-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1962175221299149736101164069416', 'a10': [0, 0], 'a2': [0, 0], 'a3': [4.597288882620143, -2.4217627732164932], 'a4': [0, 0], 'a5': [0, 2.411117735848002], 'a6': [0, 0], 'a7': [0, -7.0], 'a8': [0, 0], 'a9': [15.27013014052552, -22.267086147303022], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.824641761928856, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-4.597288882620143, 2.4217627732164932]]], [7, [[1.0, 0], [0, 7.0]]]], 'bad_primes': [2, 3, 7], 'central_character': '336.239', 'coefficient_field': 'CDF', 'conductor': 336, 'conductor_radical': 42, 'conjugate': '1176562226185568563323233488907', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-4.597288882620143, 2.4217627732164932]], [[1.0, 0], [0, -2.411117735848002], [-125.0, 0]], [[1.0, 0], [0, 7.0]], [[1.0, 0], [-37.75071226521376, 0], [1331.0, 0]], [[1.0, 0], [24.82415826292883, 0], [2197.0, 0]], [[1.0, 0], [0, 22.238989797923956], [-4913.0, 0]], [[1.0, 0], [0, 68.44493910608195], [-6859.0, 0]], [[1.0, 0], [-44.46155744665687, 0], [12167.0, 0]], [[1.0, 0], [0, 178.08049647966604], [-24389.0, 0]], [[1.0, 0], [0, -109.91436246678299], [-29791.0, 0]], [[1.0, 0], [-168.15897558117467, 0], [50653.0, 0]], [[1.0, 0], [0, 383.22221822895204], [-68921.0, 0]], [[1.0, 0], [0, -371.3975067823775], [-79507.0, 0]], [[1.0, 0], [323.41751641127973, 0], [103823.0, 0]], [[1.0, 0], [0, 401.88541100203827], [-148877.0, 0]], [[1.0, 0], [34.0931560825075, 0], [205379.0, 0]], [[1.0, 0], [-25.47245384580443, 0], [226981.0, 0]], [[1.0, 0], [0, 118.40969155173724], [-300763.0, 0]], [[1.0, 0], [106.74271400885463, 0], [357911.0, 0]], [[1.0, 0], [-1016.987585798841, 0], [389017.0, 0]], [[1.0, 0], [0, -649.6757584356446], [-493039.0, 0]], [[1.0, 0], [-250.8121651519684, 0], [571787.0, 0]], [[1.0, 0], [0, 4.027908261723821], [-704969.0, 0]], [[1.0, 0], [454.70336694828467, 0], [912673.0, 0]], [[1.0, 0], [0, -1954.3135630587733], [-1030301.0, 0]], [[1.0, 0], [0, -981.0366899669609], [-1092727.0, 0]], [[1.0, 0], [-1587.1963237005134, 0], [1225043.0, 0]], [[1.0, 0], [1665.6785594889486, 0], [1295029.0, 0]], [[1.0, 0], [0, 1200.2669312531953], [-1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 27, 'label': '2-336-12.11-c3-0-27', 'leading_term': '2.626216230259914562217807090421825898904825053198663653', '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/336/4/h/a/239/9', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [2.6262162302599146, 2.729691443239354, 2.812930482798124, 2.8750190531710094, 2.915132131506835, 2.932543100473101, 2.926638543402944, 2.8969383925443926, 2.843120825232074, 2.7650510281251948, 2.6628127049152615, 2.5367409951285027, 2.387455306121606, 2.2158904409390003, 2.02332433413305, 1.811400687994553, 1.5821448344997409, 1.337971234934114, 1.0816811705480294, 0.8164493741788387, 0.5457986042110002, 0.2735614670938936, 0.0038291499693512143, -0.259112873979007, -0.5108616649262704, -0.7469851884390143, -0.963120780337754, -1.15508175272708, -1.3189697095733222, -1.4512896900469332, -1.5490648567144076, -1.6099471135250722, -1.6323197953486375, -1.61538843569804, -1.5592556095898162, -1.4649759789247354, -1.3345879493359007, -1.1711187866006287, -0.9785606384902343, -0.7618156592701191, -0.5266093272515217, -0.2793720621785043, -0.02709036316109585, 0.22287013304599002, 0.46296606791285017, 0.6856974571101261, 0.8838425489732532, 1.0506995194455597, 1.1803272350912148, 1.2677766886717998, 1.30930434554371, 1.3025585732294125, 1.2467305920052076, 1.1426620016789995, 0.9929019167672611, 0.8017080726806317, 0.5749879275909572, 0.3201777407248862, 0.04605980436596437, -0.2374796248030921, -0.5197466914394065, -0.7895831467070414, -1.0357465866899085, -1.2473157810405249, -1.4141073300796712, -1.5270884896787347, -1.578770116643344, -1.5635633909129505, -1.4780843234201164, -1.3213910950973404, -1.0951410012897764, -0.8036561748800548, -0.4538902775110423, -0.05529189656204934, 0.38043564917596656, 0.8396741525591827, 1.3073217192202697, 1.767302762737028, 2.2031402245843306, 2.5985699079417715, 2.938173924728196, 3.208008189546266, 3.396197798866076, 3.4934741205087105, 3.493628556627565, 3.393860253403836, 3.194998479692057, 2.9015848963927526, 2.5218063446430454, 2.067274898067571, 1.5526585101019574, 0.9951723619230097, 0.41394767342361455, -0.1706990406444662, -0.7380678227219596, -1.2679153771636973, -1.7412974857556323, -2.1413762462301795, -2.454154795357899, -2.669104102978657, -2.7796501202153334, -2.7834949424032582, -2.6827525242250694, -2.483887595255118, -2.197455426103048, -1.837649582680043, -1.4216743267384149, -0.9689673973853846, -0.5003070615037031, -0.03684409479295594, 0.40089565828319623, 0.7939896331882834, 1.1260287893030168, 