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lfunc_lfunctions • Show schema
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{'Lhash': '2862277257528964811154095382844', 'a10': [4.608020735548774, 0.0], 'a2': [2.1832197461544998, 0.0], 'a3': [1.7584187567602252, 0.0], 'a4': [2.7664484599989176, 0.0], 'a5': [2.1106536543860477, 0.0], 'a6': [3.8390145517673697, 0.0], 'a7': [0.0, 0.0], 'a8': [1.6733254122793442, 0.0], 'a9': [0.09203652412617583, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [7, 13], 'central_character': '637.1', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '2862277257528964811154095382844', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.1832197461544998, 0], [2.0, 0]], [[1.0, 0], [-1.7584187567602252, 0], [3.0, 0]], [[1.0, 0], [-2.1106536543860477, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.768894090170476, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 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'3.88347837931537938364368641706154', '5.21774013402822909505358741877243', '5.64094557731621943140048115826898', '6.79374558171729159830936010030801', '7.897206772037433024041259848287373', '8.782647831158466788744230640033244', '9.767552868421186991330341901708828', '10.67802031495921849066054587245660'], 'prelabel': '2-637-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.25793862836781430891558143955', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.81676841237292859568487250860', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.88347837931537938364368641706', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '1.1', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 35, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/a/n/1/6'], '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': '2-637-1.1-c1-0-35', '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': '2-637-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.25793862836781430891558143955', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2862277257528964811154095382844', 'Lhash_array': ['2862277257528964811154095382844'], 'label': '2-637-1.1-c1-0-35', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/a/n/1/6'}