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lfunc_lfunctions • Show schema
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{'Lhash': '744065524398897701320314016476', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, -0.08647931008852482], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.67882563723714, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', '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': '8100.649', 'coefficient_field': 'CDF', 'conductor': 8100, 'conductor_radical': 30, 'conjugate': '960586950065135779320577370309', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0.08647931008852482], [-7.0, 0]], [[1.0, 0], [-0.9135206899114752, 0], [11.0, 0]], [[1.0, 0], [0, -2.6249865818372897], [-13.0, 0]], [[1.0, 0], [0, -2.086479310088525], [-17.0, 0]], [[1.0, 0], [4.938472920514738, 0], [19.0, 0]], [[1.0, 0], [0, 8.476980192263504], [-23.0, 0]], 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'2.62437178286639209039982698159086', '3.47310418290975718616008135051580', '4.16113057035459589422276546434032', '5.08925496586377511130375452102904', '5.61530449389149773368470751216551', '6.46172357572007415983995697413650', '7.03832625238680315570861566395357', '7.86016523101154801789090335179788'], 'prelabel': '2-90e2-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.042314693994332, 'root_angle': -0.07379180882521663, 'root_number': '0.8944271909999158785636694674925104941762473438446102897 - 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.07379180882521663', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58696420312106128655798756174', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.70227411346612584715228358013', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.62437178286639209039982698159', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.67882563723714, 'bad_primes': [2, 3, 5], 'central_character': '5.4', 'conductor': 8100, 'conductor_radical': 30, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8100/2/d/s/649/4'], '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': '2-90e2-5.4-c1-0-30', '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': '2-90e2-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.042314693994332, 'root_angle': -0.07379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.58696420312106128655798756174', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '744065524398897701320314016476', 'Lhash_array': ['744065524398897701320314016476'], 'factors': ['2-90e2-5.4-c1-0-30'], 'label': '2-90e2-5.4-c1-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8100/2/d/s/649/4'}