-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1912710660324147637308994700696', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -5, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 42.481375204133265, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 5]]], 'bad_primes': [2, 3, 5], 'central_character': '720.1', 'coefficient_field': '1.1.1.1', 'conductor': 720, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1], [1, 5], [1, 0, 343], [1, -4, 1331], [1, -54, 2197], [1, 114, 4913], [1, 44, 6859], [1, -96, 12167], [1, 134, 24389], [1, -272, 29791], [1, 98, 50653], [1, -6, 68921], [1, 12, 79507], [1, 200, 103823], [1, 654, 148877], [1, -36, 205379], [1, 442, 226981], [1, -188, 300763], [1, 632, 357911], [1, 390, 389017], [1, 688, 493039], [1, -1188, 571787], [1, -694, 704969], [1, 1726, 912673], [1, 1182, 1030301], [1, 1968, 1092727], [1, -796, 1225043], [1, -342, 1295029], [1, 114, 1442897]], 'euler_factors_factorization': [[1], [1], [[[1, 5], 1]], [[[1, 0, 343], 1]], [[[1, -4, 1331], 1]], [[[1, -54, 2197], 1]], [[[1, 114, 4913], 1]], [[[1, 44, 6859], 1]], [[[1, -96, 12167], 1]], [[[1, 134, 24389], 1]], [[[1, -272, 29791], 1]], [[[1, 98, 50653], 1]], [[[1, -6, 68921], 1]], [[[1, 12, 79507], 1]], [[[1, 200, 103823], 1]], [[[1, 654, 148877], 1]], [[[1, -36, 205379], 1]], [[[1, 442, 226981], 1]], [[[1, -188, 300763], 1]], [[[1, 632, 357911], 1]], [[[1, 390, 389017], 1]], [[[1, 688, 493039], 1]], [[[1, -1188, 571787], 1]], [[[1, -694, 704969], 1]], [[[1, 1726, 912673], 1]], [[[1, 1182, 1030301], 1]], [[[1, 1968, 1092727], 1]], [[[1, -796, 1225043], 1]], [[[1, -342, 1295029], 1]], [[[1, 114, 1442897], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 21, 'label': '2-720-1.1-c3-0-21', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/720/4/a/i', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-1.3564228613462957e-60, 0.21106238443271672, 0.4196191917640864, 0.6231764514918199, 0.8192640697010589, 1.0054493910499493, 1.179352613182402, 1.338664515111217, 1.4811668353543326, 1.6047554877468029, 1.7074666383631596, 1.787505491791277, 1.8432774552390607, 1.8734211707824384, 1.8768427354807173, 1.8527502718237285, 1.800687872403997, 1.7205678277743068, 1.6126999596359015, 1.477816826773096, 1.3170935519129419, 1.1321610367265615, 0.9251113915819287, 0.6984945076894279, 0.45530484233230856, 0.1989576723120801, -0.06674570518774578, -0.3376640843727112, -0.609373742132916, -0.8772367557430314, -1.1364795538877968, -1.3822806561959355, -1.6098662022915862, -1.8146115251209884, -1.9921466961423266, -2.138463673567742, -2.250022431116319, -2.3238532454132965, -2.357652186427288, -2.349866797352151, -2.2997689768530725, -2.207512194468342, -2.0741703837499514, -1.9017561693142226, -1.6932164922215855, -1.45240419860714, -1.1840247414009317, -0.893557802974997, -0.5871543628636108, -0.2715104913058435, 0.046280074689242875, 0.3588917441689239, 0.6589477028433209, 0.9392111036569121, 1.1927819554358678, 1.4132943525232955, 1.5951083267021162, 1.7334903968525859, 1.8247768603330299, 1.8665140271442122, 1.8575699522979154, 1.7982127760807145, 1.690151531973243, 1.536536216609434, 1.3419150167938338, 1.1121478294795935, 0.854276559137944, 0.5763540943163077, 0.2872353073181209, -0.0036651602800350123, -0.2866422188487855, -0.5519894322465472, -0.7902995307208963, -0.992767147993113, -1.1514840444837524, -1.2597168313581162, -1.3121572939712993, -1.3051358456836042, -1.2367894295537163, -1.1071763190769186, -0.918331729614247, -0.6742599057367867, -0.3808603496351502, -0.04578804315055104, 