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lfunc_lfunctions • Show schema
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{'Lhash': '2360921445786251147084481909900', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -15.588457268119896], 'a4': [32.0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [-243.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.57642151250816, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 15.588457268119896]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '147.146', 'coefficient_field': 'CDF', 'conductor': 147, 'conductor_radical': 21, 'conjugate': '777315534292912285246254340658', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-32.0, 0]], [[1.0, 0], [0, 15.588457268119896]], [[1.0, 0], [0, 0], [3125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-161051.0, 0]], [[1.0, 0], [0, 1141.4214821878902], [-371293.0, 0]], [[1.0, 0], [0, 0], [1419857.0, 0]], [[1.0, 0], [0, 161.0807251039056], [-2476099.0, 0]], [[1.0, 0], [0, 0], [-6436343.0, 0]], [[1.0, 0], [0, 0], 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'10.52176348900673877468694182112004', '11.49734065026930261320698469912410', '12.05209667589065974776508992130437'], 'prelabel': '2-147-21.20-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.855555736731704, 'root_angle': 0.7271855258285052, 'root_number': '-0.6546536707079771437982924562468583555692080823954245576 + 0.7559289460184544544290330724683601216315026237378429087*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3635927629142526', 'prec': 60}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.86243862887864202761484032072', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.33781404314844089602731556852', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.61818483850676143900332679746', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.57642151250816, 'bad_primes': [3, 7], 'central_character': '21.20', 'conductor': 147, 'conductor_radical': 21, 'degree': 2, 'index': 52, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/147/6/c/a/146/1'], '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': '2-147-21.20-c5-0-52', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-147-21.20-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.855555736731704, 'root_angle': 0.3635927629142526, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.86243862887864202761484032072', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2360921445786251147084481909900', 'Lhash_array': ['2360921445786251147084481909900'], 'label': '2-147-21.20-c5-0-52', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/147/6/c/a/146/1'}