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lfunc_lfunctions • Show schema
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{'Lhash': '787154050678235043858691705228', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.8020699111944452, 0.0], 'a4': [0.0, 0.0], 'a5': [0.702207910932084, 0.0], 'a6': [0.0, 0.0], 'a7': [1.702207910932084, 0.0], 'a8': [0.0, 0.0], 'a9': [0.24745596483235535, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.701974435916174, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 11, 19], 'central_character': '3344.1', 'coefficient_field': 'CDF', 'conductor': 3344, 'conductor_radical': 418, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.8020699111944452, 0], [3.0, 0]], [[1.0, 0], [-0.702207910932084, 0], [5.0, 0]], [[1.0, 0], [-1.702207910932084, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [6.290789071027275, 0], [13.0, 0]], [[1.0, 0], [6.353247381649906, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], 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[[1.0, 0], [-8.589747263875454, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 16, 'label': '2-3344-1.1-c1-0-16', 'leading_term': '1.0336730210099262395837336973069', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3344/2/a/z/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.0336730210099263, 1.0269147074183358, 1.0066025102787668, 0.9726306219373099, 0.9248421719997848, 0.8630570990396623, 0.7871086343562187, 0.6968861737909466, 0.592382055982702, 0.47373969281908523, 0.34130057702011085, 0.1956478783791916, 0.03764458989566567, -0.13153553825554118, -0.3103857593380317, -0.4970539970134391, -0.6893413707433339, -0.8847122785897388, -1.0803164821837588, -1.2730233755115339, -1.4594683408490532, -1.6361107981592462, 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'4.46006045629973264748530640801611', '4.70473906276920899316032121881303', '5.61042748507577702707448712078429', '6.29500230478553142542960856616898', '7.05520229971382857982143753063004', '7.71666117215643306162498303133617', '8.727013715659749262900440043583404'], 'prelabel': '2-3344-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.167395324137313, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.62095505696641869837863423990', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.02708795273781507568250668110', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.82008542631433658807943530586', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.701974435916174, 'bad_primes': [2, 11, 19], 'central_character': '1.1', 'conductor': 3344, 'conductor_radical': 418, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3344/2/a/z/1/1'], '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': '2-3344-1.1-c1-0-16', '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': '2-3344-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.167395324137313, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.62095505696641869837863423990', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '787154050678235043858691705228', 'Lhash_array': ['787154050678235043858691705228'], 'label': '2-3344-1.1-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3344/2/a/z/1/1'}