-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1556266778930572451414901204946', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [4.209049769721573, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.0193554789367, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '1380.1', 'coefficient_field': 'CDF', 'conductor': 1380, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-4.209049769721573, 0], [7.0, 0]], [[1.0, 0], [-2.753525097135825, 0], [11.0, 0]], [[1.0, 0], [0.753525097135825, 0], [13.0, 0]], [[1.0, 0], [4.9625748668573975, 0], [17.0, 0]], [[1.0, 0], [-4.753525097135825, 0], [19.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-4.9625748668573975, 0], [29.0, 0]], [[1.0, 0], [0.20904976972157252, 0], [31.0, 0]], [[1.0, 0], [5.716099963993223, 0], [37.0, 0]], [[1.0, 0], [9.380674406300543, 0], [41.0, 0]], [[1.0, 0], [-12.418099539443146, 0], [43.0, 0]], [[1.0, 0], [-7.17162463657897, 0], [47.0, 0]], [[1.0, 0], [9.380674406300543, 0], [53.0, 0]], [[1.0, 0], [4.9625748668573975, 0], [59.0, 0]], [[1.0, 0], [5.17162463657897, 0], [61.0, 0]], [[1.0, 0], [0.20904976972157252, 0], [67.0, 0]], [[1.0, 0], [-9.380674406300543, 0], [71.0, 0]], [[1.0, 0], [-10.260575291407475, 0], [73.0, 0]], [[1.0, 0], [2.418099539443145, 0], [79.0, 0]], [[1.0, 0], [-5.455524672585748, 0], [83.0, 0]], [[1.0, 0], [-4.911049345171495, 0], [89.0, 0]], [[1.0, 0], [-10.34324927315794, 0], [97.0, 0]], [[1.0, 0], [-14.887724600572193, 0], [101.0, 0]], [[1.0, 0], [-17.925149733714797, 0], [103.0, 0]], [[1.0, 0], [16.469625061129047, 0], [107.0, 0]], [[1.0, 0], [6.260575291407475, 0], [109.0, 0]], [[1.0, 0], [9.380674406300543, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-1380-1.1-c1-0-7', 'leading_term': '2.3937679675405644969536042756503', '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/1380/2/a/j/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.3937679675405645, 2.3901335457165076, 2.3790905763998538, 2.3602295928263657, 2.3328995346229386, 2.2962522753880554, 2.249300289141957, 2.190983652614003, 2.1202424684170005, 2.0360910578446307, 1.9376907637022578, 1.8244187741352615, 1.6959309128966724, 1.5522167739389001, 1.3936458889305876, 1.2210038192668085, 1.0355171919806734, 0.8388667902307344, 0.6331878996581859, 0.4210572306262125, 0.2054659031350826, -0.010221792593079664, -0.22232385748725772, -0.42690991461313915, -0.6198836545982613, -0.7970771965158658, -0.9543556956280559, -1.0877300517012438, -1.1934751055070107, -1.268250277532675, -1.3092192233603643, -1.3141647760045339, -1.2815952371760995, -1.210837985662502, -1.102116407857767, -0.9566063355496893, -0.7764685076744539, -0.5648540591277522, -0.3258806784259121, -0.0645778584131217, 0.21319942478052079, 0.5008882513223744, 0.7913650655231708, 1.077120159282214, 1.3504555895768044, 1.603701675831503, 1.829446192107718, 2.020769466358421, 2.171477870243268, 2.276327671265142, 2.331230962644072, 2.3334354170516636, 2.2816699511134693, 2.176249051090654, 2.0191294971669156, 1.8139145221305175, 1.5658020241902693, 1.2814752837037489, 0.9689366569512043, 0.6372868717666156, 0.2964547543116625, -0.043115610223344925, -0.37081122685649126, -0.676219151893318, -0.9495056267921922, -1.181791789832975, -1.365511674128115, -1.49473802433917, -1.5654618521960535, -1.575812625706502, -1.52620754889641, -1.4194205133457822, -1.2605639393906225, -1.0569797980402889, -0.8180395149177296, -0.5548560840953735, -0.27991542428919497, -0.006637641528975992, 0.2511177367215928, 0.47958547923108774, 0.665647772629153, 0.7973854067032593, 0.8646046861457177, 0.8593176195795079, 0.7761537657491107, 0.6126839047825247, 0.36963842599410407, 0.051006916427018434, -0.33599021281146035, -0.7810622617928317, -1.2711397490965497, -1.7907901027488462, -2.322745173983216, -2.8485229161883803, -3.349120800007624, -3.805754529222467, -4.200612598305159, -4.517595375324336, -4.7430068431345545, -4.866167974259713, -4.8799229772365615, -4.781013296369665, -4.570299168434811, -4.252814569472114, -3.837648292761979, -3.3376514032802143, -2.768979090724147, -2.1504826408682103, -1.5029744993764609, -0.8483958537278025, -0.20892147043589807, 0.393959600924765, 0.9403466489543909, 1.4127720901576042, 1.7969488560526703, 2.0823843226354604, 2.262830074694306, 2.3365437830603506, 2.3063478142297584, 