-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2171307917683320438018903874408', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.137261107234623, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, -1]], [19, [1, 1]]], 'bad_primes': [2, 5, 19], 'central_character': '1520.1', 'coefficient_field': '1.1.1.1', 'conductor': 1520, 'conductor_radical': 190, 'degree': 2, 'euler_factors': [[1], [1, 1, 3], [1, -1], [1, -1, 7], [1, 0, 11], [1, 1, 13], [1, 3, 17], [1, 1], [1, 3, 23], [1, 3, 29], [1, 2, 31], [1, 10, 37], [1, -6, 41], [1, 2, 43], [1, 0, 47], [1, -3, 53], [1, 3, 59], [1, -8, 61], [1, -7, 67], [1, 12, 71], [1, 13, 73], [1, 14, 79], [1, 6, 83], [1, -6, 89], [1, 10, 97], [1, -12, 101], [1, 8, 103], [1, 15, 107], [1, -11, 109], [1, 12, 113]], 'euler_factors_factorization': [[1], [[[1, 1, 3], 1]], [[[1, -1], 1]], [[[1, -1, 7], 1]], [[[1, 0, 11], 1]], [[[1, 1, 13], 1]], [[[1, 3, 17], 1]], [[[1, 1], 1]], [[[1, 3, 23], 1]], [[[1, 3, 29], 1]], [[[1, 2, 31], 1]], [[[1, 10, 37], 1]], [[[1, -6, 41], 1]], [[[1, 2, 43], 1]], [[[1, 0, 47], 1]], [[[1, -3, 53], 1]], [[[1, 3, 59], 1]], [[[1, -8, 61], 1]], [[[1, -7, 67], 1]], [[[1, 12, 71], 1]], [[[1, 13, 73], 1]], [[[1, 14, 79], 1]], [[[1, 6, 83], 1]], [[[1, -6, 89], 1]], [[[1, 10, 97], 1]], [[[1, -12, 101], 1]], [[[1, 8, 103], 1]], [[[1, 15, 107], 1]], [[[1, -11, 109], 1]], [[[1, 12, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 28, 'label': '2-1520-1.1-c1-0-28', '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/1520/2/a/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.3144904341810205e-60, 0.12823913415115612, 0.2564384149407785, 0.3845237023210272, 0.5123540053835957, 0.6396922251875882, 0.7661805363608983, 0.8913214122260561, 1.0144649441269158, 1.1348027679430381, 1.2513686211635442, 1.3630453287496846, 1.4685778572117911, 1.5665919748902888, 1.6556179973895986, 1.7341190639755941, 1.8005233687646605, 1.8532597485279387, 1.8907959998877109, 1.911679259472865, 1.91457773129729, 1.8983229886384207, 1.8619520169640755, 1.8047481047834584, 1.7262796358239114, 1.626435793766574, 1.5054581647219756, 1.3639672170177424, 1.2029826564138468, 1.0239367005434192, 0.8286793913802758, 0.6194751701608673, 0.39899007580090073, 0.1702690948168282, -0.06329661356704662, -0.29801267177819635, -0.5299344284608061, -0.7549294425907954, -0.9687487833396191, -1.1671061435880432, -1.3457634888958967, -1.5006216977941862, -1.6278144018497134, -1.723803013627051, -1.785470745965273, -1.8102132851219341, -1.7960236909611524, -1.7415690662617382, -1.6462565700378478, -1.5102864507272133, -1.3346899467745668, -1.1213501451991836, -0.8730042017993644, -0.5932257061318068, -0.2863864144625438, 0.042402933601006165, 0.38737246444435236, 0.7421928710066885, 1.1000935699223537, 1.4539973409407867, 1.7966689118525028, 2.120874424530046, 2.4195482428205977, 2.685963158478442, 2.9138997337818595, 3.097810304130161, 3.2329730638688985, 3.315631684298521, 3.343116071559704, 3.3139401674947444, 3.227873128283598, 3.085980778987901, 2.8906349280196144, 2.6454889204554255, 2.3554186952119798, 2.0264295665342003, 1.6655299496125207, 1.280574265042831, 0.8800782566440594, 0.47301090984475114, 