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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': -2, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '2301363548084272557', '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': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 2479.0675213134805, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1]], [11, [1, -1]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '310464.1', 'coefficient_field': '1.1.1.1', 'conductor': 310464, 'conductor_radical': 462, 'degree': 2, 'euler_factors': [[1], [1], [1, 2, 5], [1], [1, -1], [1, 6, 13], [1, 2, 17], [1, 8, 19], [1, -4, 23], [1, -2, 29], [1, -8, 31], [1, 6, 37], [1, 2, 41], [1, 8, 43], [1, 4, 47], [1, -2, 53], [1, -12, 59], [1, -10, 61], [1, -12, 67], [1, -12, 71], [1, 10, 73], [1, 8, 79], [1, 12, 83], [1, -10, 89], [1, -14, 97]], 'gamma_factors': [[], [0]], 'index': 28, 'label': '2-310464-1.1-c1-0-28', 'leading_term': '0.638751221015', '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': 0, 'origin': 'EllipticCurve/Q/310464/dz', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.6387512210145504, -0.04043193559603016, -1.343546883052269, -1.516244569749432, 0.5821346875157138, 3.6465232642151, 4.653036137123424, 2.440185186193967, -0.2901092204830698, -0.2399440560191485, 1.738506780648401, 1.741212615705498, -1.032895550665365, -2.637223181445871, -0.6356986652699487, 1.718930538218805, 0.9002937167404499, -0.9242145113648002, -0.1892959481684107, 1.22306203754467, -0.1018530705969036, -1.383814927127947, 2.003766919569671, 6.785286635256386, 5.917635898740129, 0.7832007659748804, -1.231432755582684, 0.336917485446666, 0.04966594234944843, -1.555134465628773, 0.2601710102786795, 3.337660501939238, 2.35728612962357, -0.2254976241925528, 0.1128390174813101, -0.2037505096221458, -4.424795449178469, -6.373121866896546, -2.28666774006271, 0.6828829149503309, -1.255350615348186, -1.406958636671017, 1.942463074731928, 1.549315101294664, -2.459087539151332, -2.486489741966878, 0.3354729179435557, -0.05117432329457276, -0.855247624413176, 1.359249183030364, 1.418298844093717, -1.632503270967475, -1.106526010941604, 0.8901422486076803, -3.114485279354032, -7.518465921754031, -3.736568330776179, 1.532897145341668, 0.7641731501005473, -0.2249368601610983, 1.625315490135336, 0.8379908304421441, -0.8275822228645732, 1.135672790387776, 0.9182231206480799, -3.749142925235569, -3.92759234486934, 0.6625555587931643, 1.225672628595678, -0.2856513754928624, 0.5272792926264225, -2.704553322005755, -9.127066436764983, -7.103041515101689, 0.6360674147017172, 1.871460231209259, -0.6082131628167284, -7.195582885218498e-05, -0.2591093256759899, -1.48364881567422, 0.2096859069455106, -0.995925849416535, -6.306236917330286, -5.191452534463396, 0.6580962400816046, 0.4204031477238944, -1.207945443173448, 1.931387518605434, 1.615380683564802, -2.525933094880632, -1.200651510949478, 1.40621862784308, -0.7193523397437588, -0.780080966905026, 1.204393120270458, -1.32501612502571, -2.602369998182082, 0.6835700539695854, 0.4757800391631781, -0.8680208869814987, 2.549487096375821, 2.422283631107305, -2.003505306185142, 0.4598604618592128, 4.535218569190914, 0.5328213346694907, -2.457299320291457, 0.2517805682048763, 0.5787430356456523, 0.197045922468215, 1.737377233119903, -0.8667800443716867, -3.354908261312338, -0.3030779058002765, -1.021143511738571, -5.050663659079922, -1.448733624716421, 2.864739845851444, 0.2001305703890477, -0.3385238617854437, 0.778413849844777], 'positive_zeros': ['0.2417033310922690', '0.9497607783380719', '1.961495143655530', '2.284697759632389', '2.917142197531854', '3.552125725201456', '4.102323953329624', '4.525120873600140', '4.988960606459846', '5.394980240168084', '6.297047453268597', '6.696965151088800', '7.006830854995141', '7.481212610046694', '8.213775121041411', '8.475898327518072', '8.728242819460748', '9.635015863524433', '9.877994129850838', '10.35877065517698', '10.84618988149637', '11.45832078435328', '11.74266089975753', '12.11769200492812', '12.61499853809400', '13.09443032471994', '13.35409700862344', '14.14842447380793', '14.58920024166904', '14.79117285087118', '15.33430310661328', '15.63977469330277', '16.05731130097212', '16.70831395315890', '17.15682760829417', '17.35875500777278', '17.60892096850227', '18.47387474689436', '18.91470075574941', '19.25001560430828', '19.45727841422725', '19.97220997259897'], 'prelabel': '2-310464-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 49.79023520042339, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2301363548084272557, 'z1': {'__RealLiteral__': 0, 'data': '0.2417033310922690', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '0.9497607783380719', 'prec': 60}, 'z3': {'__RealLiteral__': 0, 'data': '1.961495143655530', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2479.0675213134805, 'bad_primes': [2, 3, 7, 11], 'central_character': '1.1', 'conductor': 310464, 'conductor_radical': 462, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, -6, 0, 0, 0, -2, 0, -8, 0, 0, 0, 4, 0, -1, 0, 0, 0, 2, 0, 8, 0, 0, 0, 0, 0, -6, 0, 0, 0, -2, 0, -8, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 12, 0, 10, 0, 0, 0, 12, 0, 12, 0, 0, 0, 12, 0, -10, 0, 0, 0, 0, 0, -8, 0, 0, 0, -12, 0, 4, 0, 0, 0, 10, 0, 0, 0, 0, 0, 16, 0, 14, 0, 0, 0], 'euler11': [1, -1, 0], 'euler13': [1, 6, 13], 'euler17': [1, 2, 17], 'euler19': [1, 8, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, -2, 29], 'euler3': [1, 0, 0], 'euler31': [1, -8, 31], 'euler37': [1, 6, 37], 'euler41': [1, 2, 41], 'euler43': [1, 8, 43], 'euler47': [1, 4, 47], 'euler5': [1, 2, 5], 'euler53': [1, -2, 53], 'euler59': [1, -12, 59], 'euler61': [1, -10, 61], 'euler67': [1, -12, 67], 'euler7': [1, 0, 0], 'euler71': [1, -12, 71], 'euler73': [1, 10, 73], 'euler79': [1, 8, 79], 'euler83': [1, 12, 83], 'euler89': [1, -10, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 2, 5], [1, 0, 0], [1, -1, 0], [1, 6, 13], [1, 2, 17], [1, 8, 19], [1, -4, 23], [1, -2, 29], [1, -8, 31], [1, 6, 37], [1, 2, 41], [1, 8, 43], [1, 4, 47], [1, -2, 53], [1, -12, 59], [1, -10, 61], [1, -12, 67], [1, -12, 71], [1, 10, 73], [1, 8, 79], [1, 12, 83], [1, -10, 89], [1, -14, 97]], 'index': 28, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/310464/dz'], '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': '2-310464-1.1-c1-0-28', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-310464-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 49.79023520042339, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2301363548084272557, 'z1': {'__RealLiteral__': 0, 'data': '0.2417033310922690', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2301363548084272557', 'Lhash_array': ['2301363548084272557'], 'label': '2-310464-1.1-c1-0-28', 'type': 'ECQ', 'url': 'EllipticCurve/Q/310464/dz'}