-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1862761483758797773987466238171', 'a10': [-1.0434612111041195e-60, 3.891114489450113], 'a2': [0.8660254037844386, 0.5], 'a3': [0.0, 0.0], 'a4': [0.5, 0.8660254037844386], 'a5': [1.9455572447250564, 3.369803996897514], 'a6': [0.0, 0.0], 'a7': [2.0998492315008552, -1.6095444091311266], 'a8': [0.0, 1.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.0183451964044, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, -0.5]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.0998492315008552, 1.6095444091311266]]]], 'bad_primes': [2, 3, 7], 'central_character': '378.251', 'coefficient_field': 'CDF', 'conductor': 378, 'conductor_radical': 42, 'conjugate': '2886781492941681625961747501138', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.9455572447250564, -3.369803996897514], [-2.5, 4.330127018922194]], [[1.0, 0], [-2.0998492315008552, 1.6095444091311266]], [[1.0, 0], [3.416140736228188, 1.9723097736509907], [5.5, 9.526279441628825]], [[1.0, 0], [2.4668677372776555, -1.4242467521724573], [6.5, -11.258330249197702]], [[1.0, 0], [-0.7421169263931052, 0], [17.0, 0]], [[1.0, 0], [0, 1.7847379114983033], [-19.0, 0]], [[1.0, 0], [-5.415352151503404, 3.1265550224271093], [11.5, -19.91858428704209]], [[1.0, 0], [-2.500788584724784, -1.4438309625771972], [14.5, 25.11473670974872]], [[1.0, 0], [3.0412517220942243, -1.7558675004245132], [15.5, -26.846787517317598]], [[1.0, 0], [-3.001577169449568, 0], [37.0, 0]], [[1.0, 0], [5.247053115604284, 9.088162586239193], [-20.5, 35.50704155516198]], [[1.0, 0], [-0.47152118892620665, 0.8166986560654733], [-21.5, -37.239092362730865]], [[1.0, 0], [-1.0926260039204017, 1.892483752461087], [-23.5, -40.703193977868615]], [[1.0, 0], [0, 0], [-53.0, 0]], [[1.0, 0], [-0.010567303870706729, -0.018303107203083313], [-29.5, 51.09549882328188]], [[1.0, 0], [-2.138315462474366, -1.2345570078719141], [30.5, 52.827549630850754]], [[1.0, 0], [6.724631233780425, 11.64740295907228], [-33.5, 58.023702053557386]], [[1.0, 0], [0, 1.9430423778524133], [-71.0, 0]], [[1.0, 0], [0, -4.854860044666317], [-73.0, 0]], [[1.0, 0], [1.818064524874872, -3.148980128521849], [-39.5, -68.41600689897065]], [[1.0, 0], [4.0299770199528595, -6.980124951893368], [-41.5, -71.88010851410841]], [[1.0, 0], [9.266462831686436, 0], [89.0, 0]], [[1.0, 0], [16.298253858789025, 9.409801252692699], [48.5, 84.00446416709055]], [[1.0, 0], [-4.140791334364409, 7.172060974660083], [-50.5, -87.4685657822283]], [[1.0, 0], [-14.764600209259767, 8.52434590529333], [51.5, -89.20061658979718]], [[1.0, 0], [0, -14.336924392715245], [-107.0, 0]], [[1.0, 0], [-11.279966770567658, 0], [109.0, 0]], [[1.0, 0], [-8.515005532306288, 4.916140736228188], [56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-378-63.20-c1-0-5', '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/m/a/251/8', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.163091095646396, 2.057334759870124, 1.9578299660611755, 1.8569021079632255, 1.7456229656459943, 1.6152321565645078, 1.4583854893860413, 1.2701465533702576, 1.048728800953545, 0.7960144231924481, 0.5178532988279793, 0.22411490543011203, -0.07155215349163359, -0.35229833898853624, -0.5990168545730086, -0.7916486687588808, -0.9108026285337459, -0.9395969749263391, -0.8655814926223473, -0.6825592068401732, -0.39209972576827196, -0.004529418652953907, 0.46079821126016596, 0.9761023959298397, 1.5067215861726428, 2.0135849870117903, 2.4564738698393302, 2.797819838588862, 3.0066807492900636, 3.06245592509179, 2.957866401744295, 2.7007458789471395, 2.314271047355103, 1.8354055922464427, 1.3115309969040838, 0.7954704996401044, 0.3393531424229844, -0.012020005463321982, -0.22749028544122657, -0.2946559276107235, -0.22295727422755562, -0.04407938160496119, 0.19068810741700912, 0.4161093701918562, 0.561222575653027, 0.5592432893744999, 0.35792507547248975, -0.07105942946007435, -0.7251775641480732, -1.567805496006909, -2.5295725934836866, -3.514565330676447, -4.410983251153628, -5.1051322829438215, -5.497026084471118, -5.51545103594252, -5.130222754455148, -4.359573387858267, -3.2711622107154295, -1.9760445880612845, -0.6159603952872628, 0.6546349070554317, 1.6894440157537496, 2.3711213962233435, 2.628797231575584, 2.449437242269538, 1.8809328231779738, 1.0260084444842514, 0.02746193794624376, -0.953304624313031, -1.7612944661164993, -2.2725410715350445, -2.414285993132476, -2.177194899879626, -1.6172817513365654, -0.846865790574622, -0.015748460983100152, 0.7144515253822131, 1.1985477138509733, 1.3337393268820807, 1.078612835425532, 0.46161478325867844, -0.4228016845605116, -1.4299684634858476, -2.3901405705702747, -3.138581650357958, -3.5451486306643525, -3.5378714395941846, -3.1160164944428486, -2.350017105905109, -1.3681179316486687, -0.332152429221963, 0.5929541434449624, 1.2700386870346572, 1.6148173073391991, 1.6102232825335476, 1.3070342087706253, 0.8106292005183042, 