-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2459960771778726717799055783040', 'a10': [-2.732050807568877, 0.0], 'a2': [-2.732050807568877, 0.0], 'a3': [0.0, 0.0], 'a4': [5.464101615137754, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.2679491924311228, 0.0], 'a8': [-9.464101615137755, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.233941281861857, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 5], 'central_character': '405.1', 'coefficient_field': 'CDF', 'conductor': 405, 'conductor_radical': 15, 'conjugate': '2459960771778726717799055783040', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.732050807568877, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.2679491924311228, 0], [7.0, 0]], [[1.0, 0], [2.267949192431123, 0], [11.0, 0]], [[1.0, 0], [5.464101615137754, 0], [13.0, 0]], [[1.0, 0], [-0.7320508075688773, 0], [17.0, 0]], [[1.0, 0], [2.4641016151377544, 0], [19.0, 0]], [[1.0, 0], [-3.4641016151377544, 0], [23.0, 0]], [[1.0, 0], [7.196152422706632, 0], [29.0, 0]], [[1.0, 0], [3.0, 0], [31.0, 0]], [[1.0, 0], [-0.7320508075688773, 0], [37.0, 0]], [[1.0, 0], [-3.196152422706632, 0], [41.0, 0]], [[1.0, 0], [10.196152422706632, 0], [43.0, 0]], [[1.0, 0], [5.267949192431122, 0], [47.0, 0]], [[1.0, 0], [-3.267949192431123, 0], [53.0, 0]], [[1.0, 0], [11.732050807568877, 0], [59.0, 0]], [[1.0, 0], [-4.0, 0], [61.0, 0]], [[1.0, 0], [3.4641016151377544, 0], [67.0, 0]], [[1.0, 0], [0.2679491924311227, 0], [71.0, 0]], [[1.0, 0], [-9.660254037844387, 0], [73.0, 0]], [[1.0, 0], [-8.535898384862245, 0], [79.0, 0]], [[1.0, 0], [8.196152422706632, 0], [83.0, 0]], [[1.0, 0], [5.196152422706632, 0], [89.0, 0]], [[1.0, 0], [-7.660254037844386, 0], [97.0, 0]], [[1.0, 0], [-14.660254037844387, 0], [101.0, 0]], [[1.0, 0], [7.464101615137754, 0], [103.0, 0]], [[1.0, 0], [15.464101615137755, 0], [107.0, 0]], [[1.0, 0], [19.92820323027551, 0], [109.0, 0]], [[1.0, 0], [-5.124355652982141, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-405-1.1-c1-0-9', '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/405/2/a/g/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [-1.3431199918236437e-120, 0.11610322714279203, 0.2340344709130254, 0.35469165626089333, 0.47730003091091133, 0.5989682293868607, 0.714564028317874, 0.8168818889485773, 0.8970706098686991, 0.9453034953467387, 0.9516807323653734, 0.9073446257038698, 0.805764324795639, 0.644113331545683, 0.42462686285955353, 0.15579336979723313, -0.14678873508808987, -0.4600661076564795, -0.7538620818469606, -0.9920139066465258, -1.1343840146353388, -1.1397299454195209, -0.9693158410789118, -0.5910376392600356, 0.01627366760619009, 0.8587965756780965, 1.9243946301848074, 3.180516371823973, 4.573765020210347, 6.031471658943917, 7.465432655392098, 8.777748459309512, 9.868446635708235, 10.644314747195251, 11.028141680864973, 10.967404054427917, 10.44136922584984, 9.46564177737104, 8.093366742820479, 6.412614165814636, 4.539881149192384, 2.6101168954790337, 0.7641466011571433, -0.8652232131019064, -2.166856324404403, -3.0630361101479378, -3.5177707220701993, -3.540450933958528, -3.1841910270865443, -2.5388531989908194, -1.7194772844157213, -0.8515079473603805, -0.05472636568773665, 0.5719378014766401, 0.9625761739741262, 1.091676876322839, 0.9755815922790656, 0.6677613597121411, 0.24859257200805296, -0.18880462641833223, -0.5544352801682565, -0.7764444531561369, -0.8127982084636596, -0.6576557168503564, -0.3413220612777941, 0.07623556955417703, 0.5171854254873955, 0.900835036359068, 1.1590932036890895, 1.2494827884185344, 1.1631763100296446, 0.9264035031945201, 0.5948160583653253, 0.24177185716107144, -0.05724196338753731, -0.24094725515094256, -0.27597115388538096, -0.16487106652486053, 0.05351870636994811, 0.31191812618305803, 0.529392302346988, 0.6302980755056269, 0.5634702501428357, 0.31736625340598634, -0.07259013771512848, -0.5268502439653678, -0.93513962162865, -1.1785098666051035, -1.1560558201165616, -0.8108863960674962, -0.1495364575043113, 0.7501869366829217, 1.745974048180606, 2.6526461529466454, 3.275768196894644, 3.4515209077945106, 3.0852039006666243, 2.180245059767581, 0.8507408654762457, -0.686745907716818, -2.142578403834931, -3.200824275110535, -3.575788142548113, -3.0680835597804332, -1.6093231666273562, 0.7140438462337694, 3.66375802138785, 6.880759089514018, 9.939888540884754, 12.419146495728805, 13.971100466195406, 14.3831146193594, 