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lfunc_lfunctions • Show schema
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{'Lhash': '1035694943335285188720593629016,1570459614657294041435086306874', 'a10': 0, 'a2': -11, 'a3': 0, 'a4': 32, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 275, 'a9': 243, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 61.76085014838417, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[7, [1]]], 'bad_primes': [7], 'central_character': '49.1', 'coefficient_field': '1.1.1.1', 'conductor': 2401, 'conductor_radical': 7, 'degree': 4, 'euler_factors': [[1, 11, 89, 352, 1024], [1, 0, -243, 0, 59049], [1, 0, -3125, 0, 9765625], [1], [1, -76, -155275, -12239876, 25937424601], [1, 0, 742586, 0, 137858491849], [1, 0, -1419857, 0, 2015993900449], [1, 0, -2476099, 0, 6131066257801], [1, -4952, 18085961, -31872770536, 41426511213649], [1, -14564, 94049822, -298724374036, 420707233300201], [1, 0, -28629151, 0, 819628286980801], [1, -8886, 9617039, -616190401902, 4808584372417849], [1, 0, 231712402, 0, 13422659310152401], [1, -23496, 432032390, 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'15.02803088170051434083531658119129'], 'prelabel': '4-7e4-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.803356411667281, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c5e2-0', 'trace_hash': 637504280237240417, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.817019250532297601689552575162', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.23887419323159435713920577928', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.85586637449605103085036914909', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 61.76085014838417, 'bad_primes': [7], 'central_character': '1.1', 'conductor': 2401, 'conductor_radical': 7, 'degree': 4, 'dirichlet_coefficients': [1, -11, 0, 32, 0, 0, 0, 275, 243, 0, 76, 0, 0, 0, 0, -3025, 0, -2673, 0, 0, 0, -836, 4952, 0, 3125, 0, 0, 0, 14564, 0, 0, 8800, 0, 0, 0, 7776, 8886, 0, 0, 0, 0, 0, 23496, 2432, 0, -54472, 0, 0, 0, -34375, 0, 0, -24550, 0, 0, 0, 0, -160204, 0, 0, 0, 0, 0, 42857, 0, 0, -69364, 0, 0, 0, -4448, 66825, 0, -97746, 0, 0, 0, 0, -80168, 0, 0, 0, 0, 0, 0, -258456, 0, 20900, 0, 0, 0, 158464, 0, 0, 0, 0, 0, 0, 18468, 100000], 'euler11': [1, -76, -155275, -12239876, 25937424601], 'euler13': [1, 0, 742586, 0, 137858491849], 'euler17': [1, 0, -1419857, 0, 2015993900449], 'euler19': [1, 0, -2476099, 0, 6131066257801], 'euler2': [1, 11, 89, 352, 1024], 'euler23': [1, -4952, 18085961, -31872770536, 41426511213649], 'euler29': [1, -14564, 94049822, -298724374036, 420707233300201], 'euler3': [1, 0, -243, 0, 59049], 'euler31': [1, 0, -28629151, 0, 819628286980801], 'euler37': [1, -8886, 9617039, -616190401902, 4808584372417849], 'euler41': [1, 0, 231712402, 0, 13422659310152401], 'euler43': [1, -23496, 432032390, -3454110376728, 21611482313284249], 'euler47': [1, 0, -229345007, 0, 52599132235830049], 'euler5': [1, 0, -3125, 0, 9765625], 'euler53': [1, 24550, 184507007, 10266699353150, 174887470365513049], 'euler59': [1, 0, -714924299, 0, 511116753300641401], 'euler61': [1, 0, -844596301, 0, 713342911662882601], 'euler67': [1, 69364, 3461239389, 93650077921948, 1822837804551761449], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 4448, 3613404878, 8025212153248, 3255243551009881201], 'euler73': [1, 0, -2073071593, 0, 4297625829703557649], 'euler79': [1, 80168, 3349851825, 246681457395032, 9468276082626847201], 'euler83': [1, 0, 7878081286, 0, 15516041187205853449], 'euler89': [1, 0, -5584059449, 0, 31181719929966183601], 'euler97': [1, 0, 17174680514, 0, 73742412689492826049], 'euler_factors': [[1, 11, 89, 352, 1024], [1, 0, -243, 0, 59049], [1, 0, -3125, 0, 9765625], [1, 0, 0, 0, 0], [1, -76, -155275, -12239876, 25937424601], [1, 0, 742586, 0, 137858491849], [1, 0, -1419857, 0, 2015993900449], [1, 0, -2476099, 0, 6131066257801], [1, -4952, 18085961, -31872770536, 41426511213649], [1, -14564, 94049822, -298724374036, 420707233300201], [1, 0, -28629151, 0, 819628286980801], [1, -8886, 9617039, -616190401902, 4808584372417849], [1, 0, 231712402, 0, 13422659310152401], [1, -23496, 432032390, -3454110376728, 21611482313284249], [1, 0, -229345007, 0, 52599132235830049], [1, 24550, 184507007, 10266699353150, 174887470365513049], [1, 0, -714924299, 0, 511116753300641401], [1, 0, -844596301, 0, 713342911662882601], [1, 69364, 3461239389, 93650077921948, 1822837804551761449], [1, 4448, 3613404878, 8025212153248, 3255243551009881201], [1, 0, -2073071593, 0, 4297625829703557649], [1, 80168, 3349851825, 246681457395032, 9468276082626847201], [1, 0, 7878081286, 0, 15516041187205853449], [1, 0, -5584059449, 0, 31181719929966183601], [1, 0, 17174680514, 0, 73742412689492826049]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/49/6/c/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': '4-7e4-1.1-c5e2-0-2', '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': '4-7e4-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.803356411667281, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e2-0', 'trace_hash': 637504280237240417, 'z1': {'__RealLiteral__': 0, 'data': '0.817019250532297601689552575162', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1035694943335285188720593629016,1570459614657294041435086306874', 'Lhash_array': ['1035694943335285188720593629016', '1570459614657294041435086306874'], 'label': '4-7e4-1.1-c5e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/49/6/c/a'}