Table lfunc_lfunctions
L-functions
{'Lhash': '2767441569538895973477127428043', 'a10': [9.796853143207976, -2.005409806103483], 'a2': [1.7500097792596925, -0.9682281613831745], 'a3': [4.247075489155944, 0.0], 'a4': [2.125068455009115, -3.388817501950374], 'a5': [4.771570763992094, 1.4940255835212133], 'a6': [7.432423639277044, -4.112138092121006], 'a7': [-7.863056894291424, 0.0], 'a8': [0.4377420386857037, -7.988014891546415], 'a9': [9.0376502105892, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.354250045691284, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [-1.7500097792596925, 0.9682281613831745]]], [5, [[1.0, 0], [-4.771570763992094, -1.4940255835212133]]], [19, [[1.0, 0], [0, 4.358898943540674]]]], 'bad_primes': [2, 5, 19], 'central_character': '380.39', 'coefficient_field': 'CDF', 'conductor': 380, 'conductor_radical': 190, 'conjugate': '2140063659500310463543682717897', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.7500097792596925, 0.9682281613831745]], [[1.0, 0], [-4.247075489155944, 0], [9.0, 0]], [[1.0, 0], [-4.771570763992094, -1.4940255835212133]], [[1.0, 0], [7.863056894291424, 0], [49.0, 0]], [[1.0, 0], [0, 2.6370129431869738], [-121.0, 0]], [[1.0, 0], [0, 5.112572323791855], [-169.0, 0]], [[1.0, 0], [0, -12.26802867327835], [-289.0, 0]], [[1.0, 0], [0, 4.358898943540674]], [[1.0, 0], [-17.25073093391742, 0], [529.0, 0]], [[1.0, 0], [-4.9596583820146485, 0], [841.0, 0]], [[1.0, 0], [0, -59.46506213541342], [-961.0, 0]], [[1.0, 0], [0, -47.86766037344452], [-1369.0, 0]], [[1.0, 0], [4.385127752825953, 0], [1681.0, 0]], [[1.0, 0], [51.23624832428055, 0], [1849.0, 0]], [[1.0, 0], [41.36094532535327, 0], [2209.0, 0]], [[1.0, 0], [0, -42.98204279003986], [-2809.0, 0]], [[1.0, 0], [0, 103.3362376223377], [-3481.0, 0]], [[1.0, 0], [-68.72790014003313, 0], [3721.0, 0]], [[1.0, 0], [69.79302835628863, 0], [4489.0, 0]], [[1.0, 0], [0, 55.14747335299192], [-5041.0, 0]], [[1.0, 0], [0, 45.6446945062504], [-5329.0, 0]], [[1.0, 0], [0, 84.15134012075379], [-6241.0, 0]], [[1.0, 0], [-2.1621996309076787, 0], [6889.0, 0]], [[1.0, 0], [-89.65221906634252, 0], [7921.0, 0]], [[1.0, 0], [0, -36.54474324426752], [-9409.0, 0]], [[1.0, 0], [105.73860174475348, 0], [10201.0, 0]], [[1.0, 0], [187.5696065774794, 0], [10609.0, 0]], [[1.0, 0], [-111.6933637526349, 0], [11449.0, 0]], [[1.0, 0], [-88.20724985428757, 0], [11881.0, 0]], [[1.0, 0], [0, 108.160724292978], [-12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 15716288, 'index': 100, 'label': '2-380-20.19-c2-0-100', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/380/3/h/a/39/93', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [4.515863025839914, 4.644803417650717, 4.741425091195253, 4.801608723578741, 4.819359185783416, 4.78739476718572, 4.698011273043216, 4.544127200050768, 4.320407021932372, 4.024358624951727, 3.6573026673757423, 3.2251142214328667, 2.738642029958843, 2.2137213995870777, 1.6707165112904356, 1.1335588744196152, 0.628290968243087, 0.18117579236073691, -0.18351009531695248, -0.44582650103391414, -0.5924412559655384, -0.6185710215089594, -0.5293311409673584, -0.34025679099941647, -0.07681311823979224, 0.22720002938925096, 0.5323278820113543, 0.797071396941124, 0.9821391738731988, 1.0549292852687435, 0.9937408907628035, 0.7911773097387114, 0.4562283293408005, 0.014616994955007198, -0.49283687261728876, -1.0138597560058866, -1.4901379455186725, -1.8640018638086817, -2.0856509255430944, -2.120028394166376, -1.9523989722410011, -1.5917513930695233, -1.0713512880743934, -0.4460942507631172, 0.21327667899568806, 0.8285711040847197, 1.324220848443006, 1.6377326645037333, 1.7290541160279342, 1.5874006326337184, 1.2343323001439237, 0.7223204900874968, 0.12866008112114288, -0.4547162594562432, -0.9342818585167632, -1.2290236132456296, -1.2834972731804373, -1.0777021375372677, -0.631978538074095, -0.005787499445151094, 0.709863957716958, 1.4055629415426838, 1.9704214108550315, 2.3102475367848454, 2.3639961395435076, 2.115593996876409, 1.5987965544663245, 0.8937462990618523, 0.11523459727477414, -0.6058865382245386, -1.1453831285342877, -1.4087115191908122, -1.3504262174825417, -0.9861947964960708, -0.39471220901362974, 0.2916060434307739, 0.9063581538691362, 1.276602036677622, 1.253716106011354, 0.7424512968579713, -0.2771015380582575, -1.739008080888637, -3.4950798371811183, -5.332842805646046, -7.005628379995777, -8.27024054611191, -8.92605884994513, -8.848873436715655, -8.013380016393558, -6.500035173394158, -4.484611609787649, -2.2118432136810346, 