2.17947852787161, 1.9672301234903504, 1.684406902593509, 1.348607423397548, 0.9793727484499363, 0.5972383546608032, 0.2227348743471846, -0.12461367609562053, -0.42724439203711495, -0.6704142722005886, -0.8429187365788166, -0.9376315416153524, -0.9518361375806529, -0.8873286530826642, -0.7502841244631402, -0.5508897555133676, -0.302761279177542, -0.02217025356924503, 0.27287927886828867, 0.5636775064285998, 0.8318851285140338, 1.0606015535319935, 1.2353665234628521, 1.3450389631647044, 1.3825022443374464, 1.345153350027321, 1.2351442616187476, 1.0593567512252902, 0.8291060047070349, 0.5595833832200389, 0.26906335335937553, -0.022086640845355453, -0.2925426176004554, -0.5212465773876743, -0.6886484787097296, -0.7778981926819957, -0.7759189142892028, -0.6742983299515722, -0.4699423743082711, -0.16544828350025803, 0.2308317035594634, 0.7050479769649766, 1.2384266961240729, 1.8081346482755845, 2.3883949264179347, 2.951797276773955, 3.4707344967073928, 3.918887369625909, 4.2726759151380165, 4.512594598826409, 4.624353721896728, 4.599758363275777, 4.437269572458099, 4.142209352912167, 3.726590451429068, 3.2085730173497455, 2.6115716335664394, 1.9630568084814184, 1.2931135296584193, 0.6328347786345349, 0.012639013249250012, -0.5393932191706563, -0.9990676527786061, -1.3474186628246119, -1.5717649657252337, -1.666413333752949, -1.6329645032714706, -1.4801980789627718, -1.2235377006466, -0.8841226227181143, -0.48753567640786144, -0.06225888660114485, 0.36205454122227904, 0.7563907002649117, 1.0941601739754494, 1.3528499797088593, 1.515440631175263, 1.571499299537421, 1.5178783145761836, 1.3589711577191403, 1.1065043492714557, 0.778871678466138, 0.4000453767289771, -0.0018746426819345754, -0.39638913352652766, -0.7525026907144118, -1.0406866086749864, -1.2347808310067452, -1.313716343547728, -1.2629487222986595, -1.0755098727624308, -0.7526073920546068, -0.303728152185099, 0.2537669830567134, 0.8955387911801149, 1.5916062390991044, 2.3080462486001068, 3.008955213337827, 3.6585531144114, 4.2233007023061, 4.6738979220278765, 4.987037830021659, 5.146804426100531, 5.145624312938541, 4.984709623719043, 4.673961534867783, 4.231337902742731, 3.681722940675377, 3.0553691485417565, 2.3860097827093742, 1.7087621132119173, 1.0579560325983195, 0.4650282122198231, -0.04338153975414948, -0.44700766381113327, -0.7331068611780182, -0.8971016041642795, -0.9426772754805451, -0.8813274347806018, -0.7313787812025321, -0.5165626631508643, -0.2642310712749293, -0.0033397741296154523, 0.23766214722968942, 0.4328898795759051, 0.5608838438424779, 0.6061430092843981, 0.5602214052704833, 0.4223083845486988, 0.19924876887630683, -0.09500192350446397, -0.44045207251063684, -0.8126053190049084, -1.1843423020109145, -1.528020059818994, -1.817639047611289, -2.030920731690482, -2.151142736806403], 'positive_zeros': ['1.22767801999255964670496877027612', '2.29904300338527129077219014903463', '3.56670292035907263607382784902803', '4.51317189637090511227030872574067', '5.10597839717954388070057587370353', '6.46511903164147711739279338069223', '7.36106031408583522974286330676496', '7.973207165389061169146942735373293', '8.784524163453622519273792604468212', '9.283847332152058150982953246763453'], 'prelabel': '2-1380-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3195414561256347, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.22767801999255964670496877028', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.29904300338527129077219014903', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.56670292035907263607382784903', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 11.0193554789367, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 1380, 'conductor_radical': 690, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1380/2/a/j/1/3'], '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': '2-1380-1.1-c1-0-7', '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': '2-1380-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.3195414561256347, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.22767801999255964670496877028', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1556266778930572451414901204946', 'Lhash_array': ['1556266778930572451414901204946'], 'label': '2-1380-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1380/2/a/j/1/3'}