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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 2, 'A4': 0, 'A5': -4, 'A6': 0, 'A7': -4, 'A8': 0, 'A9': 1, 'Lhash': '1002437063159710372', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [1.1547005383792517, 0], 'a4': [0.0, 0], 'a5': [-1.7888543819998317, 0], 'a6': [0.0, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 3064.5945492551255, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [17, [1]], [83, [1, 1]]], 'bad_primes': [2, 17, 83], 'central_character': '383792.1', 'coefficient_field': '1.1.1.1', 'conductor': 383792, 'conductor_radical': 2822, 'degree': 2, 'euler_factors': [[1], [1, -2, 3], [1, 4, 5], [1, 4, 7], [1, 2, 11], [1, 2, 13], [1], [1, -4, 19], [1, -4, 23], [1, 2, 29], [1, 4, 31], [1, -2, 37], [1, 4, 41], [1, 4, 43], [1, -8, 47], [1, 10, 53], [1, 12, 59], [1, -10, 61], [1, -8, 67], [1, 2, 71], [1, -2, 73], [1, -6, 79], [1, 1], [1, -14, 89], [1, 10, 97]], 'gamma_factors': [[], [0]], 'index': 4, 'label': '2-383792-1.1-c1-0-4', 'leading_term': '0.89378471904', '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/383792/q', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.8937847190400815, 0.1524915185566752, -1.173464717608607, -0.9859609388237613, 1.943251679698915, 5.768896657611205, 6.613625895582485, 3.026246065539186, -1.606153023052329, -2.886515049293748, -0.8905208766909068, 0.6618864330470868, 0.226734974489248, -0.1804995451705359, 0.2495046979177181, -0.3365831027346611, -1.594661301516652, -0.2146374283402488, 3.209823977837817, 3.119279076276481, -0.9953625661764751, -1.394571513226199, 4.879182509966736, 8.735230487845005, 3.335191261466517, -3.774415992052382, -3.194164025318575, 1.339643916971593, 1.839909926033338, -0.1169797011857265, 0.1212992020467261, 0.4918237105069179, -0.9541352722462588, -0.6912031839522359, 1.547154088706468, 1.266779545959121, -0.4291065535981839, 0.8362982385691561, 2.003554661546684, -0.4182711565822598, -0.4493203778921727, 4.677058589805479, 5.873440757681443, 0.3282442993475463, -1.495661823526298, 2.57867193360843, 2.46355260754384, -1.872226947828081, -1.276000810981375, 1.971327229460815, 0.7039202134236923, -0.9231643097202527, 0.6979034350232132, -0.409565785105551, -3.749643651620014, -1.948104838781504, 1.309172974934343, -1.060426698088285, -3.427169921450293, -0.8923665074300314, 0.4972269492232699, -0.7347878073477382, -0.06800230245130914, 0.1852676868440317, -1.289386453251883, 0.3136151366000878, 1.540877280635534, -2.1503107639913, -0.5302978593596713, 8.639140956957952, 6.557618551901329, -9.03658550078555, -14.8000734948883, -5.750350313438834, 0.2151973158134648, -0.6126301232786256, -0.1952404380072992, 0.136786455961173, -0.9381981788574562, -0.1645679476789907, 0.3249104738817703, -0.05868143460608641, 1.060957096186453, -1.309773760038341, -6.091750418639173, -1.16372694103326, 8.339819713253089, 5.918252404544726, -1.445049087297886, -0.5766706870312298, 0.290206695857637, -3.170084635561176, -1.833894051988412, 1.064400690246903, -0.1545085166156123, 1.763143708978476, 4.638526437000949, 0.08728674985441887, -3.00248544833293, 0.9538528430990747, 1.333765707044892, -1.169164270400293, 1.293810839622912, 2.525794169331041, -0.08173196197570284, 0.2250050991626849, 0.9255113194865504, -0.1694643332822258, 0.9806154959791666, -0.1849763656475985, -3.500646867497053, 1.091189166378625, 6.187845859142105, 1.231649677742128, -1.397462125596787, 2.199621642627724, 