-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1386815407654798519831933517879', 'a10': [0.0, 0.0], 'a2': [1.043065098825747, 1.806641746768046], 'a3': [0.0, 0.0], 'a4': [-1.1759696007767309, 2.036839096701787], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [2.043065098825747, 3.538692554336923], 'a8': [-0.7341909960980323, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.389902136436429, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '675.226', 'coefficient_field': 'CDF', 'conductor': 675, 'conductor_radical': 15, 'conjugate': '2574784020450595882277188123362', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.043065098825747, -1.806641746768046], [-1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.043065098825747, -3.538692554336923], [-3.5, 6.06217782649107]], [[1.0, 0], [0.6759696007767309, 1.1708136929173483], [-5.5, 9.526279441628825]], [[1.0, 0], [-0.3240303992232691, 0.5612371146515289], [-6.5, -11.258330249197702]], [[1.0, 0], [1.3519392015534617, 0], [17.0, 0]], [[1.0, 0], [-0.6480607984465382, 0], [19.0, 0]], [[1.0, 0], [2.3950043003792088, -4.148269132602743], [-11.5, -19.91858428704209]], [[1.0, 0], [-1.9380693992049558, -3.3568346680174725], [-14.5, 25.11473670974872]], [[1.0, 0], [-3.848229996079719, 6.665329872420655], [-15.5, -26.846787517317598]], [[1.0, 0], [7.52419959685645, 0], [37.0, 0]], [[1.0, 0], [0.0898394031252368, -0.15560641073457235], [-20.5, -35.50704155516198]], [[1.0, 0], [0.4101605968747632, 0.7104189930498663], [-21.5, 37.239092362730865]], [[1.0, 0], [5.45322569570051, 9.445263970093421], [-23.5, 40.703193977868615]], [[1.0, 0], [-4.172260395302988, 0], [53.0, 0]], [[1.0, 0], [-2.086130197651494, 3.613283493536092], [-29.5, -51.09549882328188]], [[1.0, 0], [-1.9101605968747633, -3.308495204403182], [-30.5, 52.827549630850754]], [[1.0, 0], [-4.07097390115594, 7.051133633088968], [-33.5, -58.023702053557386]], [[1.0, 0], [-6.116442790642603, 0], [71.0, 0]], [[1.0, 0], [-12.344520790605976, 0], [73.0, 0]], [[1.0, 0], [5.172260395302988, 8.95861779464106], [-39.5, 68.41600689897065]], [[1.0, 0], [-6.129195296477241, -10.61607766301077], [-41.5, 71.88010851410841]], [[1.0, 0], [-3.0, 0], [89.0, 0]], [[1.0, 0], [6.7900086007584175, 11.76063988034324], [-48.5, 84.00446416709055]], [[1.0, 0], [0.7341909960980323, 1.2716561077013953], [-50.5, 87.4685657822283]], [[1.0, 0], [-3.762099798428225, 6.516147994022318], [-51.5, -89.20061658979718]], [[1.0, 0], [-1.2099913992415823, 0], [107.0, 0]], [[1.0, 0], [-14.104216798373285, 0], [109.0, 0]], [[1.0, 0], [-5.962268996061406, 10.326952829571038], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-675-9.4-c1-0-6', '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/675/2/e/b/226/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.341790646265291, 2.1021310023203568, 1.8668307254080352, 1.627749403968843, 1.3772942779265787, 1.110444197760094, 0.8261468286455128, 0.5280227666538005, 0.22443123535133536, -0.07202557345565912, -0.34549805456512406, -0.5783291118377569, -0.75286207146994, -0.8534962345276738, -0.8688150349062241, -0.7935608790174346, -0.6301974419687647, -0.3897962121722146, -0.09201785542741012, 0.23596570009231874, 0.5616478468733126, 0.8503568579988356, 1.0691531938444203, 1.1910371083192044, 1.1989296004793004, 1.0888285440291972, 0.871560445704391, 0.5726597122375938, 0.23011191739315798, -0.11001962233428773, -0.3997346171103957, -0.5963222905410656, -0.6697114924103272, -0.6088093139073687, -0.42567530381876867, -0.15654606091595907, 0.14091792908535622, 0.39427269354422934, 0.5263082837057519, 0.4673012231644872, 0.1678209070321538, -0.3899296187559847, -1.1843069824814598, -2.1517297273044402, -3.1906271345499664, -4.172051373069499, -4.956084050976911, -5.4120837954201635, -5.439928033549312, -4.9888821690776, -4.070723519548116, -2.7643227865482944, -1.2100133985732313, 0.40637408447901424, 1.8781949123236497, 3.0081273705704614, 3.6392559104642226, 3.6820133432893978, 3.1321571055917397, 2.076093349995479, 0.6817557381491746, -0.8243823362501005, -2.1911249661897174, -3.1820635846775507, -3.614319342470664, -3.3898173574632215, -2.513359502262879, -1.0938406992716363, 0.672175912024961, 2.5321432484977002, 4.219218824049256, 5.4966922166219625, 6.197175073245635, 6.249368421723881, 5.687428389397061, 4.641194664673813, 3.3092167046861243, 1.9198833808545734, 0.6883332985943876, -0.2223256383667874, -0.7278496966620162, -0.8326006131768013, -0.6206530880900012, -0.2306912830765438, 0.17941347415757294, 0.4702527580998253, 0.5522563603950551, 0.40379521439561117, 0.07213049402556591, -0.34263236692523086, -0.7163872296635166, -0.9353890395364494, -0.9274891835038401, -0.6823237395289163, -0.25522590747609913, 0.24631427736288836, 0.6903758488558964, 0.9555192588636772, 0.9638370752117928, 0.7033164402079267, 