-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2215322513259914091467220207514', 'a10': [-2.940852007452475, -1.6979016981495378], 'a2': [-0.984807753012208, 0.17364817766693036], 'a3': [1.3446542256860443, -1.0917440237274785], 'a4': [0.9396926207859084, -0.3420201433256687], 'a5': [2.60133632165946, 2.182780348072515], 'a6': [-1.134646546377205, 1.3086547347540836], 'a7': [1.1823612958041676, -2.3668590507641745], 'a8': [-0.8660254037844386, 0.5], 'a9': [0.6161899733106703, -2.9360364297452772], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.0183451964044, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.984807753012208, -0.17364817766693036]]], [3, [[1.0, 0], [-1.3446542256860443, 1.0917440237274785]]], [7, [[1.0, 0], [-1.1823612958041676, 2.3668590507641745]]]], 'bad_primes': [2, 3, 7], 'central_character': '378.41', 'coefficient_field': 'CDF', 'conductor': 378, 'conductor_radical': 42, 'conjugate': '2014920286540379316249547765212', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.984807753012208, -0.17364817766693036]], [[1.0, 0], [-1.3446542256860443, 1.0917440237274785]], [[1.0, 0], [-2.60133632165946, -2.182780348072515], [0.8682408883346517, 4.924038765061041]], [[1.0, 0], [-1.1823612958041676, 2.3668590507641745]], [[1.0, 0], [-0.6047330959419076, -0.7206928396493874], [-1.9101299543362338, 10.832885283134289]], [[1.0, 0], [-0.43641498898892334, -0.07695173734433483], [12.216004070216808, 4.446261863233693]], [[1.0, 0], [1.112822399071603, -1.9274649349927055], [-8.5, -14.722431864335457]], [[1.0, 0], [6.85516180457265, -3.95782951320846], [9.5, -16.454482671904334]], [[1.0, 0], [0.17107190195940897, 0.4700161877366311], [-17.619022191736494, 14.784115022790404]], [[1.0, 0], [-8.00321772856588, 1.4111832180304809], [27.251086002791343, -9.918584156444393]], [[1.0, 0], [2.6849737119816015, 7.376904645498708], [-23.747377736688318, 19.92641590028272]], [[1.0, 0], [0.25036939581299816, -0.43365251420843537], [-18.5, -32.04293994002423]], [[1.0, 0], [1.1670814999240562, -6.618848092531468], [-38.527397452222246, -14.022825876352417]], [[1.0, 0], [-3.7901111200013777, 3.1802808429140637], [7.466871639678005, -42.34673337952495]], [[1.0, 0], [2.1730360310434786, 0.7909204332877935], [36.00408882659197, 30.211017655267348]], [[1.0, 0], [0, -7.3673126116122685], [-53.0, 0]], [[1.0, 0], [-0.002539271665924668, -0.0021307019183363063], [10.24524248234889, 58.10365742772028]], [[1.0, 0], [4.170418070320738, -11.458129477891747], [-46.728711030257664, -39.2100441908789]], [[1.0, 0], [-2.6702626903466147, 15.143812249366228], [-62.95940559265586, -22.915349602819806]], [[1.0, 0], [10.360495873099296, 5.981635081271885], [35.5, 61.48780366869514]], [[1.0, 0], [-3.871948794541162, 2.2354706788167866], [36.5, -63.21985447626402]], [[1.0, 0], [-1.9391846393200103, -10.9976625898575], [-74.23571704208676, 27.01959132272783]], [[1.0, 0], [-2.343179041618547, -13.288828698840515], [-77.9944875252304, 28.387671896030504]], [[1.0, 0], [4.969710316873727, 8.607790767724522], [-44.5, 77.07626093681505]], [[1.0, 0], [1.0227456613284676, 1.2188608161983425], [-16.843873233692243, 95.52635204218419]], [[1.0, 0], [13.32799739396594, 4.850994333781118], [77.37048875501678, 64.92154857834048]], [[1.0, 0], [6.250579997815904, -7.4491511681946125], [-17.885762299693827, -101.43519856025743]], [[1.0, 0], [0, -10.675104540535337], [-107.0, 0]], [[1.0, 0], [3.0631299445737734, 0], [109.0, 0]], [[1.0, 0], [8.27790552826942, -9.865223652470553], [-19.62224407636313, -111.28327609037952]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 