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lfunc_lfunctions • Show schema
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{'Lhash': '277191431036738248098790164925,1032629199814077939821980643344', 'a10': 3, 'a2': -1, 'a3': 0, 'a4': 0, 'a5': -3, 'a6': 0, 'a7': -2, 'a8': 1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 365.42857651126263, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1, 1]], [3, [1]], [7, [1, 2, 1]], [19, [1, 1, 19]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '2394.1', 'coefficient_field': '1.1.1.1', 'conductor': 5731236, 'conductor_radical': 798, 'degree': 4, 'euler_factors': [[1, 1, 1], [1], [1, 3, 4, 15, 25], [1, 2, 1], [1, 8, 38, 88, 121], [1, 3, -4, 39, 169], [1, 2, -13, 34, 289], [1, 1, 19], [1, -1, -22, -23, 529], [1, 0, -29, 0, 841], [1, 12, 98, 372, 961], [1, -8, 90, -296, 1369], [1, -4, -25, -164, 1681], [1, -6, -7, -258, 1849], [1, 2, -43, 94, 2209], [1, 4, -37, 212, 2809], [1, -13, 110, -767, 3481], [1, 5, -36, 305, 3721], [1, -12, 77, -804, 4489], [1, 7, -22, 497, 5041], [1, -2, -69, -146, 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'3.96268734758562281318611646834143', '4.37195260222924538857240390963164', '4.72005707002373851847232298018949', '5.22089256028457055065771119046218', '5.71827095948449913959230065036800', '5.87346395470072600320149432100687', '6.78065127179588594301743962304593', '6.98274740298103474054795386629481', '7.47686521122505276793023086035782', '7.65775925697095361332967329053982', '7.903842742194320840529669973277608', '8.380985307150271879563876966086942', '8.703384850718296031286339079442825', '9.133970303705775399907781801249222'], 'prelabel': '4-2394e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.3722061072065825, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 635094066407606957, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.21866548320714900126141631064', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.814600805322982599120281158000', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '2.17906795911070252714031494425', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 365.42857651126263, 'bad_primes': [2, 3, 7, 19], 'central_character': '1.1', 'conductor': 5731236, 'conductor_radical': 798, 'degree': 4, 'dirichlet_coefficients': [1, -1, 0, 0, -3, 0, -2, 1, 0, 3, -8, 0, -3, 2, 0, -1, -2, 0, -1, 0, 0, 8, 1, 0, 5, 3, 0, 0, 0, 0, -12, 0, 0, 2, 6, 0, 8, 1, 0, -3, 4, 0, 6, 0, 0, -1, -2, 0, 3, -5, 0, 0, -4, 0, 24, -2, 0, 0, 13, 0, -5, 12, 0, 1, 9, 0, 12, 0, 0, -6, -7, 0, 2, -8, 0, 0, 16, 0, 8, 3, 0, -4, -34, 0, 6, -6, 0, -8, 4, 0, 6, 0, 0, 2, 3, 0, 10, -3, 0, 0], 'euler11': [1, 8, 38, 88, 121], 'euler13': [1, 3, -4, 39, 169], 'euler17': [1, 2, -13, 34, 289], 'euler19': [1, 1, 19, 0, 0], 'euler2': [1, 1, 1, 0, 0], 'euler23': [1, -1, -22, -23, 529], 'euler29': [1, 0, -29, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 12, 98, 372, 961], 'euler37': [1, -8, 90, -296, 1369], 'euler41': [1, -4, -25, -164, 1681], 'euler43': [1, -6, -7, -258, 1849], 'euler47': [1, 2, -43, 94, 2209], 'euler5': [1, 3, 4, 15, 25], 'euler53': [1, 4, -37, 212, 2809], 'euler59': [1, -13, 110, -767, 3481], 'euler61': [1, 5, -36, 305, 3721], 'euler67': [1, -12, 77, -804, 4489], 'euler7': [1, 2, 1, 0, 0], 'euler71': [1, 7, -22, 497, 5041], 'euler73': [1, -2, -69, -146, 5329], 'euler79': [1, -8, -15, -632, 6241], 'euler83': [1, 34, 455, 2822, 6889], 'euler89': [1, -4, -73, -356, 7921], 'euler97': [1, -10, 3, -970, 9409], 'euler_factors': [[1, 1, 1, 0, 0], [1, 0, 0, 0, 0], [1, 3, 4, 15, 25], [1, 2, 1, 0, 0], [1, 8, 38, 88, 121], [1, 3, -4, 39, 169], [1, 2, -13, 34, 289], [1, 1, 19, 0, 0], [1, -1, -22, -23, 529], [1, 0, -29, 0, 841], [1, 12, 98, 372, 961], [1, -8, 90, -296, 1369], [1, -4, -25, -164, 1681], [1, -6, -7, -258, 1849], [1, 2, -43, 94, 2209], [1, 4, -37, 212, 2809], [1, -13, 110, -767, 3481], [1, 5, -36, 305, 3721], [1, -12, 77, -804, 4489], [1, 7, -22, 497, 5041], [1, -2, -69, -146, 5329], [1, -8, -15, -632, 6241], [1, 34, 455, 2822, 6889], [1, -4, -73, -356, 7921], [1, -10, 3, -970, 9409]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2394/2/o/a'], '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': '4-2394e2-1.1-c1e2-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-2394e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.3722061072065825, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 635094066407606957, 'z1': {'__RealLiteral__': 0, 'data': '0.21866548320714900126141631064', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '277191431036738248098790164925,1032629199814077939821980643344', 'Lhash_array': ['277191431036738248098790164925', '1032629199814077939821980643344'], 'label': '4-2394e2-1.1-c1e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2394/2/o/a'}