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lfunc_lfunctions • Show schema
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{'Lhash': '536673171449891376287383357484', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 28.0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 53.10171900516658, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '900.649', 'coefficient_field': 'CDF', 'conductor': 900, 'conductor_radical': 30, 'conjugate': '1678790607360723866404418389686', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -28.0], [-343.0, 0]], [[1.0, 0], [-24.0, 0], [1331.0, 0]], [[1.0, 0], [0, 70.0], [-2197.0, 0]], [[1.0, 0], [0, -102.0], [-4913.0, 0]], [[1.0, 0], [20.0, 0], [6859.0, 0]], [[1.0, 0], [0, -72.0], [-12167.0, 0]], [[1.0, 0], [-306.0, 0], [24389.0, 0]], [[1.0, 0], [136.0, 0], [29791.0, 0]], [[1.0, 0], 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'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/900/4/d/h/649/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.5698748016771158, 1.37229032374173, 1.1633670536283771, 0.9458737450744125, 0.7226948504742484, 0.4968126895702645, 0.27128792714831773, 0.04923763630683255, -0.16618970625146529, -0.371842833826863, -0.5646003018872726, -0.7414073040857849, -0.8993166866407755, -1.0355339259076566, -1.1474655935048061, -1.2327705905459643, -1.2894131959420547, -1.315716751874414, -1.310416610704362, -1.272710799713905, -1.2023067306211994, -1.0994621965973863, -0.9650188665462294, -0.8004265097365022, -0.6077562673708707, -0.38970143382988726, -0.14956442005855228, 0.10877115600186989, 0.3808839747147192, 0.6618744512698187, 0.9464400037459626, 1.2289655792752678, 1.5036283639559636, 1.7645150875270108, 2.0057498206787554, 2.221629667892848, 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'primitive': True, 'rational': False, 'root_analytic_conductor': 7.287092630477987, 'root_angle': -0.6475836176504333, 'root_number': '-0.4472135954999579392818347337462552470881236719223051449 - 0.8944271909999158785636694674925104941762473438446102897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.32379180882521663', 'prec': 67}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.42336048383779257978793941050', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.55779943933213546956746539738', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.01550772510457730470272697926', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 53.10171900516658, 'bad_primes': [2, 3, 5], 'central_character': '5.4', 'conductor': 900, 'conductor_radical': 30, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/900/4/d/h/649/2'], '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': '2-30e2-5.4-c3-0-2', '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': '2-30e2-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.287092630477987, 'root_angle': -0.32379180882521663, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.42336048383779257978793941050', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '536673171449891376287383357484', 'Lhash_array': ['536673171449891376287383357484'], 'label': '2-30e2-5.4-c3-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/900/4/d/h/649/2'}