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lfunc_lfunctions • Show schema
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{'A10': 4, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': -4, 'A6': 0, 'A7': -1, 'A8': -1, 'A9': 0, 'Lhash': '624333790150648504', 'a10': [1.2649110640673518, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [-1.7888543819998317, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 412.9383690128496, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [13, [1]], [17, [1, -1]]], 'bad_primes': [2, 3, 13, 17], 'central_character': '51714.1', 'coefficient_field': '1.1.1.1', 'conductor': 51714, 'conductor_radical': 1326, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, 4, 5], [1, 1, 7], [1, 4, 11], [1], [1, -1], [1, -2, 19], [1, -7, 23], [1, 10, 29], [1, 5, 31], [1, -2, 37], [1, -2, 41], [1, -6, 43], [1, -4, 47], [1, 11, 53], [1, 0, 59], [1, -6, 61], [1, -8, 67], [1, 12, 71], [1, -2, 73], [1, 1, 79], [1, 0, 83], [1, 1, 89], [1, 12, 97]], 'gamma_factors': [[], [0]], 'index': 10, 'label': '2-51714-1.1-c1-0-10', 'leading_term': '2.22473862408', '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/51714/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.4572138015221962, 0.3671633295167097, -0.5100628806375062, -1.706123531457579, -2.060239423932037, -0.6062616473149424, 2.222771368813151, 4.455871390056475, 4.206103462896226, 1.729142177493537, -0.5156810556195098, -0.4340586474842957, 1.196946551667807, 1.607627734981394, -0.2612669817161059, -1.91507250942616, -0.352544210711334, 3.491993956982881, 5.234398489644005, 2.725325123746838, -0.52819218479678, 0.3679998370709713, 4.882216960489153, 7.296889015813801, 4.244755584752034, -0.8389545372871968, -2.619792321690519, -0.8333884544722281, 0.6546340416676814, 0.2495236744416185, 0.06908930800685452, 1.050469387901118, 1.009386006369873, -0.8987557720390112, -1.852273800784216, -0.1803587078164363, 1.105630820329979, -0.7517879682889668, -2.933851231320768, -1.3193188089641, 2.358559847481642, 3.127612189362367, 0.8921531194723521, -0.2528088571301705, 0.1457643283738504, -1.231477329848941, -3.845951196558504, -3.316030903694923, -0.009607509681625385, 0.7507866291772068, -1.179822362252033, 0.135251506996168, 4.459799233662041, 2.886151737670938, -7.041479698198728, -14.41960703111166, -10.70352450676653, -2.459599083023428, 0.1994775789425043, -1.428830349468305, -0.8187562157587494, 1.322332801647338, 1.006645381510678, -0.1390215564340804, 0.4932513221032366, 0.1454524886021051, -2.682057053132872, -3.23642935698384, 0.3274666559827412, 1.821526993703248, -1.948573003251231, -4.927423248990424, -2.883388657717201, -0.1582000468357771, -0.1042701553075686, 0.07582587817213061, 1.168446223579489, 0.1578578522130147, -1.686170357666674, -0.5830664724031507, 1.097611841238399, -0.1912251028430606, -0.5059036967505443, 2.659609229831163, 1.677657213847173, -7.067326896391554, -12.42029643036051, -6.590474324903897, 0.4882162869007825, -0.6476185122576233, -3.302017770695272, -0.4950590878257694, 2.079255366662795, 0.3713398794920532, -0.07701675672108667, 1.743032164212811, 0.05193802742707181, -2.871081470401191, 0.1091961436338265, 4.777897339943228, 2.637096264725693, -2.155779287043035, -1.525441118190476, 1.1543214003888, 0.2496279747810714, -0.9247272087162632, 0.3195543831242154, 0.3779602322302074, -0.7793911034884926, 0.3723875742627879, 