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lfunc_lfunctions • Show schema
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{'Lhash': '1549281443927982710591470153776', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.7560440518242527, 1.6555055496602549], 'a4': [0.0, 0.0], 'a5': [-2.7278032398369554, 3.1480527546811063], 'a6': [0.0, 0.0], 'a7': [1.7018477873843525, -1.0937111620321902], 'a8': [0.0, 0.0], 'a9': [-0.20451381482121414, -0.2360215241025767], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7346236985957799, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [-4.780450709765122, -0.38378511110533914]]]], 'bad_primes': [2, 23], 'central_character': '92.49', 'coefficient_field': 'CDF', 'conductor': 92, 'conductor_radical': 46, 'conjugate': '4414342072231847197566480557727', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.7560440518242527, -1.6555055496602549], [-1.9645822018358552, -2.267248723062775]], [[1.0, 0], [2.7278032398369554, -3.1480527546811063], [-0.7115741913664257, 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[-28.159011559647258, -32.497231697233104]], [[1.0, 0], [-9.109562060128601, 0], [47.0, 0]], [[1.0, 0], [-4.083926917019418, 2.624580463175749], [22.016995689099982, -48.21049575378947]], [[1.0, 0], [6.648299342394281, 4.272602551890682], [24.5094857671113, 53.668287725916585]], [[1.0, 0], [2.1990480722917995, 4.8152436076502925], [-39.946504770662386, 46.10072403560976]], [[1.0, 0], [0.33941558403128747, 2.360687240058321], [-64.28602923217133, 18.876081308375788]], [[1.0, 0], [-0.2003138237167383, -1.3932132462480153], [-68.12400112662931, 20.003011535741507]], [[1.0, 0], [-6.3023030250977, 1.8505231346942972], [61.41150789667623, -39.466779674258625]], [[1.0, 0], [14.802398916298607, 9.512924151983908], [32.817786027149026, 71.86092763300695]], [[1.0, 0], [6.674417601569188, 7.70268852593922], [-11.812131576682667, 82.15517967611741]], [[1.0, 0], [-5.33707326852115, 11.68656031835833], [-58.28260532113037, -67.26171211752899]], [[1.0, 0], [-6.501922393373881, 7.503618443684685], [-13.804539312508659, -96.01267986245047]], [[1.0, 0], [-4.315489510953815, -4.980340386855612], [-14.373798665601798, 99.9719656299742]], [[1.0, 0], [1.9482303041423812, -13.550239399908959], [-98.82777628229323, -29.01845335466726]], [[1.0, 0], [-1.6860320778815436, -3.6918952739634108], [-70.07009853214551, 80.86520445590564]], [[1.0, 0], [14.52322420820071, 4.264403390411562], [91.69663507859875, 58.929849102660135]], [[1.0, 0], [-0.37600166669710483, -2.6151490343198143], [-108.4227060184382, 31.835778923081556]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-92-23.3-c1-0-0', '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/92/2/e/a/49/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.7925811814276842, 0.7331704334148818, 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['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.22216756229914468491495340579', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.17651643449771260480765615458', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.46632332746696099202642608604', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7346236985957799, 'bad_primes': [2, 23], 'central_character': '23.3', 'conductor': 92, 'conductor_radical': 46, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/92/2/e/a/49/1'], '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': '2-92-23.3-c1-0-0', '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': '2-92-23.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8571019184413134, 'root_angle': -0.2541241675781718, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.22216756229914468491495340579', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1549281443927982710591470153776', 'Lhash_array': ['1549281443927982710591470153776'], 'label': '2-92-23.3-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/92/2/e/a/49/1'}