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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_547.53', 'a10': [-0.9287562401253023, 0.3706910390450675], 'a2': [-0.9448296081386656, 0.32756222551529895], 'a3': [-0.2225209339563144, -0.9749279121818236], 'a4': [0.7854059768309288, -0.6189809783492982], 'a5': [0.9989407761421107, -0.04601440818480051], 'a6': [0.5295939234638565, 0.8482513048797266], 'a7': [0.9830972584622324, 0.18308408014910135], 'a8': [-0.5393200344991992, 0.8421008849228118], 'a9': [-0.9009688679024191, 0.4338837391175581], 'algebraic': True, 'analytic_conductor': 2.540257320534655, 'analytic_normalization': 0, 'bad_lfactors': [[547, [1]]], 'bad_primes': [547], 'central_character': '547.53', 'coeff_info': ['x^273 - 1', '0.999735158965141 + 0.0230132989583119*I', '\\\\zeta_{273}'], 'conductor': 547, 'conductor_radical': 547, 'conjugate': 'dirichlet_L_547.289', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^122', 'a^195', 'a^244', 'a^271', 'a^44', 'a^8', 'a^93', 'a^117', 'a^120', 'a^77', 'a^166', 'a^221', 'a^130', 'a^193', 'a^215', 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'195.97066420951862094827828360205', '196.62671604996077697889952972579', '197.047697497578956308574147889963', '197.61088724911865689587965473397', '198.449911689791346897695924079643', '199.189706795488804828726364848419', '199.51166758142701133477344128852'], 'prelabel': '1-547-547.53-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.540257320534655, 'root_angle': -0.2546174371518499, 'root_number': '0.696775378630217025864456123538-0.717289391901704972346558976690*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.127308718576', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(273)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.851346347643521269755934419866-0.176966830752470075558036199836*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.942899420824', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.96190244195', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.58540409255', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.540257320534655, 'bad_primes': [547], 'central_character': '547.53', 'conductor': 547, 'conductor_radical': 547, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/547/53'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-547-547.53-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-547-547.53-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.540257320534655, 'root_angle': -0.12730871857592496, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.942899420824', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_547.53', 'Lhash_array': ['dirichlet_L_547.53'], 'label': '1-547-547.53-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/547/53'}