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lfunc_lfunctions • Show schema
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{'Lhash': '330818173041016919950287501128', 'a10': [0, 0], 'a2': [0, 0], 'a3': [3.4755484731284145, 3.862714435592508], 'a4': [0, 0], 'a5': [0.6237055409197864, -1.0802896858352995], 'a6': [0, 0], 'a7': [-10.080841909304873, 15.536300280298475], 'a8': [0, 0], 'a9': [-2.8411256218694922, 26.850102517509253], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.824641761928856, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-3.4755484731284145, -3.862714435592508]]], [7, [[1.0, 0], [10.080841909304873, -15.536300280298475]]]], 'bad_primes': [2, 3, 7], 'central_character': '336.257', 'coefficient_field': 'CDF', 'conductor': 336, 'conductor_radical': 42, 'conjugate': '2934959518379016369015145819133', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-3.4755484731284145, -3.862714435592508]], [[1.0, 0], [-0.6237055409197864, 1.0802896858352995], [-62.5, -108.25317547305482]], [[1.0, 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[-1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-336-21.5-c3-0-4', 'leading_term': '0.874156259464912234787841672370564551235866836473311099', '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/336/4/bc/d/257/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.8741562594649123, 0.6604768518300134, 0.44852680162222847, 0.2396787708369614, 0.03530552857285, -0.16321638917958597, -0.3545047515843283, -0.5371719320005962, -0.7098278502703932, -0.8710858813933685, -1.01957194936448, -1.1539369123851786, -1.272872227901981, -1.3751287658366693, -1.4595385186079524, -1.5250388395553656, -1.570698729435292, -1.5957465859154543, -1.5995987355355914, -1.5818879835104493, -1.5424913461426817, -1.481556075652156, -1.3995230501133233, 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'6.73077227159969238674231165222978', '7.974542046356813571624458160295403', '8.464571637361225100856178275397284', '9.807319686572748599357962344139711', '10.51833535998373708054093387009954'], 'prelabel': '2-336-21.5-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.452487143376032, 'root_angle': 0.9903344433942588, 'root_number': '-0.999539011473272196383183382728763903208234636313649853353 + 0.0303605754727052656162369978275118898717714136925581885*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.49516722169712946', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.26096952344869793127910113342', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.92054676043969794898203573390', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.20958424895438755211897050278', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.824641761928856, 'bad_primes': [2, 3, 7], 'central_character': '21.5', 'conductor': 336, 'conductor_radical': 42, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/336/4/bc/d/257/5'], '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': '2-336-21.5-c3-0-4', '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': '2-336-21.5-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.452487143376032, 'root_angle': 0.4951672216971294, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.26096952344869793127910113342', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '330818173041016919950287501128', 'Lhash_array': ['330818173041016919950287501128'], 'label': '2-336-21.5-c3-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/336/4/bc/d/257/5'}