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lfunc_lfunctions • Show schema
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{'Lhash': '874473328642531582077429125384', 'a10': [0, 0], 'a2': [0, 1.0], 'a3': [0, 1.0], 'a4': [-1.0, 0], 'a5': [0, 0], 'a6': [-1.0, 0], 'a7': [0, 2.0], 'a8': [0, -1.0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.570828394149682, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.0]]], [3, [[1.0, 0], [0, -1.0]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1950.1249', 'coefficient_field': 'CDF', 'conductor': 1950, 'conductor_radical': 390, 'conjugate': '1786113523400978305720705886580', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -2.0], [-7.0, 0]], [[1.0, 0], [-4.0, 0], [11.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, -8.0], [-17.0, 0]], [[1.0, 0], [-6.0, 0], [19.0, 0]], [[1.0, 0], [0, 6.0], [-23.0, 0]], [[1.0, 0], [-4.0, 0], [29.0, 0]], [[1.0, 0], [0, 0], 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[1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1950/2/e/f/1249/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.670077939608031, 1.5336328884712047, 1.3946544351465837, 1.2534393012988663, 1.1102554096792545, 0.9654222592652404, 0.8193846355726756, 0.672774983654518, 0.5264609691527661, 0.38157603530875617, 0.239531949879847, 0.10201331712597782, -0.029045226758501814, -0.15149788762056737, -0.2630410411493483, -0.36127912983623506, -0.443801022819746, -0.5082645231511461, -0.5524864933738567, -0.5745358511198198, -0.5728264723831453, -0.5462068495389997, -0.49404320627904785, -0.41629269568096416, -0.3135633226162164, -0.1871573566766605, -0.0390952515770783, 0.12788252885123247, 0.3103378558284415, 0.5041828725515477, 0.7047541611336284, 0.906912887153085, 1.10516969418614, 1.2938320911689614, 1.4671710276693424, 1.6196023270115774, 1.74587768906222, 1.8412791296288187, 1.9018100381977288, 1.9243755545207215, 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-0.8524163823495667, 'root_number': '-0.89442719099991587856366946749251049417624734384461028971 - 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.42620819117478337', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.68983782162457881447637227363', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.53772617662272086988607589872', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.93028893992715558285640521905', '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': '5.4', 'conductor': 1950, 'conductor_radical': 390, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1950/2/e/f/1249/2'], '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': '2-1950-5.4-c1-0-12', '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': '2-1950-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9459888993951417, 'root_angle': -0.42620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.68983782162457881447637227363', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '874473328642531582077429125384', 'Lhash_array': ['874473328642531582077429125384'], 'label': '2-1950-5.4-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1950/2/e/f/1249/2'}