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lfunc_lfunctions • Show schema
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{'Lhash': '1361065928488767362958728894140', 'a10': [0.0, 0.0], 'a2': [1.0728993766568748, -1.858316231778685], 'a3': [-2.661460776595966, 4.4628047833891635], 'a4': [1.6977738551385793, 2.940630576862102], 'a5': [0.0, 0.0], 'a6': [5.437822960025107, 9.733976231630141], 'a7': [11.628206767364656, -20.14064492199184], 'a8': [24.452552070040078, 0.0], 'a9': [-12.833253069282396, -23.75515976919023], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.275429751291645, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [2.661460776595966, -4.4628047833891635]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '225.151', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '1743660824893256880738504081922', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0728993766568748, 1.858316231778685], [-4.0, -6.928203230275509]], [[1.0, 0], [2.661460776595966, -4.4628047833891635]], 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1861.9846111445775], [-721448.5, 1249585.457044355]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 27, 'label': '2-15e2-9.7-c3-0-27', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/225/4/e/f/151/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.250658705569377, 2.1467486744458606, 1.9930165194491403, 1.7917066505578518, 1.5457859943268397, 1.2592914501375396, 0.9377148601846806, 0.5883719419839785, 0.22069862510797, -0.15358040301911646, -0.5204606438311139, -0.8638844514423357, -1.166212213076006, -1.4089475299496825, -1.5737049687438112, -1.643385176345128, -1.603496825898504, -1.4435399285514956, -1.158342990146475, -0.7492301704021788, -0.2248869571528366, 0.3982034231550947, 1.0958635648826645, 1.8369447423326672, 2.584703207350455, 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'8.234831817731694838886566225853971', '9.922535271797209236269019246411086', '11.10588421426745836167831072977550', '11.68381719116397045391322512618961'], 'prelabel': '2-15e2-9.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': -0.10210696658457033, 'root_number': '0.9489902416208023 - 0.3153054412922354*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0510534832923', 'prec': 54}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07369170041312594241777947219', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.54721445897063188406019456334', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.85663961485999195239295522058', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.275429751291645, 'bad_primes': [3, 5], 'central_character': '9.7', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/4/e/f/151/8'], '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': '2-15e2-9.7-c3-0-27', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-15e2-9.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': -0.051053483292285165, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.07369170041312594241777947219', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1361065928488767362958728894140', 'Lhash_array': ['1361065928488767362958728894140'], 'label': '2-15e2-9.7-c3-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/4/e/f/151/8'}