-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '805941973861451247101089055314', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': -5, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.0193554789367, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, 1]], [23, [1, 1]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '1380.1', 'coefficient_field': '1.1.1.1', 'conductor': 1380, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 1], [1, 5, 7], [1, 0, 11], [1, -4, 13], [1, 3, 17], [1, 4, 19], [1, 1], [1, -1, 29], [1, -1, 31], [1, 1, 37], [1, -11, 41], [1, -4, 43], [1, -6, 47], [1, -1, 53], [1, 1, 59], [1, -6, 61], [1, 9, 67], [1, -13, 71], [1, 0, 73], [1, -16, 79], [1, -9, 83], [1, -8, 89], [1, -2, 97], [1, 7, 101], [1, 16, 103], [1, 3, 107], [1, 12, 109], [1, -1, 113]], 'euler_factors_factorization': [[1], [[[1, 1], 1]], [[[1, 1], 1]], [[[1, 5, 7], 1]], [[[1, 0, 11], 1]], [[[1, -4, 13], 1]], [[[1, 3, 17], 1]], [[[1, 4, 19], 1]], [[[1, 1], 1]], [[[1, -1, 29], 1]], [[[1, -1, 31], 1]], [[[1, 1, 37], 1]], [[[1, -11, 41], 1]], [[[1, -4, 43], 1]], [[[1, -6, 47], 1]], [[[1, -1, 53], 1]], [[[1, 1, 59], 1]], [[[1, -6, 61], 1]], [[[1, 9, 67], 1]], [[[1, -13, 71], 1]], [[[1, 0, 73], 1]], [[[1, -16, 79], 1]], [[[1, -9, 83], 1]], [[[1, -8, 89], 1]], [[[1, -2, 97], 1]], [[[1, 7, 101], 1]], [[[1, 16, 103], 1]], [[[1, 3, 107], 1]], [[[1, 12, 109], 1]], [[[1, -1, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-1380-1.1-c1-0-0', 'leading_term': '0.783399245727423219807639209095840000000000000000000000000000000000000000000000000000000000', '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/1380/2/a/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.7833992457274233, 0.7774221643575224, 0.759394043336352, 0.7290324516293151, 0.6858933999352693, 0.6294094178313211, 0.5589391428438272, 0.47382534603945303, 0.37345816592659214, 0.2573404556825457, 0.12515246223502854, -0.023186558589095366, -0.18746181311207777, -0.367113237157574, -0.561194034490046, -0.7683387931025301, -0.986742361635814, -1.2141505586253234, -1.4478636655032349, -1.6847534984604629, -1.9212946491884486, -2.153610221750165, -2.377532070173699, -2.588675162039677, -2.782525265164161, -2.9545386891329444, -3.1002523257815744, -3.2154017401738377, -3.2960445856205327, -3.338686173558846, -3.340403643111624, -3.2989648672297314, -3.2129380229873394, -3.0817876616296527, -2.9059531555486116, -2.6869055871917937, -2.4271794873805255, -2.130376330924318, -1.8011373533286439, -1.4450840551255297, -1.068725694704162, -0.6793341146799365, -0.28478737261835707, 0.1066151797849456, 0.4863625434220308, 0.8459614722541107, 1.1771795900317372, 1.4722952486066072, 1.724346390835414, 1.9273701373746788, 2.0766245308453377, 2.1687838754545306, 2.202099429118936, 2.1765178519651522, 2.093750791429704, 1.9572902786765045, 1.7723661986407904, 1.5458439378060307, 1.2860623575224002, 1.0026144216059887, 0.7060750497281335, 0.4076829888802458, 0.11898560453144218, -0.14854260076773024, -0.38389532100158746, -0.5769299781902134, -0.7187490176678776, -0.8020522698098373, -0.8214459795009283, -0.7736949901351803, -0.6579060434633427, -0.4756321976566328, -0.23089092551491439, 0.06990854047608877, 0.4181296967322834, 0.803162589008263, 1.2127607872947885, 1.6334517179421155, 2.05100714789849, 2.450957576990343, 2.819131774848087, 3.1422008367577026, 3.408205044340436, 3.6070415924672714, 3.730891940315325, 