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lfunc_lfunctions • Show schema
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{'Lhash': '2893276115287581789923580761019', 'a10': [-0.2606118103373942, 0.4513928965568707], 'a2': [0.0, -0.4999866260092949], 'a3': [-0.424800749203603, 0.7357764807139646], 'a4': [1.7500133738118415, 0.0], 'a5': [-0.9028099414572724, -0.5212375627274265], 'a6': [0.3678784000891682, 0.21239469332053013], 'a7': [2.634907079128189, 0.23930040610111034], 'a8': [0.0, -1.8749565342619154], 'a9': [1.139088646952115, 1.972959410845951], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-2.634907079128189, -0.23930040610111034]]], [13, [[1.0, 0], [3.5750364856214603, 0.4680962790659202]]]], 'bad_primes': [7, 13], 'central_character': '91.23', 'coefficient_field': 'CDF', 'conductor': 91, 'conductor_radical': 91, 'conjugate': '2919770029741599017221086795252', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0.4999866260092949], [-2.0, 0]], [[1.0, 0], 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'7.993788606721441201525239310965092', '9.932774443759250510199029162230741', '11.12561083645861939869369257615955', '11.92118513877710938426060781466786', '12.86745599132455115972728932611168', '14.46419863401419939318891532825995'], 'prelabel': '2-91-91.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': 0.05418059157746057, 'root_number': '0.9855486496843238 + 0.16939261821403556*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0270902957887', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.28239241536009428385497676937', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.62307160903893714184466982493', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.20812773878653709232275452849', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'bad_primes': [7, 13], 'central_character': '91.23', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/2/k/b/23/3'], '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': '2-91-91.23-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': '2-91-91.23-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': 0.027090295788730286, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.28239241536009428385497676937', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2893276115287581789923580761019', 'Lhash_array': ['2893276115287581789923580761019'], 'label': '2-91-91.23-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/2/k/b/23/3'}