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lfunc_lfunctions • Show schema
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{'Lhash': '1317363379124486788851038093687', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -1.0], 'a4': [0, 0], 'a5': [-0.3536238856195162, 2.207928927189314], 'a6': [0, 0], 'a7': [0, 3.09417374111494], 'a8': [0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.913325430639492, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [0.3536238856195162, -2.207928927189314]]], [13, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '3120.1249', 'coefficient_field': 'CDF', 'conductor': 3120, 'conductor_radical': 390, 'conjugate': '284557800279145156913925829493', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0.3536238856195162, -2.207928927189314]], [[1.0, 0], [0, -3.09417374111494], [-7.0, 0]], [[1.0, 0], [5.510031595493568, 0], [11.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 6.2172793667326], 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'4.30340885097817407273187894169447', '4.89769666884773485199101022056018', '5.68773367131032109904761694149071', '6.62028335349042304410717046350687', '7.66148298874686436508471564607882', '8.188593629209589241085243951933738', '8.738589910775866032484805010073754'], 'prelabel': '2-3120-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.991325017531867, 'root_angle': 0.5505514750633276, 'root_number': '-0.1581454093425697171171376302381601763207317053588698572 + 0.9874158341366979835240071648112467629480106354745291161*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2752757375316638', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.03921646776115361471717209972', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.36248764995748573307530239664', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.58341198009767310795105480982', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 24.913325430639492, 'bad_primes': [2, 3, 5, 13], 'central_character': '5.4', 'conductor': 3120, 'conductor_radical': 390, 'degree': 2, 'index': 43, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3120/2/l/n/1249/3'], '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': '2-3120-5.4-c1-0-43', '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': '2-3120-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.991325017531867, 'root_angle': 0.2752757375316638, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03921646776115361471717209972', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1317363379124486788851038093687', 'Lhash_array': ['1317363379124486788851038093687'], 'label': '2-3120-5.4-c1-0-43', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3120/2/l/n/1249/3'}