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lfunc_lfunctions • Show schema
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{'Lhash': '110331981310789773437384798702', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, -1.3643255096084355], 'a6': [0, 0], 'a7': [0, 1.242125236073976], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 62.77945290861241, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '2304.127', 'coefficient_field': 'CDF', 'conductor': 2304, 'conductor_radical': 6, 'conjugate': '1445851014077246895354890993792', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.3643255096084355], [-25.0, 0]], [[1.0, 0], [0, -1.242125236073976], [-49.0, 0]], [[1.0, 0], [5.797958971132712, 0], [121.0, 0]], [[1.0, 0], [0, 16.3830164509006], [-169.0, 0]], [[1.0, 0], [-5.0108604624975355, 0], [289.0, 0]], [[1.0, 0], [26.183464239841964, 0], [361.0, 0]], [[1.0, 0], [0, 25.111667470117474], 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'1.64447603055918544278546263486753', '2.54714638873836532051339456506296', '3.69676263717660006867180655235648', '4.43444603919222453450663804289633', '5.38045182719581677490613960034106', '6.29496452966241910995735605171877', '6.98796633714866658698848492921281', '7.69119724573228078719805389124313', '8.641040515322010188562024589331845'], 'prelabel': '2-48e2-8.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.923348591890452, 'root_angle': -0.75, 'root_number': '-0.7071067811865475244008443621048490392848359376884740366 - 0.7071067811865475244008443621048490392848359376884740366*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.375', 'prec': 20}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.087036586651657377322711075310', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.64447603055918544278546263487', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.54714638873836532051339456506', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 62.77945290861241, 'bad_primes': [2, 3], 'central_character': '8.3', 'conductor': 2304, 'conductor_radical': 6, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2304/3/b/t/127/4'], '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': '2-48e2-8.3-c2-0-3', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-48e2-8.3-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.923348591890452, 'root_angle': -0.375, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.087036586651657377322711075310', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '110331981310789773437384798702', 'Lhash_array': ['110331981310789773437384798702'], 'label': '2-48e2-8.3-c2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2304/3/b/t/127/4'}