-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '954108383484355550277667478582', 'a10': [0.0, 0.0], 'a2': [-1.0, -1.0], 'a3': [-1.224744871391589, 1.224744871391589], 'a4': [0.0, 2.0], 'a5': [0.0, 0.0], 'a6': [2.449489742783178, 6.223015277861142e-61], 'a7': [0.0, 0.0], 'a8': [2.0, -2.0], 'a9': [0.0, -3.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.791024121276825, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 1.0]]], [3, [[1.0, 0], [1.224744871391589, -1.224744871391589]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '600.293', 'coefficient_field': 'CDF', 'conductor': 600, 'conductor_radical': 30, 'conjugate': '1472825717829200395568278482181', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 1.0]], [[1.0, 0], [1.224744871391589, -1.224744871391589]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0, -7.0]], [[1.0, 0], [-4.898979485566356, 0], [11.0, 0]], [[1.0, 0], [2.449489742783178, -2.449489742783178], [0, -13.0]], [[1.0, 0], [2.0, 2.0], [0, 17.0]], [[1.0, 0], [0, 0], [19.0, 0]], [[1.0, 0], [-4.0, 4.0], [0, -23.0]], [[1.0, 0], [0, -9.797958971132712], [-29.0, 0]], [[1.0, 0], [-2.0, 0], [31.0, 0]], [[1.0, 0], [-7.3484692283495345, -7.3484692283495345], [0, 37.0]], [[1.0, 0], [0, 0], [-41.0, 0]], [[1.0, 0], [2.449489742783178, -2.449489742783178], [0, -43.0]], [[1.0, 0], [-8.0, -8.0], [0, 47.0]], [[1.0, 0], [0, 0], [0, 53.0]], [[1.0, 0], [0, 14.696938456699069], [-59.0, 0]], [[1.0, 0], [0, 0], [-61.0, 0]], [[1.0, 0], [-7.3484692283495345, -7.3484692283495345], [0, 67.0]], [[1.0, 0], [0, 0], [-71.0, 0]], [[1.0, 0], [0, 0], [0, 73.0]], [[1.0, 0], [0, -14.0], [-79.0, 0]], [[1.0, 0], [0, 0], [0, 83.0]], [[1.0, 0], [0, 0], [89.0, 0]], [[1.0, 0], [0, 0], [0, -97.0]], [[1.0, 0], [19.595917942265423, 0], [101.0, 0]], [[1.0, 0], [0, 0], [0, 103.0]], [[1.0, 0], [0, 0], [0, -107.0]], [[1.0, 0], [0, 0], [109.0, 0]], [[1.0, 0], [-14.0, 14.0], [0, -113.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-600-120.53-c1-0-15', '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/600/2/w/a/293/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.7858330887170176, 0.7172725151981703, 0.6284942498254176, 0.5160038976435165, 0.3759266563156009, 0.20551450265772866, 0.004586753693303234, -0.22324831326119116, -0.46967954273652995, -0.7211586163298923, -0.9588261072423877, -1.1589853673253776, -1.2941992410017302, -1.3350466005578492, -1.2525132957709226, -1.0209109452126208, -0.621126002981527, -0.04391233939158192, 0.7071332457203163, 1.6133173004451946, 2.639723707584242, 3.7355694539352435, 4.836286690464687, 5.867411007844735, 6.7501476045988715, 7.408255325488224, 7.775661291069839, 7.804028938748862, 7.469383625534093, 6.776882262755352, 5.76291694461026, 4.493972786486376, 3.0620045868045236, 1.5765233108000243, 0.15404171540149159, -1.09404434008156, -2.0737342738602305, -2.7192901683200685, -3.001165053018324, -2.9297353580465395, -2.5540674031793094, -1.9555994720385286, -1.2373543112177707, -0.5100043446116176, 0.12332290824657945, 0.5812953878984011, 0.8154888470132717, 0.8165328570883068, 0.6141573111311619, 0.2709426980213262, -0.12938377414601115, -0.4972946085571705, -0.753915928138926, -0.8457263958007306, -0.7548000104004281, -0.5025533650828395, -0.14603986499176855, 0.2328311498487594, 0.5434137744467648, 0.7049212037787774, 0.6639780951393062, 0.4075867002495151, -0.03136846824118565, -0.5776681219931069, -1.1262506041303655, -1.5617353591845438, -1.781502347212693, -1.7178726408659633, -1.354785268751931, -0.7351446152627334, 0.04336134653051896, 0.8439644339025107, 1.5156548459248245, 1.9226995819356256, 1.9730842810537756, 1.6399245643126408, 0.970929398236801, 0.08314844679075839, -0.8568708312930983, -1.6643111467689609, -2.172872475749397, -2.2697277240199525, -1.921164119757562, -1.182936430089473, -0.1922576512992237, 0.8578883256909141, 1.7575697741468925, 2.3242056778122393, 2.443038068394173, 2.0947734421117206, 1.3636869049868556, 0.42340241625264724, -0.49766613980184604, -1.164618580917742, -1.3881180826427075, -1.0688284110779989, -0.2239929973309573, 1.0106130211710291, 2.4049407070078574, 3.680908729307494, 4.571261186111625, 4.8784141006328205, 4.520125649608969, 3.551268641694767, 2.1559852136735187, 0.611022389423708, -0.7723635314011777, -1.7154170484464646, -2.032879692158596, -1.674018685263195, -0.7339888358659851, 0.5675284651174614, 1.9359300411369489, 3.0683981519517842, 3.722395671202096, 3.7700182340393593, 3.2254490696573255, 2.2390498913573613, 