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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': 1, 'A4': 1, 'A5': 0, 'A6': 1, 'A7': 0, 'A8': 1, 'A9': 1, 'Lhash': '435802243076457371', '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': [0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1349.8710461697456, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -1]], [5, [1]], [7, [1]], [23, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '169050.1', 'coefficient_field': '1.1.1.1', 'conductor': 169050, 'conductor_radical': 4830, 'degree': 2, 'euler_factors': [[1, -1], [1, -1], [1], [1], [1, 0, 11], [1, 4, 13], [1, 0, 17], [1, 2, 19], [1, 1], [1, -6, 29], [1, 2, 31], [1, -10, 37], [1, 6, 41], [1, -4, 43], [1, -6, 47], [1, -6, 53], [1, 12, 59], [1, -10, 61], [1, -4, 67], [1, 0, 71], [1, -14, 73], [1, -8, 79], [1, -6, 83], [1, 0, 89], [1, -8, 97]], 'gamma_factors': [[], [0]], 'index': 70, 'label': '2-169050-1.1-c1-0-70', 'leading_term': '5.10367423236', '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/169050/hx', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [5.103674232364988, 3.840796598765937, 0.7096395102721135, -2.357836005690447, -3.075084363791479, -0.8451482285465992, 2.215595016380499, 3.210677216557118, 1.678941889247934, 0.03074991732807527, 0.2320738165606438, 1.121722711830586, 0.396909461152344, -1.532484438279737, -1.973909069834243, -0.3521061650430758, 0.6168315823463081, -0.5986405663117015, -1.625869079684728, -0.3796399241309063, 0.8686425901616779, -0.6294727980346262, -2.559227439475571, -0.9571968989161169, 2.473530849845337, 2.669435434088887, 0.053062304535972, -0.1756070617833514, 2.30068931553159, 2.289154450272301, -0.8140519758983762, -1.661446588126475, 0.3148151652348386, -0.746724401567961, -5.175167539926293, -5.720342876879394, -1.178265048848714, 0.5408010252118474, -2.803287384384436, -3.670237687520457, 0.129186291150542, 1.177455497002499, -2.172507745703137, -2.218092394492546, 2.130227343043283, 2.597968904458924, -1.989850530788496, -3.58066282386767, -0.8062702057180233, -0.06599837386389686, -1.505939453899876, -0.2757882469657096, 1.767833036415476, 0.5091277380830878, -0.9100412731108637, 0.6402264388585529, 1.346726431167565, -0.4121276886050726, -0.6466764097557646, 0.3327128235677517, -1.016343104873445, -2.018662665316023, -0.1034211179284867, -0.4589833017013295, -4.139709915477046, -3.468662060335165, 0.9968270790675171, 0.1216839809219045, -3.322036708221785, -0.05845998188575413, 3.514412427559181, -2.325875878991833, -8.098481375471795, -3.671206288958749, 0.7742602895715516, -3.051454110957154, -5.24285895831018, -0.8328234565945882, 1.276838083752964, -0.3713751831322922, 0.4833302682045356, 1.177798122010749, -1.63708638242199, -1.921383126250783, 1.331528342070062, 1.314381977868939, -0.5794156901904159, 0.6209596129227871, 1.089564478765488, -0.4956842016467863, 1.786928997131328, 5.245623592508681, 2.845152529906585, -0.3304034025633151, 1.055895232051162, 0.8472601469081926, -2.159246684897359, -1.469027344314203, 0.1583198453910948, -2.033851289131483, -2.456167571144255, 0.0922482711094587, -0.3881658379913648, -0.06119939259849674, 5.06658876444699, 5.748311937586113, 0.5285836572552848, 0.3184043246365384, 2.21267444222757, -1.97773167635647, -2.692990171133413, 4.064701796526605, 3.210736604947042, -5.075212657783489, -4.328287037439566, 1.788910019211411, 0.6778318342093894, -1.193475242349675, 1.630511477931554, 1.030771762872154, -1.899190650198922], 'positive_zeros': ['0.5508556152887117', '1.314875777848118', '2.260014259032830', '2.430087574340452', '3.053858997783579', '3.800574613440426', '4.160441946530364', '4.799975366543878', '5.183877933745804', '5.816431957226966', '6.506188688236026', '6.772639077058095', '7.435116547639356', '7.953713078134887', '8.189117563787593', '9.076062565095513', '9.309882152845506', '9.991532256589131', '10.35027052241135', '10.88146120615214', '11.39828454436008', '12.10270022865794', '12.23505192233718', '12.77594241654326', '13.30519454044430', '13.67341715219894', '14.19341243923045', '14.62848974910548', '14.86667019459660', '15.51423654225025', '15.70380136837325', '16.43243997927025', '16.75742223509072', '17.25248262891335', '17.68121335296425', '18.40147574516785', '18.59694066931448', '19.29670890307724', '19.68393881197648', '19.93684388990694'], 'prelabel': '2-169050-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 36.740591260481175, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 435802243076457371, 'z1': {'__RealLiteral__': 0, 'data': '0.5508556152887117', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.314875777848118', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.260014259032830', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1349.8710461697456, 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '1.1', 'conductor': 169050, 'conductor_radical': 4830, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, -4, 0, 0, 1, 0, 1, -2, 0, 0, 0, -1, 1, 0, -4, 1, 0, 6, 0, -2, 1, 0, 0, 0, 1, 10, -2, -4, 0, -6, 0, 4, 0, 0, -1, 6, 1, 0, 0, 0, -4, 6, 1, 0, 0, -2, 6, -12, 0, 10, -2, 0, 1, 0, 0, 4, 0, -1, 0, 0, 1, 14, 10, 0, -2, 0, -4, 8, 0, 1, -6, 6, 0, 0, 4, 6, 0, 0, 0, 0, -1, -2, 6, 0, 1, 8, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 4, 13], 'euler17': [1, 0, 17], 'euler19': [1, 2, 19], 'euler2': [1, -1, 0], 'euler23': [1, 1, 0], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, 2, 31], 'euler37': [1, -10, 37], 'euler41': [1, 6, 41], 'euler43': [1, -4, 43], 'euler47': [1, -6, 47], 'euler5': [1, 0, 0], 'euler53': [1, -6, 53], 'euler59': [1, 12, 59], 'euler61': [1, -10, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 0], 'euler71': [1, 0, 71], 'euler73': [1, -14, 73], 'euler79': [1, -8, 79], 'euler83': [1, -6, 83], 'euler89': [1, 0, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, -1, 0], [1, -1, 0], [1, 0, 0], [1, 0, 0], [1, 0, 11], [1, 4, 13], [1, 0, 17], [1, 2, 19], [1, 1, 0], [1, -6, 29], [1, 2, 31], [1, -10, 37], [1, 6, 41], [1, -4, 43], [1, -6, 47], [1, -6, 53], [1, 12, 59], [1, -10, 61], [1, -4, 67], [1, 0, 71], [1, -14, 73], [1, -8, 79], [1, -6, 83], [1, 0, 89], [1, -8, 97]], 'index': 70, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/169050/hx'], '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': '2-169050-1.1-c1-0-70', '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': '2-169050-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 36.740591260481175, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 435802243076457371, 'z1': {'__RealLiteral__': 0, 'data': '0.5508556152887117', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '435802243076457371', 'Lhash_array': ['435802243076457371'], 'label': '2-169050-1.1-c1-0-70', 'type': 'ECQ', 'url': 'EllipticCurve/Q/169050/hx'}