-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '698482643034038674886203163744', 'a10': [0.0, 0.0], 'a2': [-3.2463526858891694, -1.8742825970825765], 'a3': [-3.2463526858891694, 4.057239731494822], 'a4': [3.0258705074532157, 5.24096145603319], 'a5': [0.0, 0.0], 'a6': [18.143219582112554, -7.086648756480118], 'a7': [27.149184200009397, 15.67458880615416], 'a8': [0.0, 7.303175820741278], 'a9': [-5.922388477640354, -26.342462199268937], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.275429751291645, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [3.2463526858891694, -4.057239731494822]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '225.124', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '1539228952877531440514005599496', 'degree': 2, 'euler_factors': [[[1.0, 0], [3.2463526858891694, 1.8742825970825765], [4.0, 6.928203230275509]], [[1.0, 0], [3.2463526858891694, -4.057239731494822]], [[1.0, 0], [0, 0]], [[1.0, 0], [-27.149184200009397, -15.67458880615416], [171.5, 297.04671349806245]], [[1.0, 0], [-10.416649254300966, 18.042165753073732], [-665.5, -1152.6798124370878]], [[1.0, 0], [51.901804254110054, -29.965520657537702], [1098.5, -1902.6578121144116]], [[1.0, 0], [0, 74.04600179156704], [-4913.0, 0]], [[1.0, 0], [-63.83903773194132, 0], [6859.0, 0]], [[1.0, 0], [-28.448388997429713, 16.424685045677233], [6083.5, -10536.931087845265]], [[1.0, 0], [80.00440065702762, -138.57168676706868], [-12194.5, -21121.493572898675]], [[1.0, 0], [-127.18672830131769, -220.2938754663407], [-14895.5, 25799.76280414221]], [[1.0, 0], [0, -215.36524919506087], [-50653.0, 0]], [[1.0, 0], [70.84071725391942, 122.69972152840963], [-34460.5, 59687.336854227295]], [[1.0, 0], [-119.42991941508268, -68.9528961235933], [39753.5, 68855.08177868936]], [[1.0, 0], [29.080276179286685, 16.789505280219828], [51911.5, 89913.35549711177]], [[1.0, 0], [0, -41.991407634333186], [-148877.0, 0]], [[1.0, 0], [-307.5708582190325, -532.7283533629279], [-102689.5, 177863.43140384424]], [[1.0, 0], [-67.15345551788926, 116.31319686080077], [-113490.5, -196571.31217639567]], [[1.0, 0], [742.6455988208597, -428.7666363917142], [150381.5, -260468.39851841913]], [[1.0, 0], [-588.6653717120976, 0], [357911.0, 0]], [[1.0, 0], [0, -618.1909012638845], [-389017.0, 0]], [[1.0, 0], [172.64423403032703, -299.0285849743382], [-246519.5, -426984.29905647587]], [[1.0, 0], [946.7108084395405, 546.583740097297], [285893.5, 495182.06755369285]], [[1.0, 0], [414.84924036080673, 0], [704969.0, 0]], [[1.0, 0], [-174.4267456243236, -100.7053285400736], [456336.5, 790398.003348155]], [[1.0, 0], [132.69146991401163, -229.82836762206523], [-515150.5, -892266.8395445109]], [[1.0, 0], [-456.93054908614425, 263.8089755158489], [546363.5, -946329.3414011582]], [[1.0, 0], [0, -2084.2433880433023], [-1225043.0, 0]], [[1.0, 0], [925.6507652973338, 0], [1295029.0, 0]], [[1.0, 0], [472.86622362346986, -273.00944149969206], [721448.5, -1249585.457044355]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-15e2-45.34-c3-0-12', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/225/4/k/c/124/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.7075222803282003, 0.5811107059195091, 0.42978986039368583, 0.25929679819448326, 0.07639779075847718, -0.11091393433779054, -0.29326019223793676, -0.4598088803485472, -0.5983394842184215, -0.6954804656971721, -0.7371442121292554, -0.7091701137815511, -0.5981682271777895, -0.39253543968649335, -0.0835940049755594, 0.33321981800755224, 0.8572096000979277, 1.4814237735927365, 2.191929992075859, 2.9674770945302162, 3.7796516815480974, 4.593612228290497, 5.369446462523086, 6.064148531446119, 6.634153968362459, 7.038306981060712, 7.241071921035201, 7.215745851091622, 6.947389296468157, 6.43517463437992, 5.693862031358803, 4.7541550986960255, 3.661763198031478, 2.4751016069650116, 1.2616875783093713, 0.09342888865385844, -0.9588622015219302, -1.8312784985250519, -2.472416097766328, -2.8481915761122685, -2.945333155494055, -2.7730899668105753, -2.362854632702826, -1.7655968748755808, -1.0472412643147377, -0.28236548880781653, 0.4531826818468342, 1.0899813649214969, 1.5721836277051298, 1.8632669873912902, 1.9496456587354827, 1.841626294608929, 1.571491024406659, 1.1888467781236254, 0.7537439750563019, 0.3283916192120404, -0.031468810689229444, -0.2843624133640775, -0.4089345748769893, -0.40695329735310104, -0.30291190600217455, -0.1401473882321976, 0.026100672630364235, 0.13778183745252143, 0.1439857754407924, 0.010246119836928136, -0.27430895236259106, -0.6932321379970853, -1.2032809954747006, -1.7393985153005531, -2.2236625615098027, -2.5770435056545105, -2.732269017629747, -2.6457857315467597, -2.3067993030262355, -1.741694298501286, -1.0127590126771229, -0.21099092495606572, 0.5562852640807414, 1.1813430310791275, 1.5731667384575714, 1.6730191510020866, 1.4657817385825345, 0.9848897795177791, 0.3095937532135068, -0.44552798315869635, -1.14758299549148, -1.6664950177858127, -1.8969742036824313, -1.7776796130401105, -1.3041517203298858, -0.5329212678847812, 