-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1165145107818499242089247474318', 'a10': [0.0, 0.0], 'a2': [-2.302775637731995, 0.0], 'a3': [-1.0, 0.0], 'a4': [3.302775637731995, 0.0], 'a5': [0.0, 0.0], 'a6': [2.302775637731995, 0.0], 'a7': [-1.0, 0.0], 'a8': [-3.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 46.113607167289445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [11, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 5, 7, 11], 'central_character': '5775.1', 'coefficient_field': 'CDF', 'conductor': 5775, 'conductor_radical': 1155, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.302775637731995, 0], [2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.3027756377319946, 0], [13.0, 0]], [[1.0, 0], [4.60555127546399, 0], [17.0, 0]], [[1.0, 0], [6.302775637731995, 0], [19.0, 0]], [[1.0, 0], [1.6055512754639893, 0], [23.0, 0]], [[1.0, 0], [-9.21110255092798, 0], [29.0, 0]], [[1.0, 0], [-9.60555127546399, 0], [31.0, 0]], [[1.0, 0], [7.513878188659973, 0], [37.0, 0]], [[1.0, 0], [-9.0, 0], [41.0, 0]], [[1.0, 0], [-7.211102550927978, 0], [43.0, 0]], [[1.0, 0], [-6.211102550927978, 0], [47.0, 0]], [[1.0, 0], [4.39444872453601, 0], [53.0, 0]], [[1.0, 0], [-2.302775637731995, 0], [59.0, 0]], [[1.0, 0], [2.394448724536011, 0], [61.0, 0]], [[1.0, 0], [6.60555127546399, 0], [67.0, 0]], [[1.0, 0], [10.816653826391969, 0], [71.0, 0]], [[1.0, 0], [1.7888974490720213, 0], [73.0, 0]], [[1.0, 0], [-11.0, 0], [79.0, 0]], [[1.0, 0], [-8.302775637731994, 0], [83.0, 0]], [[1.0, 0], [9.0, 0], [89.0, 0]], [[1.0, 0], [4.302775637731995, 0], [97.0, 0]], [[1.0, 0], [-15.422205101855956, 0], [101.0, 0]], [[1.0, 0], [1.091673086804016, 0], [103.0, 0]], [[1.0, 0], [-16.816653826391967, 0], [107.0, 0]], [[1.0, 0], [1.6972243622680054, 0], [109.0, 0]], [[1.0, 0], [-14.724980739587952, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 88, 'label': '2-5775-1.1-c1-0-88', '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/5775/2/a/bf/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [9.46822051065201e-61, 0.06322411545366993, 0.12551062200986302, 0.1859084185982675, 0.24344108242435364, 0.29709824346496727, 0.34583147633189426, 0.38855571335810946, 0.4241568236215627, 0.4515056259216459, 0.4694782371702663, 0.47698232158341847, 0.47298851258195607, 0.45656603329059864, 0.4269213425765817, 0.3834384784029752, 0.32571965476733006, 0.25362458919779873, 0.16730699271478833, 0.0672466430808486, -0.04572451368732153, -0.17040372687733005, -0.3052076610375897, -0.448172718710658, -0.596966522484635, -0.7489113773858445, -0.901020254166792, -1.0500455111381386, -1.1925402113191628, -1.3249314993266625, -1.443605087076357, -1.544999469412748, -1.6257080622880253, -1.6825870405728494, -1.712866264564836, -1.7142603389738187, -1.6850765609798493, -1.6243162998850569, -1.5317662239813907, -1.4080757630750729, -1.2548172780732327, -1.07452560989309, -0.8707140032328162, -0.6478638473056736, -0.41138624229562687, -0.1675540795374296, 0.07659589670334502, 0.313390713882743, 0.5346772226736664, 0.732004349200623, 0.896828344589708, 1.0207368711407696, 1.0956868600193168, 1.1142502576010338, 1.0698610801574346, 0.9570566518363794, 0.7717055387380429, 0.5112145384269845, 0.1747071605927058, -0.23683364419402744, -0.7204651766667963, -1.2712329442646682, -1.8821716511032098, -2.544362696307956, -3.247050156793032, -3.977815567930732, -4.722810031352953, -5.467040323923137, -6.194703812244354, -6.889565153844904, -7.535366052883809, -8.116257798817955, -8.6172450132152, -9.024628020981417, -9.326430599513023, -9.512799585869807, -9.576362970428344, -9.512533695483288, -9.319747414680192, -8.99962394457561, -8.557044027830129, -8.000135287504015, -7.340163827273547, -6.591330752538771, -5.7704758692723805, -4.896693867764797, -3.99087131642535, -3.075155671583219, -2.1723701472609256, -1.3053905818288423, -0.4965022910535035, 0.23324377495374718, 0.8646555196582983, 1.3809846939442616, 1.7684528462019784, 2.016699953332552, 2.1191394004980966, 2.073205548245183, 1.8804832583407263, 1.5467123552994864, 1.0816639691673726, 0.49888990884654205, -0.18464948751535182, -0.9490693385008405, -1.7721423268082959, -2.6299615489277737, -3.4976635727943037, -4.3501886539965495, -5.163053298000815, -5.9131094323754025, -6.5792644282485275, -7.143137111341993, -7.589626722838336, -7.907374486829249, -8.08910093711995, -8.131806341658878, -8.036826297888503, -7.809739691551323, -7.4601315299063975, -7.001218479858743, -6.449350058545293, -5.823403137200517, -5.144091537897184, -4.433215854780871, -3.712881070459749, -3.0047109507492733, -2.32908851175407, -1.7044510294881887, -1.1466661160622367, -0.6685123758006594, -0.2792841819751529, 