-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '4144894427891345587933520533760', 'a10': [-4.381966011250105, -1.7746502784700094e-60], 'a2': [0.9510565162951535, 0.30901699437494745], 'a3': [2.932361769047729, 0.6334464897900012], 'a4': [-2.4270509831248424, -1.7633557568774194], 'a5': [-4.167497329183295, 1.3541019662496845], 'a6': [2.59309603821536, 1.508593032130205], 'a7': [1.7360679774997898, 1.2613272171618513], 'a8': [-4.114496766047312, -5.663118960624632], 'a9': [8.197491089145451, 3.714988538795364], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8991848723889799, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-2.932361769047729, -0.6334464897900012]]], [11, [[1.0, 0], [9.06153718637195, 6.23606797749979]]]], 'bad_primes': [3, 11], 'central_character': '33.20', 'coefficient_field': 'CDF', 'conductor': 33, 'conductor_radical': 33, 'conjugate': '4392524721869678138645932827225', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.9510565162951535, -0.30901699437494745], [3.23606797749979, 2.3511410091698925]], [[1.0, 0], [-2.932361769047729, -0.6334464897900012]], [[1.0, 0], [4.167497329183295, -1.3541019662496845], [20.225424859373685, -14.694631307311829]], [[1.0, 0], [-1.7360679774997898, -1.2613272171618513], [15.141832724372424, 46.60176929846253]], [[1.0, 0], [9.06153718637195, 6.23606797749979]], [[1.0, 0], [2.708203932499369, -8.33499465836659], [-136.72387204936612, -99.33570763742796]], [[1.0, 0], [-5.706339097770922, 1.8541019662496845], [233.8059113743598, -169.86993791252473]], [[1.0, 0], [-25.18033988749895, 18.294587797897712], [111.55513496935602, -343.33140238255044]], [[1.0, 0], [0, -26.47213595499958], [-529.0, 0]], [[1.0, 0], [-27.85815352398523, 38.34345884812358], [-259.8832922693308, -799.8385302042242]], [[1.0, 0], [9.517220926874316, -29.29099416630089], [-777.4653315943244, -564.8616274530667]], [[1.0, 0], [23.94427190999916, 17.39653184473854], [423.04426529930305, 1301.9963708080652]], [[1.0, 0], [25.625525376833163, 35.270509831248425], [-519.4575675442866, 1598.7260038921531]], [[1.0, 0], [39.708203932499366, 0], [1849.0, 0]], [[1.0, 0], [2.5226544343237025, 3.4721359549995796], [-682.6185405742589, 2100.8838444959943]], [[1.0, 0], [-10.718891816977404, -3.4827790731256836], [2272.528737199227, 1651.088773689557]], [[1.0, 0], [19.449913888787595, -26.77050983124842], [-1075.688157419192, -3310.6277332234295]], [[1.0, 0], [-8.458980337503155, -26.03406452602263], [-3010.3522360691795, 2187.1489237802925]], [[1.0, 0], [-70.79024325749306, 0], [4489.0, 0]], [[1.0, 0], [83.86448685912733, -27.249223594996213], [4078.25466864411, -2963.025456806357]], [[1.0, 0], [50.14183272437242, 36.43017390638747], [1646.7515630240948, 5068.180175336874]], [[1.0, 0], [19.486844382503577, -59.97434014752732], [-5049.0750618940465, -3668.367759557325]], [[1.0, 0], [-104.79250927541736, 34.04915028125263], [5573.318074249013, -4049.2526030428476]], [[1.0, 0], [0, 9.665631459994954], [-7921.0, 0]], [[1.0, 0], [-30.958980337503153, 95.28194411246582], [-7612.04090007388, -5530.47143881988]], [[1.0, 0], [-12.754983067483938, -4.144345223742745], [8252.78235961884, 5995.997358635518]], [[1.0, 0], [0.3328157299974764, 0.2418047818323161], [3278.3612933238173, 10089.758581375285]], [[1.0, 0], [-120.36790574234584, -165.67220926874316], [-3537.935568598773, 10888.646055063213]], [[1.0, 0], [-107.33126291998991, 0], [11881.0, 0]], [[1.0, 0], [-44.47514227758243, -61.214781741247585], [-3945.8380011737036, 