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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 0, 'Lhash': '9108611463966850', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 194.03647691171142, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '24300.1', 'coefficient_field': '1.1.1.1', 'conductor': 24300, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, -1, 7], [1, 5, 11], [1, 6, 13], [1, 7, 17], [1, 6, 19], [1, -2, 23], [1, 0, 29], [1, 8, 31], [1, 8, 37], [1, 8, 41], [1, -1, 43], [1, 8, 47], [1, -3, 53], [1, 4, 59], [1, -11, 61], [1, 1, 67], [1, -15, 71], [1, -4, 73], [1, 0, 79], [1, 16, 83], [1, 2, 89], [1, 10, 97]], 'gamma_factors': [[], [0]], 'index': 25, 'label': '2-24300-1.1-c1-0-25', 'leading_term': '7.70780443545', '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': 2, 'origin': 'EllipticCurve/Q/24300/l', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, -0.4722910812038382, -1.754701088212049, -3.351532549273029, -4.402417279527344, -4.120248234412508, -2.481095870534975, -0.4921035916410767, 0.4727840460518951, -0.08106658187552931, -1.115635650895115, -0.9217887570312508, 1.056596427463632, 3.307917307729498, 3.553380604018295, 1.209832196065782, -1.706903030116463, -2.588615118981599, -1.108855262346869, 0.4912901614304503, 0.2975584618474722, -0.7211806162881319, 0.02370865139355108, 3.016422001022554, 5.437523250143154, 4.537492999126081, 1.355210376862498, -0.4443681581122275, 0.6156841242926951, 1.948704378040567, 0.7659937939191361, -1.777760884315956, -2.321407678089602, -0.4844310330530397, 0.3992660930377957, -1.561599064514383, -3.580703711951146, -2.240762972104281, 1.083129397763514, 1.997230161001578, -0.3353526399720546, -2.041411025761669, -0.7235985939513909, 0.9211584605428382, -0.03722311147546249, -1.508667730426136, 0.2148381293443819, 3.804869191581324, 4.387410216048098, 1.230147967151359, -1.106325437453308, -0.2423695994426147, 0.5343549871502553, -1.32087710801813, -2.646093459484678, -0.1112823070986021, 3.298525727867435, 2.684040735105344, -0.6614998825368987, -1.590329037024019, 0.1762704424801271, 0.3649546231556681, -1.395006373413774, -0.7779969022097679, 2.663147537974895, 3.639187503149299, 0.2335689131865019, -2.361968377847615, -0.7050350767410237, 1.284877137857575, 0.01089901035174098, -1.335650313136619, 0.4762440633500872, 1.984147445207372, -0.3992366828414276, -3.009087183976733, -1.40922103254665, 1.198077031599159, -0.0857075345273682, -2.643000620382674, -1.571141818567591, 0.7097251523456835, -0.7926411213631387, -3.731048211304979, -2.807011727285794, 0.1001683454603615, -0.0136779681742611, -1.286484627706355, 0.810697283767923, 3.599745861538053, 2.092425816582721, -0.6223894911511819, 1.238133903786137, 4.891374577010402, 4.095390358320091, 0.675979704018534, 0.002352578073359143, 0.4267529356639844, -1.750978659718022, -3.015817364900265, 0.5298798299786273, 3.931289414139969, 1.893979255553959, -1.121608556111756, 0.2577596409537438, 2.165319114474777, 0.1783699843161323, -1.711000733052436, -0.1890894065061898, 0.2035939098545064, -2.602090690046467, -2.732193812257635, 1.500588547838137, 3.06594369535511, -0.305717736752585, -2.021829998891744, -0.0245472068558683, 0.453989373682785, -0.5810469333603956, 1.843065031528794, 5.085361725653483], 'positive_zeros': ['1.833851997379005', '2.230800230487833', '2.887670105649176', '3.845502885274559', '4.648451954005399', '5.066621139496848', '5.497169882961472', '6.637020180258046', '6.909194026578516', '7.573916920453696', '8.316841588370769', '8.584971549212875', '9.413843375747077', '9.970367195936702', '10.58275652063573', '10.99523781031088', '11.48388678364705', '12.34340946234677', '12.78828714933758', '13.10615598761012', '13.75699388056656', '14.44660891790859', '14.97441512676472', '15.30766016142869', '15.81433854854494', '16.51428712652969', '17.06262568481143', '17.50121807288776', '17.95489907810798', '18.47199139427529', '19.10890412106579', '19.49274566590372'], 'prelabel': '2-24300-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 13.92969766045593, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 9108611463966850, 'z1': {'__RealLiteral__': 0, 'data': '1.833851997379005', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '2.230800230487833', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.887670105649176', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 194.03647691171142, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 24300, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -5, 0, -6, 0, 0, 0, -7, 0, -6, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, 1, 0, 0, 0, -8, 0, -6, 0, 0, 0, 3, 0, 0, 0, 0, 0, -4, 0, 11, 0, 0, 0, 0, 0, -1, 0, 0, 0, 15, 0, 4, 0, 0, 0, -5, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, -2, 0, -6, 0, 0, 0, 0, 0, -10, 0, 0, 0], 'euler11': [1, 5, 11], 'euler13': [1, 6, 13], 'euler17': [1, 7, 17], 'euler19': [1, 6, 19], 'euler2': [1, 0, 0], 'euler23': [1, -2, 23], 'euler29': [1, 0, 29], 'euler3': [1, 0, 0], 'euler31': [1, 8, 31], 'euler37': [1, 8, 37], 'euler41': [1, 8, 41], 'euler43': [1, -1, 43], 'euler47': [1, 8, 47], 'euler5': [1, 0, 0], 'euler53': [1, -3, 53], 'euler59': [1, 4, 59], 'euler61': [1, -11, 61], 'euler67': [1, 1, 67], 'euler7': [1, -1, 7], 'euler71': [1, -15, 71], 'euler73': [1, -4, 73], 'euler79': [1, 0, 79], 'euler83': [1, 16, 83], 'euler89': [1, 2, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, -1, 7], [1, 5, 11], [1, 6, 13], [1, 7, 17], [1, 6, 19], [1, -2, 23], [1, 0, 29], [1, 8, 31], [1, 8, 37], [1, 8, 41], [1, -1, 43], [1, 8, 47], [1, -3, 53], [1, 4, 59], [1, -11, 61], [1, 1, 67], [1, -15, 71], [1, -4, 73], [1, 0, 79], [1, 16, 83], [1, 2, 89], [1, 10, 97]], 'index': 25, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/24300/l'], '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': '2-24300-1.1-c1-0-25', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 2, 'prelabel': '2-24300-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 13.92969766045593, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 9108611463966850, 'z1': {'__RealLiteral__': 0, 'data': '1.833851997379005', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '9108611463966850', 'Lhash_array': ['9108611463966850'], 'factors': ['2-24300-1.1-c1-0-25'], 'label': '2-24300-1.1-c1-0-25', 'type': 'ECQ', 'url': 'EllipticCurve/Q/24300/l'}