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lfunc_lfunctions • Show schema
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{'Lhash': '2344713849964476212962824481797', 'a10': [-6.634043150526015, 0], 'a2': [-0.6634043150526014, 1.1490499796315363], 'a3': [0, 0], 'a4': [3.1197894295391775, 5.403633800878179], 'a5': [2.5, 4.330127018922194], 'a6': [0, 0], 'a7': [12.05213376819672, -20.874908026133266], 'a8': [-18.89319611928876, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.89577355232496, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.5, -4.330127018922194]]]], 'bad_primes': [3, 5], 'central_character': '405.136', 'coefficient_field': 'CDF', 'conductor': 405, 'conductor_radical': 15, 'conjugate': '267395101843022796478117903794', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.6634043150526014, -1.1490499796315363], [-4.0, -6.928203230275509]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.5, -4.330127018922194]], [[1.0, 0], [-12.05213376819672, 20.874908026133266], [-171.5, -297.04671349806245]], 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'2-405-9.7-c3-0-41', 'leading_term': '0.663489366207036120215774381655941780288626602847209258', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/405/4/e/s/136/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [0.6634893662070361, 0.8610682293089617, 1.0437991753976017, 1.2100505873121163, 1.3583259525237823, 1.48727039438478, 1.5956826195437845, 1.6825324556573056, 1.7469837756882256, 1.7884222299027803, 1.8064868489555927, 1.8011042544099003, 1.7725239280512872, 1.7213527579394858, 1.6485869051449566, 1.5556389269485351, 1.444358055167365, 1.3170415663897987, 1.1764352974047936, 1.0257215559755177, 0.8684929548665592, 0.7087110544088162, 0.5506491323598374, 0.3988189032209076, 0.2578815733207861, 0.13254423040905958, 0.027443211364343714, -0.052983250282121454, 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'10.11295849969109473251308773306245', '11.26854910877770581719742397095703'], 'prelabel': '2-405-9.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8883303440259604, 'root_angle': 0.5555555555555556, 'root_number': '-0.173648177666930348851716626769314796000375677184069388 + 0.984807753012208059366743024589523013670643251719842419*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2777777777777778', 'prec': 60}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.84965309016722036436336019522', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.22382195018894353396034697457', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.29262516568776356789584558125', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.89577355232496, 'bad_primes': [3, 5], 'central_character': '9.7', 'conductor': 405, 'conductor_radical': 15, 'degree': 2, 'index': 41, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/405/4/e/s/136/2'], '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': '2-405-9.7-c3-0-41', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-405-9.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8883303440259604, 'root_angle': 0.2777777777777778, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.84965309016722036436336019522', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2344713849964476212962824481797', 'Lhash_array': ['2344713849964476212962824481797'], 'label': '2-405-9.7-c3-0-41', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/4/e/s/136/2'}