0.23321347979962964, -0.32958366297071967, -0.8402357349482219, -1.16427959294892, -1.214531730152101, -0.9763863838633619, -0.5139495808996046, 0.04573135852701947, 0.5472270407819385, 0.8515721489470317, 0.8794641936167695, 0.6404628635486408, 0.2387625282236379, -0.14816889512752537, -0.3146111010762049, -0.0849854659053844, 0.6292475371231608, 1.7900026032818848, 3.2228808931861455, 4.643095989849611, 5.71377385407966, 6.124555616483169, 5.6720756687462215, 4.321864278834104, 2.23437768514837, -0.25427496338525535, -2.6954953467318052, -4.622647939235866, -5.655544438265371, -5.589978250288797, -4.449762672148018, -2.487016144890588, -0.12872652813686067, 2.1190754878271174, 3.78728402918365, 4.551944414511383, 4.308148683385466, 3.191110345595408, 1.5389249816943953, -0.1938394551925513, -1.5500786457786446, -2.182911599614117, -1.938876042873193, -0.8908642988235694, 0.6867912991591741, 2.3936039173521677, 3.80808496074597, 4.594774928868808, 4.585222890854179, 3.812539435458599, 2.4920845448232334, 0.9555691959762563, -0.44174169341301484, -1.414362547990918, -1.8149403574411624, -1.6601133656440312, -1.1091042738698562, -0.40399947729891084, 0.20864452211556309, 0.5506497170877631, 0.5580747731674846, 0.2877830939942008, -0.11495217242006162, -0.47530254328267973, -0.6537356599256673, -0.5951016325530428, -0.3459005959617182, -0.03452950927672598, 0.17820846880379523, 0.16098644951061503, -0.13544339466837782, -0.6536965216491544, -1.2427407441037028, -1.705210152585629, -1.8638892790252128, -1.6250368266871347, -1.0163927797254892, -0.18544063041576384, 0.6435302352944278, 1.240954519131544, 1.449054951229346, 1.2382478361164315, 0.7223116946988697, 0.12467182443683368, -0.29555633259893993, -0.33477368967214244, 0.07709449258641411, 0.8398693823797254, 1.7037252315934868, 2.3449064267827464, 2.475471975564882, 1.9527822908325747, 0.8516512353652382, -0.5286654947180424, -1.7314002432874231, -2.2685343449620405, -1.7714800734437621, -0.12071591744823311, 2.4878910061384767, 5.565576036729631, 8.441691262694379, 10.435780955623873, 11.04315866017579, 10.080010924990773, 7.74389918929905, 4.569213742873971, 1.2878031947559168, -1.3665953743250165, -2.8541769951795013, -2.9685175169942135, -1.8794952185347495, -0.06828658769395307, 1.8246791003142948, 3.192071571180338, 3.6341819142787664, 3.0640353649809318, 1.7138770537826138, 0.044838121050022016, -1.408584980437006, -2.2083871208099226, -2.143706589947404, -1.283104744469314, 0.06425008938651146, 1.4615359814179263, 2.491228526406491, 2.8866447147012755, 2.605984733122926, 1.8277475529643186, 0.8735997515595156, 0.08885497952071375, -0.2764017231223919, -0.14488472766839586, 0.37596544820109695, 1.0478887200589186, 1.5984722295579128, 1.8233389858463283, 1.656353040899028, 1.1836918860600096, 0.5994216186228, 0.12223915694190503, -0.09285161578122586, -0.013143240510450536, 0.2653701531581291, 0.565387401968381, 0.7096599604432123, 0.6027543539278702, 0.27904367818303233, -0.10428923663868706, -0.32870116098191193, -0.20739496752928538, 0.32674847147017455, 1.1752252601710564, 2.0920887651752347, 2.764126278562385, 2.926046328947527, 2.467906113838874, 1.4919410569394869], 'positive_zeros': ['1.09400445785701086496586887869902', '2.28573164272010022827509085848686', '3.58336647593880266171882191332454', '4.44044203061591774518737120079727', '5.04417334236876156555514805269748', '6.59315371632598908634299970123281', '7.55649236473732089647968734035574', '8.454194027182124167696840263414802', '9.839068588663890039645758185878752', '10.44310386278615968036993698302943'], 'prelabel': '2-675-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.321616276742655, 'root_angle': -0.7612701264735351, 'root_number': '-0.7316943104660002 - 0.6816329188292511*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.380635063237', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09400445785701086496586887870', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.28573164272010022827509085849', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.58336647593880266171882191332', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.389902136436429, 'bad_primes': [3, 5], 'central_character': '9.4', 'conductor': 675, 'conductor_radical': 15, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/675/2/e/b/226/3'], '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': '2-675-9.4-c1-0-6', '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': '2-675-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.321616276742655, 'root_angle': -0.38063506323676755, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.09400445785701086496586887870', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1386815407654798519831933517879', 'Lhash_array': ['1386815407654798519831933517879'], 'label': '2-675-9.4-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/675/2/e/b/226/3'}