-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1007557718171389306989056516235', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.28250763410477725, 0.6345225351080066], 'a4': [0.0, 0.0], 'a5': [-1.465929128292288, 2.5390637304973978], 'a6': [0.0, 0.0], 'a7': [-4.759067774771153, 5.285480229581161], 'a8': [0.0, 0.0], 'a9': [5.699367172997311, 6.329788508937491], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.3787552780676817, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [31, [[1.0, 0], [17.22318406797071, 25.77521931159461]]]], 'bad_primes': [2, 31], 'central_character': '124.105', 'coefficient_field': 'CDF', 'conductor': 124, 'conductor_radical': 62, 'conjugate': '3087238989035593009679658016902', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.28250763410477725, -0.6345225351080066], [-6.022175457229724, -6.688303429296548]], [[1.0, 0], [1.465929128292288, -2.5390637304973978], [-12.5, -21.650635094610966]], [[1.0, 0], [4.759067774771153, -5.285480229581161], [-5.12189470011502, -48.731572873045394]], [[1.0, 0], [1.4391240344275935, -6.770546263642164], [-110.5390003747547, -49.21513381217183]], [[1.0, 0], [2.6583631616953336, -0.27940522716843386], [165.30694452401315, -35.137075748201326]], [[1.0, 0], [-1.1601975614452649, -5.458300380518872], [-264.0146372587117, 117.54688984890626]], [[1.0, 0], [0.5983076809303283, -5.692517332131863], [-353.11128386490384, -75.05612038521112]], [[1.0, 0], [-0.007155554053800397, -0.0023249804495389663], [427.96999002434717, 310.9383984627183]], [[1.0, 0], [-24.968147709018243, 34.36570709434646], [-259.8832922693308, -799.8385302042242]], [[1.0, 0], [17.22318406797071, 25.77521931159461]], [[1.0, 0], [-24.23910312162348, 13.994452712184414], [684.5, -1185.5887777808964]], [[1.0, 0], [-49.236869215598915, 21.92166654956944], [1124.8085492892405, -1249.2264516274997]], [[1.0, 0], [39.85005312388373, 4.188409358882381], [1808.5949137568066, 384.428716322037]], [[1.0, 0], [3.3714123112791095, -2.449474423585121], [682.6185405742589, -2100.8838444959943]], [[1.0, 0], [-36.14963610527132, 32.54927854908151], [293.6204533188386, -2793.61200408948]], [[1.0, 0], [-32.415882416639654, -14.432480711476567], [2329.2436407351856, 2586.8871374868095]], [[1.0, 0], [0, -11.468472933101301], [-3721.0, 0]], [[1.0, 0], [1.394694711513145, -2.4156821013883847], [-2244.5, -3887.5880375883453]], [[1.0, 0], [-54.22794484402712, -60.22623419724372], [-526.9279833322412, 5013.384874551466]], [[1.0, 0], [19.700850441305924, -92.68521416849975], [-4868.283743777421, -2167.4995709509394]], [[1.0, 0], [-15.322651590958772, -72.08740803187258], [-5701.4372011474725, 2538.443389436069]], [[1.0, 0], [0.665832553326987, 1.4954844000349528], [-4609.640747206175, 5119.524702713769]], [[1.0, 0], [-31.154541708432475, 10.12272422817929], [6408.223612443959, -4655.84698340868]], [[1.0, 0], [-13.220919921472198, -40.689807588627325], [-7612.04090007388, 5530.47143881988]], [[1.0, 0], [-4.532713100720394, 13.950256488825753], [-8252.78235961884, -5995.997358635518]], [[1.0, 0], [93.48437767720601, -41.6219265701091], [7098.8066028611265, -7884.023453489675]], [[1.0, 0], [-100.8064519996544, 21.427072831200665], [10459.181944550137, -4656.727826574836]], [[1.0, 0], [53.23221004351738, -38.67546445632948], [3671.4309101687504, -11299.50247010272]], [[1.0, 0], [61.72067694297173, 13.119134874944283], [11665.061948638371, 5193.620195434893]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-124-31.12-c2-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/124/3/o/a/105/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.0884391272211984, 