-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1499542124727475452437263713512', 'a10': [1.0, -5.034525116044599e-61], 'a2': [-0.8090169943749475, -0.5877852522924731], 'a3': [0.30901699437494745, -0.9510565162951535], 'a4': [0.30901699437494745, 0.9510565162951535], 'a5': [-0.8090169943749475, 0.5877852522924731], 'a6': [-0.8090169943749475, 0.5877852522924731], 'a7': [0.8863606526745702, 2.7279375887364377], 'a8': [0.30901699437494745, -0.9510565162951535], 'a9': [-0.8090169943749475, -0.5877852522924731], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.6350632667022538, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8090169943749475, 0.5877852522924731]]], [3, [[1.0, 0], [-0.30901699437494745, 0.9510565162951535]]], [5, [[1.0, 0], [0.8090169943749475, -0.5877852522924731]]], [11, [[1.0, 0], [-3.129539309367513, 1.0981728967350777]]]], 'bad_primes': [2, 3, 5, 11], 'central_character': '330.301', 'coefficient_field': 'CDF', 'conductor': 330, 'conductor_radical': 330, 'conjugate': '1852647162135183643879777849242', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [-0.8863606526745702, -2.7279375887364377], [-5.663118960624632, 4.114496766047312]], [[1.0, 0], [-3.129539309367513, 1.0981728967350777]], [[1.0, 0], [-4.2546839773105605, -3.091208852739118], [4.017220926874317, 12.363734711836996]], [[1.0, 0], [0.12514466794304763, -0.09092292341373327], [5.253288904374106, -16.167960777017612]], [[1.0, 0], [-0.4521989903565752, 1.3917253881477027], [-15.371322893124, -11.16791979355699]], [[1.0, 0], [-3.786942663735446, 0], [23.0, 0]], [[1.0, 0], [1.0773436582996228, 3.3157228410289106], [-23.461492836873475, 17.04577231648172]], [[1.0, 0], [2.4155456625072245, 1.754996652150383], [9.57952682562337, 29.48275200514976]], [[1.0, 0], [-2.73606797749979, -8.420751370943494], [-29.933628791873055, 21.748054334821507]], [[1.0, 0], [-2.5999966607113145, 8.001966919381847], [-33.16969676937284, -24.099195343991397]], [[1.0, 0], [-7.862891249098615, 0], [43.0, 0]], [[1.0, 0], [3.397865973292188, -10.457556167529336], [-38.02379873562253, -27.625906857746237]], [[1.0, 0], [8.556590292492356, 6.216726742213526], [16.377900701872214, 50.405995363643136]], [[1.0, 0], [-2.449703985536534, -7.539413627238396], [-47.7320026681219, 34.67932988525592]], [[1.0, 0], [1.4049766524853409, -1.020775288885209], [18.850036656871794, -58.014447494004365]], [[1.0, 0], [11.240582528355725, 0], [67.0, 0]], [[1.0, 0], [2.8683233246359903, -2.0839588794177737], [21.940206600621266, -67.52501265695591]], [[1.0, 0], [1.8541019662496845, 5.706339097770922], [-59.05824058937116, 42.90832341735054]], [[1.0, 0], [-5.492889320806847, -3.9908176931926564], [24.412342555620846, 75.13346478731714]], [[1.0, 0], [-1.2360679774997898, 0.8980559531591708], [25.648410533120636, -78.93769085249775]], [[1.0, 0], [10.88590189033385, 0], [89.0, 0]], [[1.0, 0], [15.731214573734604, 11.429396404995915], [29.974648454369902, 92.2524820806299]], [[1.0, 0], [3.3612126454428375, 2.442063932583626], [31.210716431869688, 96.05670814581052]], [[1.0, 0], [-1.6882669678563649, -5.195951453328317], [-83.32875042061958, 60.54188098612473]], [[1.0, 0], [4.8771126074849205, -15.010209181006212], [-86.56481839811937, -62.893021995294625]], [[1.0, 0], [5.52786404500042, 0], [109.0, 0]], [[1.0, 0], [-0.8500649636487633, 2.616230944151279], [-91.41892036436906, -66.41973350904946]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-330-11.4-c1-0-2', '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/330/2/m/e/301/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.1082979688540846, 