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lfunc_lfunctions • Show schema
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{'Lhash': '1839378020989566524266553187189', 'a10': [3.9038820320220755, 6.761722026217466], 'a2': [-0.3797064023253841, 0.21922359359558485], 'a3': [1.8423292192132454, 3.191007811946041], 'a4': [-3.9038820320220755, 6.761722026217466], 'a5': [0.0, -17.80776406404415], 'a6': [-1.3990883994527907, -0.8077640640441514], 'a7': [4.709833421247577, 2.719223593595585], 'a8': [0.0, -6.930869689661812], 'a9': [6.711646096066227, -11.624912040808011], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.971322790970168, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[13, [[1.0, 0], [0, 0]]]], 'bad_primes': [13], 'central_character': '169.23', 'coefficient_field': 'CDF', 'conductor': 169, 'conductor_radical': 13, 'conjugate': '1195089000578688059007316407291', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.3797064023253841, -0.21922359359558485], [4.0, -6.928203230275509]], [[1.0, 0], [-1.8423292192132454, -3.191007811946041], [-13.5, 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'9.472195319188194044972502599831404', '10.52886900369382060526098909828315', '10.98302949629026934917012339909255', '12.42717192599003141065051955902215'], 'prelabel': '2-13e2-13.10-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.157740139873794, 'root_angle': 0.08129238194076664, 'root_number': '0.9675654653395972 + 0.2526204074934736*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0406461909704', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.45101341068146270114417406577', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.88822270051944047622947185141', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.62712156217080825869590955680', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.971322790970168, 'bad_primes': [13], 'central_character': '13.10', 'conductor': 169, 'conductor_radical': 13, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/169/4/e/g/23/2'], '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': '2-13e2-13.10-c3-0-21', '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': '2-13e2-13.10-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.157740139873794, 'root_angle': 0.04064619097038332, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.45101341068146270114417406577', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1839378020989566524266553187189', 'Lhash_array': ['1839378020989566524266553187189'], 'label': '2-13e2-13.10-c3-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/169/4/e/g/23/2'}