-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2960573630953271004877838317902', 'a10': [-0.8542086167161369, 0.3052261766502505], 'a2': [-0.3812038627913328, 0.13874685924334265], 'a3': [1.0407727417334454, -2.859499606696519], 'a4': [-1.4060231921808148, 1.1797935419856236], 'a5': [2.236029263758839, 0.013157948704307402], 'a6': [-1.0634812187410401e-60, 1.234456244824608], 'a7': [1.768682229113811, -0.31186639729235577], 'a8': [0.7779575010919367, -1.3474619180205547], 'a9': [-4.795396771405258, -4.023815662234871], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.4772324373936878, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-2.236029263758839, -0.013157948704307402]]], [37, [[1.0, 0], [1.5738484391521015, -5.875627718855109]]]], 'bad_primes': [5, 37], 'central_character': '185.104', 'coefficient_field': 'CDF', 'conductor': 185, 'conductor_radical': 185, 'conjugate': '1857298439933655555671872776389', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.3812038627913328, -0.13874685924334265], [1.532088886237956, -1.2855752193730787]], [[1.0, 0], [-1.0407727417334454, 2.859499606696519], [-2.298133329356934, -1.928362829059618]], [[1.0, 0], [-2.236029263758839, -0.013157948704307402]], [[1.0, 0], [-1.768682229113811, 0.31186639729235577], [6.5778483455013586, -2.3941410032796813]], [[1.0, 0], [0.4019136302911807, -0.6961348279187788], [-5.5, -9.526279441628825]], [[1.0, 0], [-0.7379163974512997, 0.6191853769410527], [2.2574263096700946, -12.802500789158705]], [[1.0, 0], [4.968951249951612, 4.169445161172282], [2.952019020337816, 16.741731801207536]], [[1.0, 0], [1.5759734860114272, -4.3299515664755805], [-14.554844419260583, -12.212964584044247]], [[1.0, 0], [-1.1653337421924226, -2.0184172492516477], [-11.5, 19.91858428704209]], [[1.0, 0], [-8.395494667591493, -4.847141106314016], [14.5, 25.11473670974872]], [[1.0, 0], [0, -5.059583765628236], [-31.0, 0]], [[1.0, 0], [1.5738484391521015, -5.875627718855109]], [[1.0, 0], [-1.5062956943884698, 1.2639321616052899], [7.119575284344144, -40.37711787350053]], [[1.0, 0], [8.699149190110187, 0], [43.0, 0]], [[1.0, 0], [-2.168059613290747, 1.2517298013525686], [23.5, -40.703193977868615]], [[1.0, 0], [-8.746949435760976, -1.5423231844173442], [49.803708901653145, 18.127067596260442]], [[1.0, 0], [-3.739417968491663, -0.6593602799911167], [55.44186462636859, 20.179188456214455]], [[1.0, 0], [1.1035383080882144, 1.3151457432294658], [-10.592538837682751, 60.07327293374469]], [[1.0, 0], [12.309678797150863, -2.1705284957926203], [62.95940559265586, -22.915349602819806]], [[1.0, 0], [12.437063724462977, 4.5267209973764775], [54.38915546144744, 45.63792028774429]], [[1.0, 0], [0, 2.7296417185811523], [-73.0, 0]], [[1.0, 0], [-8.150461330727314, 1.437146237828245], [74.23571704208676, -27.01959132272783]], [[1.0, 0], [0.4663985941487555, -0.5558322001576683], [-14.412798746355218, -81.73904350001327]], [[1.0, 0], [-4.751276651326452, -0.8377782664390194], [83.63264324994584, 30.439792755984517]], [[1.0, 0], [2.8761122312255076, 4.981572512752866], [-48.5, 84.00446416709055]], [[1.0, 0], [4.944502388139579, 8.5641293544034], [-50.5, 87.4685657822283]], [[1.0, 0], [8.016609588849004, -13.885175112330321], [-51.5, -89.20061658979718]], [[1.0, 0], [-7.5944842047321774, -9.050753834889553], [-18.580355010361547, 105.37442957230627]], [[1.0, 0], [3.9189669352896757, 10.767273162297668], [-83.49884429996861, 70.06384945583278]], [[1.0, 0], [-15.114750317610197, 