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lfunc_lfunctions • Show schema
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{'Lhash': '1124422693728584698444188217978', 'a10': [3.049442222412977, -5.281788863965029], 'a2': [-0.849814074137659, 1.47192115339353], 'a3': [-1.6439960694802112, -0.5452310735216923], 'a4': [-0.4443679212048931, -0.7696678167806383], 'a5': [-3.5883639906851044, 0.0], 'a6': [2.199628148275318, -1.9564875508278232], 'a7': [0.0, 0.0], 'a8': [-1.8887358424097862, 0.0], 'a9': [2.405446152932766, 1.7927154836562764], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.6439960694802112, 0.5452310735216923]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '441.67', 'coefficient_field': 'CDF', 'conductor': 441, 'conductor_radical': 21, 'conjugate': '564044629930770593201686927765', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.849814074137659, -1.47192115339353], [-1.0, -1.7320508075688772]], [[1.0, 0], [1.6439960694802112, 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'7.64446204078661168171069134534366', '8.441134526147027625770782853315914', '9.677458486929656422802148768792385', '10.43446109344799436383524391777965', '11.19411396464162412101084154311985'], 'prelabel': '2-21e2-63.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': -0.05870040692494346, 'root_number': '0.9830441005906101 - 0.18336928939710273*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0293502034625', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.887013104025779839170708036383', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.97232722948196740474873912056', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.03554219161213524718551211512', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'bad_primes': [3, 7], 'central_character': '63.4', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/2/g/e/67/1'], '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': '2-21e2-63.4-c1-0-8', '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': '2-21e2-63.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': -0.02935020346247173, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.887013104025779839170708036383', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1124422693728584698444188217978', 'Lhash_array': ['1124422693728584698444188217978'], 'label': '2-21e2-63.4-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/2/g/e/67/1'}