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lfunc_lfunctions • Show schema
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{'Lhash': '755336639298761940417681067114,1410678176585321925640126192275', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1619.6280399391142, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 2, 5]], [7, [1, 0, 1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '5040.1', 'coefficient_field': '1.1.1.1', 'conductor': 25401600, 'conductor_radical': 210, 'degree': 4, 'euler_factors': [[1], [1], [1, 2, 5], [1, 0, 1], [1, -12, 58, -132, 121], [1, 0, -22, 0, 169], [1, 0, -30, 0, 289], [1, -8, 54, -152, 361], [1, 0, -30, 0, 529], [1, -4, 62, -116, 841], [1, -4, 66, -124, 961], [1, 0, 26, 0, 1369], [1, 12, 118, 492, 1681], [1, 0, -82, 0, 1849], [1, 0, -90, 0, 2209], [1, 0, -70, 0, 2809], [1, -8, 134, -472, 3481], [1, 24, 266, 1464, 3721], [1, 0, -34, 0, 4489], [1, -24, 286, -1704, 5041], [1, 0, -142, 0, 5329], [1, 32, 414, 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'positive_zeros': ['0.59585554502381822404249494612593', '1.11282886335662339463885988936527', '1.54687819882890179495122354879798', '1.88834890380341325451942590923332', '2.93602546988935205610830885606465', '3.15858759785414045170008819792109', '3.58317391838343549071027362999735', '3.92611637615677545031048206575208', '4.34371805850461078144904530455386', '4.46152639399575343392414033538144', '5.27594188110129571461131574342401', '5.31528950753101128554555254061776', '6.20162334697453255935169739522805', '6.23531266231085847618114554260460', '6.74441008379582629140608651838979', '6.83080839185318661308765045518381', '7.36095340221376516654939139370882', '7.61092480550294512553826920739872', '8.155807575656471432744686544768437', '8.347878784668809701242172101138283'], 'prelabel': '4-5040e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.343863382728646, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 357116799533805555, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.59585554502381822404249494613', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.11282886335662339463885988937', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.54687819882890179495122354880', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1619.6280399391142, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 25401600, 'conductor_radical': 210, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -1, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -24, 0, 0, 0, 8, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0], 'euler11': [1, -12, 58, -132, 121], 'euler13': [1, 0, -22, 0, 169], 'euler17': [1, 0, -30, 0, 289], 'euler19': [1, -8, 54, -152, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -30, 0, 529], 'euler29': [1, -4, 62, -116, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -4, 66, -124, 961], 'euler37': [1, 0, 26, 0, 1369], 'euler41': [1, 12, 118, 492, 1681], 'euler43': [1, 0, -82, 0, 1849], 'euler47': [1, 0, -90, 0, 2209], 'euler5': [1, 2, 5, 0, 0], 'euler53': [1, 0, -70, 0, 2809], 'euler59': [1, -8, 134, -472, 3481], 'euler61': [1, 24, 266, 1464, 3721], 'euler67': [1, 0, -34, 0, 4489], 'euler7': [1, 0, 1, 0, 0], 'euler71': [1, -24, 286, -1704, 5041], 'euler73': [1, 0, -142, 0, 5329], 'euler79': [1, 32, 414, 2528, 6241], 'euler83': [1, 0, -22, 0, 6889], 'euler89': [1, -28, 374, -2492, 7921], 'euler97': [1, 0, 130, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 2, 5, 0, 0], [1, 0, 1, 0, 0], [1, -12, 58, -132, 121], [1, 0, -22, 0, 169], [1, 0, -30, 0, 289], [1, -8, 54, -152, 361], [1, 0, -30, 0, 529], [1, -4, 62, -116, 841], [1, -4, 66, -124, 961], [1, 0, 26, 0, 1369], [1, 12, 118, 492, 1681], [1, 0, -82, 0, 1849], [1, 0, -90, 0, 2209], [1, 0, -70, 0, 2809], [1, -8, 134, -472, 3481], [1, 24, 266, 1464, 3721], [1, 0, -34, 0, 4489], [1, -24, 286, -1704, 5041], [1, 0, -142, 0, 5329], [1, 32, 414, 2528, 6241], [1, 0, -22, 0, 6889], [1, -28, 374, -2492, 7921], [1, 0, 130, 0, 9409]], 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5040/2/t/i'], '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': '4-5040e2-1.1-c1e2-0-13', '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': '4-5040e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.343863382728646, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 357116799533805555, 'z1': {'__RealLiteral__': 0, 'data': '0.59585554502381822404249494613', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '755336639298761940417681067114,1410678176585321925640126192275', 'Lhash_array': ['755336639298761940417681067114', '1410678176585321925640126192275'], 'label': '4-5040e2-1.1-c1e2-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5040/2/t/i'}