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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': -2, 'A8': 0, 'A9': 1, 'Lhash': '802429776038623301', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [-0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2767.295532449494, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, -1]], [19, [1]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '346560.1', 'coefficient_field': '1.1.1.1', 'conductor': 346560, 'conductor_radical': 570, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, -1], [1, 2, 7], [1, 0, 11], [1, -2, 13], [1, 6, 17], [1], [1, 6, 23], [1, 4, 29], [1, 0, 31], [1, -10, 37], [1, -8, 41], [1, -2, 43], [1, -2, 47], [1, 2, 53], [1, 0, 59], [1, 14, 61], [1, 4, 67], [1, -12, 71], [1, -6, 73], [1, 8, 79], [1, -2, 83], [1, -8, 89], [1, -6, 97]], 'gamma_factors': [[], [0]], 'index': 144, 'label': '2-346560-1.1-c1-0-144', 'leading_term': '5.53768422583', '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/346560/dr', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.114412858827021, 0.8604753780879947, -0.8735302424964261, -2.35789148001706, -1.573739881200408, 1.008215132912531, 2.343255039056359, 0.7557323890228805, -1.199463697002955, -0.1201550119546926, 2.678874163599802, 2.505393711612251, -1.276986496911029, -3.553810813450377, -1.372157299450131, 1.24385095075885, 0.3052022389325954, -1.189803426794254, 0.9442615610683924, 3.871993691122039, 2.630130090868852, -0.7559278095651514, -1.226664302358641, 0.1827621059578578, -0.1263834496254116, -0.364402370433355, 1.739483526171707, 2.093865709626678, -1.765307064737496, -3.680235305124152, -0.205383857301884, 1.317300608557091, -3.318948107518364, -6.036019713547337, -1.837114440807881, 1.815886192062846, 0.3687574518866141, -0.2762563101269444, 1.609670093065844, 0.266982125318335, -3.167396021383164, -2.356546993308135, 0.2193872238012723, -0.5767201511538907, -0.7351224093184653, 2.373925288836959, 2.277078045357502, -1.82677382594158, -2.060185236235009, 0.9743811923613247, 0.22393137374058, -1.732162889739749, -0.3828495577236448, -0.6778649945909191, -3.383668716041443, -1.147698218028254, 2.751280469516256, -0.8676574446996552, -5.603822076259347, -2.053387531034752, 1.999423312634746, -0.5264914930991015, -1.971131535311795, 0.3078656840499033, -0.1243444178734641, -0.9560578471381446, 1.94477513578016, 2.373265040901791, -0.8825987538370138, -0.4918788373653951, 1.392635063477244, -0.55445882357477, -1.185808346976208, 0.3303005803904188, -2.553786389043367, -4.604510319624096, 0.7657057801127766, 3.82835362925344, 0.01009968753333117, -0.7682385886339815, 0.19000950067131, -4.860586476640008, -7.410632732661965, -1.828981991672111, 0.6742578764884789, -1.713109375305971, -0.1640225367671408, 1.907314426120374, 0.1277626905188999, 0.2573188558516923, 0.9643024518101972, -1.547795482068666, -0.452821807261606, 3.655273293239626, 1.863216328186265, -0.6066251905911939, 2.105032603650264, 1.88876154685437, -0.08725503554909007, 4.235832197773052, 6.465400328160473, 1.412573663326472, -0.1473154151753421, 1.33086133953829, -0.9964307426379951, -5.648500009206593e-06, 4.018423413304609, 0.5975611756000815, -3.231868137931186, 0.4225276736697958, 0.8685872244027848, -3.245153585896374, -2.087505120161385, 0.3081581768565609, -0.2274973519619101, 1.054324744273295, 0.5570396943520692, -2.889729462699342, -1.44770439144281, 0.5877492633550873], 'positive_zeros': ['0.6396882605074185', '1.406279438522073', '2.076015340508380', '2.511140818045928', '3.173947100329994', '3.852625786573656', '4.284166766014956', '4.679332175193812', '5.433882714130920', '5.954620059130478', '6.217927166117728', '6.562486980552241', '7.151255258484986', '7.762530935466804', '8.097020637130353', '8.837524880120246', '9.293744749150279', '9.542757940661712', '10.01834279196882', '10.71045248501089', '10.91240844140777', '11.32114468828303', '11.88838810639051', '12.40633758736576', '12.77069841227180', '13.32763703434495', '13.39837915674818', '14.05586898232422', '14.46629157231403', '15.08744160958069', '15.46506608483165', '15.96060353066646', '16.23377128919038', '16.60475149752848', '17.17498457017965', '17.54598153971047', '17.94822003854810', '18.40385161170607', '18.57611644367131', '19.22135700649781', '19.75066138093366'], 'prelabel': '2-346560-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 52.605090366327616, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 802429776038623301, 'z1': {'__RealLiteral__': 0, 'data': '0.6396882605074185', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.406279438522073', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.076015340508380', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2767.295532449494, 'bad_primes': [2, 3, 5, 19], 'central_character': '1.1', 'conductor': 346560, 'conductor_radical': 570, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 1, 0, -2, 0, 1, 0, 0, 0, 2, 0, -1, 0, -6, 0, 0, 0, 2, 0, -6, 0, 1, 0, -1, 0, -4, 0, 0, 0, 0, 0, -2, 0, 10, 0, -2, 0, 8, 0, 2, 0, 1, 0, 2, 0, -3, 0, 6, 0, -2, 0, 0, 0, 0, 0, 0, 0, -14, 0, -2, 0, 2, 0, -4, 0, 6, 0, 12, 0, 6, 0, -1, 0, 0, 0, -8, 0, 1, 0, 2, 0, -6, 0, 4, 0, 8, 0, -4, 0, 0, 0, 0, 0, 6, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -2, 13], 'euler17': [1, 6, 17], 'euler19': [1, 0, 0], 'euler2': [1, 0, 0], 'euler23': [1, 6, 23], 'euler29': [1, 4, 29], 'euler3': [1, 1, 0], 'euler31': [1, 0, 31], 'euler37': [1, -10, 37], 'euler41': [1, -8, 41], 'euler43': [1, -2, 43], 'euler47': [1, -2, 47], 'euler5': [1, -1, 0], 'euler53': [1, 2, 53], 'euler59': [1, 0, 59], 'euler61': [1, 14, 61], 'euler67': [1, 4, 67], 'euler7': [1, 2, 7], 'euler71': [1, -12, 71], 'euler73': [1, -6, 73], 'euler79': [1, 8, 79], 'euler83': [1, -2, 83], 'euler89': [1, -8, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, -1, 0], [1, 2, 7], [1, 0, 11], [1, -2, 13], [1, 6, 17], [1, 0, 0], [1, 6, 23], [1, 4, 29], [1, 0, 31], [1, -10, 37], [1, -8, 41], [1, -2, 43], [1, -2, 47], [1, 2, 53], [1, 0, 59], [1, 14, 61], [1, 4, 67], [1, -12, 71], [1, -6, 73], [1, 8, 79], [1, -2, 83], [1, -8, 89], [1, -6, 97]], 'index': 144, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/346560/dr'], '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': '2-346560-1.1-c1-0-144', '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': '2-346560-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 52.605090366327616, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 802429776038623301, 'z1': {'__RealLiteral__': 0, 'data': '0.6396882605074185', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '802429776038623301', 'Lhash_array': ['802429776038623301'], 'label': '2-346560-1.1-c1-0-144', 'type': 'ECQ', 'url': 'EllipticCurve/Q/346560/dr'}