-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1916127877466835155248757804254', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 35.13417688936339, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [11, [1, -1]]], 'bad_primes': [2, 5, 11], 'central_character': '4400.1', 'coefficient_field': '1.1.1.1', 'conductor': 4400, 'conductor_radical': 110, 'degree': 2, 'euler_factors': [[1], [1, -1, 3], [1], [1, 1, 7], [1, -1], [1, 0, 13], [1, -1, 17], [1, 1, 19], [1, 0, 23], [1, 1, 29], [1, -1, 31], [1, -1, 37], [1, 0, 41], [1, 6, 43], [1, 8, 47], [1, -9, 53], [1, 4, 59], [1, 7, 61], [1, -4, 67], [1, 5, 71], [1, -14, 73], [1, 4, 79], [1, 16, 83], [1, 7, 89], [1, 16, 97], [1, 10, 101], [1, 8, 103], [1, 8, 107], [1, -10, 109], [1, -2, 113]], 'euler_factors_factorization': [[1], [[[1, -1, 3], 1]], [1], [[[1, 1, 7], 1]], [[[1, -1], 1]], [[[1, 0, 13], 1]], [[[1, -1, 17], 1]], [[[1, 1, 19], 1]], [[[1, 0, 23], 1]], [[[1, 1, 29], 1]], [[[1, -1, 31], 1]], [[[1, -1, 37], 1]], [[[1, 0, 41], 1]], [[[1, 6, 43], 1]], [[[1, 8, 47], 1]], [[[1, -9, 53], 1]], [[[1, 4, 59], 1]], [[[1, 7, 61], 1]], [[[1, -4, 67], 1]], [[[1, 5, 71], 1]], [[[1, -14, 73], 1]], [[[1, 4, 79], 1]], [[[1, 16, 83], 1]], [[[1, 7, 89], 1]], [[[1, 16, 97], 1]], [[[1, 10, 101], 1]], [[[1, 8, 103], 1]], [[[1, 8, 107], 1]], [[[1, -10, 109], 1]], [[[1, -2, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 77, 'label': '2-4400-1.1-c1-0-77', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/4400/2/a/u', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.6127333031032015e-58, 0.21114466915066452, 0.42144849098701515, 0.6300123611556303, 0.8358248033858376, 1.0377158015695371, 1.2343217608187522, 1.4240639617625568, 1.6051419664808915, 1.7755425406914436, 1.9330638511886793, 2.075354023991512, 2.1999626200972844, 2.3044031916275096, 2.3862247976410877, 2.4430901583340896, 2.4728579842592455, 2.4736669161658558, 2.4440184419378257, 2.3828561183480828, 2.2896384212871244, 2.164402586884788, 2.007816897397134, 1.821219019726645, 1.6066382294086383, 1.3667996547685586, 1.1051090574371176, 0.8256171254831262, 0.5329627890755989, 0.23229566673447305, -0.07082160019007251, -0.37052968294952804, -0.660805430141561, -0.9356084308113436, -1.1890377879671519, -1.415495017212532, -1.6098484740782226, -1.7675943146834587, -1.8850087317441127, -1.9592861029920252, -1.9886577591443542, -1.9724863360494742, -1.9113311270090207, -1.8069804963115965, -1.6624482462091708, -1.4819318317883212, -1.2707314685930442, -1.0351304461167212, -0.7822383091273661, -0.5197999548758003, -0.2559750693241852, 0.0009063620195914614, 0.2426055365665083, 0.4612453507359176, 0.6495811819187951, 0.8012626259456801, 0.9110766416904883, 0.9751626513340256, 0.9911905960939803, 0.9584937600205651, 0.8781493422772236, 0.7530012603323091, 0.587621467251321, 0.38820811614047673, 0.16242114083262643, -0.08084183045679359, -0.33172393659200017, -0.5797343162152563, -0.8141103532803439, -1.0242052740498593, -1.1998878728515043, -1.3319400062923814, -1.4124368519639914, -1.435094832525593, -1.39557259513164, -1.2917115235694083, -1.1237039367129005, -0.8941793578056653, -0.6082019656670228, -0.2731754782889607, 0.10134483331243957, 0.5039296712759103, 0.9216357693659852, 1.340437899816774, 1.745718922318325, 2.1228010502705255, 2.457499135480676, 2.7366750689425126, 2.948771466329925, 3.084302729195738, 