-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '988450520108209884655823970915', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.0673972285404627, 1.3640612730021109], 'a4': [0, 0], 'a5': [-0.34982785653220866, -0.6059196214167014], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [-0.7213263130082783, -2.9119904447236573], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.085610916553867, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0673972285404627, -1.3640612730021109]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '1764.509', 'coefficient_field': 'CDF', 'conductor': 1764, 'conductor_radical': 42, 'conjugate': '991655512383149551245540368528', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0673972285404627, -1.3640612730021109]], [[1.0, 0], [0.34982785653220866, 0.6059196214167014], [-2.5, 4.330127018922194]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.22968455234698068, -0.132608438126228], [5.5, 9.526279441628825]], [[1.0, 0], [1.1382279301574316, 0.6571562018755437], [6.5, 11.258330249197702]], [[1.0, 0], [-1.8639194435795374, -3.22840317749527], [-8.5, 14.722431864335457]], [[1.0, 0], [-0.38244872402037333, -0.22080687376439143], [9.5, 16.454482671904334]], [[1.0, 0], [4.299494607553523, -2.482314369050371], [11.5, -19.91858428704209]], [[1.0, 0], [0.27328651786161556, -0.15778204465329923], [14.5, -25.11473670974872]], [[1.0, 0], [0, 5.606318988632277], [-31.0, 0]], [[1.0, 0], [0.3511238706350093, -0.6081643836900779], [-18.5, -32.04293994002423]], [[1.0, 0], [-5.393543257948673, 9.341890955587672], [-20.5, -35.50704155516198]], [[1.0, 0], [-3.731313761232715, -6.462825013435989], [-21.5, 37.239092362730865]], [[1.0, 0], [-7.005701673570909, 0], [47.0, 0]], [[1.0, 0], [-8.519193604899469, 4.918558721067247], [26.5, -45.89934640057525]], [[1.0, 0], [-13.463630999981048, 0], [59.0, 0]], [[1.0, 0], [0, -5.652073542717741], [-61.0, 0]], [[1.0, 0], [5.941196936839257, 0], [67.0, 0]], [[1.0, 0], [0, -13.43229819247676], [-71.0, 0]], [[1.0, 0], [-6.661819598895202, 3.84620333871487], [36.5, -63.21985447626402]], [[1.0, 0], [-1.3967193979232333, 0], [79.0, 0]], [[1.0, 0], [-3.723990474405878, -6.450140708573507], [-41.5, 71.88010851410841]], [[1.0, 0], [5.592606419958775, -9.686678466104484], [-44.5, -77.07626093681505]], [[1.0, 0], [-9.182251091137926, 5.301375139235217], [48.5, -84.00446416709055]], [[1.0, 0], [8.75357465921981, -15.16163605761613], [-50.5, -87.4685657822283]], [[1.0, 0], [7.39775428661144, -4.2710954287738225], [51.5, -89.20061658979718]], [[1.0, 0], [-9.094885264188003, -5.2509344555277035], [53.5, 92.66471820493493]], [[1.0, 0], [7.121103806670353, 12.334113599125192], [-54.5, 94.39676901250381]], [[1.0, 0], [-13.378296313082505, -7.723962977656762], [56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-42e2-63.5-c1-0-11', 'leading_term': '1.221071227018973601733600243175685835307110526572887805', '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/1764/2/w/b/509/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.2210712270189736, 1.2047238236204025, 1.1764554293338647, 1.1362552736001001, 1.0839668867959336, 1.0193411785887654, 0.9421004736415614, 0.8520091173101293, 0.7489462623965331, 0.6329767931491612, 0.5044168908831698, 0.3638913606760563, 0.21238042153549275, 0.05125416136775457, -0.11770673709421996, -0.2923050641039024, -0.46993672327843844, -0.6476164459806553, -0.822019782685429, -0.9895412341457561, -1.1463679926822843, -1.288568317939874, -1.4121930790028439, -1.5133884695205007, -1.5885173633350487, -1.6342862477129443, -1.647874174910836, -1.6270597370930695, -1.5703417214221078, -1.4770488674025095, -1.3474340511163256, -1.1827482814212027, -0.9852901276534948, -0.7584266175364375, -0.5065822519828379, -0.23519357710701178, 0.04937227814063021, 0.33993556722363616, 0.6286576124773516, 0.9072280897709144, 1.1670823992751822, 1.3996442230993893, 1.5965870399976534, 1.750107151067438, 1.8531997270177996, 1.8999285743767582, 1.8856797881063119, 1.8073892579824267, 1.6637341629363158, 1.455279146701821, 1.1845688309301914, 0.8561596839840334, 0.47658600341936636, 0.05425684854747664, -0.40071688028798197, -0.8767634503598629, -1.3611549388726707, -1.8403683462639535, -2.3004933995363643, -2.7276748511505624, -3.108574985192931, -3.430840378623483, -3.6835558316267707, -3.8576678624066347, -3.946360322919816, -3.94536557305164, -3.853196263190461, -3.6712850995244977, -3.4040229505368975, -3.058689212310429, -2.6452723683325723, -2.1761830122420434, -1.665866081427328, -1.130323489955586, -0.5865625549760026, -0.0519893834435768, 0.4562304653525423, 0.9218193761920167, 1.3300170663256032, 1.6681655604372132, 1.9262241445893284, 2.0971906510356844, 2.1774085198339983, 2.166743230575222, 2.0686167632557346, 1.889894545733653, 1.6406256459178912, 1.3336435030327507, 0.984040971507878, 0.6085395677970425, 0.22477826038532103, -0.1494483618809063, -0.49696942538034844, -0.8019996347133799, -1.0508484048343183, -1.2325423829833726, -1.3393305271257891, -1.367045545312598, -1.3153015718604115, -1.1875152247457332, -0.990745346304609, -0.7353554092618197, -0.43451136181941497, -0.10353615379819817, 