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lfunc_lfunctions • Show schema
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{'Lhash': '1519407192953365966212426696701', 'a10': [0, 0], 'a2': [1.4142135623730951, 0], 'a3': [0, 1.7320508075688772], 'a4': [2.0, 0], 'a5': [0, 0], 'a6': [0, 2.449489742783178], 'a7': [0.8532176147806924, -6.947806826749571], 'a8': [2.8284271247461903, 0], 'a9': [-3.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.61042775783118, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.4142135623730951, 0]]], [3, [[1.0, 0], [0, -1.7320508075688772]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.8532176147806924, 6.947806826749571]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1050.601', 'coefficient_field': 'CDF', 'conductor': 1050, 'conductor_radical': 210, 'conjugate': '1169544737494185410050090717741', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.4142135623730951, 0]], [[1.0, 0], [0, -1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.8532176147806924, 6.947806826749571]], [[1.0, 0], 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0.6149646947647102, 0.3946389093774144, 0.14192219210335022, -0.1168871037240136], 'positive_zeros': ['1.19860093363250882577272438285892', '2.44827555866032364155504977619421', '3.30302378784278220076602761500055', '4.57165321641677291367542774596416', '5.62316461568368475069672308641803', '6.11751460816205523785188869656793', '7.07927223809592867581793438535175', '8.145979249620987237545000224167710', '8.608082779417859172081043545514663', '9.816476552199578528242316586118382'], 'prelabel': '2-1050-7.6-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.348871634076778, 'root_angle': 0.03889494605234016, 'root_number': '0.99254383239279588613635661910445885751605454443501269951 + 0.1218882306829560464535922949977411425342738916850589300*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.01944747302617008', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.19860093363250882577272438286', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.44827555866032364155504977619', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.30302378784278220076602761500', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 28.61042775783118, 'bad_primes': [2, 3, 5, 7], 'central_character': '7.6', 'conductor': 1050, 'conductor_radical': 210, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1050/3/f/e/601/15'], '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': '2-1050-7.6-c2-0-34', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-1050-7.6-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.348871634076778, 'root_angle': 0.01944747302617008, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.19860093363250882577272438286', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1519407192953365966212426696701', 'Lhash_array': ['1519407192953365966212426696701'], 'label': '2-1050-7.6-c2-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1050/3/f/e/601/15'}