5.50131921397574], [86.56302207244451, -72.63499989457894]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-185-185.104-c1-0-10', '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/185/2/v/a/104/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.240908114238653, 1.311271818379083, 1.3931953787938394, 1.486052104213281, 1.5871473687264734, 1.6919667340755178, 1.7945040641954582, 1.8876013571875423, 1.9632863496763346, 2.013127705334788, 2.0286354364894508, 2.001725329332354, 1.9252502864995327, 1.7935843998615832, 1.6032297613369113, 1.353402607848494, 1.0465451473310583, 0.6887031924098203, 0.28970852702441496, -0.1368902892151265, -0.5741934929991979, -1.002638435669446, -1.4010120015145489, -1.747758073197015, -2.0225172358844947, -2.2078016752589757, -2.290677061211273, -2.264299096578464, -2.1291393766997317, -1.8937368641448906, -1.5748303156082835, -1.1967646408115378, -0.7901197711812794, -0.38958131808052754, -0.031152965539070376, 0.25110608728043393, 0.4285581454962677, 0.48135680925946894, 0.4013522275835285, 0.1941727192086979, -0.11983867463874867, -0.5060751931785354, -0.9176299879954366, -1.2987494865990596, -1.5895879138780062, -1.7319079891755667, -1.675225281189884, -1.382785195639534, -0.8367103073512115, -0.041675377481641775, 0.9734354310028317, 2.1562621242657483, 3.4342304240955825, 4.720201024928118, 5.920076859405148, 6.941672095197084, 7.703938906497015, 8.145531819700091, 8.231688842028348, 7.958535238840082, 7.354165614358338, 6.476211781673982, 5.406020702457471, 4.239998853308412, 3.079070049703697, 2.0174866131813975, 1.132380725667702, 0.47541190999314425, 0.06764821909835643, -0.10157066075532035, -0.07155798028252394, 0.09665705167231256, 0.3302123185575954, 0.5558623908236242, 0.7113278361331091, 0.7548225503645778, 0.6712398410413164, 0.47392509773692737, 0.2016031672258665, -0.08922376317737932, -0.33534645028068516, -0.47970042965712967, -0.48391615806233607, -0.33839683915318286, -0.06801244256383787, 0.2679117226884107, 0.5817837925053965, 0.769592749841168, 0.7269156739907936, 0.36677848319705386, -0.36342520571870945, -1.4688181613682962, -2.9001874017507827, -4.555022314944181, -6.286907688052128, -7.922416422242901, -9.283377098753261, -10.211386967503975, -10.590886444037926, -10.36712842357365, -9.555997363277534, -8.243791104140405, -6.576608859491743, -4.740653850837219, -2.9362835636616125, -1.349757761603389, -0.12713322520563075, 0.6454799833739383, 0.952045346322794, 0.8454032397789457, 0.434935530402056, -0.1348098371590188, -0.7108374783053792, -1.1590847207465462, -1.387608840057798, -1.361425912164824, -1.1063183274548, -0.7009287689430618, -0.25863367355602346, 0.09736213021162397, 0.2609204477445249, 0.16659484585725345, -0.19474733276660997, -0.7715830036524807, -1.4598112449014113, -2.1219644569101734, -2.614014557038739, -2.814608396430374, -2.6509080638040166, -2.115690136203564, -1.271922321028552, -0.2434166020405365, 0.8070896897682451, 1.708487871236373, 2.314658966552094, 2.5340275707024515, 2.3492165011270614, 1.8224874747613073, 1.085373792556586, 0.31405787235185856, -0.3050067588214562, -0.6125936249718696, -0.5098302490659734, 0.019890138793900888, 0.9049841388524071, 1.9973933534994823, 3.100033526095644, 4.004798610372524, 4.533641867683897, 4.574441667168645, 4.1042451341808075, 3.1949323780973082, 1.9998866448346986, 0.7241733581152238, -0.41579637352061316, -1.2348639841907485, -1.6151605644706937, -1.5280610837178537, -1.0374656799292643, -0.2837798836390178, 0.5478836987812313, 1.268325033243054, 1.7247917293345927, 1.832521058931092, 1.5903620891355552, 1.0771113893826927, 