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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': -1, 'A8': -3, 'A9': 0, 'Lhash': '621937958716732939', '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': [-0.3779644730092272, 0], 'a8': [-1.0606601717798212, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 304.34980730411036, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, -1]], [7, [1, 1]], [11, [1]]], 'bad_primes': [3, 5, 7, 11], 'central_character': '38115.1', 'coefficient_field': '1.1.1.1', 'conductor': 38115, 'conductor_radical': 1155, 'degree': 2, 'euler_factors': [[1, -1, 2], [1], [1, -1], [1, 1], [1], [1, -2, 13], [1, -6, 17], [1, 4, 19], [1, -4, 23], [1, -10, 29], [1, 4, 31], [1, 2, 37], [1, -10, 41], [1, 12, 43], [1, 0, 47], [1, 10, 53], [1, -12, 59], [1, -2, 61], [1, -4, 67], [1, 8, 71], [1, -14, 73], [1, 4, 79], [1, -8, 83], [1, 6, 89], [1, 10, 97]], 'gamma_factors': [[], [0]], 'index': 9, 'label': '2-38115-1.1-c1-0-9', 'leading_term': '2.94046929215', '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/38115/y', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.940469292152584, 2.352325483954512, 0.7904825841812818, -1.021262521415972, -1.903873568981884, -0.9476856980719068, 1.521153954615597, 3.794222115336242, 4.011722820775054, 1.901226740951117, -0.7602561356961794, -1.772059437185312, -0.7505064239431593, 0.530675270343915, 0.2965388535916765, -1.044564871372897, -1.484604507248139, -0.1659756825022157, 1.341589716367142, 1.15536174637036, -0.2231924580093721, -0.5925992974578188, 0.6369523369808974, 1.438110437865549, 0.3399241659311746, -0.9234324712602717, 0.08551678487459238, 2.104171639197391, 1.11087658256026, -3.601779795357763, -7.171833524099061, -5.270756412281104, -0.3622888907533119, 1.547471899303087, -0.5790764304694522, -1.833656073766295, 0.5679243359255515, 2.991799728797198, 1.737985805253682, -0.5984013918008964, 0.3780104770442068, 2.9890306419232, 2.009887257915548, -2.096546117269369, -3.089754826527122, 1.04050958454577, 4.498969040614017, 2.736812540927349, -0.8582666324827609, -1.266531153804075, 0.3870993525108038, 0.379940810815322, -0.6183161329997343, 0.1326144492229968, 1.497365975111104, 0.8316021227332263, -0.4686488374750684, 0.2379975099250932, 1.258984671407673, 0.05620583261006426, -0.7520347331294852, 2.038056232715312, 4.862757652110362, 2.78454220984047, -0.8843041577635636, 0.3236626248724843, 4.190241145236848, 3.593399941708449, -0.3015286833249892, -0.2992403289867683, 3.166316604366329, 3.164840144641071, -0.1189100298373444, -0.04131211607760637, 3.037638296908727, 2.561934678969152, -0.6808703276529776, -0.02101672958808416, 2.847168807984595, -0.03454687651304383, -7.063236671157266, -8.484730479612761, -3.273291425797342, 0.1413614282833081, -0.7896991160645852, -0.9312308980252607, 0.5556043546882191, 0.00800837706995425, -1.320544744674794, 0.1514432353964532, 2.085743028098108, 1.013672353570275, -0.4413208935808346, 0.2512480528846869, 0.3400988497961028, -0.4809176978341815, 2.069479639068237, 6.403693410169947, 5.507961123373329, 0.6224762001818619, -0.3265007163362467, 1.966377687276612, 0.8512510216103795, -1.27615500318431, 1.609286591210605, 4.588563972813338, 0.7982632822839087, -3.800843985193799, -2.064176858250525, 0.112146582204427, -2.856531192169689, -4.247841064349046, -0.2624663489569914, 