-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '4726249230954150727421912463136', 'a10': [1.2595105213686244, 2.0032942418180195e-61], 'a2': [-0.5, -0.8660254037844386], 'a3': [1.5256871208655185, -2.6425676097925566], 'a4': [-0.5, 0.8660254037844386], 'a5': [-0.6297552606843122, 1.090768107839012], 'a6': [-3.051374241731037, 8.365999869889135e-61], 'a7': [-1.5256871208655185, 2.6425676097925566], 'a8': [1.0, 0.0], 'a9': [-3.1554423815498307, -5.465386525200445], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [37, [[1.0, 0], [1.3702447393156878, 5.926417919314979]]]], 'bad_primes': [2, 37], 'central_character': '74.63', 'coefficient_field': 'CDF', 'conductor': 74, 'conductor_radical': 74, 'conjugate': '2550345943523087096792934957688', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-1.5256871208655185, 2.6425676097925566], [-1.5, -2.598076211353316]], [[1.0, 0], [0.6297552606843122, -1.090768107839012], [-2.5, -4.330127018922194]], [[1.0, 0], [1.5256871208655185, -2.6425676097925566], [-3.5, -6.06217782649107]], [[1.0, 0], [-5.310884763099661, 0], [11.0, 0]], [[1.0, 0], [1.0, -1.7320508075688772], [-6.5, -11.258330249197702]], [[1.0, 0], [2.551374241731037, 4.419109815800675], [-8.5, 14.722431864335457]], [[1.0, 0], [2.3959318601812063, -4.1498757133068604], [-9.5, -16.454482671904334]], [[1.0, 0], [-1.7404894786313756, 0], [23.0, 0]], [[1.0, 0], [4.051374241731037, 0], [29.0, 0]], [[1.0, 0], [0.7918637203624126, 0], [31.0, 0]], [[1.0, 0], [1.3702447393156878, 5.926417919314979]], [[1.0, 0], [-0.10406813981879369, 0.18025130561533245], [-20.5, -35.50704155516198]], [[1.0, 0], [4.362259004830698, 0], [43.0, 0]], [[1.0, 0], [3.2081362796375874, 0], [47.0, 0]], [[1.0, 0], [5.655442381549831, 9.795513544122638], [-26.5, 45.89934640057525]], [[1.0, 0], [-6.362259004830698, -11.019755847279374], [-29.5, 51.09549882328188]], [[1.0, 0], [3.0256871208655185, -5.240643821145873], [-30.5, -52.827549630850754]], [[1.0, 0], [-4.655442381549831, 8.063462736553761], [-33.5, -58.023702053557386]], [[1.0, 0], [-3.5256871208655185, 6.106669224930311], [-35.5, -61.48780366869514]], [[1.0, 0], [3.3108847630996614, 0], [73.0, 0]], [[1.0, 0], [-5.706816623280868, 9.884496341001121], [-39.5, -68.41600689897065]], [[1.0, 0], [-1.7851976422341431, -3.092053017901703], [-41.5, 71.88010851410841]], [[1.0, 0], [1.636421338812582, 2.834364901413276], [-44.5, 77.07626093681505]], [[1.0, 0], [-2.2081362796375874, 0], [97.0, 0]], [[1.0, 0], [-3.362259004830699, 0], [101.0, 0]], [[1.0, 0], [-17.154122725193112, 0], [103.0, 0]], [[1.0, 0], [0.18112950241534934, -0.31372550093305474], [-53.5, -92.66471820493493]], [[1.0, 0], [0.23382340050310593, 0.4049940096699057], [-54.5, 94.39676901250381]], [[1.0, 0], [-0.3445576184501692, -0.5967913012906246], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-74-37.26-c1-0-4', '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/74/2/c/c/63/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9248786305970339, 0.976675025468038, 1.0446412595622823, 1.1297391095060956, 1.2320636673491128, 1.3509362036290133, 1.484999605494617, 1.632278019268559, 1.790194081247064, 1.9555578877296502, 2.1245491018766187, 2.2927125981837047, 2.4549840019903715, 2.6057570951449014, 2.739001108960479, 2.8484323097833943, 2.9277406801169112, 2.97086865535284, 2.9723346885470354, 2.9275899321062577, 2.8333917274525824, 2.688173171892656, 2.492384158980805, 2.248776391731167, 1.9626033949532204, 1.6417069331609881, 1.2964638404667843, 0.9395723445790328, 0.5856646162298916, 0.25074239436264545, -0.04855521263946818, -0.29582886125622765, -0.47590367319328986, -0.5758700304570249, -0.5861165170418273, -0.5012815468116437, -0.3210449960003589, -0.05068141695518838, 0.2986969403964285, 0.7102655321057811, 1.162019186574924, 1.6277212884413281, 2.0782503073502534, 2.4832892391419477, 2.813269035657518, 3.0414454153550388, 3.1459628244046627, 3.111742943814728, 2.9320308080395083, 2.6094413801954324, 2.1563743347073334, 1.5947045331013996, 0.9547084631629899, 0.27324944141962415, -0.40868806394529894, -1.0489579019570703, -1.607489057346021, -2.049538064221125, -2.3486700933835962, -2.4891815937315793, -2.467705002331162, -2.2937918415092016, -1.989351939280822, -1.5869279932153082, -1.1268979239648749, -0.6538118902924249, -0.21217457840987153, 0.1579356463980416, 0.42497189183857637, 0.569304332579167, 0.5854843449027919, 0.48307430738805246, 0.2858611194026291, 0.029433895968361972, -0.24271488623406795, -0.4842287940039468, -0.6515769335324434, -0.7097905356360206, -0.6375898057704231, -0.4312607566514754, -0.10673322628315206, 0.3005260619043963, 0.7379702495873799, 1.1406845062702162, 1.4379891361747346, 1.5613192346174922, 1.4525681014476373, 1.071962767469945, 0.4045215755242134, -0.5357636934878177, -1.7046772443639555, -3.0298216559425435, -4.415955067329996, -5.75323920305672, -6.927647315818008, -7.832479231581297, -8.379735527833523, -8.51004588610509, -8.199944174815268, -7.465532815367179, -6.3619599340769915, -4.978605000583834, -3.4303780630674283, -1.8460219929268866, -0.35470336897593197, 