-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '431801039029751010876770234081', 'a10': [0.0, 0.0], 'a2': [-0.15555390873299094, 0.2694272732414724], 'a3': [-0.514917304110508, 0.8918629324157945], 'a4': [0.9516059629557766, 1.6482298766249122], 'a5': [0.0, 0.0], 'a6': [-0.1601947986572874, -0.27746553038268834], 'a7': [-3.2803831053972643, 0.0], 'a8': [-1.2143197433775352, 0.0], 'a9': [0.9697203398551333, 1.67960489776205], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-2.423458161492814, 3.62309957625979]]]], 'bad_primes': [5, 19], 'central_character': '475.201', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'conjugate': '3396396542594273916498502485735', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.15555390873299094, -0.2694272732414724], [-1.0, -1.7320508075688772]], [[1.0, 0], [0.514917304110508, -0.8918629324157945], [-1.5, -2.598076211353316]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.2803831053972643, 0], [7.0, 0]], [[1.0, 0], [5.167919105882527, 0], [11.0, 0]], [[1.0, 0], [1.767354670346055, 3.0611480840335115], [-6.5, 11.258330249197702]], [[1.0, 0], [-0.5046408899242965, 0.8740636609256546], [-8.5, -14.722431864335457]], [[1.0, 0], [-2.423458161492814, 3.62309957625979]], [[1.0, 0], [-3.831756029252514, -6.636796124873732], [-11.5, 19.91858428704209]], [[1.0, 0], [-2.0130284350512095, -3.4866675265895606], [-14.5, 25.11473670974872]], [[1.0, 0], [4.600772702711839, 0], [31.0, 0]], [[1.0, 0], [6.488308703197102, 0], [37.0, 0]], [[1.0, 0], [-3.4027668739877024, 5.893765112059024], [-20.5, -35.50704155516198]], [[1.0, 0], [3.1551088568091403, -5.464808843403988], [-21.5, -37.239092362730865]], [[1.0, 0], [-1.9207858674729499, -3.326898712923409], [-23.5, 40.703193977868615]], [[1.0, 0], [-3.5594580070649786, -6.165162115644403], [-26.5, 45.89934640057525]], [[1.0, 0], [6.736491499144649, -11.667945541274367], [-29.5, -51.09549882328188]], [[1.0, 0], [3.0685018134927957, 5.314801044086761], [-30.5, 52.827549630850754]], [[1.0, 0], [-5.598972240465881, -9.697704390654655], [-33.5, 58.023702053557386]], [[1.0, 0], [-0.22770197781246443, 0.3943913945551096], [-35.5, -61.48780366869514]], [[1.0, 0], [2.066910390148852, -3.5799938104298223], [-36.5, -63.21985447626402]], [[1.0, 0], [1.4441403019221173, -2.5013243761869655], [-39.5, -68.41600689897065]], [[1.0, 0], [5.500611015107286, 0], [83.0, 0]], [[1.0, 0], [-3.5643286086620942, -6.173598245074033], [-44.5, 77.07626093681505]], [[1.0, 0], [-5.412518509404929, 9.374757055196303], [-48.5, -84.00446416709055]], [[1.0, 0], [-3.090110708896356, -5.352228748821169], [-50.5, 87.4685657822283]], [[1.0, 0], [-18.32167952897033, 0], [103.0, 0]], [[1.0, 0], [-8.73445232347089, 0], [107.0, 0]], [[1.0, 0], [-3.0483940370442233, 5.279973353650597], [-54.5, -94.39676901250381]], [[1.0, 0], [-10.344316039203104, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-475-19.11-c1-0-1', '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/475/2/e/f/201/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.5701408766666323, 0.35697678568803026, 0.14949394261149063, -0.05675632701410346, -0.26380783569206645, -0.470519619363138, -0.6723164228560088, -0.8613683425046869, -1.027131700039708, -1.1571962118562715, -1.2384034986859866, -1.2582000703146001, -1.2061645399938468, -1.0756124805088128, -0.8651429385454504, -0.5799572766435492, -0.23276163334982214, 0.15593453136684268, 0.5582848081868039, 0.9404439613670085, 1.264803846225425, 1.4930506971745154, 1.5898523106208058, 1.5268689226705239, 1.2866829123511634, 0.8661767160615991, 0.2788712830623095, -0.44421889417252186, -1.2555478974536558, -2.0939772872124855, -2.889626019348232, -3.5703112544842783, -4.069007479733582, -4.331536938100433, -4.3235649023370915, -4.035941000060563, -3.4875241418607072, -2.7248593282602775, -1.8184259519622337, -0.8556148218529003, 0.06893787744378434, 0.8645931260044399, 1.4561264731762857, 1.793751491309637, 1.8602283814130405, 1.673819369283432, 1.2863542985261904, 0.7763381003089013, 0.23778007058711478, -0.23385739176675063, -0.5566248719865969, -0.6756914993068961, -0.5733419644971737, -0.273512380333131, 0.1602517777868535, 0.6335447769653076, 1.0355880334380636, 1.2574547831653768, 1.211247257436761, 0.8470649790873112, 0.16473632329972723, -0.782047753395548, -1.8904284997932392, -3.021698559111971, -4.0215313149519245, -4.744084442337091, -5.076061594907694, -4.956572137351723, -4.389114862705719, -3.4431941484602393, -2.244789668905964, -0.9568642952299784, 0.2470395332657199, 1.211653887217364, 1.8261697562831742, 2.042898482460016, 1.8847568794836032, 1.4398817320491941, 0.8440624045351464, 0.2540458548880856, -0.1833508424403316, -0.3603899977260855, -0.23003235464496694, 0.1844618387217029, 0.7941679619714336, 1.462766178928053, 2.0350231650655637, 2.369831769351796, 2.371003550166849, 2.0092387894423602, 1.3303299715744275, 