3.136282391274162, 3.1005673825841575, 2.976102442864791, 2.765051321903846, 2.4728055111203497, 2.107865916454223, 1.6815979342439122, 1.2078656312925569, 0.7025559420553896, 0.18300875515341927, -0.3326267559220892, -0.8260854106443177, -1.2797018514900846, -1.6771200070258092, -2.003966576261229, -2.2484594776658544, -2.401924034758912, -2.4591927419608446, -2.4188686825254027, -2.2834379124783513, -2.0592221867090243, -1.7561700469061765, -1.3874912411419735, -0.9691464019110442, -0.5192105614572061, -0.057135120093121494, 0.3970619891086171, 0.8236442409872696, 1.2040063035544801, 1.5214884004854008, 1.7621186303964806, 1.9152489472609806, 1.9740544561379019, 1.935871122635368, 1.8023537280072293, 1.5794436516167274, 1.2771444985683063, 0.9091123388599718, 0.4920759843631499, 0.045110891150800934, -0.411202462604452, -0.8556988784599399, -1.2675861689546986, -1.6273965055454858, -1.917887024452999, -2.1248468828974234, -2.2377715881906877, -2.250371010427609, -2.160884816269557, -1.9721878149527523, -1.69167749725613, -1.330946420347296, -0.9052525509576235, -0.4328107125888913, 0.06606261740522251, 0.5699112222895325, 1.0571619648909847, 1.507158996104298, 1.901158527427077, 2.223234550131674, 2.4610496074714643, 2.6064508344226365, 2.6558597152567844, 2.610434000347404, 2.4759914977555364, 2.262697461701774, 1.9845294364124912, 1.6585450553483698, 1.3039888277390475, 0.9412827943467259, 0.5909526038556522, 0.2725446536747136, 0.003591183546019523, -0.20132151982146299, -0.33133132638171964, -0.37988183408086407, -0.34507413369717344, -0.22976741132240755, -0.041420212401148356, 0.20832194556846742, 0.5042731094508707, 0.8285550535047269, 1.1616030431026536, 1.483275844006497, 1.7740100222684607, 2.015955129399669, 2.194026324525363, 2.29681442766278, 2.317300214448131, 2.253329652728312, 2.107819268765447, 1.8886752835896012, 1.6084258222305978, 1.2835815285226195, 0.9337554331986965, 0.5805870473876593, 0.2465275677718119, -0.046447932705647565, -0.278129963668487, -0.4312927544485686, -0.49277055631455086, -0.4543280743852554, -0.3132712196303756, -0.07275785540629076, 0.258215730308897, 0.6651591140302643, 1.1287507331339643, 1.6257892668602827, 2.130386124683632, 2.6153371154361875, 3.0535999103570135, 3.4197963651980934, 3.691655647562986, 3.8513157018559347, 3.8864068890588266, 3.7908524057235704, 3.5653347981590517, 3.2173957878005655, 2.761156755956143, 2.2166684945309005, 1.6089200185555226, 0.9665561387140631, 0.3203709376640543, -0.2983417703987925, -0.8594903643164507, -1.3358445584996488, -1.7045574424881993, -1.948462374960038, -2.0570681404433135, -2.02719183325844, -1.863188748043893, -1.5767610466097703, -1.1863508763706765, -0.716147568794972, -0.19476115110680517, 0.34636568199954726, 0.874718976908466, 1.3585490392012403, 1.768675311816952, 2.0801564272504445, 2.2737279134169537, 2.3369224996548827, 2.2648055870070745, 2.060280247961344, 1.7339408728244992, 1.3034808545783236, 0.7926859595841963, 0.23006970322527937, -0.3527713560412492, -0.9229873047594319, -1.4483827529269475, -1.8992906821781257, -2.2503012796768704, -2.48174267996157, -2.5808247123106396, -2.5423764083281726, -2.3691320314947633, -2.0715473348619384, -1.6671560241282795, -1.1795042880958324, -0.6367270459207732, -0.06985164718155668, 0.4890682484645934, 1.0088750874726153, 1.4611687316846271, 1.8219926049400275, 2.073241053026321], 