-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2047185133385395364283589703760', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.5962345814256191, -0.6723356015123536], 'a4': [0.0, 0.0], 'a5': [4.186899254070199, -0.7382633040007224], 'a6': [0.0, 0.0], 'a7': [1.269435256500177, -1.512854027499838], 'a8': [0.0, 0.0], 'a9': [2.0959296778780434, 2.146410674915227], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.4495373673193144, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.5962345814256191, 0.6723356015123536]]]], 'bad_primes': [2, 3], 'central_character': '432.47', 'coefficient_field': 'CDF', 'conductor': 432, 'conductor_radical': 6, 'conjugate': '1587656008349499075808357220560', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.5962345814256191, 0.6723356015123536]], [[1.0, 0], [-4.186899254070199, 0.7382633040007224], [4.698463103929542, -1.7101007166283437]], [[1.0, 0], [-1.269435256500177, 1.512854027499838], [-1.2155372436685123, -6.893654271085456]], [[1.0, 0], [0.31347357960669203, -1.7777970129539173], [-10.336618828644992, -3.762221576582356]], [[1.0, 0], [3.1673183499372337, 1.1528096018222964], [9.958577760546714, 8.35623892592501]], [[1.0, 0], [1.5130814905501735, -0.8735780058749829], [8.5, -14.722431864335457]], [[1.0, 0], [-3.627648311957317, -2.094423729433849], [9.5, 16.454482671904334]], [[1.0, 0], [-5.409016269073145, 4.538703556411184], [3.993908086339398, -22.650578319280786]], [[1.0, 0], [3.007524577006193, 8.26310586377933], [-22.215288850450364, 18.64084068090964]], [[1.0, 0], [-3.172184979305398, -3.7804628454605975], [-5.3830935076748405, 30.52904034337845]], [[1.0, 0], [-0.8644280071765903, -1.4972332279153686], [-18.5, 32.04293994002423]], [[1.0, 0], [1.5814022519035735, -4.344866978179759], [-31.4078221678781, -26.354291997148113]], [[1.0, 0], [9.924582467826458, 1.7499716613440055], [40.406782693794064, 14.706866163003756]], [[1.0, 0], [2.6329147475294157, 2.209277793573154], [8.161464350345726, 46.28596439157378]], [[1.0, 0], [0, 0.5118323728677252], [-53.0, 0]], [[1.0, 0], [1.7598768139096115, 9.980757379492319], [-55.44186462636859, 20.179188456214455]], [[1.0, 0], [-0.7526712435737004, -0.6315661628804368], [10.592538837682751, 60.07327293374469]], [[1.0, 0], [4.1074223660458715, -11.28505020287391], [-51.32497768897153, -43.066769848998135]], [[1.0, 0], [-1.033194918007402, -1.7895460921107804], [-35.5, 61.48780366869514]], [[1.0, 0], [-1.3130227661610303, 2.274222142485534], [-36.5, -63.21985447626402]], [[1.0, 0], [-6.021765947272796, -16.54466596537278], [-60.51751100639927, 50.780221165236604]], [[1.0, 0], [-3.4587905961002163, 1.2588968235403335], [63.581688778875176, -53.35137160398276]], [[1.0, 0], [6.467501884159077, 3.7340139538036548], [44.5, 77.07626093681505]], [[1.0, 0], [0.25075926509380064, -1.4221264612271691], [-91.15018421623311, -33.17595390258987]], [[1.0, 0], [4.740779353899576, -5.649840826706277], [-17.538465944359967, -99.46558305423301]], [[1.0, 0], [-12.858252190559869, 2.2672567859494275], [96.78833994094856, -35.228074762543876]], [[1.0, 0], [9.164821252882325, 0], [107.0, 0]], [[1.0, 0], [12.489757391476129, 0], [109.0, 0]], [[1.0, 0], [6.382775361773811, -1.1254555080819564], [106.18526614880764, -38.64827619580057]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-432-108.47-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/432/2/be/b/47/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.4669259986345187, 1.5240047082514114, 1.5769591955496474, 1.6218728531589957, 1.6518796693708582, 1.6580234409596473, 1.6303380625753314, 1.5590051471969484, 1.4355210235844702, 1.2538428543190936, 1.0114796221926476, 0.710467390496535, 0.35813890402903653, -0.03242248984587515, -0.4423590949788572, -0.8475457391217541, -1.2196943725780345, -1.5280720221577546, -1.7417813843772323, -1.8324777551072564, -1.777319107515262, -1.5618777723244808, -1.1826931839941366, -0.6491261170549891, 0.01580548290933511, 0.7758652813453489, 1.583460186699584, 2.382926675202344, 3.1150712728765373, 3.722614850530318, 4.1560263240505355, 4.379108313783135, 4.373639331014168, 4.142403065722738, 3.710055396147526, 3.1214918351845236, 2.437666379883957, 1.7291473327790248, 1.0680350825734106, 0.5191622449819007, 0.13169825223389856, -0.06765453979518676, -0.07878628479767198, 0.0711880520832527, 0.33117851605723303, 0.6331074055438427, 0.9019162098163177, 1.0673463985389176, 1.0758532825437945, 0.9008288060113249, 0.5493915879249638, 0.06436861785506859, -0.4792836962517227, -0.9835629346322207, -1.3410699139338864, -1.4514654586418034, -1.2383612238934087, -0.6639838725627767, 0.26092591300305623, 1.4739659317835636, 2.8657314795038724, 4.292146696774199, 5.593065280440847, 6.614598932549444, 7.231830668023726, 7.3682737729720875, 7.00873947986017, 6.203172954079808, 5.06039694689678, 3.732358011643605, 2.3911268678756077, 1.2022652274986023, 0.29896986326657393, -0.23854212230748412, -0.3946932462946371, -0.21900332126115732, 0.18494986361470644, 0.6802596145285281, 1.1234399783402305, 1.3922741154582976, 1.4094716850522144, 1.1574830457364729, 0.6813914208852486, 0.07905381909824523, -0.5198234691114741, -0.9816984537972134, -1.1987285232468026, -1.1137289729375344, -0.7351533456583069, -0.13854026104980424, 