3.7745691815673457, 3.735768385248958, 3.6152062710057176, 3.416640745036328, 3.146765589846857, 2.8149807913089036, 2.4330443896597167, 2.0146171251826237, 1.5747162706298152, 1.1290996561346667, 0.693604763817208, 0.28347068582230495, -0.08732747835797218, -0.40670169767302233, -0.6650023128745094, -0.8554705418821621, -0.9745687197503962, -1.022169597084934, -1.0015918761298166, -0.9194758551166662, -0.785500299477112, -0.6119491434284402, -0.4131440006138797, -0.20476536993137512, -0.003091510074007337, 0.17581110544624626, 0.3169083402973033, 0.40699071002459464, 0.43539821220000363, 0.39464032791567616, 0.2808776461073212, 0.0942371421094275, -0.16105969566971143, -0.47676824172054627, -0.8408945818062341, -1.2381649265190475, -1.650673783175522, -2.058684651730764, -2.441548547058901, -2.7786986146014385, -3.050673909621556, -3.2401223859229273, -3.3327325242585317, -3.318044946161629, -3.1900998026796255, -2.947882566031336, -2.5955398229150894, -2.1423473875391874, -1.602425031037857, -0.9942047878676522, -0.33967251741455373, 0.33658548793818205, 1.0084881998012662, 1.6496662150356247, 2.2347105460269114, 2.740401833432754, 3.1468573173800616, 3.4385354946804143, 3.6050441969060163, 3.641706640551851, 3.5498514509486907, 3.336806216683627, 3.0155891304382547, 2.6043089548814096, 2.125299096192001, 1.6040261316160125, 1.0678259065028266, 0.5445305483367975, 0.06105681422080546, -0.35797037739616877, -0.691485865601009, -0.9230747341577635, -1.0418248222932154, -1.0428925464074021, -0.9277480799218955, -0.7040828803215351, -0.3853807865459679, 0.009827551008942302, 0.4589893332871114, 0.9367797268674293, 1.4165104146945628, 1.8716197066738323, 2.277161624714636, 2.611210239914105, 2.856099142075743, 2.999424162227746, 3.034749975081288, 2.961977351507369, 2.787346754867723, 2.5230746396606203, 2.186640049176297, 1.7997596912036853, 1.3871083765277261, 0.9748573945801394, 0.5891150860108656, 0.2543607792502303, -0.008035120282799986, -0.18111596763024376, -0.2533889589463526, -0.21955493276229712, -0.08087070112726152, 0.1548817993264341, 0.4738218529927485, 0.8567701991676772, 1.2803785339839888, 1.718522983586279, 2.143879221530594, 2.529584636564894, 2.8508863023230435, 3.0866729794685495, 3.2207951468633422, 3.2430888779961142, 3.1500366367615307, 2.945019794155869, 2.6381425945975345, 2.245633928223772, 1.7888599538294403, 1.293005685467222, 0.7855054878382369, 0.29431957346618237, -0.15383512539541713, -0.5351867626168191, -0.8304326745056506, -1.025985057928271, -1.1148538466579438, -1.097104465078326, -0.9798546406856157, -0.7768037853154296, -0.5073187769825181, -0.19512935059773176, 0.1332871860725646, 0.45053033639258233, 0.730192636196119, 0.9487420881672538, 1.0872448548814784, 1.1328101564388806, 1.079655115790497, 0.9297101318651199, 0.6927139002378508, 0.3857797018847242, 0.032449001289766306, -0.33871747837000266, -0.695929448672201, -1.0062288470201266, -1.2376946785310714, -1.3616495096376524, -1.354722872464927, -1.2006329221726049, -0.891562998851387, -0.42903346846452667, 0.1758000331419415, 0.9024549347115796, 1.7220308471978836, 2.5986745106601616, 3.491518653957564, 4.356980567971303, 5.1512808121937095, 5.833025801546299, 6.3656913154477355, 6.719847853090745, 6.874983150125335, 6.82080129024009, 6.557910242394368, 6.097848301669529, 5.462442325121501, 4.6825340548733685, 3.7961523183487684, 2.8462456819553137, 1.8781196768861075, 