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lfunc_lfunctions • Show schema
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{'Lhash': '3165049542968033440767638171033', 'a10': [-1.3448812207611243, -1.3448812207611243], 'a2': [1.3448812207611243, 1.3448812207611243], 'a3': [-1.268038659534405, -1.1798635336030134], 'a4': [0.0, 1.6174109959118639], 'a5': [-1.0, 0.0], 'a6': [-0.11858507100337606, -3.292137689810485], 'a7': [-4.794073251792304, 0.0], 'a8': [0.5145367668678351, -0.5145367668678351], 'a9': [0.21584408414762205, 2.9922251471669834], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.4734924879256983, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.268038659534405, 1.1798635336030134]]], [5, [[1.0, 0], [1.0, 0]]], [29, [[1.0, 0], [4.769006186277564, -2.501315652860775]]]], 'bad_primes': [3, 5, 29], 'central_character': '435.191', 'coefficient_field': 'CDF', 'conductor': 435, 'conductor_radical': 435, 'conjugate': '275198422145094899311494576014', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3448812207611243, 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'-0.440895281317182 + 0.8975585501304318*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.322669493235', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.49678384753511255986315437773', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.66207898331545956095697181780', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.34561289411653848451599713622', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.4734924879256983, 'bad_primes': [3, 5, 29], 'central_character': '87.17', 'conductor': 435, 'conductor_radical': 435, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/435/2/q/c/191/16'], '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': '2-435-87.17-c1-0-36', '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': '2-435-87.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8637307981373539, 'root_angle': 0.3226694932352523, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.49678384753511255986315437773', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3165049542968033440767638171033', 'Lhash_array': ['3165049542968033440767638171033'], 'label': '2-435-87.17-c1-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/435/2/q/c/191/16'}