-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1963756491579052101232446815560', 'a10': [2.0, -3.4641016151377544], 'a2': [-0.5, -0.8660254037844386], 'a3': [0.5, 0.8660254037844386], 'a4': [-0.5, 0.8660254037844386], 'a5': [2.0, 3.4641016151377544], 'a6': [0.5, -0.8660254037844386], 'a7': [-3.0, 0.0], 'a8': [1.0, 0.0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [3, [[1.0, 0], [-0.5, -0.8660254037844386]]], [19, [[1.0, 0], [4.0, 1.7320508075688772]]]], 'bad_primes': [2, 3, 19], 'central_character': '114.7', 'coefficient_field': 'CDF', 'conductor': 114, 'conductor_radical': 114, 'conjugate': '3423630973610838372715725229335', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [-2.0, -3.4641016151377544], [-2.5, 4.330127018922194]], [[1.0, 0], [3.0, 0], [7.0, 0]], [[1.0, 0], [-2.0, 0], [11.0, 0]], [[1.0, 0], [-3.5, 6.06217782649107], [-6.5, -11.258330249197702]], [[1.0, 0], [0, 0], [-8.5, 14.722431864335457]], [[1.0, 0], [4.0, 1.7320508075688772]], [[1.0, 0], [-2.0, 3.4641016151377544], [-11.5, -19.91858428704209]], [[1.0, 0], [2.0, -3.4641016151377544], [-14.5, -25.11473670974872]], [[1.0, 0], [-1.0, 0], [31.0, 0]], [[1.0, 0], [-7.0, 0], [37.0, 0]], [[1.0, 0], [2.0, 3.4641016151377544], [-20.5, 35.50704155516198]], [[1.0, 0], [3.5, 6.06217782649107], [-21.5, 37.239092362730865]], [[1.0, 0], [1.0, -1.7320508075688772], [-23.5, -40.703193977868615]], [[1.0, 0], [-2.0, 3.4641016151377544], [-26.5, -45.89934640057525]], [[1.0, 0], [-3.0, -5.196152422706632], [-29.5, 51.09549882328188]], [[1.0, 0], [-0.5, 0.8660254037844386], [-30.5, -52.827549630850754]], [[1.0, 0], [1.5, -2.598076211353316], [-33.5, -58.023702053557386]], [[1.0, 0], [1.0, 1.7320508075688772], [-35.5, 61.48780366869514]], [[1.0, 0], [-1.5, -2.598076211353316], [-36.5, 63.21985447626402]], [[1.0, 0], [2.5, 4.330127018922194], [-39.5, 68.41600689897065]], [[1.0, 0], [12.0, 0], [83.0, 0]], [[1.0, 0], [9.0, -15.588457268119896], [-44.5, -77.07626093681505]], [[1.0, 0], [5.0, 8.660254037844387], [-48.5, 84.00446416709055]], [[1.0, 0], [1.0, -1.7320508075688772], [-50.5, -87.4685657822283]], [[1.0, 0], [-9.0, 0], [103.0, 0]], [[1.0, 0], [-2.0, 0], [107.0, 0]], [[1.0, 0], [3.0, 5.196152422706632], [-54.5, 94.39676901250381]], [[1.0, 0], [-2.0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-114-19.7-c1-0-0', '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/114/2/e/a/7/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9895600898264755, 0.9621297123187688, 0.9418766478949088, 0.9251606539009141, 0.9073894386507175, 0.8833556014021787, 0.8475359553042302, 0.7943365906869542, 0.7183036014216401, 0.6143305817103202, 0.4778875551614324, 0.3052830629776422, 0.09395835695518877, -0.15719775612985698, -0.44753279438134386, -0.7743384312667257, -1.1326115165214603, -1.5148996420520642, -1.9112625496601445, -2.309378090118714, -2.694816008690009, -3.0514943762198072, -3.3623220607575823, -3.610016586937982, -3.7780707347701394, -3.851824302437381, -3.8195809307709307, -3.673695341460526, -3.411545500831203, -3.036298807163858, -2.557382952725441, -1.9905817960180723, -1.3576949855472835, -0.6857270436014541, -0.005606105273584801, 0.649527471517119, 1.246379755903197, 1.753784679982955, 2.1450474457050976, 2.4001624057411113, 2.507705036252299, 2.466201919571104, 2.2848062837018364, 1.9831500581404995, 1.5903050379179802, 1.1428618599730698, 0.682220236996791, 0.2512696209038494, -0.10928267462715684, -0.36461812993599535, -0.4891957438642017, -0.4694679486168847, -0.3056037212445957, -0.01197150915451832, 0.38375859052421807, 0.8429007989261884, 1.319287579030855, 1.7637643574854975, 2.129228390173537, 2.3756999176849614, 2.474867634770422, 2.413564121052307, 2.1957049798775916, 1.8423654808963041, 1.38986013649936, 0.8859160074052719, 0.3842656266475994, -0.061797589198930365, -0.40618830327379535, -0.6163116801664081, -0.6780423984890983, -0.5986789249319601, -0.4073464117344028, -0.15260007325783143, 0.10268456771476064, 0.28869543708820605, 0.33757557458326665, 0.19280029259548495, -0.18212837208514518, -0.7968443558567417, -1.6301654189789356, -2.6297611317193086, -3.715762745394171, -4.788148237009495, -5.737231299820998, -6.456128990783133, -6.853744436963007, -6.866633325547063, -6.468161715116076, -5.6736181523112625, -4.540395951524147, -3.1629634955482424, -1.6630186249863295, -0.1758885067413301, 1.165204950065267, 2.2450272712469563, 2.980263132502379, 3.329575228022908, 3.2983223143107994, 2.93715241102199, 2.3345148037222674, 1.6039935632952753, 0.86813202479784, 0.24097468858131657, -0.18819251583589594, -0.36752335550934623, -0.28979127981039604, 0.007091860514687612, 0.4464131422598095, 