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lfunc_lfunctions • Show schema
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{'Lhash': '802543933264370022385818346796', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.439327801447643, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [7, [1, -1]], [13, [1, -1]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '2184.1', 'coefficient_field': '1.1.1.1', 'conductor': 2184, 'conductor_radical': 546, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 2, 5], [1, -1], [1, 4, 11], [1, -1], [1, 6, 17], [1, -4, 19], [1, 0, 23], [1, -6, 29], [1, 0, 31], [1, -6, 37], [1, 6, 41], [1, -4, 43], [1, 0, 47], [1, 2, 53], [1, -4, 59], [1, 2, 61], [1, -4, 67], [1, 0, 71], [1, 6, 73], [1, -8, 79], [1, -12, 83], [1, -10, 89], [1, 14, 97], [1, -6, 101], [1, -16, 103], [1, -12, 107], [1, -14, 109], [1, -2, 113]], 'euler_factors_factorization': [[1], [[[1, 1], 1]], [[[1, 2, 5], 1]], [[[1, -1], 1]], [[[1, 4, 11], 1]], [[[1, 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1.8576196656389226, 1.6519714819623774, 1.36076678713581, 0.995224857006594, 0.5708984358263968, 0.10694297860257408, -0.374828935676436, -0.8510614230185657, -1.2980806563527312, -1.69316784858847, -2.0158120106110915, -2.248874300516509, -2.3795991201473488, -2.400414025133148, -2.3094706927120305], 'positive_zeros': ['0.63309553367456222372713514327382', '2.18571288805244671340846045832273', '3.30940782556401294409318748139140', '4.40024854312076089724865952141510', '4.93803016248922274695356229711124', '5.88133006849509043635940278987846', '6.77795077062942325242325961481232', '7.60123667345496814600041115013045', '8.135980268495423139052960375930747', '8.951303684850219176373370636196195'], 'prelabel': '2-2184-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.176042121608407, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 2060689779552296436, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.63309553367456222372713514327', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.18571288805244671340846045832', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.30940782556401294409318748139', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.439327801447643, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 2184, 'conductor_radical': 546, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -2, 0, 1, 0, 1, 0, -4, 0, 1, 0, 2, 0, -6, 0, 4, 0, -1, 0, 0, 0, -1, 0, -1, 0, 6, 0, 0, 0, 4, 0, -2, 0, 6, 0, -1, 0, -6, 0, 4, 0, -2, 0, 0, 0, 1, 0, 6, 0, -2, 0, 8, 0, -4, 0, 4, 0, -2, 0, 1, 0, -2, 0, 4, 0, 0, 0, 0, 0, -6, 0, 1, 0, -4, 0, 8, 0, 1, 0, 12, 0, 12, 0, -6, 0, 10, 0, 1, 0, 0, 0, -8, 0, -14, 0, -4, 0], 'euler11': [1, 4, 11], 'euler13': [1, -1, 0], 'euler17': [1, 6, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 0, 31], 'euler37': [1, -6, 37], 'euler41': [1, 6, 41], 'euler43': [1, -4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 2, 5], 'euler53': [1, 2, 53], 'euler59': [1, -4, 59], 'euler61': [1, 2, 61], 'euler67': [1, -4, 67], 'euler7': [1, -1, 0], 'euler71': [1, 0, 71], 'euler73': [1, 6, 73], 'euler79': [1, -8, 79], 'euler83': [1, -12, 83], 'euler89': [1, -10, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 2, 5], [1, -1, 0], [1, 4, 11], [1, -1, 0], [1, 6, 17], [1, -4, 19], [1, 0, 23], [1, -6, 29], [1, 0, 31], [1, -6, 37], [1, 6, 41], [1, -4, 43], [1, 0, 47], [1, 2, 53], [1, -4, 59], [1, 2, 61], [1, -4, 67], [1, 0, 71], [1, 6, 73], [1, -8, 79], [1, -12, 83], [1, -10, 89], [1, 14, 97]], 'index': 3, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2184/c', 'ModularForm/GL2/Q/holomorphic/2184/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/2184/2/a/c'], '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': '2-2184-1.1-c1-0-3', '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': '2-2184-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.176042121608407, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2060689779552296436, 'z1': {'__RealLiteral__': 0, 'data': '0.63309553367456222372713514327', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20643843
{'Lhash': '802543933264370022385818346796', 'Lhash_array': ['802543933264370022385818346796'], 'label': '2-2184-1.1-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2184/2/a/c'}
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id: 24556170
{'Lhash': '802543933264370022385818346796', 'Lhash_array': ['802543933264370022385818346796'], 'label': '2-2184-1.1-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2184/2/a/c/1/1'}
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id: 90133
{'Lhash': '2060689779552296436', 'Lhash_array': ['2060689779552296436'], 'label': '2-2184-1.1-c1-0-3', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2184/c'}