1.0595555516754918, -0.026487453440562973, -0.7633790695598478, -0.9863929048004221, -0.6588686384719152, 0.12249890779386345, 1.1549987003889703, 2.1825340463128575, 2.959910303668366, 3.312341974812902, 3.1751805700593643, 2.604194202031913, 1.7545675403213985, 0.8350700154222117, 0.050349510149590306, -0.45271490380214174, -0.6200508420808332, -0.4976572945043763, -0.20985530430571234, 0.08445284490256726, 0.24421914071958928, 0.1916090898314465, -0.06339406690084183, -0.42668679489436273, -0.7511260235739015, -0.885710741981702, -0.7277981956138371, -0.2618898157985062, 0.4279160871212465, 1.1770592943941212, 1.7868885276210786, 2.085164874442892, 1.982392862284425, 1.5057941556679322, 0.7984528334863802, 0.08107960043609316, -0.41476699745258616, -0.5236408157479551, -0.2103225287713919, 0.4000141242737865, 1.0382850451930858, 1.3544896907807586, 1.0132836054321108, -0.2025695907430396, -2.3099547540044076, -5.089772433038817, -8.112103915780326, -10.820371954415974, -12.656215055309662, -13.194474652801416, -12.253232251359162, -9.948855316902513, -6.679516224325448, -3.0391880683625945, 0.31730925721397135, 2.8242167616163236, 4.13129636911747, 4.174465813396674, 3.173168191280197, 1.5568084997829519, -0.1583181317581713, -1.5071527537454945, -2.191320714867212, -2.141535388032914, -1.5124176428796174, -0.6148284658905033, 0.19149358678514236, 0.6116027561599332, 0.5014569209334825, -0.09779278247756451, -0.9849724362659743, -1.8726868222559492, -2.4842997450900937, -2.6423166500455717, -2.320204175747286, -1.642275922683858, -0.8335357872425253, -0.13771986444960435, 0.26805449225738864, 0.3329083757907748, 0.14590913985889106, -0.10065564941171601, -0.1857484048014864, 0.05394318906093856, 0.6557531717217974, 1.5055472615808412, 2.3654221996822415, 2.947067333678559, 3.007426378009434, 2.4349531595427094, 1.296883997908942, -0.16990647167393297, -1.6235649566856576, -2.71800301336327, -3.2077736557434267, -3.0229675787648698, -2.289185094834147, -1.2853345821268187, -0.3524852179658607, 0.2165576515961742, 0.27050278805663697, -0.1554373286522212, -0.8579527246273374, -1.54122968171148, -1.9239414286355347, -1.840752096497593, -1.302838637820385, -0.4956184068040665, 0.2865739974907045, 0.7469491291711615, 0.6968574145311033, 0.1309547665343427, -0.76134637003481, -1.654795735597819, -2.199466396048087, -2.146658703230678, -1.4450864851818057, -0.271285338586731, 1.0203361032947267, 2.0147458338549886, 2.383349674588076, 2.0107877491950523, 1.0555650582213358, -0.08110851901065487, -0.8737484294126493, -0.8436453453989803, 0.27194484365771626, 2.409293958167973, 5.166540903451945, 7.900244327488752, 9.904389833218996, 10.618219916665444, 9.7981225332973, 7.598558130538043, 4.5348830523486345, 1.3380940388882707, -1.254114448610616, -2.7053404755249835, -2.823478575269059], 'positive_zeros': ['0.75265880307442498912615705372819', '2.13317254319976829544608293468496', '4.26434304899191110716484966358109', '5.47320594146263700198060073408404', '6.20982010820383205626515288500698', '7.04743246135862329047633419135228', '7.74223135049702964264244641389673', '8.743339572621577243980977069258696', '9.635981160997039780835213297030608', '10.52267624712126921727177213776280'], 'prelabel': '2-600-120.53-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.188840816797061, 'root_angle': -0.1762081911747834, 'root_number': '0.8506508083520399 - 0.5257311121191337*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0881040955874', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.75265880307442498912615705373', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.13317254319976829544608293468', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.26434304899191110716484966358', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.791024121276825, 'bad_primes': [2, 3, 5], 'central_character': '120.53', 'conductor': 600, 'conductor_radical': 30, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/600/2/w/a/293/1'], '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': '2-600-120.53-c1-0-15', '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': '2-600-120.53-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.188840816797061, 'root_angle': -0.0881040955873917, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.75265880307442498912615705373', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '954108383484355550277667478582', 'Lhash_array': ['954108383484355550277667478582'], 'label': '2-600-120.53-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/600/2/w/a/293/1'}