1.611020499893401, 0.1919770066905793, 0.1066762783950679, 2.39846842863219, 1.590788387698246, -1.111712229222419, 0.6824094865735667, 2.977257988872912, -1.265262060443008, -5.349807521500748], 'positive_zeros': ['0.6299649649662659', '1.559763760750261', '2.670763151328659', '3.073720965539513', '3.722707926279229', '4.275821108777570', '5.190711297171537', '5.470837164228661', '6.452136993299975', '7.100596696551197', '7.610059405715630', '7.712243729424277', '8.395054228639809', '9.020345529711999', '9.432081757724673', '10.08690391004624', '10.87541463172556', '11.14228495728592', '11.33272088947130', '12.25085113680358', '12.59961922537141', '12.99113824888481', '13.58766389356339', '14.64859274177498', '14.79606563883795', '15.33564225675512', '15.93656735068257', '16.11774610683766', '16.51756352770945', '17.22906418031761', '17.64619843415558', '18.53774382079451', '18.70033035002635', '18.98088438605906', '19.51771109386656'], 'prelabel': '2-51714-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 20.32088504501833, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 624333790150648504, 'z1': {'__RealLiteral__': 0, 'data': '0.6299649649662659', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.559763760750261', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.670763151328659', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 412.9383690128496, 'bad_primes': [2, 3, 13, 17], 'central_character': '1.1', 'conductor': 51714, 'conductor_radical': 1326, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, -4, 0, -1, -1, 0, 4, -4, 0, 0, 1, 0, 1, 1, 0, 2, -4, 0, 4, 7, 0, 11, 0, 0, -1, -10, 0, -5, -1, 0, -1, 4, 0, 2, -2, 0, 4, 2, 0, 6, -4, 0, -7, 4, 0, -6, -11, 0, 0, -11, 0, 16, 1, 0, 10, 0, 0, 6, 5, 0, 1, 0, 0, 8, 1, 0, -4, -12, 0, 2, -2, 0, 2, 4, 0, -1, -4, 0, -2, 0, 0, -4, -6, 0, 4, -1, 0, 0, 7, 0, -4, -8, 0, -12, 6, 0, 11], 'euler11': [1, 4, 11], 'euler13': [1, 0, 0], 'euler17': [1, -1, 0], 'euler19': [1, -2, 19], 'euler2': [1, 1, 0], 'euler23': [1, -7, 23], 'euler29': [1, 10, 29], 'euler3': [1, 0, 0], 'euler31': [1, 5, 31], 'euler37': [1, -2, 37], 'euler41': [1, -2, 41], 'euler43': [1, -6, 43], 'euler47': [1, -4, 47], 'euler5': [1, 4, 5], 'euler53': [1, 11, 53], 'euler59': [1, 0, 59], 'euler61': [1, -6, 61], 'euler67': [1, -8, 67], 'euler7': [1, 1, 7], 'euler71': [1, 12, 71], 'euler73': [1, -2, 73], 'euler79': [1, 1, 79], 'euler83': [1, 0, 83], 'euler89': [1, 1, 89], 'euler97': [1, 12, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, 4, 5], [1, 1, 7], [1, 4, 11], [1, 0, 0], [1, -1, 0], [1, -2, 19], [1, -7, 23], [1, 10, 29], [1, 5, 31], [1, -2, 37], [1, -2, 41], [1, -6, 43], [1, -4, 47], [1, 11, 53], [1, 0, 59], [1, -6, 61], [1, -8, 67], [1, 12, 71], [1, -2, 73], [1, 1, 79], [1, 0, 83], [1, 1, 89], [1, 12, 97]], 'index': 10, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/51714/a'], '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': '2-51714-1.1-c1-0-10', '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': '2-51714-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 20.32088504501833, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 624333790150648504, 'z1': {'__RealLiteral__': 0, 'data': '0.6299649649662659', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '624333790150648504', 'Lhash_array': ['624333790150648504'], 'label': '2-51714-1.1-c1-0-10', 'type': 'ECQ', 'url': 'EllipticCurve/Q/51714/a'}