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lfunc_lfunctions • Show schema
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{'A10': 1, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': -1, 'A6': 0, 'A7': -1, 'A8': -1, 'A9': 0, 'Lhash': '1604784440348778703', 'a10': [0.31622776601683794, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 608.6996146082207, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [5, [1, 1]], [7, [1, 1]], [11, [1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '76230.1', 'coefficient_field': '1.1.1.1', 'conductor': 76230, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, 1], [1, 1], [1], [1, 2, 13], [1, -2, 17], [1, -4, 19], [1, 8, 23], [1, -4, 29], [1, -2, 31], [1, 4, 37], [1, -6, 41], [1, 0, 43], [1, -8, 47], [1, -2, 53], [1, -6, 59], [1, -6, 61], [1, 4, 67], [1, -16, 71], [1, -16, 73], [1, 16, 79], [1, -4, 83], [1, -12, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 22, 'label': '2-76230-1.1-c1-0-22', 'leading_term': '1.3162246049', '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/76230/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.316224604899171, 0.9084967513407347, -0.03825588493804206, -0.7339324807839531, -0.3033666672615871, 1.299736387125956, 2.818426800978352, 2.658749556408559, 0.7302083253065832, -0.9919718091881554, -0.4670728221976585, 1.757019880010614, 2.787514282069601, 0.9870482560188422, -1.457074503585254, -1.058705339098475, 1.952858124956643, 3.190304911815825, -0.1064495896543211, -4.651452148196031, -5.001681824241743, -1.081259724184009, 1.539138085992895, -0.4346569001098031, -3.425962614521275, -2.697985121172705, 0.4605698113195801, 1.239290157826724, -0.8956267573360072, -1.911716522949012, -0.3630371724177403, 0.5815220108971506, -0.6208204425160058, -1.032786237089407, 0.9619604743747974, 2.15279206423086, 0.2446344882764535, -1.688898340467678, -0.6788170923035051, 0.839296776553822, 0.04375744748707875, -0.6540298882251812, 1.295200212123255, 2.623981416443682, 0.0198922163192708, -2.873482362210441, -1.61123577697612, 0.8293958541576762, 0.09253563883060384, -0.8815681187626478, 1.460527971021294, 2.203770869461569, -3.425699462096581, -8.804003548170098, -5.749444244476544, 0.7767203358862828, 1.324082654077038, -1.369189841704602, 1.012496401907912, 5.798843607861066, 4.834880090596488, 0.2133532424869796, -0.5558529176580463, 1.384337473010161, 0.8643495252749298, -0.1020724733624757, 1.78316943459606, 2.737242616237296, 0.1136296254709182, -1.188111056912169, 1.102439671302574, 1.841514025132716, -0.3654428842813785, -0.4747212572811347, 1.568209379548969, 0.8136069308598199, -1.524851233497282, -0.9393443492124239, 0.2903194555126202, -1.079621566394896, -1.461982017144111, 0.4992281287910611, -0.4498515399674474, -3.425459716643125, -0.9834963494401272, 4.310470785919056, 3.114376903571996, -1.292842931852526, 0.5487574219980359, 4.180615595396591, 1.115270773816288, -2.423546947144839, 0.7288537130449052, 2.658589357513639, -2.269462216639949, -4.980588480893212, -1.176599192321318, 0.8023896332616395, -0.6123565737021123, 1.570679156727609, 5.00458678053764, 2.833649353926704, -0.6368263352648744, 0.2806091928817824, 0.9171548793047766, -1.312284747351641, -1.180467063931242, 1.040532205504793, 0.5060715275524594, -0.2234531383171971, 1.821551004781958, 1.84827274224483, -1.006705144275337, -0.996541960387815, 0.5605662832564303, -0.8503944145745334, -0.7948468276529017, 3.166050730258897, 3.606391191839164, -0.1408695858092708, -0.4757691682202275], 'positive_zeros': ['0.4903360735847691', '1.059692444393491', '2.083760716102660', '2.559858357103523', '3.337536920064027', '3.847752345461843', '4.494571570414696', '5.317008689397795', '5.718137853685093', '6.459367532675164', '6.907730052704127', '7.550879189638881', '7.897840613742791', '8.399159729095301', '9.022450963511346', '9.584423647186246', '10.00736207257536', '10.36701061949683', '11.00129572465569', '11.63865290807973', '12.01231791261645', '12.37588191833546', '12.87658908608413', '13.71065036425910', '14.10520526055460', '14.44636115317653', '15.26606921594202', '15.57053723022886', '16.14700611027911', '16.28412658443503', '17.00944086152206', '17.39846872732995', '17.95767606689390', '18.30880374963630', '18.82642997460195', '19.38555467028829', '19.59553253914705'], 'prelabel': '2-76230-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 24.671838492666506, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1604784440348778703, 'z1': {'__RealLiteral__': 0, 'data': '0.4903360735847691', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.059692444393491', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.083760716102660', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 608.6996146082207, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 76230, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, -1, 0, -1, -1, 0, 1, 0, 0, -2, 1, 0, 1, 2, 0, 4, -1, 0, 0, -8, 0, 1, 2, 0, -1, 4, 0, 2, -1, 0, -2, 1, 0, -4, -4, 0, 1, 6, 0, 0, 0, 0, 8, 8, 0, 1, -1, 0, -2, 2, 0, 0, 1, 0, -4, 6, 0, 6, -2, 0, 1, 2, 0, -4, 2, 0, -1, 16, 0, 16, 4, 0, 4, 0, 0, -16, -1, 0, -6, 4, 0, -2, 0, 0, 0, 12, 0, 2, -8, 0, -8, -4, 0, -2, -1, 0, 1], 'euler11': [1, 0, 0], 'euler13': [1, 2, 13], 'euler17': [1, -2, 17], 'euler19': [1, -4, 19], 'euler2': [1, 1, 0], 'euler23': [1, 8, 23], 'euler29': [1, -4, 29], 'euler3': [1, 0, 0], 'euler31': [1, -2, 31], 'euler37': [1, 4, 37], 'euler41': [1, -6, 41], 'euler43': [1, 0, 43], 'euler47': [1, -8, 47], 'euler5': [1, 1, 0], 'euler53': [1, -2, 53], 'euler59': [1, -6, 59], 'euler61': [1, -6, 61], 'euler67': [1, 4, 67], 'euler7': [1, 1, 0], 'euler71': [1, -16, 71], 'euler73': [1, -16, 73], 'euler79': [1, 16, 79], 'euler83': [1, -4, 83], 'euler89': [1, -12, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, 1, 0], [1, 1, 0], [1, 0, 0], [1, 2, 13], [1, -2, 17], [1, -4, 19], [1, 8, 23], [1, -4, 29], [1, -2, 31], [1, 4, 37], [1, -6, 41], [1, 0, 43], [1, -8, 47], [1, -2, 53], [1, -6, 59], [1, -6, 61], [1, 4, 67], [1, -16, 71], [1, -16, 73], [1, 16, 79], [1, -4, 83], [1, -12, 89], [1, 2, 97]], 'index': 22, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/76230/g'], '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': '2-76230-1.1-c1-0-22', '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': '2-76230-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 24.671838492666506, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1604784440348778703, 'z1': {'__RealLiteral__': 0, 'data': '0.4903360735847691', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1604784440348778703', 'Lhash_array': ['1604784440348778703'], 'label': '2-76230-1.1-c1-0-22', 'type': 'ECQ', 'url': 'EllipticCurve/Q/76230/g'}