-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3081504023110507838674677155831', 'a10': [1.7918887482206685, 1.3375854043761715], 'a2': [-0.7071067811865476, 0.7071067811865476], 'a3': [1.7542204894299585, -1.7542204894299585], 'a4': [0.0, -1.0], 'a5': [-0.3212409751481677, -2.2128723948492497], 'a6': [0.0, 2.480842407544616], 'a7': [-0.7071067811865476, 0.7071067811865476], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [0.0, -3.154579051071767], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.148480955638592, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [5, [[1.0, 0], [0.3212409751481677, 2.2128723948492497]]], [7, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [11, [[1.0, 0], [3.3150962120514182, 0.1006831904656339]]]], 'bad_primes': [2, 5, 7, 11], 'central_character': '770.197', 'coefficient_field': 'CDF', 'conductor': 770, 'conductor_radical': 770, 'conjugate': '604463640189783319950611795362', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [-1.7542204894299585, 1.7542204894299585], [0, -3.0]], [[1.0, 0], [0.3212409751481677, 2.2128723948492497]], [[1.0, 0], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [3.3150962120514182, 0.1006831904656339]], [[1.0, 0], [4.935017899077652, 4.935017899077652], [0, 13.0]], [[1.0, 0], [2.378021412581726, -2.378021412581726], [0, -17.0]], [[1.0, 0], [0.03784768204193145, 0], [19.0, 0]], [[1.0, 0], [-1.6686146436910878, 1.6686146436910878], [0, -23.0]], [[1.0, 0], [-7.022392318017295, 0], [29.0, 0]], [[1.0, 0], [2.617555777902949, 0], [31.0, 0]], [[1.0, 0], [-6.70165077704714, -6.70165077704714], [0, 37.0]], [[1.0, 0], [0, 7.0580927993257765], [-41.0, 0]], [[1.0, 0], [3.134511979136202, 3.134511979136202], [0, 43.0]], [[1.0, 0], [6.506717528397481, 6.506717528397481], [0, 47.0]], [[1.0, 0], [-7.39262612616608, 7.39262612616608], [0, -53.0]], [[1.0, 0], [0, -4.176723775060779], [-59.0, 0]], [[1.0, 0], [0, -0.7377747064499617], [-61.0, 0]], [[1.0, 0], [3.596614296497866, 3.596614296497866], [0, 67.0]], [[1.0, 0], [-7.758428635021159, 0], [71.0, 0]], [[1.0, 0], [3.4455407303749817, 3.4455407303749817], [0, 73.0]], [[1.0, 0], [-5.318553964577699, 0], [79.0, 0]], [[1.0, 0], [4.105869641794497, 4.105869641794497], [0, 83.0]], [[1.0, 0], [0, 13.527464382153982], [-89.0, 0]], [[1.0, 0], [8.406003994614634, 8.406003994614634], [0, 97.0]], [[1.0, 0], [0, 2.9675278292939997], [-101.0, 0]], [[1.0, 0], [0.5294805095514759, -0.5294805095514759], [0, -103.0]], [[1.0, 0], [-7.670664600031974, 7.670664600031974], [0, -107.0]], [[1.0, 0], [11.441491159232154, 0], [109.0, 0]], [[1.0, 0], [0.040068727960521695, -0.040068727960521695], [0, -113.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 33, 'label': '2-770-55.32-c1-0-33', '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/770/2/m/f/197/9', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9760476945268657, 1.2304175101522306, 1.4915850430948512, 1.7595779465066208, 2.0301251023569757, 2.2944473218754724, 2.5397818683981113, 2.7504697316889333, 2.9094533694390905, 3.0000672684251284, 3.008008141653978, 2.923342616256459, 2.742365496565544, 2.4690819692792036, 2.1160696032852377, 1.70449267679658, 1.263098818638, 0.8261268301139869, 0.43018887338040945, 0.11034696733250017, -0.10423665741104454, -0.1945578876483013, -0.15533078025703, 0.002773829100111614, 0.2527587420607085, 0.5531725360019043, 0.8523291887918231, 1.0946460000791918, 1.2285079993566883, 1.21472997752594, 1.0344354294746543, 0.6950621036386511, 0.2332805852049479, -0.2861037426019783, -0.7757143435153465, -1.1354501345979908, -1.2657294485536699, -1.0825769790363253, -0.5324820937728117, 0.39529844843786727, 1.6612311936742727, 3.1745587306431937, 4.799859264107644, 6.370970584676691, 7.71093597615854, 8.65550822858646, 9.076908462317988, 8.904158493015439, 8.1365086586393, 6.84729716987817, 5.176924965059298, 3.3153287015825033, 1.47611649445453, -0.13391492123389515, -1.3451378247591892, -2.0503183544728065, -2.2203101668876255, -1.9072577562561122, -1.2344148705451812, -0.3740313613990348, 0.4830317728407618, 1.1606651230119838, 1.5278460951197728, 1.520346522180972, 1.1497178201785312, 0.4978244826318434, -0.3020082409955971, -1.0934890881775765, -1.7297509351620215, -2.1030081848598905, -2.1653313689636016, -1.9361855604295675, -1.4951654514842028, -0.9615717334179837, -0.4654206159898646, -0.11649094157484007, 0.02140582502351635, -0.05520202156020517, -0.29004844283329745, -0.5828513119833962, -0.8166416503604618, -0.8902038512336015, -0.7475709283466001, -0.3968442377761294, 0.08714668980179043, 0.5780881664687428, 0.9286587823163328, 1.0095176580858904, 0.7474261280819341, 0.1526146030468655, -0.67257379075851, -1.5476796516226816, -2.249344969118048, -2.5609414460739806, -2.325683347261568, -1.4905719044076617, -0.12977982368035446, 1.5597658143726376, 3.2916310528563058, 4.746100367618147, 5.637631822420912, 5.778401494133665, 