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lfunc_lfunctions • Show schema
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{'Lhash': '3636963150969033887608519401692', 'a10': [88.27822185373186, 0.0], 'a2': [-3.531128874149275, 0.0], 'a3': [13.593386622447824, 0.0], 'a4': [-19.531128874149275, 0.0], 'a5': [-25.0, 0.0], 'a6': [-48.0, 0.0], 'a7': [-49.0, 0.0], 'a8': [181.96305708501592, 0.0], 'a9': [-58.21984013265653, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.613433693454323, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [25.0, 0]]], [7, [[1.0, 0], [49.0, 0]]]], 'bad_primes': [5, 7], 'central_character': '35.1', 'coefficient_field': 'CDF', 'conductor': 35, 'conductor_radical': 35, 'conjugate': '3636963150969033887608519401692', 'degree': 2, 'euler_factors': [[[1.0, 0], [3.531128874149275, 0], [32.0, 0]], [[1.0, 0], [-13.593386622447824, 0], [243.0, 0]], [[1.0, 0], [25.0, 0]], [[1.0, 0], [49.0, 0]], [[1.0, 0], [691.5195007924797, 0], [161051.0, 0]], [[1.0, 0], [502.14983032991154, 0], [371293.0, 0]], [[1.0, 0], 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'positive_zeros': ['2.86905804352889549176612019967018', '4.90416902353730511480470986203155', '7.49083378784061391460195292366513', '8.457254639796722827613336821948178', '9.557668410900609873242043847863922', '10.83543312987410794957736278271303', '12.78101222722675327510565152481092', '13.69119822940869710538499628832269', '14.94808582298613532937978421080301'], 'prelabel': '2-35-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.369268598841069, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.86905804352889549176612019967', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.90416902353730511480470986203', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.49083378784061391460195292367', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.613433693454323, 'bad_primes': [5, 7], 'central_character': '1.1', 'conductor': 35, 'conductor_radical': 35, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/35/6/a/b/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': '2-35-1.1-c5-0-8', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-35-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.369268598841069, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '2.86905804352889549176612019967', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3636963150969033887608519401692', 'Lhash_array': ['3636963150969033887608519401692'], 'label': '2-35-1.1-c5-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/35/6/a/b/1/1'}