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lfunc_lfunctions • Show schema
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{'Lhash': '1371226403783801853648916709595', 'a10': [0.0, 0.0], 'a2': [0.23594189941983992, -0.4086633574294685], 'a3': [-0.5201106888687659, 0.9008581386803511], 'a4': [0.8886628401963163, 1.5392091900184819], 'a5': [0.0, 0.0], 'a6': [0.24543180768051603, 0.42510036069612717], 'a7': [1.1753981852081028, 0.0], 'a8': [1.7824587915183538, 0.0], 'a9': [0.9589697426489155, 1.6609843171891725], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-1.5703069024525993, -4.066218910992093]]]], 'bad_primes': [5, 19], 'central_character': '475.201', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'conjugate': '2422248891507781059511107614848', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.23594189941983992, 0.4086633574294685], [-1.0, -1.7320508075688772]], [[1.0, 0], [0.5201106888687659, -0.9008581386803511], [-1.5, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-475-19.11-c1-0-9', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/475/2/e/g/201/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.6384197752058605, 1.5188259231762877, 1.393754618400897, 1.2565289092598848, 1.0998018748297644, 0.9171197357481892, 0.7042932017787219, 0.4604761914903497, 0.1889331925107173, -0.10250872556048157, -0.4013480303602434, -0.6906838584304281, -0.9499298438135477, -1.1560006882536407, -1.2849673407683055, -1.3141229496303577, -1.2243391762661027, -1.0025289775618733, -0.6439765953415933, -0.15425778364597975, 0.4495376255452784, 1.1385454399347295, 1.873031913400268, 2.604566186950907, 3.2794297183428998, 3.843077263206901, 4.245304332754652, 4.445632422459589, 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'9.291299335324386699127312829795754', '9.817098590729338979690357670119703', '11.22071492552667083934818737963755'], 'prelabel': '2-475-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': -0.3517296281276135, 'root_number': '0.44914228162499925 - 0.8934602458177363*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.175864814064', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.08170690215184257773865194515', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.40906861509876142706981586935', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.33213738152750648849238929926', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '19.11', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/e/g/201/4'], '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': '2-475-19.11-c1-0-9', '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': '2-475-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': -0.17586481406380675, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.08170690215184257773865194515', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1371226403783801853648916709595', 'Lhash_array': ['1371226403783801853648916709595'], 'label': '2-475-19.11-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/e/g/201/4'}