0.015464675837775978, 0.21402915179835597, 0.3185094439593493, 0.33461841592759456, 0.2713485186581714, 0.14051248867421684, -0.043822743279541415, -0.26598510360242195, -0.5094021184640434, -0.7573317531548553, -0.993588653736263, -1.2032352845122682, -1.3732089382583357, -1.4928583268275868, -1.5543673345917437, -1.5530483814874279, -1.4874934957277235, -1.3595774001046959, -1.1743134037649738, -0.9395693801302933, -0.6656573135734654, -0.3648155332758913, -0.05060756429003105, 0.2627347116105918, 0.5609933598731257, 0.8306407608186438, 1.0594788888304276, 1.2372120274497636, 1.35592648637998, 1.4104551665704188, 1.398610152458544, 1.3212726585927057, 1.1823363422282953, 0.9885069059178955, 0.7489677312850131, 0.47492768364917, 0.1790728987760417, -0.12505097020066328, -0.4236961395928631, -0.7035777980975677, -0.9525145253963885, -1.1600127116105607, -1.3177662813281474, -1.4200470665012928, -1.4639664532607088, -1.4495952032503963, -1.3799353225233242, -1.2607451836039343, -1.1002264393808938, -0.9085882359560516, -0.6975104829783277, -0.4795331523282043, -0.2674024744396468, -0.07340727305062837, 0.0912606154922034, 0.21708891015482187, 0.29674022371662, 0.32543424407315885, 0.3011964978135764, 0.224960208288486, 0.10051530430338118, -0.06569342909585879, -0.26490914606358834, -0.4865292776466637, -0.718671341185454, -0.9488086718403322, -1.164442541344817, -1.3537748709164499, -1.5063453611059359, -1.6135984019966645, -1.6693485424836692, -1.6701184368510553, -1.615329805351979, -1.5073357140250623, -1.351291000431912, -1.1548665006804004, -0.9278213974287084, -0.6814560357149577, -0.42797449467566945, -0.179791658529679, 0.05117682885756074, 0.2542017524333192, 0.42036527820782, 0.5430870829661337, 0.6185199625549681, 0.6457899804994292, 0.6270645230386567, 0.5674410521029973, 0.47465939917138816, 0.3586505777851814, 0.23094474913071517, 0.10396960308854661, -0.009722492287265554, -0.09825510471873383, -0.15120984820380107, -0.16034346343956465, -0.12019570908033132, -0.028548844746234706, 0.11329320006022617, 0.30042852753434623, 0.5244954749042905, 0.7740250122664115, 1.0349947121162413, 1.2915596526900668, 1.5269245851907207, 1.7243122960621693, 1.8679759103638895, 1.9441983878930915, 1.942221003463562, 1.8550443633352498, 1.680050505610143, 1.4194026991484194, 1.0801903533071127, 0.6742994769718074, 0.2180037369441638, -0.2687133899107207, -0.7630794238525556, -1.2406560947749035, -1.676611480856152, -2.047077123992503, -2.330518822412361, -2.5090460873634224, -2.5695855093496465, -2.504847639603543, -2.314025364089653, -2.0031738180463066], 'positive_zeros': ['0.919137424467534711701947506833106', '2.14146356286875620326466302852541', '2.73969082149708782507516451623570', '4.24999880457103174627469133964922', '4.76917546656680670560344310291734', '6.13772083490541776991439732456254', '6.41169136752711370773103317281853', '7.17938115583077778200203482765233', '7.85574363226124867204286252650797'], 'prelabel': '2-5775-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.790700049868898, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.919137424467534711701947506833', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.14146356286875620326466302853', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.73969082149708782507516451624', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 46.113607167289445, 'bad_primes': [3, 5, 7, 11], 'central_character': '1.1', 'conductor': 5775, 'conductor_radical': 1155, 'degree': 2, 'index': 88, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5775/2/a/bf/1/1'], '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': '2-5775-1.1-c1-0-88', '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': '2-5775-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.790700049868898, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.919137424467534711701947506833', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1165145107818499242089247474318', 'Lhash_array': ['1165145107818499242089247474318'], 'label': '2-5775-1.1-c1-0-88', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5775/2/a/bf/1/1'}