-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '6457268689446145708595529609989', 'a10': [3.0, 1.0], 'a2': [-1.0, -1.0], 'a3': [0.0, 0.0], 'a4': [0.0, 2.0], 'a5': [-2.0, 1.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [2.0, -2.0], 'a9': [0.0, -3.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.15970080404256085, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 1.0]]], [5, [[1.0, 0], [2.0, -1.0]]]], 'bad_primes': [2, 5], 'central_character': '20.7', 'coefficient_field': 'CDF', 'conductor': 20, 'conductor_radical': 10, 'conjugate': '4606030782759158937396950496407', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 1.0]], [[1.0, 0], [0, 0], [0, 3.0]], [[1.0, 0], [2.0, -1.0]], [[1.0, 0], [0, 0], [0, -7.0]], [[1.0, 0], [0, 0], [-11.0, 0]], [[1.0, 0], [1.0, -1.0], [0, -13.0]], [[1.0, 0], [-3.0, -3.0], [0, 17.0]], [[1.0, 0], [0, 0], [19.0, 0]], [[1.0, 0], [0, 0], [0, 23.0]], [[1.0, 0], [0, -4.0], [-29.0, 0]], [[1.0, 0], [0, 0], [-31.0, 0]], [[1.0, 0], [7.0, 7.0], [0, 37.0]], [[1.0, 0], [8.0, 0], [41.0, 0]], [[1.0, 0], [0, 0], [0, 43.0]], [[1.0, 0], [0, 0], [0, -47.0]], [[1.0, 0], [-9.0, 9.0], [0, -53.0]], [[1.0, 0], [0, 0], [59.0, 0]], [[1.0, 0], [-12.0, 0], [61.0, 0]], [[1.0, 0], [0, 0], [0, -67.0]], [[1.0, 0], [0, 0], [-71.0, 0]], [[1.0, 0], [11.0, -11.0], [0, -73.0]], [[1.0, 0], [0, 0], [79.0, 0]], [[1.0, 0], [0, 0], [0, 83.0]], [[1.0, 0], [0, 16.0], [-89.0, 0]], [[1.0, 0], [-13.0, -13.0], [0, 97.0]], [[1.0, 0], [-2.0, 0], [101.0, 0]], [[1.0, 0], [0, 0], [0, 103.0]], [[1.0, 0], [0, 0], [0, -107.0]], [[1.0, 0], [0, 6.0], [-109.0, 0]], [[1.0, 0], [1.0, -1.0], [0, -113.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-20-20.7-c1-0-0', '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/20/2/e/a/7/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [0.42884560674967936, 0.4450208283328996, 0.478739668480985, 0.5301432443030899, 0.5991412747648811, 0.6856258265222448, 0.7895173283030188, 0.9106657983296447, 1.0486732713372322, 1.2026881398261466, 1.3711993135495053, 1.551845523346, 1.741251629802604, 1.9349048483727103, 2.127086116969663, 2.310873640985849, 2.4782360069103926, 2.6202305874310508, 2.7273188899418814, 2.7898038134907654, 2.7983844691472117, 2.744812548556967, 2.6226207890108872, 2.4278798443440452, 2.159926164757838, 1.8219919749951359, 1.4216609977556371, 0.9710721275762474, 0.4867995750084969, -0.010646617278091812, -0.4977307599973382, -0.9492092459567875, -1.3398108924682848, -1.646188673684611, -1.8490051320056853, -1.9349725010745724, -1.8986386334389378, -1.7436973205666109, -1.4836118673945384, -1.1413775143410494, -0.7483126026516811, -0.3418580572572569, 0.03752616316357641, 0.350160331316375, 0.5613174964265994, 0.6453507078228499, 0.5892951085129485, 0.39545334936599624, 0.08252114828084792, -0.3150772048205927, -0.7497995779422059, -1.1654767847821665, -1.5033683571208165, -1.709222279477878, -1.7405689736651024, -1.5733433776917962, -1.2068953711731636, -0.6665389270699116, -0.0030104995450627803, 0.7114544963504035, 1.3902928414243678, 1.9424345325041408, 2.283736524036326, 2.34864475998282, 2.1005088450343314, 1.5389879256700416, 0.7032307377347504, -0.33002021902746276, -1.453604143922491, -2.5418525657424813, -3.465944002319541, -4.110782859103304, -4.391084112854788, -4.26426500015746, -3.7380298589543273, -2.8711767799095154, -1.767087034375138, -0.5604566864970996, 0.6010706401474796, 1.5777928200053069, 2.2582169774016654, 2.5754755349763028, 2.5171078131624056, 2.126374594463702, 1.4946012678911544, 0.7455478953219418, 0.014228372699948102, -0.5763157922781431, -0.9362605987090177, -1.0244152249691643, -0.8548546929420274, -0.49331108140022567, -0.04372005894772157, 0.3727942377977356, 0.6426572961961741, 0.683567449912637, 0.46244598082977373, 0.0037790546998146476, -0.6137362084422415, -1.2720534511582715, -1.8375810935083716, -2.189365391898331, -2.245911755314619, -1.9848505688319407, -1.4508177857201376, -0.7491443358340065, -0.025837319033901716, 0.5626778153149831, 0.8841349055601405, 0.8620594612113961, 0.49732239720300747, -0.1258277035713298, -0.8516997986601744, -1.4817643918660024, -1.8149007657149598, -1.6913725003028548, -1.031260290884535, 0.141334839191643, 1.6944761668398258, 3.407078070032632, 5.007448682521809, 6.2245784368782315, 6.841911895339268, 6.742281695093397, 5.934076047415915, 4.552375884405817, 2.8340256873591247, 