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lfunc_lfunctions • Show schema
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{'Lhash': '2018124458228017895467205516393', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-5.196149825817556, -0.005194964502347477], 'a4': [0, 0], 'a5': [8.059065891100772, -13.958711584931887], 'a6': [0, 0], 'a7': [5.679086469297357, -17.628045180173658], 'a8': [0, 0], 'a9': [26.999946024687638, 0.05398762778800246], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.824641761928856, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [5.196149825817556, 0.005194964502347477]]], [7, [[1.0, 0], [-5.679086469297357, 17.628045180173658]]]], 'bad_primes': [2, 3, 7], 'central_character': '336.257', 'coefficient_field': 'CDF', 'conductor': 336, 'conductor_radical': 42, 'conjugate': '853009331211024049623062853646', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [5.196149825817556, 0.005194964502347477]], [[1.0, 0], [-8.059065891100772, 13.958711584931887], [-62.5, -108.25317547305482]], [[1.0, 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0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 34, 'label': '2-336-21.5-c3-0-34', 'leading_term': '1.517433305396592668835798578992541029332129503654649880', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/336/4/bc/d/257/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [1.5174333053965927, 1.6539058359178413, 1.7786127511477767, 1.8898336271751621, 1.985918261802274, 2.065291875335717, 2.1264656024660393, 2.16805261854346, 2.1887899478290462, 2.1875656993451598, 2.1634511781268935, 2.115737035286706, 2.0439723574275996, 1.948005361490818, 1.8280241610551375, 1.684595909679615, 1.5187025109354872, 1.3317710178990907, 1.125696831495572, 0.9028578513715851, 0.6661178386758324, 0.4188174202397874, 0.1647514000575962, -0.09186865299229896, 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'7.22766667499837987216089684769468', '8.750370127460112968721364728385373', '9.891891692609708537911578478133002', '10.45805620955342251187035548336059', '11.50687321005123966814204461487403'], 'prelabel': '2-336-21.5-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.452487143376032, 'root_angle': 0.6398695244784978, 'root_number': '-0.4254083663468157974016363788211167742065885397451237126 + 0.9050015037789348118473483940081956299104198859551186578*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3199347622392489', 'prec': 60}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.59201948696641822343299596588', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.92059807705488800198905509585', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.59848869606365800111307149004', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.824641761928856, 'bad_primes': [2, 3, 7], 'central_character': '21.5', 'conductor': 336, 'conductor_radical': 42, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/336/4/bc/d/257/1'], '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': '2-336-21.5-c3-0-34', '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': '2-336-21.5-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.452487143376032, 'root_angle': 0.3199347622392489, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.59201948696641822343299596588', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2018124458228017895467205516393', 'Lhash_array': ['2018124458228017895467205516393'], 'label': '2-336-21.5-c3-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/336/4/bc/d/257/1'}