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lfunc_lfunctions • Show schema
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{'Lhash': '1221230488494523687669002986642', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-9.0, 0], 'a4': [0, 0], 'a5': [0, 83.5169408720482], 'a6': [0, 0], 'a7': [0, 187.36694333639812], 'a8': [0, 0], 'a9': [81.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 100.07950356329994, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [9.0, 0]]], [13, [[1.0, 0], [-259.9087564856141, -551.1265175094569]]]], 'bad_primes': [2, 3, 13], 'central_character': '624.337', 'coefficient_field': 'CDF', 'conductor': 624, 'conductor_radical': 78, 'conjugate': '193818542377696024677942719070', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [9.0, 0]], [[1.0, 0], [0, -83.5169408720482], [-3125.0, 0]], [[1.0, 0], [0, -187.36694333639812], [-16807.0, 0]], [[1.0, 0], [0, 786.3336386201817], [-161051.0, 0]], [[1.0, 0], [-259.9087564856141, -551.1265175094569]], [[1.0, 0], [-923.7874177969393, 0], [1419857.0, 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-0.6558283869363384, -1.0372396361068266, -1.306469024533449], 'positive_zeros': ['0.963380988637288398884528926224540', '1.69403688479111205930761129494234', '3.77461463984287523264616705416484', '4.53393065547026563146123251789265', '5.22403859408740727997270386529115', '6.35633110555998602886420698710128', '7.61644291505357854844930632169111', '7.903098977010899854913347713937136', '9.364807326295470978875590298694081', '10.01733038620624437497611249574412'], 'prelabel': '2-624-13.12-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.003974388376848, 'root_angle': 0.35973138067111204, 'root_number': '0.426542716636761659994268258923175373344707576106705994 + 0.904467418365156616213204364875032769234659989850476722*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.17986569033555602', 'prec': 64}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.963380988637288398884528926225', 'prec': 107}, 'z2': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 100.07950356329994, 'bad_primes': [2, 3, 13], 'central_character': '13.12', 'conductor': 624, 'conductor_radical': 78, 'degree': 2, 'index': 47, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/624/6/c/f/337/7'], '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': '2-624-13.12-c5-0-47', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-624-13.12-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.003974388376848, 'root_angle': 0.17986569033555602, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.963380988637288398884528926225', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1221230488494523687669002986642', 'Lhash_array': ['1221230488494523687669002986642'], 'label': '2-624-13.12-c5-0-47', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/624/6/c/f/337/7'}