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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': '471106997334017600', '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': 881.5484383149359, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [23, [1, 1]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '110400.1', 'coefficient_field': '1.1.1.1', 'conductor': 110400, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, 1, 7], [1, -3, 11], [1, -7, 13], [1, 8, 17], [1, 5, 19], [1, 1], [1, -9, 29], [1, 6, 31], [1, -4, 37], [1, 9, 41], [1, 9, 43], [1, -2, 47], [1, 2, 53], [1, 0, 59], [1, -4, 61], [1, -8, 67], [1, -10, 71], [1, 11, 73], [1, 13, 79], [1, -7, 83], [1, 6, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 130, 'label': '2-110400-1.1-c1-0-130', 'leading_term': '5.50638366916', '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/110400/ca', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.203922527251851, 1.459774605763185, 0.3662765310038979, -1.342966171105758, -2.085836105702402, -1.016793764283157, 0.5974748581331355, 0.3357631521067061, -2.432630419386455, -5.095981735210822, -4.434338023249139, -0.7405714631607102, 2.096113222745567, 1.39245881729107, -0.876785336550796, -1.112700270033935, 0.5295796523121926, 0.6113247964553499, -1.715109194213188, -2.793217966093506, -0.1312763329264532, 3.250317879522175, 3.240844909767023, 0.845230763554421, -0.1391577859862332, 0.3269934457317211, -0.4096436744818698, -1.154840245577179, 2.029606631813759, 7.642062489459494, 8.851134905079345, 3.952853812565033, -0.5313958199580987, -0.4160855878968058, 0.1909787033962097, -2.056669574286888, -2.970893091512371, 0.6612482295568058, 3.76049013642982, 1.620047043907477, -1.544493770706903, -0.5677224563778781, 1.59039895200353, 0.7341374495709726, -0.4869227553727142, 0.589756292405534, 0.2751181894443158, -3.173891968768894, -4.309966448265156, -0.832403567169036, 1.3560807058326, -0.3322408500773979, -0.7076154258322542, 1.195652801936553, -0.2678702755788431, -4.039336014421967, -2.500831588136227, 2.789227946292268, 2.604353815956971, -2.359143663921074, -3.200424203728935, -0.01994314415158186, 0.4563948522460316, -0.4621920860115757, 1.805912641779058, 3.609923098213703, 1.329874607635472, 0.04809592569302897, 2.259752818122581, 2.253211067372398, -0.7629698263356475, -0.9129092486048965, 0.6253835153559258, -1.327020158634666, -2.74259615965735, 1.108320282107461, 3.624949176018589, 0.2654385210726936, -1.551033746273932, 0.997754154466751, 0.3652260363588714, -2.966358265876256, -0.5265523973908659, 4.627807490042373, 3.417905147189789, -0.4680891420744678, 0.04133638199021407, 0.7535326381199366, -1.480102909842484, -1.063231112266612, 1.81077822763494, 0.979828424256133, -1.117499416110549, -0.02403260916388938, -0.2029297399526622, -2.428246754233755, 0.4141234243119677, 5.669042960276719, 4.151763154659277, -0.1330884197965803, 0.3488164505872628, 0.1222166974243965, -3.88089847522735, -3.433053886307108, 0.6928727458870916, -1.079577381541275, -5.018682319552657, -2.579512226346355, 0.4262314049704336, -1.420264340739911, -1.402992453380385, 1.44265509138399, 0.503425562461353, -1.468668617925683, 0.04376457754277195, 0.2043225068624879, -0.8923950919040478, 2.891082936853371, 6.439591933049598, 3.003503512301524], 'positive_zeros': ['0.8040671118205806', '1.642960194449752', '2.043363478470183', '3.047603411554237', '3.644795150434297', '4.169720247905147', '4.581605850429903', '5.258403268148356', '6.136928059192348', '6.334527895502599', '6.670576098796267', '7.137002770150212', '8.199952438516306', '8.574994546992738', '8.788996052072440', '9.464715166392310', '10.10343250993728', '10.55253010646837', '11.10103170763447', '11.39616103264263', '11.77712660775495', '12.55494751073723', '12.96093234659046', '13.34183651233535', '13.73182536601669', '14.36254572360647', '14.88106574724754', '15.50194885200786', '15.83005041414815', '16.09124081354633', '16.91186517082588', '16.98589549029453', '17.68163261787217', '18.11394990759821', '18.38410607835407', '18.94414648887764', '19.51612195706483', '19.90869913075483'], 'prelabel': '2-110400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 29.690881400102217, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 471106997334017600, 'z1': {'__RealLiteral__': 0, 'data': '0.8040671118205806', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.642960194449752', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.043363478470183', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 881.5484383149359, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 110400, 'conductor_radical': 690, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 3, 0, 7, 0, 0, 0, -8, 0, -5, 0, 1, 0, -1, 0, 0, 0, -1, 0, 9, 0, -6, 0, -3, 0, 0, 0, 4, 0, -7, 0, -9, 0, -9, 0, 0, 0, 2, 0, -6, 0, 8, 0, -2, 0, 0, 0, 5, 0, 0, 0, 4, 0, -1, 0, 0, 0, 8, 0, 1, 0, 10, 0, -11, 0, 0, 0, -3, 0, -13, 0, 1, 0, 7, 0, 0, 0, -9, 0, -6, 0, -7, 0, 6, 0, 0, 0, -2, 0, 3, 0], 'euler11': [1, -3, 11], 'euler13': [1, -7, 13], 'euler17': [1, 8, 17], 'euler19': [1, 5, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 0], 'euler29': [1, -9, 29], 'euler3': [1, 1, 0], 'euler31': [1, 6, 31], 'euler37': [1, -4, 37], 'euler41': [1, 9, 41], 'euler43': [1, 9, 43], 'euler47': [1, -2, 47], 'euler5': [1, 0, 0], 'euler53': [1, 2, 53], 'euler59': [1, 0, 59], 'euler61': [1, -4, 61], 'euler67': [1, -8, 67], 'euler7': [1, 1, 7], 'euler71': [1, -10, 71], 'euler73': [1, 11, 73], 'euler79': [1, 13, 79], 'euler83': [1, -7, 83], 'euler89': [1, 6, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 1, 7], [1, -3, 11], [1, -7, 13], [1, 8, 17], [1, 5, 19], [1, 1, 0], [1, -9, 29], [1, 6, 31], [1, -4, 37], [1, 9, 41], [1, 9, 43], [1, -2, 47], [1, 2, 53], [1, 0, 59], [1, -4, 61], [1, -8, 67], [1, -10, 71], [1, 11, 73], [1, 13, 79], [1, -7, 83], [1, 6, 89], [1, 2, 97]], 'index': 130, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/110400/ca'], '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': '2-110400-1.1-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': 1, 'prelabel': '2-110400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 29.690881400102217, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 471106997334017600, 'z1': {'__RealLiteral__': 0, 'data': '0.8040671118205806', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '471106997334017600', 'Lhash_array': ['471106997334017600'], 'label': '2-110400-1.1-c1-0-130', 'type': 'ECQ', 'url': 'EllipticCurve/Q/110400/ca'}