-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2550389163998100010118396565910', 'a10': [-6.049401641744878, -3.4926236662975696], 'a2': [0.0, -1.8342431843139217], 'a3': [0.0, 0.0], 'a4': [-1.3644480592020753, 0.0], 'a5': [1.904122471963251, -3.2980368652739958], 'a6': [0.0, 0.0], 'a7': [0.3177759703989623, 2.6265982625131308], 'a8': [0.0, -1.1657568156860783], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.5275177946066, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.3177759703989623, -2.6265982625131308]]]], 'bad_primes': [3, 7], 'central_character': '567.269', 'coefficient_field': 'CDF', 'conductor': 567, 'conductor_radical': 21, 'conjugate': '1448229041553183931993550041084', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.8342431843139217], [-2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.904122471963251, 3.2980368652739958], [-2.5, -4.330127018922194]], [[1.0, 0], [-0.3177759703989623, -2.6265982625131308]], [[1.0, 0], [-1.0095750170189974, 0.5828784078430391], [5.5, -9.526279441628825]], [[1.0, 0], [-4.798036865273995, 2.7701478757476896], [6.5, -11.258330249197702]], [[1.0, 0], [1.5885011943343186, -2.7513647764708824], [-8.5, -14.722431864335457]], [[1.0, 0], [0.5466720888031131, -0.31562127762893233], [9.5, -16.454482671904334]], [[1.0, 0], [1.5257900102021182, 0.8809152731170348], [11.5, 19.91858428704209]], [[1.0, 0], [-4.186577405687634, -2.4171215921569607], [14.5, 25.11473670974872]], [[1.0, 0], [0, -4.2778106409796495], [-31.0, 0]], [[1.0, 0], [2.115812835672958, 3.664695330691943], [-18.5, 32.04293994002423]], [[1.0, 0], [2.2824549337243836, 3.953327911196887], [-20.5, 35.50704155516198]], [[1.0, 0], [3.615812835672958, -6.262771542045259], [-21.5, -37.239092362730865]], [[1.0, 0], [2.5457598334107723, 0], [47.0, 0]], [[1.0, 0], [0.06271118413220032, 0.03620631903992605], [26.5, 45.89934640057525]], [[1.0, 0], [6.985247332595139, 0], [59.0, 0]], [[1.0, 0], [0, -8.086055584906152], [-61.0, 0]], [[1.0, 0], [-5.098803283489756, 0], [67.0, 0]], [[1.0, 0], [0, -4.761830546234069], [-71.0, 0]], [[1.0, 0], [-4.847438507018874, -2.7986699269075044], [36.5, 63.21985447626402]], [[1.0, 0], [-17.098803283489758, 0], [79.0, 0]], [[1.0, 0], [5.081124860631888, -8.80076641821576], [-41.5, -71.88010851410841]], [[1.0, 0], [5.775078600021953, 10.002729552941766], [-44.5, 77.07626093681505]], [[1.0, 0], [0.5960737305479913, 0.34414332878874726], [48.5, 84.00446416709055]], [[1.0, 0], [-3.292029950743381, -5.701963134726005], [-50.5, 87.4685657822283]], [[1.0, 0], [-8.09607373054799, -4.674270347710941], [51.5, 89.20061658979718]], [[1.0, 0], [-13.654873387561345, 7.8836448260588], [53.5, -92.66471820493493]], [[1.0, 0], [-7.231625671345916, 12.525543084090518], [-54.5, -94.39676901250381]], [[1.0, 0], [-17.19981343180146, 9.930316914861914], [56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 26, 'label': '2-567-63.38-c1-0-26', '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/567/2/i/f/269/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.7876213491320712, 1.986104791686333, 2.19687549739204, 2.417569149228939, 2.641068673662825, 2.8556230738385264, 3.045497999384033, 3.1920074343371754, 3.2748420439484174, 3.2736610988622443, 3.169919875706011, 2.9488701639861263, 2.6016175718583243, 2.1270635709854457, 1.533515955723167, 0.8397284642540641, 0.07513609405687119, -0.7209080004825116, -1.5010136249392574, -2.2127652263696436, -2.802744674911127, -3.221301350123544, -3.427666213839619, -3.394891938947825, -3.114032211650548, -2.596968449929038, -1.8773641813303263, -1.0093802643512597, -0.06401096465852511, 0.8768176718739089, 1.7279405486377015, 2.4097017015819286, 2.8567935553430392, 3.026096844933523, 2.902441019669956, 2.5013692693501253, 1.868307426551939, 1.0739745538060996, 0.20638429124085508, -0.6396993714748764, -1.3745497216701463, -1.92492138966928, -2.2434954856163194, -2.314853324247793, -2.1569378779260537, -1.8175978136212496, -1.3665642299197969, -0.883970182293023, -0.44715904919064386, -0.117918303481788, 0.06767116818471158, 0.10490473463338593, 0.02045776166553464, -0.13351460093305823, -0.2903542934930254, -0.38312823769456955, -0.3595424617677758, -0.19466109078861812, 0.10124528831036446, 0.4816589451982841, 0.8703398104910421, 1.1747404416054592, 1.3042047929914629, 1.1896974690119284, 0.8012020271192735, 0.15903137837459905, -0.6638405612958223, -1.5497880432787627, -2.354296837243397, -2.9308788042821, -3.1588524055478344, -2.96872914706339, -2.359944839854714, -1.4067394470779095, -0.25000237817505205, 0.9244632541308014, 1.918027955376821, 2.556088448174956, 2.7226842281592276, 2.3857775350127643, 1.6074454504515232, 0.5358718716342338, -0.6204867740726041, -1.63251292130168, -2.296654675393276, -2.4787502487962425, -2.1463150894243417, -1.3819295214189025, -0.37378820588628026, 0.6160609009050043, 1.3006241814346977, 1.42501528215139, 