0.06856803102444074, -0.3240666899319973, -0.6959666910867267, -1.0387067291640582, -1.3445990946631752, -1.6069146465650928, -1.8200816345553534, -1.979855677919664, -2.083454898638379, -2.1296550527243068, -2.118840551788759, -2.0530084918314246, -1.935724176750273, -1.7720281019207664, -1.5682959046469733, -1.3320543451695213, -1.0717579030592355, -0.7965320066792667, -0.5158902057818743, -0.2394336992524525, 0.023457504359503785, 0.26393192654334136, 0.47396231106642867, 0.6466195721099303, 0.7763152971766663, 0.8590038448344309, 0.8923361533411304, 0.8757587637825801, 0.8105532252444209, 0.6998129430073183, 0.5483565967590199, 0.3625794285665455, 0.15024590726838477, -0.07977056001892675, -0.31779315635167, -0.553682867991209, -0.7772042581216078, -0.9784034501501847, -1.147985141420667, -1.2776750849178287, -1.360554569386519, -1.3913540122816654, -1.3666938526447072, -1.2852624716877241, -1.1479228386316394, -0.9577419216706667, -0.7199395460729842, -0.4417562364450725, -0.13224254965353782, 0.1980246178639119, 0.5372903908633295, 0.8730239279039164, 1.1923607338573463, 1.4825700074155668, 1.7315303559841966, 1.9281963892009257, 2.0630385144581758, 2.128438732562212, 2.1190263739100663, 2.0319395045831623, 1.8670001209970701, 1.6267941696541468, 1.316650780385697, 0.9445187721613261, 0.5207423484151443, 0.057741800207566, -0.430391170048046, -0.9283703556151927, -1.420247903606664, -1.8899842543341612, -2.322034360858446, -2.7019282126608255, -3.0168233378592966, -3.2560074735532, -3.411330979442371, -3.47755079685841, -3.4525707600412114, -3.3375667518010705, -3.1369894339771034, -2.8584419203048075, -2.512434620439199, -2.1120243794549687, -1.6723497704926742, -1.210078773362799, -0.7427889016897141, -0.28830295525110433, 0.13599417332779398, 0.5138309320108359, 0.8306898547228593, 1.0743875575306987, 1.2355698731672629, 1.308100988275725, 1.2893293549990528, 1.1802178468375808, 0.9853309417658068, 0.712677436620958, 0.3734130962861567, -0.018586523803848704, -0.44726731934657427, -0.8950312072813835, -1.3434390882329252, -1.7739540326666918, -2.168694415682515, -2.5111658588652848, -2.7869412743709043, -2.9842600551090293, -3.094520467655435, -3.1126434776433425, -3.037291414265274, -2.8709308572378975, -2.61973566260632, -2.293332859662802, -1.9044009580231904, -1.4681367034223685, -1.0016122219024075, -0.5230495237121916, -0.05104326203482543, 0.3962347366287256, 0.8018144742780859, 1.1506559611577454, 1.4302940944139049, 1.631371108828957, 1.7480321776362573, 1.7781656109260155, 1.7234758886688009, 1.5893851834054076, 1.3847667480821009, 1.1215212207981264, 0.8140141788258359, 0.4783998186833707, 0.1318611338469417, -0.2081988643979542, -0.5249777000414395, -0.8030676241320849, -1.0291861160496591, -1.1928079221627872, -1.2866680787132518, -1.307111077732765, -1.2542682975246464, -1.1320537268351685, -0.9479765077941786, -0.7127775156634386, -0.43990567496795013, -0.14485757523638054, 0.15558918976669184, 0.4442130226854254, 0.7042158489767256, 0.9200793275080851, 1.078367856683133, 1.168438458413869, 1.1830215526656256, 1.11864237080074, 0.9758600519299753, 0.7593099979457782, 0.47754443849235256, 0.1426759366768307, -0.2301617187131084, -0.6235116130797099, -1.0184189981060405, -1.395345213137624, -1.7351266825104608, -2.019932495150165, -2.234173364804933, -2.365316369814031, -2.404563744320293, -2.3473599895076616, -2.1936994371792036, -1.9482157748069886, -1.6200454952229884, -1.222468267558637, -0.7723383025481387, -0.28933135594053605, 0.204958455941031, 0.6880298574897021, 