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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 2, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 1, 'Lhash': '1370829612212139845', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 246.83356272818205, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [7, [1, -1]], [23, [1, 1]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '30912.1', 'coefficient_field': '1.1.1.1', 'conductor': 30912, 'conductor_radical': 966, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, -2, 5], [1, -1], [1, -4, 11], [1, 2, 13], [1, -6, 17], [1, 0, 19], [1, 1], [1, -2, 29], [1, 4, 31], [1, 6, 37], [1, 6, 41], [1, -12, 43], [1, -12, 47], [1, 6, 53], [1, 4, 59], [1, -10, 61], [1, -4, 67], [1, -16, 71], [1, -2, 73], [1, 8, 79], [1, 16, 83], [1, -6, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 35, 'label': '2-30912-1.1-c1-0-35', 'leading_term': '4.65459216854', '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/30912/ch', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [4.654592168537976, 4.116345023569982, 2.613723418116238, 0.6221583423995948, -0.9658422952364341, -1.323166303885529, -0.4460062994160312, 0.6275454947606025, 0.6412920832722694, -0.584639123985985, -1.75742675244412, -1.351480505004766, 0.5873641221751607, 2.181348450817406, 1.709832539479406, -0.1998364326628185, -0.9973445867054623, 0.776420396586254, 3.406815804225555, 3.808069925675996, 1.386835123320543, -0.9952425056966961, -0.6230410736365082, 1.420895609586149, 1.671488002849144, -0.8367495081099203, -3.006369242253201, -1.96587052275117, 0.7229650652466427, 1.217858990215554, -0.9708781534079677, -2.231581928005881, -0.3229810892183771, 2.157816691311479, 1.735418155934543, -0.6438639272025097, -1.309042853545591, 0.2426749319943039, 0.9178661178564889, -0.3287618639524551, -0.5816179206073036, 1.556688589032394, 2.581144298729915, -0.4016415750288417, -3.917569715496093, -2.644941404938074, 2.109460018827951, 4.028168300140366, 1.508041659562645, -0.3341711940703824, 1.37823427566092, 2.605558037525196, -0.2046797792289726, -3.726948991268202, -3.388536837750704, -0.7621865364701046, 0.05786332952771713, -0.4147559089031228, 0.4045734004039378, 0.8696956983102059, -1.753186263001485, -4.478082258171213, -2.620495687054311, 1.189849802490783, 0.3542827810471402, -4.341059512242448, -5.668967254481294, -2.104354172219849, 0.4863450370765322, 0.01186352328104036, 0.9398560972462331, 4.14165590698356, 4.311823207207589, 0.3908244644063514, -1.597377100898456, 0.511719423266608, 1.329336563832959, -1.322861114444292, -2.314472134455968, 0.3401870990449852, 1.46187634011396, -0.9403949333418818, -1.874304574677226, 0.4160871129822625, 1.191328848835168, -0.7289561933737737, -0.7820490883506747, 1.211516412224448, 0.5183171254784983, -1.666537781688998, 0.3552814371505616, 4.166235440744704, 2.010637639332574, -4.039695565805338, -4.551582923836753, 0.3853587157255763, 2.033296020522158, -0.6690280655922172, -1.018563850099491, 1.418926437347961, 1.473226703172447, -0.2493215041885636, -0.1119812389042159, -0.3121509098892514, -3.00996066996778, -3.348710598278941, 1.012157355320576, 3.558688602856893, 1.088392138740895, -0.3741904504589976, 1.236411233934168, 0.04005786102750962, -3.605503576271218, -2.085548499794048, 3.298517045563695, 3.3406633763872, -1.368751068919701, -2.195132611787434, 0.5634587713268009, 0.4394132532001734, -1.102570354940664], 'positive_zeros': ['0.8330850967548746', '1.591591245347797', '2.149517205038994', '2.932533977299981', '3.723204571704924', '4.173118089706452', '5.120890553141965', '5.578792478720984', '6.181046667460692', '6.925796597043804', '7.403850074534330', '8.027266601411262', '8.679318329420604', '9.214898861310549', '9.693209681040915', '10.08868518265548', '10.72647295310864', '11.39044747737316', '12.14543582328445', '12.34501477144597', '12.98769012147695', '13.88256926396790', '14.03268015587650', '14.41962663853520', '14.86707167828247', '15.65559408438940', '16.02224110530195', '16.91071329553365', '17.25513503149251', '17.36150839972368', '18.27484360256825', '18.70161975281531', '19.14178043987431', '19.72166398017003'], 'prelabel': '2-30912-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 15.710937678196743, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1370829612212139845, 'z1': {'__RealLiteral__': 0, 'data': '0.8330850967548746', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.591591245347797', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.149517205038994', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 246.83356272818205, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 30912, 'conductor_radical': 966, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 4, 0, -2, 0, 2, 0, 6, 0, 0, 0, 1, 0, -1, 0, -1, 0, 1, 0, 2, 0, -4, 0, 4, 0, 2, 0, -6, 0, -2, 0, -6, 0, 12, 0, 2, 0, 12, 0, 1, 0, 6, 0, -6, 0, 8, 0, 0, 0, -4, 0, 10, 0, 1, 0, -4, 0, 4, 0, -1, 0, 16, 0, 2, 0, -1, 0, 4, 0, -8, 0, 1, 0, -16, 0, 12, 0, 2, 0, 6, 0, -2, 0, -4, 0, 0, 0, -2, 0, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, 2, 13], 'euler17': [1, -6, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 0], 'euler29': [1, -2, 29], 'euler3': [1, -1, 0], 'euler31': [1, 4, 31], 'euler37': [1, 6, 37], 'euler41': [1, 6, 41], 'euler43': [1, -12, 43], 'euler47': [1, -12, 47], 'euler5': [1, -2, 5], 'euler53': [1, 6, 53], 'euler59': [1, 4, 59], 'euler61': [1, -10, 61], 'euler67': [1, -4, 67], 'euler7': [1, -1, 0], 'euler71': [1, -16, 71], 'euler73': [1, -2, 73], 'euler79': [1, 8, 79], 'euler83': [1, 16, 83], 'euler89': [1, -6, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, -2, 5], [1, -1, 0], [1, -4, 11], [1, 2, 13], [1, -6, 17], [1, 0, 19], [1, 1, 0], [1, -2, 29], [1, 4, 31], [1, 6, 37], [1, 6, 41], [1, -12, 43], [1, -12, 47], [1, 6, 53], [1, 4, 59], [1, -10, 61], [1, -4, 67], [1, -16, 71], [1, -2, 73], [1, 8, 79], [1, 16, 83], [1, -6, 89], [1, 2, 97]], 'index': 35, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/30912/ch'], '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': '2-30912-1.1-c1-0-35', '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': '2-30912-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 15.710937678196743, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1370829612212139845, 'z1': {'__RealLiteral__': 0, 'data': '0.8330850967548746', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1370829612212139845', 'Lhash_array': ['1370829612212139845'], 'label': '2-30912-1.1-c1-0-35', 'type': 'ECQ', 'url': 'EllipticCurve/Q/30912/ch'}