0.820474620136874, -0.5557816170122754, -2.6036442255767165, -5.090558740886798, -7.6883171933144725, -10.02970646347383, -11.774219744563549, -12.669865957581568, -12.598623565618512, -11.59626024496529, -9.842467848565727, -7.623453741832724, -5.274943796414643, -3.11769198959538, -1.3991025692473207, -0.2530740391082912, 0.31402731593058286, 0.4093277844709506, 0.21577861910612475, -0.059407970132604, -0.23752783394548524, -0.2097535443174068, 0.042384641090538966, 0.4514965498653974, 0.891550064509183, 1.2198277971546638, 1.3219891443140321, 1.1479644405625342, 0.7289650619126169, 0.17101112209057628, -0.3732573108146728, -0.7467758457273079, -0.8326173069744772, -0.5884527107983808, -0.06101427070326954, 0.6239919994857567, 1.2943452597568568, 1.7776550168973115, 1.94897975203653, 1.7663738015108104, 1.2840011731792758, 0.6384568052864709, 0.011387345791203719, -0.42163532272232973, -0.5417280023544548, -0.32212005756165146, 0.16252005754015866, 0.7566776650066804, 1.2697845163985886, 1.5348648024465537, 1.4632157200719145, 1.0784510372453806, 0.5182333218466706, 0.000726295652362201, -0.23705619739844985, -0.01306298314318187, 0.7345461900406803, 1.9106174708857915, 3.268011293370636, 4.456890394574425, 5.108456039550712, 4.932874280359836, 3.805647037430481, 1.817978229574504, -0.7251851250447537, -3.3626460737113995, -5.578443611303592, -6.923370675364424, -7.126000023460765, -6.164056118869141, -4.276232962480699, -1.9095119084666619, 0.386182215835973, 2.0900385491747326, 2.8356626541277046, 2.497438516392924, 1.2156943396165634, -0.645557358998071, -2.5967023906904836, -4.150055282071606, -4.942836882368637, -4.823258870168913, -3.877877701111119, -2.394792102827438, -0.7749620290194339, 0.5820700744348709, 1.385409663337585, 1.5233560352375064, 1.0790368752356665, 0.2893012230023517, -0.5384249825925874, -1.12480211789232, -1.3025679306047235, -1.0611016516216096, -0.5395732486228468, 0.027192560510909153, 0.3915082370626449, 0.37719506892953514, -0.061399623048261597, -0.8240896527122802, -1.6973489288193135, -2.4233787132943942, -2.7829244477563932, -2.6648946216164076, -2.1004352248725917, -1.2509187465665008, -0.3544582323698211, 0.35090196924975103, 0.7016857278555528, 0.6566000236451065, 0.30195944276795444, -0.18597117501812047, -0.6078731792854598, -0.8136154379774946, -0.7540805041739025, -0.4939217791809434, -0.1804094977851409, 0.020596103874070255, -0.001943436855442314, -0.24944316187907617, -0.6001256586422643, -0.8454639879717523, -0.7675242017409963, -0.2322146590712167, 0.734718490827232, 1.9191940533212635, 2.954277379788823, 3.415475130457651, 2.9507078086389003, 1.4056156444799228, -1.0973402247322321, -4.1561366454641995, -7.170862670787413, -9.49161554386611, -10.592327642196368, -10.219672028789827, -8.471166785355203, -5.7762526692427505, -2.782818859296257, -0.18061778138279994, 1.4869473667286681, 1.9666902003712785, 1.3520937946724212, 0.035873903060730274, -1.4257180981865338, -2.493743007141732, -2.8154389033180767, -2.328040859725375, -1.2655143890779346, -0.06748674856868483, 0.7787744624006301, 0.9109110890509914, 0.2215916798734927, -1.096743294873186, -2.60742262918665, -3.767425531729835, -4.102737815189069, -3.364168470440314, -1.6131735917634162, 0.789748228806371, 3.2897503816110185, 5.301109288708342, 6.376855354960221, 6.331192208918297, 5.278061865928602], 'positive_zeros': ['2.01190230457740070590023664334514', '3.50836004016527483745364906612076', '4.77968312600438141198947721390117', '6.19166694141667797713774431217615', '6.51898752514013505984229255085812', '7.21217919635224747884834269493062', '8.150909405913302743492227020674772', '9.276056323431976429723745719986292', '10.18256335476411675131507423446079', '11.04503894087954112090159873985635'], 'prelabel': '2-567-63.38-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': 0.8102188873710148, 'root_number': '-0.8274668981144679 + 0.5615144989444357*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.405109443686', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.01190230457740070590023664335', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.50836004016527483745364906612', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.77968312600438141198947721390', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.5275177946066, 'bad_primes': [3, 7], 'central_character': '63.38', 'conductor': 567, 'conductor_radical': 21, 'degree': 2, 'index': 26, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/567/2/i/f/269/2'], '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': '2-567-63.38-c1-0-26', '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': '2-567-63.38-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': 0.4051094436855074, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.01190230457740070590023664335', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2550389163998100010118396565910', 'Lhash_array': ['2550389163998100010118396565910'], 'label': '2-567-63.38-c1-0-26', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/567/2/i/f/269/2'}