-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1774435802403619061249066844318', 'a10': [-10.0, 0], 'a2': [1.0, 1.7320508075688772], 'a3': [0, 0], 'a4': [2.0, -3.4641016151377544], 'a5': [-2.5, 4.330127018922194], 'a6': [0, 0], 'a7': [0, 0], 'a8': [24.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.89577355232496, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [2.5, -4.330127018922194]]]], 'bad_primes': [3, 5], 'central_character': '405.271', 'coefficient_field': 'CDF', 'conductor': 405, 'conductor_radical': 15, 'conjugate': '1011298300553247524285159726118', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, -1.7320508075688772], [-4.0, 6.928203230275509]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.5, -4.330127018922194]], [[1.0, 0], [0, 0], [-171.5, 297.04671349806245]], [[1.0, 0], [5.0, 8.660254037844387], [-665.5, 1152.6798124370878]], [[1.0, 0], [-40.0, 69.2820323027551], [-1098.5, -1902.6578121144116]], [[1.0, 0], [-7.0, 0], [4913.0, 0]], [[1.0, 0], [113.0, 0], [6859.0, 0]], [[1.0, 0], [-40.5, 70.14805770653953], [-6083.5, -10536.931087845265]], [[1.0, 0], [-110.0, -190.5255888325765], [-12194.5, 21121.493572898675]], [[1.0, 0], [-94.5, 163.6788013152589], [-14895.5, -25799.76280414221]], [[1.0, 0], [-170.0, 0], [50653.0, 0]], [[1.0, 0], [-65.0, 112.58330249197702], [-34460.5, -59687.336854227295]], [[1.0, 0], [5.0, 8.660254037844387], [-39753.5, 68855.08177868936]], [[1.0, 0], [80.0, 138.5640646055102], [-51911.5, 89913.35549711177]], [[1.0, 0], [-631.0, 0], [148877.0, 0]], [[1.0, 0], [-280.0, 484.9742261192856], [-102689.5, -177863.43140384424]], [[1.0, 0], [114.5, 198.31981746663644], [-113490.5, 196571.31217639567]], [[1.0, 0], [375.0, -649.519052838329], [-150381.5, -260468.39851841913]], [[1.0, 0], [-890.0, 0], [357911.0, 0]], [[1.0, 0], [890.0, 0], [389017.0, 0]], [[1.0, 0], [-13.5, -23.382685902179844], [-246519.5, 426984.29905647587]], [[1.0, 0], [214.5, 371.5248982235242], [-285893.5, 495182.06755369285]], [[1.0, 0], [750.0, 0], [704969.0, 0]], [[1.0, 0], [-740.0, -1281.7175976009692], [-456336.5, 790398.003348155]], [[1.0, 0], [-750.0, -1299.038105676658], [-515150.5, 892266.8395445109]], [[1.0, 0], [-230.0, 398.37168574084177], [-546363.5, -946329.3414011582]], [[1.0, 0], [420.0, 0], [1225043.0, 0]], [[1.0, 0], [607.0, 0], [1295029.0, 0]], [[1.0, 0], [1085.0, -1879.275126212232], [-721448.5, -1249585.457044355]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 34, 'label': '2-405-9.4-c3-0-34', 'leading_term': '2.475642903657198249920443451804452627259337825307778205', '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/405/4/e/j/271/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [2.475642903657198, 2.560241794896006, 2.6188398516277362, 2.651142597569625, 2.6570289949121277, 2.6365605687205798, 2.589995857863751, 2.517809281527521, 2.4207131896290233, 2.2996815979824445, 2.155973904298767, 1.9911567454622685, 1.807122093738242, 1.6060997010772056, 1.3906620861468548, 1.163720416422997, 0.9285098647789111, 0.6885633126956019, 0.4476726255605103, 0.20983713333423062, -0.02080059561184764, -0.24003110805455713, -0.44366545040122535, -0.6276319590914817, -0.7880803080415022, -0.9214901632367052, -1.0247813363201024, -1.0954219345943512, -1.1315306957951266, -1.131969493455905, -1.0964219224656984, -1.025453941902941, -0.9205527772810554, -0.7841406762385679, -0.619560674107925, -0.43103225584969423, -0.22357568846441458, -0.002904825414523572, 0.22471067385815469, 0.4526115439381384, 0.6739401051374855, 0.881851763339841, 1.0697409372640705, 