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lfunc_lfunctions • Show schema
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{'Lhash': '2743209126400563877306780369503,3945972102634839128455760229998', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': -1, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.38792111500809284, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 1]], [3, [1, -2, 1]], [13, [1, 6, 13]]], 'bad_primes': [2, 3, 13], 'central_character': '78.1', 'coefficient_field': '1.1.1.1', 'conductor': 6084, 'conductor_radical': 78, 'degree': 4, 'euler_factors': [[1, 0, 1], [1, -2, 1], [1, 0, -6, 0, 25], [1, 0, -10, 0, 49], [1, 0, -22, 0, 121], [1, 6, 13], [1, 4, 38, 68, 289], [1, 0, -2, 0, 361], [1, -8, 62, -184, 529], [1, 20, 158, 580, 841], [1, 0, 38, 0, 961], [1, 0, -10, 0, 1369], [1, 0, 18, 0, 1681], [1, -8, 102, -344, 1849], [1, 0, 50, 0, 2209], [1, 12, 142, 636, 2809], [1, 0, -102, 0, 3481], [1, -4, 126, -244, 3721], [1, 0, -130, 0, 4489], [1, 0, -142, 0, 5041], [1, 0, -130, 0, 5329], [1, 0, 158, 0, 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'4.09590559657322186514860263713173', '4.85249707345187774716120514420217', '5.54761891959354108169770988650783', '6.79786971902108167486082243353509', '7.41831476835950984450226175228518', '7.66415074492954259569590107456343', '8.851745622938911644148999350723467', '8.984026452504948289969072761145226', '9.511202414981599377293774012324024', '10.08531224531131389879503994585660', '11.10594759747666845413619050873589', '11.12830875965079958923609098612128', '12.35987154513940471821027925502653', '12.89700338987594582710171365238308', '12.91154339683631396817715304872815', '13.74217914458887684779145517637453', '14.21173017908092884179812633888664', '14.81502284481490964825941282865752'], 'prelabel': '4-78e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.7891977798790284, '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': 618607681433556058, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.16401043466288981441025505835', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.11282312486137849791066275163', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.09590559657322186514860263713', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.38792111500809284, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 6084, 'conductor_radical': 78, 'degree': 4, 'dirichlet_coefficients': [1, 0, 2, -1, 0, 0, 0, 0, 3, 0, 0, -2, -6, 0, 0, 1, -4, 0, 0, 0, 0, 0, 8, 0, 6, 0, 4, 0, -20, 0, 0, 0, 0, 0, 0, -3, 0, 0, -12, 0, 0, 0, 8, 0, 0, 0, 0, 2, 10, 0, -8, 6, -12, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -1, 0, 0, 0, 4, 16, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -6], 'euler11': [1, 0, -22, 0, 121], 'euler13': [1, 6, 13, 0, 0], 'euler17': [1, 4, 38, 68, 289], 'euler19': [1, 0, -2, 0, 361], 'euler2': [1, 0, 1, 0, 0], 'euler23': [1, -8, 62, -184, 529], 'euler29': [1, 20, 158, 580, 841], 'euler3': [1, -2, 1, 0, 0], 'euler31': [1, 0, 38, 0, 961], 'euler37': [1, 0, -10, 0, 1369], 'euler41': [1, 0, 18, 0, 1681], 'euler43': [1, -8, 102, -344, 1849], 'euler47': [1, 0, 50, 0, 2209], 'euler5': [1, 0, -6, 0, 25], 'euler53': [1, 12, 142, 636, 2809], 'euler59': [1, 0, -102, 0, 3481], 'euler61': [1, -4, 126, -244, 3721], 'euler67': [1, 0, -130, 0, 4489], 'euler7': [1, 0, -10, 0, 49], 'euler71': [1, 0, -142, 0, 5041], 'euler73': [1, 0, -130, 0, 5329], 'euler79': [1, 0, 158, 0, 6241], 'euler83': [1, 0, -150, 0, 6889], 'euler89': [1, 0, -142, 0, 7921], 'euler97': [1, 0, -50, 0, 9409], 'euler_factors': [[1, 0, 1, 0, 0], [1, -2, 1, 0, 0], [1, 0, -6, 0, 25], [1, 0, -10, 0, 49], [1, 0, -22, 0, 121], [1, 6, 13, 0, 0], [1, 4, 38, 68, 289], [1, 0, -2, 0, 361], [1, -8, 62, -184, 529], [1, 20, 158, 580, 841], [1, 0, 38, 0, 961], [1, 0, -10, 0, 1369], [1, 0, 18, 0, 1681], [1, -8, 102, -344, 1849], [1, 0, 50, 0, 2209], [1, 12, 142, 636, 2809], [1, 0, -102, 0, 3481], [1, -4, 126, -244, 3721], [1, 0, -130, 0, 4489], [1, 0, -142, 0, 5041], [1, 0, -130, 0, 5329], [1, 0, 158, 0, 6241], [1, 0, -150, 0, 6889], [1, 0, -142, 0, 7921], [1, 0, -50, 0, 9409]], 'index': 2, 'instance_types': ['HMF', 'ECNF', 'CMF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-36.1-a', 'EllipticCurve/2.2.13.1/36.1/a', 'ModularForm/GL2/Q/holomorphic/78/2/b/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-78e2-1.1-c1e2-0-2', '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': 0, 'prelabel': '4-78e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.7891977798790284, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 618607681433556058, 'z1': {'__RealLiteral__': 0, 'data': '2.16401043466288981441025505835', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9959679
{'Lhash': '2743209126400563877306780369503,3945972102634839128455760229998', 'Lhash_array': ['2743209126400563877306780369503', '3945972102634839128455760229998'], 'factors': ['2-78-13.12-c1-0-0', '2-78-13.12-c1-0-1'], 'label': '4-78e2-1.1-c1e2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/78/2/b/a'}
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id: 9526838
{'Lhash': '_2743209126400563877306780369503', 'Lhash_array': ['_2743209126400563877306780369503'], 'factors': ['4-78e2-1.1-c1e2-0-2'], 'label': '4-78e2-1.1-c1e2-0-2', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.13.1/36.1/a'}
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id: 9526254
{'Lhash': '_2743209126400563877306780369503', 'Lhash_array': ['_2743209126400563877306780369503'], 'factors': ['4-78e2-1.1-c1e2-0-2'], 'label': '4-78e2-1.1-c1e2-0-2', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-36.1-a'}