-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1212191100384154938364503211079', 'a10': [-1.3377572421303165, 2.3170635115629286], 'a2': [1.2497242961956476, 2.164585976464118], 'a3': [0.0, 0.0], 'a4': [-2.1236216330034132, 3.6782205644143], 'a5': [0.535220946813091, 0.9270298731553933], 'a6': [0.0, 0.0], 'a7': [-0.19355986010541465, 0.0], 'a8': [-5.616869017981579, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.096325623691686, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [1.50782783625368, -4.089798921245218]]]], 'bad_primes': [3, 19], 'central_character': '513.406', 'coefficient_field': 'CDF', 'conductor': 513, 'conductor_radical': 57, 'conjugate': '3266445681323858873960708779238', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.2497242961956476, -2.164585976464118], [-1.0, 1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.535220946813091, -0.9270298731553933], [-2.5, 4.330127018922194]], [[1.0, 0], [0.19355986010541465, 0], [7.0, 0]], [[1.0, 0], [-0.5717287817461935, 0], [11.0, 0]], [[1.0, 0], [2.8436554558038805, -4.925355728672755], [-6.5, -11.258330249197702]], [[1.0, 0], [1.0225701181176927, 1.771143398881552], [-8.5, 14.722431864335457]], [[1.0, 0], [1.50782783625368, -4.089798921245218]], [[1.0, 0], [-0.7771174067550584, 1.3460068319459304], [-11.5, -19.91858428704209]], [[1.0, 0], [-3.0494118210683987, 5.2817362072916], [-14.5, -25.11473670974872]], [[1.0, 0], [-5.869809824877354, 0], [31.0, 0]], [[1.0, 0], [-9.366684641028627, 0], [37.0, 0]], [[1.0, 0], [0.964779053186909, 1.6710463381979226], [-20.5, 35.50704155516198]], [[1.0, 0], [-1.6060305806949262, -2.78172656427296], [-21.5, 37.239092362730865]], [[1.0, 0], [-5.308802249246443, 9.195115223030774], [-23.5, -40.703193977868615]], [[1.0, 0], [3.8482947808925467, -6.665442083008031], [-26.5, -45.89934640057525]], [[1.0, 0], [-5.89825800956965, -10.216082548724712], [-29.5, 51.09549882328188]], [[1.0, 0], [4.011548013477989, -6.948204976345875], [-30.5, -52.827549630850754]], [[1.0, 0], [-3.370129418498933, 5.837235380922707], [-33.5, -58.023702053557386]], [[1.0, 0], [3.50280102935995, 6.067029351655996], [-35.5, 61.48780366869514]], [[1.0, 0], [-4.036760992373001, -6.991875136802197], [-36.5, 63.21985447626402]], [[1.0, 0], [-2.440186971987448, -4.226527815449913], [-39.5, 68.41600689897065]], [[1.0, 0], [-6.02878937741464, 0], [83.0, 0]], [[1.0, 0], [-8.795232272686686, 15.233789160662827], [-44.5, -77.07626093681505]], [[1.0, 0], [-3.7951150415153156, -6.573332072473396], [-48.5, 84.00446416709055]], [[1.0, 0], [-3.621140602814592, 6.271999505425465], [-50.5, -87.4685657822283]], [[1.0, 0], [-4.751981770383046, 0], [103.0, 0]], [[1.0, 0], [-3.664214884651784, 0], [107.0, 0]], [[1.0, 0], [6.169471445430134, 10.685837999330394], [-54.5, 94.39676901250381]], [[1.0, 0], [16.60307413762404, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-513-19.7-c1-0-4', '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/513/2/f/h/406/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.0195105642831024, 1.7444357028782704, 1.485195770747679, 1.2323482183880625, 0.9780102995635199, 0.7172950207088314, 0.44913257503194526, 0.17651111562194857, -0.09375798216404113, -0.35165533089227047, -0.5848862916867285, -0.7800846898738031, -0.9242318628680605, -1.0062070974752175, -1.0183488017362332, -0.9578715299724053, -0.8279616843014455, -0.6383719898245522, -0.40535710045338313, -0.15084247683002117, 0.09920509253596246, 0.3171395491015956, 0.47655544737876354, 0.5554838489600582, 0.5394934439237059, 0.4242722033499532, 0.2172612830369739, -0.06202956218501066, -0.3832735110715377, -0.7082122662216185, -0.9950184547109503, -1.2037362439349666, -1.3021770904030903, -1.2714777033002564, -1.1104484956236758, -0.8378817613533502, -0.49216449051654004, -0.12784714240391984, 0.19076893552781315, 0.3984937767952399, 0.43956748315587646, 0.2780627979009712, -0.09322369727000142, -0.646992356545707, -1.3201266729957761, -2.0176996738891373, -2.6224476332437314, -3.0090254126300024, -3.0615169192341427, -2.691961102388074, -1.8572025968524069, -0.5712956352621135, 1.0889579339113837, 2.9869733405204886, 4.938350000722221, 6.73099366533481, 8.151187341797083, 9.012257729135822, 9.181762182111644, 8.602989178983606, 7.307103793431038, 5.413452499028281, 3.1172283867882022, 0.6656470867650292, -1.67431426587515, -3.652036599489966, -5.067798901334251, -5.800303050388285, -5.822669769580749, -5.204129475279473, -4.096926412874527, -2.7104288792180364, -1.2766581371541001, -0.01300008380752053, 0.9115662541911613, 1.4009466387680067, 1.44296370103424, 1.1052155452667463, 0.5168240049436765, -0.16023194864720408, -0.7645437742140594, -1.1669262166425074, -1.2941565899085132, -1.1402874459367118, -0.763571168354749, -0.27000688657461414, 0.21269836665463926, 0.5649618396998797, 0.7023819076480201, 0.5940920262731965, 0.2684326996192202, -0.19518415786800444, -0.6862033953796768, -1.089908317757651, -1.3150439004880152, -1.3154636271509337, -1.1005348582225998, -0.7316794316745416, -0.3057713709186496, 