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lfunc_lfunctions • Show schema
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{'Lhash': '722994730362148881711032174663', 'a10': [3.0, 0.0], 'a2': [-1.7320508075688772, 0.0], 'a3': [0.0, 0.0], 'a4': [-5.0, 0.0], 'a5': [-1.7320508075688772, 0.0], 'a6': [0.0, 0.0], 'a7': [-13.856406460551018, 0.0], 'a8': [22.516660498395403, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 89.74190511873151, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': 'CDF', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.7320508075688772, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.7320508075688772, 0], [125.0, 0]], [[1.0, 0], [13.856406460551018, 0], [343.0, 0]], [[1.0, 0], [-13.856406460551018, 0], [1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-117.0, 0], [4913.0, 0]], [[1.0, 0], [-114.3153532995459, 0], [6859.0, 0]], [[1.0, 0], [78.0, 0], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 40, 'label': '2-39e2-1.1-c3-0-40', 'leading_term': '1.0037318720243189548795217602977', '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/1521/4/a/o/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.003731872024319, 0.9912662407425884, 0.9541144783341137, 0.8930103341456385, 0.8091711148500647, 0.7042888400655997, 0.5805170297630075, 0.4404523650192629, 0.2871103456464464, 0.12389401713424869, -0.04544513719405839, -0.21685494090922905, -0.3860395273840029, -0.548525966007545, -0.6997405522156556, -0.8350944189183169, -0.9500776986550226, -1.0403610076635634, -1.1019025524339445, -1.1310586951748192, -1.1246953768847536, -1.0802974057826555, -0.9960722949517167, -0.8710450956424997, -0.7051405397457706, 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'6.83742857468351378204704595839295', '7.77423134477657699827200500137728', '8.206063465790956996325082526316566', '9.327486932291249285724095862797442'], 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.57034227746350611523180720085', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.57727971356795834644781448684', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.22096572160771695183392359924', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 89.74190511873151, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'index': 40, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/4/a/o/1/1'], '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': '2-39e2-1.1-c3-0-40', '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': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.57034227746350611523180720085', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '722994730362148881711032174663', 'Lhash_array': ['722994730362148881711032174663'], 'label': '2-39e2-1.1-c3-0-40', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/4/a/o/1/1'}