-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': -2, 'A4': -1, 'A5': 0, 'A6': 0, 'A7': 6, 'A8': 0, 'A9': 1, 'Lhash': '1628118118519929866317331741862', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792515, 0], 'a4': [-0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [2.2677868380553634, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 55.14677389390195, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 1]], [3, [1, 2, 3]], [5, [1, 0, -1]], [31, [1, 0, 31]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '864900.1', 'coefficient_field': '1.1.1.1', 'conductor': 864900, 'conductor_radical': 930, 'degree': 4, 'euler_factors': [[1, 0, 1], [1, 2, 3], [1, 0, -1], [1, -6, 22, -42, 49], [1, 0, 10, 0, 121], [1, -2, 18, -26, 169], [1, 0, -2, 0, 289], [1, 0, 22, 0, 361], [1, 0, -2, 0, 529], [1, 0, -22, 0, 841], [1, 0, 31], [1, 10, 74, 370, 1369], [1, 0, 42, 0, 1681], [1, 12, 86, 516, 1849], [1, 0, 10, 0, 2209], [1, 0, -10, 0, 2809], [1, 0, 2, 0, 3481], [1, 4, 62, 244, 3721], [1, 6, 134, 402, 4489], [1, 0, 2, 0, 5041], [1, -22, 258, -1606, 5329], [1, 0, 94, 0, 6241], [1, 0, -10, 0, 6889], [1, 0, -102, 0, 7921], [1, 24, 322, 2328, 9409], [1, 0, 98, 0, 10201], [1, 18, 262, 1854, 10609], [1, 0, 146, 0, 11449], [1, 12, 190, 1308, 11881], [1, 0, 54, 0, 12769]], 'gamma_factors': [[], [0, 0]], 'index': 17, 'label': '4-930e2-1.1-c1e2-0-17', 'load_key': 'Costa', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/2.0.3.1/96100.1/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.048828125', 'prec': 37}, 'plot_values': [-1.2717023599729662e-74, 0.16607535211575852, 0.331323447228449, 0.4948301141269787, 0.6555131501245641, 0.8120526612708393, 0.9628382383865441, 1.1059379018172508, 1.239093116184963, 1.3597433339296587, 1.4650824511596439, 1.5521482372493294, 1.6179442299147762, 1.6595917876010848, 1.674508000984657, 1.6606030510503837, 1.6164884556266494, 1.541685589163145, 1.4368220351945467, 1.3038018984347812, 1.1459353341995027, 0.9680124154997648, 0.7763072062592099, 0.5784996662905475, 0.3835058579746738, 0.20121087331282572, 0.04210389621774197, -0.08317928299745782, -0.16439440799529056, -0.19228873122502507, -0.15923712936988263, -0.05988232041709683, 0.10825815419816404, 0.3442592343487148, 0.6433726060244506, 0.996769678484903, 1.3914812240252525, 1.8105647605081487, 2.233520822815367, 2.636966497424628, 2.995559450302772, 3.2831488704675933, 3.4741122142736915, 3.5448194926638092, 3.4751513516779813, 3.249984667967604, 2.860551092462076, 2.305571064339253, 1.5920691760581562, 0.7357869423397907, -0.23887388151577063, -1.2994206701324782, -2.406366019543241, -3.5148312646097724, -4.576602633269348, -5.542549934391496, -6.365285143581165, -7.0019111814504, -7.416692128116227, -7.583467299596276, -7.487634681341314, -7.127545072974742, -6.5151769403809965, -5.67600238726672, -4.648004813660914, -3.4798657260562633, -2.2283979933098426, -0.9553612177964571, 0.2761528406431024, 1.4055352462488135, 2.378418860563984, 3.1501159457602217, 3.6884799812909015, 3.975968584956406, 4.0107349064106925, 3.806641614436259, 3.39217015159241, 2.8082824853256736, 2.1053764371619317, 1.339551729686072, 0.5684652816095973, -0.15290501731531483, -0.7762533726205668, -1.263373712143167, -1.588740081326633, -1.741024308727373, -1.7234227778137077, -1.5527655506258298, -1.2574879272495902, -0.8746471795860558, -0.4462559495769679, -0.015269756295291844, 0.3783979431942907, 0.7014582615291655, 0.930086681205563, 1.0517484966868702, 1.065835409844348, 0.9830558764478493, 0.8236477719839501, 0.6146043222888697, 0.38621031727208, 0.1682637552845962, -0.013601039138297636, -0.14107495238818119, -0.20545319898668274, -0.20875324583319907, -0.16351484166248162, -0.09126951114334951, -0.019818145135703256, 