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lfunc_lfunctions • Show schema
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{'Lhash': '2540769942297836939566519478843', 'a10': [-1.2167778322259388, 1.8760201776642875], 'a2': [-0.7071067811865476, 0.7071067811865476], 'a3': [-1.7025814073026342, -0.31814548795697456], 'a4': [0.0, -1.0], 'a5': [2.186938445633638, -0.4661547329047808], 'a6': [1.4288696905641078, -0.9789440266875482], 'a7': [-2.6815506212698486, -2.6815506212698486], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [2.797566896985237, 1.083337185225538], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.072370503085302, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [3, [[1.0, 0], [1.7025814073026342, 0.31814548795697456]]], [5, [[1.0, 0], [-2.186938445633638, 0.4661547329047808]]], [17, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]]], 'bad_primes': [2, 3, 5, 17], 'central_character': '510.137', 'coefficient_field': 'CDF', 'conductor': 510, 'conductor_radical': 510, 'conjugate': '234506205468238344522686217872', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [1.7025814073026342, 0.31814548795697456]], [[1.0, 0], [-2.186938445633638, 0.4661547329047808]], [[1.0, 0], [2.6815506212698486, 2.6815506212698486], [0, 7.0]], [[1.0, 0], [0, 4.1056944586214215], [-11.0, 0]], [[1.0, 0], [4.653422689094253, -4.653422689094253], [0, -13.0]], [[1.0, 0], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, -2.505361861411482], [-19.0, 0]], [[1.0, 0], [-0.10686083195883966, -0.10686083195883966], [0, 23.0]], [[1.0, 0], [5.150286945103412, 0], [29.0, 0]], [[1.0, 0], [9.651533500203488, 0], [31.0, 0]], [[1.0, 0], [6.883978124413046, 6.883978124413046], [0, 37.0]], [[1.0, 0], [0, 2.1272428438860116], [-41.0, 0]], [[1.0, 0], [-4.8082414600001115, 4.8082414600001115], [0, -43.0]], [[1.0, 0], [3.7551023181913323, -3.7551023181913323], [0, -47.0]], [[1.0, 0], [3.1392403620120413, 3.1392403620120413], [0, 53.0]], [[1.0, 0], [3.3853555513982125, 0], [59.0, 0]], [[1.0, 0], [4.4255876000600125, 0], [61.0, 0]], [[1.0, 0], [-7.732818774423836, -7.732818774423836], [0, 67.0]], [[1.0, 0], [0, 12.432121264480276], [-71.0, 0]], [[1.0, 0], [2.675044682342795, -2.675044682342795], [0, -73.0]], [[1.0, 0], [0, -8.139484725154471], [-79.0, 0]], [[1.0, 0], [3.247416627439758, 3.247416627439758], [0, 83.0]], [[1.0, 0], [-12.992512166232627, 0], [89.0, 0]], [[1.0, 0], [5.965851989236719, 5.965851989236719], [0, 97.0]], [[1.0, 0], [0, 1.2593754890661226], [-101.0, 0]], [[1.0, 0], [5.479382337283656, -5.479382337283656], [0, -103.0]], [[1.0, 0], [-0.8693449330230338, 0.8693449330230338], [0, -107.0]], [[1.0, 0], [0, -8.864105573071894], [-109.0, 0]], [[1.0, 0], [-0.6847995589852903, -0.6847995589852903], [0, 113.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 23, 'label': '2-510-15.2-c1-0-23', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': 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2.018011522039778, 'root_angle': 0.815744672516669, 'root_number': '-0.8370894886480594 + 0.547065981390664*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.407872336258', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.00431407663940957977197321645', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.09741450118128093695955246937', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.89413979136942808224440197282', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.072370503085302, 'bad_primes': [2, 3, 5, 17], 'central_character': '15.2', 'conductor': 510, 'conductor_radical': 510, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/510/2/l/g/137/1'], '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': '2-510-15.2-c1-0-23', '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': '2-510-15.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.018011522039778, 'root_angle': 0.4078723362583345, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.00431407663940957977197321645', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2540769942297836939566519478843', 'Lhash_array': ['2540769942297836939566519478843'], 'label': '2-510-15.2-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/510/2/l/g/137/1'}