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lfunc_lfunctions • Show schema
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{'Lhash': '1072487868140195668360642119813', 'a10': [-37.40992905766792, 0.0], 'a2': [2.0, 0.0], 'a3': [-7.176926701687154, 0.0], 'a4': [4.0, 0.0], 'a5': [-18.70496452883396, 0.0], 'a6': [-14.353853403374307, 0.0], 'a7': [0.0, 0.0], 'a8': [8.0, 0.0], 'a9': [24.50827688139005, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 132.9903051529394, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-2.0, 0]]], [7, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [-23.0, 0]]]], 'bad_primes': [2, 7, 23], 'central_character': '2254.1', 'coefficient_field': 'CDF', 'conductor': 2254, 'conductor_radical': 322, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.0, 0]], [[1.0, 0], [7.176926701687154, 0], [27.0, 0]], [[1.0, 0], [18.70496452883396, 0], [125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [36.894867676204846, 0], [1331.0, 0]], [[1.0, 0], [22.790012344011565, 0], [2197.0, 0]], [[1.0, 0], [66.69409123534365, 0], [4913.0, 0]], [[1.0, 0], 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'3.54063398001694768403749582154198', '4.55500603692004924480532023663489', '4.92195948375850964002006743786170', '5.79175468821126784880144600066254', '6.65409063275538606004758090843768', '7.50722505410815247527426742746617', '7.81668494591790018903695330043354'], 'prelabel': '2-2254-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.532142262083806, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.846043750499627901839896537967', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.57879205759713552607542495647', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.54063398001694768403749582154', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 132.9903051529394, 'bad_primes': [2, 7, 23], 'central_character': '1.1', 'conductor': 2254, 'conductor_radical': 322, 'degree': 2, 'index': 92, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2254/4/a/l/1/2'], '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': '2-2254-1.1-c3-0-92', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-2254-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.532142262083806, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.846043750499627901839896537967', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1072487868140195668360642119813', 'Lhash_array': ['1072487868140195668360642119813'], 'factors': ['2-2254-1.1-c3-0-92'], 'label': '2-2254-1.1-c3-0-92', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2254/4/a/l/1/2'}