-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1541539875003221657748191052860', 'a10': [0.0, 0.0], 'a2': [1.0, 0.0], 'a3': [1.0, 0.0], 'a4': [-1.0, 0.0], 'a5': [0.0, 0.0], 'a6': [1.0, 0.0], 'a7': [4.47213595499958, 0.0], 'a8': [-3.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.97195037899008, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '1875.1', 'coefficient_field': 'CDF', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4.47213595499958, 0], [7.0, 0]], [[1.0, 0], [-3.23606797749979, 0], [11.0, 0]], [[1.0, 0], [-3.381966011250105, 0], [13.0, 0]], [[1.0, 0], [2.8541019662496847, 0], [17.0, 0]], [[1.0, 0], [3.23606797749979, 0], [19.0, 0]], [[1.0, 0], [4.47213595499958, 0], [23.0, 0]], [[1.0, 0], [-4.381966011250105, 0], [29.0, 0]], [[1.0, 0], [-7.23606797749979, 0], [31.0, 0]], [[1.0, 0], [-8.090169943749475, 0], [37.0, 0]], [[1.0, 0], [1.381966011250105, 0], [41.0, 0]], [[1.0, 0], [5.708203932499369, 0], [43.0, 0]], [[1.0, 0], [5.23606797749979, 0], [47.0, 0]], [[1.0, 0], [-1.381966011250105, 0], [53.0, 0]], [[1.0, 0], [4.0, 0], [59.0, 0]], [[1.0, 0], [0.6180339887498949, 0], [61.0, 0]], [[1.0, 0], [-5.23606797749979, 0], [67.0, 0]], [[1.0, 0], [0.7639320225002103, 0], [71.0, 0]], [[1.0, 0], [-3.090169943749474, 0], [73.0, 0]], [[1.0, 0], [0, 0], [79.0, 0]], [[1.0, 0], [-3.5278640450004204, 0], [83.0, 0]], [[1.0, 0], [-7.618033988749895, 0], [89.0, 0]], [[1.0, 0], [-8.854101966249685, 0], [97.0, 0]], [[1.0, 0], [16.562305898749052, 0], [101.0, 0]], [[1.0, 0], [1.2360679774997898, 0], [103.0, 0]], [[1.0, 0], [-16.47213595499958, 0], [107.0, 0]], [[1.0, 0], [19.090169943749473, 0], [109.0, 0]], [[1.0, 0], [-2.673762078750736, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 38, 'label': '2-1875-1.1-c1-0-38', 'leading_term': '3.28239146238213767741083220701', '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/1875/2/a/d/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [3.2823914623821375, 3.2770277928757077, 3.260748723810057, 3.233003860688184, 3.192920720411623, 3.1393682716563784, 3.071039060941769, 2.986544345826662, 2.884516470234283, 2.763713078483217, 2.6231184653046093, 2.46203818719562, 2.28018385211768, 2.077745665271023, 1.8554508094170659, 1.6146060975173018, 1.3571235980180516, 1.0855281516353674, 0.8029459214042809, 0.5130733826402316, 0.22012649077237864, -0.07122982565053411, -0.3559712118279773, -0.6288212816218285, -0.884375059153261, -1.1172360258308087, -1.3221636878800904, -1.4942279614335345, -1.628966110965272, -1.7225375037520838, -1.7718710886132212, -1.7748002997054342, -1.7301800503406601, -1.6379806374956878, -1.4993537386118656, -1.3166662548900878, -1.0934985377990616, -0.8346045172185705, -0.5458324104627306, -0.23400600188541176, 0.09323209569576954, 0.42761230076364515, 0.7604606510170526, 1.0829462794366007, 1.3863466033533804, 1.662321891746288, 1.9031899538575154, 2.1021910649389466, 2.253732962345437, 2.353605846663919, 2.3991578343858113, 2.3894222416195703, 2.3251894260268866, 2.209017651552599, 2.04517952359757, 1.8395429083852162, 1.5993878193030393, 1.3331634296023966, 1.0501920474476, 0.7603294500384034, 0.47359329880857814, 0.19977332943304435, -0.05196148250013033, -0.27344263511296524, -0.457852246929191, -0.6000275888510872, -0.6967050804755425, -0.7466906824487831, -0.7509461588254076, -0.7125838446759455, -0.6367662302243916, -0.5305107281560272, -0.4024042629600969, -0.26223662658321173, -0.12056568563996764, 0.011768701116371925, 0.1241619895309832, 0.20677096050030352, 0.2510243719751106, 0.25009369005104115, 0.19929996398698474, 0.09643470218782331, -0.05802445349352806, -0.26081844295998324, -0.5059421216882929, -0.7848147245186142, -1.0865837274628747, -1.3985538803038546, -1.7067267381295055, -1.9964299442771694, -2.253010129445912, -2.462558895616182, -2.6126382208830834, -2.6929699769578535, -2.6960542578101663, -2.617682964850202, -2.4573185875821837, -2.2183132771944414, -1.9079499634609824, -1.537295156538176, -1.1208618714655456, -0.6760904167328442, -0.22266415401202327, 0.21831370806426328, 0.6252481533946254, 0.9770443699259177, 1.2541178941159328, 1.4393741618749736, 1.5191081908660997, 1.4837770479831414, 1.3286021786379836, 1.0539654775780662, 0.665571920138428, 