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lfunc_lfunctions • Show schema
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{'Lhash': '4152817659920058010557366076958', 'a10': [9.575507653592549, 1.221590464344673e-60], 'a2': [2.0, -3.4641016151377544], 'a3': [14.696938456699069, -5.196152422706632], 'a4': [-8.0, -13.856406460551018], 'a5': [1.1969384566990686, 2.0731582205358676], 'a6': [11.393876913398136, -61.303993090844685], 'a7': [25.848469228349533, -44.770862001382085], 'a8': [-64.0, 0.0], 'a9': [189.0, -152.73506473629428], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.8869087566336518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-2.0, 3.4641016151377544]]], [3, [[1.0, 0], [-14.696938456699069, 5.196152422706632]]]], 'bad_primes': [2, 3], 'central_character': '18.7', 'coefficient_field': 'CDF', 'conductor': 18, 'conductor_radical': 6, 'conjugate': '2647505226657465402487347849210', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.0, 3.4641016151377544]], [[1.0, 0], [-14.696938456699069, 5.196152422706632]], [[1.0, 0], 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'7.82096121188874813614081769065562', '8.915779079601797956667019923252011', '10.86555498261630164020485736686043', '13.07345333670908913539755920854109', '13.91870354183291055219471895791500', '15.42430084666835328961304996437055', '16.01295061274648738798662263328712', '17.86105684230720304584628448099043'], 'prelabel': '2-18-9.7-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.699090567519475, 'root_angle': 0.3392086596167701, 'root_number': '0.48393074209907105 + 0.8751063003152488*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.169604329808', 'prec': 47}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.27599549842234091842542519150', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.50062149911938647193123872670', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.82096121188874813614081769066', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.8869087566336518, 'bad_primes': [2, 3], 'central_character': '9.7', 'conductor': 18, 'conductor_radical': 6, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/18/6/c/a/7/2'], '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': '2-18-9.7-c5-0-3', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-18-9.7-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.699090567519475, 'root_angle': 0.16960432980838505, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '3.27599549842234091842542519150', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4152817659920058010557366076958', 'Lhash_array': ['4152817659920058010557366076958'], 'label': '2-18-9.7-c5-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/6/c/a/7/2'}