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  • lfunc_lfunctions • Show schema
    {'Lhash': '2271395069144030647790707537596', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-80.08541470522664, -138.71200721467622], 'a6': [0, 0], 'a7': [-254.68201816318287, -871.0224277389924], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 78.72102642199872, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [254.68201816318287, 871.0224277389924]]]], 'bad_primes': [2, 3, 7], 'central_character': '252.109', 'coefficient_field': 'CDF', 'conductor': 252, 'conductor_radical': 42, 'conjugate': '104793989388145059766332123220', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [80.08541470522664, 138.71200721467622], [-39062.5, 67658.23467065927]], [[1.0, 0], [254.68201816318287, 871.0224277389924]], [[1.0, 0], [-1581.929460099053, 2739.9821988815625], [-9743585.5, -16876385.133891404]], 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'6.46507389596911090519745351072185', '7.43316624707313081510932717255531', '8.518225566511710669785563627971597', '9.563627339598153489686795659364475', '10.31716985145336871664149009997097', '11.64585394054968346294205795703909'], 'prelabel': '2-252-7.4-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.87248704828577, 'root_angle': -0.36852080266598836, 'root_number': '-0.6777425520262721273541915226820053664309006076211266198 - 0.7352992813629806742518474354970999615799338896377386858*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.36852080266598847', 'prec': 57}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.79181477035950271719873405015', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.86970790358564565307432731827', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.11640199178377804158937536517', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 78.72102642199872, 'bad_primes': [2, 3, 7], 'central_character': '7.4', 'conductor': 252, 'conductor_radical': 42, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/252/8/k/b/109/1'], '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': '2-252-7.4-c7-0-22', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-252-7.4-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.87248704828577, 'root_angle': -0.36852080266598836, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '1.79181477035950271719873405015', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2271395069144030647790707537596', 'Lhash_array': ['2271395069144030647790707537596'], 'factors': ['2-252-7.4-c7-0-22'], 'label': '2-252-7.4-c7-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/252/8/k/b/109/1'}