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lfunc_lfunctions • Show schema
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{'Lhash': '131765251687767847741440409680', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-1.0, 0], 'a6': [0, 0], 'a7': [0, -4.6479323660930625], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 66.11613287362019, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [-2.230330334932171, 4.24565973637565]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '8280.1241', 'coefficient_field': 'CDF', 'conductor': 8280, 'conductor_radical': 690, 'conjugate': '1138646637657993851600743087809', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 4.6479323660930625], [-7.0, 0]], [[1.0, 0], [-3.8484137229574986, 0], [11.0, 0]], [[1.0, 0], [6.831075054996286, 0], [13.0, 0]], [[1.0, 0], [4.298288370284648, 0], [17.0, 0]], [[1.0, 0], [0, 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'2.61536906276129318127018955288039', '2.94433449934479477334050862916790', '4.26084102806689099513469619915513', '4.84907172913961990765620448677747', '5.39317622166987179363941993979400', '6.42811813225367282067921024722855', '6.80187900202195149184565553425762', '7.59395427254856676063155281826783'], 'prelabel': '2-8280-69.68-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.131182747523278, 'root_angle': -0.5419474548061359, 'root_number': '-0.1314007166034130815474667057065484543404982820462576790 - 0.9913293356277264539557104530703593646487075436379889588*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.270973727403068', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.10394445572308699796525927407', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.63704729800727634906097947501', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.61536906276129318127018955288', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 66.11613287362019, 'bad_primes': [2, 3, 5, 23], 'central_character': '69.68', 'conductor': 8280, 'conductor_radical': 690, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8280/2/p/a/1241/2'], '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': '2-8280-69.68-c1-0-4', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-8280-69.68-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.131182747523278, 'root_angle': -0.27097372740306797, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.10394445572308699796525927407', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '131765251687767847741440409680', 'Lhash_array': ['131765251687767847741440409680'], 'label': '2-8280-69.68-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8280/2/p/a/1241/2'}