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lfunc_lfunctions • Show schema
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{'Lhash': '354814495774295370889270507027,2040368739895899052423473018175', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -6, 'a6': 0, 'a7': 16, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1948.4987567619592, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 6, 25]]], 'bad_primes': [2, 3, 5], 'central_character': '1620.1', 'coefficient_field': '1.1.1.1', 'conductor': 2624400, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1], [1, 6, 25], [1, -16, 128, -784, 2401], [1, 34, 531, 4114, 14641], [1, -24, 288, -4056, 28561], [1, -8, 32, -2312, 83521], [1, 0, 239, 0, 130321], [1, 46, 1058, 24334, 279841], [1, 0, -1681, 0, 707281], [1, -50, 2547, -48050, 923521], [1, -18, 162, -24642, 1874161], [1, -146, 8691, -245426, 2825761], [1, 78, 3042, 144222, 3418801], [1, 90, 4050, 198810, 4879681], [1, -16, 128, -44944, 7890481], [1, 0, -4561, 0, 12117361], [1, 192, 16658, 714432, 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25, 5041], 2]], [[[1, -80, 3200, -426320, 28398241], 1]], [[[1, 0, -8126, 0, 38950081], 1]], [[[1, -150, 11250, -1033350, 47458321], 1]], [[[1, 0, -12817, 0, 62742241], 1]], [[[1, 186, 17298, 1750074, 88529281], 1]], [[[1, 193, 10201], 2]], [[[1, 22, 242, 233398, 112550881], 1]], [[[1, 58, 1682, 664042, 131079601], 1]], [[[1, 0, -18433, 0, 141158161], 1]], [[[1, 128, 8192, 1634432, 163047361], 1]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 0, 'label': '4-1620e2-1.1-c2e2-0-0', 'leading_term': '1.01093570897547110425351617323635483099983586780414112497053794561679749198083710797881962', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1620/3/l/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.029296875', 'prec': 37}, 'plot_values': 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'9.738129180411592991650752842294835'], 'prelabel': '4-1620e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.643929772835359, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c2e2-0', 'trace_hash': 2172871574514466567, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.27989928432204751431434974277', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.29483368525883241912780721627', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.60956713113893411119346962396', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1948.4987567619592, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 2624400, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -6, 0, 16, 0, 0, 0, -34, 0, 24, 0, 0, 0, 8, 0, 0, 0, 0, 0, -46, 0, 11, 0, 0, 0, 0, 0, 50, 0, 0, 0, -96, 0, 18, 0, 0, 0, 146, 0, -78, 0, 0, 0, -90, 0, 128, 0, 0, 0, 16, 0, 204, 0, 0, 0, 0, 0, -192, 0, 0, 0, -144, 0, -134, 0, 0, 0, -50, 0, 80, 0, 0, 0, -544, 0, 0, 0, 0, 0, 150, 0, -48, 0, 0, 0, 0, 0, 384, 0, 0, 0, 0, 0, -186, 0, 0, 0], 'euler11': [1, 34, 531, 4114, 14641], 'euler13': [1, -24, 288, -4056, 28561], 'euler17': [1, -8, 32, -2312, 83521], 'euler19': [1, 0, 239, 0, 130321], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 46, 1058, 24334, 279841], 'euler29': [1, 0, -1681, 0, 707281], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -50, 2547, -48050, 923521], 'euler37': [1, -18, 162, -24642, 1874161], 'euler41': [1, -146, 8691, -245426, 2825761], 'euler43': [1, 78, 3042, 144222, 3418801], 'euler47': [1, 90, 4050, 198810, 4879681], 'euler5': [1, 6, 25, 0, 0], 'euler53': [1, -16, 128, -44944, 7890481], 'euler59': [1, 0, -4561, 0, 12117361], 'euler61': [1, 192, 16658, 714432, 13845841], 'euler67': [1, 134, 8978, 601526, 20151121], 'euler7': [1, -16, 128, -784, 2401], 'euler71': [1, 50, 10707, 252050, 25411681], 'euler73': [1, -80, 3200, -426320, 28398241], 'euler79': [1, 0, -8126, 0, 38950081], 'euler83': [1, -150, 11250, -1033350, 47458321], 'euler89': [1, 0, -12817, 0, 62742241], 'euler97': [1, 186, 17298, 1750074, 88529281], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 6, 25, 0, 0], [1, -16, 128, -784, 2401], [1, 34, 531, 4114, 14641], [1, -24, 288, -4056, 28561], [1, -8, 32, -2312, 83521], [1, 0, 239, 0, 130321], [1, 46, 1058, 24334, 279841], [1, 0, -1681, 0, 707281], [1, -50, 2547, -48050, 923521], [1, -18, 162, -24642, 1874161], [1, -146, 8691, -245426, 2825761], [1, 78, 3042, 144222, 3418801], [1, 90, 4050, 198810, 4879681], [1, -16, 128, -44944, 7890481], [1, 0, -4561, 0, 12117361], [1, 192, 16658, 714432, 13845841], [1, 134, 8978, 601526, 20151121], [1, 50, 10707, 252050, 25411681], [1, -80, 3200, -426320, 28398241], [1, 0, -8126, 0, 38950081], [1, -150, 11250, -1033350, 47458321], [1, 0, -12817, 0, 62742241], [1, 186, 17298, 1750074, 88529281]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1620/3/l/a'], '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': '4-1620e2-1.1-c2e2-0-0', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2], 'order_of_vanishing': 0, 'prelabel': '4-1620e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.643929772835359, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e2-0', 'trace_hash': 2172871574514466567, 'z1': {'__RealLiteral__': 0, 'data': '0.27989928432204751431434974277', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '354814495774295370889270507027,2040368739895899052423473018175', 'Lhash_array': ['354814495774295370889270507027', '2040368739895899052423473018175'], 'label': '4-1620e2-1.1-c2e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1620/3/l/a'}