0.9275695830144183, 1.9100940652885394, 2.536708610356106, 2.7909669332689173, 2.6965837975404123, 2.3130743564895244, 1.7271243108716356, 1.0407910113111314, 0.358067038590111, -0.2284260778031929, -0.6488452067639451, -0.8641076780496374, -0.8693822965810308, -0.6926446330989172, -0.3885502892590989, -0.028557459878374918, 0.31121228565071196, 0.5625344654605837, 0.6761364337391457, 0.6295204921586094, 0.4302979978370652, 0.11445191684840506, -0.2602690612756663, -0.6248419312329131, -0.911710626133027, -1.0677228614855472, -1.0650996203380458, -0.9085063420034808, -0.6368463031181993, -0.3191947194652505, -0.04522120295167076, 0.08863385329648539, -0.0047956954459557844, -0.38763037009987733, -1.0840339944763264, -2.072428461835471, -3.2843970257496693, -4.610848429647404, -5.914881916419896, -7.04969504569613, -7.87899171517858, -8.296830475927765, -8.24380449986485, -7.716894118417637, -6.771230239390438, -5.513225798314455, -4.085887564416808, -2.64839599162823, -1.3530237505860234, -0.32298057239997013, 0.36528047424961857, 0.6923951200925902, 0.6972917469294533, 0.468961075277606, 0.13004082431186592, -0.18514466723426967, -0.3544637923962442, -0.2897496004331751, 0.047288926897309846, 0.6378472325613895, 1.4088939648117949, 2.2458094368958643, 3.0127660172606814, 3.5774174639831555, 3.835617748118059, 3.731768576894857, 3.271043616707431, 2.5210672814209865, 1.602424408400553, 0.6693412608802111, -0.1163348315333798, -0.613443458104715, -0.7271520167181947, -0.42729925182490186, 0.24402992328356685, 1.1773581759356098, 2.212598832917321, 3.1651396071139155, 3.8568819761367683, 4.146908191279809, 3.9563946364362548, 3.2832997922735903, 2.2040859392752337, 0.8619908371407937, -0.5562498991876391, -1.8512489423394543, -2.844011123682869, -3.405370899045631, -3.476637445291588, -3.077832269715221, -2.302149212936124, -1.297776097034647, -0.240524661884954, 0.6976146275109855, 1.3781646306575484, 1.7186610067059087, 1.7039418751290547, 1.3843982899985832, 0.8618898137861497, 0.26641610804716287, -0.27159510947128584, -0.6477252498656407, -0.8034071602650513, -0.735267345312719, -0.49227565258095396, -0.16157576415842936, 0.1537360833698887, 0.35989366763286584, 0.39513291749492846, 0.24460504215936266, -0.055975413182326954, -0.4290138345870741, -0.7743784323156113, -0.9952725755141619, -1.0248649403613421, -0.8474647206339989, -0.5089310739913281, -0.11311395317086562, 0.19596130897858088, 0.2633179569667114, -0.04188331365265488, -0.7925945869096048, -1.9788943155049457, -3.4978486516925806, -5.161607066607305, -6.723558702594334, -7.918651666079034, -8.510852481929888, -8.338869510562171, -7.351120034315102, -5.622589037807513, -3.349442732717996, -0.8214285789004745, 1.6235933094247514, 3.6550504045709657, 5.004926459529819, 5.512641777066535, 5.1511114013324, 4.0290622793573005, 2.36921867433284, 0.46660888493891794, -1.3649307060636215, -2.847756866078647, -3.7864688224548733, -4.096488245991419, -3.8102944171204878, -3.0610283338841042, -2.047759700062225, -0.9903247924273704, -0.08353747884064852, 0.5396371317778773, 0.828611715178696], 'positive_zeros': ['3.72835324663060223169942872203945', '4.64489223391926068959373998079075', '6.67466518249955352430153828514743', '8.317900127744862278149754496246105', '9.138490409215562991005082762444902', '10.03470392558039367002711832799244', '11.05802304320704398615953571511546', '13.03222204767425692862954533229913', '14.19773089507496903442810739687917', '15.00987700516465633440538993369230'], 'prelabel': '2-74-37.26-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, 'root_angle': 0.4744986764920295, 'root_number': '0.08002909696199592 + 0.9967925278810267*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.237249338246', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.72835324663060223169942872204', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.64489223391926068959373998079', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.67466518249955352430153828515', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'bad_primes': [2, 37], 'central_character': '37.26', 'conductor': 74, 'conductor_radical': 74, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/74/2/c/c/63/3'], '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': '2-74-37.26-c1-0-4', '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': '2-74-37.26-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, 'root_angle': 0.23724933824601474, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.72835324663060223169942872204', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '4726249230954150727421912463136', 'Lhash_array': ['4726249230954150727421912463136'], 'label': '2-74-37.26-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/74/2/c/c/63/3'}