-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '443425113229140378701054704987', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.0, 1.7320508075688772], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [14.0, -12.12435565298214], 'a8': [0, 0], 'a9': [11.5, 19.91858428704209], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.30133700401845, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-14.0, 12.12435565298214]]]], 'bad_primes': [2, 5, 7], 'central_character': '700.501', 'coefficient_field': 'CDF', 'conductor': 700, 'conductor_radical': 70, 'conjugate': '1770332524663226846515582264944', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, -1.7320508075688772], [-13.5, -23.382685902179844]], [[1.0, 0], [0, 0]], [[1.0, 0], [-14.0, 12.12435565298214]], [[1.0, 0], [13.5, -23.382685902179844], [-665.5, -1152.6798124370878]], [[1.0, 0], [41.0, 0], [2197.0, 0]], [[1.0, 0], [-3.0, 5.196152422706632], [-2456.5, -4254.782808792947]], [[1.0, 0], [-24.5, -42.4352447854375], [-3429.5, 5940.068244557465]], [[1.0, 0], [40.5, 70.14805770653953], [-6083.5, 10536.931087845265]], [[1.0, 0], [-66.0, 0], [24389.0, 0]], [[1.0, 0], [94.0, -162.81277591147446], [-14895.5, -25799.76280414221]], [[1.0, 0], [-11.5, -19.91858428704209], [-25326.5, 43866.78477789317]], [[1.0, 0], [-51.0, 0], [68921.0, 0]], [[1.0, 0], [-202.0, 0], [79507.0, 0]], [[1.0, 0], [-163.5, -283.19030703751145], [-51911.5, 89913.35549711177]], [[1.0, 0], [100.5, -174.07110616067217], [-74438.5, -128931.26403921588]], [[1.0, 0], [-12.0, 20.784609690826528], [-102689.5, -177863.43140384424]], [[1.0, 0], [-98.0, -169.74097914175], [-113490.5, 196571.31217639567]], [[1.0, 0], [482.0, -834.8484892481988], [-150381.5, -260468.39851841913]], [[1.0, 0], [1140.0, 0], [357911.0, 0]], [[1.0, 0], [434.0, -751.7100504848927], [-194508.5, -336898.604504011]], [[1.0, 0], [319.0, 552.5242076144718], [-246519.5, 426984.29905647587]], [[1.0, 0], [36.0, 0], [571787.0, 0]], [[1.0, 0], [-405.0, -701.4805770653953], [-352484.5, 610521.062880512]], [[1.0, 0], [1550.0, 0], [912673.0, 0]], [[1.0, 0], [930.0, -1610.807251039056], [-515150.5, -892266.8395445109]], [[1.0, 0], [566.0, 980.3407570839845], [-546363.5, 946329.3414011582]], [[1.0, 0], [-90.0, -155.88457268119896], [-612521.5, 1060918.3587283]], [[1.0, 0], [-962.0, 1666.23287688126], [-647514.5, -1121528.0126375577]], [[1.0, 0], [108.0, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-700-7.4-c3-0-7', 'leading_term': '1.225490756033447228006555640723773970094003969491554118', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/700/4/i/c/501/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.2254907560334471, 1.0340041368680082, 0.8339005474589429, 0.6274473882306644, 0.41698422285374287, 0.20491265648425527, -0.00631499908903136, -0.21420891178215334, -0.41625734725550767, -0.6099452100146967, -0.7927758825090812, -0.9622965971606118, -1.1161274173197555, -1.2519937303977167, -1.3677619752811123, -1.4614781421642828, -1.5314084017401801, -1.5760810478293865, -1.5943287784405975, -1.5853302002185574, -1.548649325297568, -1.4842717425043237, -1.3926360910413307, -1.2746594481659128, -1.1317552663121808, -0.9658425622194748, -0.7793451727015613, -0.5751800494712261, -0.35673376851607624, -0.12782667619686489, 0.10733561860572413, 0.3442233739381134, 0.5780560806734264, 0.8038873048232781, 1.0166998582858549, 1.2115097594765485, 1.3834770635864977, 1.5280212817822523, 1.6409387824483832, 1.7185192887288354, 1.7576583680641145, 1.755962663396701, 1.7118445533204103, 1.6246029591345894, 1.4944871478644886, 1.3227406165825628, 1.111622486583478, 0.8644042845674796, 0.5853405368167822, 0.27961224249589517, -0.04675698904191198, -0.38701157112647944, -0.7337999537964288, -1.0793337874849032, -1.415567168746363, -1.7343920981554855, -2.027845540802247, -2.28832283154361, -2.5087916384921303, -2.6830003154522206, -2.805674260589748, -2.8726938740130326, -2.881247885649839, -2.8299562154263875, -2.7189571322155204, -2.5499542909704824, -2.3262202358905077, -2.0525541405817815, -1.7351928855556829, -1.3816760134318706, -1.0006666108377926, -0.6017316957862654, -0.19508718878986092, 0.20868603879778155, 0.5989472693165128, 0.9653133419842098, 1.2979786581165922, 1.5880275356938731, 1.8277284276774912, 2.0107996361633464, 2.132636639059498, 2.190492001356827, 2.183600059633002, 2.1132401226279502, 1.9827337849879811, 1.7973740545544377, 1.5642862824410166, 1.2922232854306848, 0.9912994791998606, 0.6726712099255767, 0.34817268952004543, 0.02991891521612555, -0.27011139918328575, -0.5404986142335474, -0.7707956481494762, -0.9519168869402959, -1.0764875830317115, -1.1391397090415358, -1.1367417092264454, -1.0685516079784447, -0.9362854398524229, -0.7440958840849141, -0.4984592232571503, -0.20797218795217567, 0.11693622966804522, 0.464369446596855, 0.8213926311761379, 