0.4474112848925789, -0.4815857442265317, -1.2868643599311809, -1.8232417817244342, -2.0022848248767824, -1.8128470535207366, -1.3250203678123733, -0.6759946791116886, -0.04029997416621103, 0.4094795583755705, 0.5430111842511515, 0.30441722167616964, -0.2713214945719838, -1.0622172297917043, -1.8834202018014934, -2.5270545963982434, -2.8093335535793256, -2.6144801066243715, -1.9252333245938362, -0.832341208768379, 0.4800575201037862, 1.7708374664475484, 2.7926260586150864, 3.3458131443512564, 3.3235769966012167, 2.7372994414068113, 1.7159239070998442, 0.47866688583967953, -0.7132930893002741, -1.61541758092599, -2.0552315813425577, -1.9714752491364766, -1.4274105281867557, -0.5946372898687912, 0.289237400948792, 0.9793433947888394, 1.2847579480709186, 1.1173011737704515, 0.5157153909075952, -0.36122304105108627, -1.2716176930770016, -1.9489187114213322, -2.167949538607073, -1.8023252335068554, -0.8588981334451219, 0.519697042890137, 2.0855360574400774, 3.5418420733968787, 4.6116801539806636, 5.101985509535798, 4.9470185128676585, 4.220433944299357, 3.113085431195191, 1.882450605594354, 0.7868855247281933, 0.021852971518575105, -0.3252752276973067, -0.2901936312715224, -0.012874584349824336, 0.3093940220500455, 0.4838511444928122, 0.3815415674218908, -0.02280423184947103, -0.6418301733405463, -1.3004790927456817, -1.7880910954770053, -1.923037929937693, -1.6112559519808944, -0.8812323242807693, 0.11579211150358498, 1.1420085408266818, 1.9367812905889674, 2.2908020104063604, 2.1097746596304883, 1.448813588713528, 0.5062415797393114, -0.4235017033364953, -1.0265790468067353, -1.0560142630630645, -0.4038986819375786, 0.8610412866495103, 2.5022110450484965, 4.169478035713724, 5.485654778361383, 6.142472158337499, 5.980222359353771, 5.029239334356411, 3.5015666535540304, 1.7347937004671652, 0.10332405787534599, -1.0785111666713032, -1.6347482453553628, -1.56600023301631, -1.0375208858709402, -0.32145075194171147, 0.28923081203518425, 0.5693881237092858, 0.4267581588170968, -0.07581152663531249, -0.7471561415756984, -1.3349948695968308, -1.6125248536695498, -1.4572524102520372, -0.8969845179352028, -0.10772064824706032, 0.6371024218677945, 1.0513527830777327, 0.9292290813845981, 0.21748900627168927, -0.9566671609076729, -2.312619620821429, -3.492168381331062, -4.162801185457762, -4.117807450261732, -3.342570478129532, -2.0256879190399917, -0.5097029041013156, 0.8055778117459746, 1.5794615293704426, 1.6320366067044219, 1.00032684698977, -0.068833449087836, -1.188281761892107, -1.9426951923742273, -2.010682120473863, -1.2606900223380952, 0.207826770557135, 2.0902731793219327, 3.962035396495083, 5.397332525110775, 6.086315654079883, 5.915856758337319, 4.990987969205972, 3.592458974758388, 2.0855632308903767, 0.8100453759114202, -0.014067294626726692, -0.3360041771996171, -0.2657104337216965, -0.013141269874775813, 0.2015667872581094, 0.23475854439481425, 0.07216605979673334, -0.17043471723178238, -0.2988350472754962, -0.12565369968236526, 0.4418097174836323, 1.3440419290537293, 2.365409545304203, 3.1891024532275476, 3.495546713250307, 3.0727669517484735, 1.9011895431140204, 0.18196869465894946, -1.7046622246537548, -3.301732459788391, -4.208615338956281, -4.203346873423277, -3.3144448393445956, -1.8174474252752746, -0.15500234414423977, 1.1959514994915086, 1.8686975192653723, 1.7171291071872916, 0.8564764588203302, -0.37905353037041195], 'positive_zeros': ['0.34063095852438283157953935223598', '2.07592140050854673686409899300862', '3.30063317785917401012725033145085', '4.99020000725626619349971781804425', '6.05934850837609855269038378922616', '6.70663990490204204668848719097679', '7.52413151649876329748431709849690', '8.972735366119844676683989734949875', '9.939863288178888537540994607591060', '10.32809884221326706579902005773766'], 'prelabel': '2-475-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.9532367241269469, 'root_number': '-0.9892279502109887 + 0.14638327268293158*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.476618362063', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.34063095852438283157953935224', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.07592140050854673686409899301', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.30063317785917401012725033145', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '19.11', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/e/f/201/3'], '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': '2-475-19.11-c1-0-1', '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': '2-475-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.47661836206347347, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.34063095852438283157953935224', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '431801039029751010876770234081', 'Lhash_array': ['431801039029751010876770234081'], 'label': '2-475-19.11-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/e/f/201/3'}