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lfunc_lfunctions • Show schema
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{'Lhash': '1666539074339603444196383961605', 'a10': [0.3980897868116001, 1.658163297481701], 'a2': [-0.2667646159650939, -1.6842854981113178], 'a3': [0.0, 0.0], 'a4': [-1.814597762521932, 0.5895985537835376], 'a5': [-0.996917333733128, 0.07845909572784494], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.7029417004690527, 1.3796007660982177], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.4597651619515322, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.996917333733128, -0.07845909572784494]]], [13, [[1.0, 0], [-0.9876883405951378, -0.15643446504023087]]]], 'bad_primes': [3, 5, 13], 'central_character': '2925.2638', 'coefficient_field': 'CDF', 'conductor': 2925, 'conductor_radical': 195, 'conjugate': '769144260775052611509530525526', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.2667646159650939, 1.6842854981113178], [-0.9510565162951535, 0.30901699437494745]], [[1.0, 0], 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[0.9510565162951535, 0.30901699437494745]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-2925-325.38-c0-0-2', 'leading_term': '0.74987592201775652866370209409970', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2925/1/er/a/2638/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.7498759220177565, 0.8136869566526214, 0.8839772173982351, 0.9613497753621003, 1.04582724000134, 1.1368429310256065, 1.233273667186264, 1.3334947259383, 1.4354410288364572, 1.5366652624015937, 1.6343897385343826, 1.7255527583910348, 1.8068521033172038, 1.874788703078286, 1.9257131950385675, 1.955877442264132, 1.9614923676263276, 1.9387927899367885, 1.8841093486415181, 1.793947075831089, 1.6650697089847437, 1.4945884258941662, 1.2800533191326313, 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'6.40841487338747149679612153924580', '7.23510992889748587776234168788090', '7.61407447242019246944723227580428', '8.439891811136631572789462839813553', '8.986674201494742171845964755991842'], 'prelabel': '2-2925-325.38-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.208207416775585, 'root_angle': -0.9600000000000001, 'root_number': '-0.99211470131447783104979304278575 - 0.12533323356430424537311875981616*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.48', 'prec': 17}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.31466752276972665993886313193', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.17198057759203287069557669707', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.42283803442721487772942778831', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.4597651619515322, 'bad_primes': [3, 5, 13], 'central_character': '325.38', 'conductor': 2925, 'conductor_radical': 195, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2925/1/er/a/2638/1'], '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': '2-2925-325.38-c0-0-2', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-2925-325.38-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.208207416775585, 'root_angle': -0.48000000000000004, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.31466752276972665993886313193', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1666539074339603444196383961605', 'Lhash_array': ['1666539074339603444196383961605'], 'label': '2-2925-325.38-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2925/1/er/a/2638/1'}