0.42956302653755074, -0.19252701431834562, -0.6462931914410454, -0.8409539349514863, -0.7598498752876477, -0.46382451043854545, -0.07481089383445484, 0.25675799081639616, 0.39306218644442686, 0.24853868835264675, -0.1819653215907937, -0.8141773479218513, -1.4878616243896254, -2.0007992378692516, -2.1562553957552204, -1.813269934741407, -0.927836333731076, 0.4254697364008054, 2.0578197663451463, 3.6970974263714735, 5.0400205904172966, 5.814781434118719, 5.840646647891458, 5.071049353975969, 3.6098936292676354, 1.6964509683194444, -0.33887332978315515, -2.139044519104798, -3.3915796294835996, -3.8910639066487605, -3.5793702139402894, -2.554787535957634, -1.0481633435402222, 0.628449505638429, 2.1489912445058836, 3.2413048666076247, 3.740646557298996, 3.6172243842967053, 2.972411035686943, 2.0056913253550688, 0.9612356069952787, 0.0675891312764526, -0.514772406984354, -0.725637997652018, -0.6100090984967979, -0.2958416027899087, 0.048464887083345815, 0.26484863082133336, 0.2507914594889297, -0.013124759755625178, -0.4604368060577953, -0.9610928332093703, -1.3622120306112486, -1.5355627815334842, -1.418037380175472, -1.0331790890587427, -0.4869373459610071, 0.06202708623389632, 0.4498897844243105, 0.5600471680977305, 0.3653068280911414, -0.05307930296197109, -0.5167501793361052, -0.7911236235815109, -0.6467961246784687, 0.07379649016336985, 1.4021392094510732, 3.2173256648750335, 5.256767078387193, 7.163871753565926, 8.563060979033127, 9.144960014563843, 8.741179977826045, 7.369831969419271, 5.239520398471832, 2.70949696414859, 0.2144556748983042, -1.8286427908026037, -3.1096421392670197, -3.488897618468363, -3.02055220165038, -1.930353104460796, -0.5543084682081121, 0.7458207030252406, 1.668658216586661, 2.039505281433238, 1.8409451301140223, 1.2016090213574264, 0.34810510244298737, -0.46527370457326805, -1.0289536824058125], 'positive_zeros': ['2.33548079448725510084952997883250', '4.26209626328205523845242534571500', '4.95637854344335492935082227758321', '6.13068130023450235690068745340892', '8.533532869213636891352763802039134', '8.812732500287962301417106856898668', '9.835862978973817561573373975447494', '10.52637759279915991368139519590874', '11.19582796704918853679503411385015', '13.26627474640684129029005041825411'], 'prelabel': '2-185-185.104-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2154145125814846, 'root_angle': 0.18279678652599943, 'root_number': '0.4098140914073248 + 0.9121690690239331*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.182796786526', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.33548079448725510084952997883', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.26209626328205523845242534571', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.95637854344335492935082227758', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.4772324373936878, 'bad_primes': [5, 37], 'central_character': '185.104', 'conductor': 185, 'conductor_radical': 185, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/185/2/v/a/104/7'], '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': '2-185-185.104-c1-0-10', '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': '2-185-185.104-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2154145125814846, 'root_angle': 0.18279678652599943, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.33548079448725510084952997883', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2960573630953271004877838317902', 'Lhash_array': ['2960573630953271004877838317902'], 'factors': ['2-185-185.104-c1-0-10'], 'label': '2-185-185.104-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/185/2/v/a/104/7'}