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lfunc_lfunctions • Show schema
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{'Lhash': '838939434826796305407366573536', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 5, 'a6': 0, 'a7': -20, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 42.481375204133265, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -5]]], 'bad_primes': [2, 3, 5], 'central_character': '720.1', 'coefficient_field': '1.1.1.1', 'conductor': 720, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1], [1, -5], [1, 20, 343], [1, 56, 1331], [1, 86, 2197], [1, -106, 4913], [1, 4, 6859], [1, -136, 12167], [1, -206, 24389], [1, -152, 29791], [1, -282, 50653], [1, -246, 68921], [1, 412, 79507], [1, -40, 103823], [1, -126, 148877], [1, -56, 205379], [1, 2, 226981], [1, -388, 300763], [1, 672, 357911], [1, -1170, 389017], [1, 408, 493039], [1, -668, 571787], [1, 66, 704969], [1, 926, 912673], [1, -198, 1030301], [1, -1532, 1092727], [1, 444, 1225043], [1, -62, 1295029], [1, 414, 1442897]], 'euler_factors_factorization': [[1], [1], [[[1, -5], 1]], [[[1, 20, 343], 1]], [[[1, 56, 1331], 1]], [[[1, 86, 2197], 1]], [[[1, -106, 4913], 1]], [[[1, 4, 6859], 1]], [[[1, -136, 12167], 1]], [[[1, -206, 24389], 1]], [[[1, -152, 29791], 1]], [[[1, -282, 50653], 1]], [[[1, -246, 68921], 1]], [[[1, 412, 79507], 1]], [[[1, -40, 103823], 1]], [[[1, -126, 148877], 1]], [[[1, -56, 205379], 1]], [[[1, 2, 226981], 1]], [[[1, -388, 300763], 1]], [[[1, 672, 357911], 1]], [[[1, -1170, 389017], 1]], [[[1, 408, 493039], 1]], [[[1, -668, 571787], 1]], [[[1, 66, 704969], 1]], [[[1, 926, 912673], 1]], [[[1, -198, 1030301], 1]], [[[1, -1532, 1092727], 1]], [[[1, 444, 1225043], 1]], [[[1, -62, 1295029], 1]], [[[1, 414, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-720-1.1-c3-0-4', 'leading_term': '1.445930648885617896229721785580200000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': 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2.382699132404758, 2.462897833606534, 2.437275370676562, 2.301868983481945, 2.0589317650229195, 1.7169256904662868, 1.2901548740539277, 0.7980548908698523, 0.26417409764149463, -0.28509876191311057, -0.8219908708701682, -1.3189040565151755, -1.7499872173088353, -2.092631626095733, -2.3288013903703333, -2.446119628572576, -2.4386439698046454, -2.3072821216073067, -2.05981854159088, -1.710545555335306, -1.2795153062249636, -0.7914513564488376, -0.2743792470039124, 0.24194737642094752, 0.7277354333260626, 1.1548583154994418, 1.4984792182305395], 'positive_zeros': ['0.66180652198307057085647703255216', '2.56337424129377760391774000580818', '3.05806569117810373200245554216807', '4.77375497356854754717661725197838', '5.42853774452513999255338041521864', '6.50942037724942214409297562249005', '7.41528957462770992748127007712802', '8.166099746388934360114435975072500', '9.493864387188800645835462542261904', '9.966096515770255838195583686179139'], 'prelabel': '2-720-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.517773792034613, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 2287856987517022173, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.66180652198307057085647703255', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.56337424129377760391774000581', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.05806569117810373200245554217', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 42.481375204133265, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 720, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 5, 0, -20, 0, 0, 0, -56, 0, -86, 0, 0, 0, 106, 0, -4, 0, 0, 0, 136, 0, 25, 0, 0, 0, 206, 0, 152, 0, 0, 0, -100, 0, 282, 0, 0, 0, 246, 0, -412, 0, 0, 0, 40, 0, 57, 0, 0, 0, 126, 0, -280, 0, 0, 0, 56, 0, -2, 0, 0, 0, -430, 0, 388, 0, 0, 0, -672, 0, 1170, 0, 0, 0, 1120, 0, -408, 0, 0, 0, 668, 0, 530, 0, 0, 0, -66, 0, 1720, 0, 0, 0, -20, 0, -926, 0, 0, 0], 'euler11': [1, 56, 1331], 'euler13': [1, 86, 2197], 'euler17': [1, -106, 4913], 'euler19': [1, 4, 6859], 'euler2': [1, 0, 0], 'euler23': [1, -136, 12167], 'euler29': [1, -206, 24389], 'euler3': [1, 0, 0], 'euler31': [1, -152, 29791], 'euler37': [1, -282, 50653], 'euler41': [1, -246, 68921], 'euler43': [1, 412, 79507], 'euler47': [1, -40, 103823], 'euler5': [1, -5, 0], 'euler53': [1, -126, 148877], 'euler59': [1, -56, 205379], 'euler61': [1, 2, 226981], 'euler67': [1, -388, 300763], 'euler7': [1, 20, 343], 'euler71': [1, 672, 357911], 'euler73': [1, -1170, 389017], 'euler79': [1, 408, 493039], 'euler83': [1, -668, 571787], 'euler89': [1, 66, 704969], 'euler97': [1, 926, 912673], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -5, 0], [1, 20, 343], [1, 56, 1331], [1, 86, 2197], [1, -106, 4913], [1, 4, 6859], [1, -136, 12167], [1, -206, 24389], [1, -152, 29791], [1, -282, 50653], [1, -246, 68921], [1, 412, 79507], [1, -40, 103823], [1, -126, 148877], [1, -56, 205379], [1, 2, 226981], [1, -388, 300763], [1, 672, 357911], [1, -1170, 389017], [1, 408, 493039], [1, -668, 571787], [1, 66, 704969], [1, 926, 912673]], 'index': 4, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/720/4/a/q/1/1', 'ModularForm/GL2/Q/holomorphic/720/4/a/q'], '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': '2-720-1.1-c3-0-4', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-720-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.517773792034613, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 2287856987517022173, 'z1': {'__RealLiteral__': 0, 'data': '0.66180652198307057085647703255', 'prec': 103}}
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lfunc_instances • Show schema
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id: 19979587
{'Lhash': '838939434826796305407366573536', 'Lhash_array': ['838939434826796305407366573536'], 'label': '2-720-1.1-c3-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/4/a/q'}
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id: 24569824
{'Lhash': '838939434826796305407366573536', 'Lhash_array': ['838939434826796305407366573536'], 'label': '2-720-1.1-c3-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/4/a/q/1/1'}