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lfunc_lfunctions • Show schema
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{'Lhash': '3477945567743091489041791302473', 'a10': [-0.4543170543003763, 2.576560050395996], 'a2': [-0.8936326403234123, -0.44879918020046217], 'a3': [0.6475685200403952, -1.606441723764884], 'a4': [0.5971585917027862, 0.8021231927550437], 'a5': [-0.7503654895765841, -2.506395282308296], 'a6': [-1.2996580950195202, 1.1449405382159512], 'a7': [0.3184892519150703, 0.7383410768520693], 'a8': [-0.17364817766693036, -0.984807753012208], 'a9': [-2.1613100237053846, -2.0805621791791347], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.293576512744743, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8936326403234123, 0.44879918020046217]]], [3, [[1.0, 0], [-0.6475685200403952, 1.606441723764884]]]], 'bad_primes': [2, 3], 'central_character': '162.13', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '1350575078894933175696727240021', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[47.17552874452011, 63.36773222764846]], [[1.0, 0], [-1.9484807930868375, -0.9785638338559786], [49.564163111331254, 66.57622499866864]], [[1.0, 0], [0.5877285789666551, 3.3331744047633425], [-83.63264324994584, 30.439792755984517]], [[1.0, 0], [-2.074748086286508, 6.9301412280847305], [-81.04231770705483, -53.30237087286819]], [[1.0, 0], [4.130210916632976, -5.547836057678748], [-28.967126503820115, -96.75694074386438]], [[1.0, 0], [-12.177411970459513, -2.8860996546680378], [92.04416195331146, 46.226315560647606]], [[1.0, 0], [-4.444095959536888, -7.697399995629452], [-53.5, 92.66471820493493]], [[1.0, 0], [5.811254686232484, -10.065388372277397], [-54.5, -94.39676901250381]], [[1.0, 0], [8.523559505828064, -9.034445266500505], [-6.570365666883768, -112.80882188465331]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-162-81.13-c1-0-7', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': 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False, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': 0.6483766618900068, 'root_number': '-0.4494406007695463 + 0.8933102184459267*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.324188330945', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.74361528887922098859392503470', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.13436773128561259978791859694', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.74509898166297266145120865565', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.293576512744743, 'bad_primes': [2, 3], 'central_character': '81.13', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/2/g/a/13/3'], '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': '2-162-81.13-c1-0-7', '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': '2-162-81.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': 0.3241883309450034, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.74361528887922098859392503470', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3477945567743091489041791302473', 'Lhash_array': ['3477945567743091489041791302473'], 'label': '2-162-81.13-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/2/g/a/13/3'}