13, 'label': '2-378-189.41-c1-0-13', '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/378/2/z/a/41/10', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.5658860400407837, 1.5883708448838858, 1.6112556624770455, 1.6305291414619059, 1.6398310000682228, 1.6313656519203037, 1.5969233026179868, 1.528888702684758, 1.421192966394484, 1.2701959781466345, 1.0754798421049936, 0.8405089149811856, 0.5730871419808191, 0.2855286123163599, -0.0055432464756881685, -0.2798372153311343, -0.5145152564283083, -0.6857869733054027, -0.7709161889320557, -0.7505169037084904, -0.6109551781556772, -0.3466213812802368, 0.038197599349251106, 0.5281258448746752, 1.0964421161843543, 1.7059568306528936, 2.311123580223609, 2.861359413657836, 3.305400060180663, 3.596362503926843, 3.697046951343867, 3.584904308062634, 3.2560441330714758, 2.727678237518662, 2.0384963362980804, 1.2466525577386303, 0.425293921773146, -0.34413891426980675, -0.980295779337509, -1.4111580564871464, -1.5830946586083765, -1.4685877168931436, -1.0715206113666766, -0.42911377248411553, 0.3900651643027925, 1.2921300938645008, 2.1675290198138466, 2.9033768114748155, 3.3970721235241554, 3.569501129826534, 3.3760414388947657, 2.8137382923850036, 1.9234339694811082, 0.7862538848799543, -0.4853844047849786, -1.7612735479782657, -2.9097478771719723, -3.8146469702290515, -4.39049886242978, -4.593653111692061, -4.4276000818454975, -3.9415286274020365, -3.2221897945023366, -2.3801962862183292, -1.5328227098538252, -0.7860139729771096, -0.2185298027631167, 0.12911327828649202, 0.25897999299198043, 0.2125227624674038, 0.060353718296233275, -0.11323713678295096, -0.22821403452282094, -0.22581628536689066, -0.0813467728472315, 0.18992313790868515, 0.5351699006161493, 0.8746312215645313, 1.118659997204009, 1.1880706650470236, 1.0337683775498647, 0.6515272444434537, 0.08847541184524214, -0.5607248782098375, -1.1680744710542774, -1.59478423311215, -1.7182931276402638, -1.4586672321423824, -0.7990102871174624, 0.204702915566007, 1.4271953612293065, 2.6912196510571396, 3.7962949917901927, 4.554050175619926, 4.823724211054526, 4.540909839065938, 3.7335180802270274, 2.5211043824983737, 1.0967718457765048, -0.30571477934262664, -1.4538867102970372, -2.159785173032685, -2.3159935460214385, -1.9171116395468046, -1.0619156467628377, 0.06483776041574343, 1.2279119017158828, 2.187709078792192, 2.7479280770257586, 2.795085872121168, 2.321637174734783, 1.4276192004224446, 0.30011838393093976, -0.8254904531844771, -1.7146347896564924, -2.1827049784060426, -2.1338140888991126, -1.5807429596189102, -0.6415990514109267, 0.486267563991259, 1.569543177153631, 2.389999492583783, 2.792039220868744, 2.7161148387226897, 2.2104622853732567, 1.4184318178214523, 0.54424591437725, -0.19499499586384011, -0.6199759835622973, -0.6306854747475681, -0.22900129015758, 0.48306843215099465, 1.3291701923281316, 2.102341803766864, 2.616229647485281, 2.7513681061156214, 2.4851343288813212, 1.8978208948451736, 1.1530261665846078, 0.45687905990604344, 0.005946508917304462, -0.06332722615324504, 0.2890653439703735, 0.9940271095874703, 1.8879885725223546, 2.751699603161157, 3.363884368101633, 3.5565191737556865, 3.2578179382484267, 2.5118575941532217, 1.4695058748616217, 0.352528588213933, -0.6003670731835618, -1.192036152355931, -1.3150711471522045, -0.9772494928168782, -0.2976050619168154, 0.525933545084042, 1.2689246841808797, 1.7390355294024464, 1.825340920176526, 1.5250990825252102, 0.9407789600449015, 0.24817390010278526, -0.355559242258291, -0.7093443455598464, -0.7346782960925956, -0.45744215736576493, 