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lfunc_lfunctions • Show schema
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{'Lhash': '1577157603667616301750730882372', 'a10': [27064144198.07591, 0], 'a2': [1271.9551395599815, 0], 'a3': [0, 0], 'a4': [-479282.12294694775, 0], 'a5': [21277593.33354983, 0], 'a6': [0, 0], 'a7': [632075570.6821496, 0], 'a8': [-3277108624.4200835, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.15296098583559, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '10.5', 'prec': 14}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '9.1', 'coefficient_field': 'CDF', 'conductor': 9, 'conductor_radical': 3, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1271.9551395599815, 0], [2097152.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-21277593.33354983, 0], [476837158203125.0, 0]], [[1.0, 0], [-632075570.6821496, 0], [558545864083284030, 0]], [[1.0, 0], [59758476606.34392, 0], [7400249944258161000000, 0]], [[1.0, 0], [-738499392407.168, 0], [247064529073450400000000, 0]], [[1.0, 0], [-8358762709708.16, 0], 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'group': 'GL2', 'index': 3, 'label': '2-3e2-1.1-c21-0-3', 'leading_term': '3.564208383577649258657800073586804407698990420928939278', 'load_key': 'CMFs-workshop', 'motivic_weight': 21, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [21], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/9/22/a/e/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.09375', 'prec': 24}, 'plot_values': [3.5642083835776495, 3.536876364460945, 3.4554287897394858, 3.321499555766707, 3.137773556573937, 2.907930114389222, 2.636565426690669, 2.3290956361673905, 1.9916425354093807, 1.6309042846829795, 1.2540138414658737, 0.868388067990177, 0.4815706922494303, 0.10107244414890855, -0.2657882317947569, -0.612040474898359, -0.9312089646026652, -1.2174513100132478, -1.4656818449614766, -1.6716790630229357, -1.8321742502284641, -1.9449192521871914, -2.008731740355964, -2.023516811454417, -1.9902642557419115, -1.9110213543595937, 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'13.52145812722002435240906711501711', '14.07258330141691945639913971775284', '15.71950741249817679745562138072350'], 'prelabel': '2-3e2-1.1-c21-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.015272772824584, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c21-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.24415797490543756439724998456', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.14767765435172049491292905417', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.93956968454570441006330021795', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.15296098583559, 'bad_primes': [3], 'central_character': '1.1', 'conductor': 9, 'conductor_radical': 3, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9/22/a/e/1/2'], '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': '2-3e2-1.1-c21-0-3', 'motivic_weight': 21, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [21], 'order_of_vanishing': 0, 'prelabel': '2-3e2-1.1-c21-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.015272772824584, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c21-0', 'z1': {'__RealLiteral__': 0, 'data': '1.24415797490543756439724998456', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1577157603667616301750730882372', 'Lhash_array': ['1577157603667616301750730882372'], 'label': '2-3e2-1.1-c21-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9/22/a/e/1/2'}