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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': -4, 'A8': 0, 'A9': 1, 'Lhash': '2198679968040662893', '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': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 553.842388419601, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, 1]], [17, [1]]], 'bad_primes': [2, 3, 5, 17], 'central_character': '69360.1', 'coefficient_field': '1.1.1.1', 'conductor': 69360, 'conductor_radical': 510, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 1], [1, 4, 7], [1, 0, 11], [1, 2, 13], [1], [1, 4, 19], [1, 0, 23], [1, 2, 29], [1, 10, 31], [1, -10, 37], [1, 6, 41], [1, 12, 43], [1, 6, 47], [1, -12, 53], [1, -12, 59], [1, -8, 61], [1, 8, 67], [1, 8, 71], [1, -14, 73], [1, -10, 79], [1, 2, 83], [1, 14, 89], [1, 10, 97]], 'gamma_factors': [[], [0]], 'index': 29, 'label': '2-69360-1.1-c1-0-29', 'leading_term': '2.68905249643', '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/69360/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.5334171606514125, 0.3003168235202565, -1.037878010308986, -2.864799657740353, -3.678142513001291, -2.29635011642307, 0.6525322055219458, 2.770538062024348, 2.079954545114742, -0.6619283758432988, -2.447678458199861, -1.34592306221068, 1.130886903549254, 1.912018459900285, 0.4600093415280591, -0.4463340829456961, 1.286745459754876, 3.742030427150165, 3.479538731279601, 0.6414099877475955, -0.9843277950276151, 0.5230103989047745, 2.376717798456914, 1.50065291236118, -0.6706389272674393, -0.813053526739869, 0.5918821225989227, 0.3260862897875955, -1.322910546304053, -0.385408468605986, 3.58448385795216, 5.387476559724949, 2.199422407072761, -1.184688069473752, 0.3795426052716429, 4.092145769366713, 4.026387521425606, 0.8941056582029543, -0.05693782403876628, 1.316763320974562, 0.5285535244293443, -2.339560339672967, -2.460256063342612, 0.4080188020827528, 1.106966025645721, -1.286377893771038, -1.82996802593853, 0.6877997715379273, 1.61037212475109, -0.2798680307212278, -0.7876953528668986, 0.5772169894880009, -0.2333846353544564, -1.855025426395888, 1.77295499375108, 8.740103642739964, 9.71330319303417, 3.527210944572443, -0.8368525978892649, -0.05481406907726145, -0.3933119554365413, -3.799936607773306, -4.467169986874855, -1.246913589679797, 0.450008342869539, -0.1506784442485204, 0.5368611905033525, 0.6740422599443776, -3.087454415932504, -5.975750616793975, -2.758484966185008, 1.40044434286686, 0.5067713036827559, -0.9947964436425657, 1.565714977884118, 3.342239389771108, 1.007875496441573, -0.3181668382158391, 0.788949242934681, -0.9998222155804373, -4.014747634805549, -1.034805266206585, 4.295512544126089, 2.270175437764537, -3.970771682794466, -4.325923046513316, -0.4423703174512568, 0.318543598944195, -0.1801140121635292, 1.744410281320478, 2.199961637024766, -0.2894604952921441, -0.7549695423636275, 0.4376088661958139, -0.9928403436002746, -1.373850601722257, 3.129095126132608, 5.167365356893811, 0.09908936737413852, -3.383099883340916, -0.7847990497242052, 0.06453164520448909, -2.421336266621755, -0.7417655621310543, 3.18661527912011, 1.630197790743492, -1.474721861191577, 0.2932464836110071, 1.507564279459565, -1.580959013100936, -1.974622960349155, 1.630650400626949, 1.870667988870266, -0.4932918973798748, 0.2659404849822351, 1.022923116974568, -1.225045100894085, -1.311106620607955, 0.6585276767003644, -0.9682452286862487], 'positive_zeros': ['0.5769452518079123', '1.696793296782448', '2.442858106700009', '3.131995165136124', '3.820672174588508', '4.108617668693572', '5.059137987347134', '5.443697682369514', '6.161521950553261', '6.639681677580560', '7.049569635812454', '7.530115001818864', '8.380199743054326', '8.723726796043708', '9.611793179492992', '9.765197663122597', '10.29851381628911', '10.96344130192702', '11.37777241583555', '11.93717166781056', '12.46529851910061', '12.88788524818827', '13.22237891288116', '13.67504122588402', '14.66215246417236', '15.00993867547106', '15.20308129829399', '16.11822817552825', '16.43121079705002', '16.63462750674293', '17.06801430746845', '17.88751894703573', '18.29904005110026', '18.63293438565309', '19.35559223519451', '19.57985798027337', '19.92338531391800'], 'prelabel': '2-69360-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.533856216514984, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2198679968040662893, 'z1': {'__RealLiteral__': 0, 'data': '0.5769452518079123', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.696793296782448', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.442858106700009', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 553.842388419601, 'bad_primes': [2, 3, 5, 17], 'central_character': '1.1', 'conductor': 69360, 'conductor_radical': 510, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, -4, 0, 1, 0, 0, 0, -2, 0, 1, 0, 0, 0, -4, 0, 4, 0, 0, 0, 1, 0, -1, 0, -2, 0, -10, 0, 0, 0, 4, 0, 10, 0, 2, 0, -6, 0, -12, 0, -1, 0, -6, 0, 9, 0, 0, 0, 12, 0, 0, 0, 4, 0, 12, 0, 8, 0, -4, 0, 2, 0, -8, 0, 0, 0, -8, 0, 14, 0, -1, 0, 0, 0, 10, 0, 1, 0, -2, 0, 0, 0, 2, 0, -14, 0, 8, 0, 10, 0, 4, 0, -10, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 2, 13], 'euler17': [1, 0, 0], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 2, 29], 'euler3': [1, 1, 0], 'euler31': [1, 10, 31], 'euler37': [1, -10, 37], 'euler41': [1, 6, 41], 'euler43': [1, 12, 43], 'euler47': [1, 6, 47], 'euler5': [1, 1, 0], 'euler53': [1, -12, 53], 'euler59': [1, -12, 59], 'euler61': [1, -8, 61], 'euler67': [1, 8, 67], 'euler7': [1, 4, 7], 'euler71': [1, 8, 71], 'euler73': [1, -14, 73], 'euler79': [1, -10, 79], 'euler83': [1, 2, 83], 'euler89': [1, 14, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 1, 0], [1, 4, 7], [1, 0, 11], [1, 2, 13], [1, 0, 0], [1, 4, 19], [1, 0, 23], [1, 2, 29], [1, 10, 31], [1, -10, 37], [1, 6, 41], [1, 12, 43], [1, 6, 47], [1, -12, 53], [1, -12, 59], [1, -8, 61], [1, 8, 67], [1, 8, 71], [1, -14, 73], [1, -10, 79], [1, 2, 83], [1, 14, 89], [1, 10, 97]], 'index': 29, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/69360/a'], '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': '2-69360-1.1-c1-0-29', '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': '2-69360-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.533856216514984, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2198679968040662893, 'z1': {'__RealLiteral__': 0, 'data': '0.5769452518079123', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2198679968040662893', 'Lhash_array': ['2198679968040662893'], 'label': '2-69360-1.1-c1-0-29', 'type': 'ECQ', 'url': 'EllipticCurve/Q/69360/a'}