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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -5, 'A8': 0, 'A9': 1, 'Lhash': '2238871682284673178', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-1.889822365046136, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 498.26650861278983, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [13, [1, 1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '62400.1', 'coefficient_field': '1.1.1.1', 'conductor': 62400, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, 5, 7], [1, 5, 11], [1, 1], [1, 3, 17], [1, -4, 19], [1, -5, 23], [1, -4, 29], [1, 0, 31], [1, -7, 37], [1, -11, 41], [1, -12, 43], [1, -6, 47], [1, 1, 53], [1, 12, 59], [1, -7, 61], [1, 4, 67], [1, 7, 71], [1, 14, 73], [1, 5, 79], [1, -2, 83], [1, 3, 89], [1, 1, 97]], 'gamma_factors': [[], [0]], 'index': 20, 'label': '2-62400-1.1-c1-0-20', 'leading_term': '0.988168190685', '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/62400/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.9881681906851034, 0.5973663067869105, -0.2809040282816829, -0.7857263264361992, 0.1072289068053869, 2.607408672702826, 5.397601694500652, 6.340259225513187, 4.449591618384872, 1.190152449222566, -0.7459438286568145, -0.3376282230157085, 0.5217089423652577, -0.6172033863409032, -3.370053534520645, -4.645895625034916, -2.678492471352558, 0.2455698577349417, 0.5120530922955286, -1.938061510239169, -3.477056586570663, -1.917433872901582, 0.4828425572207572, 0.6877006736477494, -0.4310729601092358, 0.1464378997786278, 2.234585249666378, 2.559472299519497, 0.4879008648210468, -0.5202138605855909, 0.9922872094946622, 1.082954137948831, -3.307160891386855, -8.09454780187945, -7.205316894918972, -1.916862676369757, 0.9598687999607793, -0.5263742520404456, -1.559677395526065, 0.3618265046804374, 1.637962587265002, 0.112010933104271, -0.7634493378008104, 1.005772739979293, 1.561237020481869, -1.369702364700625, -3.181511385849732, -0.2192290122380754, 3.305739860272894, 2.529915744414039, -0.003487657502382708, -0.2073018737002978, -0.007543365635271917, -1.769937016197075, -2.059633509201514, 0.9390525000021139, 1.181756331217071, -4.952440059859791, -9.84571891508484, -6.119507353017548, 0.8329628000173426, 2.208262693609127, -0.333071090969124, -0.701632851397873, 0.1580011856391819, -0.6919454389728414, -0.4459552849473573, 2.450634868055389, 2.966907572002664, -0.603601985019522, -2.074493751436279, 0.6579881742608777, 1.42034594244807, -1.391458738304204, -1.689844616815095, 1.209961304929786, 1.419418479633382, -0.46363152734491, 1.01319241052187, 3.12950246393531, 0.09902369234067591, -3.488532498298555, -1.042624231937471, 2.015946398068466, -1.067108812687406, -4.472300558466326, -1.73699774763529, 1.666865613803945, 0.542779639207381, -0.4298914531044293, 1.369211489037306, 1.425616357798539, -0.3728269224470574, 0.03468656570157609, 0.1598784944549695, -3.052688673351526, -3.748018803783825, 1.0570921579161, 3.195502565924872, -0.4043443641635864, -1.113448178525562, 2.893073945892801, 3.031545967288883, -0.8814774396753006, -1.133748384359256, 0.7661366839112206, -0.5260028536691856, -0.8274998928522949, 2.416803224278163, 1.425861491220412, -4.891382604488803, -6.055356744713551, -0.5870830092135335, 1.856244609242291, -0.04164485973892918, -0.3379644425352943, 0.1919549158094328, -0.3717265918220506, 0.8269699816060372, 1.027300425555109, -4.832772759354277], 'positive_zeros': ['0.4228559436044133', '0.9844871708355888', '2.365429694178106', '2.823038671928265', '3.172865260553151', '4.221956937238725', '4.567714737985983', '5.435595033819698', '5.892077171048054', '6.228312497618771', '7.060588858224556', '7.363994519322160', '7.837692323645034', '8.862250555530726', '9.191339335277397', '9.713136150650387', '10.26424860829858', '10.63269560403113', '11.15285543547952', '11.76233421783435', '12.49945571520379', '12.82127258692678', '12.99784026868604', '13.67836805489337', '14.06841834251549', '14.96173618617562', '15.46291035548194', '15.91134758473482', '16.09504291541563', '16.54855663655798', '17.21110618211962', '17.69690258126765', '18.13508189324740', '18.64595566895077', '19.16495532141440', '19.40622605547395'], 'prelabel': '2-62400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 22.321884073993168, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2238871682284673178, 'z1': {'__RealLiteral__': 0, 'data': '0.4228559436044133', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '0.9844871708355888', 'prec': 60}, 'z3': {'__RealLiteral__': 0, 'data': '2.365429694178106', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 498.26650861278983, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 62400, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, -5, 0, 1, 0, -5, 0, -1, 0, 0, 0, -3, 0, 4, 0, 5, 0, 5, 0, 0, 0, -1, 0, 4, 0, 0, 0, 5, 0, 0, 0, 7, 0, 1, 0, 11, 0, 12, 0, 0, 0, 6, 0, 18, 0, 3, 0, -1, 0, 0, 0, -4, 0, -12, 0, 7, 0, -5, 0, 0, 0, -4, 0, -5, 0, -7, 0, -14, 0, 0, 0, 25, 0, -5, 0, 1, 0, 2, 0, 0, 0, -4, 0, -3, 0, 5, 0, 0, 0, 0, 0, -1, 0, -5, 0], 'euler11': [1, 5, 11], 'euler13': [1, 1, 0], 'euler17': [1, 3, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -5, 23], 'euler29': [1, -4, 29], 'euler3': [1, 1, 0], 'euler31': [1, 0, 31], 'euler37': [1, -7, 37], 'euler41': [1, -11, 41], 'euler43': [1, -12, 43], 'euler47': [1, -6, 47], 'euler5': [1, 0, 0], 'euler53': [1, 1, 53], 'euler59': [1, 12, 59], 'euler61': [1, -7, 61], 'euler67': [1, 4, 67], 'euler7': [1, 5, 7], 'euler71': [1, 7, 71], 'euler73': [1, 14, 73], 'euler79': [1, 5, 79], 'euler83': [1, -2, 83], 'euler89': [1, 3, 89], 'euler97': [1, 1, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 5, 7], [1, 5, 11], [1, 1, 0], [1, 3, 17], [1, -4, 19], [1, -5, 23], [1, -4, 29], [1, 0, 31], [1, -7, 37], [1, -11, 41], [1, -12, 43], [1, -6, 47], [1, 1, 53], [1, 12, 59], [1, -7, 61], [1, 4, 67], [1, 7, 71], [1, 14, 73], [1, 5, 79], [1, -2, 83], [1, 3, 89], [1, 1, 97]], 'index': 20, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/62400/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': '2-62400-1.1-c1-0-20', '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': '2-62400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 22.321884073993168, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2238871682284673178, 'z1': {'__RealLiteral__': 0, 'data': '0.4228559436044133', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2238871682284673178', 'Lhash_array': ['2238871682284673178'], 'label': '2-62400-1.1-c1-0-20', 'type': 'ECQ', 'url': 'EllipticCurve/Q/62400/a'}