-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3527385774234096446542101058032', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-2.8632039700232084, -1.6530715828377047], 'a4': [0.0, 0.0], 'a5': [0.8772357852101692, -2.056807569304114], 'a6': [0.0, 0.0], 'a7': [-0.5170631895759412, -0.8955797150691486], 'a8': [0.0, 0.0], 'a9': [3.9652913159711085, 6.868086026073614], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.076110452553291, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.8772357852101692, 2.056807569304114]]], [13, [[1.0, 0], [3.576723722706811, -0.4550246272745375]]]], 'bad_primes': [2, 5, 13], 'central_character': '260.69', 'coefficient_field': 'CDF', 'conductor': 260, 'conductor_radical': 130, 'conjugate': '367852758816551790034775522461', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.8632039700232084, 1.6530715828377047], [1.5, 2.598076211353316]], [[1.0, 0], [-0.8772357852101692, 2.056807569304114]], [[1.0, 0], [0.5170631895759412, 0.8955797150691486], [-3.5, 6.06217782649107]], [[1.0, 0], [2.960914754293396, 1.7094849304388267], [5.5, 9.526279441628825]], [[1.0, 0], [3.576723722706811, -0.4550246272745375]], [[1.0, 0], [2.0750781968886187, -1.1980469555631672], [8.5, -14.722431864335457]], [[1.0, 0], [5.37246398219296, -3.101793526330674], [9.5, -16.454482671904334]], [[1.0, 0], [-6.283037098788307, -3.6275131603138338], [11.5, 19.91858428704209]], [[1.0, 0], [-0.9027961045441382, 1.5636887219457112], [-14.5, -25.11473670974872]], [[1.0, 0], [0, 5.800534191917004], [-31.0, 0]], [[1.0, 0], [-0.7135197526836023, 1.235852463851979], [-18.5, -32.04293994002423]], [[1.0, 0], [3.6015804571335743, 2.0793734464341647], [20.5, 35.50704155516198]], [[1.0, 0], [1.868643560037274, -1.0788618624069806], [21.5, -37.239092362730865]], [[1.0, 0], [3.508943140840677, 0], [47.0, 0]], [[1.0, 0], [0, 4.5538176359402955], [-53.0, 0]], [[1.0, 0], [5.06249521142697, -2.9228329730885525], [29.5, -51.09549882328188]], [[1.0, 0], [1.9027961045441382, 3.2957395295145884], [-30.5, 52.827549630850754]], [[1.0, 0], [-3.808220337099512, 6.596031110273432], [-33.5, -58.023702053557386]], [[1.0, 0], [-9.4974544050469, 5.483357857370025], [35.5, -61.48780366869514]], [[1.0, 0], [7.153447445413622, 0], [73.0, 0]], [[1.0, 0], [12.852412140529008, 0], [79.0, 0]], [[1.0, 0], [-0.7066943140987488, 0], [83.0, 0]], [[1.0, 0], [-5.06249521142697, -2.9228329730885525], [44.5, 77.07626093681505]], [[1.0, 0], [7.997942700042697, 13.85284311249856], [-48.5, 84.00446416709055]], [[1.0, 0], [-2.9956234383222875, 5.188571995518375], [-50.5, -87.4685657822283]], [[1.0, 0], [0, 11.709588927164525], [-103.0, 0]], [[1.0, 0], [-11.745207893860927, -6.781098939208724], [53.5, 92.66471820493493]], [[1.0, 0], [0, -1.395326636322545], [-109.0, 0]], [[1.0, 0], [3.6513297431577985, -2.108096210112242], [56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-260-65.4-c1-0-7', '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/260/2/z/a/69/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.32137025125404317, 0.4719623873756405, 0.6366563049957262, 0.819474434333362, 1.022942676432381, 1.247559788516312, 1.4914709765635998, 1.7502986247642545, 2.017095256510633, 2.2824142934476526, 2.5345187791188097, 2.759758144383648, 2.9431391439427954, 3.0691029444316693, 3.122499407961831, 3.0897246144627943, 2.959961056867929, 2.7264343234376534, 2.3875783564793216, 1.9479866784932334, 1.4190224008853864, 0.8189680507031197, 0.17261907239471913, -0.4897372263106291, -1.1339637181830557, -1.724280383305332, -2.225911844162109, -2.607984309000721, -2.846423162991366, -2.926562840784983, -2.8451670037380925, -2.6115757636708095, -2.2477511981852603, -1.7870822496520864, -1.271930262457639, -0.7500370757160406, -0.27006457179797944, 0.12332955117163927, 0.3943691844019092, 0.5204221024636252, 0.49508397951428107, 0.32959754150671927, 0.052268730167056576, -0.2942471109078019, -0.6576613213033806, -0.9823722198312479, -1.216739679476994, -1.3204671517679438, -1.2711363953798451, -1.068947517080044, -0.738853219071017, -0.32953862642099574, 0.09093430479786437, 0.4425648279268066, 0.6432338810670356, 0.6198086689934759, 0.3191457179215108, -0.28251598461462074, -1.1732026694475648, -2.303037211690043, -3.586918550335275, -4.912094362388781, -6.149989799961893, -7.171003669935723, -7.860462538466312, -8.133622500094944, -7.947592458919984, -7.3083487416130195, -6.271599927372989, -4.937076796995286, -3.4367577076361937, -1.9184588390867832, -0.526977204677741, 0.6145584265657941, 1.4203914528103636, 1.8525007635189423, 1.9239660792943873, 1.6947172682675162, 1.2602383663324532, 0.7349475811664591, 0.23289267242438846, -0.1510811828871706, -0.35652719896970436, -0.36632645477799536, -0.2077327042324462, 0.054747065598934275, 0.33346863434160484, 0.536291620456455, 0.5863563576914185, 0.43926381443195817, 0.09425232617527865, -0.40305957300205003, -0.9673127143990746, -1.488634547504248, -1.853965814267689, -1.9706762725282503, -1.7879815627824, -1.3118096082957558, -0.6097409895177682, 