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lfunc_lfunctions • Show schema
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{'Lhash': '1015455540423523017991551538920', 'a10': [0.0, 0.0], 'a2': [0.698938694557896, -0.44918062442533513], 'a3': [0.0, 0.0], 'a4': [-0.12866294761072453, 0.28173255684142967], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.6548607339452851, 0.7557495743542583], 'a8': [0.15486073394528507, 1.0770800629384238], 'a9': [-0.9594929736144974, -0.28173255684142967], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.848037741780008, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-0.6548607339452851, -0.7557495743542583]]], [23, [[1.0, 0], [0, 0]]]], 'bad_primes': [7, 23], 'central_character': '3703.1392', 'coefficient_field': 'CDF', 'conductor': 3703, 'conductor_radical': 161, 'conjugate': '2013918800956426621547912482824', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.698938694557896, 0.44918062442533513], [0.41541501300188644, -0.9096319953545183]], [[1.0, 0], [0, 0], [0.9594929736144974, 0.28173255684142967]], 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[-1.6143537075597825, 1.0374821311956879], [0.41541501300188644, -0.9096319953545183]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-3703-161.104-c0-0-4', 'leading_term': '1.68877222749429112745718434978', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3703/1/l/f/1392/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.6887722274942911, 1.6269613058190726, 1.572641161918996, 1.5228625176533985, 1.4741657318241752, 1.4228717259215156, 1.3653455860264885, 1.2982047962724896, 1.2184660896095114, 1.1236395048691812, 1.0117838912458377, 0.8815375033834801, 0.7321338982398903, 0.5634094529139398, 0.37580559667678176, 0.1703665861883462, -0.05126774459206026, -0.28687556999943603, -0.5336745916370013, -0.7883530759572056, -1.0471117879102285, 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'4.08373899483667326298675608506514', '5.02656655502578780356207087864102', '5.37782849012031554411862724686415', '6.35247704947148116322248291913717', '6.93472878378162833666245196308538', '7.76318505263070530218111071516628', '8.535926452707160811557331325151552'], 'prelabel': '2-3703-161.104-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3594255190263305, 'root_angle': -0.2935904482631465, 'root_number': '0.60395552035409220422144242207937 - 0.79701802328041347575585005759008*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.14679522413157325', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.801053176830192113565491968779', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.09845574106582462391295239088', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.39598790496021404620966804628', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.848037741780008, 'bad_primes': [7, 23], 'central_character': '161.104', 'conductor': 3703, 'conductor_radical': 161, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3703/1/l/f/1392/1'], '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': '2-3703-161.104-c0-0-4', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3703-161.104-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3594255190263305, 'root_angle': -0.14679522413157325, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.801053176830192113565491968779', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1015455540423523017991551538920', 'Lhash_array': ['1015455540423523017991551538920'], 'label': '2-3703-161.104-c0-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3703/1/l/f/1392/1'}