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lfunc_lfunctions • Show schema
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{'Lhash': '3739296694386281063959788296876', 'a10': [-9.815078528040072, -0.5024544501145287], 'a2': [0.7612682588392865, 0.4395184341663798], 'a3': [2.598076211353316, -1.5], 'a4': [-3.613647092055867, -6.25902036406429], 'a5': [-9.955594453139959, 5.087842281813469], 'a6': [2.637110604998279, 1.0222002110365684e-60], 'a7': [-18.518420468935542, -0.26096615816845947], 'a8': [0.0, -13.385352992783222], 'a9': [4.5, -7.794228634059948], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.195200550602768, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-2.598076211353316, 1.5]]], [5, [[1.0, 0], [9.955594453139959, -5.087842281813469]]], [7, [[1.0, 0], [18.518420468935542, 0.26096615816845947]]]], 'bad_primes': [3, 5, 7], 'central_character': '105.79', 'coefficient_field': 'CDF', 'conductor': 105, 'conductor_radical': 105, 'conjugate': '408922946241766818607783699833', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'7.55710087626819957110745613093899', '8.021387570021474869644447906709171', '9.434180807523485592177690842783098', '10.35635050342149155786990036848008', '12.12991822049490579187857367184661', '12.63119130097775941728059560460733', '13.39689594305191727621175906141489'], 'prelabel': '2-105-35.9-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.489015980383165, 'root_angle': 0.8339265234586598, 'root_number': '-0.8669556803219902 + 0.49838524091051806*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.416963261729', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.94978497522349881309610208781', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.98735124042121794617582223068', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.26512445501543956866522602366', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.195200550602768, 'bad_primes': [3, 5, 7], 'central_character': '35.9', 'conductor': 105, 'conductor_radical': 105, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/105/4/q/b/79/13'], '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': '2-105-35.9-c3-0-22', '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': '2-105-35.9-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.489015980383165, 'root_angle': 0.4169632617293299, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.94978497522349881309610208781', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3739296694386281063959788296876', 'Lhash_array': ['3739296694386281063959788296876'], 'label': '2-105-35.9-c3-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/105/4/q/b/79/13'}