1.1375454233428095, 1.5324104456430458, 1.8538064903526044], 'positive_zeros': ['1.71285992945721434713256047960836', '2.78657644407780172553397041532100', '4.07122685411677794871025218408621', '5.07343753056513176169564111606663', '5.72097876958001523126129137905581', '6.52061944989712916278916517958419', '7.36939617775242477603507597422482', '8.412887815220587989400052076942710', '8.985992202019533467038785145213075'], 'prelabel': '2-1520-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.483857216826577, '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': 2293407573598342556, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.71285992945721434713256047961', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.78657644407780172553397041532', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.07122685411677794871025218409', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 12.137261107234623, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 1520, 'conductor_radical': 190, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 1, 0, 1, 0, -2, 0, 0, 0, -1, 0, -1, 0, -3, 0, -1, 0, -1, 0, -3, 0, 1, 0, 5, 0, -3, 0, -2, 0, 0, 0, 1, 0, -10, 0, 1, 0, 6, 0, -2, 0, -2, 0, 0, 0, -6, 0, 3, 0, 3, 0, 0, 0, 1, 0, -3, 0, 8, 0, -2, 0, -1, 0, 7, 0, 3, 0, -12, 0, -13, 0, -1, 0, 0, 0, -14, 0, 1, 0, -6, 0, -3, 0, 3, 0, 6, 0, -1, 0, 2, 0, -1, 0, -10, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 1, 13], 'euler17': [1, 3, 17], 'euler19': [1, 1, 0], 'euler2': [1, 0, 0], 'euler23': [1, 3, 23], 'euler29': [1, 3, 29], 'euler3': [1, 1, 3], 'euler31': [1, 2, 31], 'euler37': [1, 10, 37], 'euler41': [1, -6, 41], 'euler43': [1, 2, 43], 'euler47': [1, 0, 47], 'euler5': [1, -1, 0], 'euler53': [1, -3, 53], 'euler59': [1, 3, 59], 'euler61': [1, -8, 61], 'euler67': [1, -7, 67], 'euler7': [1, -1, 7], 'euler71': [1, 12, 71], 'euler73': [1, 13, 73], 'euler79': [1, 14, 79], 'euler83': [1, 6, 83], 'euler89': [1, -6, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 0, 0], [1, 1, 3], [1, -1, 0], [1, -1, 7], [1, 0, 11], [1, 1, 13], [1, 3, 17], [1, 1, 0], [1, 3, 23], [1, 3, 29], [1, 2, 31], [1, 10, 37], [1, -6, 41], [1, 2, 43], [1, 0, 47], [1, -3, 53], [1, 3, 59], [1, -8, 61], [1, -7, 67], [1, 12, 71], [1, 13, 73], [1, 14, 79], [1, 6, 83], [1, -6, 89], [1, 10, 97]], 'index': 28, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1520/d', 'ModularForm/GL2/Q/holomorphic/1520/2/a/d/1/1', 'ModularForm/GL2/Q/holomorphic/1520/2/a/d'], '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': '2-1520-1.1-c1-0-28', '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': '2-1520-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2293407573598342556, 'z1': {'__RealLiteral__': 0, 'data': '1.71285992945721434713256047961', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20676482
{'Lhash': '2171307917683320438018903874408', 'Lhash_array': ['2171307917683320438018903874408'], 'label': '2-1520-1.1-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1520/2/a/d'}
-
id: 24553458
{'Lhash': '2171307917683320438018903874408', 'Lhash_array': ['2171307917683320438018903874408'], 'label': '2-1520-1.1-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1520/2/a/d/1/1'}
-
id: 96114
{'Lhash': '2293407573598342556', 'Lhash_array': ['2293407573598342556'], 'label': '2-1520-1.1-c1-0-28', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1520/d'}