0.9367429341014317, 0.06409598292803328, -0.70326567872328], 'positive_zeros': ['0.63577611505595346610175523130106', '2.50345116392380435330633055071364', '3.65815898084270096861369071239315', '4.26457759009902094548130755028358', '5.66910598157464769461844955537261', '6.38765866408695998791678634939392', '6.82030863704119938120900900769038', '7.939682391816145384225408893687152', '8.972782544307586558194185458056258', '9.490834483076530112950594729522188'], 'prelabel': '2-1380-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.3195414561256347, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 2104018330926093201, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.63577611505595346610175523130', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.50345116392380435330633055071', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.65815898084270096861369071239', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 11.0193554789367, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 1380, 'conductor_radical': 690, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, -5, 0, 1, 0, 0, 0, 4, 0, 1, 0, -3, 0, -4, 0, 5, 0, -1, 0, 1, 0, -1, 0, 1, 0, 1, 0, 0, 0, 5, 0, -1, 0, -4, 0, 11, 0, 4, 0, -1, 0, 6, 0, 18, 0, 3, 0, 1, 0, 0, 0, 4, 0, -1, 0, 6, 0, -5, 0, -4, 0, -9, 0, 1, 0, 13, 0, 0, 0, -1, 0, 0, 0, 16, 0, 1, 0, 9, 0, 3, 0, -1, 0, 8, 0, -20, 0, -1, 0, 4, 0, 2, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -4, 13], 'euler17': [1, 3, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 0], 'euler29': [1, -1, 29], 'euler3': [1, 1, 0], 'euler31': [1, -1, 31], 'euler37': [1, 1, 37], 'euler41': [1, -11, 41], 'euler43': [1, -4, 43], 'euler47': [1, -6, 47], 'euler5': [1, 1, 0], 'euler53': [1, -1, 53], 'euler59': [1, 1, 59], 'euler61': [1, -6, 61], 'euler67': [1, 9, 67], 'euler7': [1, 5, 7], 'euler71': [1, -13, 71], 'euler73': [1, 0, 73], 'euler79': [1, -16, 79], 'euler83': [1, -9, 83], 'euler89': [1, -8, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 1, 0], [1, 5, 7], [1, 0, 11], [1, -4, 13], [1, 3, 17], [1, 4, 19], [1, 1, 0], [1, -1, 29], [1, -1, 31], [1, 1, 37], [1, -11, 41], [1, -4, 43], [1, -6, 47], [1, -1, 53], [1, 1, 59], [1, -6, 61], [1, 9, 67], [1, -13, 71], [1, 0, 73], [1, -16, 79], [1, -9, 83], [1, -8, 89], [1, -2, 97]], 'index': 0, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1380/a', 'ModularForm/GL2/Q/holomorphic/1380/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/1380/2/a/a'], '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': '2-1380-1.1-c1-0-0', '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': '2-1380-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.3195414561256347, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2104018330926093201, 'z1': {'__RealLiteral__': 0, 'data': '0.63577611505595346610175523130', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 20617408
{'Lhash': '805941973861451247101089055314', 'Lhash_array': ['805941973861451247101089055314'], 'label': '2-1380-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1380/2/a/a'}
-
id: 24552897
{'Lhash': '805941973861451247101089055314', 'Lhash_array': ['805941973861451247101089055314'], 'label': '2-1380-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1380/2/a/a/1/1'}
-
id: 42773
{'Lhash': '2104018330926093201', 'Lhash_array': ['2104018330926093201'], 'label': '2-1380-1.1-c1-0-0', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1380/a'}