0.9250167352690433, 1.3299084561162844, 1.5566328860167014, 1.5266086367744929, 1.2006937244226676, 0.5867701397670377, -0.2599801113986349, -1.2443123805238319, -2.2446833560869366, -3.1314840018517773, -3.7869122084636992, -4.123320704492862, -4.0970480319375815, -3.7154100373662367, -3.035602857714239, -2.1555805915379316, -1.1983094140443524, -0.2919392904660541, 0.45082606193770064, 0.9506809393382536, 1.1739045120812175, 1.1366341734185512, 0.900414306585907, 0.5597254083596973, 0.22363160026953546, -0.005222423398910993, -0.050487878232322404, 0.12279730505511002, 0.5007780510544825, 1.0225542893345114, 1.5910402242000712, 2.0911040956630136, 2.411767235441186, 2.468375574270263, 2.220522444723499, 1.682152980862702, 0.9216279031348584, 0.05134399969249846, -0.7915224865269073, -1.4698304480780489, -1.87233164251667, -1.9356694899781897, -1.6581475004298571, -1.1022841519821458, -0.3851903165384555, 0.341902147824404, 0.921493024048242, 1.2200117392928678, 1.154654446868109, 0.7115506653487504, -0.04861439388304024, -0.9991512477272667, -1.9690643750822878, -2.7742964663777445, -3.2529271418777643, -3.2977366508728005, -2.8797748616297305, -2.0580399689727655, -0.9728367343005433, 0.17658668803182345, 1.1664959694071042, 1.789153784213541, 1.891902024959164, 1.4074402965532256, 0.3693463881812661, -1.0904790717879331, -2.76241403006314, -4.3943058072359396, -5.734954349403708, -6.57790662070758, -6.797408158993641, -6.369762011908005, -5.376079576668329, -3.9859549135442944, -2.42526336932653, -0.9343487325694401, 0.27529797881726925, 1.0575312085923307, 1.354309087750281, 1.2006270078842103, 0.7111688766891509, 0.05192425721289768, -0.5969678584731378, -1.079198091458319, -1.2931280810518395, -1.2092084638608303, -0.8706923697289225, -0.37805471553989634, 0.13889285386061312, 0.5545164485201133, 0.7786343870366127, 0.7782535366676894, 0.5846945761801825, 0.2844296387816105, -0.004229585670618815, -0.16308370872182573, -0.10697818189002582, 0.19035211729151927, 0.6841294144074944, 1.2636239589596538, 1.7740694667764394, 2.0509787836015656, 1.9593257377701014, 1.428593225881143, 0.4752603049033925, -0.7931492252278721, -2.194326873087939, -3.5050262528877254, -4.505636154888046, -5.025903955477599, -4.981616578054323, -4.39374319030981, -3.3852438336241284, -2.1556678015942903, -0.9387133068837207, 0.04806212625355744, 0.6501617685653691, 0.8089715018790729, 0.5727291537470821, 0.08273522397202687, -0.46244453099102906, -0.8568553676812878, -0.9396941365873027, -0.6381680046296012, 0.009760239899190185, 0.8587720001260777, 1.6858351530828288, 2.240053997518701, 2.301784073867958, 1.7375625934077747, 0.5379504363505052, -1.1710655964004393, -3.1466487904930944, -5.074426774763067, -6.631111655494584, -7.55083896004545, -7.680528883582884, -7.0118255203510484, -5.682318928888464, -3.9456485437426374, -2.11714280773325, -0.5072240587555467, 0.6424194740142972, 1.205595726929654, 1.1910440104005364, 0.7307205736514333, 0.040434183631929466, -0.6372023508396459], 'positive_zeros': ['1.54913072358068928721326785821206', '4.25104104797604112613275752221054', '5.95861093515340541713444358494610', '6.62925058745666810014651140037743', '8.356139788180140540496179767920068', '9.197588431634538098208427051469955', '9.698975745534639055029712035201362', '11.64041903378439221298354564433070', '12.93675058068021834249048812864088', '13.37268083446081823670774685785691'], 'prelabel': '2-114-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': -0.13550657612455358, 'root_number': '0.9107472158164717 - 0.4129642949245674*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0677532880623', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.54913072358068928721326785821', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.25104104797604112613275752221', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.95861093515340541713444358495', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'bad_primes': [2, 3, 19], 'central_character': '19.7', 'conductor': 114, 'conductor_radical': 114, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/114/2/e/a/7/1'], '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': '2-114-19.7-c1-0-0', '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': '2-114-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': -0.06775328806227679, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.54913072358068928721326785821', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1963756491579052101232446815560', 'Lhash_array': ['1963756491579052101232446815560'], 'label': '2-114-19.7-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/2/e/a/7/1'}