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lfunc_lfunctions • Show schema
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{'Lhash': '781844104023719745532954587966', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0.8660254037844386, -0.5], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.559608545745714, '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], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '2700.1549', 'coefficient_field': 'CDF', 'conductor': 2700, 'conductor_radical': 30, 'conjugate': '1605396664475104902767445787518', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.8660254037844386, 0.5], [3.5, -6.06217782649107]], [[1.0, 0], [-1.5, -2.598076211353316], [-5.5, 9.526279441628825]], [[1.0, 0], [-0.8660254037844386, -0.5], [6.5, 11.258330249197702]], [[1.0, 0], [0, -6.0], [-17.0, 0]], [[1.0, 0], [-4.0, 0], [19.0, 0]], [[1.0, 0], 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-0.07253767907706453], 'positive_zeros': ['0.61676624764186247690829387858563', '1.86912232728428613208869045672430', '3.06484990658246662407741500861316', '3.75643694598376137151292525559227', '4.95650211689555763466934952525521', '5.48720345880660625204335646196261', '6.42378866198112025309059830247320', '7.19977647717467135593469769996700', '7.999670839821001784581991155496563', '8.653417634573923489201025580640082'], 'prelabel': '2-2700-45.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.64323255348531, 'root_angle': -0.3698058398726555, 'root_number': '0.3977076213692615180895209818637189278454218449969980281 - 0.91751220586148286896577549520636145370209503449153755958*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.18490291993632776', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.61676624764186247690829387859', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.86912232728428613208869045672', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.06484990658246662407741500861', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.559608545745714, 'bad_primes': [2, 3, 5], 'central_character': '45.4', 'conductor': 2700, 'conductor_radical': 30, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2700/2/s/b/1549/2'], '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': '2-2700-45.4-c1-0-6', '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': '2-2700-45.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.64323255348531, 'root_angle': -0.18490291993632774, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.61676624764186247690829387859', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '781844104023719745532954587966', 'Lhash_array': ['781844104023719745532954587966'], 'label': '2-2700-45.4-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2700/2/s/b/1549/2'}