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lfunc_lfunctions • Show schema
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{'Lhash': '2162486082498618245507909174284', 'a10': [938.4832776244069, 813.2003891707293], 'a2': [8.096937833925024, -5.203585980421486], 'a3': [2.218468775042499, -15.42978924982974], 'a4': [11.896534398686688, -26.049776691223954], 'a5': [36.34894080019265, 123.7931238303569], 'a6': [-62.32743126324928, -136.47803736225], 'a7': [399.32002958760484, -346.0127753009014], 'a8': [48.43780750185985, 336.89235110519047], 'a9': [-233.15679258832287, -68.46101131246742], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.873731769769721, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-2.218468775042499, 15.42978924982974]]], [23, [[1.0, 0], [11905.521527134075, -2508.8734856399487]]]], 'bad_primes': [3, 23], 'central_character': '69.34', 'coefficient_field': 'CDF', 'conductor': 69, 'conductor_radical': 69, 'conjugate': '1705826755414722817386480638915', 'degree': 2, 'euler_factors': [[[1.0, 0], [-8.096937833925024, 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9.838005275693966, 9.00822132896399, 7.548508411187483, 5.669110573577046, 3.63545728253757, 1.7216692282643806, 0.16376181545738425, -0.8786136112861299, -1.3448656763766857, -1.2767642728816662, -0.8024321642376114, -0.10494788843651189, 0.6175497212497327, 1.1918668512459536, 1.5017489884469488, 1.5056989908307168, 1.237662316334763, 0.7913837084061143, 0.2927369763454682, -0.1331921576213929, -0.39256117110110855, -0.4438634516231931], 'positive_zeros': ['1.70590072856769960367163723652026', '4.17809164550118701754089359454059', '5.01565350641605906649809706868777', '5.92900738601405694930879521389349', '7.78632997776625863407994453944811', '9.093733370451544766502096305618096', '10.14018829822798488956749359952728', '12.17091009291751374908968332756499', '12.45123219635644384214488221555375', '14.08985396058648469425983881824485'], 'prelabel': '2-69-23.11-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9841852077645337, 'root_angle': 0.3675715111416033, 'root_number': '0.40413811070901934 + 0.9146979760951395*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.183785755571', 'prec': 47}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.70590072856769960367163723652', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.17809164550118701754089359454', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.01565350641605906649809706869', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.873731769769721, 'bad_primes': [3, 23], 'central_character': '23.11', 'conductor': 69, 'conductor_radical': 69, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/69/7/f/a/34/19'], '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': '2-69-23.11-c6-0-18', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-69-23.11-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9841852077645337, 'root_angle': 0.18378575557080165, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '1.70590072856769960367163723652', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2162486082498618245507909174284', 'Lhash_array': ['2162486082498618245507909174284'], 'label': '2-69-23.11-c6-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/69/7/f/a/34/19'}