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lfunc_lfunctions • Show schema
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{'Lhash': '1041322105976279726869568477378', 'a10': [-315.92565009908117, -13.819681959905731], 'a2': [-4.740639164757656, -3.086477006161852], 'a3': [-1.8155998055464246, 1.8155998055464246], 'a4': [12.947319380868342, 29.263747553069667], 'a5': [48.13573876915458, -28.424472785747653], 'a6': [14.210910597910736, -3.0032964934887967], 'a7': [-66.78790881601526, 0.0], 'a8': [28.94331460110438, -178.69047131814696], 'a9': [0.0, 236.40719469219957], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.830705585038453, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [4.740639164757656, 3.086477006161852]]], [5, [[1.0, 0], [-48.13573876915458, 28.424472785747653]]]], 'bad_primes': [2, 5], 'central_character': '80.29', 'coefficient_field': 'CDF', 'conductor': 80, 'conductor_radical': 10, 'conjugate': '1586522849932120395596320572234', 'degree': 2, 'euler_factors': [[[1.0, 0], [4.740639164757656, 3.086477006161852]], [[1.0, 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'prelabel': '2-80-80.29-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5819974295130996, 'root_angle': -0.05997070466894665, 'root_number': '0.9823044920198628 - 0.18729090997055678*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0299853523345', 'prec': 54}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.821458299147098412528441532335', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.75922534454767334050822510585', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.34215498178925685171822764776', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.830705585038453, 'bad_primes': [2, 5], 'central_character': '80.29', 'conductor': 80, 'conductor_radical': 10, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/80/6/q/a/29/11'], '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': '2-80-80.29-c5-0-22', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-80-80.29-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5819974295130996, 'root_angle': -0.029985352334473324, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.821458299147098412528441532335', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1041322105976279726869568477378', 'Lhash_array': ['1041322105976279726869568477378'], 'label': '2-80-80.29-c5-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/80/6/q/a/29/11'}