0.9456819968813259, 0.795235115938025, 0.6350383282127093, 0.462938009471672, 0.2770192813339694, 0.07592940040982474, -0.1408256278708327, -0.3726243816674962, -0.6175237481188915, -0.8721131200789566, -1.131440276333505, -1.3890214927493014, -1.6369487741834714, -1.866105611033067, -2.066498909440198, -2.227708622050755, -2.3394483029447293, -2.39221976109878, -2.378033858209743, -2.2911581714583935, -2.1288417892283347, -1.8919591313989852, -1.5855096418724741, -1.2189096892574354, -0.806018043670288, -0.36484755251366513, 0.0830666802697686, 0.5136485941409935, 0.9015892716765167, 1.2219273465796483, 1.4518147422619456, 1.5723506304805073, 1.5703420882713608, 1.4398346570462162, 1.1832529749602285, 0.8120032621346457, 0.34641698979977154, -0.1850415818447588, -0.7473239861894633, -1.3010545634046782, -1.805375505859357, -2.2211885287168283, -2.5145400734060828, -2.659852400639825, -2.642682660621089, -2.4617016082173637, -2.1296261613654783, -1.672915377053974, -1.130143850922157, -0.5490924424782192, 0.01726748301737782, 0.5155871832699526, 0.8973275842014806, 1.123816093434293, 1.170635090449569, 1.0308261117419963, 0.7164757813758582, 0.25838874219401137, -0.2962606698226015, -0.888189223669838, -1.4518440404140769, -1.9222787343041405, -2.2423617158652713, -2.3695172308047407, -2.281191761806676, -1.9783266209283341, -1.4863002332680058, -0.8530669836211979, -0.14453814358008657, 0.5624107086000496, 1.1886032845241576, 1.6619397759925225, 1.9263765492866771, 1.9493732472253458, 1.7267917529734995, 1.284490667907095, 0.6762348925185422, -0.022008027248926632, -0.7208393031279948, -1.3282889452397384, -1.7614534932129382, -1.9574230633334724, -1.882021775129958, -1.5350997192635976, -0.9515148162769222, -0.1974861634603424, 0.6373798200939357, 1.4514754390125324, 2.1445549204109455, 2.631293835471313, 2.8531529188296956, 2.7868093258634508, 2.4478327747998376, 1.8889129076243991, 1.1927075383523569, 0.46017374870117195, -0.20405174056052564, -0.7071509008447736, -0.9822105615935413, -0.9987229554901328, -0.7677816755775632, -0.34099430141707726, 0.19694006268649122, 0.7410605572684886, 1.1825723081518587, 1.4264232002398802, 1.4072970861467717, 1.1014268749378837, 0.53218677415943, -0.23166903526862978, -1.0851222967420928, -1.9021787713696139, -2.5551010761935546, -2.9346296727410075, -2.967957283895473, -2.6314624695296054, -1.9559519601545599, -1.02330856058226, 0.04518090294943357, 1.1071554995596307, 2.0213415028160124, 2.6699842357580303, 2.9778286174995907, 2.9243909991649755, 2.547301474366594, 1.935949965921394, 1.2163067199763922, 0.5293314406706144, 0.006562187103293199, -0.2529352759897649, -0.20020125489788734, 0.15461392915768643, 0.7436487401859267, 1.4531028272642477, 2.143499334826153, 2.6749782862397655, 2.933161395039953, 2.8509046660280055, 2.421876702418224, 1.7032840889564904, 0.8069832450570561, -0.11966444092231623, -0.9199059147056792, -1.4560100654163448, -1.6347618694016977, -1.4252255126691074, -0.865288728928264, -0.05552078399167533, 0.8587664956188475, 1.7141086958547063, 2.3592618108878587, 2.6836502181267767, 2.638413669520226, 2.245871361712429, 1.5953605447108445, 0.8260030224980024, 0.09951342894607476, -0.43181398906287854, -0.6557324437621671, -0.5231979096397665, -0.05929527157762074, 0.6405132665359307, 1.4284053862573198, 2.1332102520143077, 2.5948578227399928, 2.6974734935279376, 2.3944203796906676, 1.7200379487194855, 