5.122895597143529, 3.7822772748424187, 2.00396418616823, 0.11999580345666228, -1.5246037611608225, -2.6470729362620897, -3.0880290737425797, -2.843708196743124, -2.0613372432392008, -0.9985961357672708, 0.04292747893092827, 0.7937307098940134, 1.0826901131730884, 0.8767945071644334, 0.28414941824139217, -0.4804254856310445, -1.1580282279535488, -1.5197374177747665, -1.432020748911936, -0.8954551796342921, -0.04571391037623493, 0.8840528485096704, 1.629644431629753, 1.9729855791235944, 1.808498446372484, 1.1795057742145665, 0.2733016543324812, -0.6252490950218088, -1.210088230745411, -1.2400155453601016, -0.6106883193173713, 0.6080588337211058, 2.181235065865306, 3.7632097791679584, 4.984232155115207, 5.546222686875723, 5.301967875104658, 4.295856257051343, 2.7544917372825357, 1.02916997508622, -0.4944840743769269, -1.4952237843423235, -1.7963403644302482, -1.4055545555124664, -0.5042732498376573, 0.6098317044832289, 1.609786590394302, 2.230488398894075, 2.3379567922106785, 1.9573912698676212, 1.253249912827818, 0.4689675266654642, -0.15408849282258055, -0.45290141090476704, -0.3907522057473065, -0.06248794731785483, 0.3435632438820099, 0.6138677268777378, 0.5853527083237371, 0.20333118582503032, -0.45764857949552007, -1.217197665395183, -1.8492127440526693, -2.1587795933364515, -2.0498423457437567, -1.5601269858443962, -0.8502910916812441, -0.14951091674078182, 0.32520998754308905, 0.44888252957352465, 0.23932299640474167, -0.1408272028542197, -0.4348998120827898, -0.38187372609644693, 0.1834163843455012, 1.2536494572032475, 2.6247622857811885, 3.937527817779132, 4.77749924371137, 4.805863339097458, 3.8813022801767083, 2.1325939860514724, -0.04573939232689273, -2.080154944491616, -3.3671912006410634, -3.4442904817258846, -2.1325310643587376, 0.3927539778296952, 3.6279164640493606, 6.860103668582199, 9.348388299793566, 10.51663659968831, 10.103437871598748, 8.226398657450321, 5.343020779948271, 2.1207065540344785, -0.7451284837899891, -2.71143831879302, -3.515005257869132, -3.213125859545068, -2.1311074511245933, -0.7386402371804927, 0.5023929004933003, 1.269909025534995, 1.4543126155814914, 1.1545948094653544, 0.6069312744014401, 0.07680644238931543, -0.24407036686924824, -0.2993719482232179, -0.1689279398194928, -0.012904213514016504, 0.015121290099277956, -0.1505541385808607, -0.4460785042119609, -0.6942433131730372, -0.674014361182846, -0.21740250413603918, 0.7043078597695006, 1.9407488162836042, 3.1888671340077592, 4.0810871139853235, 4.30706827465965, 3.7265206813641525, 2.4312400416885405, 0.7306641571449011, -0.9384402394132259, -2.1502575520500984, -2.6298644088433236, -2.346014940874315, -1.5228224106382464, -0.5638918114221347, 0.08686638433525305, 0.10055944826785984, -0.6192012602624788, -1.8984025915974405, -3.3487496628158095, -4.499255619040142, -4.957823394150626, -4.546235948092669, -3.3609518694580154, -1.7382483239284257, -0.1363656372825768, 1.0228658855984964, 1.4957935748376245, 1.2910497765069864, 0.6497500903220866, -0.059819806328411086, -0.4928169074524124, -0.4664006010437037, -0.03302298432015325, 0.5405485318243294, 0.8818904289363497, 0.6688792660665451, -0.2266796791690483], 'positive_zeros': ['2.43087805311314489615765810397223', '2.87334285462749743962574884289605', '4.05670258563211338494904553406863', '4.82754907071417576585320001055097', '6.61347807842903719458679408833406', '7.42790278619944519293686370864030', '8.203965765483477931350091784027583', '9.457830846721158206639130177713094', '9.573460400696741237849742376354555', '10.47864177329621184746739518366128'], 'prelabel': '2-770-55.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4796130657097675, 'root_angle': 0.7875680255701335, 'root_number': '-0.7854492186670915 + 0.6189261061671704*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.393784012785', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.43087805311314489615765810397', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.87334285462749743962574884290', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.05670258563211338494904553407', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 6.148480955638592, 'bad_primes': [2, 5, 7, 11], 'central_character': '55.32', 'conductor': 770, 'conductor_radical': 770, 'degree': 2, 'index': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/770/2/m/f/197/9'], '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': '2-770-55.32-c1-0-33', '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': '2-770-55.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4796130657097675, 'root_angle': 0.39378401278506675, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.43087805311314489615765810397', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3081504023110507838674677155831', 'Lhash_array': ['3081504023110507838674677155831'], 'label': '2-770-55.32-c1-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/770/2/m/f/197/9'}