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lfunc_lfunctions • Show schema
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{'Lhash': '1548507632068709606908358167154', 'a10': [0.0, 0.0], 'a2': [0.6180339887498949, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.618033988749895, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.0, 0.0], 'a8': [-2.23606797749979, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.91585113697024, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '5625.1', 'coefficient_field': 'CDF', 'conductor': 5625, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6180339887498949, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.0, 0], [7.0, 0]], [[1.0, 0], [-3.0, 0], [11.0, 0]], [[1.0, 0], [1.0, 0], [13.0, 0]], [[1.0, 0], [0.2360679774997897, 0], [17.0, 0]], [[1.0, 0], [-6.708203932499369, 0], [19.0, 0]], [[1.0, 0], [7.618033988749895, 0], [23.0, 0]], [[1.0, 0], [-1.381966011250105, 0], 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129, 'label': '2-75e2-1.1-c1-0-129', '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/5625/2/a/b/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-1.127921519112332e-60, 0.1784297211080093, 0.35567575541301705, 0.530514985510583, 0.7016482464117827, 0.8676691396267218, 1.0270405285022004, 1.1780804712800352, 1.3189587830156841, 1.447704835280841, 1.562226649367883, 1.660340846391402, 1.7398126028132777, 1.798404425739594, 1.8339323026410124, 1.8443275836952462, 1.8277028093625434, 1.782419590348694, 1.707156574248064, 1.600975489035471, 1.4633832377313225, 1.2943880331999091, 1.0945476110837133, 0.8650076470347734, 0.6075286363090128, 0.32449967328108664, 0.018937798003124316, -0.3055281427075451, -0.6446898423323335, -0.9938084367696929, -1.347679892478111, 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'prelabel': '2-75e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.701928911661943, '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': '1.22155713237536775014526789573', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.56768649451905884485716367257', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.54728059228494985462628079567', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 44.91585113697024, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 5625, 'conductor_radical': 15, 'degree': 2, 'index': 129, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5625/2/a/b/1/2'], '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': '2-75e2-1.1-c1-0-129', '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': '2-75e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.701928911661943, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.22155713237536775014526789573', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1548507632068709606908358167154', 'Lhash_array': ['1548507632068709606908358167154'], 'label': '2-75e2-1.1-c1-0-129', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5625/2/a/b/1/2'}