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lfunc_lfunctions • Show schema
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{'Lhash': '1285554158119047512054078997815,1869426807312480903524454544665', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -32, 'a5': 0, 'a6': 0, 'a7': 484, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 133.34787470604897, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 32]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '72.1', 'coefficient_field': '1.1.1.1', 'conductor': 5184, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1, 0, 32], [1], [1, 0, -5282, 0, 9765625], [1, -484, 92178, -8134588, 282475249], [1, 0, 227050, 0, 25937424601], [1, 0, -742586, 0, 137858491849], [1, 0, 2839714, 0, 2015993900449], [1, 0, -4952198, 0, 6131066257801], [1, 0, 12872686, 0, 41426511213649], [1, 0, 36304750, 0, 420707233300201], [1, -13900, 105560802, -397945198900, 819628286980801], [1, 0, -138687914, 0, 4808584372417849], [1, 0, 231712402, 0, 13422659310152401], [1, 0, -294016886, 0, 21611482313284249], [1, 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{'algebraic': True, 'analytic_conductor': 133.34787470604897, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 5184, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -32, 0, 0, 484, 0, 0, 0, 0, 0, 0, 0, 0, 1024, 0, 0, 0, 0, 0, 0, 0, 0, 5282, 0, 0, -15488, 0, 0, 13900, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 142078, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32768, 0, 0, 0, 0, 0, 0, 0, 0, -181412, 0, 0, 0, 0, 0, -34100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 180484, 0, 0, -169024], 'euler11': [1, 0, 227050, 0, 25937424601], 'euler13': [1, 0, -742586, 0, 137858491849], 'euler17': [1, 0, 2839714, 0, 2015993900449], 'euler19': [1, 0, -4952198, 0, 6131066257801], 'euler2': [1, 0, 32, 0, 0], 'euler23': [1, 0, 12872686, 0, 41426511213649], 'euler29': [1, 0, 36304750, 0, 420707233300201], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -13900, 105560802, -397945198900, 819628286980801], 'euler37': [1, 0, -138687914, 0, 4808584372417849], 'euler41': [1, 0, 231712402, 0, 13422659310152401], 'euler43': [1, 0, -294016886, 0, 21611482313284249], 'euler47': [1, 0, 458690014, 0, 52599132235830049], 'euler5': [1, 0, -5282, 0, 9765625], 'euler53': [1, 0, -617985986, 0, 174887470365513049], 'euler59': [1, 0, 588563050, 0, 511116753300641401], 'euler61': [1, 0, -1689192602, 0, 713342911662882601], 'euler67': [1, 0, -2700250214, 0, 1822837804551761449], 'euler7': [1, -484, 92178, -8134588, 282475249], 'euler71': [1, 0, 3608458702, 0, 3255243551009881201], 'euler73': [1, 181412, 12373721622, 376080063829316, 4297625829703557649], 'euler79': [1, 34100, 6444815298, 104927623205900, 9468276082626847201], 'euler83': [1, 0, 7877173786, 0, 15516041187205853449], 'euler89': [1, 0, 11168118898, 0, 31181719929966183601], 'euler97': [1, -180484, 25318299078, -1549877518944388, 73742412689492826049], 'euler_factors': [[1, 0, 32, 0, 0], [1, 0, 0, 0, 0], [1, 0, -5282, 0, 9765625], [1, -484, 92178, -8134588, 282475249], [1, 0, 227050, 0, 25937424601], [1, 0, -742586, 0, 137858491849], [1, 0, 2839714, 0, 2015993900449], [1, 0, -4952198, 0, 6131066257801], [1, 0, 12872686, 0, 41426511213649], [1, 0, 36304750, 0, 420707233300201], [1, -13900, 105560802, -397945198900, 819628286980801], [1, 0, -138687914, 0, 4808584372417849], [1, 0, 231712402, 0, 13422659310152401], [1, 0, -294016886, 0, 21611482313284249], [1, 0, 458690014, 0, 52599132235830049], [1, 0, -617985986, 0, 174887470365513049], [1, 0, 588563050, 0, 511116753300641401], [1, 0, -1689192602, 0, 713342911662882601], [1, 0, -2700250214, 0, 1822837804551761449], [1, 0, 3608458702, 0, 3255243551009881201], [1, 181412, 12373721622, 376080063829316, 4297625829703557649], [1, 34100, 6444815298, 104927623205900, 9468276082626847201], [1, 0, 7877173786, 0, 15516041187205853449], [1, 0, 11168118898, 0, 31181719929966183601], [1, -180484, 25318299078, -1549877518944388, 73742412689492826049]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/72/6/d/a'], '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': '4-72e2-1.1-c5e2-0-0', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5, 5], 'order_of_vanishing': 0, 'prelabel': '4-72e2-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.3981811350389504, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e2-0', 'trace_hash': 2227411682368404976, 'z1': {'__RealLiteral__': 0, 'data': '1.01412341688442756353742463179', 'prec': 103}}
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{'Lhash': '1285554158119047512054078997815,1869426807312480903524454544665', 'Lhash_array': ['1285554158119047512054078997815', '1869426807312480903524454544665'], 'label': '4-72e2-1.1-c5e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/72/6/d/a'}