12144.040656572815]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-33-33.20-c2-0-2', '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/33/3/h/a/20/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.2908547250959, 1.289277583536046, 1.2954881766137836, 1.3088708984066855, 1.32851437621483, 1.3532394797688712, 1.3816297423895556, 1.4120609371492798, 1.4427285856125578, 1.4716742374634046, 1.4968128329466857, 1.5159641444450573, 1.5268912837207134, 1.5273487690162386, 1.5151418709926796, 1.4881980346807904, 1.4446501802305391, 1.3829306520937514, 1.3018735314282877, 1.2008219671975044, 1.0797361446720402, 0.9392965366076139, 0.7809962270563777, 0.6072154271828264, 0.42127089125333445, 0.22743286685156322, 0.030902551106114912, -0.16225616063435896, -0.3452355076207221, -0.5106562637944493, -0.6507942623442442, -0.7578586790910288, -0.8243163810459949, -0.8432530478899433, -0.8087580848917323, -0.716316787522121, -0.5631900463947911, -0.34875937417350183, -0.07481347821930608, 0.25424773448998406, 0.6313147141401886, 1.0465956276220723, 1.4877852824637923, 1.9403851835979362, 2.3881765213899886, 2.81383881563439, 3.1996969757329876, 3.5285692280405065, 3.78467836811971, 3.9545798630725484, 4.028053243026854, 3.9988987547361283, 3.8655801035676918, 3.631656842280985, 3.3059569293905517, 2.902451264180215, 2.439807383343937, 1.940618405643385, 1.4303248153426655, 0.9358695329106264, 0.4841494058746641, 0.10034704290135943, -0.19375599323555584, -0.38137197398595224, -0.4520884669200778, -0.4029247016164536, -0.23896147958425804, 0.026535393612490736, 0.37254856750723314, 0.7713134426631667, 1.1898660608554692, 1.592064217212269, 1.9409696095103686, 2.2014418631187334, 2.3427666349498923, 2.3411228935173156, 2.181691448423507, 1.8602194843398445, 1.3838846855259315, 0.7713466105178028, 0.051929967979005696, -0.7360493343030761, -1.5477339089736009, -2.334799689850005, -3.048943401835184, -3.645522117975274, -4.087055090131732, -4.346291897041113, -4.408570306604564, -4.273232366050406, -3.953936013195965, -3.477787451329267, -2.8833199723351512, -2.217449430634983, -1.5316356668332618, -0.877563108018548, -0.30271347193540993, 0.15376844123391578, 0.4645233650781847, 0.6163947645874339, 0.6115516577243378, 0.4671673835611871, 0.2136390551980166, -0.10852411813271606, -0.45287689223628974, -0.7718924271918026, -1.0220226119647255, -1.168449080930772, -1.1890180273175774, -1.07691356333045, -0.8417362243014594, -0.5088065495001514, -0.11669472831636585, 0.2868316258519931, 0.6500684209742026, 0.9233207636424587, 1.0649071339896488, 1.0465563810945364, 0.8575634438407702, 0.5071731853587161, 0.02483002175407771, -0.5418506950921944, -1.1312867327794123, -1.6739562811655209, -2.099672390778485, -2.345356855312774, -2.3624692027443874, -2.1232401596439994, -1.6249489543819573, -0.8916653180151668, 0.026865686133448037, 1.0592102952151359, 2.1187934023669404, 3.1123902240161594, 3.9496962027790663, 4.552947518163171, 4.865514594808233, 4.858464059052848, 4.534278108095651, 3.927217066245531, 3.1001805432032565, 2.138324269458871, 1.1400766314872994, 0.2065239294716696, -0.5696455057784976, -1.114362141292341, -1.3803497818333974, -1.3522565606496244, -1.0480874740275488, -0.5167167105310622, 0.16826860032318497, 0.9176857987254603, 1.6377475816893812, 2.24158464992803, 2.659867152370238, 2.849180561922032, 2.797074505798901, 2.523111835811868, 2.0757512946286236, 1.5254373442844729, 0.9547750484004425, 0.44706849631680584, 0.07474163559038202, -0.11079652729425375, -0.08644641850967448, 0.13916477990051604, 0.5266705940512837, 1.0112906821432033, 