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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 0, 'Lhash': '1598088297784130071', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 804.8920523745066, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [7, [1, -1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '100800.1', 'coefficient_field': '1.1.1.1', 'conductor': 100800, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, -1], [1, 0, 11], [1, -2, 13], [1, 6, 17], [1, -8, 19], [1, 0, 23], [1, -6, 29], [1, -4, 31], [1, 10, 37], [1, -6, 41], [1, -4, 43], [1, 0, 47], [1, -6, 53], [1, -12, 59], [1, -10, 61], [1, -4, 67], [1, -12, 71], [1, -10, 73], [1, 8, 79], [1, -12, 83], [1, -6, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 186, 'label': '2-100800-1.1-c1-0-186', 'leading_term': '3.43725284568', '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/100800/mj', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.437252845681319, 2.779269610974591, 1.173262766431119, -0.2983320441639733, -0.3703215839791446, 1.186118912711736, 2.911470163282339, 2.880763425488927, 0.9668987331424205, -0.6106359007166458, 0.2275401087201902, 2.575674219607099, 3.338997964606404, 1.297497595814039, -0.9419764306407775, -0.3816972506579587, 1.965808499103273, 2.358711700130187, -0.08243070090810115, -1.924555827092518, -0.8065428030043624, 0.6611803013888587, -0.8419458646206845, -3.51982175584169, -3.056048112136921, 0.1126145559578387, 1.21414959272439, -0.8980331040243812, -1.844644980521128, 0.4337573088131354, 1.813340768851009, -0.63558980721437, -3.115271835625555, -1.772549387776005, 0.417689432269914, -0.5412722842172388, -1.962380341970746, 0.2335392210448233, 3.089474811991452, 1.739627351907125, -1.123879517996277, 0.006172754489283808, 3.028327066831908, 2.311955213095696, -0.5096586674786544, -0.1763664130688988, 1.656789975230415, 0.3833551722427344, -1.407712403080721, 0.8694179180991689, 3.461631508103785, 0.8935102398418981, -2.913589220028787, -1.922520661731265, 0.6493241670145585, -0.2407568035041225, -1.306726062824624, 0.6812656783277792, 0.751949299932309, -3.612423778634266, -5.657176898019725, -2.169210334704125, 0.4308486653365575, -0.5686485724953794, -0.1287670129034349, 1.393591183417442, -1.789975296678493, -6.761567259353346, -5.60003864254799, -0.8781487114357404, -0.06835068423736018, -1.055052431272027, 0.5751570518560325, 0.7600769481469654, -2.452184331940306, -2.369759265723425, 1.81978734145785, 1.995053264520805, -1.89792953803602, -2.042786581014404, 0.2534476416930782, -1.314455271278393, -3.199407378552619, -0.6842940029327927, 0.8543467273470755, -1.115193984530339, 0.1880330966622514, 4.652710462952929, 4.190404667950858, 0.3240833384976981, 0.04520342719541908, 0.0260912392139216, -3.686665287355603, -4.320016879693849, 0.2850903788867812, 1.427597993240081, -1.809414915340057, -1.734109507567441, 0.2364581799694032, -0.7150833730380509, 0.3163313393758587, 4.942359734802231, 4.599287594991863, -0.5613339771205199, -1.059757460519161, 1.472288906824632, -0.04294232614469502, -1.417185799406576, 0.7488671144820901, -0.1556668723355516, -3.556113957068486, -1.502700786856002, 2.211590361377481, 0.3210401683405834, -1.61265485658442, 0.2116660477158918, -0.6908357261003814, -3.017222710548023, 0.0565454997167986, 2.590633407963725, -1.533078757240031], 'positive_zeros': ['0.6836987412878588', '1.081965406257777', '2.119082647396861', '2.470453630491154', '3.370559186635375', '3.793808810733583', '4.492826947409687', '5.100825484711666', '5.416621215808470', '6.240431052219112', '6.660707658770153', '7.211650752449551', '7.703779888895508', '8.423656997091192', '8.681801316190183', '9.233602205554709', '9.879799813542370', '10.24951026146921', '10.94136561331743', '11.27091909306667', '11.78639111425988', '12.18934870429066', '12.79792550839560', '13.40946540132388', '13.72034005000020', '14.17935175064679', '14.55752112813232', '15.40875925382511', '15.64599791082022', '16.01611012132140', '16.40925501613528', '17.34006821243874', '17.48562474312852', '17.93294894710763', '18.32010325430515', '18.89158625497275', '19.37683170216474', '19.95044302241611'], 'prelabel': '2-100800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 28.370619527506033, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1598088297784130071, 'z1': {'__RealLiteral__': 0, 'data': '0.6836987412878588', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.081965406257777', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.119082647396861', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 804.8920523745066, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 100800, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, -6, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, -10, 0, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 6, 0, 0, 0, 0, 0, 12, 0, 10, 0, 0, 0, 0, 0, 4, 0, 0, 0, 12, 0, 10, 0, 0, 0, 0, 0, -8, 0, 0, 0, 12, 0, 0, 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 0, 10, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -2, 13], 'euler17': [1, 6, 17], 'euler19': [1, -8, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, 10, 37], 'euler41': [1, -6, 41], 'euler43': [1, -4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, -6, 53], 'euler59': [1, -12, 59], 'euler61': [1, -10, 61], 'euler67': [1, -4, 67], 'euler7': [1, -1, 0], 'euler71': [1, -12, 71], 'euler73': [1, -10, 73], 'euler79': [1, 8, 79], 'euler83': [1, -12, 83], 'euler89': [1, -6, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, -1, 0], [1, 0, 11], [1, -2, 13], [1, 6, 17], [1, -8, 19], [1, 0, 23], [1, -6, 29], [1, -4, 31], [1, 10, 37], [1, -6, 41], [1, -4, 43], [1, 0, 47], [1, -6, 53], [1, -12, 59], [1, -10, 61], [1, -4, 67], [1, -12, 71], [1, -10, 73], [1, 8, 79], [1, -12, 83], [1, -6, 89], [1, -10, 97]], 'index': 186, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/100800/mj'], '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': '2-100800-1.1-c1-0-186', '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': '2-100800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 28.370619527506033, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1598088297784130071, 'z1': {'__RealLiteral__': 0, 'data': '0.6836987412878588', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1598088297784130071', 'Lhash_array': ['1598088297784130071'], 'label': '2-100800-1.1-c1-0-186', 'type': 'ECQ', 'url': 'EllipticCurve/Q/100800/mj'}