0.02040253978387551, 0.00046709173005455933, -0.10285281781110281, -0.30336549315554473, -0.60267205730166, -0.9887033189179953, -1.4358354601209276, -1.9066693691818262, -2.3553693187212477, -2.732268931017501, -2.9892875333038273, -3.085578289773488, -2.9927673620277173, -2.6991513969345617, -2.212302039281113, -1.559675835402549, -0.7870325866022873, 0.04529544942382071, 0.8679927041386869, 1.6096876389680939, 2.2045154023668605, 2.599500564919179, 2.760919645588355, 2.6788731615280734, 2.3694591505242615, 1.874180753765074, 1.2565158215808045, 0.5958952460784986, -0.020356954918281305, -0.5063111019139739, -0.786959532052002, -0.8069260979241865, -0.5373469359842814, 0.019921342232754446, 0.8313384152691388, 1.834185304014609, 2.9423720785268963, 4.0549978516491745, 5.0667778052743735, 5.87920862164613, 6.411224313238984, 6.60811799618842, 6.447674105983244, 5.94275488288609, 5.139983202901733, 4.1146162664466415, 2.9621582172743706, 1.7876592590944895, 0.6939437043948906, -0.22983982915230214, -0.9179691489373033, -1.3350095567910731, -1.478932869402498, -1.3800941803866693, -1.09617877154434, -0.7037416362013645, -0.28740478074186643, 0.07190554486931741, 0.3081524868065224, 0.37933063108180803, 0.27331415380723767, 0.00957698520847915, -0.36352093619947906, -0.7756044248610587, -1.1444711262416127, -1.3882889976234205, -1.4381863457666704, -1.2495138703429234, -0.81018013462987, -0.14480086905218276, 0.6860791787832169, 1.5917982553069092, 2.4618588109861252, 3.1794939212802698, 3.6368513953954738, 3.749849111852224, 3.470724635830863, 2.796532337591785, 1.772309887077027, 0.4882884805219454, -0.9287234282283909, -2.328891839474334, -3.556286872725851, -4.467152189809419, -4.94724954957108, -4.926078028366455, -4.386120503054512, -3.3658714942622625, -1.9561756800653056, -0.29025564404268134, 1.4713809107713647, 3.1592988003424476, 4.614473668350363, 5.706195290612764, 6.346306289853033, 6.498027920609449, 6.178337964241125, 5.453715795636374, 4.4299412058981975, 3.2374076171964483, 2.0139807264908667, 0.8877220503333233, -0.038235791812451105, -0.6967229147634786, -1.0621481041229315, -1.1501580261994404, -1.0116515651128546, -0.7222517594485509, -0.36895465901819674, -0.036029325578844036, 0.2077133595597046, 0.3184367720676764, 0.28227574646160275, 0.11524065449396427, -0.14174181846978284, -0.43166642706191305, -0.6925912080486347, -0.8691753437932832, -0.922678555662122, -0.8377715865601678, -0.6250562799905324, -0.3189198180006646, 0.028865809426394953, 0.35866846149465964, 0.6139793655106949, 0.7519301506160525, 0.7514788114587679, 0.6177763637442514, 0.38186086914774664, 0.09561834207099218, -0.177228120883957, -0.3726257071085536, -0.43823709287017837, -0.3439000170973424, -0.08856938023594818, 0.2976619083134153, 0.7570790403757822, 1.2130882075283733, 1.582961892357568, 1.792612708084908, 1.790969069775694, 1.5614577432793755, 1.1284429559247875, 0.5571907780760043, -0.05308059932343377, -0.5823896371684024, -0.9076839170397261, -0.9224699480610982], 'positive_zeros': ['1.28435873278236245967725570034781', '1.53347833820744832754504858838756', '2.42989353523414900304035353582141', '3.30908920407833803053253029557452', '3.94426177116844605090509920301046', '4.44514379194632604451878223602530', '4.97630027277575908068295367976731', '5.29117441073688713850944236676171', '5.37148186282783477747388186443452', '6.14970985396899297248183326190079', '6.68770055729895198216161364579581', '6.93218152688057401872567142051067', '7.70158203757975610770315706406065', '8.094516989884481716872748546887895'], 'prelabel': '4-930e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.725084840510306, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 