1.1745119749589998, 1.5101866930921064, 1.8153546819050579, 2.0779515825991175, 2.28740258804945, 2.435066735249006, 2.5146146667299347, 2.5223229043874738, 2.457270507562139, 2.32142749857605, 2.1196285151860286, 1.8594296435298632, 1.5508511258189925, 1.206013434980775, 0.838678863681218, 0.46371508510315607, 0.09650091105052035, -0.247702482144882, -0.5543894258328649, -0.8104301394769312, -1.0046469693854185, -1.1283209154540286, -1.1756050908008635, -1.1438250557829615, -1.0336502420789335, -0.8491257831498308, -0.5975598006916873, -0.28926733315589803, 0.06282162444333968, 0.44367634342767487, 0.8367824685695715, 1.2248375532284554, 1.5904964137814082, 1.9171346853487112, 2.189597269289366, 2.394898110298547, 2.5228389872471713, 2.5665177409652786, 2.5227005191840877, 2.3920380511814607, 2.179112465834701, 1.892308473579169, 1.5435105354129692, 1.1476355969222536, 0.7220187096572325, 0.2856760307312162, -0.14152406661683672, -0.5397460428191454, -0.8900891948109015, -1.17546565203357, -1.3814135133911165, -1.4968062910273183, -1.514423716386831, -1.4313545957391263, -1.2492095594286352, -0.9741299348947278, -0.6165882230188379, -0.19098535274479375, 0.2849404220197118, 0.7908689021093975, 1.3047852298929998, 1.8039597790559092, 2.265976134181913, 2.6697594613991376, 2.996556616812416, 3.230820719562304, 3.360956622595386, 3.379889622800528, 3.285427626613374, 3.080396486805841, 2.7725389199163053, 2.3741787992331886, 1.901664144862912, 1.374613227906957, 0.8149983045123488, 0.2461100675279532, -0.3085475176559319, -0.8263781178025124, -1.2867742290235897, -1.6721044194397274, -1.9685563441086666, -2.166791862253673, -2.2623795369355713, -2.2559806835842773, -2.1532774351736936, -1.9646444010837048, -1.704578749951717, -1.3909162568051188, -1.043872346371928, -0.6849568106617216, -0.33581813517526715, -0.017077803466242204, 0.25278372731339016, 0.4584296097774069, 0.5885031096155919, 0.6362515206384799, 0.5999017392900572, 0.48276460359869056, 0.29305941112016276, 0.043465050277820404, -0.2495808877349461, -0.566799614379343, -0.8871575075731037, -1.189063602709121, -1.4516134844249098, -1.655811276985757, -1.7857015402598146, -1.8293467407540605, -1.7795934464380028, -1.634581150806053, -1.3979611376471568, -1.0788083609532673, -0.6912261122828834, -0.25366037165687777, 0.2120427597201411, 0.6817881996731142, 1.1305307286511763, 1.5336513161723482, 1.868335120958288, 2.1148739195878736, 2.2578185998629774, 2.2869144784036455, 2.197763250282492, 1.9921698055149033, 1.6781492031128402, 1.2695878627405428, 0.7855724841050571, 0.24941924147917519, -0.31254666811523757, -0.8723960498460553, -1.402108684348552, -1.875110244193022, -2.2677464426934284, -2.560609917904797, -2.7396424537992705, -2.796946808319617, -2.731258066587849, -2.5480432366565378, -2.259218724853077, -1.8824971940492663, -1.440396868619275, -0.9589663449663984, -0.4662952034657897, 0.009105858334198814, 0.4399628922938099, 0.8018385874507064, 1.0745802570862866, 1.2435295916827456, 1.300420613446447, 1.2439095540787362], 'positive_zeros': ['0.34980073621966933635382921840585', '1.73119121991548992887474259626081', '2.92147241796739193179961975788136', '4.24691272149273105435321020939076', '5.33768252040448818706634074620555', '6.07323850817422622056525166691816', '7.22296399279699807822996801947534', '7.900114619198913075860363100156639', '8.945122767897129582860551465107984', '9.633502034282451949391886512691034'], 'prelabel': '2-700-7.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.426611626978749, 'root_angle': -0.3535062863872795, 'root_number': '-0.6054643436493673635071294605077551469423497523567868621 - 0.7958724323465669471984178169629224157856347934855379281*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3535062863872795', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.34980073621966933635382921841', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.73119121991548992887474259626', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.92147241796739193179961975788', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 41.30133700401845, 'bad_primes': [2, 5, 7], 'central_character': '7.4', 'conductor': 700, 'conductor_radical': 70, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/700/4/i/c/501/1'], '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': '2-700-7.4-c3-0-7', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-700-7.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.426611626978749, 'root_angle': -0.3535062863872795, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.34980073621966933635382921841', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '443425113229140378701054704987', 'Lhash_array': ['443425113229140378701054704987'], 'factors': ['2-700-7.4-c3-0-7'], 'label': '2-700-7.4-c3-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/700/4/i/c/501/1'}