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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 0, 'Lhash': '1995915036138527670', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 925.6258602306826, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -1]], [7, [1, -1]], [23, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '115920.1', 'coefficient_field': '1.1.1.1', 'conductor': 115920, 'conductor_radical': 4830, 'degree': 2, 'euler_factors': [[1], [1], [1, -1], [1, -1], [1, 0, 11], [1, 2, 13], [1, -6, 17], [1, 0, 19], [1, 1], [1, -10, 29], [1, 8, 31], [1, 6, 37], [1, -6, 41], [1, 0, 43], [1, -8, 47], [1, -14, 53], [1, -4, 59], [1, 14, 61], [1, 16, 67], [1, 8, 71], [1, 6, 73], [1, 0, 79], [1, 0, 83], [1, -14, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 127, 'label': '2-115920-1.1-c1-0-127', 'leading_term': '8.5097043534', '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/115920/es', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.933547042712708, 2.782925212143567, 2.002645774830826, 0.2638581634040945, -0.724015478899952, 0.1918427918340428, 2.077584387313995, 2.653601301201462, 1.065346675072245, -0.687839347300638, -0.1264576546921658, 2.141907328479495, 2.815534006901959, 0.4921633803261469, -1.867554776999034, -0.852661523349386, 2.278214394435382, 3.199070811014828, 0.973009118702092, -0.6079448491775484, 0.787656595549857, 2.324764619449001, 1.165340927559883, -0.2427459468730687, 1.622655838679837, 4.562524592149235, 3.720866259427965, -0.06789029353853725, -1.516253195866527, -0.06770647805770055, -0.5200812427725984, -3.666643768003421, -4.34778227117253, -1.044396351933186, 0.9403925291759209, -0.7791277656317664, -1.331908771820505, 1.808689275297378, 3.757763231207983, 1.629499401922858, -0.199976443019609, 0.5543000346566428, -0.6303047821364591, -4.945791510898904, -6.076951709080281, -1.867569547838889, 1.09803628311061, -0.1884674579768929, -0.4869702718123548, 1.61676193350195, 0.5189534684375151, -3.772403768607123, -4.244951346041663, -0.6684076367041842, 0.08145537298825561, -2.08844242019299, -1.534456798755935, 0.4429558609276411, -0.5865911363280581, -0.9876445589825825, 3.166434336681207, 5.712136379217049, 1.974865838668872, -1.160068051151961, 0.9705412711346254, 2.036091998783782, -0.7904028921185055, -1.248898219778106, 1.293803016693612, 0.6502606442020837, -1.726012594349385, -0.3188981132908836, 1.273139344571554, -1.208791166836583, -1.943675892197182, 1.938153738631562, 2.942038693351889, -0.372851399060541, -0.2041578755643424, 2.553554446018552, 0.2719362311905169, -3.744714587044735, -2.339066272233758, 0.2067102921153874, -0.8060129416892547, -0.4697686056517485, 1.865105038010617, 0.1689647169778942, -2.542288855767577, 0.2272815671330019, 2.797021598306569, -0.3759158285753896, -2.029151513347566, 0.9521291871862427, 0.8274914945086927, -1.980817957683229, -0.04106384275427471, 2.851593091715851, 0.6002630153608971, -0.961530740666317, 1.283762934824192, 0.8275278969879013, -1.221502938860124, 1.203527419900426, 2.728042602970194, -1.281334333302694, -2.507836880155008, 1.399237327110051, 1.711444365200597, -0.6788269630184327, 0.692274878380362, 0.7686855729527163, -3.466393314401634, -3.314602443676436, 1.321443144738118, 1.239073443212626, -1.014099933517301, 0.5679615765857452, 0.5294985546942645, -2.315167299146073], 'positive_zeros': ['1.041296958217104', '1.471360455139734', '2.377128920823502', '2.766498642794259', '3.539956050333846', '4.070592229210582', '4.852456229941591', '5.155018241828905', '5.908191976301997', '6.086783835251668', '6.995021182117281', '7.513881593374227', '7.680027932499163', '8.578601387213138', '8.914693959221073', '9.376992190151071', '10.17878304200834', '10.36145981422068', '10.69602203301174', '11.60919382784761', '11.97500383417856', '12.31391181692414', '12.78326196502938', '13.56415050743485', '13.76192798531835', '14.41536910568954', '14.67247708881319', '15.08292523315911', '15.85764808608575', '16.17124138743800', '16.68528186070539', '17.12016250332462', '17.55700787400871', '18.02834064761837', '18.40511721835539', '18.88758729372587', '19.46850373268642', '19.76733257628584'], 'prelabel': '2-115920-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 30.424099990479302, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1995915036138527670, 'z1': {'__RealLiteral__': 0, 'data': '1.041296958217104', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.471360455139734', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.377128920823502', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 925.6258602306826, 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '1.1', 'conductor': 115920, 'conductor_radical': 4830, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 6, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 10, 0, -8, 0, 0, 0, 1, 0, -6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 8, 0, 1, 0, 0, 0, 14, 0, 0, 0, 0, 0, 4, 0, -14, 0, 0, 0, -2, 0, -16, 0, 0, 0, -8, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 14, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 2, 13], 'euler17': [1, -6, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 0], 'euler29': [1, -10, 29], 'euler3': [1, 0, 0], 'euler31': [1, 8, 31], 'euler37': [1, 6, 37], 'euler41': [1, -6, 41], 'euler43': [1, 0, 43], 'euler47': [1, -8, 47], 'euler5': [1, -1, 0], 'euler53': [1, -14, 53], 'euler59': [1, -4, 59], 'euler61': [1, 14, 61], 'euler67': [1, 16, 67], 'euler7': [1, -1, 0], 'euler71': [1, 8, 71], 'euler73': [1, 6, 73], 'euler79': [1, 0, 79], 'euler83': [1, 0, 83], 'euler89': [1, -14, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -1, 0], [1, -1, 0], [1, 0, 11], [1, 2, 13], [1, -6, 17], [1, 0, 19], [1, 1, 0], [1, -10, 29], [1, 8, 31], [1, 6, 37], [1, -6, 41], [1, 0, 43], [1, -8, 47], [1, -14, 53], [1, -4, 59], [1, 14, 61], [1, 16, 67], [1, 8, 71], [1, 6, 73], [1, 0, 79], [1, 0, 83], [1, -14, 89], [1, -2, 97]], 'index': 127, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/115920/es'], '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': '2-115920-1.1-c1-0-127', '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': '2-115920-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 30.424099990479302, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1995915036138527670, 'z1': {'__RealLiteral__': 0, 'data': '1.041296958217104', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1995915036138527670', 'Lhash_array': ['1995915036138527670'], 'label': '2-115920-1.1-c1-0-127', 'type': 'ECQ', 'url': 'EllipticCurve/Q/115920/es'}