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lfunc_lfunctions • Show schema
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{'Lhash': '981777695975635439065406728311,1249156609887894181433510265305', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 167.334019432485, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 1, 1]]], 'bad_primes': [2, 3, 5], 'central_character': '1620.1', 'coefficient_field': '1.1.1.1', 'conductor': 2624400, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1], [1, 1, 1], [1, 2, -3, 14, 49], [1, 0, -11, 0, 121], [1, 2, -9, 26, 169], [1, -12, 70, -204, 289], [1, 8, 54, 152, 361], [1, -6, 13, -138, 529], [1, -6, 7, -174, 841], [1, -4, -15, -124, 961], [1, -4, 78, -148, 1369], [1, -6, -5, -246, 1681], [1, -10, 57, -430, 1849], [1, 6, -11, 282, 2209], [1, -12, 142, -636, 2809], [1, -12, 85, -708, 3481], [1, 2, -57, 122, 3721], [1, 2, -63, 134, 4489], [1, -24, 286, -1704, 5041], [1, -4, 150, -292, 5329], [1, 8, 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['0.77448604197313909151175145248901', '0.985410814038974510103190904705562', '2.35000714234537269357006211758138', '2.47721962337422856461379687633311', '3.39485230222342112397070753470629', '3.39884688204924552232079268051836', '4.22556459238636769494077186937889', '4.45586560799290528528078787306997', '5.18225187955212691209606686313405', '5.46693619519736486074087230697012', '6.00586804970885833955879536878375', '6.32755156734376256877235140711114', '6.89646202038817991171433881561650', '7.13867389319388351197198050246455', '7.71566523213339628157756761593779', '7.920019884955751442423591008299603', '8.490249047453280027012231826293586', '8.621809818729676507247985036694433', '9.444033007247618621045438384566470', '9.458662684714851864404080516705546'], 'prelabel': '4-1620e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.596632470443349, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1757909081664729997, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.77448604197313909151175145249', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.985410814038974510103190904706', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '2.35000714234537269357006211758', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 167.334019432485, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 2624400, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 12, 0, -8, 0, 0, 0, 6, 0, 0, 0, 0, 0, 6, 0, 4, 0, 0, 0, 2, 0, 4, 0, 0, 0, 6, 0, 10, 0, 0, 0, -6, 0, 7, 0, 0, 0, 12, 0, 0, 0, 0, 0, 12, 0, -2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 24, 0, 4, 0, 0, 0, 0, 0, -8, 0, 0, 0, 6, 0, -12, 0, 0, 0, 12, 0, 4, 0, 0, 0, 8, 0, -2, 0, 0, 0], 'euler11': [1, 0, -11, 0, 121], 'euler13': [1, 2, -9, 26, 169], 'euler17': [1, -12, 70, -204, 289], 'euler19': [1, 8, 54, 152, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -6, 13, -138, 529], 'euler29': [1, -6, 7, -174, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -4, -15, -124, 961], 'euler37': [1, -4, 78, -148, 1369], 'euler41': [1, -6, -5, -246, 1681], 'euler43': [1, -10, 57, -430, 1849], 'euler47': [1, 6, -11, 282, 2209], 'euler5': [1, 1, 1, 0, 0], 'euler53': [1, -12, 142, -636, 2809], 'euler59': [1, -12, 85, -708, 3481], 'euler61': [1, 2, -57, 122, 3721], 'euler67': [1, 2, -63, 134, 4489], 'euler7': [1, 2, -3, 14, 49], 'euler71': [1, -24, 286, -1704, 5041], 'euler73': [1, -4, 150, -292, 5329], 'euler79': [1, 8, -15, 632, 6241], 'euler83': [1, -6, -47, -498, 6889], 'euler89': [1, -12, 214, -1068, 7921], 'euler97': [1, 2, -93, 194, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 1, 1, 0, 0], [1, 2, -3, 14, 49], [1, 0, -11, 0, 121], [1, 2, -9, 26, 169], [1, -12, 70, -204, 289], [1, 8, 54, 152, 361], [1, -6, 13, -138, 529], [1, -6, 7, -174, 841], [1, -4, -15, -124, 961], [1, -4, 78, -148, 1369], [1, -6, -5, -246, 1681], [1, -10, 57, -430, 1849], [1, 6, -11, 282, 2209], [1, -12, 142, -636, 2809], [1, -12, 85, -708, 3481], [1, 2, -57, 122, 3721], [1, 2, -63, 134, 4489], [1, -24, 286, -1704, 5041], [1, -4, 150, -292, 5329], [1, 8, -15, 632, 6241], [1, -6, -47, -498, 6889], [1, -12, 214, -1068, 7921], [1, 2, -93, 194, 9409]], 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1620/2/i/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': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-1620e2-1.1-c1e2-0-9', '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': '4-1620e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.596632470443349, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1757909081664729997, 'z1': {'__RealLiteral__': 0, 'data': '0.77448604197313909151175145249', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '981777695975635439065406728311,1249156609887894181433510265305', 'Lhash_array': ['981777695975635439065406728311', '1249156609887894181433510265305'], 'label': '4-1620e2-1.1-c1e2-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1620/2/i/b'}