0, 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[-107.0, 0]], [[1.0, 0], [8.393115187488524, 0], [109.0, 0]], [[1.0, 0], [0, 7.957154287240315], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-975-5.4-c1-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/975/2/c/i/274/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.13134845313533508, -0.15703695166688353, -0.48496345469088126, -0.8577773663296313, -1.277629354511294, -1.7411537114500613, -2.2377525587023936, -2.7486397252771235, -3.246724698997543, -3.69740739632132, -4.06034847057418, -4.292237400248922, -4.350491432126532, -4.1976919919541755, -3.806420795677194, -3.1640198105963404, -2.276693634703248, -1.1723252881055684, 0.09859173104111578, 1.4643775610416492, 2.8361995572180247, 4.114668260871265, 5.19859616083014, 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'6.57565638892244278597245708981464', '7.31948693479767534053386853108161', '7.85004914491059140278042041109471', '9.028551265913521836087276876695039', '9.122731980486811315230740012852849'], 'prelabel': '2-975-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.790235509249146, 'root_angle': -0.35241638234956674, 'root_number': '0.44721359549995804 - 0.8944271909999159*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.176208191175', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.05889724693817678428696016877', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.24072169709271762784196079828', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.88456014434641877908589326214', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.785414197074841, 'bad_primes': [3, 5, 13], 'central_character': '5.4', 'conductor': 975, 'conductor_radical': 195, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/975/2/c/i/274/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-975-5.4-c1-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-975-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.790235509249146, 'root_angle': -0.17620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.05889724693817678428696016877', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '74661130432970046925939252966', 'Lhash_array': ['74661130432970046925939252966'], 'label': '2-975-5.4-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/975/2/c/i/274/2'}