Formats: - HTML - YAML - JSON - 2026-10-24T15:06:08.597310
  • lfunc_lfunctions • Show schema
    {'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '1795171592948384154431640222434', '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': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 42.30865083922584, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '663552.1', 'coefficient_field': '1.1.1.1', 'conductor': 663552, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1], [1, 0, -2, 0, 25], [1, 0, 10, 0, 49], [1, -4, 10, -44, 121], [1, 0, 18, 0, 169], [1, 2, 10, 34, 289], [1, 0, 22, 0, 361], [1, 0, 2, 0, 529], [1, 0, 38, 0, 841], [1, 0, -14, 0, 961], [1, 0, -10, 0, 1369], [1, 2, 82, 82, 1681], [1, 12, 118, 516, 1849], [1, 0, 2, 0, 2209], [1, 0, 62, 0, 2809], [1, 4, 86, 236, 3481], [1, 0, 38, 0, 3721], [1, 16, 182, 1072, 4489], [1, 0, -94, 0, 5041], [1, 20, 230, 1460, 5329], [1, 0, -102, 0, 6241], [1, 12, 202, 996, 6889], [1, 18, 178, 1602, 7921], [1, 0, -2, 0, 9409], [1, 0, -130, 0, 10201], [1, 0, 146, 0, 10609], [1, 4, 214, 428, 11449], [1, 0, -158, 0, 11881], [1, 18, 186, 2034, 12769]], 'gamma_factors': [[], [0, 0]], 'index': 27, 'label': '4-663552-1.1-c1e2-0-27', 'load_key': 'Costa', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/2.0.8.1/10368.3/p', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.048828125', 'prec': 27}, 'plot_values': [-1.3469216471210805e-74, 0.20909017950385905, 0.41787793790783323, 0.6259572316376958, 0.8327197785265628, 1.0372663912422087, 1.2383330669552468, 1.43423641083475, 1.6228426228490742, 1.8015637796725872, 1.9673844651663754, 2.11692091651942, 2.246513739525159, 2.3523538991919875, 2.4306401214764595, 2.4777640794318483, 2.490517836553794, 2.466316059783133, 2.403423596209616, 2.3011772536250477, 2.1601891744446577, 1.9825181930515887, 1.7717951663208056, 1.533288603197409, 1.2738981060962353, 1.0020652532472711, 0.7275946274380886, 0.4613817039380656, 0.2150491513759612, 0.000498602786861298, -0.17060912600458394, -0.2874263732242397, -0.34051878099889976, -0.3224634652676996, -0.22841149428419477, -0.05657860727003769, 0.19137230275728337, 0.5100915645499138, 0.8904762704688827, 1.319800459387319, 1.78205617622386, 2.2585082973466517, 2.7284530491855854, 3.170156245721681, 3.5619332655039577, 3.883319637836663, 4.11626983418447, 4.246313486066253, 4.2635937165278035, 4.163712358495521, 3.94831207665617, 3.625336030673342, 3.2089215633902444, 2.718904905477232, 2.179938077865391, 1.6202456730859045, 1.0700763016285226, 0.5599292567795876, 0.11865932557825397, -0.2284203634051471, -0.4613078277008503, -0.5668233583336713, -0.5397401062016866, -0.38343029584964455, -0.10995091569916911, 0.26047155106463, 0.7005561095260899, 1.1776358065890915, 1.6557888689092024, 2.0983002262425905, 2.470287246169465, 2.741300109127142, 2.887697197559891, 2.8946010565696945, 2.7572616911430465, 2.4816906994465646, 2.0844801472950865, 1.5917809894978288, 1.0374829010095477, 0.4607053715056119, -0.09722688388346296, -0.5960985006298598, -1.000145532743883, -1.2811458731590541, -1.420985248946943, -1.413456403536393, -1.2651024446510943, -0.9949884852210457, -0.6333734195252093, -0.21934904375736056, 0.20239135636944436, 0.5854070026150773, 0.8856699160166422, 1.0656717103820816, 1.098103969958926, 0.968759619506552, 0.6783566022808379, 0.24306963988087113, -0.30633526650320086, -0.9267444638690464, -1.5661701125515068, -2.1681833653732867, -2.6769346905915463, -3.0423166132300463, -3.2247908956751843, -3.199413139208571, -2.958644241440488, -2.5136369514801364, -1.893819408697911, -1.144754625112654, -0.32442099439254446, 0.5017819928295061, 