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lfunc_lfunctions • Show schema
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{'Lhash': '1140753581359510655769805135807', 'a10': [0, 0], 'a2': [-0.5, 0.8660254037844386], 'a3': [-0.8660254037844386, -0.5], 'a4': [-0.5, -0.8660254037844386], 'a5': [0, 0], 'a6': [0.8660254037844386, -0.5], 'a7': [-2.366025403784439, -4.098076211353316], 'a8': [1.0, 0], 'a9': [0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.570828394149682, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, -0.8660254037844386]]], [3, [[1.0, 0], [0.8660254037844386, 0.5]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-0.2320508075688773, -3.598076211353316]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1950.199', 'coefficient_field': 'CDF', 'conductor': 1950, 'conductor_radical': 390, 'conjugate': '827236940691357572637556647491', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.366025403784439, 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'prelabel': '2-1950-65.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9459888993951417, 'root_angle': 0.06150066986048387, 'root_number': '0.9262641648144649158437223610756721051072976774306212530 + 0.3768749089294241866988208819399386368026220643324462946*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.061500669860483866', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.899895902825374714813872590449', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.36053324898845470639438050208', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.33767152909756901003176324416', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.570828394149682, 'bad_primes': [2, 3, 5, 13], 'central_character': '65.4', 'conductor': 1950, 'conductor_radical': 390, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1950/2/y/a/199/1'], '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': '2-1950-65.4-c1-0-19', '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': '2-1950-65.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9459888993951417, 'root_angle': 0.06150066986048387, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.899895902825374714813872590449', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1140753581359510655769805135807', 'Lhash_array': ['1140753581359510655769805135807'], 'factors': ['2-1950-65.4-c1-0-19'], 'label': '2-1950-65.4-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1950/2/y/a/199/1'}