-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1777801372846071357969813053622', 'a10': [3.128244944068297, 0.0], 'a2': [-2.373485943580927, 0.0], 'a3': [1.0, 0.0], 'a4': [3.633435524376243, 0.0], 'a5': [-1.3179959849893401, 0.0], 'a6': [-2.373485943580927, 0.0], 'a7': [-0.8592906728134033, 0.0], 'a8': [-3.8769362568527526, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.978065444458213, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [23, [[1.0, 0], [-1.0, 0]]], [29, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 23, 29], 'central_character': '2001.1', 'coefficient_field': 'CDF', 'conductor': 2001, 'conductor_radical': 2001, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.373485943580927, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.3179959849893401, 0], [5.0, 0]], [[1.0, 0], [0.8592906728134033, 0], [7.0, 0]], [[1.0, 0], [-4.308468604627704, 0], [11.0, 0]], [[1.0, 0], [4.155417908469283, 0], [13.0, 0]], [[1.0, 0], [-2.089203833795516, 0], [17.0, 0]], [[1.0, 0], [2.4561488665734994, 0], [19.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [4.707457553789044, 0], [31.0, 0]], [[1.0, 0], [3.9423173926857817, 0], [37.0, 0]], [[1.0, 0], [3.174423202390526, 0], [41.0, 0]], [[1.0, 0], [-11.015306901168916, 0], [43.0, 0]], [[1.0, 0], [-11.110311193133313, 0], [47.0, 0]], [[1.0, 0], [14.016503636889459, 0], [53.0, 0]], [[1.0, 0], [-8.472220396866978, 0], [59.0, 0]], [[1.0, 0], [6.3924912375021705, 0], [61.0, 0]], [[1.0, 0], [-4.747146450750084, 0], [67.0, 0]], [[1.0, 0], [12.490936463351497, 0], [71.0, 0]], [[1.0, 0], [-8.541055987730457, 0], [73.0, 0]], [[1.0, 0], [13.009239213466001, 0], [79.0, 0]], [[1.0, 0], [14.2415458458892, 0], [83.0, 0]], [[1.0, 0], [-0.7958076073303042, 0], [89.0, 0]], [[1.0, 0], [-3.9236887545187953, 0], [97.0, 0]], [[1.0, 0], [-3.906518116391636, 0], [101.0, 0]], [[1.0, 0], [-1.6805432888849818, 0], [103.0, 0]], [[1.0, 0], [-11.297726886260904, 0], [107.0, 0]], [[1.0, 0], [17.589693936638874, 0], [109.0, 0]], [[1.0, 0], [3.9825322186777794, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 64, 'label': '2-2001-1.1-c1-0-64', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/2001/2/a/i/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.4402877156768463e-60, 0.08308929487915773, 0.1658345301921574, 0.24786660848715172, 0.3287679630544899, 0.408052215623183, 0.48514817733141763, 0.5593891484174897, 0.6300081428781501, 0.6961393418330111, 0.7568257911899648, 0.8110331206243624, 0.8576688751100487, 0.8956069115385612, 0.9237162105712852, 0.9408933756971489, 0.9460980268206673, 0.9383902368280286, 0.9169691021760508, 0.8812114815799492, 0.8307098819591512, 0.7653084214703834, 0.6851357604381045, 0.5906338675668649, 0.48258148631906533, 0.3621111897460394, 0.23071896569783165, 0.09026536164804055, -0.05703265827256367, -0.20861983087213976, -0.3616311753370797, -0.5129312945948732, -0.6591643870323227, -0.7968146652871242, -0.9222765629359166, -1.031933779078381, -1.1222458735751903, -1.1898407916476055, -1.2316113761911343, -1.2448136306362056, -1.2271642359852706, -1.176934614247364, -1.0930386779831454, -0.9751113223998105, -0.8235747115478053, -0.6396894912278075, -0.4255882337817829, -0.18428868721689942, 0.08031523639531392, 0.363486343041729, 0.6597019767899537, 0.9627372243807408, 1.2657732642093127, 1.5615298818318464, 1.8424204038866783, 2.1007265203926893, 2.3287896948255558, 2.519215126815618, 2.665083559320267, 2.7601656364201195, 2.7991330445199476, 2.777760332196243, 2.6931111232601164, 2.5437024314815666, 2.3296409673266147, 2.052725705481109, 1.7165115596995473, 1.3263297852500595, 0.8892616889889496, 0.4140633562158908, -0.08895962142668039, -0.6081270414056967, -1.1306067615766044, -1.6426817880312719, -2.1300569135937653, -2.578198587240141, -2.9727003430644303, -3.299664917141721, -3.54609317926363, -3.700269248111808, -3.7521306818968276, -3.6936124739041194, -3.518953757478475, -3.22495665176541, -2.8111875612388517, -2.28011247032996, -1.6371593289767834, -0.8907024732498082, -0.051966123344467985, 0.8651537056712143, 1.8443471212911013, 2.8672238581177694, 3.9137156661557215, 4.96253851834829, 5.991703395078418, 6.97906248905413, 7.902876098294596, 8.742384305035968, 9.478366830822093, 10.09367425614944, 10.5737141247003, 10.90687632816292, 11.084883580265684, 11.103054711332778, 10.960470901878011, 10.660037761825533, 10.208439270546057, 9.615982927186717, 8.896338914218036, 8.066179534869768, 7.144728527851558, 6.153232970840643, 