1.266862808206706, 1.9083638535938505, 2.374198256588395, 2.627619994083711, 2.6508169184429704, 2.4467375747066606, 2.038928165709751, 1.469350470757377, 0.7943560159524604, 0.07918543755010826, -0.6084759553512632, -1.2052432683432477, -1.6583862509114744, -1.93112425321466, -2.0062883701307266, -1.8879364717031797, -1.6007156980069213, -1.1870047334302178, -0.7021099287907311, -0.20800875920343015, 0.23369381429852887, 0.5688265802064136, 0.7569397148961147, 0.7760936397465165, 0.6255734619166441, 0.32617267997571825, -0.0820433320582464, -0.5442977767581934, -0.9975177386728106, -1.3779071712442874, -1.6288248960947072, -1.7080526748823017, -1.593580039566651, -1.2871771121145767, -0.8152610924448138, -0.22686239102580458, 0.4111702042995797, 1.0212573337957849, 1.5237169030721083, 1.8459729195867012, 1.9312862660036132, 1.7459700165923402, 1.2841969891493596, 0.5697627581515806, -0.34549335594392694, -1.3865214973400868, -2.462674181795486, -3.4772827571522003, -4.338127269270072, -4.967596641427861, -5.311344020859307, -5.344394267643692, -5.073942592926177, -4.5384646033296745, -3.803194572459901, -2.9524685112199314, -2.079817405452955, -1.2769843773623943, -0.6231890989592506, -0.1759513851417012, 0.03538904827396565, 0.012640173858815024, -0.21217476985208136, -0.5815510761626633, -1.0204567011773782, -1.4465085339345203, -1.7810756849220917, -1.959878937680537, -1.9417021868674225, -1.7140588858586912, -1.295038782561835, -0.7310511109939835, -0.09071800841643417, 0.5443134856880136, 1.0904494813845833, 1.4736528049028845, 1.6398241368628848, 1.5626348278883755, 1.2477016476657297, 0.7324662793974198, 0.08171157392388197, -0.6207620026718518, -1.2832421375158092, -1.818532084726016, -2.156025490646032, -2.2517640303845226, -2.0950506450098896, -1.7106297597903724, -1.1560308033614586, -0.5143261750981412, 0.11680866326177684, 0.6383151644370366, 0.9634860369408302, 1.0303353043901786, 0.8108690661035206, 0.3159087609690749, -0.40529878138131453, -1.2707480818762709, -2.175955010744803, -3.0075350255978592, -3.658281380242798, -4.041701381102526, -4.104004219046016, -3.8318496973232006, -3.2547250954306475, -2.4415441755059395, -1.4918591118704518, -0.5228319122370897, 0.34628093334537763, 1.0100071170161038, 1.390701605141376, 1.4487901045477194, 1.187765768725863, 0.6532217475500888, -0.07395654848245883, -0.8892821591947652, -1.6795778341112917, -2.3389727325832994, -2.7836813873322708, -2.9634272819087335, -2.8678531361310298, -2.526988027104607, -2.0057140701445593, -1.3930655662200397, -0.7879694109697536, -0.28357988883845126, 0.047411109363611544, 0.16423497322735414, 0.06449438987018857, -0.2154393022195484, -0.6062025845738911, -1.0165659302432455, -1.3482490170938217, -1.5121679854259094, -1.4435970903938442, -1.1138483896744908, -0.5365652036917274, 0.23248011746394642, 1.1022120220163314, 1.9588078094377483, 2.682185866734379, 3.163981698022322, 3.324284312478077, 3.124537008040352, 2.574540899020662], 'positive_zeros': ['1.41614068784030805713397454470907', '1.72152769979827701933766706186162', '2.84715959744495461923339727677976', '3.14073274970007574415170213426335', '3.89745822559605834211808654809907', '4.37087036507384903100010666531004', '4.75898201686463271520699744061092', '5.39008847706981631272183454865059', '5.91364219632269512929721021496667', '6.41837735856575227473623505272053', '6.72917333213766140722446789447886', '7.19523487874934462858002412970074', '7.59975611036620556892906241169429', '8.384621070850913416153815772139857'], 'prelabel': '4-663552-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.5503940947170642, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 