634171777344130420, 'z1': {'__RealLiteral__': 0, 'data': '1.28435873278236245967725570034781', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.53347833820744832754504858838756', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.42989353523414900304035353582141', 'prec': 113}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 55.14677389390195, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 864900, 'conductor_radical': 930, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, -1, 0, 0, 6, 0, 1, 0, 0, 2, 2, 0, 0, 1, 0, 0, 0, 0, -12, 0, 0, 0, 1, 0, 4, -6, 0, 0, 0, 0, 0, 0, 0, -1, -10, 0, -4, 0, 0, 0, -12, 0, 0, 0, 0, -2, 14, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 6, -1, 0, 0, -6, 0, 0, 0, 0, 0, 22, 0, -2, 0, 0, 0, 0, 0, -11, 0, 0, 12, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, -24, 0, 0, -1], 'euler11': [1, 0, 10, 0, 121], 'euler13': [1, -2, 18, -26, 169], 'euler17': [1, 0, -2, 0, 289], 'euler19': [1, 0, 22, 0, 361], 'euler2': [1, 0, 1, 0, 0], 'euler23': [1, 0, -2, 0, 529], 'euler29': [1, 0, -22, 0, 841], 'euler3': [1, 2, 3, 0, 0], 'euler31': [1, 0, 31, 0, 0], 'euler37': [1, 10, 74, 370, 1369], 'euler41': [1, 0, 42, 0, 1681], 'euler43': [1, 12, 86, 516, 1849], 'euler47': [1, 0, 10, 0, 2209], 'euler5': [1, 0, -1, 0, 0], 'euler53': [1, 0, -10, 0, 2809], 'euler59': [1, 0, 2, 0, 3481], 'euler61': [1, 4, 62, 244, 3721], 'euler67': [1, 6, 134, 402, 4489], 'euler7': [1, -6, 22, -42, 49], 'euler71': [1, 0, 2, 0, 5041], 'euler73': [1, -22, 258, -1606, 5329], 'euler79': [1, 0, 94, 0, 6241], 'euler83': [1, 0, -10, 0, 6889], 'euler89': [1, 0, -102, 0, 7921], 'euler97': [1, 24, 322, 2328, 9409], 'euler_factors': [[1, 0, 1, 0, 0], [1, 2, 3, 0, 0], [1, 0, -1, 0, 0], [1, -6, 22, -42, 49], [1, 0, 10, 0, 121], [1, -2, 18, -26, 169], [1, 0, -2, 0, 289], [1, 0, 22, 0, 361], [1, 0, -2, 0, 529], [1, 0, -22, 0, 841], [1, 0, 31, 0, 0], [1, 10, 74, 370, 1369], [1, 0, 42, 0, 1681], [1, 12, 86, 516, 1849], [1, 0, 10, 0, 2209], [1, 0, -10, 0, 2809], [1, 0, 2, 0, 3481], [1, 4, 62, 244, 3721], [1, 6, 134, 402, 4489], [1, 0, 2, 0, 5041], [1, -22, 258, -1606, 5329], [1, 0, 94, 0, 6241], [1, 0, -10, 0, 6889], [1, 0, -102, 0, 7921], [1, 24, 322, 2328, 9409]], 'index': 17, 'instance_types': ['BMF', 'ECNF', 'ECNF', 'BMF'], 'instance_urls': ['ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/96100.1/a', 'EllipticCurve/2.0.3.1/96100.1/a', 'EllipticCurve/2.0.3.1/96100.3/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/96100.3/a'], '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': '4-930e2-1.1-c1e2-0-17', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'prelabel': '4-930e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.725084840510306, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 634171777344130420, 'z1': {'__RealLiteral__': 0, 'data': '1.28435873278236245967725570034781', 'prec': 113}}
-
lfunc_instances • Show schema
Hide schema
-
id: 9811665
{'Lhash': '1628118118519929866317331741862', 'Lhash_array': ['1628118118519929866317331741862'], 'label': '4-930e2-1.1-c1e2-0-17', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/96100.3/a'}
-
id: 9811664
{'Lhash': '1628118118519929866317331741862', 'Lhash_array': ['1628118118519929866317331741862'], 'label': '4-930e2-1.1-c1e2-0-17', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/96100.3/a'}
-
id: 9811327
{'Lhash': '1628118118519929866317331741862', 'Lhash_array': ['1628118118519929866317331741862'], 'label': '4-930e2-1.1-c1e2-0-17', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/96100.1/a'}
-
id: 9811221
{'Lhash': '1628118118519929866317331741862', 'Lhash_array': ['1628118118519929866317331741862'], 'label': '4-930e2-1.1-c1e2-0-17', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/96100.1/a'}