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lfunc_lfunctions • Show schema
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{'Lhash': '3611374030549376890077903489615', 'a10': [-11.005159322219379, -19.061495091474235], 'a2': [1.0, -1.7320508075688772], 'a3': [-2.2467312283971053, -3.891452638535422], 'a4': [-2.0, -3.4641016151377544], 'a5': [5.5025796611096895, -9.530747545737118], 'a6': [-8.986924913588421, 1.9713556858627316e-60], 'a7': [-18.49323377586725, 1.0001522439722592], 'a8': [-8.0, 0.0], 'a9': [3.404397574690469, -5.896589568528154], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.086294140884059, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 1.7320508075688772]]], [7, [[1.0, 0], [18.49323377586725, -1.0001522439722592]]], [11, [[1.0, 0], [-5.5, -9.526279441628825]]]], 'bad_primes': [2, 7, 11], 'central_character': '154.23', 'coefficient_field': 'CDF', 'conductor': 154, 'conductor_radical': 154, 'conjugate': '626619091475422415491518399796', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 1.7320508075688772]], 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'6.48149549736111806778519359707772', '7.51553160221845447025200360553143', '9.156647428421606334938717614141635', '10.10535800568836981763797751057631', '10.80460691258233071814495916945454', '12.17572441257995565988115547461776', '13.21269617713243176886312303671540'], 'prelabel': '2-154-7.2-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.014348045744562, 'root_angle': -0.8707043875315696, 'root_number': '-0.9186312259305357 - 0.3951160218788415*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.435352193766', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.84887178683083539520168924372', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.21593794753903874807638667769', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.57392744124917705366604165490', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.086294140884059, 'bad_primes': [2, 7, 11], 'central_character': '7.2', 'conductor': 154, 'conductor_radical': 154, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/154/4/e/c/23/2'], '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': '2-154-7.2-c3-0-18', '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': '2-154-7.2-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.014348045744562, 'root_angle': -0.4353521937657848, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.84887178683083539520168924372', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3611374030549376890077903489615', 'Lhash_array': ['3611374030549376890077903489615'], 'label': '2-154-7.2-c3-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/154/4/e/c/23/2'}