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lfunc_lfunctions • Show schema
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{'Lhash': '2492116389520305717896004637386', 'a10': [-0.7071067811865476, 0.819495500447568], 'a2': [-1.2633011408170578, 0.635665185148849], 'a3': [-1.0794708255183387, 2.6060731071524543], 'a4': [1.1918595447793592, -1.6060731071524543], 'a5': [0.7071067811865476, -0.2928932188134525], 'a6': [-0.2928932188134525, -3.9784371514842456], 'a7': [1.6855439326707928, -1.6855439326707928], 'a8': [-0.48475276359281166, 2.786577606704886], 'a9': [-3.5050394331183607, -3.5050394331183607], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.25552128646809735, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.2633011408170578, -0.635665185148849]]]], 'bad_primes': [2], 'central_character': '32.13', 'coefficient_field': 'CDF', 'conductor': 32, 'conductor_radical': 2, 'conjugate': '5865671050677948027066131722188', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.2633011408170578, -0.635665185148849]], [[1.0, 0], 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'positive_zeros': ['1.96593319095310802704015827057145', '6.03542308789259743903214383661633', '7.43248478488102221700541271465924', '8.615721821083829182468653933697167', '10.52658754860998971080776408403349', '11.82818646825443887129531170663284', '12.48711000067748710808361182241514', '13.87399620616605496962080468136191', '15.78028704778179298679005002875580', '17.40897769943251374550937180754910'], 'prelabel': '2-2e5-32.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5054911339164094, 'root_angle': -0.4294591405298531, 'root_number': '0.21980116455301507 - 0.9755446930105962*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.214729570265', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.96593319095310802704015827057', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.03542308789259743903214383662', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.43248478488102221700541271466', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.25552128646809735, 'bad_primes': [2], 'central_character': '32.13', 'conductor': 32, 'conductor_radical': 2, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/32/2/g/b/13/1'], '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': '2-2e5-32.13-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': '2-2e5-32.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5054911339164094, 'root_angle': -0.21472957026492656, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.96593319095310802704015827057', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2492116389520305717896004637386', 'Lhash_array': ['2492116389520305717896004637386'], 'label': '2-2e5-32.13-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/32/2/g/b/13/1'}