1.3839127269166784, 1.5584871413736625, 1.6449879318459628, 1.6432652417544067, 1.5577713880886581, 1.3973085417155342, 1.1745445649766344, 0.9053179494885134, 0.607764649760321, 0.301310107185561, 0.005578278148916429, -0.2607245257789691, -0.48089013831460586, -0.6411927331610574, -0.7317196245193817, -0.7469984347132392, -0.6863802783371279, -0.5541511032077293, -0.3593578202202211, -0.11535160557725545, 0.16093307526021766, 0.44992949699336066, 0.7305712623101361, 0.9815459615554041, 1.1826004826697993, 1.315823304945775, 1.3668280008673033, 1.3257654193641328, 1.1880996082288253, 0.9550941749239661, 0.633970955164148, 0.23772079940739396, -0.2154339539470247, -0.7029052721324031, -1.1988934306041186, -1.6757708269795901, -2.1056216925352094, -2.4618521234891557, -2.720777879387679, -2.8630956968550065, -2.8751477344688694, -2.7498981634102653, -2.4875554767094306, -2.095793107609223, -1.589543427286131, -0.9903648882997778, -0.3254075661226566, 0.37397289935968403, 1.073880482608742, 1.7397318345206139, 2.338192223819605, 2.8390815803968956, 3.2171367489783256, 3.453521879212887, 3.5369914770154143, 3.4646294414222973, 3.242111423095263, 2.883465717249382, 2.410338011332471, 1.8507958206231394, 1.2377374558995777, 0.6069960073338456, -0.004750611912792132, -0.5621384751367524, -1.0332137474759715, -1.3913362355145324, -1.6167705007218427, -1.697862451865422, -1.6317239895135975, -1.4243783616245609, -1.0903525757154038, -0.6517383889934512, -0.13677779922899969, 0.4219396847285121, 0.9895545297778193, 1.5311567841975984, 2.014004411769138, 2.409595522873448, 2.69545782436853, 2.856536003082565, 2.8860834033939287, 2.785996688087374, 2.566569122815175, 2.2456772740319058, 1.847454627497801, 1.400541257591467, 0.9360286969511441, 0.48524139147485296, 0.07750888762520478, -0.2619148817911698, -0.5136375280214279, -0.6654908504055732, -0.7133702311249709, -0.6614868830602038, -0.5220102389080854, -0.3141212519424857, -0.06254010487700598, 0.20436927645472447, 0.45678330109166504, 0.6657337205936392, 0.8053838489060026, 0.8550963301148445, 0.8011352080284401, 0.6378692018151849, 0.36837747389758985, 0.004401508523663003, -0.43436591503025934, -0.9216146281916365, -1.4262866738524016, -1.91485265776422, -2.3538327455079813, -2.712378289036209, -2.9647212925907565, -3.0923042549087225, -3.0854222992984277, -2.9442418302250166, -2.6791031514295116, -2.310065603826825, -1.8657092256204162, -1.3812626839736968, -0.8961791352962896, -0.45132578020481284, -0.08598571310214542, 0.1651104954112207, 0.2745029435928998, 0.22426297270449283, 0.007617852404158052, -0.3701958191748444, -0.8919314230730971, -1.5292045169571982, -2.244194019667663, -2.9920662889972474, -3.723960404720178, -4.390328283298673, -4.944393056710044, -5.345476010900957, -5.5619476286143845, -5.573581880200694, -5.373133424482875, -4.967012074800343, -4.374993874560226, -3.628978673156393, -2.770874943547308, -1.8497583625246836], 'positive_zeros': ['1.54788332127628642474475857619291', '2.96067673348780749747650606310058', '4.08963852445967881276114490342988', '5.14203177216306998374926482682231', '6.51842909171855911651886790999194', '7.66978320113491969639642014927744', '8.649819971417102236790524203028282', '9.311333854816332717378886009534154', '10.16277346956762314809764642862594', '11.21262955430959619496009339638551'], 'prelabel': '2-336-12.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.452487143376032, 'root_angle': 0.34567003844972854, 'root_number': '0.46606846300998567199182275111721764541413007875806277060 + 0.8847486579744043993818316677348385567532983851186430971*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.17283501922486427', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.54788332127628642474475857619', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.96067673348780749747650606310', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.08963852445967881276114490343', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 19.824641761928856, 'bad_primes': [2, 3, 7], 'central_character': '12.11', 'conductor': 336, 'conductor_radical': 42, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/336/4/h/a/239/9'], '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': '2-336-12.11-c3-0-27', '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': '2-336-12.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.452487143376032, 'root_angle': 0.17283501922486427, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.54788332127628642474475857619', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1962175221299149736101164069416', 'Lhash_array': ['1962175221299149736101164069416'], 'label': '2-336-12.11-c3-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/336/4/h/a/239/9'}