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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1228339685491236421', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1507.2561885536893, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, 1]], [11, [1]], [13, [1, 1]]], 'bad_primes': [2, 3, 5, 11, 13], 'central_character': '188760.1', 'coefficient_field': '1.1.1.1', 'conductor': 188760, 'conductor_radical': 4290, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 1], [1, 0, 7], [1], [1, 1], [1, 6, 17], [1, 4, 19], [1, 0, 23], [1, -6, 29], [1, -4, 31], [1, 2, 37], [1, 2, 41], [1, 0, 43], [1, 0, 47], [1, -6, 53], [1, -4, 59], [1, 14, 61], [1, -8, 67], [1, 0, 71], [1, 10, 73], [1, -4, 79], [1, 12, 83], [1, -14, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 1, 'label': '2-188760-1.1-c1-0-1', 'leading_term': '0.599541805312', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/Q/188760/l', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.5995418053123135, 0.002594250012878762, -1.254189761424478, -1.816942779234933, -0.5999972239953156, 1.712902874330051, 2.765813462325289, 1.090785388686212, -1.589752312970836, -1.95871373248784, 0.4905692266222384, 2.194729481148677, 0.1624241090468358, -3.440560629491264, -3.947016471928779, -0.9228860517570608, 1.228294360176128, 0.09438563694751718, -1.365117958738298, -0.5048263306852177, 0.1538188457482486, -2.225935042106376, -4.787324832003007, -3.32756381364645, 0.1869081301822737, 0.9142228505726852, -0.3581107965581226, 0.5592491462101482, 2.502255463197778, 1.109925833851607, -1.744106634272901, -0.4861620975290695, 3.264484438794587, 3.097460852135887, 0.006197898852785152, 0.276765927891472, 2.534052041306064, 0.1451704251460945, -4.927355710914001, -4.88233202053867, -0.7929706745947663, -0.02705467105910386, -1.992999922876102, -1.031528917531447, 1.143903808499541, 0.01486090924680452, -1.468771254807375, 0.07281202404744339, 0.5331502044821553, -2.006806655546112, -2.186427895045727, 0.4505829659545021, -0.246405528814465, -2.800873319159222, -0.4859730616808652, 2.907316886921384, -0.09499148595115749, -3.904780224354886, -0.6010966114399915, 3.582082077473066, 1.516219994731937, -0.9067550105936211, 0.7443435682508871, 0.8615849954583049, -1.149681328902358, 0.6144860727730396, 3.449692336193825, 1.464846706838027, -0.7931564128310865, 0.923484612438127, 1.148527238123242, -1.143170720281542, -0.02321568592256506, 1.709282027545735, -1.799470063373991, -4.465397899268169, -1.292182527770738, 0.2484061082049328, -2.066502464512905, -0.9562107783581762, 1.150101178066086, -2.378400906476132, -4.487383640876294, 0.4361823819790669, 2.713940644282543, -1.258366682077076, -2.115102275785285, 0.0782684458688672, -1.812349876510646, -3.463909900071659, -0.4346347891232885, 0.8576519615643869, -0.4203233920270928, 1.350958807728676, 2.442297971466387, -0.5801087246095963, -1.043596931453848, 1.041055592550683, -0.644661609929906, -1.110112049526977, 3.137500865313502, 2.026285069058341, -4.356353235979991, -3.433920586581619, 1.30440994681433, -0.9743141229589704, -3.689874777401474, -0.784540289090905, -0.2828637558214211, -2.38839605304732, -0.4010858906940282, 0.8893799133696929, -1.344964765094441, 0.08697540739572206, 2.976324327182567, 0.9046956032580906, -0.5641361844121427, 0.2794242050067398, -3.032065556240742, -5.370910278335562, -1.149952167424525], 'positive_zeros': ['0.2505877294903689', '1.067704765085995', '1.845153588856554', '2.457551067026903', '3.011115576552671', '3.822316716985345', '4.261482785364121', '4.842526413292723', '5.035987007487548', '5.983037306883935', '6.414110030639037', '6.678512444088167', '7.333771210425090', '7.782270959452463', '8.500723534827324', '8.718902149920911', '9.257111583090646', '10.07656932709080', '10.24573581160062', '10.84553017112281', '11.25158728168455', '11.74104150856392', '12.06612107224891', '12.69832165897069', '12.97768109416446', '13.52641997461458', '13.99558590892607', '14.52611456422981', '15.10587509525226', '15.41538050618909', '15.84486828628388', '16.20618072593451', '16.86104415823169', '17.15010177655325', '17.61698998889916', '18.00201270543836', '18.40540851159652', '19.10035135753865', '19.28645174040189', '19.82295050142948'], 'prelabel': '2-188760-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 38.82339743703131, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1228339685491236421, 'z1': {'__RealLiteral__': 0, 'data': '0.2505877294903689', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.067704765085995', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.845153588856554', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1507.2561885536893, 'bad_primes': [2, 3, 5, 11, 13], 'central_character': '1.1', 'conductor': 188760, 'conductor_radical': 4290, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 1, 0, -6, 0, -4, 0, 0, 0, 0, 0, 1, 0, -1, 0, 6, 0, 4, 0, 0, 0, 0, 0, -2, 0, 1, 0, -2, 0, 0, 0, -1, 0, 0, 0, -7, 0, 6, 0, 6, 0, 0, 0, 4, 0, 4, 0, -14, 0, 0, 0, 1, 0, 8, 0, 0, 0, 0, 0, -10, 0, -1, 0, 0, 0, 4, 0, 1, 0, -12, 0, 6, 0, -6, 0, 14, 0, 0, 0, -4, 0, 4, 0, 2, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, 1, 0], 'euler17': [1, 6, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, -4, 31], 'euler37': [1, 2, 37], 'euler41': [1, 2, 41], 'euler43': [1, 0, 43], 'euler47': [1, 0, 47], 'euler5': [1, 1, 0], 'euler53': [1, -6, 53], 'euler59': [1, -4, 59], 'euler61': [1, 14, 61], 'euler67': [1, -8, 67], 'euler7': [1, 0, 7], 'euler71': [1, 0, 71], 'euler73': [1, 10, 73], 'euler79': [1, -4, 79], 'euler83': [1, 12, 83], 'euler89': [1, -14, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 1, 0], [1, 0, 7], [1, 0, 0], [1, 1, 0], [1, 6, 17], [1, 4, 19], [1, 0, 23], [1, -6, 29], [1, -4, 31], [1, 2, 37], [1, 2, 41], [1, 0, 43], [1, 0, 47], [1, -6, 53], [1, -4, 59], [1, 14, 61], [1, -8, 67], [1, 0, 71], [1, 10, 73], [1, -4, 79], [1, 12, 83], [1, -14, 89], [1, -2, 97]], 'index': 1, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/188760/l'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-188760-1.1-c1-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-188760-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 38.82339743703131, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1228339685491236421, 'z1': {'__RealLiteral__': 0, 'data': '0.2505877294903689', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1228339685491236421', 'Lhash_array': ['1228339685491236421'], 'label': '2-188760-1.1-c1-0-1', 'type': 'ECQ', 'url': 'EllipticCurve/Q/188760/l'}