-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '4158304755948162771790342950166', 'a10': [-9.18992785308158e-61, -0.753677828861482], 'a2': [1.3447343791642639, -1.602592027453956], 'a3': [0.06485682972085959, -1.7308360961219174], 'a4': [-0.41269430061882234, -2.340505684159373], 'a5': [0.27597560553091577, -0.23157102881491792], 'a6': [-2.6866089198252716, -2.4314538413901934], 'a7': [2.187887303196571, 1.4876656709460083], 'a8': [-0.6823285078914505, -0.39394254770688464], 'a9': [-2.991587183277119, -0.22451308392179312], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5091725982022, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.06485682972085959, 1.7308360961219174]]], [7, [[1.0, 0], [-2.187887303196571, -1.4876656709460083]]]], 'bad_primes': [3, 7], 'central_character': '189.101', 'coefficient_field': 'CDF', 'conductor': 189, 'conductor_radical': 21, 'conjugate': '2381738983363134481969110490214', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3447343791642639, 1.602592027453956], [-0.3472963553338607, -1.969615506024416]], [[1.0, 0], [-0.06485682972085959, 1.7308360961219174]], [[1.0, 0], [-0.27597560553091577, 0.23157102881491792], [0.8682408883346517, -4.924038765061041]], [[1.0, 0], [-2.187887303196571, -1.4876656709460083]], [[1.0, 0], [4.022419161728971, -4.793732486910291], [-1.9101299543362338, -10.832885283134289]], [[1.0, 0], [0.42989027072019403, -1.1811138116469677], [-9.958577760546714, -8.35623892592501]], [[1.0, 0], [0.9372189357934537, 0], [17.0, 0]], [[1.0, 0], [0, 7.643435517556281], [-19.0, 0]], [[1.0, 0], [0.5849188711240634, -1.6070513906262522], [-17.619022191736494, -14.784115022790404]], [[1.0, 0], [0.7315675118351651, 2.009965219573718], [-22.215288850450364, 18.64084068090964]], [[1.0, 0], [-5.714944588384285, 1.0076989241859822], [29.13047124436316, -10.602624443095731]], [[1.0, 0], [-1.6675650653819876, 2.8883074181685195], [-18.5, -32.04293994002423]], [[1.0, 0], [8.666691256580588, 3.1544176469704843], [31.4078221678781, 26.354291997148113]], [[1.0, 0], [0.6886690368649885, -3.9056361885060475], [-40.406782693794064, -14.706866163003756]], [[1.0, 0], [-0.8760046443445361, 4.9680692133718445], [-44.16555317693769, -16.07494673630643]], [[1.0, 0], [3.010370585569883, 1.7380382679393032], [26.5, 45.89934640057525]], [[1.0, 0], [-6.005624484980157, -2.185868550713069], [45.196622144019706, 37.92446897150582]], [[1.0, 0], [10.301529363116595, 1.8164375692779453], [57.32124986794041, 20.863228742865793]], [[1.0, 0], [0.22267827972268786, -0.18684926238649857], [11.634427903684333, -65.98211945181794]], [[1.0, 0], [4.183158943592727, -2.4151479421462514], [35.5, -61.48780366869514]], [[1.0, 0], [3.196382353476547, -1.8454322122126539], [36.5, -63.21985447626402]], [[1.0, 0], [-7.908244544846824, -6.635805080840707], [13.718206035687498, 77.79981248796443]], [[1.0, 0], [-6.069170502710595, 2.2089974096731004], [63.581688778875176, -53.35137160398276]], [[1.0, 0], [-5.123906208752111, 0], [89.0, 0]], [[1.0, 0], [7.915668053230308, 1.395745848116553], [91.15018421623311, 33.17595390258987]], [[1.0, 0], [13.380859658499851, -4.8702346245873676], [77.37048875501678, -64.92154857834048]], [[1.0, 0], [-4.112632197787744, -4.901244196732166], [-17.885762299693827, 101.43519856025743]], [[1.0, 0], [2.8141344097883847, -1.6247412590271126], [53.5, -92.66471820493493]], [[1.0, 0], [-6.303348193970418, 10.917719329754288], [-54.5, -94.39676901250381]], [[1.0, 0], [14.553018022882508, -2.566089728170747], [106.18526614880764, -38.64827619580057]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 