-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1308687529849245164078115498680', 'a10': [0.0, 0.0], 'a2': [0.0, -2.585786437626905], 'a3': [0.0, 6.656854249492381], 'a4': [1.3137084989847605, 0.0], 'a5': [0.0, 0.0], 'a6': [17.213203435596427, 0.0], 'a7': [0.0, 7.0], 'a8': [0.0, -24.083261120685233], 'a9': [-17.31370849898476, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.325334251004612, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, -7.0]]]], 'bad_primes': [5, 7], 'central_character': '175.99', 'coefficient_field': 'CDF', 'conductor': 175, 'conductor_radical': 35, 'conjugate': '2087455940439187697049694751024', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.585786437626905], [-8.0, 0]], [[1.0, 0], [0, -6.656854249492381], [-27.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -7.0]], [[1.0, 0], [-38.254833995939045, 0], [1331.0, 0]], [[1.0, 0], [0, -19.34314575050762], [-2197.0, 0]], [[1.0, 0], [0, -87.22539674441619], [-4913.0, 0]], [[1.0, 0], [-44.22539674441618, 0], [6859.0, 0]], [[1.0, 0], [0, -218.16652224137047], [-12167.0, 0]], [[1.0, 0], [-46.94112549695428, 0], [24389.0, 0]], [[1.0, 0], [-194.55844122715712, 0], [29791.0, 0]], [[1.0, 0], [0, 366.8528137423857], [-50653.0, 0]], [[1.0, 0], [339.3624817342638, 0], [68921.0, 0]], [[1.0, 0], [0, 226.16652224137047], [-79507.0, 0]], [[1.0, 0], [0, 11.676190233248546], [-103823.0, 0]], [[1.0, 0], [0, 209.01933598375618], [-148877.0, 0]], [[1.0, 0], [-616.0, 0], [205379.0, 0]], [[1.0, 0], [-320.73506473629425, 0], [226981.0, 0]], [[1.0, 0], [0, 14.509667991878084], [-300763.0, 0]], [[1.0, 0], [952.0, 0], [357911.0, 0]], [[1.0, 0], [0, -824.4894654563446], [-389017.0, 0]], [[1.0, 0], [156.27503653147244, 0], [493039.0, 0]], [[1.0, 0], [0, 1036.528137423857], [-571787.0, 0]], [[1.0, 0], [-170.22539674441617, 0], [704969.0, 0]], [[1.0, 0], [0, 1059.873016277919], [-912673.0, 0]], [[1.0, 0], [241.83347775862953, 0], [1030301.0, 0]], [[1.0, 0], [0, 1679.576910659136], [-1092727.0, 0]], [[1.0, 0], [0, 1506.8813844421313], [-1225043.0, 0]], [[1.0, 0], [-1252.4095218659884, 0], [1295029.0, 0]], [[1.0, 0], [0, -1370.2034611053284], [-1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-175-5.4-c3-0-9', '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/175/4/b/c/99/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.0203592063506943, 1.89299085479825, 1.728409664520741, 1.5280633918996676, 1.2938162657197059, 1.0282565702116069, 0.7350358608156385, 0.419201814042259, 0.08748459113232035, -0.2515030733231636, -0.5871892530797542, -0.9071220447314201, -1.1972297500616922, -1.4422773101808974, -1.6265216609118582, -1.7345534156642899, -1.7522948651549484, -1.6681056561935965, -1.4739290682984287, -1.1663953278916628, -0.747785926073854, -0.2267565542522629, 0.38128199641616256, 1.0542142671904433, 1.7637693503140865, 2.476604108677696, 3.1559141854586352, 3.763518428572623, 4.26231111237648, 4.618926721101793, 4.806419481603391, 4.806729945734517, 4.612698998500734, 4.229399923346628, 3.6745940624828837, 2.9781752895921803, 2.1805503030143045, 1.3300000348031573, 0.4791738510684107, -0.3190279604457074, -1.0158386421983678, -1.5708689226051316, -1.9557776881790678, -2.1569563248283496, -2.176881967949924, -2.033909773881214, -1.76042785077073, -1.399476891953382, -1.000121147434849, -0.6120262488261635, -0.27982985580132647, -0.03796244765117437, 0.09342778395334689, 0.11087790660172805, 0.027939482598279962, -0.12673351963419502, -0.3134276148880539, -0.48714293199605513, -0.6044316148845845, -0.6304361417574522, -0.5451598922257814, -0.34802239594054857, -0.05990430827090049, 0.27783504709876555, 0.6075075152897117, 0.8621193225356208, 0.9745384004699651, 0.8877016295776708, 0.5645028101464031, -0.004084251953784761, -0.793981649638567, -1.747103316956636, -2.7751028813265726, -3.7676938183869253, -4.604805700040787, -5.171230039773188, -5.371938709349434, -5.146008706794874, -4.477115417023793, -3.3988822962335026, -1.9939751643293182, -0.38663770541439507, 1.270722088026028, 2.815394932176287, 4.09445147641718, 4.984358532554072, 5.4073628925976385, 5.342196849656706, 4.8273648031022836, 3.956276066558149, 2.86465919451006, 1.711856776233116, 0.6585755167225551, -0.15570838787951408, -0.6323310729302754, -0.7270116395957467, -0.4552573028244925, 0.11133443372610333, 0.8574038833350996, 1.6429320849699318, 2.326135364867823, 2.7864925866055343, 2.9441528370196868, 2.7724991236677328, 2.301727406403246, 1.6127765730582417, 0.8225753564441871, 0.06308087296375993, -0.5422961978141644, -0.9007626566097475, -0.9667819684924068, -0.7502447430108593, -0.31459182519426065, 0.23490676192214607, 