-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1077319405705960089865063496995', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-2.0, 3.4641016151377544], 'a6': [0, 0], 'a7': [1.0, 1.7320508075688772], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33.63298933136331, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0.5, -0.8660254037844386]]]], 'bad_primes': [2, 3, 13], 'central_character': '4212.1405', 'coefficient_field': 'CDF', 'conductor': 4212, 'conductor_radical': 78, 'conjugate': '495373296027747763219512231610', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.0, -3.4641016151377544], [-2.5, -4.330127018922194]], [[1.0, 0], [-1.0, -1.7320508075688772], [-3.5, 6.06217782649107]], [[1.0, 0], [2.0, 3.4641016151377544], [-5.5, 9.526279441628825]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [2.0, 0], [17.0, 0]], [[1.0, 0], [2.0, 0], [19.0, 0]], [[1.0, 0], [0, 0], [-11.5, -19.91858428704209]], [[1.0, 0], [3.0, 5.196152422706632], [-14.5, 25.11473670974872]], [[1.0, 0], [-5.0, 8.660254037844387], [-15.5, -26.846787517317598]], [[1.0, 0], [-10.0, 0], [37.0, 0]], [[1.0, 0], [-4.0, 6.928203230275509], [-20.5, -35.50704155516198]], [[1.0, 0], [2.0, 3.4641016151377544], [-21.5, 37.239092362730865]], [[1.0, 0], [2.0, 3.4641016151377544], [-23.5, 40.703193977868615]], [[1.0, 0], [-10.0, 0], [53.0, 0]], [[1.0, 0], [4.0, -6.928203230275509], [-29.5, -51.09549882328188]], [[1.0, 0], [-7.0, -12.12435565298214], [-30.5, 52.827549630850754]], [[1.0, 0], [1.0, -1.7320508075688772], [-33.5, -58.023702053557386]], [[1.0, 0], [16.0, 0], [71.0, 0]], [[1.0, 0], [10.0, 0], [73.0, 0]], [[1.0, 0], [-8.0, -13.856406460551018], [-39.5, 68.41600689897065]], [[1.0, 0], [0, 0], [-41.5, 71.88010851410841]], [[1.0, 0], [-4.0, 0], [89.0, 0]], [[1.0, 0], [-1.0, -1.7320508075688772], [-48.5, 84.00446416709055]], [[1.0, 0], [-5.0, -8.660254037844387], [-50.5, 87.4685657822283]], [[1.0, 0], [-4.0, 6.928203230275509], [-51.5, -89.20061658979718]], [[1.0, 0], [12.0, 0], [107.0, 0]], [[1.0, 0], [2.0, 0], [109.0, 0]], [[1.0, 0], [-3.0, 5.196152422706632], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 25, 'label': '2-4212-9.4-c1-0-25', 'leading_term': '1.054791164349961185836133267828091455443560819801792847', '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/4212/2/i/b/1405/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.0547911643499612, 1.1177112497478638, 1.1641016079883277, 1.1939831998322423, 1.2073056195652447, 1.2039686232051654, 1.1838560497278308, 1.1468798426491582, 1.0930313662062212, 1.0224369337106205, 0.9354144032587522, 0.8325278041321338, 0.7146371845055565, 0.5829411700404549, 0.439010057192773, 0.28480761178491765, 0.1227000922111485, -0.044548633498989174, -0.2137966522060836, -0.38155865998323124, -0.5440557295751962, -0.6972798086432315, -0.837072140251222, -0.9592143545320497, -1.0595305295576494, -1.1339980713798101, -1.1788648320006379, -1.1907694856787945, -1.1668618357254181, -1.1049194434589316, -1.0034567755256436, -0.8618229713614318, -0.6802843531123984, -0.46008794694554306, -0.20350256488938734, 0.08616558653743764, 0.40458525205280454, 0.7464422273196488, 1.1055122137565105, 1.4747645314075573, 1.8464958175906596, 2.212491814171111, 2.5642143035111156, 2.8930092275638386, 3.190331053762312, 3.447977574028994, 3.6583285779416768, 3.814581264695995, 3.9109748846295953, 3.9429969585467397, 3.9075635344286557, 3.8031663211662003, 3.629980193647803, 3.3899254889792347, 3.086680695432968, 2.725642548815198, 2.3138321595913105, 1.8597475525981024, 1.3731648547713475, 0.8648922527837118, 0.3464826939384089, -0.17008695115576009, -0.6727609787442648, -1.1497635910500061, -1.589959675483598, -1.9832053807743162, -2.320676029786969, -2.5951591421201083, -2.801301040907889, -2.9357966878274024, -2.9975140098878845, -2.987546013892417, -2.9091863735359818, -2.767826846303132, -2.5707777432537315, -2.3270156319415887, -2.0468653889123387, -1.7416265156328257, -1.4231561713593108, -1.1034235431689356, -0.7940518607749125, -0.5058654792237688, -0.2484599220279639, -0.02981254931588475, 0.14404943502515144, 0.26930859291332, 0.34453178895782516, 0.3707499410582839, 0.3514367738837435, 0.2923842731768547, 0.20147670922111574, 0.08836936696278008, -0.035917687069942666, -0.15947653549945348, -0.270041273412102, -0.35555014419767944, -0.40471714816525517, -0.4075890650962535, -0.3560635464791238, -0.24434467649875047, -0.06931418565703751, 0.16920070511357815, 0.4682781069202326, 0.821881715584981, 1.2209760802419516, 1.6537768510605781, 2.106130130656395, 2.5620092471501783, 3.004111749861249, 3.414534457040928, 3.775500201130595, 4.07010673788376, 4.283066292259103, 4.401403541135651, 