-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2100416803952929507318819241661', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [2.2221891785620707, -0.2487473712054658], 'a6': [0, 0], 'a7': [1.519303833105563, -2.166036902435123], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.061150654681333, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.2221891785620707, 0.2487473712054658]]], [7, [[1.0, 0], [-1.519303833105563, 2.166036902435123]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1260.433', 'coefficient_field': 'CDF', 'conductor': 1260, 'conductor_radical': 210, 'conjugate': '1130329073405640976495313865016', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.2221891785620707, 0.2487473712054658]], [[1.0, 0], [-1.519303833105563, 2.166036902435123]], [[1.0, 0], [1.105527432977097, 0], [11.0, 0]], [[1.0, 0], [-3.5226482450460015, 3.5226482450460015], [0, -13.0]], [[1.0, 0], [3.2384170428110717, 3.2384170428110717], [0, 17.0]], [[1.0, 0], [-0.9167188199621634, 0], [19.0, 0]], [[1.0, 0], [4.439086262554359, 4.439086262554359], [0, 23.0]], [[1.0, 0], [0, -8.285300148962415], [-29.0, 0]], [[1.0, 0], [0, 4.59361668404277], [-31.0, 0]], [[1.0, 0], [2.3035232253485782, -2.3035232253485782], [0, -37.0]], [[1.0, 0], [0, -3.150912218465021], [-41.0, 0]], [[1.0, 0], [-2.703563811926849, -2.703563811926849], [0, 43.0]], [[1.0, 0], [4.714364107756745, 4.714364107756745], [0, 47.0]], [[1.0, 0], [-6.418940151696219, -6.418940151696219], [0, 53.0]], [[1.0, 0], [-4.36338811083326, 0], [59.0, 0]], [[1.0, 0], [0, 10.868713099660056], [-61.0, 0]], [[1.0, 0], [6.811014279375923, -6.811014279375923], [0, -67.0]], [[1.0, 0], [4.79795520579321, 0], [71.0, 0]], [[1.0, 0], [-9.72949658003554, 9.72949658003554], [0, -73.0]], [[1.0, 0], [0, -12.57060029792483], [-79.0, 0]], [[1.0, 0], [0.22750899177832812, -0.22750899177832812], [0, -83.0]], [[1.0, 0], [-8.931233473102559, 0], [89.0, 0]], [[1.0, 0], [-12.411404959294284, -12.411404959294284], [0, 97.0]], [[1.0, 0], [0, 4.917864659653499], [-101.0, 0]], [[1.0, 0], [1.9117083047840266, -1.9117083047840266], [0, -103.0]], [[1.0, 0], [-14.342568901324666, 14.342568901324666], [0, -107.0]], [[1.0, 0], [0, -9.159626605127178], [-109.0, 0]], [[1.0, 0], [-6.704240300658634, -6.704240300658634], [0, 113.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-1260-35.13-c1-0-15', 'leading_term': '2.0317893979258157053569193440962453974581132589331496932', '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/1260/2/ba/b/433/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.0317893979258157, 2.1089900582668593, 2.1810397862322337, 2.247710641221775, 2.3085108267796506, 2.362691998328921, 2.4092724688337346, 2.447074272561965, 2.474771470580663, 2.490946875633724, 2.4941544584930027, 2.482984958018146, 2.4561325411759425, 2.412460662571901, 2.3510655071416107, 2.2713355491667415, 2.1730058344451146, 2.056205612875757, 1.9214979439226532, 1.76990989496682, 1.6029519762870321, 1.4226255249925304, 1.2314168768509954, 1.0322773575757325, 0.8285883869702105, 0.6241113193219436, 0.42292203669412204, 0.22933075989808374, 0.047788033386440026, -0.11722163932942527, -0.26129650078811084, -0.3802420509592691, -0.4702003330011757, -0.527780513145833, -0.5501868973381543, -0.5353402428358265, -0.4819880514244677, -0.38979949017543686, -0.25944069061160174, -0.09262643858508553, 0.10785530888751899, 0.3381490567005691, 0.593369787382015, 0.867674703062086, 1.1543690220956615, 1.4460450430893077, 1.7347525048283292, 2.012197055240864, 2.269962438257066, 2.499750859859337, 2.6936349513741966, 2.8443138569697886, 2.945365279583912, 2.991484867642073, 2.9787041507510748, 2.9045783651786943, 2.768335968887492, 2.57098243950364, 2.3153520726684222, 2.00610293510805, 1.6496518449816238, 1.2540482064162721, 0.8287876573939857, 0.3845687304226343, -0.0670020059213688, -0.5137486462835947, -0.9432987496001528, -1.3434786832696404, -1.702718461871605, -2.0104519532669682, -2.2574977280841426, -2.4364057691890704, -2.5417557730870306, -2.5703938813737635, -2.521596369903969, -2.397151063951438, -2.20134998169404, -1.9408898536805819, -1.6246806175835566, -1.2635656207914365, -0.8699609378179247, -0.4574247740314373, -0.040171226023154274, 0.36745445198596455, 0.7515196122725074, 1.0990459255039666, 1.3985271401434878, 1.640401051988144, 1.81745483423037, 1.9251447975177662, 1.9618144655699017, 1.9287984889754999, 1.8304042610375613, 1.6737679902241436, 1.4685872360470351, 1.2267373146550786, 0.961784294501235, 0.688412289961448, 0.4217871826599352, 0.17688253066188267, -0.032203936700363506, -0.1929133618867225, -0.2948382649299867, -0.3302555861799041, -0.2945538466567386, -0.1865318162292018, -0.008551075218359348, 0.2334691423907624, 0.5302196607523977, 0.8693291999913612, 1.2358424737796265, 