0.24085010823471675, 0.5813689054298059, 0.9010605169549453, 1.1841561767735915, 1.4169006815659992, 1.5882822220934556, 1.690629744800452, 1.7200438577353485, 1.676634962901354, 1.5645516015183356, 1.3917925145376524, 1.1698071407622386, 0.9129006325308026, 0.6374703660344055, 0.36111076106474793, 0.10163143599708051, -0.12396019554421184, -0.30045723924567924, -0.4153771872333763, -0.459758243912704, -0.42878024891226746, -0.32217036365194196, -0.14436418009597754, 0.09559461485582926, 0.3844190381643727, 0.7051965816120198, 1.0382340680866053, 1.362090225654718, 1.6547448285982247, 1.8948438874760463, 2.0629540315433355, 2.142756383179845, 2.1221111640757035, 1.9939290838925452, 1.7567941162162322, 1.415294219769976, 0.9800313655123694, 0.4672991504982104, -0.10156556242859872, -0.7011321267495901, -1.3030842290655493, -1.8776283241127116, -2.3950310084122752, -2.827204492624748, -3.149254134480702, -3.340901495358675, -3.3877007657557274, -3.2819755740385905, -3.023416774917911, -2.619299166819385, -2.0842953284715486, -1.4398868157109228, -0.7133956008996618, 0.06331942223712327, 0.8554360968514078, 1.6269313091544233, 2.342437950295619, 2.9690951726691766, 3.4782888829623606, 3.8471836355090345, 4.059957129448607, 4.108663924222011, 3.993674990262282, 3.7236632304911654, 3.3151308297983855, 2.7915007343873404, 2.1818201701537956, 1.519147330434181, 0.8387117566072689, 0.17595325622637562, -0.4354475116540916, -0.9654320233035145, -1.3892109357621438, -1.688597609031161, -1.8529485293807773, -1.8796541402701517, -1.7741504105180175, -1.5494504379674672, -1.2252247385805592, -0.8264867835615523, -0.3819650526346337, 0.07773723073862786, 0.5220797542940062, 0.9224985711825712, 1.2541747284146048, 1.4975460908259073, 1.63946626860496, 1.6739367689032358, 1.6023656898422425, 1.4333367697900998, 1.1819044618493886, 0.8684618641559826, 0.51725674952632, 0.1546546945786603, -0.19273422825804473, -0.4999388135156507, -0.7453921571468685, -0.9124581316108255, -0.9906130433960698, -0.9761991198269774, -0.872694911181927, -0.6904802429904564, -0.4461078745318552, -0.16112820041300766, 0.13945516240086178, 0.4289944289712391, 0.6811470239395254, 0.8718293900547294, 0.9810369816442531, 0.9943993983869228, 0.904356055644977, 0.7108625082602749, 0.42156899267309544, 0.05144887587670528, -0.3781069212939783, -0.8406754546673553, -1.306578201176583, -1.74492995498687, -2.1258200144541397, -2.4224732115983985, -2.613236526367327, -2.6832460536152882, -2.625648556515599, -2.442280608894711, -2.143744583348817, -1.748862095823032, -1.2835291699621036, -0.7790403082505647, -0.26998780506222564, 0.2081248417179677, 0.6213931178498489, 0.9399704697351594, 1.1403008290387229, 1.2069613871775444, 1.1339760790128597, 0.9254943894170308, 0.595772462901034, 0.16844125782870983, -0.3249036208878878, -0.8467072413865396, -1.35592893803696, -1.8108216174982381, -2.171829262272712, -2.4044028829648765, -2.48153678812075, -2.385842675235994, -2.1110078676857555, -1.6625242410812093, -1.0576233599555838, -0.3244077646011707, 0.4997755623807202, 1.3706197217349605, 2.2396529517631074], 'positive_zeros': ['0.77974997205874238154881648764050', '2.09933947743555807307715312117177', '3.11265401102460310356583558868039', '4.40035734869422157261677206278381', '5.30827590087902491369571606410186', '6.05287843913856321241231978838183', '6.99773234521987824029692641114758', '7.41965055533702294854602617623765', '8.310155657990479607455503402386542', '9.194520731742051067264317875747065'], 'prelabel': '2-42e2-63.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7530801905306883, 'root_angle': -0.15302092626686517, 'root_number': '0.886657856893346174647763238923069167191244138551058701 - 0.462426042529287547308822074587800812163649593010966311*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.07651046313343259', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.77974997205874238154881648764', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.09933947743555807307715312117', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.11265401102460310356583558868', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 14.085610916553867, 'bad_primes': [2, 3, 7], 'central_character': '63.5', 'conductor': 1764, 'conductor_radical': 42, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1764/2/w/b/509/3'], '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': '2-42e2-63.5-c1-0-11', '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': '2-42e2-63.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7530801905306883, 'root_angle': -0.07651046313343259, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.77974997205874238154881648764', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '988450520108209884655823970915', 'Lhash_array': ['988450520108209884655823970915'], 'label': '2-42e2-63.5-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1764/2/w/b/509/3'}