20, 'label': '2-189-189.101-c1-0-20', '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/189/2/ba/a/101/19', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.9061623631330897, 2.043740009448713, 2.211068247720876, 2.409816451768096, 2.6390984466162175, 2.8955954935876256, 3.1737801902399534, 3.4661447725540775, 3.763409205293544, 4.054735828506429, 4.327996263494901, 4.5701322277990775, 4.767636857876927, 4.90716448969185, 4.976257813711804, 4.964163071924413, 4.862687162181493, 4.667036000281207, 4.376562439621676, 3.9953458761334533, 3.5325258159636723, 3.002319379196056, 2.4236687051459023, 1.8194885560352132, 1.2155162339474597, 0.6388033726706368, 0.11592936906716665, -0.32894459086094163, -0.67602818792111, -0.9116848987273868, -1.0298595897458624, -1.0329740236065759, -0.9321425690551892, -0.7466098031035607, -0.5023792412189354, -0.23008338478332802, 0.03776753382713842, 0.26993644188697496, 0.439717231168435, 0.5279593520068818, 0.5255045297447464, 0.4347058766363201, 0.26976683889396164, 0.05574468334741568, -0.17379693329215187, -0.38034216796519876, -0.5248777161965041, -0.5727973209618585, -0.4986992291087822, -0.2904707790441662, 0.0479236828365493, 0.49543593178476725, 1.0150185753547813, 1.5568770096013977, 2.063691796157399, 2.477336158688251, 2.7463654451761896, 2.833375354663862, 2.721246102555693, 2.4173333569868296, 1.9548422996293875, 1.390919766403633, 0.8013939837733675, 0.2725380275505859, -0.10932468090332459, -0.26917919439258947, -0.15420011269751985, 0.2573599988937439, 0.9506582295121788, 1.873170064553633, 2.938546591198651, 4.035306695008737, 5.039567108985266, 5.8303813468591965, 6.305775072764146, 6.3973143516390065, 6.081082061955467, 5.383286284963273, 4.379357918822506, 3.1862432618065353, 1.9485524421219165, 0.8201524669276334, -0.05644660990356237, -0.5700990739913411, -0.657532791495621, -0.3138157842003287, 0.40501546918972475, 1.3878989577905982, 2.4827610502386004, 3.51687721125147, 4.32083091705177, 4.7526681530360735, 4.718683812839868, 4.187659184809587, 3.196262918565905, 1.8446133757171905, 0.28248988969464633, -1.3118570992775511, -2.7571500410661804, -3.8949093206175642, -4.611667385133009, -4.854108500604708, -4.634778919995905, -4.027531028288642, -3.153548224553483, -2.160361306594601, -1.1974391667961861, -0.39250365192625986, 0.16743214883114646, 0.4471588772653059, 0.4647771080540391, 0.28363206024250137, -0.0035616450839324456, -0.2952176051935565, -0.5019751416649516, -0.5642993946372854, -0.46320072560044884, -0.2220703284845665, 0.10058100377921804, 0.4258393162531858, 0.6733679004558003, 0.7805377604956262, 0.7175057296858117, 0.494829230994611, 0.16174518969220186, -0.2047666208308052, -0.5179693385439343, -0.7025695141942192, -0.7143829539836559, -0.5537905300604375, -0.269412069551107, 0.04961618434286259, 0.29193155948722005, 0.3495383853890342, 0.14553936222333005, -0.34208198906262044, -1.0663872713524118, -1.9112790617145556, -2.7067058039542036, -3.257648504057755, -3.382180833676617, -2.951553858391848, -1.9242026929346099, -0.3661188086422338, 1.5478206518151127, 3.5535590081545747, 5.336527183315653, 6.583271601836282, 7.037069039995857, 6.5471960083153835, 5.102144404279538, 2.8396623433693704, 0.03062551336980489, -2.9613500540588262, -5.737913101455755, -7.9313654204692465, -9.265505916329495, -9.600615680928023, -8.954130862107265, -7.493139470667174, -5.500262714169082, -3.319652613723413, -1.2936950552384188, 0.2972566945757912, 1.2805560872791886, 1.6139023891682924, 1.3813346087561778, 