0.4244663394395888, 1.4171292018749369, 2.2781589023233746, 2.85204803736446, 3.0217925185364694, 2.7310102496468995, 1.9970005178060986, 0.9119987989457616, -0.36822787731398526, -1.6471495224704793, -2.7182662711101386, -3.3990190287240996, -3.562126797785476, -3.158842788820962, -2.22978998036136, -0.9010311290071311, 0.6344709282692798, 2.1472683276063775, 3.4087928643331606, 4.229356367418772, 4.4901744950172775, 4.163690281226859, 3.318428983407121, 2.1073125545336, 0.7413231472796088, -0.546914372289793, -1.543171424252883, -2.088094702175067, -2.1035530497017167, -1.604132903951422, -0.691827251124517, 0.46487952936802934, 1.6633859161586648, 2.70451269723177, 3.427991420281965, 3.739184909906494, 3.622154796412939, 3.1369933771634213, 2.4025426514623622, 1.568572474406599, 0.783566833153714, 0.1650317816507098, -0.2214766864906923, -0.37045314211919256, -0.3304581508248657, -0.18602286252250863, -0.0321456188776459, 0.052266355240203566, 0.025474466334154074, -0.10668095574027428, -0.2936281040959083, -0.45549831440941696, -0.5073054754509062, -0.3857046679910273, -0.07127777315284119, 0.3998848337927553, 0.9391306217177602, 1.4230580077044168, 1.7227612635526242, 1.7379117739562022, 1.4273379752964332, 0.8279545598851915, 0.056091232233155486, -0.710912412382508, -1.2703520553680263, -1.4401622918728771, -1.1053108443878854, -0.25365379406786376, 1.0081390379887145, 2.464128147559245, 3.8242351528932046, 4.779239500218507, 5.064989343996054, 4.522343579909477, 3.139406618541937, 1.0656948386824399, -1.4065486322212173, -3.891730166560376, -5.9820053939274445, -7.326008066908354, -7.6988944330576095, -7.048693198962668, -5.508613112140929, -3.372043515071051, -1.0349671018585713, 1.0823844609606883, 2.6181848978713615, 3.338500088121512, 3.178976914652067, 2.2502331890106273, 0.8064951459002828, -0.8148333174387308, -2.2686283338595477, -3.2753851180376503, -3.676160556196981, -3.4574661975826118, -2.741731912785147, -1.747139117737671, -0.7277438331518559, 0.09083192807784714, 0.5642972986504539, 0.6586616252960329, 0.44911258230834555, 0.09040620747864711, -0.23241533587036212, -0.35932331339834356, -0.2017134337466855, 0.23234505555118215, 0.8404847126891057, 1.4550422068341782, 1.8905430721880547, 1.9965765898843653, 1.7015348099247087, 1.0351616770717147, 0.1235903562678101, -0.8419835348319902, -1.6546422097188636, -2.145767404304376, -2.2290287871040686, -1.922259528127644, -1.341121947807472, -0.6661990406325247, -0.09252566037531859, 0.22445060450519635, 0.21133848050013077, -0.10436887181076424, -0.6046584864681661, -1.1178892162355065, -1.4718994758786876, -1.5481199410447708, -1.3207882409237428, -0.8692023119653505, -0.3583747645133403, 0.007528431835562372, 0.04647799348718626, -0.3427277458454776, -1.1417662898399596, -2.2065604926342557, -3.2972594176291437, -4.137962361638036, -4.490853654834468, -4.224479662912533, -3.356474369611196, -2.057224425945314, -0.611279993508055, 0.6549448309270778, 1.460711091077102, 1.6500179107761552, 1.2396030135221696, 0.420784917304354, -0.48788498035199285, -1.1266928924541912, -1.1978265351939474, -0.5578883847013262, 0.7262163837317704, 2.3754337185467445, 3.9543993441657483, 4.973268163493739, 5.011041983451243, 3.8291887870088614, 1.4457157273862176, -1.8508269104300679, -5.552963694643466, -9.040332635998926, -11.714830855099072], 'positive_zeros': ['0.55100565006499660486143982023270', '1.77789298359951485185831749656837', '4.38545776763668880380813152235343', '5.67173272888122824496574119372161', '6.98759522951534803491759936105099', '7.72864938084019278294532489999634', '8.131006410246310506542025868502536', '9.658085246418327916446413491634224', '10.55162727790593677387055468480111', '11.44637910194286520151470285842303'], 'prelabel': '2-15e2-45.34-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': -0.3672537403120919, 'root_number': '0.4050510581104219 - 0.9142940666566899*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.183626870156', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.55100565006499660486143982023', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.77789298359951485185831749657', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.38545776763668880380813152235', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 13.275429751291645, 'bad_primes': [3, 5], 'central_character': '45.34', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/4/k/c/124/2'], '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': '2-15e2-45.34-c3-0-12', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-15e2-45.34-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': -0.18362687015604595, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.55100565006499660486143982023', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '698482643034038674886203163744', 'Lhash_array': ['698482643034038674886203163744'], 'label': '2-15e2-45.34-c3-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/4/k/c/124/2'}