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lfunc_lfunctions • Show schema
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{'Lhash': '2257215029850855746463916506591', 'a10': [0, 0], 'a2': [1.4142135623730951, 0], 'a3': [0, 0], 'a4': [2.0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, -4.0], 'a8': [2.8284271247461903, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.261611896213362, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.4142135623730951, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '450.449', 'coefficient_field': 'CDF', 'conductor': 450, 'conductor_radical': 30, 'conjugate': '1124781607404127061008513939294', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.4142135623730951, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 4.0], [-49.0, 0]], [[1.0, 0], [0, 16.97056274847714], [-121.0, 0]], [[1.0, 0], [0, 8.0], [-169.0, 0]], [[1.0, 0], [12.727922061357855, 0], [289.0, 0]], [[1.0, 0], [-16.0, 0], [361.0, 0]], [[1.0, 0], [-16.97056274847714, 0], 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'2-450-15.14-c2-0-9', 'leading_term': '2.5592497818477604886899837479180292131473573919178442516', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/450/3/b/b/449/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [2.5592497818477606, 2.677137796368188, 2.781225469076359, 2.871008270542003, 2.945828586465965, 3.004879690883185, 3.047222686146771, 3.071815733327861, 3.0775543866146196, 3.0633214380700315, 3.028044377715278, 2.970758367528293, 2.890672497855605, 2.78723702045666, 2.6602092166841325, 2.509715551138888, 2.336307776751583, 2.141010699499087, 1.9253593877494408, 1.691423733390061, 1.4418184511513905, 1.1796968496392424, 0.9087270308074905, 0.6330495786115253, 0.3572162826692337, 0.086110004336178, -0.17515357900571202, -0.4213409352114292, 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'8.222961778580255333538752901795060', '9.390982866838975194978286840224136', '10.08851724843839726043903431332778', '11.35891645531985118184119722082700'], 'prelabel': '2-450-15.14-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5016584493941383, 'root_angle': 0.34349689366573694, 'root_number': '0.47209785359306035893067535041557620454813147964453828386 + 0.8815461511644329936618819085048547040795526907042009464*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.17174844683286847', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.78062869172661924812980214033', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.95119353443851788897824654717', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.43100603770608651664440440118', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.261611896213362, 'bad_primes': [2, 3, 5], 'central_character': '15.14', 'conductor': 450, 'conductor_radical': 30, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/450/3/b/b/449/3'], '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': '2-450-15.14-c2-0-9', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-450-15.14-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.5016584493941383, 'root_angle': 0.17174844683286847, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.78062869172661924812980214033', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2257215029850855746463916506591', 'Lhash_array': ['2257215029850855746463916506591'], 'label': '2-450-15.14-c2-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/450/3/b/b/449/3'}