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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 3, 'A4': 0, 'A5': 2, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 6, 'Lhash': '1288315388509425401', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [1.7320508075688774, 0], 'a4': [0.0, 0], 'a5': [0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [2.0, 0], 'algebraic': True, 'analytic_conductor': 2972.2874845185256, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, 1]], [17, [1]], [23, [1, -1]]], 'bad_primes': [2, 7, 17, 23], 'central_character': '372232.1', 'coefficient_field': '1.1.1.1', 'conductor': 372232, 'conductor_radical': 5474, 'degree': 2, 'euler_factors': [[1], [1, -3, 3], [1, -2, 5], [1, 1], [1, -2, 11], [1, 0, 13], [1], [1, -1, 19], [1, -1], [1, 1, 29], [1, 3, 31], [1, 2, 37], [1, -6, 41], [1, -2, 43], [1, 1, 47], [1, 7, 53], [1, -5, 59], [1, 12, 61], [1, 8, 67], [1, 10, 71], [1, 10, 73], [1, -4, 79], [1, -3, 83], [1, 10, 89], [1, -16, 97]], 'gamma_factors': [[], [0]], 'index': 14, 'label': '2-372232-1.1-c1-0-14', 'leading_term': '19.996072371', '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/372232/p', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 4.541118711953465, 6.574122939930083, 5.006627515775758, 1.433061268090098, -0.9147734479096543, -0.5660077477925453, 0.5930041661135692, 0.215827788353535, -1.037382851228925, -0.9199087679156646, 0.3029218036713639, 0.2833361544256537, -0.8579474274795522, -0.4204727818165833, 1.456727382511289, 1.222755904528243, -1.086760879530065, -0.3691016723611732, 4.195431757286801, 5.426605365824212, -0.2714153582679263, -5.34365953642933, -3.121883940217348, 0.7725665567141466, -1.034604233870323, -4.380831814615247, -2.366579207434546, 1.425198571989499, 0.8621038990268934, -0.8039975221943315, 1.0596933925202, 2.629225768054526, 0.4623939718018856, -1.109480817134337, 0.3817212364505491, 1.031942829988828, 0.06111136028527816, 0.2898064225815892, -0.1118075872326848, -2.57516880698165, -2.070667257544567, 1.062051928153587, -1.875024870236083, -8.289503523030215, -4.444964526374643, 6.978253649359622, 8.522991661898892, 0.3016517808150141, -1.77091118387501, 3.010489123029087, 3.274097107746352, -0.02596021836119699, -0.0940899658294847, 0.4256979891973022, -0.7971378616289776, -0.2245428515168052, 0.94644003824836, 0.0485932646189928, 0.3753568715011845, 1.30060793005021, -1.720083297633455, -3.815986240488585, -0.516176059633289, 0.02911671443521695, -3.538062985990153, -0.1783397648312186, 6.649367470359874, 3.717312971789649, -2.090482118070853, 0.8852603664749067, 3.206699391406089, -1.996935141833788, -3.56964802262824, 0.2983868744870721, -0.2733950963916046, -2.635347516408246, -0.8075051216420629, 0.07690447067720209, -0.9554123660157586, 0.5583532246946545, 0.9547602270650631, -1.318531250980041, -0.8197327925242637, 0.1110523352362665, -1.606066441856742, -0.3871043945629186, 1.334983131459488, -2.50011349490061, -3.325933989755723, 0.6003258768854636, -4.420353860053762, -11.73006533244051, -3.368251818539477, 7.929160771039553, 4.457354524196771, -0.8023074297896001, 2.265809163309577, 2.93132198212966, -0.03838983551361431, 0.08642014221918914, 0.2614696881885659, -0.2912690540509827, 0.8984906072746691, 0.3342015254178989, -0.541269814562859, 1.315647514063888, 0.4503236078954818, -0.66087596835536, 4.132506625554384, 4.681495536076583, -0.9796870643642959, 2.025873803344514, 