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lfunc_lfunctions • Show schema
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{'Lhash': '1058453162727299784973529968254', 'a10': [0, -8.5554709920982], 'a2': [0, -2.6709287611501553], 'a3': [0, 0], 'a4': [-5.133860447139104, 0], 'a5': [3.2031820228758345, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 8.37031800169472], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.5642081874154, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '1323.1322', 'coefficient_field': 'CDF', 'conductor': 1323, 'conductor_radical': 21, 'conjugate': '1729805448386935745796959476633', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.6709287611501553], [-2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.2031820228758345, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -4.063570503928894], [-11.0, 0]], [[1.0, 0], [0, -2.998620486725213], [-13.0, 0]], [[1.0, 0], [-2.5425495494569192, 0], [17.0, 0]], [[1.0, 0], [0, 0.1652993229337411], 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'5.30019487451808637572094064701533', '5.90889862889434803073879106191665', '6.20289103669361852511290104530397', '7.30766264815843300002758601965187', '8.146268921553860353416428668490692', '8.737335623231802020425733255300395', '9.616115835023916139679908551688716'], 'prelabel': '2-1323-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.250262787439717, 'root_angle': 0.4499601835622111, 'root_number': '0.1565580108156215421545904255253269822922515178137538237 + 0.987668764945746235695785342701200843915484362829692257*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.22498009178110556', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.834972320083100621018638902163', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.82757764577683708240378394099', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.18373421213912666596018209716', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.5642081874154, 'bad_primes': [3, 7], 'central_character': '21.20', 'conductor': 1323, 'conductor_radical': 21, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1323/2/c/f/1322/2'], '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': '2-1323-21.20-c1-0-21', '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': '2-1323-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.250262787439717, 'root_angle': 0.22498009178110556, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.834972320083100621018638902163', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1058453162727299784973529968254', 'Lhash_array': ['1058453162727299784973529968254'], 'label': '2-1323-21.20-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1323/2/c/f/1322/2'}