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  • lfunc_lfunctions • Show schema
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'6.40988289477296954632353735709730', '6.49218341582208978978483180541977', '6.51981227620683655741980806628218', '6.63073626598302217238338339938510', '7.09774573983824873003900070955410', '7.12671927009422318074590099473099', '7.23050593983810284879852892642146', '7.27623667072786889571435163015318', '7.35857659609785144308927250081066', '7.55385573503427758923733934729036', '7.64954197726042963057891539770644', '7.78402734726918564674868823413542', '7.943903926113686598589588030201312', '7.968827118582327799829550267383787', '8.027705190648413747996943294257008', '8.080673331679851061784471026837342'], 'prelabel': '12-4840e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.216718956032975, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e6-0', 'trace_hash': 573857895409722983, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.05051714408409494809684222310', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.13474647368702925186738467154', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '1.24727254661942786622784116891', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 3332228787.247679, 'bad_primes': [2, 5, 11], 'central_character': '1.1', 'conductor': 12855002631049216000000, 'conductor_radical': 110, 'degree': 12, 'dirichlet_coefficients': [1, 0, -3, 0, -6, 0, 7, 0, -2, 0, 0, 0, -1, 0, 18, 0, -6, 0, 7, 0, -21, 0, -9, 0, 21, 0, 11, 0, -10, 0, 1, 0, 0, 0, -42, 0, 3, 0, 3, 0, 6, 0, -18, 0, 12, 0, -3, 0, 12, 0, 18, 0, -23, 0, 0, 0, -21, 0, -2, 0, -6, 0, -14, 0, 6, 0, -22, 0, 27, 0, -13, 0, -10, 0, -63, 0, 0, 0, 22, 0, 6, 0, -10, 0, 36, 0, 30, 0, -25, 0, -7, 0, -3, 0, -42, 0, -33, 0, 0, 0], 'euler11': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler13': [1, 1, 45, -6, 910, -859, 12924, -11167, 153790, -13182, 1285245, 371293, 4826809], 'euler17': [1, 6, 72, 313, 2374, 8118, 48321, 138006, 686086, 1537769, 6013512, 8519142, 24137569], 'euler19': [1, -7, 63, -372, 2629, -11785, 58343, -223915, 949069, -2551548, 8210223, -17332693, 47045881], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 9, 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97604778, 205111490, 594823321], [1, -1, 91, -256, 4818, -12597, 186992, -390507, 4630098, -7626496, 84040411, -28629151, 887503681], [1, -3, 166, -457, 12968, -30812, 604530, -1140044, 17753192, -23148421, 311110726, -208031871, 2565726409], [1, -6, 160, -865, 12776, -61540, 651329, -2523140, 21476456, -59616665, 452121760, -695137206, 4750104241], [1, 18, 343, 3709, 40406, 309587, 2369267, 13312241, 74710694, 294891463, 1172648743, 2646151974, 6321363049], [1, 3, 143, 812, 10526, 74947, 556032, 3522509, 23251934, 84304276, 697794383, 688035021, 10779215329], [1, 23, 371, 4184, 42556, 368457, 2924216, 19528221, 119539804, 622901368, 2927368451, 9618496339, 22164361129], [1, 2, 177, -199, 16248, -37789, 1107507, -2229551, 56559288, -40870421, 2144772897, 1429848598, 42180533641], [1, 6, 221, 538, 18774, -8906, 1106328, -543266, 69858054, 122115778, 3059930861, 5067577806, 51520374361], [1, 22, 298, 3305, 30898, 261640, 2192889, 17529880, 138701122, 994021715, 6005034058, 29702752354, 90458382169], [1, 13, 404, 3933, 67568, 509214, 6237970, 36154194, 340610288, 1407663963, 10266319124, 23454981563, 128100283921], [1, 10, 158, 1819, 25610, 203566, 2001099, 14860318, 136475690, 707621923, 4486922078, 20730715930, 151334226289], [1, -22, 506, -7637, 99482, -1123377, 10395066, -88746783, 620867162, -3765338843, 19708740986, -67695240778, 243087455521], [1, 10, 313, 2275, 49590, 301275, 5061625, 25005825, 341625510, 1300815425, 14854454473, 39390406430, 326940373369], [1, 25, 475, 6627, 81130, 837405, 8303699, 74529045, 642630730, 4671829563, 29802564475, 139601486225, 496981290961], [1, 33, 817, 13611, 195654, 2268901, 24243221, 220083397, 1840908486, 12422392203, 72328422577, 283382228481, 832972004929]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4840/2/a/bb'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '12-4840e6-1.1-c1e6-0-5', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0, 0, 0, 0], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 6, 'prelabel': '12-4840e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.216718956032975, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e6-0', 'trace_hash': 573857895409722983, 'z1': {'__RealLiteral__': 0, 'data': '1.05051714408409494809684222310', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1331688688248248310468269818623,1438462048476229351887326457699,1581105792370309973098663463234,1644914134201513368833893832205,1956918853286724725588845595903,2243825559003882588712122282907', 'Lhash_array': ['1331688688248248310468269818623', '1438462048476229351887326457699', '1581105792370309973098663463234', '1644914134201513368833893832205', '1956918853286724725588845595903', '2243825559003882588712122282907'], 'factors': ['2-4840-1.1-c1-0-56', '2-4840-1.1-c1-0-61', '2-4840-1.1-c1-0-73', '2-4840-1.1-c1-0-79', '2-4840-1.1-c1-0-92', '2-4840-1.1-c1-0-103'], 'label': '12-4840e6-1.1-c1e6-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4840/2/a/bb'}