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lfunc_lfunctions • Show schema
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{'Lhash': '1510570044102383522516967032350', 'a10': [0, 0], 'a2': [0, 0], 'a3': [2.41750033973273, 0], 'a4': [0, 0], 'a5': [1.944981280181697, -1.1031989030735874], 'a6': [0, 0], 'a7': [0, 1.0], 'a8': [0, 0], 'a9': [2.844307892607865, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.886490052766813, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.944981280181697, 1.1031989030735874]]], [7, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 5, 7], 'central_character': '2240.1569', 'coefficient_field': 'CDF', 'conductor': 2240, 'conductor_radical': 70, 'conjugate': '1971013958207286007968396116747', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.41750033973273, 0], [3.0, 0]], [[1.0, 0], [-1.944981280181697, 1.1031989030735874]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, -2.554434421962928], [-11.0, 0]], [[1.0, 0], [-5.477106886377047, 0], [13.0, 0]], [[1.0, 0], [0, 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['1.19162965239034999087776471512595', '2.34169601284022830775207065382808', '3.15511679872184560435257592611665', '3.73604700327661269757209242524654', '4.98117075158384369076160157358106', '6.05151993606923606190083182474920', '6.68122626469747173639442611634998', '7.61572194819950549265180057283278', '8.330249639394402300412170187429754', '9.101304744803129054051659083991741'], 'prelabel': '2-2240-40.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.22924225515243, 'root_angle': -0.0809001686576334, 'root_number': '0.96787600314719566026358185494905266215090213294832297834 - 0.25142800665759114343885832115200669397656607494501447461*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0404500843288167', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.19162965239034999087776471513', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.34169601284022830775207065383', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.15511679872184560435257592612', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.886490052766813, 'bad_primes': [2, 5, 7], 'central_character': '40.29', 'conductor': 2240, 'conductor_radical': 70, 'degree': 2, 'index': 48, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2240/2/l/d/1569/22'], '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': '2-2240-40.29-c1-0-48', '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': '2-2240-40.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.22924225515243, 'root_angle': -0.0404500843288167, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.19162965239034999087776471513', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1510570044102383522516967032350', 'Lhash_array': ['1510570044102383522516967032350'], 'label': '2-2240-40.29-c1-0-48', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2240/2/l/d/1569/22'}