13.614773109443506, 11.804971279939666, 9.246891263868632, 6.335333847347083, 3.4963656351986843, 1.112798014300429, -0.5401440147206119, -1.3367058236136096, -1.3124247122358201, -0.6444979961140124, 0.39420773335940107, 1.4970621379769036, 2.387998431220831, 2.874684832036836, 2.8798468781107727, 2.4452342102392617, 1.7090216564945173, 0.8633898594035692, 0.10327448571731436, -0.4211623668074218, -0.6372303326115192, -0.5605349336864812, -0.28254498356557395, 0.06063281110600146, 0.32922829590285185, 0.4193086366995726, 0.29033212619982723, -0.026258758512732346, -0.4391657353819338, -0.8261851260940677, -1.071516238382444, -1.1007203749841143, -0.9033214656755649, -0.5365165703855428, -0.10880109760149308, 0.25193723440086696, 0.43673493408420716, 0.38908621708439145, 0.12357885788114438, -0.2764525424083934, -0.6823982061893122, -0.9588762654174482, -1.006419703665654, -0.7956667399315985, -0.38214534875345424, 0.10418866668894644, 0.49339780098089897, 0.625513077526311, 0.402247382686498, -0.17492374082583173, -0.9930233351734786, -1.8483056649504748, -2.496696372973197, -2.7223174102826713, -2.4061581604231725, -1.5751611941415735, -0.4155837464834425, 0.7570966505387108, 1.5681869341792023, 1.6788774542124625, 0.8834330507837919, -0.8171748607051026, -3.186843086120624, -5.782718103549654, -8.038161233745738, -9.383894555427819, -9.380096094803735, -7.827757006288563, -4.831020956102742, -0.7929865901728241, 3.6568956986921903, 7.78900353182875, 10.924976542438245, 12.579343079792688, 12.558175934455344, 10.991821323484192, 8.294760980990318, 5.063433879116245, 1.9378045992007478, -0.5392298273690745, -2.030959725594823, -2.45988001665335, -1.9950484999577454, -0.9812898927591086, 0.16776316354430953, 1.082686353227243, 1.5274828960868678, 1.4434270136980043, 0.9396991000405867, 0.23817979997504665, -0.4078975701750316, -0.7956600059497405, -0.8305722601636254, -0.5452106858955589, -0.07614395287398272, 0.3908078142801835, 0.6874344163457011, 0.719808142340773, 0.4967393975201916, 0.12182753906092304, -0.24691382329189807, -0.45529758879569654, -0.4088823871078558, -0.10746428630060643, 0.3535790571439535, 0.8155635056278664, 1.111455809194904, 1.1247820094186358, 0.8321977430653661, 0.31470706771776236, -0.26703109247046136, -0.7256514409820198, -0.9107228334028411, -0.7613380911276365, -0.32904946349849, 0.2378119408786013, 0.744288575055841, 1.0170387309655369, 0.9671455637670813, 0.624628995583178, 0.13045528649503754, -0.3140026296872098, -0.5249491252765963, -0.41546189859919247, -0.04712156005537317, 0.3680892786321429, 0.5225842158376739, 0.11277108596119953, -1.0450945477561602, -2.920080081484521, -5.22734755607432, -7.464891171235973, -9.024518443681796, -9.351803284927719, -8.11204818667709, -5.313423855496467, -1.3470545236190723, 3.0748018339261365, 7.072894598741544, 9.810565262533377, 10.703991414565085, 9.57555127453652, 6.706588168187624, 2.772730353388701, -1.3226796700812053], 'positive_zeros': ['1.94056688123354518976348832487330', '2.99718508586738244117959337162164', '5.30600954979009837211133848160254', '6.50951253662799041173106328615038', '7.31996317957000879743322008349490', '8.103368373131588726861552509454161', '9.222697266578735014282348495177995', '9.722832552934395336803449497776851', '10.47901817533946089705980451277083'], 'prelabel': '2-405-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7983162352216746, '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': '1.94056688123354518976348832487', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.99718508586738244117959337162', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.30600954979009837211133848160', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.233941281861857, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 405, 'conductor_radical': 15, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/405/2/a/g/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': '2-405-1.1-c1-0-9', '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': '2-405-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7983162352216746, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.94056688123354518976348832487', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2459960771778726717799055783040', 'Lhash_array': ['2459960771778726717799055783040'], 'label': '2-405-1.1-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/2/a/g/1/1'}