706865773648310561, 'z1': {'__RealLiteral__': 0, 'data': '1.41614068784030805713397454470907', 'prec': 110}, 'z2': {'__RealLiteral__': 0, 'data': '1.72152769979827701933766706186162', 'prec': 110}, 'z3': {'__RealLiteral__': 0, 'data': '2.84715959744495461923339727677976', 'prec': 110}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 42.30865083922584, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 663552, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -12, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, -4, 10, -44, 121], 'euler13': [1, 0, 18, 0, 169], 'euler17': [1, 2, 10, 34, 289], 'euler19': [1, 0, 22, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 2, 0, 529], 'euler29': [1, 0, 38, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, -14, 0, 961], 'euler37': [1, 0, -10, 0, 1369], 'euler41': [1, 2, 82, 82, 1681], 'euler43': [1, 12, 118, 516, 1849], 'euler47': [1, 0, 2, 0, 2209], 'euler5': [1, 0, -2, 0, 25], 'euler53': [1, 0, 62, 0, 2809], 'euler59': [1, 4, 86, 236, 3481], 'euler61': [1, 0, 38, 0, 3721], 'euler67': [1, 16, 182, 1072, 4489], 'euler7': [1, 0, 10, 0, 49], 'euler71': [1, 0, -94, 0, 5041], 'euler73': [1, 20, 230, 1460, 5329], 'euler79': [1, 0, -102, 0, 6241], 'euler83': [1, 12, 202, 996, 6889], 'euler89': [1, 18, 178, 1602, 7921], 'euler97': [1, 0, -2, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 0, -2, 0, 25], [1, 0, 10, 0, 49], [1, -4, 10, -44, 121], [1, 0, 18, 0, 169], [1, 2, 10, 34, 289], [1, 0, 22, 0, 361], [1, 0, 2, 0, 529], [1, 0, 38, 0, 841], [1, 0, -14, 0, 961], [1, 0, -10, 0, 1369], [1, 2, 82, 82, 1681], [1, 12, 118, 516, 1849], [1, 0, 2, 0, 2209], [1, 0, 62, 0, 2809], [1, 4, 86, 236, 3481], [1, 0, 38, 0, 3721], [1, 16, 182, 1072, 4489], [1, 0, -94, 0, 5041], [1, 20, 230, 1460, 5329], [1, 0, -102, 0, 6241], [1, 12, 202, 996, 6889], [1, 18, 178, 1602, 7921], [1, 0, -2, 0, 9409]], 'index': 27, 'instance_types': ['ECNF', 'ECNF', 'BMF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.8.1/10368.3/g', 'EllipticCurve/2.0.8.1/10368.3/p', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/10368.3/p', 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/10368.3/g'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-663552-1.1-c1e2-0-27', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'prelabel': '4-663552-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.5503940947170642, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 706865773648310561, 'z1': {'__RealLiteral__': 0, 'data': '1.41614068784030805713397454470907', 'prec': 110}}
  • lfunc_instances • Show schema
    • id: 9814516
      {'Lhash': '1795171592948384154431640222434', 'Lhash_array': ['1795171592948384154431640222434'], 'factors': ['4-663552-1.1-c1e2-0-27'], 'label': '4-663552-1.1-c1e2-0-27', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/10368.3/g'}
    • id: 9814584
      {'Lhash': '1795171592948384154431640222434', 'Lhash_array': ['1795171592948384154431640222434'], 'factors': ['4-663552-1.1-c1e2-0-27'], 'label': '4-663552-1.1-c1e2-0-27', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.8.1/10368.3/p'}
    • id: 9814921
      {'Lhash': '1795171592948384154431640222434', 'Lhash_array': ['1795171592948384154431640222434'], 'factors': ['4-663552-1.1-c1e2-0-27'], 'label': '4-663552-1.1-c1e2-0-27', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/10368.3/p'}
    • id: 9815174
      {'Lhash': '1795171592948384154431640222434', 'Lhash_array': ['1795171592948384154431640222434'], 'factors': ['4-663552-1.1-c1e2-0-27'], 'label': '4-663552-1.1-c1e2-0-27', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.8.1/10368.3/g'}