0.002029506671707183, 0.46875853687131325, 0.7721752870956656, 0.8076184420507823, 0.5818009042510525, 0.2272415531529629, -0.021391415254088456, 0.11435165534482947, 0.8771486509519715, 2.393725914843806, 4.616408729539905, 7.304532882915282, 10.054419905602321, 12.374270379345232, 13.78824706860147, 13.945461731546985, 12.706994729764746, 10.188404173623367, 6.745538690024932, 2.9053246317020043, -0.7429926329865832, -3.6705473197209737, -5.51618118135031, -6.152886742294337, -5.698237622896108, -4.467959376781326, -2.8861994745651196, -1.3767486901872121, -0.2636011761503966, 0.29424801863542743, 0.3189556188072113, -0.0200390446505163, -0.4771580745663906, -0.8165798875409563, -0.8872108449961131, -0.6653202289113617, -0.2537524442910608, 0.16006213392029292, 0.37272313690764447, 0.2377645790492779, -0.28039980868944336, -1.0885699083108735, -1.9886225312336134, -2.735806161583051, -3.1133286540826397, -2.999891363965461, -2.408843607033059, -1.4863130236109523, -0.4683843067902399, 0.3897568673295258, 0.8908308278607167, 0.9545127560248977, 0.6397444549685104, 0.12288237716061379, -0.36182382146513187, -0.6007777322590763, -0.47347171371815466, 0.004952791011612214, 0.6857684569372329, 1.3340803376722508, 1.7076213474496258, 1.6422113384010657, 1.1159666379638902, 0.26998070792547013, -0.6237927162821725, -1.240181916787288, -1.3017305981166143, -0.6721085284829872, 0.5880372800376025, 2.222553413899088, 3.8414055842158463, 5.026743366426189, 5.453253118017345, 4.986976218948862, 3.7319391729384206, 2.008720532295912, 0.2692038959089814, -1.028819496999854, -1.5508409094606932, -1.1803711805582104, -0.050730159365386794, 1.49597844355549, 3.0106524714888927, 4.069188037746897, 4.394847603983736, 3.9340746662645745, 2.8631829586380935, 1.5247721802808711, 0.3145700607716345], 'positive_zeros': ['1.74758132316670275864190571825705', '2.73905438584388191501318456596633', '4.56718389560642235209748961601834', '5.44298530360082775478107301841229', '6.70304531176080283546597875637840', '8.318477658737538395286648138071838', '8.792123721401644163989834563289673', '9.293186419590988552750284828453036', '10.26752208469111144518895170451332', '11.10210875852608005233194034441617'], 'prelabel': '2-378-189.41-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.737338538225754, 'root_angle': 0.08883392642758903, 'root_number': '0.9613092758179554 + 0.27547137097411417*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0444169632138', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.74758132316670275864190571826', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.73905438584388191501318456597', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.56718389560642235209748961602', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.0183451964044, 'bad_primes': [2, 3, 7], 'central_character': '189.41', 'conductor': 378, 'conductor_radical': 42, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/378/2/z/a/41/10'], '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': '2-378-189.41-c1-0-13', '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': '2-378-189.41-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.737338538225754, 'root_angle': 0.044416963213794514, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.74758132316670275864190571826', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2215322513259914091467220207514', 'Lhash_array': ['2215322513259914091467220207514'], 'label': '2-378-189.41-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/378/2/z/a/41/10'}