0.02296210634533835, -0.5734667149869461, 7.578538258840161, 8.293087376445007, 0.5966055835263167], 'positive_zeros': ['0.2780096521275995', '0.8606680582008911', '1.901840208481210', '2.603537028710119', '3.073097874409672', '3.362535626961727', '3.679690807424800', '4.266714867613377', '4.939725233876331', '5.324086026609846', '6.098939719494675', '6.665827723224463', '7.226844121151965', '7.471202398302364', '7.850063131056281', '8.327877623596181', '8.906602054745743', '9.152692805874992', '9.713146631189196', '10.03034035121655', '10.76515759765027', '11.10349897480911', '11.63436308664939', '12.08303596672845', '12.56290486411554', '12.90394600840209', '13.21876520484843', '13.86419616243534', '14.18303893472698', '14.83047386227188', '15.10332323215814', '15.51261754685221', '15.78290793798692', '16.22326018969837', '16.62157951131775', '17.01713252899174', '17.61215482476971', '18.46883506367972', '18.63501951560100', '19.04088920487420', '19.28315173008265', '19.78185639310972'], 'prelabel': '2-383792-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 55.35878023633763, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1002437063159710372, 'z1': {'__RealLiteral__': 0, 'data': '0.2780096521275995', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '0.8606680582008911', 'prec': 60}, 'z3': {'__RealLiteral__': 0, 'data': '1.901840208481210', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3064.5945492551255, 'bad_primes': [2, 17, 83], 'central_character': '1.1', 'conductor': 383792, 'conductor_radical': 2822, 'degree': 2, 'dirichlet_coefficients': [1, 0, 2, 0, -4, 0, -4, 0, 1, 0, -2, 0, -2, 0, -8, 0, 0, 0, 4, 0, -8, 0, 4, 0, 11, 0, -4, 0, -2, 0, -4, 0, -4, 0, 16, 0, 2, 0, -4, 0, -4, 0, -4, 0, -4, 0, 8, 0, 9, 0, 0, 0, -10, 0, 8, 0, 8, 0, -12, 0, 10, 0, -4, 0, 8, 0, 8, 0, 8, 0, -2, 0, 2, 0, 22, 0, 8, 0, 6, 0, -11, 0, -1, 0, 0, 0, -4, 0, 14, 0, 8, 0, -8, 0, -16, 0, -10, 0, -2, 0], 'euler11': [1, 2, 11], 'euler13': [1, 2, 13], 'euler17': [1, 0, 0], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, 2, 29], 'euler3': [1, -2, 3], 'euler31': [1, 4, 31], 'euler37': [1, -2, 37], 'euler41': [1, 4, 41], 'euler43': [1, 4, 43], 'euler47': [1, -8, 47], 'euler5': [1, 4, 5], 'euler53': [1, 10, 53], 'euler59': [1, 12, 59], 'euler61': [1, -10, 61], 'euler67': [1, -8, 67], 'euler7': [1, 4, 7], 'euler71': [1, 2, 71], 'euler73': [1, -2, 73], 'euler79': [1, -6, 79], 'euler83': [1, 1, 0], 'euler89': [1, -14, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 0, 0], [1, -2, 3], [1, 4, 5], [1, 4, 7], [1, 2, 11], [1, 2, 13], [1, 0, 0], [1, -4, 19], [1, -4, 23], [1, 2, 29], [1, 4, 31], [1, -2, 37], [1, 4, 41], [1, 4, 43], [1, -8, 47], [1, 10, 53], [1, 12, 59], [1, -10, 61], [1, -8, 67], [1, 2, 71], [1, -2, 73], [1, -6, 79], [1, 1, 0], [1, -14, 89], [1, 10, 97]], 'index': 4, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/383792/q'], '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': '2-383792-1.1-c1-0-4', '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': '2-383792-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 55.35878023633763, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1002437063159710372, 'z1': {'__RealLiteral__': 0, 'data': '0.2780096521275995', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1002437063159710372', 'Lhash_array': ['1002437063159710372'], 'factors': ['2-383792-1.1-c1-0-4'], 'label': '2-383792-1.1-c1-0-4', 'type': 'ECQ', 'url': 'EllipticCurve/Q/383792/q'}