-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3363443588430400426233428741450', 'a10': [9.0, 15.588457268119896], 'a2': [-1.0, 1.7320508075688772], 'a3': [2.5, 4.330127018922194], 'a4': [-2.0, -3.4641016151377544], 'a5': [4.5, -7.794228634059948], 'a6': [-10.0, 3.111507638930571e-61], 'a7': [-14.0, -12.12435565298214], 'a8': [8.0, 0.0], 'a9': [1.0, -1.7320508075688772], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.826026740080369, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, -1.7320508075688772]]], [7, [[1.0, 0], [14.0, 12.12435565298214]]]], 'bad_primes': [2, 7], 'central_character': '14.9', 'coefficient_field': 'CDF', 'conductor': 14, 'conductor_radical': 14, 'conjugate': '5791102070762442892224478751270', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, -1.7320508075688772]], [[1.0, 0], [-2.5, -4.330127018922194], [-13.5, 23.382685902179844]], [[1.0, 0], [-4.5, 7.794228634059948], [-62.5, -108.25317547305482]], [[1.0, 0], [14.0, 12.12435565298214]], [[1.0, 0], [-28.5, -49.363448015713004], [-665.5, 1152.6798124370878]], [[1.0, 0], [70.0, 0], [2197.0, 0]], [[1.0, 0], [25.5, 44.16729559300637], [-2456.5, 4254.782808792947]], [[1.0, 0], [2.5, -4.330127018922194], [-3429.5, -5940.068244557465]], [[1.0, 0], [34.5, -59.75575286112627], [-6083.5, -10536.931087845265]], [[1.0, 0], [-114.0, 0], [24389.0, 0]], [[1.0, 0], [11.5, 19.91858428704209], [-14895.5, 25799.76280414221]], [[1.0, 0], [-126.5, 219.10442715746296], [-25326.5, -43866.78477789317]], [[1.0, 0], [42.0, 0], [68921.0, 0]], [[1.0, 0], [124.0, 0], [79507.0, 0]], [[1.0, 0], [100.5, -174.07110616067217], [-51911.5, -89913.35549711177]], [[1.0, 0], [-196.5, -340.3479836872844], [-74438.5, 128931.26403921588]], [[1.0, 0], [109.5, 189.65956342879207], [-102689.5, 177863.43140384424]], [[1.0, 0], [-354.5, 614.012011283167], [-113490.5, -196571.31217639567]], [[1.0, 0], [209.5, 362.86464418567977], [-150381.5, 260468.39851841913]], [[1.0, 0], [96.0, 0], [357911.0, 0]], [[1.0, 0], [-156.5, -271.0659513845293], [-194508.5, 336898.604504011]], [[1.0, 0], [230.5, -399.2377111446262], [-246519.5, -426984.29905647587]], [[1.0, 0], [588.0, 0], [571787.0, 0]], [[1.0, 0], [-508.5, 880.7478356487741], [-352484.5, -610521.062880512]], [[1.0, 0], [1834.0, 0], [912673.0, 0]], [[1.0, 0], [-142.5, -246.81724007856502], [-515150.5, 892266.8395445109]], [[1.0, 0], [-249.5, 432.1466764884349], [-546363.5, -946329.3414011582]], [[1.0, 0], [-553.5, 958.6901219893736], [-612521.5, -1060918.3587283]], [[1.0, 0], [461.5, 799.3414476930369], [-647514.5, 1121528.0126375577]], [[1.0, 0], [-1542.0, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-14-7.2-c3-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/14/4/c/a/9/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [0.9179932624685974, 0.8884274939708666, 0.8645270052331742, 0.844699180588219, 0.8270500123613765, 0.8094049251710231, 0.789329415521619, 0.7641513579832973, 0.7309891721638829, 0.6867917050556056, 0.6283962789767871, 0.552610911030858, 0.4563254254497235, 0.3366542459580967, 0.19111118599616678, 0.0178136067504076, -0.184290065432062, -0.41517919210993837, -0.6735197809937586, -0.9564408236523788, -1.2593490214416219, -1.575805417772695, -1.8974887629383865, -2.214269949591452, -2.5144191089158565, -2.7849615783591006, -3.012190731712099, -3.182334623784847, -3.28235986465944, -3.3008807691817585, -3.229125663312966, -3.0618966653885833, -2.798445991856937, -2.443182747814116, -2.006121163708098, -1.5029860593703581, -0.954905257223519, -0.38764234782431173, 0.16964366986848575, 0.6860842081028157, 1.1311581639729882, 1.4769979188066111, 1.7007770597785057, 1.7869764920685127, 1.729303891790457, 1.5320393222283752, 1.2106012637965837, 0.7911742985300864, 0.30931163379365445, -0.19248114290555696, -0.668067153870849, -1.0716783506648129, -1.362264929403054, -1.5077819497764082, -1.488953608910384, -1.302054395320653, -0.960298826299487, -0.4935395919045532, 0.053867152735082524, 0.6269730628016555, 1.1656521462408278, 1.6110335155680693, 1.9122886933069352, 2.0329921507719533, 1.9562408321564613, 1.6877861177683544, 1.2566045230084155, 0.7126021364788854, 0.12148850796044851, -0.4427688405780476, -0.9071351524798364, -1.2092717484964786, -1.3066147488778814, -1.1834813829019464, -0.8550618890343027, -0.36747711268735617, 0.20644583970115638, 0.7754567041139647, 1.2414038550983164, 1.512636897881814, 1.5175395503815514, 1.2162689628849253, 0.608872409762559, -0.2616718078721455, -1.3123146032098973, -2.428714837721492, -3.4790732848148287, -4.331335536562267, -4.871446324163729, -5.020014976827626, -4.744815688392513, -4.067019592352116, -3.059896070146486, -1.8398214795227168, -0.5506350117410655, 0.6565067311340811, 1.6447941548543732, 2.311576057007769, 2.603094407200755, 2.521617690973989, 2.123614142075581, 1.509068377182514, 0.8035662812851626, 