-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2224378771425939687697033407276', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.4116292664269173, -0.11029572952010794], 'a4': [0.0, 0.0], 'a5': [0.17187087807271884, -2.2294529376666627], 'a6': [0.0, 0.0], 'a7': [2.476349413629793, 1.429721000566733], 'a8': [0.0, 0.0], 'a9': [-2.4408027063245266, -1.4091980995352327], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.152220905106582, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.17187087807271884, 2.2294529376666627]]], [13, [[1.0, 0], [-1.2550625292306228, -3.3800618408131577]]]], 'bad_primes': [2, 5, 13], 'central_character': '520.457', 'coefficient_field': 'CDF', 'conductor': 520, 'conductor_radical': 130, 'conjugate': '1093624718059330950389729878583', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.4116292664269173, 0.11029572952010794], [2.598076211353316, 1.5]], [[1.0, 0], [-0.17187087807271884, 2.2294529376666627]], [[1.0, 0], [-2.476349413629793, -1.429721000566733], [3.5, 6.06217782649107]], [[1.0, 0], [-0.8584345557064504, 3.2037213768692885], [-9.526279441628825, -5.5]], [[1.0, 0], [-1.2550625292306228, -3.3800618408131577]], [[1.0, 0], [1.434544957418386, 5.353794666827148], [-14.722431864335457, 8.5]], [[1.0, 0], [-1.5182391569807772, 0.4068109560303078], [16.454482671904334, -9.5]], [[1.0, 0], [-1.3786802410173926, 5.145304706868215], [-19.91858428704209, -11.5]], [[1.0, 0], [3.012571473139402, -1.7393089509700213], [14.5, -25.11473670974872]], [[1.0, 0], [-3.172102550995019, 3.172102550995019], [0, -31.0]], [[1.0, 0], [-2.3582488502802343, 1.3615356085254187], [18.5, -32.04293994002423]], [[1.0, 0], [0.43208901620143236, 0.1157779029495321], [35.50704155516198, 20.5]], [[1.0, 0], [-4.842456088575686, 1.2975321983170283], [37.239092362730865, -21.5]], [[1.0, 0], [0, 9.915888586645485], [-47.0, 0]], [[1.0, 0], [-3.959069126993961, 3.959069126993961], [0, -53.0]], [[1.0, 0], [-2.5939753665937815, -9.680847861710097], [-51.09549882328188, 29.5]], [[1.0, 0], [4.435876017414831, -7.683162638238773], [-30.5, -52.827549630850754]], [[1.0, 0], [-1.296328547512575, -2.2453069075937453], [-33.5, 58.023702053557386]], [[1.0, 0], [-3.500368213007156, -13.063552016141784], [-61.48780366869514, 35.5]], [[1.0, 0], [-1.2172997095152973, 0], [73.0, 0]], [[1.0, 0], [0, -0.9329569092505471], [-79.0, 0]], [[1.0, 0], [0, -16.11555895330593], [-83.0, 0]], [[1.0, 0], [10.335842352333525, 2.7694806114031634], [77.07626093681505, 44.5]], [[1.0, 0], [-1.8126198028419722, 3.1395495933277773], [-48.5, -84.00446416709055]], [[1.0, 0], [6.109212771061667, -3.527155637909153], [50.5, -87.4685657822283]], [[1.0, 0], [-3.1357140249101967, -3.1357140249101967], [0, 103.0]], [[1.0, 0], [-0.6926735790428878, 2.585092990048634], [-92.66471820493493, -53.5]], [[1.0, 0], [10.76208676430961, 10.76208676430961], [0, 109.0]], [[1.0, 0], [-4.7187105215469884, -17.610467412623194], [-97.86087062764156, 56.5]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 13, 'label': '2-520-65.2-c1-0-13', 'load_key': 'CMFs-workshop', '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': 'ModularForm/GL2/Q/holomorphic/520/2/cw/c/457/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.3325919496690881, 1.4598714465840594, 1.5817218708763803, 1.695593175561165, 1.7952399342823135, 1.8713744727330033, 1.9127092392793263, 1.9072121355181182, 1.843468794453406, 1.7120909982944073, 1.5071132951043664, 1.2272946065546158, 0.8772086842320114, 0.4679822508762469, 0.017532160332763277, -0.44983178587343786, -0.9045314925422746, -1.3136014779288714, -1.6432703813791227, -1.8620903411519532, -1.9443625380182874, -1.8735196939395047, -1.645064967255847, -1.2686456657454224, -0.768870922389063, -0.1845712691899745, 0.43365594883327996, 1.027577599960323, 1.5368713768834095, 1.9056010446448624, 2.088936258586624, 2.0592983357508565, 1.8110717232741527, 1.3630938855154682, 0.7583319740245976, 0.06046356842229449, -0.6525274482047457, -1.2971964471459068, -1.794970348750015, -2.0826875327325522, -2.12189073178197, -1.9054393559851683, -1.4602485436250565, -0.8454139224646209, -0.1455992061893207, 0.5397293166387859, 1.1099442929769456, 1.477932387177355, 1.5836301007199203, 1.404233244308796, 0.9592327052246541, 0.3091050310822235, -0.45257913794072635, -1.2128037166608716, -1.8566664061487514, -2.286200988221997, -2.4373951995201155, -2.2924082079988555, -1.884589118837422, -1.2949648896448072, -0.6402557277144422, -0.053968465070117114, 0.33654666037765846, 0.4332690794171319, 0.18680002332057705, -0.3919164201597028, -1.230006576520959, -2.2020980604022418, -3.1496896344505396, -3.9074854588616086, -4.332253241403392, -4.3290408349322504, -3.869793766850586, -3.000582004085051, -1.8356069050289694, -0.5385884122865829, 0.7054190893821519, 1.7227492835443625, 2.3822549105685136, 2.6187814603133766, 2.4441985092024088, 1.9435109772990764, 1.2564925337087338, 0.5482482808801995, -0.025489243125123642, -0.3512296300898358, -0.38179347052161844, -0.14622878474098752, 0.25694852803484364, 0.6822150298405324, 0.9707768961557521, 