-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '805772678161234125227049861443', 'a10': [-2.9270509831248424, 5.069801019116659], 'a2': [1.3090169943749475, 2.267283942228512], 'a3': [-1.3090169943749475, 2.267283942228512], 'a4': [-2.4270509831248424, 4.203775615332221], 'a5': [1.118033988749895, 1.9364916731037085], 'a6': [-6.854101966249685, -1.4109342611737269e-60], 'a7': [0.0, 0.0], 'a8': [-7.47213595499958, 0.0], 'a9': [-1.9270509831248424, -3.337750211547782], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.434072428181207, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [0.5, 0.8660254037844386]]]], 'bad_primes': [7, 19], 'central_character': '931.704', 'coefficient_field': 'CDF', 'conductor': 931, 'conductor_radical': 133, 'conjugate': '4002159780262654691301110276939', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3090169943749475, -2.267283942228512], [-1.0, 1.7320508075688772]], [[1.0, 0], [1.3090169943749475, -2.267283942228512], [-1.5, -2.598076211353316]], [[1.0, 0], [-1.118033988749895, -1.9364916731037085], [-2.5, 4.330127018922194]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.8090169943749475, 4.865360153581828], [-5.5, -9.526279441628825]], [[1.0, 0], [1.0, 0], [13.0, 0]], [[1.0, 0], [2.4270509831248424, -4.203775615332221], [-8.5, -14.722431864335457]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-1.5, -2.598076211353316], [-11.5, 19.91858428704209]], [[1.0, 0], [5.618033988749895, 0], [29.0, 0]], [[1.0, 0], [0.4270509831248423, -0.739674000194466], [-15.5, -26.846787517317598]], [[1.0, 0], [-5.354101966249685, -9.27357663444888], [-18.5, 32.04293994002423]], [[1.0, 0], [0.38196601125010515, 0], [41.0, 0]], [[1.0, 0], [2.0, 0], [43.0, 0]], [[1.0, 0], [-5.5901699437494745, -9.682458365518542], [-23.5, 40.703193977868615]], [[1.0, 0], [0.5450849718747371, -0.9441148657292971], [-26.5, -45.89934640057525]], [[1.0, 0], [-0.35410196624968454, 0.6133225966044934], [-29.5, -51.09549882328188]], [[1.0, 0], [3.3541019662496847, 5.809475019311125], [-30.5, 52.827549630850754]], [[1.0, 0], [3.2811529493745266, -5.683123615721152], [-33.5, -58.023702053557386]], [[1.0, 0], [-7.47213595499958, 0], [71.0, 0]], [[1.0, 0], [-2.0729490168751576, 3.590453018727727], [-36.5, -63.21985447626402]], [[1.0, 0], [-5.0, -8.660254037844387], [-39.5, 68.41600689897065]], [[1.0, 0], [-7.854101966249685, 0], [83.0, 0]], [[1.0, 0], [-1.1458980337503155, -1.9847536147488225], [-44.5, 77.07626093681505]], [[1.0, 0], [14.416407864998739, 0], [97.0, 0]], [[1.0, 0], [-6.73606797749979, 11.667211980267364], [-50.5, -87.4685657822283]], [[1.0, 0], [2.3541019662496847, 4.077424211742248], [-51.5, 89.20061658979718]], [[1.0, 0], [0.7360679774997897, 1.274907134854101], [-53.5, 92.66471820493493]], [[1.0, 0], [-5.208203932499369, 9.020873827268934], [-54.5, -94.39676901250381]], [[1.0, 0], [4.145898033750315, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 14, 'label': '2-931-7.4-c1-0-14', '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/931/2/f/j/704/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.6418635042578544, 1.2261961733527325, 0.86310199735346, 0.543208790366962, 0.2617722017324914, 0.01880714056610778, -0.18185316887597897, -0.33422105164496346, -0.4321817767119277, -0.47158411597574457, -0.45214496723207775, -0.3789432762904135, -0.26329170325150913, -0.12279992864122162, 0.019501805943912907, 0.13701961736494622, 0.20235073086826857, 0.19070990253267284, 0.08365738799644289, -0.1273613779082255, -0.4382234463146051, -0.830637712660874, -1.2724158429395585, -1.7197767372679307, -2.121687098983067, -2.425918666811154, -2.5861723947610273, -2.569336419675756, -2.3617660857518694, -1.973451546093124, -1.4391045030406424, -0.8155557041321376, -0.17537984278430163, 0.40271005809861754, 0.8455257110744825, 1.0974273756759612, 1.1307083949211498, 0.952348924327041, 0.6055162957337941, 0.16490786285563128, -0.2739790248065127, -0.6104493976527191, -0.756832450733858, -0.6562891822845733, -0.2968517447341783, 0.28139231856511077, 0.9881697451100024, 1.694718551523031, 2.2543236231818047, 2.5288983973325183, 2.417319286764032, 1.8803533606192495, 0.9570390000690844, -0.2316084743945109, -1.4937648663678187, -2.5924595025678974, -3.282556655422632, -3.353392268519329, -2.669745730117486, -1.203417367486244, 0.9512702663342878, 3.582288945372944, 6.385799942732485, 9.009965313023615, 11.109891268773486, 12.404349087120314, 12.72399711296534, 12.041861252802178, 10.479747389236927, 8.288587604096818, 5.805665705655237, 3.39624752072338, 1.3903949293485907, 0.026932150773722602, -0.5846789873307319, -0.47724997390709034, 0.1887030311004586, 1.163673809600825, 2.1637239937361303, 2.9293373004586885, 3.2762494594074587, 3.1278421574006443, 2.5228889005304405, 1.5980035494510207, 0.5498046478691024, -0.4137412670153376, -1.1211438571293675, -1.4733187618900325, -1.4597893531771966, -1.1523973810258392, -0.6794100426619663, -0.1877188927899851, 0.1964329565873276, 0.3977887877342598, 0.40586214193348596, 