5.114373242155441, 4.05162881083724, 2.988619374875647, 1.9484419882010662, 0.9530252523373256, 0.022521364501898903, -0.8252441979461751, -1.575247298308749, -2.215648394314067, -2.7380717322563264, -3.13777126696159, -3.413677952814043, -3.5683271584263907, -3.607669165338216, -3.540769864617495, -3.3794127078218574, -3.137616548080695, -2.8310870810736466, -2.4766220386597495, -2.091491995834509, -1.6928195470254597, -1.296979643273598, -0.9190430434360175, -0.5722831405466519, -0.267763933850145, -0.014023716000352094, 0.1831347477931509, 0.3207410111867019, 0.39863869097756566, 0.41935476599679156, 0.38786356337473826, 0.31125681952071726, 0.19833500164588833, 0.059138254383433585, -0.09556224526477011, -0.2547901931655849, -0.407884389153388, -0.544990737874032, -0.6575048162833159, -0.738446083831326, -0.7827479265465836, -0.7874515491757141, -0.7517960985001836, -0.6772021272272724, -0.5671503835824607, -0.4269627188292538, -0.26349642470784473, -0.08476733579722959, 0.10047963232413988, 0.2832313517418152, 0.454676089151074, 0.6066587297913842, 0.7320991380837574, 0.8253528943213949, 0.8824963789503164, 0.9015218055873309, 0.8824321710417313, 0.8272309970139753, 0.7398069557931349, 0.6257187534255715, 0.4918907324041522, 0.3462342995964946, 0.197214247546246, 0.053382109916542596, -0.07709929517323903, -0.18691514877258678, -0.27001717349986665, -0.32197853866453985, -0.3402651042673245, -0.32440693626638656, -0.27605889275074436, -0.19894463589618255, -0.09868440431287265, 0.017487007403380255, 0.14109967733363468, 0.2629075521084252, 0.3734044855186924, 0.4633711460999597, 0.5244242216028199, 0.5495383609943358, 0.5335118119269029, 0.4733487535397092, 0.36853483426525474, 0.2211872687474933, 0.03606682149163088, -0.1795541624019544, -0.41616614978944466, -0.662430160791046, -0.9057024459724929, -1.1326529394583484, -1.3299485401219238, -1.4849677759082398, -1.5865104774367689, -1.6254649332975137, -1.595395744503232, -1.4930182703392012, -1.318530095755945, -1.075776187216887, -0.7722320824747766, -0.41879823998905663, -0.029408146773126965, 0.3795375098309103, 0.7898888486064931, 1.182586516272585, 1.5385851770302885, 1.8398169859172326, 2.070147434060912, 2.216274405096244, 2.26852217707513, 2.2214854895667004, 2.074484592800317, 1.8318002006689196, 1.502667158652211, 1.1010169803198613, 0.6449716818246813, 0.15610396647124775, -0.3415088437288567, -0.8223982985723629, -1.260936987327003, -1.6326327985130336, -1.9154233889248073, -2.0909065796772723, -2.1454431185114022, -2.0710721623391586, -1.8661868561384474, -1.535927268600777, -1.092260294068429, -0.5537304100443171, 0.05511925856918129, 0.7046400068926283, 1.3612533126697466, 1.9888630149448434, 2.550444588641882, 3.0097416575084313, 3.3329924518023226, 3.4906050419689807, 3.4587001599651592, 3.220444365734738, 2.7671041421460973, 2.0987629255326787, 1.2246576314298732, 0.16310827805164987, -1.0589669354407443, -2.406939156695167, -3.839727611831389], 'positive_zeros': ['1.40243800028650936821880551474445', '2.42250102426845090066656055727121', '3.54585864728428179566093507798741', '4.47173938147046130968370335787854', '5.94269005872411107390701131634725', '6.96020473791284007231526869620869', '7.38310019795180556257865664146285', '8.097528670896476681481933623374272', '8.906707116878849210428990540734578'], 'prelabel': '2-2001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9972572402158724, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.40243800028650936821880551474', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.42250102426845090066656055727', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.54585864728428179566093507799', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 15.978065444458213, 'bad_primes': [3, 23, 29], 'central_character': '1.1', 'conductor': 2001, 'conductor_radical': 2001, 'degree': 2, 'index': 64, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2001/2/a/i/1/1'], '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': '2-2001-1.1-c1-0-64', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-2001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9972572402158724, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.40243800028650936821880551474', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1777801372846071357969813053622', 'Lhash_array': ['1777801372846071357969813053622'], 'label': '2-2001-1.1-c1-0-64', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2001/2/a/i/1/1'}