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lfunc_lfunctions • Show schema
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{'Lhash': '1786619652440772558141819479133', 'a10': [0.0, 0.0], 'a2': [-1.5061824469076126, 2.073082288854671], 'a3': [1.7048596988969624, 0.5539424954853253], 'a4': [-1.4110506242404242, -4.342767276345619], 'a5': [0.0, 0.0], 'a6': [-3.716198129353389, 2.699975983469204], 'a7': [3.614849727459788, -1.1745358753738384], 'a8': [6.254104822428695, 2.032081839112286], 'a9': [0.17264332149368988, 0.1254327152412677], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1958860555852118, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-3.1948869259927086, -0.8903356277948562]]]], 'bad_primes': [5, 11], 'central_character': '275.224', 'coefficient_field': 'CDF', 'conductor': 275, 'conductor_radical': 55, 'conjugate': '2106491361199560606065178915695', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.5061824469076126, -2.073082288854671], [-0.6180339887498949, -1.902113032590307]], [[1.0, 0], 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-1.2655752114175907, -0.7513036848073819, 0.22528675753137098, 1.4136066005093404, 2.406397733322231, 2.7342725313863983], 'positive_zeros': ['1.40939439631007733408493097753035', '2.52768999716686690903569483837773', '3.55639606111170845414864348508355', '5.20539406878363757963061716023624', '7.52741896372073991047947564288401', '8.077957830000254947291985144049930', '8.841578559802135610886573580922180', '9.635621172882501441278780177003597', '10.66385361851648578171651839634299', '11.65672205864489682027423438868957'], 'prelabel': '2-275-55.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4818522381078392, 'root_angle': -0.5734736727322179, 'root_number': '-0.22878008835047214 - 0.9734781308146322*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.286736836366', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.40939439631007733408493097753', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.52768999716686690903569483838', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.55639606111170845414864348508', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1958860555852118, 'bad_primes': [5, 11], 'central_character': '55.4', 'conductor': 275, 'conductor_radical': 55, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/275/2/z/c/224/1'], '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': '2-275-55.4-c1-0-4', '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': '2-275-55.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4818522381078392, 'root_angle': -0.28673683636610897, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.40939439631007733408493097753', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1786619652440772558141819479133', 'Lhash_array': ['1786619652440772558141819479133'], 'label': '2-275-55.4-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/275/2/z/c/224/1'}