1.151042267044488, -2.359990546599332, -1.916006401621262, 3.631654327118364, 4.838388170646747, 0.8355690656230654, -0.2790078758290893, 1.359452100923703], 'positive_zeros': ['0.6046894761928077', '1.357081293099334', '2.419835324269949', '3.124469347498214', '3.561650095309919', '4.272765555159141', '4.957252561537985', '5.391471359077858', '6.049945865361782', '6.489764787487302', '7.072047599940292', '8.022248085386611', '8.446727706387882', '8.957305393167842', '9.661605242899338', '9.962209174162658', '10.62451128215824', '11.19891416035812', '11.92704085790548', '12.43335557468375', '12.83129137691636', '13.22896319558037', '13.88075913153497', '14.20885430910133', '14.75767525037512', '15.10325350127992', '15.91800513702751', '16.22773960463193', '16.97564122545721', '17.27512598577268', '17.98856488682672', '18.25395349198197', '18.93562119010498', '19.25170013356030', '19.74865187104420'], 'prelabel': '2-38115-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 17.445624302503777, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 621937958716732939, 'z1': {'__RealLiteral__': 0, 'data': '0.6046894761928077', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.357081293099334', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.419835324269949', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 304.34980730411036, 'bad_primes': [3, 5, 7, 11], 'central_character': '1.1', 'conductor': 38115, 'conductor_radical': 1155, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, -1, 1, 0, -1, -3, 0, 1, 0, 0, 2, -1, 0, -1, 6, 0, -4, -1, 0, 0, 4, 0, 1, 2, 0, 1, 10, 0, -4, 5, 0, 6, -1, 0, -2, -4, 0, -3, 10, 0, -12, 0, 0, 4, 0, 0, 1, 1, 0, -2, -10, 0, 0, 3, 0, 10, 12, 0, 2, -4, 0, 7, 2, 0, 4, -6, 0, -1, -8, 0, 14, -2, 0, 4, 0, 0, -4, -1, 0, 10, 8, 0, 6, -12, 0, 0, -6, 0, -2, -4, 0, 0, -4, 0, -10, 1, 0, -1], 'euler11': [1, 0, 0], 'euler13': [1, -2, 13], 'euler17': [1, -6, 17], 'euler19': [1, 4, 19], 'euler2': [1, -1, 2], 'euler23': [1, -4, 23], 'euler29': [1, -10, 29], 'euler3': [1, 0, 0], 'euler31': [1, 4, 31], 'euler37': [1, 2, 37], 'euler41': [1, -10, 41], 'euler43': [1, 12, 43], 'euler47': [1, 0, 47], 'euler5': [1, -1, 0], 'euler53': [1, 10, 53], 'euler59': [1, -12, 59], 'euler61': [1, -2, 61], 'euler67': [1, -4, 67], 'euler7': [1, 1, 0], 'euler71': [1, 8, 71], 'euler73': [1, -14, 73], 'euler79': [1, 4, 79], 'euler83': [1, -8, 83], 'euler89': [1, 6, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, -1, 2], [1, 0, 0], [1, -1, 0], [1, 1, 0], [1, 0, 0], [1, -2, 13], [1, -6, 17], [1, 4, 19], [1, -4, 23], [1, -10, 29], [1, 4, 31], [1, 2, 37], [1, -10, 41], [1, 12, 43], [1, 0, 47], [1, 10, 53], [1, -12, 59], [1, -2, 61], [1, -4, 67], [1, 8, 71], [1, -14, 73], [1, 4, 79], [1, -8, 83], [1, 6, 89], [1, 10, 97]], 'index': 9, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/38115/y'], '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': '2-38115-1.1-c1-0-9', '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': '2-38115-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 17.445624302503777, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 621937958716732939, 'z1': {'__RealLiteral__': 0, 'data': '0.6046894761928077', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '621937958716732939', 'Lhash_array': ['621937958716732939'], 'label': '2-38115-1.1-c1-0-9', 'type': 'ECQ', 'url': 'EllipticCurve/Q/38115/y'}