0.26934546295365375, 0.07383074831191751, -0.08977062507408005, -0.15615791523258635, -0.10630420015044766, 0.02857032225469598, 0.18094739292596726, 0.2744043322575116, 0.25544197937340646, 0.11881845442010036, -0.08310347300303254, -0.25191557929308694, -0.27402124827062896, -0.06255651929128572, 0.4025375289195375, 1.0503031005407348, 1.7212433511263174, 2.2003684609676215, 2.275667606380054, 1.808251595835963, 0.7948191947202856, -0.5974789551702449, -2.0385387150992598, -3.0898682145676113, -3.298329506828318, -2.3093265812909296, 0.027971460274322277, 3.5917688834601025, 7.976938027247708, 12.5512154708459, 16.570561242522384, 19.330208710297175, 20.317223702749285, 19.327894418762387, 16.52013823423773, 12.386012102375567, 7.648779898525389, 3.107879306370011, -0.5314749595509721, -2.803126416595386, -3.564672254051771, -3.002822437297232, -1.5606443189336254, 0.1920791740296808, 1.709965053640905, 2.6046956045476506, 2.725656332130026, 2.1703215862248, 1.226130556951263, 0.264492309637199, -0.37996536751386395, -0.5091861027479194, -0.11261473344365602, 0.64291424807247, 1.4777231502157233, 2.095498337572932, 2.2796620075983376, 1.9596327144922359, 1.2272741444711062, 0.30028249871024704, -0.5536870252626183, -1.106116493497373, -1.2403163915163111, -0.9841817570027679, -0.49317965531853936, 0.00951790818345605, 0.3145753449965226, 0.301457895642544, -0.018967937675137114, -0.5088101897126124, -0.9529721329257802, -1.1372127047761815, -0.9273667548003843, -0.3219910289468464, 0.540405700911749, 1.4228820464525354, 2.0667898912870815, 2.27772724833634, 1.9911279691680355, 1.2945300085408262, 0.39832491271767034, -0.4353157258179426, -0.9808300739163046, -1.1240265114080878, -0.8966831400576173, -0.45843092497740584, -0.032173855095303745, 0.1836680613854193, 0.09375475104173395, -0.2545841317377959, -0.6870321925884364, -0.9693420993024514, -0.9022115673564383, -0.40855894404661214, 0.42148671073727473, 1.3487400798161537, 2.064472312441503, 2.3058024741939493, 1.965427597577095, 1.1522379114654766, 0.1734532702315298, -0.564783083094052, -0.7113869330624665, -0.12864677733303076, 1.002990189775792, 2.179378769355, 2.682714676155236, 1.78553668526841, -1.00714565584911, -5.752043171525686, -11.968115232379708, -18.68583271655551, -24.644311692503372, -28.589684523607577, -29.59440087615322, -27.306864787509472, -22.05804907030662, -14.79187079917379, -6.837078133934478, 0.41557199373741344, 5.840327665096625, 8.817936506017734, 9.329701463831471, 7.887776763671285, 5.334059275391812, 2.5764043401458157, 0.3440099995031491, -0.9693417042509241, -1.3392110586670538, -1.0286551582099295, -0.4336440796744852, 0.08286133186951453, 0.310862687624819, 0.23333384943737687, -0.014880320919394173, -0.24067176662088455, -0.2940376248424117, -0.1348516623606801, 0.15874036808302497, 0.437675616239303, 0.5591570880543782, 0.45673168335595554, 0.1714904232896822, -0.168841677532137, -0.4124282632664465, -0.45821768201488733, -0.30820641738721694, -0.071778738903705, 0.0820052932734322, 0.004654381030615757, -0.3543948518873255, -0.9096395154005191, -1.4617658491862924, -1.7759549974274669, -1.6864575617987716, -1.1832718333749077, -0.4403775142575864, 0.23362172981214344, 0.5101178685148268, 0.17896711631173315, -0.744929890002145, -1.9950691828112435], 'positive_zeros': ['0.63564256429663016229535194794547', '1.73210041136115963931350398324895', '2.30724127734697957801375055040216', '4.03581133418457785877301080629876', '4.92038500154101764890966539901255', '5.56900259590831948666934771215736', '6.60190952824381732880754182277575', '7.44899061934584344894117090403740', '9.128423253861746337120930793920660', '9.471545840926141479630714793073811'], 'prelabel': '2-931-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7265495462546077, 'root_angle': 0.41402514554911785, 'root_number': '0.26682585713848156 + 0.9637447597586793*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.207012572775', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.63564256429663016229535194795', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.73210041136115963931350398325', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.30724127734697957801375055040', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 7.434072428181207, 'bad_primes': [7, 19], 'central_character': '7.4', 'conductor': 931, 'conductor_radical': 133, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/931/2/f/j/704/2'], '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': '2-931-7.4-c1-0-14', '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': '2-931-7.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7265495462546077, 'root_angle': 0.20701257277455892, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.63564256429663016229535194795', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '805772678161234125227049861443', 'Lhash_array': ['805772678161234125227049861443'], 'label': '2-931-7.4-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/931/2/f/j/704/2'}