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lfunc_lfunctions • Show schema
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{'Lhash': '446634941431713331818044761234', 'a10': [2.7863275492553456, 0.0], 'a2': [-1.0, 0.0], 'a3': [0.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-2.7863275492553456, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.211124970764842, 0.0], 'a8': [-1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 30.039721240405694, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 11, 19], 'central_character': '3762.1', 'coefficient_field': 'CDF', 'conductor': 3762, 'conductor_radical': 1254, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.7863275492553456, 0], [5.0, 0]], [[1.0, 0], [2.211124970764842, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-0.9772936624839548, 0], [13.0, 0]], [[1.0, 0], [7.9245396326278, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], 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[[1.0, 0], [17.150971742144385, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-3762-1.1-c1-0-0', 'leading_term': '0.33223857149652312312154997126374', '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/3762/2/a/bi/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.33223857149652314, 0.3253563647599613, 0.30469713165148654, 0.2702285024735447, 0.221914380672584, 0.15974044219272243, 0.08374740905079094, -0.005930041354137481, -0.10902113183295058, -0.22507609471148138, -0.3534249658129851, -0.4931403286328557, -0.6430060400770425, -0.8014936985060186, -0.9667483296957433, -1.1365844782283805, -1.3084936038021924, -1.479663391512289, -1.647009287278239, -1.8072182592056345, -1.956804459386364, -2.0921761178071514, 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'3.79758214121094209836604188574131', '4.52587678529126126195174397740849', '5.69365001247478908566129585552190', '6.54732978509392928095530686559869', '7.17213692253874559001951615103318', '7.76510341662592968695141054910299', '8.595106246587903644348277897279569'], 'prelabel': '2-3762-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.480850412153728, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.35233284420115496940433269703', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.93089431857362079195219434723', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.99342368764984659903806855563', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 30.039721240405694, 'bad_primes': [2, 3, 11, 19], 'central_character': '1.1', 'conductor': 3762, 'conductor_radical': 1254, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3762/2/a/bi/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': '2-3762-1.1-c1-0-0', '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': '2-3762-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.480850412153728, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.35233284420115496940433269703', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '446634941431713331818044761234', 'Lhash_array': ['446634941431713331818044761234'], 'label': '2-3762-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3762/2/a/bi/1/2'}