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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': '2221551179919946280', '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, 0, 11], [1, 4, 13], [1, 0, 17], [1, -6, 19], [1, -1], [1, -6, 29], [1, -10, 31], [1, -6, 37], [1, 2, 41], [1, -12, 43], [1, 10, 47], [1, -10, 53], [1, 12, 59], [1, -14, 61], [1, 12, 67], [1, -12, 71], [1, -14, 73], [1, 0, 79], [1, -2, 83], [1, 12, 89], [1, -12, 97]], 'gamma_factors': [[], [0]], 'index': 24, 'label': '2-30912-1.1-c1-0-24', 'leading_term': '2.6873047366', '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/ba', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.687304736596533, 2.264719249608494, 1.136266585514578, -0.19245731917957, -0.8920177603868991, -0.3339862316621787, 1.211950140399445, 2.505827816561696, 2.311814946490845, 0.7315331013853018, -0.548113045433833, 0.2160526903051852, 2.774274578531365, 4.643160608277903, 3.45715528112444, -0.3237646628196095, -3.550897418695808, -3.644582730260061, -1.382407370480291, 0.219342170119013, -0.3251746503770411, -1.353855959351268, -0.7290870140313893, 0.9302398337330308, 1.165671576511216, -0.4421512958649626, -1.281048140261937, 0.4608095212005855, 2.677179268224294, 2.123065214970549, -0.510174729784801, -1.109528703860799, 1.732915275498526, 4.014187000865732, 1.794897673580093, -2.823618172064147, -4.403235961250877, -1.816328635052891, 0.6816546951817626, 0.3277387429846497, -0.4197247365842856, 1.018025091289663, 2.436813148819647, 0.6912854371483728, -2.361650263791299, -2.458665751459048, 0.005448266197726848, 0.7339843078531005, -0.9594165992494658, -1.093566051749233, 1.48242784018524, 2.472615213712461, -0.3841413465294598, -2.887276227908606, -1.378808768571413, 1.029240281451825, 0.3603385521524674, -0.8225239286537798, 1.625407025314497, 4.957931877046601, 3.702984361709584, -0.3385762609914743, -0.6942120525823773, 2.577094419093987, 3.177391646803074, -0.1667925737802357, -1.877909942778711, 0.160229423844463, 1.531465377165886, 0.1740751383705329, -0.5324789895859154, 0.4847386565759373, 0.06607022336488895, -1.384481398513154, 0.4752319999535861, 4.453361878973128, 4.01311319603629, -0.7941518643076381, -2.402262900974826, 0.6640164095669776, 0.9661829767725714, -3.808874775784201, -6.280143909771582, -2.853221740237582, 0.5001456660502726, 0.1369646743928776, 0.2573130144922178, 2.625119035338544, 2.895434910921155, 0.491244436547382, 0.1391073451266772, 1.508349885700845, -0.3893682282783669, -3.889936975596248, -2.690464583878837, 1.545521809247421, 1.881749454800053, -0.7673821925689597, -0.6131797559596445, 0.9054584228034003, -0.4621275175514789, -1.162023561278155, 2.812114781854129, 5.672823547670979, 2.103280895977259, -1.789028004497021, -0.051407106919833, 2.134198806728374, 0.1752188874691589, -0.672514416605477, 2.42941429149088, 3.126469403949832, -0.7422145157900816, -2.404191827766354, 0.06623153371732766, 0.9395989400461207, -0.5071212148147827, -0.1528571293591805, 0.2966503718979912, -2.202490924460573, -3.120719380698418], 'positive_zeros': ['0.7101791279007846', '1.313250954845261', '2.360614215205117', '2.720076233142973', '3.730432317229636', '4.683109941253797', '4.927925463424645', '5.607390310267763', '6.189681495986510', '6.704630709276035', '7.449030770835865', '7.872030342750887', '8.595876031050859', '9.400897153400539', '9.816181090792265', '10.11622788491750', '10.80248714412314', '11.49939445754561', '11.87222297200218', '12.37015229162099', '12.97408903039033', '13.61825202547115', '14.04769989584290', '14.38168236402920', '15.22398966297961', '15.56237314373398', '16.23837150856697', '16.73468220309394', '17.27648851595635', '17.63792936016597', '18.01021095954535', '18.46783719153928', '19.20795528212531', '19.69971686455895'], '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': 2221551179919946280, 'z1': {'__RealLiteral__': 0, 'data': '0.7101791279007846', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.313250954845261', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.360614215205117', '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, 0, 0, -4, 0, -2, 0, 0, 0, 6, 0, -1, 0, 1, 0, -1, 0, -1, 0, 6, 0, 10, 0, 0, 0, 2, 0, 6, 0, 4, 0, -2, 0, 12, 0, 2, 0, -10, 0, 1, 0, 0, 0, 10, 0, 0, 0, -6, 0, -12, 0, 14, 0, 1, 0, -8, 0, -12, 0, -1, 0, 12, 0, 14, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, -6, 0, -12, 0, -4, 0, -10, 0, 12, 0, 12, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 4, 13], 'euler17': [1, 0, 17], 'euler19': [1, -6, 19], 'euler2': [1, 0, 0], 'euler23': [1, -1, 0], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, -10, 31], 'euler37': [1, -6, 37], 'euler41': [1, 2, 41], 'euler43': [1, -12, 43], 'euler47': [1, 10, 47], 'euler5': [1, -2, 5], 'euler53': [1, -10, 53], 'euler59': [1, 12, 59], 'euler61': [1, -14, 61], 'euler67': [1, 12, 67], 'euler7': [1, -1, 0], 'euler71': [1, -12, 71], 'euler73': [1, -14, 73], 'euler79': [1, 0, 79], 'euler83': [1, -2, 83], 'euler89': [1, 12, 89], 'euler97': [1, -12, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, -2, 5], [1, -1, 0], [1, 0, 11], [1, 4, 13], [1, 0, 17], [1, -6, 19], [1, -1, 0], [1, -6, 29], [1, -10, 31], [1, -6, 37], [1, 2, 41], [1, -12, 43], [1, 10, 47], [1, -10, 53], [1, 12, 59], [1, -14, 61], [1, 12, 67], [1, -12, 71], [1, -14, 73], [1, 0, 79], [1, -2, 83], [1, 12, 89], [1, -12, 97]], 'index': 24, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/30912/ba'], '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-c1-0-24', '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': 2221551179919946280, 'z1': {'__RealLiteral__': 0, 'data': '0.7101791279007846', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2221551179919946280', 'Lhash_array': ['2221551179919946280'], 'factors': ['2-30912-1.1-c1-0-24'], 'label': '2-30912-1.1-c1-0-24', 'type': 'ECQ', 'url': 'EllipticCurve/Q/30912/ba'}