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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': 1, 'A8': 0, 'A9': 1, 'Lhash': '363901728729932392', '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': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [7, [1, -1]], [11, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '369600.1', 'coefficient_field': '1.1.1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, -1], [1, 1], [1, -7, 13], [1, -3, 17], [1, 1, 19], [1, -4, 23], [1, 8, 29], [1, 6, 31], [1, -7, 37], [1, 9, 41], [1, 6, 43], [1, -2, 47], [1, -3, 53], [1, -14, 59], [1, 3, 61], [1, 5, 67], [1, -13, 71], [1, 9, 73], [1, -10, 79], [1, 4, 83], [1, 6, 89], [1, 10, 97]], 'gamma_factors': [[], [0]], 'index': 130, 'label': '2-369600-1.1-c1-0-130', 'leading_term': '2.37699926222', '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/369600/jg', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.37699926221556, 1.508190240299019, -0.3679356686890868, -1.506239811262915, -0.7604711112180399, 0.7451376010887961, 0.6490649468922565, -1.160844588183983, -1.540774301701527, 1.603995008084184, 5.24061730247881, 4.565672964704967, 0.1503999209594082, -2.403024245880393, -0.8944919995648654, 0.3742679757616272, -1.538992499403204, -2.869145719362447, -0.1588290161081617, 2.939655713622186, 1.994913430228938, -0.3624464814562929, -0.006008121788773517, 0.8248630368761903, -0.902925123278881, -1.848731804629148, 0.7425902656770736, 2.250662751998339, -0.2865883940639732, -1.347658684385817, 2.014314670219841, 3.476566360113561, 0.2777969510891058, -0.8655514874038712, 1.957699973193268, 1.802625233096657, -1.515589742070956, -0.3035925816054543, 3.980594711422716, 2.799770455894555, -1.621080472097638, -1.102859354906916, 1.752753255383886, 0.7876720620378069, -0.7147521470194917, 0.3006998344443693, -0.2289923070697903, -1.430372885339311, 1.847925503649474, 5.113715721636321, 2.132019973190329, -1.15163402763753, 0.222362151119392, 0.189888054734611, -1.880341940027124, 0.7514503526170488, 3.644984667565081, -0.9736959474074574, -5.379340888665805, -2.212972286573727, 0.2288817506188741, -1.701211745830046, 0.008757455504449018, 3.721394239195521, 1.690445573465812, -1.269126005990339, 0.05988547419206716, 0.1682227750028283, -0.6468811205119521, 3.094295282647792, 5.541513613125613, 1.701826132287945, -0.7469172625683412, 0.2609817414723054, -0.8782366632875321, -0.9870998090361057, 1.081202274140832, -3.005984717863018, -8.63586963881082, -3.670982701128012, 3.644582462238572, 1.71181811446977, -0.9663438348620408, 0.9544232169532807, 0.1795979881414473, -0.7685324144009954, 2.585034852626006, 2.330108338578516, -1.37999845593109, 0.405486980818808, 2.527514959960814, -1.001549836145649, -2.175852594153902, 0.1814904507660029, -0.0930033280374615, 0.345843345534376, 1.252385029904683, -3.158830131450199, -4.841984980425322, 1.363200623602537, 3.071365997287364, -0.8349695141295636, -0.006034812431108559, 0.3380741093423161, -3.145377331750803, -0.1115026248078868, 4.849918541011226, 1.210868677228275, -1.458260221843693, 1.926474453028368, 1.602356533667284, -0.168929862549182, 1.884168196098432, 1.293722411995484, -0.5771886955766434, 0.6308832529381114, -1.697131419491883, -4.728281018166505, -0.3241353958881084, 2.620585795918972, -0.08667746781671817], 'positive_zeros': ['0.4512023749204111', '1.116778874496764', '1.600319135639052', '2.149967783750685', '3.008544782883084', '3.607496569150947', '3.836579046893385', '4.509956011737354', '5.193413506753086', '5.501049618136210', '5.900720694280754', '6.442906247028624', '6.977085798648079', '7.371895921238356', '8.020669435625334', '8.340552395340641', '8.877893643053314', '9.267508936145016', '9.894008754591832', '10.33181500131491', '10.83591542370758', '11.18651245725674', '11.46772690887382', '11.89870318994087', '12.61959443003241', '12.97245128010079', '13.27091668417118', '13.70892564311175', '14.21418670251561', '14.90320216656978', '15.04837117698794', '15.49949384380469', '16.10385054367572', '16.49182945724090', '16.77642063193018', '17.07425124956171', '17.85764622302359', '18.17293933059702', '18.37557051035222', '18.84782419630461', '19.12741367638432', '19.84980123375236'], 'prelabel': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 363901728729932392, 'z1': {'__RealLiteral__': 0, 'data': '0.4512023749204111', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.116778874496764', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.600319135639052', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, 1, 0, 1, 0, -1, 0, 7, 0, 0, 0, 3, 0, -1, 0, -1, 0, 4, 0, 0, 0, -1, 0, -8, 0, -6, 0, 1, 0, 0, 0, 7, 0, -7, 0, -9, 0, -6, 0, 0, 0, 2, 0, 1, 0, -3, 0, 3, 0, 0, 0, 1, 0, 14, 0, -3, 0, 1, 0, 0, 0, -5, 0, -4, 0, 13, 0, -9, 0, 0, 0, -1, 0, 10, 0, 1, 0, -4, 0, 0, 0, 8, 0, -6, 0, 7, 0, 6, 0, 0, 0, -10, 0, -1, 0], 'euler11': [1, 1, 0], 'euler13': [1, -7, 13], 'euler17': [1, -3, 17], 'euler19': [1, 1, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, 8, 29], 'euler3': [1, 1, 0], 'euler31': [1, 6, 31], 'euler37': [1, -7, 37], 'euler41': [1, 9, 41], 'euler43': [1, 6, 43], 'euler47': [1, -2, 47], 'euler5': [1, 0, 0], 'euler53': [1, -3, 53], 'euler59': [1, -14, 59], 'euler61': [1, 3, 61], 'euler67': [1, 5, 67], 'euler7': [1, -1, 0], 'euler71': [1, -13, 71], 'euler73': [1, 9, 73], 'euler79': [1, -10, 79], 'euler83': [1, 4, 83], 'euler89': [1, 6, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, -1, 0], [1, 1, 0], [1, -7, 13], [1, -3, 17], [1, 1, 19], [1, -4, 23], [1, 8, 29], [1, 6, 31], [1, -7, 37], [1, 9, 41], [1, 6, 43], [1, -2, 47], [1, -3, 53], [1, -14, 59], [1, 3, 61], [1, 5, 67], [1, -13, 71], [1, 9, 73], [1, -10, 79], [1, 4, 83], [1, 6, 89], [1, 10, 97]], 'index': 130, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/369600/jg'], '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': '2-369600-1.1-c1-0-130', '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': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 363901728729932392, 'z1': {'__RealLiteral__': 0, 'data': '0.4512023749204111', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '363901728729932392', 'Lhash_array': ['363901728729932392'], 'label': '2-369600-1.1-c1-0-130', 'type': 'ECQ', 'url': 'EllipticCurve/Q/369600/jg'}