1.0712857845801809, -0.44641937522535075, -1.4902432593271073, -1.9365549612063127, -1.7885667553922915, -1.170087781361234, -0.29283925840119784, 0.59512007404444, 1.2678404660903042, 1.5730772355400024, 1.464866688090925, 1.0094366186672978, 0.3632742725339363, -0.27096133995415705, -0.6994379735890449, -0.7889958561966987, -0.502484887230314, 0.09161435744484417, 0.8378821559959574, 1.5361367794829148, 1.995959080687985, 2.088929689605103, 1.7842825541521032, 1.1578889400479566, 0.37156576755728593, -0.37216835930224934, -0.8877698480992441, -1.060766731508445, -0.8826796430595373, -0.4559746164466822, 0.033691653120434116, 0.3714654489955034, 0.37922123248775635, -0.02508534037305923, -0.7923208036128868, -1.7431420167955483, -2.6072830393345705, -3.0926698123092575, -2.9668962120160955, -2.1290136057883617, -0.6509296178953162, 1.2250741503551237, 3.134821459192018, 4.676269965179775, 5.508343918678837, 5.438783896531001, 4.477089869153563, 2.8371828714661036, 0.8875302059131422, -0.9393236096187749, -2.254538348147767, -2.8095806808122408, -2.5557239570222126, -1.650353734951314, -0.40848466589580107, 0.786953688872381, 1.5910004289365547, 1.7891527107915863, 1.3507972928141034, 0.4292032365517465, -0.6908400407761238, -1.6814960522212654, -2.2698417397324233, -2.3162066372525483, -1.8499906282535081, -1.0531458668775127, -0.19754060215678715, 0.4434854448277246, 0.6812712581747299, 0.46856166788755543, -0.09080599757550689, -0.7817430268552346, -1.353762846074063, -1.6075702521675468, -1.4634490252221104, -0.9882850136682606, -0.3715802160804459, 0.14218234543569183, 0.3424934644769808, 0.1328494016393128, -0.4263792046150009, -1.1288797910895134, -1.6860855798331096, -1.8244772480981843, -1.3848950178381867, -0.3898545173640028, 0.9462133571504824, 2.27106680697934, 3.199189329732544, 3.435188501160118, 2.876398852460787, 1.6596589261776191, 0.13365964326756166, -1.238379341333825, -2.018030628756718, -1.9303748014757047, -0.9578026013920721, 0.6427971093029536, 2.4078169812598316, 3.801177542701039, 4.3748109692465995, 3.9057767338819422, 2.4667646082099948, 0.4071459105694381, -1.7501683685735634, -3.4640388080411926, -4.333883833023181, -4.212245543130602, -3.2365711585094155, -1.7720158137541984, -0.28598651523586216, 0.8030098702737749, 1.2521731967214846, 1.0561808897038052, 0.4261592185522759, -0.3033153784168593, -0.8039659522038485, -0.8733341784184407, -0.5019736233038822, 0.134069317945102, 0.7504185447707156, 1.0707659434673829, 0.9380109392868793, 0.3779581526424485, -0.40869129630547185, -1.1232858026996064, -1.4861175478307302, -1.3486462946127569, -0.7574154955677163, 0.056426993134613086], 'positive_zeros': ['5.09388682361178306352765485359104', '7.36427401884056470781626500805036', '8.476557285997462789360043827499739', '10.19606565450750423970831368887720', '11.72375060446644028152469300010512', '13.61776821454158890200258592320509', '15.12087754482813165213151877279967', '16.18889154393944071424592053478892', '17.05197663834121013206113169629376', '18.63950642032327279407698589487207'], 'prelabel': '2-20-20.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.399625830049261, 'root_angle': 0.1762081911747834, 'root_number': '0.8506508083520399 + 0.5257311121191337*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0881040955874', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '5.09388682361178306352765485359', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '7.36427401884056470781626500805', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.476557285997462789360043827500', 'prec': 107}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.15970080404256085, 'bad_primes': [2, 5], 'central_character': '20.7', 'conductor': 20, 'conductor_radical': 10, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/20/2/e/a/7/1'], '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': '2-20-20.7-c1-0-0', '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': '2-20-20.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.399625830049261, 'root_angle': 0.0881040955873917, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '5.09388682361178306352765485359', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '6457268689446145708595529609989', 'Lhash_array': ['6457268689446145708595529609989'], 'label': '2-20-20.7-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/20/2/e/a/7/1'}