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lfunc_lfunctions • Show schema
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{'Lhash': '3717752967789786984468130753754', 'a10': [19.17885704861269, 11.496583940844312], 'a2': [1.4142135623730951, 1.4142135623730951], 'a3': [2.0116967252593523, -4.790936890168853], 'a4': [0.0, 4.0], 'a5': [10.845406169766411, -2.716093704715036], 'a6': [9.62037671879369, -3.930439134307053], 'a7': [-16.17885704861269, 16.17885704861269], 'a8': [-5.656854249492381, 5.656854249492381], 'a9': [-18.906152571161595, -19.275824105753813], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7700573001722193, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.4142135623730951, -1.4142135623730951]]], [3, [[1.0, 0], [-2.0116967252593523, 4.790936890168853]]], [5, [[1.0, 0], [-10.845406169766411, 2.716093704715036]]]], 'bad_primes': [2, 3, 5], 'central_character': '30.23', 'coefficient_field': 'CDF', 'conductor': 30, 'conductor_radical': 30, 'conjugate': '3342594945876676989265118881418', 'degree': 2, 'euler_factors': 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[{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/30/4/e/a/23/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [1.6859491326179137, 1.6890819101360075, 1.6931533068722815, 1.6966855827092957, 1.6971862168572998, 1.691299555363229, 1.6750037612862239, 1.643850403462099, 1.5932476279941004, 1.518789354273782, 1.4166308266844116, 1.2839049709699804, 1.1191651200725554, 0.9228290097520765, 0.6975878970460345, 0.44873471705486495, 0.18435794843315959, -0.08465505153815918, -0.3448584563451526, -0.5807750097880444, -0.775734061186305, -0.9130181223556794, -0.9772812170117259, -0.9561627625790512, -0.8419793876864207, -0.6333386651622208, -0.3364889105376591, 0.03379591912443857, 0.45399177310720845, 0.8924254970148716, 1.31080819167994, 1.6667230627132177, 1.9169830165186492, 2.0216532423662743, 1.9484137816413436, 1.6768326793148027, 1.202049315989412, 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'root_analytic_conductor': 1.3304350041141504, 'root_angle': -0.02536105634362312, 'root_number': '0.9968276969050557 - 0.07958984032502159*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0126805281718', 'prec': 54}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.93278997155875450581078334757', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.73115582973570092952389375873', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.62191064057652483505732774680', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.7700573001722193, 'bad_primes': [2, 3, 5], 'central_character': '15.8', 'conductor': 30, 'conductor_radical': 30, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/30/4/e/a/23/5'], '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': '2-30-15.8-c3-0-4', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-30-15.8-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3304350041141504, 'root_angle': -0.01268052817181156, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.93278997155875450581078334757', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3717752967789786984468130753754', 'Lhash_array': ['3717752967789786984468130753754'], 'label': '2-30-15.8-c3-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/30/4/e/a/23/5'}