0.5464526762045597, 1.1613147232843373, 1.551435605829615, 1.599715074594517, 1.2538899228460045, 0.5414268906322012, -0.4318179016768329, -1.4996840605548711, -2.4674797632211125, -3.151293585904654, -3.41677653786794, -3.209057859325211, -2.566988933568172, -1.6179981394671992, -0.5538880692992686, 0.407927509504357, 1.0698807301194195, 1.2967485581175842, 1.0458116899646583, 0.3776549609535547, -0.5553846248771207, -1.5412587648219194, -2.354241298425638, -2.805106389560284, -2.7843476495565285, -2.288546036531698, -1.4234958614576474, -0.3827765381787246, 0.5939952063111478, 1.2742450090374102, 1.4850351301874127, 1.1531736522600613, 0.32343443275630906, -0.8496623700581684, -2.135019316557929, -3.275756373510553, -4.046070059678915, -4.301009201500178, -4.007533097350979, -3.2495450267974886, -2.2057544206293906, -1.1057563147752572, -0.17503306729156143, 0.4176585165486955, 0.5975935714650966, 0.3969383720942743, -0.05983823799455567, -0.5940038465633305, -1.0239646238827729, -1.21634966866489, -1.1229959593789114, -0.7935711721850417, -0.35990033812547717, 0.004370699395579609, 0.13829074501729463, -0.05248156779868302, -0.5576403981213855, -1.2517637926197704, -1.9162111861572344, -2.2896738556608733, -2.1357234576371233, -1.3104652431506825, 0.18762272359099078, 2.199933769134606, 4.428760492172893, 6.494138753576941, 8.014222574392857, 8.690389419511725, 8.37636736992142, 7.1140297856820585, 5.126408623306396, 2.7690011059719932, 0.45090502203198957, -1.4550202203045786, -2.690966833019591, -3.162836115543705, -2.947468582195475, -2.257988736915008, -1.3777122774094337, -0.5811307677475577, -0.06351892501081638, 0.10214489548637253, -0.029770390162374562, -0.3103402930232697, -0.5557448897012055, -0.6151959698967544, -0.4262593953889282, -0.04049135305264647, 0.3888619975592467, 0.6539719253968265, 0.5605622499821028, -0.0034863619458981826, -1.0204427402762577, -2.331786002320788, -3.669423960853461, -4.722061467575439, -5.21893207064706, -5.007194131467715, -4.100153656475622, -2.6810864205860727, -1.05978119010674, 0.4074556746277659, 1.412661437382684, 1.7793162521540027, 1.5097120573796723, 0.7823433370701645, -0.10079392907061362, -0.8025862406451474, -1.0498032351672306, -0.71408728415028, 0.14894001888123506, 1.3144600262391177, 2.4534983759299567, 3.2297336031191275, 3.399910117676545, 2.8881884689203123, 1.8120361981868653, 0.45130913722736726, -0.8310701759738089, -1.6939223297684476, -1.9173153263223213, -1.4671876311801362, -0.505602086386384, 0.6568077448333748, 1.6523839471133757, 2.1649073042654807, 2.022691273130576, 1.2485270799939592, 0.05164251506053449, -1.2356606483439487, -2.2572834219639692, -2.7382741503114834, -2.563629568133857, -1.8073789756589458, -0.7039013656539133, 0.42858236995852067, 1.2875724306855094, 1.6771626228175411, 1.5615969417471047, 1.0651558289024783, 0.4195586370111758, -0.12274079151606894, -0.3797318494526917, -0.3042866978558798, 0.0005887444017288426, 0.3217448086435567, 0.41839707191405606, 0.11944501303977265, -0.5982320276103753, -1.5792910499798298, -2.521138918620845, -3.0605513577043997, -2.8904261334451626, -1.8699115177823618, -0.09121217040887107, 2.1215895489437107, 4.285804421744653, 5.886867928601038, 6.522218995304688, 6.0192160152980705, 4.490560988447731, 2.30892314513601, 0.006806132152512832, -1.8693978164979497, -2.9080373140662394, -2.9395005366311135, -2.070977547253021], 'positive_zeros': ['1.61494431747740078319311383829276', '2.99725029280773316134367900886328', '5.06752127975404585826035010112233', '5.32897063722612185762602741738631', '6.39010766529543474552921794177614', '7.21882671812877477438786849493155', '9.058354509156747454514625791428295', '9.448738356573156956485406767017905', '10.39086214265061525166813269722953', '11.15069037382645044141741379689420'], 'prelabel': '2-432-108.47-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.857293021394124, 'root_angle': 0.23253309407093467, 'root_number': '0.7448246868477917 + 0.6672602085109594*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.116266547035', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.61494431747740078319311383829', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.99725029280773316134367900886', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.06752127975404585826035010112', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.4495373673193144, 'bad_primes': [2, 3], 'central_character': '108.47', 'conductor': 432, 'conductor_radical': 6, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/432/2/be/b/47/2'], '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': '2-432-108.47-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': '2-432-108.47-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.857293021394124, 'root_angle': 0.11626654703546734, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.61494431747740078319311383829', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2047185133385395364283589703760', 'Lhash_array': ['2047185133385395364283589703760'], 'label': '2-432-108.47-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/432/2/be/b/47/2'}