- 
              lfunc_lfunctions •   Show schema
  Hide schema
   
        
{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 2, 'A6': 0, 'A7': 2, 'A8': 0, 'A9': 0, 'Lhash': '1445756724384246418', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 1182.6163940959716, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [11, [1]], [17, [1, 1]]], 'bad_primes': [2, 3, 11, 17], 'central_character': '148104.1', 'coefficient_field': '1.1.1.1', 'conductor': 148104, 'conductor_radical': 1122, 'degree': 2, 'euler_factors': [[1], [1], [1, -2, 5], [1, -2, 7], [1], [1, 0, 13], [1, 1], [1, 2, 19], [1, 2, 23], [1, -10, 29], [1, -8, 31], [1, 6, 37], [1, -2, 41], [1, 2, 43], [1, 0, 47], [1, -12, 53], [1, 10, 59], [1, 10, 61], [1, 4, 67], [1, 6, 71], [1, 0, 73], [1, -10, 79], [1, 4, 83], [1, -10, 89], [1, 14, 97]], 'gamma_factors': [[], [0]], 'index': 62, 'label': '2-148104-1.1-c1-0-62', 'leading_term': '9.75934818421', '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/148104/cd', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 2.213245734800497, 3.166575537360528, 2.249433874743002, 0.2464831182509561, -0.9698514198079174, -0.2766283434949492, 1.219896717205756, 1.366830549238226, -0.09643016825035952, -0.8305367196697779, 0.8516435547862424, 2.934824429657361, 1.913382925855679, -1.954024340567237, -4.167278252685589, -2.02808516570655, 1.382772104262315, 1.801719308180918, 0.1720744386144491, 0.544963328561106, 2.888470480212304, 3.118851927556923, 0.4742772906370114, -0.9388386380996401, 0.3868424610905752, 0.5025539933572223, -2.31521526724969, -3.436481635616419, -0.04012762129449061, 2.949379444598597, 1.04432058584691, -1.880905112341246, -0.8648801552249459, 1.18229767057559, -0.1297606344600281, -1.650108077056256, 0.9043218869949444, 3.854440055035989, 2.387506599354175, -0.1927639179778247, 0.4304602056771229, 0.9245725252310779, -1.726985518749479, -2.665166435830813, 0.9581933910464238, 2.992478293299411, 0.08895003909632264, -1.634755663321559, 0.4363259730031687, -0.1154603452266213, -4.678445009104066, -5.695974513540705, -1.671960537024527, 0.3750974406756133, -0.6447247145470111, 0.1210188887884928, 1.015960487562082, -1.735733463849121, -3.380355317449181, -0.07633199733556563, 1.824680962915804, -0.7242252673295132, -0.3348486198840848, 4.275515639669483, 4.275254260350891, -0.6364252371569377, -1.43642002982307, 1.56347027147562, 1.204654036178227, -0.775275469161782, -0.1004591282024913, -0.2399474802419038, -1.671507422858553, 1.374172247520261, 5.849578785662646, 3.610904167272812, -0.7899486957293002, 0.4429512738955297, 1.389016293466604, -3.217777954480328, -5.157213267873565, -0.9515576781905726, 0.9843411607798579, -0.7285789635946757, -0.07300033585132923, 0.9539889779260783, -0.2794487010820899, 1.603389552498566, 5.352725881438502, 2.74042287089755, -2.261024104713111, -1.196477005246655, 0.08545094486428113, -3.769498190573253, -4.324757715431396, 0.5215464467091373, 1.438947579848108, -1.031709164425761, -0.2548359382710443, -0.1814206175034495, -3.209241383516046, -2.49472922613584, 0.4532691292914283, -1.219136316373848, -2.267133804881867, 1.415355678490533, 1.459035170119542, -2.38092444701028, -0.8352666179853122, 2.514022696275568, 0.6666244853110188, 0.4231847165375604, 4.169384331492639, 3.114164264773467, -0.7016753354147611, 0.3734887434479264, 1.134809636773122, -1.49206023618821, -0.3987435709557559, 2.091461325523386], 'positive_zeros': ['1.032885967990084', '1.545258277800815', '2.235016960078651', '2.658482097162713', '3.381172179092251', '4.134993214322514', '4.797546801334067', '4.895961813175433', '5.795154091885851', '6.191390994450575', '6.559801680403236', '7.252267029079879', '7.821200773994078', '8.331273885950734', '8.736950241689572', '9.190556438919811', '9.964849387023205', '10.17857295391047', '10.60994973762156', '11.19462324613105', '11.75617710216884', '12.20120325842017', '12.49131116037208', '13.38270952712041', '13.60846208374603', '13.98309233052158', '14.37444126549152', '15.00470801655056', '15.43623355761651', '15.77194155292651', '16.46409948310395', '16.86669441771495', '17.37396229336201', '17.77304156832669', '17.95731866963581', '18.43075617784447', '19.18003695773975', '19.46212377405096', '19.84776111304817'], 'prelabel': '2-148104-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 34.38919007618487, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1445756724384246418, 'z1': {'__RealLiteral__': 0, 'data': '1.032885967990084', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.545258277800815', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.235016960078651', 'prec': 57}}
           