0.1360882373965295, -0.38368779873530273, -0.684547750720107, -0.7458349335566175, -0.6001069227370135, -0.3256466321895759, -0.029993644491746557, 0.17258790716746886, 0.18550383136504137, -0.0486587358738425, -0.5339017721551869, -1.217041732164246, -1.995643950846775, -2.7366431327455003, -3.3024215139534907, -3.579427746746016, -3.503620429243786, -3.0773293029682116, -2.3735536197443934, -1.5260430268720226, -0.7063143047040645, -0.09150235909438767, 0.17094327302637588, -0.005298651311512789, -0.6244703915759099, -1.6031309143344123, -2.781865229627665, -3.9528149442351026, -4.89819677401248, -5.432463706317691, -5.439657712578847, -4.898115716566905, -3.886984659634102, -2.5725759969235815, -1.1767446322603228, 0.06665269090186028, 0.9584290005176923, 1.3741239532577485, 1.288817362795288, 0.7811042704112767, 0.015001406860120371, -0.7966592106393705, -1.439634763976053, -1.7461822698882086, -1.632828540734149, -1.1193835106045529, -0.3246230340793007, 0.5607318587061251, 1.3179079936066134, 1.7510097993458185, 1.733317388460307, 1.238123575975741, 0.34668054074634236, -0.7689344681698509, -1.884336109066554, -2.7738820716274044, -3.262260096611631, -3.2642863965548043, -2.8032522845003354, -2.0032416719011708, -1.057170794554203, -0.17833998922681063, 0.4524809767675204, 0.7311063344443356, 0.653839799842927, 0.3149213664469654, -0.12206167410521118, -0.47155954568684616, -0.5798632782221376, -0.3708913287982802, 0.12879635218586508, 0.7933871141200539, 1.4298729926793363, 1.8312897509661579, 1.8375484665548298, 1.3875167772343064, 0.5474932501058708, -0.4932454410926823, -1.46083394366626, -2.061142872770654, -2.054688193555669, -1.3231206792067483, 0.09052182171377694, 1.979675996603281, 4.012769172117126, 5.804520958825314, 7.003385987559769, 7.373735626300352, 6.852042924805559, 5.562436007074175, 3.7870782560498646, 1.8983583589363933, 0.26980390500799034, -0.8117168090776986, -1.2101719451304502, -0.9647530758957851, -0.268833381281374, 0.5900374808056775, 1.312242668426399, 1.6676432799931113, 1.5543190315944595, 1.0188673599362266, 0.23360210176482984, -0.5617215578072482, -1.1359267654596372, -1.337453033893412, -1.139292789826449, -0.6445235009575532, -0.05094426182688464, 0.414301616844674, 0.5699756302816261, 0.34240443603382653, -0.2061586242675174, -0.8923285646372898, -1.4662727093197443, -1.6905178072243983, -1.4190728060891906, -0.6520720839487981, 0.45225281732180045, 1.6140294082114814, 2.507717505325074, 2.856199993982831, 2.515185031805497, 1.5219726924552774, 0.09249502741605468, -1.434338201434655, -2.690009273802089, -3.380585064057437, -3.3707479463565098, -2.721927465116655, -1.6720748152663591, -0.5621088853200421, 0.2694950331772779, 0.5922056962327296, 0.3564694886658686, -0.289033382529098, -1.042514336112494, -1.5439899240066592, -1.491593389953023, -0.7435049935227731, 0.6267340919292035, 2.3401003417047512, 3.985964159901941, 5.138907988422655, 5.483679310263609, 4.910261947604902, 3.549599887921829, 1.7383628637510637, -0.07713700172177583, -1.4689445221999233, -2.148477765475178, -2.0437985554523017, -1.3100531006173615, -0.2709692014296453], 'positive_zeros': ['2.65328915382901394963039405638191', '6.62525929767708568596055772993536', '8.545662963510313431303726219308188', '10.17866315908668252753946338986827', '11.98950982979369141487438511313117', '13.29749318027771018416356786077907', '14.54147840467397320909262650281576', '16.60088533217385288874447020366855', '18.14594227112232935887102024855180', '19.18029280225304998422878326827368'], 'prelabel': '2-14-7.2-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9088601322977969, 'root_angle': -0.14649371361272054, 'root_number': '0.6054643436493674 - 0.7958724323465669*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.146493713613', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.65328915382901394963039405638', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.62525929767708568596055772994', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.545662963510313431303726219308', 'prec': 107}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.826026740080369, 'bad_primes': [2, 7], 'central_character': '7.2', 'conductor': 14, 'conductor_radical': 14, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/14/4/c/a/9/1'], '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': '2-14-7.2-c3-0-0', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-14-7.2-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9088601322977969, 'root_angle': -0.14649371361272054, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.65328915382901394963039405638', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3363443588430400426233428741450', 'Lhash_array': ['3363443588430400426233428741450'], 'factors': ['2-14-7.2-c3-0-0'], 'label': '2-14-7.2-c3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/14/4/c/a/9/1'}