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lfunc_lfunctions • Show schema
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{'Lhash': '3168103333843600129258625553093', 'a10': [-1.953183041196372, 8.051130152867911], 'a2': [0.6792295239778572, -1.9625048254307564], 'a3': [0.4582265217274104, 0.8888354486549235], 'a4': [-1.8179662541102428, -1.4296644643219507], 'a5': [-3.971231910457765, 0.3792066696122323], 'a6': [2.055584839226137, -0.2955484813458655], 'a7': [0.9212234205465101, -2.4801910026118126], 'a8': [-0.5464388379562397, 0.35117491756368435], 'a9': [-0.5800569095711982, 0.8145759520503357], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.4582265217274104, -0.8888354486549235]]], [7, [[1.0, 0], [-0.9212234205465101, 2.4801910026118126]]], [23, [[1.0, 0], [-4.305169502196397, 2.113176650769648]]]], 'bad_primes': [3, 7, 23], 'central_character': '483.10', 'coefficient_field': 'CDF', 'conductor': 483, 'conductor_radical': 483, 'conjugate': 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[-3.7589713500756416, -78.91051979545763]], [[1.0, 0], [1.6337032405866132, 3.57731110345113], [-54.35344091745866, 62.72721467140344]], [[1.0, 0], [0.4037942317003111, -8.476684110198875], [-88.59700110900452, -8.459987854072256]], [[1.0, 0], [-1.2153128797947448, 2.6611640052178847], [-63.52149119269265, -73.30770871236305]], [[1.0, 0], [0.5216563700743271, -5.4630326656731025], [-99.17479842353337, -19.11437568040143]], [[1.0, 0], [-1.6694722076259028, -0.3217643945014406], [95.62189710065547, 38.28123293301373]], [[1.0, 0], [-4.563679994834274, 8.852304184477273], [-62.0660893241182, -87.15962686938592]], [[1.0, 0], [1.7158039929535833, -4.285871177299745], [-78.88701015345265, -75.21861225155021]], [[1.0, 0], [-10.72949535145139, 9.297160645730493], [16.08157672488122, -111.8498229325454]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 29, 'label': '2-483-161.10-c1-0-29', '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/483/2/bf/a/10/28', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.8081881948042858, 1.082705653413735, 1.3780818142940028, 1.6990264199352691, 2.046506977805618, 2.4169391866087655, 2.8018639359141266, 3.1880243334465703, 3.5577819018218646, 3.8898617725898297, 4.160446363301201, 4.344632580034515, 4.418234924471636, 4.359867027595235, 4.153177567170895, 3.789062445547467, 3.2676319437689516, 2.599687228200888, 1.8074620269794837, 0.9244176624963691, -0.006054819333225904, -0.9330745858733163, -1.8017797921025362, -2.557695301374063, -3.1516138107700535, -3.5445284506983885, -3.712076981014885, -3.6479356786039316, -3.3656477540799656, -2.898492045562069, -2.2971885185403824, -1.6254825863884086, -0.9539247212300828, -0.3524309718337578, 0.11756521749602208, 0.41041771994842685, 0.5020501662538981, 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'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': -0.8833745629546105, 'root_number': '-0.9336268368747018 - 0.3582470229706575*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.441687281477', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.49919286376956776396876662545', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.21436500325569975080952243460', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.78701512615799384354402755175', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.8567744176278445, 'bad_primes': [3, 7, 23], 'central_character': '161.10', 'conductor': 483, 'conductor_radical': 483, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/483/2/bf/a/10/28'], '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': '2-483-161.10-c1-0-29', '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': '2-483-161.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9638672097745928, 'root_angle': -0.44168728147730524, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.49919286376956776396876662545', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3168103333843600129258625553093', 'Lhash_array': ['3168103333843600129258625553093'], 'label': '2-483-161.10-c1-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/483/2/bf/a/10/28'}