0.25659894130849353, -0.21967851237998437, -0.5130093687393548, -0.5713903190306344, -0.40691567358823644, -0.09199238238286335, 0.2585361020423884, 0.5155841194255497, 0.5681161181201553, 0.3521712018753302, -0.1302749955351797, -0.807449846002988, -1.5505117622491849, -2.200687135108241, -2.605188212740773, -2.6539593787048963, -2.3086906135319496, -1.6168751068132043, -0.7067688718769346, 0.23668361506180868, 1.0104743059086154, 1.4386033894741002, 1.4135572338730764, 0.9244393643700586, 0.06456782188702177, -0.9842772181367911, -1.9885192966043652, -2.7129732584775064, -2.973676981910594, -2.6813635109743217, -1.8651855584447377, -0.6704182605681839, 0.6703668859606988, 1.8870214561809853, 2.7317084531653557, 3.035447475356537, 2.748078205690015, 1.951805309384964, 0.8443415553363874, -0.30531905088782013, -1.2189139490806915, -1.6746169924016192, -1.5610294427213964, -0.9063641262768289, 0.12475930810036066, 1.2669990737509844, 2.214815700106075, 2.6940823761268406, 2.5280562355131715, 1.6819638833647998, 0.27524753255459383, -1.4419470756054746, -3.1429587450990812, -4.496983773165467, -5.242663006418029, -5.245513033746515, -4.525672031631244, -3.2496140872646393, -1.6882610480191629, -0.15210837849732914, 1.0804811824884148, 1.8241902466970352, 2.022224751840504, 1.7484076958169705, 1.1766186362922408, 0.5267239734642428, 0.0020888168077214044, -0.26433550409012874, -0.2410071899835233, 0.0019595304944723425, 0.3225125871227703, 0.5571744458476415, 0.5773305407611034, 0.3346097974385331, -0.11829555437170446, -0.6380750326368473, -1.03023522582771, -1.1067383981247638, -0.7454347976636571, 0.0661844478994722, 1.216466487315036, 2.4899309291445357, 3.618283913420252, 4.349006479322036, 4.5129227234117275, 4.071780738361603, 3.1318929349127846, 1.9190232694209177, 0.7204982287363384, -0.1900748728954179, -0.6248081800497896, -0.5300450756877084, 0.0025591148691453632, 0.765896429916642, 1.4999968151619465, 1.9694913742486784, 2.0333730789829185, 1.6862258798436778, 1.0580041857274005, 0.3714143689331969, -0.1313894514511834, -0.27142602911337205, 0.00024378458709109263, 0.5728828054477733, 1.195051867416057, 1.53962816945906, 1.2984623875485075, 0.28058125970588155, -1.5146873862511925, -3.8726217942792545, -6.396436550163011, -8.593319972978662, -9.99231226863782, -10.263344054640156, -9.305262271271092, -7.278180758196702, -4.570118499406488, -1.7056497280789236, 0.7797861041411794, 2.466727753631737, 3.1461431599178815, 2.8569590632423023, 1.8580303079993912, 0.544159409916011, -0.6688452196592694, -1.457002226996799, -1.6673344628450562, -1.3424666629999158, -0.686255594800785, 0.01642498815353098, 0.49935647426849594, 0.6026304342158065, 0.32136438594214284, -0.19872324172071543, -0.7161508232272249, -0.9803040749549792, -0.8213110944594009, -0.2137286095320943, 0.7069659269657065, 1.6809833801666436, 2.402818994738548, 2.6171565337801717, 2.201614954277827, 1.209754061403555, -0.13985750800296065, -1.5256966754292849, -2.617401039239431, -3.172600575365155, -3.1061436112938003, -2.5101095441914216, -1.6186829716946656, -0.7296119515652102, -0.10789548427457224, 0.09700428419162299, -0.10634194643431195, -0.5625801797603159, -1.0302144019512767, -1.2708124650640649, -1.1362862028130705], 'positive_zeros': ['1.46945971028880029227670026913152', '2.62631417185724535138000997669989', '4.61981961141611085277305970270413', '5.14981541485944442005752997840498', '5.85822237630093570191734312151693', '7.55858109744833825527441284287271', '8.503376647617699923128331876207480', '9.502441909431485061153093772389430', '10.19374051481165300861058679344830', '11.41716715531014159784390201246997'], 'prelabel': '2-378-63.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.737338538225754, 'root_angle': -0.37176668896873133, 'root_number': '0.3920480623463852 - 0.9199447357371229*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.185883344484', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.46945971028880029227670026913', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.62631417185724535138000997670', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.61981961141611085277305970270', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.0183451964044, 'bad_primes': [2, 3, 7], 'central_character': '63.20', 'conductor': 378, 'conductor_radical': 42, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/378/2/m/a/251/8'], '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': '2-378-63.20-c1-0-5', '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': '2-378-63.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.737338538225754, 'root_angle': -0.18588334448436566, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.46945971028880029227670026913', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1862761483758797773987466238171', 'Lhash_array': ['1862761483758797773987466238171'], 'label': '2-378-63.20-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/378/2/m/a/251/8'}