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lfunc_lfunctions • Show schema
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{'Lhash': '1620896885525426081225894927798', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [31.176914536239792, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33.98510016330661, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '576.289', 'coefficient_field': 'CDF', 'conductor': 576, 'conductor_radical': 6, 'conjugate': '1006946395995781729348371023340', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-125.0, 0]], [[1.0, 0], [-31.176914536239792, 0], [343.0, 0]], [[1.0, 0], [0, 0], [-1331.0, 0]], [[1.0, 0], [0, 62.353829072479584], [-2197.0, 0]], [[1.0, 0], [0, 0], [4913.0, 0]], [[1.0, 0], [0, 56.0], [-6859.0, 0]], [[1.0, 0], [0, 0], [12167.0, 0]], [[1.0, 0], [0, 0], [-24389.0, 0]], [[1.0, 0], [155.88457268119896, 0], 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'2-24e2-8.5-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.82967410438239, 'root_angle': 0.25, 'root_number': '0.70710678118654752440084436210484903928483593768847403659 + 0.7071067811865475244008443621048490392848359376884740366*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.27866218438550636600268532293', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.24831316230899120951329007367', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.95357947718611103681208369815', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 33.98510016330661, 'bad_primes': [2, 3], 'central_character': '8.5', 'conductor': 576, 'conductor_radical': 6, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/576/4/d/d/289/3'], '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': '2-24e2-8.5-c3-0-22', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-24e2-8.5-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.82967410438239, 'root_angle': 0.125, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.27866218438550636600268532293', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1620896885525426081225894927798', 'Lhash_array': ['1620896885525426081225894927798'], 'label': '2-24e2-8.5-c3-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/576/4/d/d/289/3'}