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lfunc_lfunctions • Show schema
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{'Lhash': '1320626268799745629629279883429', 'a10': [2.0, -5.034525116044599e-61], 'a2': [0.8090169943749475, -0.5877852522924731], 'a3': [-0.30901699437494745, -0.9510565162951535], 'a4': [-0.30901699437494745, 0.9510565162951535], 'a5': [1.618033988749895, 1.1755705045849463], 'a6': [-0.8090169943749475, -0.5877852522924731], 'a7': [-1.2360679774997898, 3.804226065180614], 'a8': [0.9270509831248422, 2.853169548885461], 'a9': [-0.8090169943749475, 0.5877852522924731], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8985695933724793, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.30901699437494745, 0.9510565162951535]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '363.124', 'coefficient_field': 'CDF', 'conductor': 363, 'conductor_radical': 33, 'conjugate': '2991997480081553711727588881548', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8090169943749475, 0.5877852522924731], 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'positive_zeros': ['1.04179043386401459710073506741300', '3.41392332888437310674738873241551', '4.64689388108015808252163385028110', '5.21566021857320539991304636464297', '6.45536507269735971089444455844771', '7.14275722682849799658408568502047', '8.741389982839601996509955212134196', '9.751132638106307679571016945128944', '10.26096586068518123325551155818300', '11.04374390321835708829616362652757'], 'prelabel': '2-363-11.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7025186029446138, 'root_angle': -0.21399653131288596, 'root_number': '0.7823975971743531 - 0.6227792545804642*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.106998265656', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.04179043386401459710073506741', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.41392332888437310674738873242', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.64689388108015808252163385028', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.8985695933724793, 'bad_primes': [3, 11], 'central_character': '11.3', 'conductor': 363, 'conductor_radical': 33, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/363/2/e/g/124/1'], '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': '2-363-11.3-c1-0-4', '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': '2-363-11.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7025186029446138, 'root_angle': -0.10699826565644298, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.04179043386401459710073506741', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1320626268799745629629279883429', 'Lhash_array': ['1320626268799745629629279883429'], 'label': '2-363-11.3-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/363/2/e/g/124/1'}