1.0959449825319343, 1.0757952056100832, 1.0428226534737681, 0.9899630162321732, 0.9089273478530445, 0.791099344822026, 0.6284323797385892, 0.4143222586637625, 0.14445285889068302, -0.1823994062812602, -0.5636416256686647, -0.9922851856034891, -1.4565924350094348, -1.9400357126012662, -2.421647716192934, -2.876821365580752, -3.2785836329581834, -3.5993229078485527, -3.812896380690664, -3.896987283578866, -3.835527675246125, -3.620957909500101, -3.256066478926111, -2.7551505665668277, -2.14426379872538, -1.4603761692748976, -0.7493611079232528, -0.06284114635750082, 0.5459429111862292, 1.0269375759081114, 1.3383317158259147, 1.4513434393855478, 1.3541773019947458, 1.0546085366305622, 0.5807391404366237, -0.02037164413637341, -0.6862824741866136, -1.3447731273473689, -1.9210287851468273, -2.3457112700570533, -2.5630347427094056, -2.537867185885952, -2.2609003610357696, -1.7510820455824119, -1.0547806079808868, -0.24153008290993308, 0.6033572199606256, 1.3885791406169818, 2.0279147423018467, 2.4511923267456712, 2.613672755605862, 2.502473950360968, 2.1389782523599807, 1.5766620187766465, 0.8944090854071118, 0.1860337341663559, -0.4526534825055978, -0.9374515466962713, -1.208048832523331, -1.2370618992973266, -1.0343071968464241, -0.6454386744435459, -0.144928695898595, 0.375723609553688, 0.8228481292288691, 1.1162172965309018, 1.2028577122582214, 1.066661422575184, 0.7319785812662302, 0.2603044011326931, -0.2596796784935599, -0.7272725279918097, -1.0476860573245335, -1.1496658513115672, -0.9995933076718536, -0.609305151968799, -0.035841791648721276, 0.6272930235591073, 1.266234489682839, 1.7676491974685453, 2.0407764987247448, 2.0365123054326646, 1.759701459748119, 1.2718204912405124, 0.6828561087417732, 0.13315450866470438, -0.232016027106716, -0.2908573464763335, 0.02882245441834086, 0.7308871152387483, 1.7436795125955817, 2.9265685646618027, 4.089985392012728, 5.026117421488196, 5.54521849973839, 5.51110556507323, 4.869170822331402, 3.661262404000405, 2.0239549367654126, 0.16968981303655337, -1.6465190614950453, -3.169259855173012, -4.186302264945306, -4.56554731205601, -4.27829161557172, -3.404142683613872, -2.1163130899284477, -0.649775229761452, 0.7418641738438984, 1.8326035483341792, 2.4645002423279254, 2.5744780201146575, 2.202278567577852, 1.4781075435347109, 0.5926433213172597, -0.24430047092338902, -0.847812996259723, -1.095419432404694, -0.950294582688395, -0.46542099974116996, 0.2319143247834876, 0.9715947102454481, 1.5809129314576358, 1.9244255070471201, 1.9343688250936713, 1.624732828823439, 1.0858384628759379, 0.4607867027769901, -0.09059065230082507, -0.43164372669399154, -0.4830325089315807, -0.24268544155077107, 0.21349764671177143, 0.7506858800968454, 1.2095575656159159, 1.4478929972238028, 1.3790712625720236, 0.997673452748668, 0.3852715942355439, -0.30583323352944475, -0.8877531259016955, -1.1830395666898499, -1.0705653820779832, -0.5198159215149226, 0.3954542304656727, 1.508501031264003, 2.5941108968550877, 3.4188486641544573, 3.7953421100053832, 3.627474656983591, 2.9351305653909043, 1.851802353135773, 0.5948734145444368, -0.5848298784057998, -1.4622559537416928, -1.891608188961782, -1.8406008351954624, -1.3964672526543604, -0.7415979207086112, -0.10435985632475098, 0.30283117302983076, 0.3424579174760823, -0.007608703104304195, -0.6433142456476039, -1.3572649485007555, -1.8905749006821047, -2.0013692777381533, -1.5327794811714552, -0.4626946974743582, 