6.641121924065141, -2.281877101795412, -9.314177334762588, -3.259530549039528, -0.1141153284490083, -2.305543736017777, -0.08619422615808069, 0.2499535974719507], 'positive_zeros': ['1.118133823616930', '1.605159183416547', '2.042227933107593', '2.681467106785270', '3.063947949281236', '3.558073586512651', '4.129575773159313', '4.525768154748569', '5.240610743761671', '5.921807713150558', '6.181258553532346', '6.884465081588990', '7.340670242264791', '7.652626506566513', '8.291326144462187', '8.699660077514387', '9.281884571292421', '9.372815923948667', '9.734061487485344', '10.39583795869586', '10.66898199646093', '11.34576659834962', '12.01053803586098', '12.34954912691300', '12.99696155805139', '13.26886009332605', '13.59516563055588', '14.03297992607114', '14.51319735686909', '14.67675252470418', '15.14271132552331', '15.78855538479747', '16.00241299807047', '16.50579439641019', '17.12684777812863', '17.45894109957855', '17.91722886597870', '18.47528852158272', '18.72743087530497', '19.34984990134183', '19.51843445296808', '19.93538129792654'], 'prelabel': '2-372232-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.518689314018964, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1288315388509425401, 'z1': {'__RealLiteral__': 0, 'data': '1.118133823616930', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.605159183416547', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.042227933107593', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2972.2874845185256, 'bad_primes': [2, 7, 17, 23], 'central_character': '1.1', 'conductor': 372232, 'conductor_radical': 5474, 'degree': 2, 'dirichlet_coefficients': [1, 0, 3, 0, 2, 0, -1, 0, 6, 0, 2, 0, 0, 0, 6, 0, 0, 0, 1, 0, -3, 0, 1, 0, -1, 0, 9, 0, -1, 0, -3, 0, 6, 0, -2, 0, -2, 0, 0, 0, 6, 0, 2, 0, 12, 0, -1, 0, 1, 0, 0, 0, -7, 0, 4, 0, 3, 0, 5, 0, -12, 0, -6, 0, 0, 0, -8, 0, 3, 0, -10, 0, -10, 0, -3, 0, -2, 0, 4, 0, 9, 0, 3, 0, 0, 0, -3, 0, -10, 0, 0, 0, -9, 0, 2, 0, 16, 0, 12, 0], 'euler11': [1, -2, 11], 'euler13': [1, 0, 13], 'euler17': [1, 0, 0], 'euler19': [1, -1, 19], 'euler2': [1, 0, 0], 'euler23': [1, -1, 0], 'euler29': [1, 1, 29], 'euler3': [1, -3, 3], 'euler31': [1, 3, 31], 'euler37': [1, 2, 37], 'euler41': [1, -6, 41], 'euler43': [1, -2, 43], 'euler47': [1, 1, 47], 'euler5': [1, -2, 5], 'euler53': [1, 7, 53], 'euler59': [1, -5, 59], 'euler61': [1, 12, 61], 'euler67': [1, 8, 67], 'euler7': [1, 1, 0], 'euler71': [1, 10, 71], 'euler73': [1, 10, 73], 'euler79': [1, -4, 79], 'euler83': [1, -3, 83], 'euler89': [1, 10, 89], 'euler97': [1, -16, 97], 'euler_factors': [[1, 0, 0], [1, -3, 3], [1, -2, 5], [1, 1, 0], [1, -2, 11], [1, 0, 13], [1, 0, 0], [1, -1, 19], [1, -1, 0], [1, 1, 29], [1, 3, 31], [1, 2, 37], [1, -6, 41], [1, -2, 43], [1, 1, 47], [1, 7, 53], [1, -5, 59], [1, 12, 61], [1, 8, 67], [1, 10, 71], [1, 10, 73], [1, -4, 79], [1, -3, 83], [1, 10, 89], [1, -16, 97]], 'index': 14, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/372232/p'], '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': '2-372232-1.1-c1-0-14', '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': '2-372232-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.518689314018964, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1288315388509425401, 'z1': {'__RealLiteral__': 0, 'data': '1.118133823616930', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1288315388509425401', 'Lhash_array': ['1288315388509425401'], 'factors': ['2-372232-1.1-c1-0-14'], 'label': '2-372232-1.1-c1-0-14', 'type': 'ECQ', 'url': 'EllipticCurve/Q/372232/p'}