0.7707200176445663, 1.166995519237273, 1.323512950176287, 1.1851930230302996, 0.7534279111086526, 0.08694276306713176, -0.7081864618498502, -1.4976914355893864, -2.143993668801456, -2.5321796672187116, -2.592113869674241, -2.3123559597941656, -1.7430292781045662, -0.9868669637784024, -0.17995566090345316, 0.5342408028993356, 1.0325795386538468, 1.236195530548575, 1.1258673371542944, 0.7455476954341778, 0.19312644193052916, -0.3999332406771631, -0.8961228319837503, -1.181033591827495, -1.188077436014248, -0.9134828183669831, -0.4181354002397685, 0.1845103035156332, 0.7523028762237184, 1.145323507106126, 1.2574627351731633, 1.0418409054386284, 0.5243073304447176, -0.19843228370306465, -0.9763537136324248, -1.63624544912344, -2.0184960723041465, -2.01287250269334, -1.585458343920519, -0.790431002658303, 0.2367000276099168, 1.303953145667116, 2.2014747021856884, 2.7463385672783205, 2.8242754387186206, 2.4192274068248127, 1.6237393377762102, 0.6269062155370517, -0.3188222807759018, -0.9461588567421116, -1.0275036213668363, -0.4244842658873809, 0.8779162119158281, 2.7602949785002044, 4.983997301398133, 7.230390516508607, 9.157102851519124, 10.46042240667102, 10.931551898433078, 10.495449531029072, 9.224390680275318, 7.323479757016779, 5.0910683325901855, 2.8621796441852867, 0.9464932161663339, -0.4265480292107929, -1.1446103015888442, -1.2244034559054262, -0.7971839943514795, -0.07200389154863172, 0.7144566018198332, 1.350015044333749, 1.689607194278374, 1.6795142817962299, 1.3588498595120388, 0.839386177202766, 0.26983345903943173, -0.20586003889325677, -0.4855506460050783, -0.5321978360960249, -0.3780978678157356, -0.10976806805711647, 0.16175855847942272, 0.3366895443868248, 0.35819359661173716, 0.23109747980049095, 0.022062295452087318, -0.15924302486383762, -0.19319584105433524, 0.01139767982765595, 0.48435938816183144, 1.1764432304557064, 1.9630486920827235, 2.670020593261192, 3.1162476586406216, 3.1628716862240016, 2.7564198032625256, 1.9538524744772074, 0.9213742117604625, -0.09494059023558955, -0.8215644290806853, -1.021624828338817, -0.5556513561266518, 0.5762162388032593, 2.2220729363236704, 4.100942027042481, 5.8568755898948845, 7.1332476542116465, 7.650667818360623, 7.2704220211827275, 6.028180565192923, 4.129350797427458, 1.9063756579535396, -0.2526451495542109, -1.9876419691497502, -3.04306598791069, -3.3192589566905593, -2.886764827639411, -1.9606268093608912, -0.8414895694878045, 0.1615388857138304, 0.80688076656222, 0.9763821210681053, 0.6973756138948612, 0.1259098488187126, -0.5038322513143999, -0.9501508925181448, -1.0355005872580145, -0.6999537932488438, -0.02196173931169689, 0.7994697851728766, 1.49683242981613, 1.8068483885453965, 1.5446339526315631, 0.6593730952451301, -0.7438153547798272, -2.4224084817020053, -4.051413740426867, -5.301049305234949, -5.91734434336887, -5.784835037946499, -4.955021140149904, -3.6330818350533134], 'positive_zeros': ['1.03237242944832544739333277365196', '2.67352045577803876477612793985670', '4.82352917790929012541746536107390', '6.40188160329373191011090938786694', '6.77644020452773905440791942022151', '7.77298554987503961263365679155762', '8.624255205988623097960181033632280', '10.15404941878339276654717952646824', '11.59700987177039495360289214854970', '12.10399213872292715096570306754549'], 'prelabel': '2-175-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2133058134893746, 'root_angle': -0.07379180882521663, 'root_number': '0.894427190999916 - 0.44721359549995787*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0737918088252', 'prec': 54}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.03237242944832544739333277365', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.67352045577803876477612793986', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.82352917790929012541746536107', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 10.325334251004612, 'bad_primes': [5, 7], 'central_character': '5.4', 'conductor': 175, 'conductor_radical': 35, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/175/4/b/c/99/2'], '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': '2-175-5.4-c3-0-9', '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': '2-175-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2133058134893746, 'root_angle': -0.07379180882521663, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03237242944832544739333277365', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1308687529849245164078115498680', 'Lhash_array': ['1308687529849245164078115498680'], 'factors': ['2-175-5.4-c3-0-9'], 'label': '2-175-5.4-c3-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/175/4/b/c/99/2'}