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lfunc_lfunctions • Show schema
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{'Lhash': '1555078343682469065674315891826', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': 4, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.24768683659657, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -1]]], 'bad_primes': [2, 3, 5], 'central_character': '2160.1', 'coefficient_field': '1.1.1.1', 'conductor': 2160, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1], [1, -1], [1, -4, 7], [1, -2, 11], [1, -4, 13], [1, 1, 17], [1, -5, 19], [1, -5, 23], [1, 8, 29], [1, 7, 31], [1, 6, 37], [1, 6, 41], [1, -2, 43], [1, -8, 47], [1, 9, 53], [1, -4, 59], [1, -13, 61], [1, -10, 67], [1, 6, 71], [1, 6, 73], [1, 9, 79], [1, 17, 83], [1, -6, 89], [1, 8, 97], [1, 12, 101], [1, 4, 103], [1, -12, 107], [1, -17, 109], [1, 6, 113]], 'euler_factors_factorization': [[1], [1], [[[1, -1], 1]], [[[1, -4, 7], 1]], [[[1, -2, 11], 1]], [[[1, -4, 13], 1]], [[[1, 1, 17], 1]], [[[1, -5, 19], 1]], [[[1, -5, 23], 1]], [[[1, 8, 29], 1]], [[[1, 7, 31], 1]], [[[1, 6, 37], 1]], [[[1, 6, 41], 1]], [[[1, -2, 43], 1]], [[[1, -8, 47], 1]], [[[1, 9, 53], 1]], [[[1, -4, 59], 1]], [[[1, -13, 61], 1]], [[[1, -10, 67], 1]], [[[1, 6, 71], 1]], [[[1, 6, 73], 1]], [[[1, 9, 79], 1]], [[[1, 17, 83], 1]], [[[1, -6, 89], 1]], [[[1, 8, 97], 1]], [[[1, 12, 101], 1]], [[[1, 4, 103], 1]], [[[1, -12, 107], 1]], [[[1, -17, 109], 1]], [[[1, 6, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 16, 'label': '2-2160-1.1-c1-0-16', 'leading_term': '2.61538537027493394127278472281000000000000000000000000000000000000000000000000000000000000', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2160/2/a/w', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': 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3.6109737045532433, 3.1513002651542936, 2.6085154849488617, 2.004880802033971, 1.3655832763909856, 0.7175242106213776, 0.08801102335719029, -0.49658059981886216, -1.012104973207368, -1.4378371643884722, -1.7574933084527555, -1.9600259775224544], 'positive_zeros': ['1.22674050988694425207628828008980', '1.90973494783978255742149684954108', '3.33465948715580981375117818151300', '4.20120998954151629074024789634042', '5.28222711027526819045315544759715', '5.64925836280054079608642247649938', '6.88740520144549246250126905667935', '7.46206699816106956360734624663570', '8.478833179515949977669438635262419', '8.925238629210729863020418287737466'], 'prelabel': '2-2160-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.153033449973233, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1441965826064475956, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.22674050988694425207628828009', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.90973494783978255742149684954', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.33465948715580981375117818151', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.24768683659657, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 2160, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, 4, 0, 0, 0, 2, 0, 4, 0, 0, 0, -1, 0, 5, 0, 0, 0, 5, 0, 1, 0, 0, 0, -8, 0, -7, 0, 0, 0, 4, 0, -6, 0, 0, 0, -6, 0, 2, 0, 0, 0, 8, 0, 9, 0, 0, 0, -9, 0, 2, 0, 0, 0, 4, 0, 13, 0, 0, 0, 4, 0, 10, 0, 0, 0, -6, 0, -6, 0, 0, 0, 8, 0, -9, 0, 0, 0, -17, 0, -1, 0, 0, 0, 6, 0, 16, 0, 0, 0, 5, 0, -8, 0, 0, 0], 'euler11': [1, -2, 11], 'euler13': [1, -4, 13], 'euler17': [1, 1, 17], 'euler19': [1, -5, 19], 'euler2': [1, 0, 0], 'euler23': [1, -5, 23], 'euler29': [1, 8, 29], 'euler3': [1, 0, 0], 'euler31': [1, 7, 31], 'euler37': [1, 6, 37], 'euler41': [1, 6, 41], 'euler43': [1, -2, 43], 'euler47': [1, -8, 47], 'euler5': [1, -1, 0], 'euler53': [1, 9, 53], 'euler59': [1, -4, 59], 'euler61': [1, -13, 61], 'euler67': [1, -10, 67], 'euler7': [1, -4, 7], 'euler71': [1, 6, 71], 'euler73': [1, 6, 73], 'euler79': [1, 9, 79], 'euler83': [1, 17, 83], 'euler89': [1, -6, 89], 'euler97': [1, 8, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -1, 0], [1, -4, 7], [1, -2, 11], [1, -4, 13], [1, 1, 17], [1, -5, 19], [1, -5, 23], [1, 8, 29], [1, 7, 31], [1, 6, 37], [1, 6, 41], [1, -2, 43], [1, -8, 47], [1, 9, 53], [1, -4, 59], [1, -13, 61], [1, -10, 67], [1, 6, 71], [1, 6, 73], [1, 9, 79], [1, 17, 83], [1, -6, 89], [1, 8, 97]], 'index': 16, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2160/w', 'ModularForm/GL2/Q/holomorphic/2160/2/a/w/1/1', 'ModularForm/GL2/Q/holomorphic/2160/2/a/w'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-2160-1.1-c1-0-16', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-2160-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.153033449973233, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1441965826064475956, 'z1': {'__RealLiteral__': 0, 'data': '1.22674050988694425207628828009', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20719670
{'Lhash': '1555078343682469065674315891826', 'Lhash_array': ['1555078343682469065674315891826'], 'label': '2-2160-1.1-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2160/2/a/w'}
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id: 24556082
{'Lhash': '1555078343682469065674315891826', 'Lhash_array': ['1555078343682469065674315891826'], 'label': '2-2160-1.1-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2160/2/a/w/1/1'}
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id: 37853
{'Lhash': '1441965826064475956', 'Lhash_array': ['1441965826064475956'], 'label': '2-2160-1.1-c1-0-16', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2160/w'}