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lfunc_lfunctions • Show schema
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{'Lhash': '3215493580359635013185270442741,5269452124129753591630258332412', 'a10': -2, 'a2': -1, 'a3': -1, 'a4': 1, 'a5': 2, 'a6': 1, 'a7': -2, 'a8': -3, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.0781070621112613, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1, -2, 1]], [7, [1, 2, 1]]], 'bad_primes': [5, 7], 'central_character': '35.1', 'coefficient_field': '1.1.1.1', 'conductor': 1225, 'conductor_radical': 35, 'degree': 4, 'euler_factors': [[1, 1, 0, 2, 4], [1, 1, 2, 3, 9], [1, -2, 1], [1, 2, 1], [1, -1, 18, -11, 121], [1, -5, 28, -65, 169], [1, 5, 36, 85, 289], [1, 6, 30, 114, 361], [1, 2, 30, 46, 529], [1, -1, 20, -29, 841], [1, 0, 62, 0, 961], [1, -12, 110, -444, 1369], [1, -2, 66, -82, 1681], [1, -10, 94, -430, 1849], [1, 5, 62, 235, 2209], [1, 2, 90, 106, 2809], [1, 8, 134, 472, 3481], [1, -6, -22, -366, 3721], [1, -4, 70, -268, 4489], [1, -16, 206, -1136, 5041], [1, 8, 94, 584, 5329], [1, 9, 174, 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-0.17174732981403176], 'positive_zeros': ['2.53657717653485394345612541605317', '4.15686477265978088320503087187603', '5.75333263909241173971323500779893', '6.44771243960593321795590797895646', '6.48150256884439156034400207857153', '8.054746333088715318280391070412932', '8.914097901089898875492127200172533', '9.212565164174387439717095614639199', '9.982496960603323626825608149425871', '10.91335028499141244772470576034716', '11.12711409504629322506872055030719', '11.90227741643907382762501423524645', '12.96793398602071777540469125016742', '12.99212700705068834617634779507722', '13.94588673316197709173832397867650', '14.58335792317703476215761000619025', '15.47778975023287695392669568728728', '15.74352143908137457099974538479815', '16.54043015310824634377959576392741', '16.90322846331634953577134877294517'], 'prelabel': '4-35e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.5286552818940539, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1488746108957299258, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.53657717653485394345612541605', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.15686477265978088320503087188', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.75333263909241173971323500780', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 0.0781070621112613, 'bad_primes': [5, 7], 'central_character': '1.1', 'conductor': 1225, 'conductor_radical': 35, 'degree': 4, 'dirichlet_coefficients': [1, -1, -1, 1, 2, 1, -2, -3, -1, -2, 1, -1, 5, 2, -2, 1, -5, 1, -6, 2, 2, -1, -2, 3, 3, -5, 0, -2, 1, 2, 0, 1, -1, 5, -4, -1, 12, 6, -5, -6, 2, -2, 10, 1, -2, 2, -5, -1, 3, -3, 5, 5, -2, 0, 2, 6, 6, -1, -8, -2, 6, 0, 2, 1, 10, 1, 4, -5, 2, 4, 16, 3, -8, -12, -3, -6, -2, 5, -9, 2, -4, -2, 8, 2, -10, -10, -1, -3, 6, 2, -10, -2, 0, 5, -12, -1, -9, -3, -1, 3], 'euler11': [1, -1, 18, -11, 121], 'euler13': [1, -5, 28, -65, 169], 'euler17': [1, 5, 36, 85, 289], 'euler19': [1, 6, 30, 114, 361], 'euler2': [1, 1, 0, 2, 4], 'euler23': [1, 2, 30, 46, 529], 'euler29': [1, -1, 20, -29, 841], 'euler3': [1, 1, 2, 3, 9], 'euler31': [1, 0, 62, 0, 961], 'euler37': [1, -12, 110, -444, 1369], 'euler41': [1, -2, 66, -82, 1681], 'euler43': [1, -10, 94, -430, 1849], 'euler47': [1, 5, 62, 235, 2209], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, 2, 90, 106, 2809], 'euler59': [1, 8, 134, 472, 3481], 'euler61': [1, -6, -22, -366, 3721], 'euler67': [1, -4, 70, -268, 4489], 'euler7': [1, 2, 1, 0, 0], 'euler71': [1, -16, 206, -1136, 5041], 'euler73': [1, 8, 94, 584, 5329], 'euler79': [1, 9, 174, 711, 6241], 'euler83': [1, -8, 182, -664, 6889], 'euler89': [1, -6, 170, -534, 7921], 'euler97': [1, 9, 108, 873, 9409], 'euler_factors': [[1, 1, 0, 2, 4], [1, 1, 2, 3, 9], [1, -2, 1, 0, 0], [1, 2, 1, 0, 0], [1, -1, 18, -11, 121], [1, -5, 28, -65, 169], [1, 5, 36, 85, 289], [1, 6, 30, 114, 361], [1, 2, 30, 46, 529], [1, -1, 20, -29, 841], [1, 0, 62, 0, 961], [1, -12, 110, -444, 1369], [1, -2, 66, -82, 1681], [1, -10, 94, -430, 1849], [1, 5, 62, 235, 2209], [1, 2, 90, 106, 2809], [1, 8, 134, 472, 3481], [1, -6, -22, -366, 3721], [1, -4, 70, -268, 4489], [1, -16, 206, -1136, 5041], [1, 8, 94, 584, 5329], [1, 9, 174, 711, 6241], [1, -8, 182, -664, 6889], [1, -6, 170, -534, 7921], [1, 9, 108, 873, 9409]], 'index': 0, 'instance_types': ['G2Q', 'CMF'], 'instance_urls': ['Genus2Curve/Q/1225/a', 'ModularForm/GL2/Q/holomorphic/35/2/a/b'], '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': True, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-35e2-1.1-c1e2-0-0', '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': '4-35e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.5286552818940539, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1488746108957299258, 'z1': {'__RealLiteral__': 0, 'data': '2.53657717653485394345612541605', 'prec': 103}}
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id: 9955771
{'Lhash': '3215493580359635013185270442741,5269452124129753591630258332412', 'Lhash_array': ['3215493580359635013185270442741', '5269452124129753591630258332412'], 'label': '4-35e2-1.1-c1e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/35/2/a/b'}
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id: 1222339
{'Lhash': '1488746108957299258', 'Lhash_array': ['1488746108957299258'], 'label': '4-35e2-1.1-c1e2-0-0', 'type': 'G2Q', 'url': 'Genus2Curve/Q/1225/a'}