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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': '979593060851052599', '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': 1220.752946101335, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, 1]], [7, [1]], [13, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 13], 'central_character': '152880.1', 'coefficient_field': '1.1.1.1', 'conductor': 152880, 'conductor_radical': 2730, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 1], [1], [1, 4, 11], [1, 1], [1, -6, 17], [1, -4, 19], [1, 8, 23], [1, -6, 29], [1, 8, 31], [1, 10, 37], [1, -6, 41], [1, 4, 43], [1, 0, 47], [1, 10, 53], [1, -4, 59], [1, -2, 61], [1, -12, 67], [1, 16, 71], [1, 2, 73], [1, -16, 79], [1, 12, 83], [1, 10, 89], [1, -6, 97]], 'gamma_factors': [[], [0]], 'index': 99, 'label': '2-152880-1.1-c1-0-99', 'leading_term': '4.3692565732', '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/152880/i', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.9016503251779295, 0.7921159443773975, -0.5988381795897125, -2.202703677029944, -2.234334735310421, -0.1945986029683697, 1.911858343140243, 1.384837649357241, -1.726173953341924, -4.043146648227941, -2.850124039536526, 0.1435195121375348, 0.9227599891912961, -1.113050059822692, -2.167661974514231, 0.1512469240186897, 2.892723014218639, 2.218479911743644, -0.5441327027571855, -1.213169357519481, 0.3364644835388264, 0.5613510847142636, -0.7733291481108323, 0.07890492189788954, 3.39133458720102, 4.24318890427163, 0.8781958580329765, -1.724828929553665, -0.348685459841761, 1.168754715263085, -0.1940589671607125, -0.8564831469114554, 1.341499351513777, 1.260037178527456, -3.979633959851091, -7.65213429381494, -4.198745440655402, 0.8247652653294665, 0.6518548175520787, -1.51596672087204, -0.6449686739089036, 0.2464833577469787, -2.050557279692485, -3.181943463181673, -0.3754369045166862, 1.319871178004108, -0.6019285960188668, -1.363907302519137, 0.2624381713155186, -0.1217938132257577, -1.29096762073362, 1.732172112966504, 5.119060501200414, 2.11049325124773, -2.589914196666461, -1.483330485966658, 0.7166974248009743, -2.100969783247497, -3.717939355075356, 1.081236974942392, 4.770434178475779, 2.197246957292774, -0.3213437989901684, 0.2506546102403154, -0.556549027469958, -1.505123266709474, 1.574421499896982, 3.748483908731672, 0.4495883959497941, -1.810616145404376, 0.7930605663056662, 1.850307752633743, 0.1003139002867874, 1.18384724327398, 2.589017594970195, -0.548270200213844, -2.186710794664326, 1.365283836008736, 1.606582624793532, -3.227520152555561, -3.425878290985551, 0.6410898488319945, 0.2203521144838779, -1.459015069628828, 1.902135333408614, 3.832773218730902, 0.4702713673893, -0.298029320080152, 2.352053871159092, 1.16075809278004, -1.139839290353825, 0.9645851994548658, 2.339365352536467, 0.2868846520303534, -0.06677460049755729, -0.2851365375444634, -3.359138102376946, -2.396283799704661, 3.115364178594479, 2.498365041040006, -2.200606141269003, 0.1351382946143843, 4.347448551362564, 1.539398264374822, -0.8842106410766102, 1.342955789804569, -0.04669090948743196, -3.611234231628149, -1.430392886454038, 1.242566606154072, -0.655935475505308, -0.7538496954758083, 0.880017254006971, -1.173538402042249, -1.846251557067901, 1.530885428832467, 1.322518637431674, -1.213453378989093, 0.190995019699698, -0.4052803947139846], 'positive_zeros': ['0.6618939752018018', '1.518836180434413', '2.124191168659763', '2.985719917597865', '3.383264016511480', '3.988717559133464', '4.695556409002214', '5.196542499688770', '5.604453608188408', '5.992388513569225', '6.806478575047569', '7.286346899645427', '7.725041366554574', '8.116312816830010', '8.579167593548984', '9.441220832738472', '9.813012607396027', '10.34234898024568', '10.54964942011916', '11.27877973069101', '11.68728959369622', '12.20461165026730', '12.48209089079895', '12.89922808477728', '13.59248796951930', '14.11523351100540', '14.35855132354830', '14.95587762995649', '15.67775037499860', '15.92025232167765', '16.16569995527346', '16.65225179731257', '17.27635606935834', '17.68893958410902', '18.29103680567506', '18.31989139495872', '18.96654515289479', '19.41539640589611', '19.83978982941332'], 'prelabel': '2-152880-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 34.93927512272307, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 979593060851052599, 'z1': {'__RealLiteral__': 0, 'data': '0.6618939752018018', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.518836180434413', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.124191168659763', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1220.752946101335, 'bad_primes': [2, 3, 5, 7, 13], 'central_character': '1.1', 'conductor': 152880, 'conductor_radical': 2730, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, 0, 0, 1, 0, -4, 0, -1, 0, 1, 0, 6, 0, 4, 0, 0, 0, -8, 0, 1, 0, -1, 0, 6, 0, -8, 0, 4, 0, 0, 0, -10, 0, 1, 0, 6, 0, -4, 0, -1, 0, 0, 0, 0, 0, -6, 0, -10, 0, 4, 0, -4, 0, 4, 0, 2, 0, 0, 0, 1, 0, 12, 0, 8, 0, -16, 0, -2, 0, -1, 0, 0, 0, 16, 0, 1, 0, -12, 0, -6, 0, -6, 0, -10, 0, 0, 0, 8, 0, -4, 0, 6, 0, -4, 0], 'euler11': [1, 4, 11], 'euler13': [1, 1, 0], 'euler17': [1, -6, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 8, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 8, 31], 'euler37': [1, 10, 37], 'euler41': [1, -6, 41], 'euler43': [1, 4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 1, 0], 'euler53': [1, 10, 53], 'euler59': [1, -4, 59], 'euler61': [1, -2, 61], 'euler67': [1, -12, 67], 'euler7': [1, 0, 0], 'euler71': [1, 16, 71], 'euler73': [1, 2, 73], 'euler79': [1, -16, 79], 'euler83': [1, 12, 83], 'euler89': [1, 10, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 1, 0], [1, 0, 0], [1, 4, 11], [1, 1, 0], [1, -6, 17], [1, -4, 19], [1, 8, 23], [1, -6, 29], [1, 8, 31], [1, 10, 37], [1, -6, 41], [1, 4, 43], [1, 0, 47], [1, 10, 53], [1, -4, 59], [1, -2, 61], [1, -12, 67], [1, 16, 71], [1, 2, 73], [1, -16, 79], [1, 12, 83], [1, 10, 89], [1, -6, 97]], 'index': 99, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/152880/i'], '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': '2-152880-1.1-c1-0-99', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-152880-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 34.93927512272307, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 979593060851052599, 'z1': {'__RealLiteral__': 0, 'data': '0.6618939752018018', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '979593060851052599', 'Lhash_array': ['979593060851052599'], 'label': '2-152880-1.1-c1-0-99', 'type': 'ECQ', 'url': 'EllipticCurve/Q/152880/i'}