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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': -3, 'A8': 1, 'A9': 0, 'Lhash': '303200303157276520', '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': [-1.1338934190276817, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 259.4339561671401, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [5, [1, 1]], [19, [1]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '32490.1', 'coefficient_field': '1.1.1.1', 'conductor': 32490, 'conductor_radical': 570, 'degree': 2, 'euler_factors': [[1, -1], [1], [1, 1], [1, 3, 7], [1, 2, 11], [1, 5, 13], [1, -5, 17], [1], [1, -3, 23], [1, 7, 29], [1, -2, 31], [1, -10, 37], [1, 0, 41], [1, -10, 43], [1, 0, 47], [1, 3, 53], [1, 13, 59], [1, -12, 61], [1, 11, 67], [1, 12, 71], [1, -1, 73], [1, -4, 79], [1, -6, 83], [1, 6, 89], [1, -12, 97]], 'gamma_factors': [[], [0]], 'index': 30, 'label': '2-32490-1.1-c1-0-30', 'leading_term': '6.49479335432', '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/32490/be', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.496773579892284, 2.22621100718671, 1.535150900136061, -0.6318820693413562, -3.302935311403248, -4.829350748611891, -4.081630877320465, -1.547402025095805, 0.8782238063619566, 1.531687908025445, 0.56340330511022, -0.3045675399726108, 0.2111927340159255, 1.405156342267092, 1.475532537683834, -0.05550370634179245, -1.488855147495854, -1.044080324992892, 0.6630485879665061, 1.253644951389179, -0.1866139139399831, -1.692271144925712, -1.131127049887787, 0.5597061212312948, 0.5069279313695654, -1.814515547754783, -3.460724266375951, -2.203809561959282, 0.04401057822115468, 0.2013192830272538, -0.7291290876939771, 1.302172962318074, 6.64022152471862, 9.822387669029926, 6.64530262507814, 0.6126132930658369, -1.438594820662047, 1.274500862717803, 3.106799078629787, 1.108935601276028, -0.7182231287594852, 1.428691664498766, 4.541536386979854, 3.649086088218819, -0.0243052185494418, -1.165076363312561, 1.047959444000895, 2.299332953191887, 0.7783408461846986, -0.4973466761123467, 0.06024220679209798, -0.05716119159409424, -1.787677253613471, -1.864643173022388, 1.075905294597336, 3.08121056877768, 1.382140279879803, -0.7421729163322731, 0.01401322767601408, 1.126107540025919, -0.4402458914499523, -2.036594138426071, -0.4918321358410336, 1.344759118493848, -0.02278605223257002, -1.68404536872745, -0.2736099387714042, 0.1998450649913898, -4.367178838927388, -8.09063891603058, -3.273495138695085, 5.352518535119323, 6.732653708688333, 0.9565311983940396, -2.191419968733018, -0.05615938216203734, 1.000122939596264, -0.6094726795480532, 0.1701195318822361, 3.217396677206343, 2.876192754048337, -0.3853027995191327, -0.5613455447032053, 1.962670180151487, 1.325611427320976, -1.985425356368096, -2.257201004148494, 0.2328712220952341, 0.660326568688754, -0.4246862792825903, 0.5044664132516978, 1.685233663654291, 0.2619970666907833, -0.8792982261290463, 0.5212736333405106, 0.4947811925819726, -2.477876701272525, -2.95865289774108, 0.4522351129211128, 1.458418329002555, -1.145254688210776, -0.9067292135052071, 2.266460237264603, 1.347013217752541, -2.642367253056977, -2.1749374137462, 0.4141263385807967, -2.929594764309118, -8.203556835034059, -5.828093369614152, 0.04850670716201339, -0.8345913659805843, -5.104694164329248, -3.501536725185028, 0.9602895399800261, 0.8844040508562505, -0.7747213617231736, 0.5476336824345917, 0.8662550833263475, -1.761466785422282], 'positive_zeros': ['0.9388154144038221', '2.144090389562155', '2.874729612062208', '3.199542192945661', '3.992618461074705', '4.653294856505688', '5.226061214317723', '5.908796603884848', '6.320330091447912', '7.242805119753324', '7.545709125257126', '7.904324545743640', '9.033314650774247', '9.405736483423848', '10.10279764621698', '10.38685936501152', '11.24808246573514', '11.64980473854544', '12.35666095065343', '12.73075335177499', '12.98764153711838', '13.67135690402657', '14.38061885217476', '14.74797457669959', '15.20353099274415', '15.79756129148294', '16.24766873459295', '16.78368589023650', '17.02120678796701', '17.83909209239714', '18.54225247083729', '19.00522942130664', '19.40601833823867', '19.73391830034630'], 'prelabel': '2-32490-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.106953658812706, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 303200303157276520, 'z1': {'__RealLiteral__': 0, 'data': '0.9388154144038221', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '2.144090389562155', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.874729612062208', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 259.4339561671401, 'bad_primes': [2, 3, 5, 19], 'central_character': '1.1', 'conductor': 32490, 'conductor_radical': 570, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, -1, 0, -3, 1, 0, -1, -2, 0, -5, -3, 0, 1, 5, 0, 0, -1, 0, -2, 3, 0, 1, -5, 0, -3, -7, 0, 2, 1, 0, 5, 3, 0, 10, 0, 0, -1, 0, 0, 10, -2, 0, 3, 0, 0, 2, 1, 0, -5, -3, 0, 2, -3, 0, -7, -13, 0, 12, 2, 0, 1, 5, 0, -11, 5, 0, 3, -12, 0, 1, 10, 0, 0, 6, 0, 4, -1, 0, 0, 6, 0, -5, 10, 0, -2, -6, 0, 15, 3, 0, 0, 0, 0, 12, 2, 0, 1], 'euler11': [1, 2, 11], 'euler13': [1, 5, 13], 'euler17': [1, -5, 17], 'euler19': [1, 0, 0], 'euler2': [1, -1, 0], 'euler23': [1, -3, 23], 'euler29': [1, 7, 29], 'euler3': [1, 0, 0], 'euler31': [1, -2, 31], 'euler37': [1, -10, 37], 'euler41': [1, 0, 41], 'euler43': [1, -10, 43], 'euler47': [1, 0, 47], 'euler5': [1, 1, 0], 'euler53': [1, 3, 53], 'euler59': [1, 13, 59], 'euler61': [1, -12, 61], 'euler67': [1, 11, 67], 'euler7': [1, 3, 7], 'euler71': [1, 12, 71], 'euler73': [1, -1, 73], 'euler79': [1, -4, 79], 'euler83': [1, -6, 83], 'euler89': [1, 6, 89], 'euler97': [1, -12, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, 1, 0], [1, 3, 7], [1, 2, 11], [1, 5, 13], [1, -5, 17], [1, 0, 0], [1, -3, 23], [1, 7, 29], [1, -2, 31], [1, -10, 37], [1, 0, 41], [1, -10, 43], [1, 0, 47], [1, 3, 53], [1, 13, 59], [1, -12, 61], [1, 11, 67], [1, 12, 71], [1, -1, 73], [1, -4, 79], [1, -6, 83], [1, 6, 89], [1, -12, 97]], 'index': 30, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/32490/be'], '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': '2-32490-1.1-c1-0-30', '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': '2-32490-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.106953658812706, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 303200303157276520, 'z1': {'__RealLiteral__': 0, 'data': '0.9388154144038221', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '303200303157276520', 'Lhash_array': ['303200303157276520'], 'label': '2-32490-1.1-c1-0-30', 'type': 'ECQ', 'url': 'EllipticCurve/Q/32490/be'}