1.6128314131608263, 1.9821156354680203, 2.3250623897318503, 2.623431497594427, 2.86022754390306, 3.0205199685935846, 3.09219191490219, 3.0665807606363407, 2.938977173117962, 2.708955167252667, 2.3805128031950527, 1.9620115451355846, 1.4659115530406126, 0.9083098741877078, 0.3082981812887308, -0.3128341086867042, -0.9325172782276528, -1.527898443184325, -2.07687248494588, -2.559097978978731, -2.9569487362236364, -3.2563534297430112, -3.447480061514719, -3.5252285982474154, -3.489503713093146, -3.345249840829282, -3.1022422170532624, -2.7746396782907317, -2.380317147944441, -1.9400072976807559, -1.476291238809911, -1.012486688633651, -0.5714883712803349, -0.17461905274678927, 0.15944969488569974, 0.41565027838553964, 0.5832941022104833, 0.6566257473423215, 0.6351239562056006, 0.523529767799146, 0.3315962002501702, 0.07356857029545256, -0.23258090219660363, -0.5661269213544311, -0.9047241428781889, -1.225640605470285, -1.5070261725820804, -1.729147403055528, -1.8755207565154108, -1.9338802728134448, -1.8969237100088234, -1.7627922432228866, -1.5352526858721693, -1.2235670952505076, -0.8420517315213192, -0.40934472636729263, 0.05258148404895217, 0.5196118551424991, 0.9668209382337185, 1.3698727688886487, 1.7064103279717775, 1.9573554928835335, 2.108043904625446, 2.1491270751623004, 2.0771860054888376, 1.8950159917533358, 1.6115603628311959, 1.2414906403697892, 0.8044509401950939, 0.32400417755887817, -0.17366436339872052, -0.6612153735101296, -1.111713679750595, -1.5001872979885473, -1.8050966734238652, -2.0096269013302592, -2.102724409232213, -2.079813070123037, -1.9431423181366851, -1.701740604877052, -1.3709703058836347, -0.9717036535903555, -0.5291620529362534, -0.07148185324255464, 0.37191297968115367, 0.7720379382588863, 1.102073865996449, 1.3389890674825382, 1.464959492030842, 1.4684992942853383, 1.3452300036065752, 1.0982370909397219, 0.7379867519424234, 0.2818018347509198, -0.24707752237948094, -0.8207974332311948, -1.4084840092813957, -1.97803460235976, -2.4980004757890133, -2.939447767897908, -3.2776833937688807, -3.493739303314894, -3.5755219840946064, -3.5185535489626907, -3.326255075784259, -3.00975063465628, -2.5871999676640347, -2.0826972528021654, -1.5248009306792925, -0.9447834282724452, -0.3747082060705548, 0.15454638467840645, 0.6151922956014455, 0.9842450625244616, 1.2449351422061525, 1.3877253862307646, 1.4108669862915018, 1.32045515611962, 1.1299776354167825, 0.8593818004210398, 0.5337176397868026, 0.18144203942823403, -0.16750717200293175, -0.4837427191154517, -0.740431906766803, -0.9151404619989342, -0.9913924968989538, -0.9598401963886474, -0.8189614034449862, -0.5752336089445909, -0.24276704070318733, 0.15758461770085597, 0.5995822170274216, 1.0533421048701201, 1.4873474937581468, 1.8705979621800501, 2.174753671587047, 2.376129189823515, 2.457399842569245, 2.408900892889687, 2.2294255625474517, 1.9264603647788567, 1.5158333401796389, 1.02079014552205, 0.4705519147659126, -0.10155525375598394], 'positive_zeros': ['1.65693670130773245850349755314580', '2.31339379714240164651414854623039', '3.74130531519848885142473600165440', '4.81036852522241907737188967623700', '5.84948904793525339432959135368113', '6.21329456213008790571371599628820', '7.35341955953755668660438254220592', '8.466569097726848797919005207272462', '8.921050777222911260504196418860446', '9.778576805642181252593532800794059'], 'prelabel': '2-1260-35.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1719316913643225, 'root_angle': 0.3354284212534218, 'root_number': '0.4942891070949620586591446974039725296317512299123660765 + 0.86929757770700427084251879186962573014430553167487082840*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.16771421062671094', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.65693670130773245850349755315', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.31339379714240164651414854623', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.74130531519848885142473600165', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 10.061150654681333, 'bad_primes': [2, 3, 5, 7], 'central_character': '35.13', 'conductor': 1260, 'conductor_radical': 210, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1260/2/ba/b/433/8'], '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': '2-1260-35.13-c1-0-15', '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': '2-1260-35.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1719316913643225, 'root_angle': 0.1677142106267109, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.65693670130773245850349755315', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2100416803952929507318819241661', 'Lhash_array': ['2100416803952929507318819241661'], 'label': '2-1260-35.13-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1260/2/ba/b/433/8'}