0.04254714631325669, 2.014946134956261, 3.4945374419336632, 4.354387546245223, 4.567455865494168, 4.204847232629009, 3.4169709057633573, 2.401520925699969, 1.36469572655879, 0.4833114010039138, -0.12484005844622936, -0.4168390595387771, -0.42409154534250787, -0.23626859399389658, 0.026103181537899253, 0.24386558741303602, 0.32880325312032055, 0.24384069599758718, 0.00939316921568732, -0.3053053284407663, -0.603486067966022, -0.7892755816125724, -0.7960118891802036, -0.6071130898665321, -0.2638781966036007, 0.14225257605574582, 0.491581803334732, 0.6671124935124123, 0.5869403223488971, 0.22966517447638554, -0.35429378972478803, -1.049430056818174, -1.699528129429275, -2.144762018088116, -2.2630014170873447, -2.005117572718665, -1.4148199698725281, -0.6267071559105224, 0.1588373309288445, 0.7196296081139202, 0.8652797849625721, 0.48804643510020607, -0.40167583311579474, -1.6650846679050542, -3.0544056197850966, -4.259725002302109, -4.9742205674424715, -4.963836081047392, -4.125521747875595, -2.5199025980692316, -0.36942233648039413, 1.9794234381410856, 4.122896606613854, 5.681998950883871, 6.381734598499114, 6.109793076427608, 4.941024966210009, 3.1216404384154113, 1.016237558972278, -0.9705951363748618, -2.4803491632697763, -3.2747135916852357, -3.2809038233283854, -2.5982139484642968, -1.4650895150127912, -0.19548303337207912, 0.8994369020595036, 1.5848321130607141, 1.7531255323432335, 1.4404368188803767, 0.8055970252244355, 0.07844399364491728, -0.5080812194455268, -0.783542258438467, -0.6857425319261936, -0.27458775434456606, 0.2891555597264001, 0.7938138442867557, 1.0411923550886277, 0.9071120961046311, 0.38082838070028335, -0.428139588696338, -1.3181920141491545, -2.051430180680127, -2.4217080631528543, -2.3158678456253923, -1.750592556373321, -0.8737793357141616, 0.07095405597569732, 0.8077206621639713, 1.1028517817735721, 0.8300579541737236, 0.00808539233529686, -1.200008656099896, -2.5263783660906505, -3.6663956580185646, -4.356841555991019, -4.443036161788331, -3.9166488882007133, -2.914075119374216, -1.676300621283733, -0.48197225494657325, 0.4271505544251781, 0.9072517224201295, 0.9430898367318693, 0.6403853031284797, 0.18353357936897388, -0.22748715474444853, -0.4410365918461943, -0.3985574889348224, -0.14628967290232642, 0.1893656888975854, 0.454396866949287, 0.5298816514829319, 0.38316875628000185, 0.08882996735164898, -0.1901560902815464, -0.25775160806032216, 0.03902271910338277, 0.7372602107462047, 1.7138893666636084, 2.6884616774051753, 3.278406346388864, 3.0962680332300376, 1.864464327742461, -0.48460236068883267, -3.753929768649946, -7.493122167041595, -11.078537316664688, -13.846253579347463, -15.245940967892057, -14.976098726985423, -13.06423565655156, -9.868970828677996, -6.001288651112372, -2.1837769356533547, 0.9164458528878745, 2.838095147598145, 3.4208116944186706, 2.821500640273254, 1.4499594686967534, -0.15628551487505277, -1.4819794678678317, -2.1673444851844548, -2.0890372047756265, -1.3694763858054748, -0.3162841306359582, 0.6864992751230209, 1.3008745505900337, 1.3342209091647885, 0.7874866646411588, -0.15897605194630987, -1.2136324125562536, -2.0715993904765972, -2.509756328748071, -2.449345155717057, -1.9681350433518108, -1.2613359884579889, -0.5671505508087767, -0.08374390293406112, 0.09392756254139413, -0.003109454610481888, -0.2413817382121979, -0.44443420484568225, -0.46544488350827534], 'positive_zeros': ['2.18312646169271116799328190342193', '3.03256349466803904483096075511246', '4.12877937009491822367267462140495', '5.45937848354214356190895719009589', '6.52668736760412028786702747639464', '7.37605071162331751205692170660449', '8.518779803276429432018757056366207', '9.322140410273127076793673739911216', '9.971288588796229813213352815966604', '11.49753433765137183986251073123213'], 'prelabel': '2-380-20.19-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.217802051974497, 'root_angle': 0.13743599566176298, 'root_number': '0.6497537939146805 + 0.7601447278600826*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.137435995662', 'prec': 40}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.18312646169271116799328190342', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.03256349466803904483096075511', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.12877937009491822367267462140', 'prec': 100}}