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lfunc_lfunctions • Show schema
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{'Lhash': '864524260022684405992949420685', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.9358988526701657, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.2470760053448295, 0.0], 'a8': [0.0, 0.0], 'a9': [0.7477043677696638, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 30.34315276808656, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 19], 'central_character': '3800.1', 'coefficient_field': 'CDF', 'conductor': 3800, 'conductor_radical': 190, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.9358988526701657, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.2470760053448295, 0], [7.0, 0]], [[1.0, 0], [0.5138596842197632, 0], [11.0, 0]], [[1.0, 0], [-6.1566977488237065, 0], [13.0, 0]], [[1.0, 0], [4.519855396829781, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [5.860844892733567, 0], 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0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 19, 'label': '2-3800-1.1-c1-0-19', 'leading_term': '1.187856709687966828295543747881', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3800/2/a/ba/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.1878567096879669, 1.181225976394978, 1.1613062921941064, 1.1280215068339663, 1.081265277745511, 1.020930458127996, 0.9469474529233175, 0.8593290959645138, 0.758219315017305, 0.6439427682582649, 0.517052720929866, 0.3783746372155753, 0.22904324238666232, 0.07053112512056317, -0.09533272658881009, -0.2663557436132388, -0.4399869242732873, -0.6133349818896098, -0.7831998487381582, -0.9461175721358942, -1.0984183008223563, -1.2362967042274358, -1.3558937950749046, -1.4533887421155636, 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'5.61983152234551653815331344413561', '6.44479818527058019354710437964054', '6.50284192652144108068409233795183', '7.983451765466953643050475616939478', '8.329969858292361094229887419795272'], 'prelabel': '2-3800-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.5084619239935355, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.68198939034702020857083765837', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.77939889325735359663450105121', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.98833209566256860990705508822', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 30.34315276808656, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 3800, 'conductor_radical': 190, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3800/2/a/ba/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': '2-3800-1.1-c1-0-19', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-3800-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.5084619239935355, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.68198939034702020857083765837', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '864524260022684405992949420685', 'Lhash_array': ['864524260022684405992949420685'], 'label': '2-3800-1.1-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3800/2/a/ba/1/2'}