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lfunc_lfunctions • Show schema
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{'Lhash': '1156275514521843662850287437176', 'a10': [0.1782296277349324, 0.0], 'a2': [-1.0, 0.0], 'a3': [-0.3504437134708287, 0.0], 'a4': [1.0, 0.0], 'a5': [-0.1782296277349324, 0.0], 'a6': [0.3504437134708287, 0.0], 'a7': [-3.9084931427938803, 0.0], 'a8': [-1.0, 0.0], 'a9': [-2.8771892036887756, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.02405234066265, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [1.0, 0]]], [211, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 19, 211], 'central_character': '8018.1', 'coefficient_field': 'CDF', 'conductor': 8018, 'conductor_radical': 8018, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [0.3504437134708287, 0], [3.0, 0]], [[1.0, 0], [0.1782296277349324, 0], [5.0, 0]], [[1.0, 0], [3.9084931427938803, 0], [7.0, 0]], [[1.0, 0], [1.5272658333655775, 0], [11.0, 0]], [[1.0, 0], [0.3151734636675137, 0], [13.0, 0]], [[1.0, 0], 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137, 'label': '2-8018-1.1-c1-0-137', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/8018/2/a/f/1/19', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-2.066235541477332e-62, 0.10143217973922054, 0.20135436729081607, 0.2982343827758462, 0.3904982981765187, 0.4765159368455603, 0.55459349974286, 0.6229748891734098, 0.6798527260994972, 0.7233894558138728, 0.7517483539714532, 0.7631337139140449, 0.7558390368745523, 0.7283016672359109, 0.6791620151987284, 0.6073252837807044, 0.5120234592767261, 0.39287522820657333, 0.2499414455251896, 0.08377379708063869, -0.1045456252901063, -0.31337598292870755, -0.5405025341118667, -0.7831363521915654, -1.037930282648304, -1.301012114790803, -1.5680354952018238, -1.8342486080551768, -2.0945801015599064, -2.3437411623963524, 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'7.76533682008439401860134800469265'], 'prelabel': '2-8018-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.001503130078914, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.912140549070592773162440665721', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.33075897667473427730153638521', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.05238024638914152179724343676', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.02405234066265, 'bad_primes': [2, 19, 211], 'central_character': '1.1', 'conductor': 8018, 'conductor_radical': 8018, 'degree': 2, 'index': 137, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8018/2/a/f/1/19'], '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': '2-8018-1.1-c1-0-137', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-8018-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.001503130078914, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.912140549070592773162440665721', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1156275514521843662850287437176', 'Lhash_array': ['1156275514521843662850287437176'], 'label': '2-8018-1.1-c1-0-137', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8018/2/a/f/1/19'}