0.3217501786531416, 0.7112585993397951, 1.1112681348892046, 1.5096954179323845, 1.894234533302941, 2.2527688431541413, 2.5737890801636674, 2.8468030781226115, 3.0627222045418048, 3.2142097973588273, 3.2959777059572346, 3.3050183932250414, 3.240761945999858, 3.1051497193883826, 2.9026191378029345, 2.6399973036112985, 2.326304416754162, 1.9724714647880834, 1.5909800714477749, 1.1954356563050261, 0.800088021473019, 0.41931601194471935, 0.06709487349864107, -0.24353374777665518, -0.5009686395034495, -0.6955123800171611, -0.8197719427586124, -0.8689791210850907, -0.8412159676809604, -0.7375337612709224, -0.5619579215064433, -0.32137565338166046, -0.025307752809312772, 0.31442923696182457, 0.6841596572069405, 1.068868908107473, 1.45278801729248, 1.8200202175904936, 2.1551847415029597, 2.444051595640855, 2.6741406956079175, 2.835259476877734, 2.9199549601095223, 2.9238592012781695, 2.845911009895325, 2.6884416368864135, 2.457117638221126, 2.1607400945865667, 1.8109055653091177, 1.421540310892798, 1.0083251590624558, 0.5880336438185644, 0.17781046149861482, -0.20557936377083275, -0.546498116799324, -0.8311466344721765, -1.0482067191674982, -1.1893845270653878, -1.249828404741488, -1.22839962367011, -1.1277805608662816, -0.9544118513799477, -0.7182576019348113, -0.43240557442164634, -0.11251696956222335, 0.22385229641762863, 0.558030477954182, 0.8710753908623113, 1.1446487557195557, 1.361879694702792, 1.508177136790835, 1.5719523165406935, 1.5452158458496148, 1.4240188945092322, 1.2087146445084205, 0.9040241138929266, 0.5188993361766815, 0.06618633133600037, -0.4379001247776469, -0.9744686927520966, -1.5227809447732046, -2.0611812300565613, -2.5680844340460816, -3.0229754576223122, -3.4073727235306177, -3.7057087882833977, -3.9060842213050977, -4.000856217371931, -3.9870307286055318, -3.8664359271228412, -3.645665133506357, -3.335788487503892, -2.9518440591396105, -2.512130234965577, -2.0373314985160738, -1.5495186167679946, -1.0710712621735483, -0.6235758416479434, -0.22675347424614847, 0.10252751359751927, 0.35110355794778186, 0.510187298703207, 0.5758219472296481, 0.5490925293585877, 0.4360799977403134, 0.2475572148003751, -0.0015608764114618413, -0.29298763765091207, -0.6060185441565946, -0.9186211129529084, -1.2086057547248017, -1.4548172044705683, -1.6382841129948238, -1.743265560748741, -1.7581376960177004, -1.676071235947517, -1.49546086703992, -1.2200801513448396, -0.8589497618621973, -0.42592200842575756, 0.061000120476607154, 0.5805766035024252, 1.1094308469733705, 1.6232802442870617, 2.098232143769797, 2.512075921394354, 2.8455009242117373, 3.0831729292564174, 3.214608372065343, 3.234795653051135, 3.1445258469523294, 2.9504104643429745, 2.6645807464395586, 2.304080415608831, 1.8899809007704356, 1.4462638541840371, 0.9985293702822563, 0.5725989079396137, 0.19308885519463362, -0.11796649895881568, -0.3423653453919667, -0.4667907203716827, -0.4836034615502719, -0.3913279513724829, -0.19479935516771843, 0.09504038782367256, 0.46169098304307643, 0.883960255682943, 1.3371039872408088, 1.7941783163373395, 2.2275310030212734, 2.610348945729787, 2.9181750047428325, 3.1303077547826503, 3.2310033154816082, 3.2104086595676335, 3.0651702646472483, 2.7986798910663713, 2.4209396561376266, 1.9480502923018512, 1.4013482828023907, 0.8062381940923329, 0.19078474591087674, -0.41585612736611083, -0.9850776860336516, -1.4904395458648396, -1.9091671798588605, -2.2234452174434027, -2.42142716400891, -2.4979000510570777, -2.4545622665120996, -2.29989529191416, -2.0486339913745923], 