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lfunc_lfunctions • Show schema
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{'Lhash': '704263153989551762224605324228', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-3.1572021606244056, 0.0], 'a4': [0.0, 0.0], 'a5': [2.2201927896747695, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [6.967925483051416, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.16778306430095, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]], [41, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 7, 41], 'central_character': '8036.1', 'coefficient_field': 'CDF', 'conductor': 8036, 'conductor_radical': 574, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [3.1572021606244056, 0], [3.0, 0]], [[1.0, 0], [-2.2201927896747695, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.125002468100489, 0], [11.0, 0]], [[1.0, 0], [-2.309891404107559, 0], [13.0, 0]], [[1.0, 0], [2.2483306063195827, 0], [17.0, 0]], [[1.0, 0], [-1.9236823007619457, 0], [19.0, 0]], [[1.0, 0], 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'4.71837231466934828786941111536140', '5.15414179427919916216171903998014', '5.73219232895437186331061904487089', '6.40777012451440833722789688790128', '6.70770860922065067955378209838982', '7.75425580621249342500531828502380'], 'prelabel': '2-8036-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.010479577672047, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.55556566917000263484103601342', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.57574216860640521640354406639', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.44570811034960381317576534209', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.16778306430095, 'bad_primes': [2, 7, 41], 'central_character': '1.1', 'conductor': 8036, 'conductor_radical': 574, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8036/2/a/t/1/1'], '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': '2-8036-1.1-c1-0-27', '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': '2-8036-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.010479577672047, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.55556566917000263484103601342', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '704263153989551762224605324228', 'Lhash_array': ['704263153989551762224605324228'], 'label': '2-8036-1.1-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8036/2/a/t/1/1'}