0.988513095342963, 0.6598294567520349, -0.010329796667066382, -0.9317856493904417, -1.943610438033881, -2.845468197408953, -3.439602058128056, -3.5745865985141294, -3.181155986696521, -2.2917562864950796, -1.0387558808656325, 0.3691705943328843, 1.6880757404488915, 2.688681613665124, 3.2043952829239264, 3.1666249708227054, 2.6191660627001645, 1.7079624378229263, 0.6481026210898455, -0.32477908209855577, -1.0077197971636667, -1.2759438586793503, -1.1098905889908408, -0.597117785921775, 0.09168889051175826, 0.7471417586996351, 1.1754606016194789, 1.249439752660113, 0.9433318905047675, 0.34254559192622286, -0.3749423199670685, -0.9815939874824163, -1.2576467582570006, -1.0487847070733707, -0.3096307734571382, 0.8783443561189509, 2.3198170758920713, 3.747211713926383, 4.881338886899414, 5.4964418423502694, 5.473534119165778, 4.828492696882518, 3.7074821083117744, 2.3504570888188394, 1.031669472565132, -0.007835798671992765, -0.6184511552670809, -0.7758456308453907, -0.5814796560738839, -0.22953842160443064, 0.05104225356772535, 0.0639736337217923, -0.29585487725112397, -1.0089384216877693, -1.9325284739425816, -2.837208068317297, -3.4693900956258106, -3.6230615061282037, -3.2010719342331195, -2.248577553761998, -0.9484284340514, 0.4214977506527548, 1.558488674155789, 2.2142596815374627, 2.261771061398744, 1.730901303400025, 0.8023619550967374, -0.23949923486557742, -1.0829689185630489, -1.4739301571082426, -1.286255058932043, -0.5579096269408349, 0.5178098749765043, 1.6441842323668712, 2.502314455566365, 2.8394503881794066, 2.539824486163674, 1.6579870190647883, 0.40496229739500755, -0.9092172057527538, -1.9606259535351462, -2.5002240779722236, -2.42109195171646, -1.7849493813334436, -0.800448698583327, 0.24029600677822816, 1.0482527171243863, 1.4215390566805737, 1.3020883175202183, 0.7880317875676296, 0.09810395989439123, -0.5011475086178928, -0.7831317593442404, -0.6368671380933508, -0.10670034064863662, 0.6170981654202805, 1.2551532018490836, 1.5267810210379094, 1.2422762776793197, 0.3710312530944524, -0.936593019675314, -2.3821766096300503, -3.5989131487174166, -4.255466180159782, -4.153380166186159, -3.2885169756410417, -1.857137390041198, -0.20355710307278477, 1.2760786691978505, 2.245815497683238, 2.5243962511352724, 2.133817860071235, 1.2871616650924524, 0.3193084089467393, -0.41834231493712226, -0.6668409119788722, -0.3387441804968877, 0.4571969521479488, 1.4533097321429032, 2.31042847820784, 2.7278258601772607, 2.540739041529027, 1.774337317649718, 0.6366885450722531, -0.5472943369689053, -1.4399481345290162, -1.7995519256598342, -1.5583489043390346, -0.8441935942286733, 0.061844219431876186, 0.8187950974354832, 1.1400642384000235, 0.8913720352420925, 0.13980035787698056, -0.8631502963256864, -1.7602506536117226, -2.204406027625548, -1.9744732552345017, -1.0531353933595717, 0.3593318878065155, 1.9010691492993002, 3.1574055884580967, 3.787951303566633, 3.631203252035451, 2.7528265671892473, 1.4219526295144045, 0.02335267382623732, -1.0655412235507857, -1.5921464598109036, -1.5019671203301836, -0.9435864067316422, -0.2044582833947787, 0.3999259861807281, 0.6448383722506792, 0.4813650366802388, 0.05720435665651518, -0.33539317229706256, -0.3678642518624925, 0.19699699787272387, 1.402544913248388, 3.0582501644260187, 4.779073230812939, 6.094482263254733, 6.593265493522175, 6.057093225603215, 4.538213260077009], 'positive_zeros': ['1.75472545118146889070446877388273', '3.16252408657571419114383743916981', '4.38550054631266867106643252105221', '5.52572346908437059806975340357424', '6.42693063139883340950551499597189', '7.63857568759059922732879651564023', '8.048276695325638384761404878798694', '9.427402137362874570039288983723202', '10.49322891574160335731103860368490', '10.92426253620670992756648179834721'], 'prelabel': '2-520-65.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.037699905556896, 'root_angle': 0.4099878937326324, 'root_number': '0.2790276286493745 + 0.9602830741246597*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.204993946866', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.75472545118146889070446877388', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.16252408657571419114383743917', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.38550054631266867106643252105', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.152220905106582, 'bad_primes': [2, 5, 13], 'central_character': '65.2', 'conductor': 520, 'conductor_radical': 130, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/520/2/cw/c/457/6'], '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': '2-520-65.2-c1-0-13', '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': '2-520-65.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.037699905556896, 'root_angle': 0.2049939468663162, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.75472545118146889070446877388', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2224378771425939687697033407276', 'Lhash_array': ['2224378771425939687697033407276'], 'label': '2-520-65.2-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/520/2/cw/c/457/6'}