0.1956688249001252, 0.94476296532981, 1.467261329892988, 1.612941691637035, 1.2810388238608548, 0.44277385406570097, -0.8476174106629344, -2.456093781491226, -4.186470107751302, -5.810046852966704, -7.102360392026965, -7.8806525907583005, -8.035255286085656, -7.548966776537675, -6.500550375341995, -5.0513593375511014, -3.4172584307496505, -1.8308583227330386, -0.5010303943926733, 0.4226922100760082, 0.8740670007138465, 0.8778929777726641, 0.5401637946596434, 0.022723567064435426, -0.49234774966326755, -0.8412899035879504, -0.912212272992581, -0.6667239365122974, -0.14523086539387534, 0.5450418104553117, 1.256526458030232, 1.8363456262067621, 2.1620450579696042, 2.169962667064575, 1.8697531112975294, 1.341657719998707, 0.7170171578491004, 0.14641032239301474, -0.23721697506733685, -0.3517072017247361, -0.18702746227466097, 0.19077709982539084, 0.6546382505600845, 1.047673851918528, 1.223698361913954, 1.0876186346196421, 0.6258361764995437, -0.08137912917915502, -0.8697493774190797, -1.5222724105719883, -1.8160284576728025, -1.574628414930871, -0.7145311389576675, 0.7258057039663844, 2.581658524063328, 4.585122331648228, 6.411960948065685, 7.743139622154241, 8.328302751529112, 8.037557246462086, 6.890074598001698, 5.052835445553924, 2.8092817753152812, 0.5042753716877146, -1.5229366801393687, -3.0033288941807044, -3.7863933017087468, -3.861956992251687, -3.3514175328768028, -2.4713006513508016, -1.4783466854329368, -0.6094243419910648, -0.030463112184723973, 0.19393331276808684, 0.10386793219059769, -0.17896546507704908, -0.4937551152714079, -0.6904992037911273, -0.673808252095238, -0.42885076724180976, -0.022635920693622726, 0.4194264343390179, 0.7549300820655082, 0.8719980669257827, 0.7291261353230619, 0.3753062486384527, -0.05648401335024347, -0.38213103736234455, -0.41785363379521273, -0.036923933638242645, 0.7839980475191206, 1.9426945904493587, 3.221481591390623, 4.329494128058854, 4.968510621142388, 4.906901658013711, 4.043229647736537, 2.442635297435774, 0.3352099440814339, -1.925323907167533, -3.934364888392702, -5.32415051855052, -5.845671413285583, -5.424850299938201, -4.178962486936858, -2.3888646638710824, -0.43348837985147143, 1.2975331115534274, 2.491750018994635, 2.9808483800299754, 2.7706113078838706, 2.027338432561833, 1.0253441451579142, 0.07006739995123346, -0.5826351896297242, -0.7898753447376368, -0.5517102053154379, -0.0009172401477432536, 0.64321339310829, 1.143123585591793, 1.3135481537972589, 1.0744287548186868, 0.4715618495635774, -0.3402158340989754, -1.1456632787099976, -1.7347804285100008, -1.9657788497809532, -1.8065504642093215, -1.3421898210979235, -0.7462325321514534, -0.22419225077717403, 0.0534905731346702, 0.008401569858682793, -0.3171220506538472, -0.7695328547900159, -1.130543519220372, -1.1878027350715437, -0.8090456066590477, 0.003138325573684707, 1.094160299316619, 2.1858847870708416, 2.9455250397881354, 3.077570274193831, 2.4135656965531997, 0.9737371969508687, -1.0189137003495108, -3.1789375642515725, -5.045109922835859, -6.192099086561755, -6.338035936449936, -5.419042401511086, -3.609990857214235, -1.2849261744936171, 1.0731755695649492, 2.989841448842867, 4.112816833929433, 4.2922148567906, 3.6065802995258305], 'positive_zeros': ['2.78261673492602890302361159345925', '4.58192183504811074584348513649013', '5.27007665067552371159395266131367', '6.47206456109769516222321192761598', '7.07388070907955516355875027971372', '9.053693597758349805491400939140871', '10.06950745968034242481675831608522', '10.60090875615577188477239826893757', '11.27628034027716776452035590016837', '12.34483223232978437372253442048462'], 'prelabel': '2-260-65.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': -0.916035810432261, 'root_number': '-0.9654109778605638 - 0.26073289747615275*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.458017905216', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.78261673492602890302361159346', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.58192183504811074584348513649', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.27007665067552371159395266131', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.076110452553291, 'bad_primes': [2, 5, 13], 'central_character': '65.4', 'conductor': 260, 'conductor_radical': 130, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/260/2/z/a/69/1'], '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': '2-260-65.4-c1-0-7', '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': '2-260-65.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4408714212424685, 'root_angle': -0.4580179052161305, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.78261673492602890302361159346', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3527385774234096446542101058032', 'Lhash_array': ['3527385774234096446542101058032'], 'label': '2-260-65.4-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/260/2/z/a/69/1'}