0.7645015002108171, -0.0038130035733506032, -0.693422686599026, -1.1260350496924918, -1.209751361515437, -0.9519806902754084, -0.4489717382221382, 0.14454171298753693, 0.6576899094655791, 0.9474092769635272, 0.9335112395208033, 0.6167856418012703, 0.07628732961588934, -0.5529496304455754, -1.1157894861297286, -1.477240530397044, -1.5568762968171652, -1.3487806999340133, -0.9220459590083706, -0.4017744411469696, 0.06451217472098099, 0.34640519762731653, 0.3658409256099971, 0.11878703858653623, -0.32248953585479345, -0.8275111145238762, -1.241699708959568, -1.4279052520112328, -1.3045982822039905, -0.8705525020984792, -0.20907614365233299, 0.5300163264037343, 1.1667361203686846, 1.5366745294161417, 1.5345181217522261, 1.1438246151000242, 0.44472897339910117, -0.40328336641416884, -1.1999679938765495, -1.7549519425874904, -1.9375230975835738, -1.712369942900957, -1.1511869259648162, -0.4159763811265275, 0.2828317276225661, 0.7434958613883432, 0.8308132976692888, 0.5192187883014471, -0.09133310251639674, -0.7927214427371102, -1.3168966030770062, -1.4044228522021684, -0.8767956540716967, 0.3060194003012909, 2.0187519950984605, 3.9837811403564984, 5.823439105281331, 7.141308994948667, 7.6143372285211255, 7.073920341748444, 5.555723831414583, 3.304665810227216, 0.7317828859615986, -1.6688347060850617, -3.4249979446217615, -4.189466665591279, -3.817160681137685, -2.3982593246097648, -0.23907897986911436, 2.2051305173378997, 4.429973412835587, 5.9911176578155665, 6.597694275870336, 6.168694787493324, 4.8403153464663236, 2.9241439600341907, 0.8278485933596408, -1.041331503329027, -2.366576948628181, -2.9838266180639756, -2.9031103526831212, -2.286391204655602, -1.3905052347100717, -0.49218593003712685, 0.18422789087897204, 0.5177726334670641, 0.5087367080198247, 0.2613281086845938, -0.06117662833712521, -0.29391145698472254], 'positive_zeros': ['3.28032405396210625880611920173063', '4.48166504837461339191298881304506', '5.40536287791748421031166734679773', '6.23468009336392138126580024873953', '7.957146340466866956713972284117308', '8.308032526988853205876890354183049', '10.24025887286840814169016381775449', '10.68672317346131645756414247450163', '12.02191921884807073847841468138560', '13.45560645780329636845273176711284'], 'prelabel': '2-189-189.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2284838615961546, 'root_angle': 0.6484603771827833, 'root_number': '-0.4496755252289462 + 0.8931919849674377*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.324230188591', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.28032405396210625880611920173', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.48166504837461339191298881305', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.40536287791748421031166734680', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.5091725982022, 'bad_primes': [3, 7], 'central_character': '189.101', 'conductor': 189, 'conductor_radical': 21, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/189/2/ba/a/101/19'], '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': '2-189-189.101-c1-0-20', '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': '2-189-189.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2284838615961546, 'root_angle': 0.32423018859139163, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.28032405396210625880611920173', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '4158304755948162771790342950166', 'Lhash_array': ['4158304755948162771790342950166'], 'label': '2-189-189.101-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/189/2/ba/a/101/19'}