      - 
              lfunc_search •   Show schema
  Hide schema
   
        
{'algebraic': True, 'analytic_conductor': 1182.6163940959716, 'bad_primes': [2, 3, 11, 17], 'central_character': '1.1', 'conductor': 148104, 'conductor_radical': 1122, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, -2, 0, -1, 0, 0, 0, 10, 0, 8, 0, 0, 0, 4, 0, -6, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, -3, 0, 0, 0, 12, 0, 0, 0, 0, 0, -10, 0, -10, 0, 0, 0, 0, 0, -4, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, -4, 0, -2, 0, 0, 0, 10, 0, 0, 0, 0, 0, -4, 0, -14, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, 0, 13], 'euler17': [1, 1, 0], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, 2, 23], 'euler29': [1, -10, 29], 'euler3': [1, 0, 0], 'euler31': [1, -8, 31], 'euler37': [1, 6, 37], 'euler41': [1, -2, 41], 'euler43': [1, 2, 43], 'euler47': [1, 0, 47], 'euler5': [1, -2, 5], 'euler53': [1, -12, 53], 'euler59': [1, 10, 59], 'euler61': [1, 10, 61], 'euler67': [1, 4, 67], 'euler7': [1, -2, 7], 'euler71': [1, 6, 71], 'euler73': [1, 0, 73], 'euler79': [1, -10, 79], 'euler83': [1, 4, 83], 'euler89': [1, -10, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -2, 5], [1, -2, 7], [1, 0, 0], [1, 0, 13], [1, 1, 0], [1, 2, 19], [1, 2, 23], [1, -10, 29], [1, -8, 31], [1, 6, 37], [1, -2, 41], [1, 2, 43], [1, 0, 47], [1, -12, 53], [1, 10, 59], [1, 10, 61], [1, 4, 67], [1, 6, 71], [1, 0, 73], [1, -10, 79], [1, 4, 83], [1, -10, 89], [1, 14, 97]], 'index': 62, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/148104/cd'], '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': '2-148104-1.1-c1-0-62', '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': '2-148104-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 34.38919007618487, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1445756724384246418, 'z1': {'__RealLiteral__': 0, 'data': '1.032885967990084', 'prec': 57}}
           
      - 
              lfunc_instances •   Show schema
  Hide schema
   
        
{'Lhash': '1445756724384246418', 'Lhash_array': ['1445756724384246418'], 'factors': ['2-148104-1.1-c1-0-62'], 'label': '2-148104-1.1-c1-0-62', 'type': 'ECQ', 'url': 'EllipticCurve/Q/148104/cd'}