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lfunc_lfunctions • Show schema
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{'Lhash': '1906213768702138400608891290547,2268922406464709365262244118766', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 237.9953425354976, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 2, 1]], [7, [1, -2, 1]], [23, [1, 2, 1]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '1932.1', 'coefficient_field': '1.1.1.1', 'conductor': 3732624, 'conductor_radical': 966, 'degree': 4, 'euler_factors': [[1], [1, 2, 1], [1, -1, 7, -5, 25], [1, -2, 1], [1, 0, 9, 0, 121], [1, 5, 29, 65, 169], [1, 6, 43, 102, 289], [1, 8, 41, 152, 361], [1, 2, 1], [1, -2, 59, -58, 841], [1, -2, 63, -62, 961], [1, 2, 23, 74, 1369], [1, 4, 73, 164, 1681], [1, 5, 63, 215, 1849], [1, 14, 130, 658, 2209], [1, -15, 133, -795, 2809], [1, -11, 119, -649, 3481], [1, 1, 41, 61, 3721], [1, 5, -19, 335, 4489], [1, 13, 155, 923, 5041], [1, 0, 29, 0, 5329], [1, 20, 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'positive_zeros': ['1.50373751912312532066113730989593', '1.78986418343998711783463871062937', '2.46817203600319115178278712920415', '2.76289467099899513060619439255924', '3.95298508279997642186992116668997', '4.16807982310039301498395542833777', '4.49217842734020754909329312001190', '5.01006435552063346040420928873007', '5.45265865247141905259912597397152', '5.62332677581800205276268885908287', '6.44940168022507556725179244511874', '6.46407624520877745263977758138217', '6.95438563857432411132635324615272', '7.25276574617372903731106419117180', '7.87823164910431246022748568391770', '8.232838705689800509783592630073202', '8.651362878125213709904818829322295', '8.865573702542904813041700199963809'], 'prelabel': '4-1932e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.9277344195491857, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1419437306171865238, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.50373751912312532066113730990', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.78986418343998711783463871063', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.46817203600319115178278712920', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 237.9953425354976, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 3732624, 'conductor_radical': 966, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 0, 1, 0, 2, 0, 3, 0, 0, 0, -5, 0, -2, 0, -6, 0, -8, 0, -4, 0, -2, 0, -6, 0, -4, 0, 2, 0, 2, 0, 0, 0, 2, 0, -2, 0, 10, 0, -4, 0, -5, 0, 3, 0, -14, 0, 3, 0, 12, 0, 15, 0, 0, 0, 16, 0, 11, 0, -1, 0, 6, 0, -5, 0, -5, 0, 4, 0, -13, 0, 0, 0, 12, 0, 0, 0, -20, 0, 5, 0, -8, 0, -6, 0, -4, 0, 3, 0, -10, 0, -4, 0, -8, 0, -22, 0, 0, 0], 'euler11': [1, 0, 9, 0, 121], 'euler13': [1, 5, 29, 65, 169], 'euler17': [1, 6, 43, 102, 289], 'euler19': [1, 8, 41, 152, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 2, 1, 0, 0], 'euler29': [1, -2, 59, -58, 841], 'euler3': [1, 2, 1, 0, 0], 'euler31': [1, -2, 63, -62, 961], 'euler37': [1, 2, 23, 74, 1369], 'euler41': [1, 4, 73, 164, 1681], 'euler43': [1, 5, 63, 215, 1849], 'euler47': [1, 14, 130, 658, 2209], 'euler5': [1, -1, 7, -5, 25], 'euler53': [1, -15, 133, -795, 2809], 'euler59': [1, -11, 119, -649, 3481], 'euler61': [1, 1, 41, 61, 3721], 'euler67': [1, 5, -19, 335, 4489], 'euler7': [1, -2, 1, 0, 0], 'euler71': [1, 13, 155, 923, 5041], 'euler73': [1, 0, 29, 0, 5329], 'euler79': [1, 20, 245, 1580, 6241], 'euler83': [1, 8, 169, 664, 6889], 'euler89': [1, -3, 177, -267, 7921], 'euler97': [1, 22, 315, 2134, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 2, 1, 0, 0], [1, -1, 7, -5, 25], [1, -2, 1, 0, 0], [1, 0, 9, 0, 121], [1, 5, 29, 65, 169], [1, 6, 43, 102, 289], [1, 8, 41, 152, 361], [1, 2, 1, 0, 0], [1, -2, 59, -58, 841], [1, -2, 63, -62, 961], [1, 2, 23, 74, 1369], [1, 4, 73, 164, 1681], [1, 5, 63, 215, 1849], [1, 14, 130, 658, 2209], [1, -15, 133, -795, 2809], [1, -11, 119, -649, 3481], [1, 1, 41, 61, 3721], [1, 5, -19, 335, 4489], [1, 13, 155, 923, 5041], [1, 0, 29, 0, 5329], [1, 20, 245, 1580, 6241], [1, 8, 169, 664, 6889], [1, -3, 177, -267, 7921], [1, 22, 315, 2134, 9409]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1932/2/a/e'], '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': '4-1932e2-1.1-c1e2-0-7', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'prelabel': '4-1932e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.9277344195491857, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1419437306171865238, 'z1': {'__RealLiteral__': 0, 'data': '1.50373751912312532066113730990', 'prec': 103}}
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{'Lhash': '1906213768702138400608891290547,2268922406464709365262244118766', 'Lhash_array': ['1906213768702138400608891290547', '2268922406464709365262244118766'], 'label': '4-1932e2-1.1-c1e2-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1932/2/a/e'}