0.17436227963683978, -0.40382854835731713, -1.048859381150899, -1.7370957137293266, -2.4424145732512734, -3.1373570667393507, -3.7943753538013776, -4.387114147553518, -4.891663112640885, -5.287716004317534, -5.559575231902266, -5.696946712635288, -5.695479204336073, -5.5570143838409205, -5.289528222900273, -4.906760010461849, -4.427541875236381, -3.8748579991018954, -3.2746779788875835, -2.654622114125164, -2.0425269685985947, -1.4649866938271894, -0.9459487990712042, -0.5054419932817107, -0.15850832591026282, 0.08559772607121384, 0.2238939373181981, 0.25980600154041406, 0.20294023681258758, 0.06849952932283099, -0.12363091474086653, -0.3500820086599559, -0.5854200657618976, -0.8037093641599415, -0.9801302914435586, -1.0925599891615039, -1.1230222705831372, -1.0589188370114027, -0.8939643263734282, -0.6287630387141764, -0.2709845454017767, 0.16488221170005474, 0.6581925139408837, 1.183198684953343, 1.7104400190569766, 2.2083964832553358, 2.645315392784862, 2.9911076946926842, 3.219203712708818, 3.3082577755261178, 3.2435972712255237, 3.0183241568695194, 2.6339952293893476, 2.1008305910829614, 1.4374264597290145, 0.6699772662207348, -0.16895882935657203, -1.0420890400740774, -1.9093229488199999, -2.729910558815846, -3.4646604163146466, -4.078109656344697, -4.540518224508281, -4.829567644796679, -4.931660208590512, -4.842736563061311, -4.568557161046968, -4.1244243206699025, -3.53435488138536, -2.829746621462272, -2.0476126682527123, -1.2284851240609818, -0.41411029912150243, 0.3549281279577447, 1.041516001796696, 1.6141066301772011, 2.048482447773901, 2.329072815428407, 2.44974703133803, 2.414033633134192, 2.2347524517211825, 1.9330824313092565, 1.5371236370667039, 1.0800438519960445, 0.5979266251391814, 0.12745680876968188, -0.2964098032370905, -0.6426449226408164, -0.8860748275831986, -1.0089139914860232, -1.0018086854012203, -0.8643258276985344, -0.6048585897706837, -0.23995850047526943, 0.20685850268307773, 0.7067499721415167, 1.2275174329354743, 1.7357762190486974, 2.1991784896666466, 2.5885401615829977, 2.8797295259573605, 3.055192048455358, 3.1050111866545214, 3.0274372973719146, 2.8288536538285847, 2.5231877039322415, 2.1308142564551504, 1.6770325745893977, 1.1902288833744668, 0.6998574397194045, 0.23438549153136792, -0.18065075449787962, -0.5243408146982291, -0.7817256950115431, -0.9446626546065799, -1.0121711129972468, -0.9902403832329022, -0.8911199549078272, -0.7321516577384586, -0.5342373404832885, -0.3200631144723947, -0.11221962670877086, 0.06863422388713974, 0.205419939731606, 0.2859705424942968, 0.30393863914321684, 0.2592086870673021, 0.15777946813350044, 0.011124649637905621, -0.1649188820302197, -0.3516467049071752, -0.5292461460062585, -0.6786754750984755, -0.7835069529084038, -0.8315774161978718, -0.8163022043112655, -0.737532077252517, -0.6018667647469421, -0.42238051961831047, -0.21776147086481298, -0.010914185875065076, 0.17288002257715895, 0.3081114572780614, 0.37133571751703176], 'positive_zeros': ['1.21606054122932682573547065652734', '2.32725131854991977661984969121202', '3.62018348495749946622227172829692', '4.38901518237591598027508741045083', '4.78481468581057925511933073923037', '6.00576252668532945349096965573197', '6.63962792386534838733971776412935', '8.062342299095762193361618769794498', '8.342916251547541267608811467252628', '9.002323657462668260045432006373220'], 'prelabel': '2-1875-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21606054122932682573547065653', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.32725131854991977661984969121', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.62018348495749946622227172830', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 14.97195037899008, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1875/2/a/d/1/2'], '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': '2-1875-1.1-c1-0-38', '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': '2-1875-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21606054122932682573547065653', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1541539875003221657748191052860', 'Lhash_array': ['1541539875003221657748191052860'], 'label': '2-1875-1.1-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1875/2/a/d/1/2'}