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lfunc_lfunctions • Show schema
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{'Lhash': '554203332100063902878357434720', 'a10': [-6.9078415788758045, 3.9882441950832352], 'a2': [2.2480463181674137, -1.2979101469447034], 'a3': [-1.5, 0.8660254037844386], 'a4': [1.3691414990840434, -2.3714226391645803], 'a5': [-3.072819951729025, 0.0], 'a6': [-2.2480463181674137, 3.8937304408341102], 'a7': [-4.266298338936697, 5.54965751044026], 'a8': [0.0, 3.2751905985005787], 'a9': [1.5, -2.598076211353316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.438711217036106, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.5, -0.8660254037844386]]], [7, [[1.0, 0], [4.266298338936697, -5.54965751044026]]], [13, [[1.0, 0], [9.118601096926438, -9.265587624923308]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.244', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '2989410054726296581736651026173', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.2480463181674137, 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[[1.0, 0], [43.92245166338124, -76.07591787396444], [-6384.5, -11058.278380923497]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-273-91.62-c2-0-6', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/273/3/bo/c/244/15', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.2146511685256671, 0.897206413254809, 0.556592007561452, 0.19128586803402503, -0.19967985805406419, -0.6159680798897899, -1.0552648168826113, -1.5127494612081955, -1.9807555475728045, -2.4486577601795494, -2.9030110187072053, -3.3279580180343116, -3.7059097901306517, -4.0184878108826005, -4.247695425685493, -4.377261901705573, -4.394076419316465, -4.289604846038837, -4.06116275631628, -3.7129075471056896, -3.2564140080734365, -2.710713896643536, -2.1017122304687303, 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'6.27946112737827686263644941666224', '7.29974279956187059610392164833980', '7.934238984995642718345902342358649', '9.783352158871361271222860798256707', '10.52808878180687860743004028313002', '11.82072689298269988642166115592611'], 'prelabel': '2-273-91.62-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7274000837860415, 'root_angle': -0.5398448134568482, 'root_number': '-0.12484953012700668 - 0.9921756874803301*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.269922406728', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.43718934223695743997508405746', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.17659313020711425189727113235', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.28182998214944525730480097335', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.438711217036106, 'bad_primes': [3, 7, 13], 'central_character': '91.62', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/3/bo/c/244/15'], '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': '2-273-91.62-c2-0-6', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-273-91.62-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7274000837860415, 'root_angle': -0.2699224067284241, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.43718934223695743997508405746', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '554203332100063902878357434720', 'Lhash_array': ['554203332100063902878357434720'], 'label': '2-273-91.62-c2-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/3/bo/c/244/15'}