1.511826725508904, 1.9421370794378832, 2.223525748349112, 2.2963166487136686, 2.128957231426003, 1.7233036367928807, 1.1152467234527097, 0.37047916708876133, -0.4241083555883392, -1.1722756437563258, -1.7819041430544897, -2.1781915006837225, -2.31465836188407, -2.1803204064885033, -1.8018895681597604, -1.2405599873471376, -0.5837116204114674, 0.06738333224485339, 0.6121501225675866, 0.9655118248323965, 1.070726421302473, 0.9083168979921732, 0.49967599243114286, -0.09532079921216693, -0.7864865443424424, -1.4662022334022236, -2.025194443932454, -2.3689183017901376, -2.4321005997426033, -2.189210606937631, -1.6591830224554314, -0.9035450043510243, -0.018079700287472102, 0.880852798155357, 1.6733708819282653, 2.2539693497064075, 2.547531984445242, 2.520952311182958, 2.1884714518352553, 1.6097681374155113, 0.8809384278122002, 0.11961512067194946, -0.5535742641095808, -1.0343802145675771, -1.2520980119315122, -1.181757159129741, -0.8492709972613366, -0.32853828302547744, 0.26926817355924776, 0.8127493143917365, 1.1711447394537335, 1.235822122890137, 0.9390122096344162, 0.2667541423168782, -0.7361507547023246, -1.9701753428764088, -3.293701033010928, -4.542497095894167, -5.553179062448031, -6.187099359563978, -6.350992616240167, -6.011149856886703, -5.19886854757262, -4.006271637435882, -2.5730969071335883, -1.0664860494008437, 0.34308246088184025, 1.5059574694641538, 2.3138078687135515, 2.7132803967181363, 2.710783434097963, 2.3678193738980835, 1.7878452792344797, 1.0970331005492588, 0.42229028045548134, -0.12968180239095398, -0.48874532200760534, -0.6303964832136115, -0.5761590495970371, -0.3854675490264556, -0.14073484860287777, 0.07147279097543625, 0.1795237179239349, 0.14239150993275432, -0.041149231099853564, -0.3316644226407384, -0.6568422569590312, -0.9265714851417511, -1.0525392009060004], 'positive_zeros': ['3.26974517043189472291427415641029', '4.78025445443902479535841473092541', '7.66322599270599920674199952731695', '8.364171713280274496926239256760787', '10.00850706701366814824703970888332', '12.07855482842601962094535192777287', '12.83472658781114521169462111132322', '14.03581535705258299118344346897143', '15.00579331371891175354484848379488', '16.24659854070756665608604884071480'], 'prelabel': '2-33-33.20-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9482535907598663, 'root_angle': -0.05498194981180036, 'root_number': '0.9851190740406888 - 0.1718732380599609*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0274909749059', 'prec': 54}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.26974517043189472291427415641', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.78025445443902479535841473093', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.66322599270599920674199952732', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.8991848723889799, 'bad_primes': [3, 11], 'central_character': '33.20', 'conductor': 33, 'conductor_radical': 33, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/33/3/h/a/20/2'], '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': '2-33-33.20-c2-0-2', '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': '2-33-33.20-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9482535907598663, 'root_angle': -0.02749097490590018, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '3.26974517043189472291427415641', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '4144894427891345587933520533760', 'Lhash_array': ['4144894427891345587933520533760'], 'label': '2-33-33.20-c2-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/33/3/h/a/20/2'}