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lfunc_lfunctions • Show schema
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{'Lhash': '1393797241892250321622560571780', 'a10': [-0.7193548914554571, 2.0784394609510155], 'a2': [1.4226244727375639, -0.7334138898862809], 'a3': [-0.7860530947427875, 0.6181589862206052], 'a4': [0.3258506374113095, -0.4575931926950805], 'a5': [-0.9945240376457353, 0.9482767545253027], 'a6': [-0.6648919827999744, 1.4559103597125325], 'a7': [1.6927227193830916, -2.0333936646120225], 'a8': [-0.32760578727241674, 2.27854829939678], 'a9': [0.23575893550942723, -0.9718115683235417], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.7860530947427875, -0.6181589862206052]]], [7, [[1.0, 0], [-1.6927227193830916, 2.0333936646120225]]], [23, [[1.0, 0], [-4.786212232215646, -0.3035991900340437]]]], 'bad_primes': [3, 7, 23], 'central_character': '483.163', 'coefficient_field': 'CDF', 'conductor': 483, 'conductor_radical': 483, 'conjugate': '2260606881496821746754366963863', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.4226244727375639, 0.7334138898862809], [1.1601138191423963, -1.6291519041006715]], [[1.0, 0], [0.7860530947427875, -0.6181589862206052]], [[1.0, 0], [0.9945240376457353, -0.9482767545253027], [0.2379095791187115, -4.99433669591504]], [[1.0, 0], [-1.6927227193830916, 2.0333936646120225]], [[1.0, 0], [-3.161634776427211, -1.6299360120785555], [6.38062600528318, 8.960335472553693]], [[1.0, 0], [-3.841662532108947, -4.433514903180343], [-1.850092897552707, 12.867678744452126]], [[1.0, 0], [4.093737837641213, -0.39090456731814566], [16.692787853466015, -3.2172711541269736]], [[1.0, 0], [0.8045020561049884, 0.07682063205334187], [18.656645247991428, 3.595773642847794]], [[1.0, 0], [-4.786212232215646, -0.3035991900340437]], [[1.0, 0], [-1.0034340979456722, 2.197214188590093], [-18.990961284413267, -21.91673765627349]], [[1.0, 0], [-2.883455665932342, 1.1543615149507167], [22.435755181257175, 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'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': -0.15555352983767948, 'root_number': '0.88295058054887 - 0.46946594371521083*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0777767649188', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09951215393367014601020819886', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.20630120331406265357319267159', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.47600084426957177066800226531', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'bad_primes': [3, 7, 23], 'central_character': '161.2', 'conductor': 483, 'conductor_radical': 483, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/483/2/y/b/163/13'], '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': '2-483-161.2-c1-0-14', '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': '2-483-161.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': -0.07777676491883974, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.09951215393367014601020819886', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1393797241892250321622560571780', 'Lhash_array': ['1393797241892250321622560571780'], 'label': '2-483-161.2-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/483/2/y/b/163/13'}