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lfunc_lfunctions • Show schema
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{'Lhash': '2106231274241214119714393499784', 'a10': [1.0, -1.7320508075688772], 'a2': [-0.5, 0.8660254037844386], 'a3': [0.5, -0.8660254037844386], 'a4': [-0.5, -0.8660254037844386], 'a5': [-2.0, 0.0], 'a6': [0.5, 0.8660254037844386], 'a7': [0.5, 0.8660254037844386], 'a8': [1.0, 0.0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, -0.8660254037844386]]], [3, [[1.0, 0], [-0.5, 0.8660254037844386]]], [7, [[1.0, 0], [-0.5, -0.8660254037844386]]], [13, [[1.0, 0], [1.5, -3.278719262151]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.295', 'coefficient_field': 'CDF', 'conductor': 546, 'conductor_radical': 546, 'conjugate': '740605407285500337517192996231', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [2.0, 0], [5.0, 0]], [[1.0, 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[-1.9105458270998632, 3.3091624427256665], [-33.5, -58.023702053557386]], [[1.0, 0], [-1.0894541729001368, -1.8869899799809653], [-35.5, 61.48780366869514]], [[1.0, 0], [-4.0, 0], [73.0, 0]], [[1.0, 0], [-13.178908345800274, 0], [79.0, 0]], [[1.0, 0], [-6.178908345800274, 0], [83.0, 0]], [[1.0, 0], [4.5, -7.794228634059948], [-44.5, -77.07626093681505]], [[1.0, 0], [-5.178908345800274, -8.970132382668563], [-48.5, 84.00446416709055]], [[1.0, 0], [3.1789083458002736, -5.506030767530808], [-50.5, -87.4685657822283]], [[1.0, 0], [8.178908345800274, 0], [103.0, 0]], [[1.0, 0], [9.589454172900137, -16.609421844316422], [-53.5, -92.66471820493493]], [[1.0, 0], [-4.0, 0], [109.0, 0]], [[1.0, 0], [9.178908345800274, 15.898335612944072], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-546-13.9-c1-0-8', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 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4.1323001530775665, 2.7602638923140135, 1.2093317025349786, -0.11766291996429587, -0.8940620294267115, -0.9695101631375342, -0.41339244119428276, 0.5132106255981186, 1.447983149456788, 2.0499928415954782, 2.1130093610906133, 1.6308865634153273, 0.792530254458064, -0.09184975767875933, -0.7075175737839483, -0.8538745399846154, -0.5225085680208987, 0.09431805971099093, 0.6696087806018736, 0.8604315463443245, 0.4384426783564125, -0.6146074154447383, -2.0823818938360374, -3.5726271711837887], 'positive_zeros': ['1.66152350960272933531137111645236', '3.26423483179434402926065797716080', '4.11893531363589770482950566249417', '4.94494751860031872216306115013377', '6.64646963877933473075456209286646', '7.76659180068789645909828552231612', '8.240579418026804574474824537766278', '9.475998439311390433559590264201842', '10.00230279821300597157895990155913', '10.97824405833601616701795341154625'], 'prelabel': '2-546-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.38861812631626375, 'root_number': '0.3428193461943569 + 0.9394013497301745*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.194309063158', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.66152350960272933531137111645', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.26423483179434402926065797716', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.11893531363589770482950566249', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '13.9', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/l/k/295/2'], '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': '2-546-13.9-c1-0-8', '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': '2-546-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.19430906315813187, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.66152350960272933531137111645', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2106231274241214119714393499784', 'Lhash_array': ['2106231274241214119714393499784'], 'label': '2-546-13.9-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/l/k/295/2'}