Formats: - HTML - YAML - JSON - 2026-03-20T10:07:23.864461
Query: /api/lfunc_lfunctions/?_offset=0
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{'A10': 0, 'A2': 1, 'A3': -1, 'A4': -1, 'A5': 0, 'A6': -1, 'A7': 0, 'A8': -3, 'A9': 1, 'Lhash': '2019893345475402302', 'a10': [0.0, 0], 'a2': [0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [-0.5, 0], 'a5': [0.0, 0], 'a6': [-0.4082482904638631, 0], 'a7': [0.0, 0], 'a8': [-1.0606601717798212, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 851.0056595417961, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 1]], [5, [1]], [7, [1]], [29, [1, 1]]], 'bad_primes': [3, 5, 7, 29], 'central_character': '106575.1', 'coefficient_field': '1.1.1.1', 'conductor': 106575, 'conductor_radical': 3045, 'degree': 2, 'euler_factors': [[1, -1, 2], [1, 1], [1], [1], [1, 2, 11], [1, 4, 13], [1, 6, 17], [1, 6, 19], [1, -8, 23], [1, 1], [1, -6, 31], [1, 6, 37], [1, -6, 41], [1, 4, 43], [1, 8, 47], [1, -8, 53], [1, -12, 59], [1, -2, 61], [1, 4, 67], [1, 8, 71], [1, 10, 73], [1, -14, 79], [1, 12, 83], [1, -6, 89], [1, 14, 97]], 'gamma_factors': [[], [0]], 'id': 8122202, 'index': 18, 'label': '2-106575-1.1-c1-0-18', 'leading_term': '4.17655005539', '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': 1, 'origin': 'EllipticCurve/Q/106575/by', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.8372169402682247, 0.541924811854648, -1.346385285787347, -3.869448559617364, -4.88183684701426, -2.892455195766012, 1.004697190326539, 3.647632308799086, 2.993616908179548, 0.5747560930358148, -0.1722812158610336, 1.817831602091073, 3.811577558709531, 2.929289101977646, 0.0695724369885301, -1.478880765102759, -0.7194358940555275, 0.1164374769104421, -0.4245309604001803, -0.8498867815617078, 0.01518705383245858, 0.367249531128658, -1.324921307873208, -2.771027553662835, -1.269447114054788, 1.169634233514039, 0.9128766373527942, -0.2747690479856937, 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-2.950277498387499, 4.838110118720191, 10.62934813363006, 5.739061572451461, -0.466869175710161, -0.1593354510272942, 0.7424024182818628, -0.9335894461576724, -0.4937085774016944, 1.310019752875487, 0.4284535188061432, -0.6081551095366237, 0.2629086835622539, -0.2065901274061028, -1.314834447693289, 0.04509822473014924, 0.5865470944400765, -1.469143473932749, -1.075148986395341, 0.8531333070126345, -1.00391268773437, -0.7987711937457228, 6.972166067512392, 10.35704282907134, 1.609354544482527, -5.14720131116907, -1.286110721559478, 1.769350871343188, -0.3162947889403808, 0.9231351810470814, 3.353322572711667, 0.4162908001209987, -1.05519923928279, 2.777869277308411, 2.7714290165262, -1.089407114186685, 0.5816048413870257, 4.043384457300973, 1.649655394037498, -0.6517625311646306, 0.5255892518324426, -1.82941488971763], 'positive_zeros': ['0.5944785510513148', '1.686639075647048', '2.583626162373048', '2.790737521627808', '3.756488840837513', '4.422648884927740', '4.614887944877146', '5.246485513763349', '5.582726386184237', '6.363643310937901', '6.890886187222153', '7.072428621178614', '8.160750000085181', '8.394014589481579', '9.100044931576983', '9.420566229808062', '10.15741016759592', '10.55821251790740', '11.01894350830010', '11.68984095045700', '11.99596443512206', '12.66958974767345', '13.00035500676697', '13.32194690498614', '13.70092409699140', '14.58358576361402', '14.88242989845637', '15.12529597792041', '15.70502577370408', '16.25237997058888', '16.81553704310609', '17.40093719623873', '17.58882708310895', '17.89240524792655', '18.66374848782087', '19.05672750683237', '19.39472111186078', '19.86955765690738'], 'prelabel': '2-106575-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 29.172001294765433, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2019893345475402302, 'z1': {'__RealLiteral__': 0, 'data': '0.5944785510513148', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.686639075647048', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.583626162373048', 'prec': 57}}