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lfunc_lfunctions • Show schema
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{'Lhash': '4884587312533140388355016419594', 'a10': [-3.79128784747792, 0.0], 'a2': [0.0, -1.0], 'a3': [-2.79128784747792, 0.0], 'a4': [-1.0, 0.0], 'a5': [0.0, -3.79128784747792], 'a6': [0.0, 2.79128784747792], 'a7': [-2.0, 0.0], 'a8': [0.0, 1.0], 'a9': [4.79128784747792, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [37, [[1.0, 0], [-4.0, -4.58257569495584]]]], 'bad_primes': [2, 37], 'central_character': '74.73', 'coefficient_field': 'CDF', 'conductor': 74, 'conductor_radical': 74, 'conjugate': '1090424961078908481949437335412', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [2.79128784747792, 0], [3.0, 0]], [[1.0, 0], [0, 3.79128784747792], [-5.0, 0]], [[1.0, 0], [2.0, 0], [7.0, 0]], [[1.0, 0], [-3.79128784747792, 0], [11.0, 0]], [[1.0, 0], [0, -0.79128784747792], [-13.0, 0]], [[1.0, 0], [0, 1.58257569495584], 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'10.60372255719571875243541001958686', '11.61663988693689817395718213544293', '12.69090853689407699925217616715432', '14.23068044913168063095737893912014', '15.03541603439504904094907466769774'], 'prelabel': '2-74-37.36-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, 'root_angle': 0.7715734282458674, 'root_number': '-0.7533708035008841 + 0.657595949221429*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.385786714123', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.85325996899596242988396231979', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.02007695550803456404350041039', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.33636746403213413824536341217', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'bad_primes': [2, 37], 'central_character': '37.36', 'conductor': 74, 'conductor_radical': 74, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/74/2/b/a/73/1'], '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': '2-74-37.36-c1-0-3', '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': '2-74-37.36-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, 'root_angle': 0.3857867141229337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.85325996899596242988396231979', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4884587312533140388355016419594', 'Lhash_array': ['4884587312533140388355016419594'], 'label': '2-74-37.36-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/74/2/b/a/73/1'}