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lfunc_lfunctions • Show schema
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{'Lhash': '561436122230140972922914514628', 'a10': [1.0, 0.0], 'a2': [-1.0, 0.0], 'a3': [0.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 55.336328600747336, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '6930.1', 'coefficient_field': 'CDF', 'conductor': 6930, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [3.6272130052966616, 0], [13.0, 0]], [[1.0, 0], [-4.205550098193282, 0], [17.0, 0]], [[1.0, 0], [8.151650961496683, 0], [19.0, 0]], [[1.0, 0], [0.8972249509033592, 0], [23.0, 0]], [[1.0, 0], 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0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-6930-1.1-c1-0-3', 'leading_term': '0.65224346999267999891304166410719', '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/6930/2/a/ce/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.65224346999268, 0.6434683376527005, 0.6171587376430859, 0.5733695183717822, 0.5122163351220795, 0.4339099186710409, 0.33880008615678514, 0.22742600313930741, 0.1005687894932097, -0.040697557051940426, -0.1949608073096259, -0.360434266584355, -0.5349327331612336, -0.7158631593553249, -0.9002319141358076, -1.08466991115898, -1.2654762189302067, -1.4386801157883662, -1.6001208936951745, -1.745544054448838, -1.870711886173361, -1.9715257674490532, -2.044156936614392, -2.085181904135808, -2.0917181992457925, 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'5.10296802760846495978631745105561', '6.07081673255192813437186709970986', '6.67107685722981853069573175068423', '7.37452533853338466293372674717307', '8.037004480467048385745426043992759'], 'prelabel': '2-6930-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.438839197129303, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44289500760624363717499421018', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.76441068357714542664903479573', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.65575464892903192954408223640', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 55.336328600747336, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 6930, 'conductor_radical': 2310, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6930/2/a/ce/1/1'], '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': '2-6930-1.1-c1-0-3', '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': '2-6930-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.438839197129303, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.44289500760624363717499421018', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '561436122230140972922914514628', 'Lhash_array': ['561436122230140972922914514628'], 'label': '2-6930-1.1-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6930/2/a/ce/1/1'}