'positive_zeros': ['1.51155837193770356965403922877638', '2.58966013719884848890127061395560', '3.28418393568304306414564053332653', '4.04919364705774213673393910854776', '5.04523007135713372903963223203927', '5.84613831007330099419015653787679', '6.55580953383084523336225101016377', '7.30585158597649557226756040516083', '8.227326837622866265008796590544483'], 'prelabel': '2-4400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.927408952431357, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 238272003255306666, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.51155837193770356965403922878', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.58966013719884848890127061396', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.28418393568304306414564053333', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 35.13417688936339, 'bad_primes': [2, 5, 11], 'central_character': '1.1', 'conductor': 4400, 'conductor_radical': 110, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, -1, 0, -2, 0, 1, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 0, 0, 0, 0, -5, 0, -1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -6, 0, 0, 0, -8, 0, -6, 0, 1, 0, 9, 0, 0, 0, -1, 0, -4, 0, -7, 0, 2, 0, 0, 0, 4, 0, 0, 0, -5, 0, 14, 0, 0, 0, -1, 0, -4, 0, 1, 0, -16, 0, 0, 0, -1, 0, -7, 0, 0, 0, 1, 0, 0, 0, -16, 0, -2, 0], 'euler11': [1, -1, 0], 'euler13': [1, 0, 13], 'euler17': [1, -1, 17], 'euler19': [1, 1, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 1, 29], 'euler3': [1, -1, 3], 'euler31': [1, -1, 31], 'euler37': [1, -1, 37], 'euler41': [1, 0, 41], 'euler43': [1, 6, 43], 'euler47': [1, 8, 47], 'euler5': [1, 0, 0], 'euler53': [1, -9, 53], 'euler59': [1, 4, 59], 'euler61': [1, 7, 61], 'euler67': [1, -4, 67], 'euler7': [1, 1, 7], 'euler71': [1, 5, 71], 'euler73': [1, -14, 73], 'euler79': [1, 4, 79], 'euler83': [1, 16, 83], 'euler89': [1, 7, 89], 'euler97': [1, 16, 97], 'euler_factors': [[1, 0, 0], [1, -1, 3], [1, 0, 0], [1, 1, 7], [1, -1, 0], [1, 0, 13], [1, -1, 17], [1, 1, 19], [1, 0, 23], [1, 1, 29], [1, -1, 31], [1, -1, 37], [1, 0, 41], [1, 6, 43], [1, 8, 47], [1, -9, 53], [1, 4, 59], [1, 7, 61], [1, -4, 67], [1, 5, 71], [1, -14, 73], [1, 4, 79], [1, 16, 83], [1, 7, 89], [1, 16, 97]], 'index': 77, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/4400/u', 'ModularForm/GL2/Q/holomorphic/4400/2/a/u/1/1', 'ModularForm/GL2/Q/holomorphic/4400/2/a/u'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-4400-1.1-c1-0-77', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-4400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.927408952431357, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 238272003255306666, 'z1': {'__RealLiteral__': 0, 'data': '1.51155837193770356965403922878', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20181134
{'Lhash': '1916127877466835155248757804254', 'Lhash_array': ['1916127877466835155248757804254'], 'label': '2-4400-1.1-c1-0-77', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4400/2/a/u'}
-
id: 24565768
{'Lhash': '1916127877466835155248757804254', 'Lhash_array': ['1916127877466835155248757804254'], 'label': '2-4400-1.1-c1-0-77', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4400/2/a/u/1/1'}
-
id: 33140
{'Lhash': '238272003255306666', 'Lhash_array': ['238272003255306666'], 'label': '2-4400-1.1-c1-0-77', 'type': 'ECQ', 'url': 'EllipticCurve/Q/4400/u'}