1.0784831957468006, 2.8281561497671097, 4.4464642850317375, 5.593397916936256, 6.009539211304896, 5.580327962627332, 4.367287347150095, 2.5975292171826103, 0.6131775322157975, -1.2074933340394438, -2.5380388598249417, -3.1791665124783917, -3.102552002934328, -2.452120509339642, -1.5025280566691166, -0.5855314459553508, -0.0032180011049794217, 0.049526503756679226, -0.4666462700139925, -1.4286980738415764, -2.5872029178620166, -3.635245866094889, -4.291601451992672, -4.3758754494985235, -3.855591625550309, -2.8528974622359695, -1.6095761989950537, -0.4203897212415363, 0.4466688027586302, 0.8212206025294162, 0.6731294309744358, 0.115619488791768, -0.6312801763344594, -1.3060177306960727, -1.6806236831385613, -1.624189299849703, -1.13685697362365, -0.3451552360950898, 0.539195143935517, 1.284258414559736, 1.7070552953457578, 1.726291840682796, 1.3830905027872036, 0.8239028013356974, 0.25129373480442485, -0.14187132267270433, -0.23413340131381488, -0.013472350152971746, 0.42069624169680747, 0.892732019378338, 1.2125458768515662, 1.2444935663970416, 0.9609661647830068, 0.46223343011832774, -0.04595784619159055, -0.3124665936232434, -0.12170208146440287, 0.6290054989321344, 1.880454526792394, 3.408622314775129, 4.872215275424704, 5.900035851719743, 6.194722614059005, 5.623068457054568, 4.265403034401661, 2.407154203557449, 0.4718700057347228, -1.0878993698985695, -1.912444982235971, -1.8351620409919962, -0.9319057285511783, 0.49616635407096243, 2.003172303884004, 3.1210873329271465, 3.4903552544711522, 2.9615955088086907, 1.6391814911197322, -0.14621146457858164, -1.9287051987120192, -3.2362387761263305, -3.720799052975246, -3.2528257741597373, -1.95325175250559, -0.15489479972170134, 1.6944690309480004, 3.158187284393937, 3.928767600260593], 'positive_zeros': ['1.18293015792955567605190311919623', '3.51203686311743178630289471281174', '4.49604526325548448957536474643237', '5.78562441477758387290308072624539', '7.03429197311164416124107814091405', '7.909303324863012373695243699847919', '8.812532251353467455192381034648509', '9.632014297824354451222270554450918', '10.78689746364518544306711154941674', '11.11787134959940746572769417936300'], 'prelabel': '2-330-11.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.62328779540236, 'root_angle': 0.08500886934132909, 'root_number': '0.9645500655622818 + 0.26389992615345254*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0425044346707', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.18293015792955567605190311920', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.51203686311743178630289471281', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.49604526325548448957536474643', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.6350632667022538, 'bad_primes': [2, 3, 5, 11], 'central_character': '11.4', 'conductor': 330, 'conductor_radical': 330, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/330/2/m/e/301/2'], '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': '2-330-11.4-c1-0-2', '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': '2-330-11.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.62328779540236, 'root_angle': 0.042504434670664545, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.18293015792955567605190311920', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1499542124727475452437263713512', 'Lhash_array': ['1499542124727475452437263713512'], 'label': '2-330-11.4-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/330/2/m/e/301/2'}