0.07061679490333542, 0.30973019608877395, 0.3666203362028503, 0.252202834294197, 0.031522561466620344, -0.19298614010414586, -0.3095547194785631, -0.22957786972951535, 0.08393358840435705, 0.5999597798447369, 1.220573506846778, 1.8007878178694157, 2.183563187260357, 2.2420825515380356, 1.9187709184630093, 1.250386381016227, 0.37108510544745377, -0.5097608167352825, -1.1520763800869733, -1.3430537618027254, -0.9554401567649434, 0.008359975091033702, 1.3987528864116021, 2.9350177765096026, 4.254449222879523, 4.986034171766375, 4.833522603430828, 3.6493061784757437, 1.481283637452651, -1.4200365995525805, -4.638516320738654, -7.667808098694651, -10.010387420933963, -11.279197897819449, -11.279385395672929, -10.051290261915693, -7.864111613041927, -5.160651931907545, -2.4647543350037697, -0.2717804316360287, 1.0534151617281333, 1.3481631118788386, 0.6774899349236994, -0.6915353066676615, -2.3595913607925763, -3.8917139778413703, -4.9173773481827405, -5.210420569561569, -4.730704473554709, -3.6192680675651543, -2.1504730048894856, -0.6551776455631504, 0.5643167828990879, 1.3056218654669245, 1.5065298396862479, 1.2457460031153509, 0.7065091014717827, 0.11535571418674326, -0.3255688071215101, -0.4933910848550999, -0.3718629679430905, -0.04501283847122577, 0.33904753219166195, 0.6216965361389378, 0.6875858908492769, 0.5019758782379682, 0.12047739604132406, -0.33113587216933876, -0.6999648485524259, -0.8576441215522731, -0.7437206090359446, -0.38650250402354497, 0.10566979064205105, 0.5802324637056777, 0.8918750528312671, 0.9528434104898585, 0.7651116393747689, 0.42287145184329183, 0.08317546612094955, -0.08692487597303025, 0.029870268522854456, 0.4543501323070249, 1.093834565876487, 1.7630562804876446, 2.2389529623070765, 2.333923708250118, 1.9647840009881115, 1.1941623300502555, 0.2280548480343738, -0.6339953108595292, -1.0847252108461263, -0.9071115273330842, -0.054588764137685514, 1.3134788087152287, 2.8565733318624513, 4.136331365589882, 4.738611304343711, 4.401110789897663, 3.1089094486012225, 1.1268609367631996, -1.0459804568848083, -2.7929853125872657, -3.5396401567839835, -2.9141539291130547, -0.8640954398631798, 2.305773268085136, 5.988823386313021, 9.414004271111548, 11.831205242510213, 12.69614411539497, 11.805486211990189, 9.345820806817814, 5.843406162646317, 2.028698402267302, -1.3471298575700097, -3.6938524647279185, -4.713745500380863, -4.449898208555265, -3.2423584397639718, -1.6092932372309996, -0.09067338126916644, 0.8992806597387993, 1.1697760916216882, 0.7771402615889248, -0.02621050531602505, -0.8958553653417596, -1.5162109376421824, -1.6991989948533703, -1.4314829041181933, -0.8594213307949864, -0.2217711414285515, 0.24332036608961538, 0.38357755574737223, 0.18124116541186647, -0.24965051654286308, -0.71352473831154, -1.010731584921123, -1.012986056934633, -0.7092875547132561, -0.2062558988693256, 0.31619470619327494, 0.6765194701821264, 0.763271115633162, 0.5796876394664577, 0.24400610288231403, -0.05517204728829682, -0.13224757371560988, 0.1206258246800209, 0.6859251671038396, 1.4193532223827097, 2.0968842408445276, 2.49428417039346, 2.470248864159919, 2.0217418811718093, 1.2892414989525576, 0.50754240596153, -0.08175927964148458, -0.3244396723758402], 'positive_zeros': ['0.956250168749898855938373201904519', '2.44925504021124640207161932027054', '3.34928075268671497688962197201431', '4.67165790119698596606100179957224', '5.22413903880472668562739293471193', '6.42083225224702747571683028608270', '7.909365132884300286144009023112852', '9.126457671415484765968836958830652', '9.845256493615956485906097629572109', '10.69245742391578599086139721844736'], 'prelabel': '2-513-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.023938147200078, 'root_angle': -0.493240213559107, 'root_number': '-0.9990981581100776 - 0.04246022210316801*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.493240213559', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.956250168749898855938373201905', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.44925504021124640207161932027', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.34928075268671497688962197201', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.096325623691686, 'bad_primes': [3, 19], 'central_character': '19.7', 'conductor': 513, 'conductor_radical': 57, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/513/2/f/h/406/6'], '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': '2-513-19.7-c1-0-4', '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': '2-513-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.023938147200078, 'root_angle': -0.493240213559107, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.956250168749898855938373201905', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1212191100384154938364503211079', 'Lhash_array': ['1212191100384154938364503211079'], 'factors': ['2-513-19.7-c1-0-4'], 'label': '2-513-19.7-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/513/2/f/h/406/6'}