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lfunc_lfunctions • Show schema
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{'Lhash': '1005883921195294504986286654985', 'a10': [0.0, 0.0], 'a2': [0.7922869913932613, 0.0], 'a3': [-1.0, 0.0], 'a4': [-1.3722813232690143, 0.0], 'a5': [0.0, 0.0], 'a6': [-0.7922869913932613, 0.0], 'a7': [2.5243377989621387, 0.0], 'a8': [-2.6718146237444933, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 72.46423983431198, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '9075.1', 'coefficient_field': 'CDF', 'conductor': 9075, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7922869913932613, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.5243377989621387, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-6.780726405493154, 0], [13.0, 0]], [[1.0, 0], [-6.6332495807108, 0], [17.0, 0]], [[1.0, 0], [7.72049022166877, 0], [19.0, 0]], 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0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 126, 'label': '2-9075-1.1-c1-0-126', 'leading_term': '2.40277835168837749443090146701', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/9075/2/a/cw/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [2.4027783516883776, 2.393119158872081, 2.3641466214782967, 2.315883023595983, 2.2483888606216818, 2.1617961193452446, 2.0563515290024004, 1.9324667984509245, 1.7907724469571615, 1.632171668122149, 1.457890715390576, 1.2695225237109786, 1.0690606391092254, 0.8589209722799286, 0.6419493877306972, 0.4214136606405184, 0.20097886328920522, -0.015334226801190384, -0.22320757766600577, -0.4181005707901113, -0.5953397282929132, -0.750221835822827, -0.878128308194509, -0.9746481809088271, 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'4.99672592731418112094011424665125', '5.66873622369709269718786454739260', '6.03976655285249975037659850029520', '6.87936316253827048392877050206076', '7.912129035466897006319350063011144'], 'prelabel': '2-9075-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.512593014723068, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.793502500621380926403010043009', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.49516997226307554681809599781', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.82517452002750547873990118415', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 72.46423983431198, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 9075, 'conductor_radical': 165, 'degree': 2, 'index': 126, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9075/2/a/cw/1/3'], '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': '2-9075-1.1-c1-0-126', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-9075-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.512593014723068, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.793502500621380926403010043009', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1005883921195294504986286654985', 'Lhash_array': ['1005883921195294504986286654985'], 'label': '2-9075-1.1-c1-0-126', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9075/2/a/cw/1/3'}