'positive_zeros': ['1.50886266292918633478968469461575', '2.92112734152836684564415836551394', '4.04222466359204504078249596148584', '4.87083806250021007745933914505149', '6.22288113544855041840252182719004', '6.80148373918685823544763409530514', '7.995268274334997955762032999022738', '8.691636308798170730205431417433168', '9.441592853999042607847323646934784'], 'prelabel': '2-720-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.517773792034613, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'trace_hash': 2134947756124042272, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.50886266292918633478968469462', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.92112734152836684564415836551', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.04222466359204504078249596149', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 42.481375204133265, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 720, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -5, 0, 0, 0, 0, 0, 4, 0, 54, 0, 0, 0, -114, 0, -44, 0, 0, 0, 96, 0, 25, 0, 0, 0, -134, 0, 272, 0, 0, 0, 0, 0, -98, 0, 0, 0, 6, 0, -12, 0, 0, 0, -200, 0, -343, 0, 0, 0, -654, 0, -20, 0, 0, 0, 36, 0, -442, 0, 0, 0, -270, 0, 188, 0, 0, 0, -632, 0, -390, 0, 0, 0, 0, 0, -688, 0, 0, 0, 1188, 0, 570, 0, 0, 0, 694, 0, 0, 0, 0, 0, 220, 0, -1726, 0, 0, 0], 'euler11': [1, -4, 1331], 'euler13': [1, -54, 2197], 'euler17': [1, 114, 4913], 'euler19': [1, 44, 6859], 'euler2': [1, 0, 0], 'euler23': [1, -96, 12167], 'euler29': [1, 134, 24389], 'euler3': [1, 0, 0], 'euler31': [1, -272, 29791], 'euler37': [1, 98, 50653], 'euler41': [1, -6, 68921], 'euler43': [1, 12, 79507], 'euler47': [1, 200, 103823], 'euler5': [1, 5, 0], 'euler53': [1, 654, 148877], 'euler59': [1, -36, 205379], 'euler61': [1, 442, 226981], 'euler67': [1, -188, 300763], 'euler7': [1, 0, 343], 'euler71': [1, 632, 357911], 'euler73': [1, 390, 389017], 'euler79': [1, 688, 493039], 'euler83': [1, -1188, 571787], 'euler89': [1, -694, 704969], 'euler97': [1, 1726, 912673], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 5, 0], [1, 0, 343], [1, -4, 1331], [1, -54, 2197], [1, 114, 4913], [1, 44, 6859], [1, -96, 12167], [1, 134, 24389], [1, -272, 29791], [1, 98, 50653], [1, -6, 68921], [1, 12, 79507], [1, 200, 103823], [1, 654, 148877], [1, -36, 205379], [1, 442, 226981], [1, -188, 300763], [1, 632, 357911], [1, 390, 389017], [1, 688, 493039], [1, -1188, 571787], [1, -694, 704969], [1, 1726, 912673]], 'index': 21, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/720/4/a/i/1/1', 'ModularForm/GL2/Q/holomorphic/720/4/a/i'], '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': '2-720-1.1-c3-0-21', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-720-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.517773792034613, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 2134947756124042272, 'z1': {'__RealLiteral__': 0, 'data': '1.50886266292918633478968469462', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20472478
{'Lhash': '1912710660324147637308994700696', 'Lhash_array': ['1912710660324147637308994700696'], 'label': '2-720-1.1-c3-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/4/a/i'}
-
id: 24569816
{'Lhash': '1912710660324147637308994700696', 'Lhash_array': ['1912710660324147637308994700696'], 'label': '2-720-1.1-c3-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/4/a/i/1/1'}