0.7853720728538414, -0.24164535285339028, -1.167953708728648, -1.8129394073702376, -2.0443869955742633, -1.8055222221113594, -1.1275158200657198, -0.12466162586491768, 1.0270750145698722, 2.1240265652451003, 2.9745587684463843, 3.436525719284878, 3.444750159618951, 3.022798786134573, 2.276522934216605, 1.3706249815500928, 0.4931011995409201, -0.18496457861488716, -0.5457058355925853, -0.5490613685386019, -0.24025919433696755, 0.26155629792889384, 0.7912258804093217, 1.1760273115165443, 1.2762845792893485, 1.019119416918249, 0.4176780780979385, -0.428765143808201, -1.3542729427137699, -2.161377964113023, -2.6644029905063067, -2.7314874411644015, -2.3159035394672327, -1.4694115977293027, -0.3342407646666903, 0.8850271839580031, 1.9638776210298365, 2.7054702912996045, 2.982964167365997, 2.767057734759446, 2.132368485010743, 1.2409042353792594, 0.30599781664252623, -0.4554636314212465, -0.8719105164022243, -0.8560409130101897, -0.42490729176562175, 0.30364421863732477, 1.137641998696226, 1.85493261709772, 2.2545265682725675, 2.2036374579755895, 1.669543044131209, 0.7287612014012377, -0.44880951654504864, -1.6373554148178735, -2.605725869923345, -3.169480049931109, -3.232292787554449, -2.8069853276450507, -2.0111487943080553, -1.038282975201536, -0.11118759652547738, 0.5713688205613845, 0.8819651309233525, 0.7944076061838806, 0.38883253217047997, -0.16940135980882856, -0.6721202434910987, -0.9218812112294982, -0.7836302433062433, -0.2217047478573253, 0.6872078968695653, 1.7688119228055752, 2.790571230144756, 3.516531338147552, 3.7644616218680635, 3.451374456677353, 2.6160787343257086, 1.412861413691253, 0.07737593702874371, -1.1273447165520825, -1.9718330397067974, -2.3132837753508984, -2.127741772808877, -1.5133308464176223, -0.6635589836152956, 0.18283557590178645], 'positive_zeros': ['0.794822893619099264168290292330944', '3.35166011477278151919742750782366', '4.70772761179925382269723651110571', '6.37101828039126239883451347087182', '7.31017546137163806532105112936933', '8.650080427199088102020330204655515', '9.746147103058010973364588337513225', '10.78011544890036009825270162059272', '12.08403469411907855341734845932852', '12.83072024737743832864286488400690'], 'prelabel': '2-124-31.12-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8381390801752955, 'root_angle': -0.5438045859518883, 'root_number': '-0.13718220925809674 - 0.9905458300669726*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.271902292976', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.794822893619099264168290292331', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.35166011477278151919742750782', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.70772761179925382269723651111', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.3787552780676817, 'bad_primes': [2, 31], 'central_character': '31.12', 'conductor': 124, 'conductor_radical': 62, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/124/3/o/a/105/3'], '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': '2-124-31.12-c2-0-1', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-124-31.12-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8381390801752955, 'root_angle': -0.27190229297594415, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.794822893619099264168290292331', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1007557718171389306989056516235', 'Lhash_array': ['1007557718171389306989056516235'], 'label': '2-124-31.12-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/124/3/o/a/105/3'}