4.415080561195526, 4.317519419967763, 4.105996615317294, 3.781888365248745, 3.350751645066526, 2.8222326349276963, 2.209801601055328, 1.5303208738363512, 0.8034601664454177, 0.05098064941663188, -0.7040843831783634, -1.438319071895231, -2.1288475954956674, -2.754250227841547, -3.29543258637768, -3.7364089696386333, -4.0649636708979715, -4.273158890320657, -4.357664178037815, -4.3198899740318994, -4.165916444786173, -3.9062180702008074, -3.555193884360857, -3.13052247472861, -2.65236934890179, -2.1424816590720877, -1.62321114640886, -1.116510207666573, -0.6429479514931056, -0.22079285422026793, 0.1347938982976072, 0.41241501676376185, 0.6049110350778176, 0.7096274023092628, 0.7284604112038117, 0.6676783576316079, 0.5375254302813676, 0.35162676812850036, 0.12622334002612584, -0.12072573682348661, -0.37052859813596994, -0.6047838327931052, -0.8063889355273365, -0.9604814836896919, -1.0552632310503993, -1.082662656961059, -1.038799261558741, -0.924222709156887, -0.7439113283436629, -0.507026919033111, -0.22643566553086908, 0.08198245524199756, 0.4002017191921878, 0.7090520064978705, 0.9893013513903213, 1.22276223131323, 1.3933617394271163, 1.4881165384456434, 1.497957432437439, 1.4183553803794542, 1.2497105077524207, 0.9974776918628103, 0.6720160095585, 0.28816404282277047, -0.13544203282775427, -0.577276302912551, -1.0140126596572854, -1.4217409178107192, -1.777246259699212, -2.059283904485463, -2.2497796298316572, -2.3348892580212555, -2.305856404702988, -2.1596174241840065, -1.899115122393324, -1.533297823103709, -1.0767969946372635, -0.5492939959582871, 0.0253963554465427, 0.6204817049297644, 1.2075299594212616, 1.7579203056620267, 2.24433129289743, 2.6421863664707415, 2.930978094620474, 3.0953975421974973, 3.1262046106899697, 3.0207882457711954, 2.783381555832681, 2.424915246269231, 1.9625123709892967, 1.418647161275012, 0.820009508336689, 0.1961334764654178, -0.42213797173865897, -1.0042698775145416, -1.5216461294663821, -1.9490858771592494, -2.2661814160375506, -2.4583825119796083, -2.517765554558946, -2.443443004120149, -2.2415884082747963, -1.9250737140727499, -1.5127374851982238, -1.0283236959790152, -0.4991497894103586, 0.0454214727696201, 0.5756201345808167, 1.0629240765368617, 1.481636381137171, 1.810294446231421, 2.0328295672824686, 2.13940985999615, 2.126917613437997, 1.9990334235184624, 1.7659225343863638, 1.4435423610137033, 1.052612782153975, 0.6173111157813113, 0.16377047319974236, -0.281527618348201, -0.6933686220856234, -1.049329770134396, -1.3311205901614274, -1.5256563451985152, -1.62579751022329, -1.6307086276734786, -1.5458131785141733, -1.382346085166401, -1.1565306120277175, -0.8884301989648353, -0.6005466642611467, -0.31625291084163887, -0.05815966665547635, 0.15347889891232608, 0.30221703666081184, 0.37663083744981274, 0.3712111641498535, 0.2868732980959737, 0.13104400520986978, -0.08268692197431796, -0.33533599875483017], 'positive_zeros': ['0.849855161597366147245000030103599', '1.76279008618299495525489044732123', '3.08084263456936232562721215805088', '4.22266355493436418796376542635870', '4.65738658527342304637210119167333', '5.09433469601001017285446215328118', '6.24951028845379239868272080901315', '7.29198842071995452148152637169481', '7.74501738217377663438555489806011', '8.365687869088255055242622477368369'], 'prelabel': '2-4212-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.799395600522809, 'root_angle': 0.1111111111111111, 'root_number': '0.93969262078590838405410927732473146993620813426446463309 + 0.3420201433256687330440996146822595807630833675141606285*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.05555555555555555', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.849855161597366147245000030104', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.76279008618299495525489044732', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.08084263456936232562721215805', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 33.63298933136331, 'bad_primes': [2, 3, 13], 'central_character': '9.4', 'conductor': 4212, 'conductor_radical': 78, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4212/2/i/b/1405/1'], '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': '2-4212-9.4-c1-0-25', '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': '2-4212-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.799395600522809, 'root_angle': 0.05555555555555555, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.849855161597366147245000030104', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1077319405705960089865063496995', 'Lhash_array': ['1077319405705960089865063496995'], 'label': '2-4212-9.4-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4212/2/i/b/1405/1'}