1.2314744488937017, 1.3616244992077502, 1.4556926627736908, 1.5103159225969502, 1.523445675786927, 1.4944909068540955, 1.4244173727848986, 1.315795682323759, 1.1727925749297246, 1.0011014889888648, 0.80781061213267, 0.6012089687967882, 0.3905336439699521, 0.18566387439109575, -0.003229646630194395, -0.16606942219671164, -0.29327670412096496, -0.3761830283223524, -0.407431445439706, -0.38135037531256394, -0.29428290328534584, -0.1448549596966314, 0.06583278547213826, 0.3341023222995791, 0.6536951127443525, 1.0158748789404186, 1.4096388255909955, 1.8220352371747552, 2.2385806377276705, 2.6437649113819215, 3.0216281728415444, 3.3563889745552062, 3.6330998660603613, 3.8383035928608513, 3.9606615254095123, 3.991525396399655, 3.9254242043492105, 3.7604402668356154, 3.498451869987451, 3.1452246887239994, 2.7103400046398187, 2.206954520302091, 1.6513939954875372, 1.0625906973371422, 0.46138240893261934, -0.13030189752369195, -0.6903380286678442, -1.1973470398390018, -1.631639102172165, -1.9761174601518985, -2.2170989471452867, -2.345009403526427, -2.354916349425642, -2.246867322525109, -2.026010211605257, -1.702481402749112, -1.2910582130797712, -0.8105834388744544, -0.28318134953069585, 0.26670446396362857, 0.8134109180869741, 1.3312440037295348, 1.7957007848125148, 2.1846656951017005, 2.479521034551547, 2.6661136508921937, 2.735524960480998, 2.6845995855352527, 2.5161986681293342, 2.2391569118570627, 1.8679370050307555, 1.4219905833704203, 0.9248505007747507, 0.40299405609316824, -0.11546986477544006, -0.6022258170610355, -1.030217175932771, -1.3750757456262734, -1.6164391603596326, -1.739083473803425, -1.733806267355966, -1.5980073500782197, -1.3359291578716392, -0.9585365608829663, -0.4830350549168497, 0.0679537876897987, 0.6675213090148099, 1.2858490771801028, 1.891763250093991, 2.4543832087013393, 2.944774577603263, 3.337514616002688, 3.6120810686316394, 3.7539838909496974, 3.7555724707154816, 3.616468421271055, 3.3435948067773484, 2.950795631516083, 2.4580632698728855, 1.890414821001662, 1.27647972061831, 0.6468789854199335, 0.032490018440550016, -0.5373009773989663, -1.036254880133053, -1.4427440207942057, -1.740935768557007, -1.9216222981560727, -1.9826445933159074, -1.928883444599108, -1.7718170423491615, -1.5286720841521784, -1.221221373258105, -0.8743039747143966, -0.5141625600513434, -0.1667053019029472, 0.14419438415226074, 0.3982483523953154, 0.5800514009782821, 0.6800388049124332, 0.695038287383771, 0.6283776524151921, 0.48953902289727513, 0.2933814876251274, 0.05898388989988798, -0.19181357475819275, -0.43606825927186393, -0.6514782895419374, -0.8180862278453463, -0.919820077416109, -0.9457579735155858, -0.8910205649633929, -0.7572199380078883, -0.552424411377643, -0.290632635399375, 0.00921415829956987, 0.32461866679668683, 0.6312190957962208, 0.9046674525439078, 1.1225593989244462, 1.2662730242716826, 1.3225765342829843, 1.2848777301291572, 1.1540106547287439, 0.938485582961736, 0.6541656598335645, 0.3233744546291837, -0.026519349797303308, -0.36495399021102753, -0.6603423082746589, -0.8824067875990492, -1.0045163431637656, -1.0058534795379617, -0.8732469627567914, -0.6025239178491162, -0.19926530004034426, 0.3211118328150876, 0.9339754723060334, 1.6067834116401876, 2.3010015586624353, 2.9745190569655167, 3.584403778120416, 4.089812218232846, 4.454850935091355, 4.651184025608849, 4.660193395442629, 4.474525263929248, 4.098895948694211, 3.550079955988604, 2.856060391313054, 2.0543817068807453, 1.1898034830834632, 0.3114069367150134, -0.530650908194788, -1.2885104187149043, -1.9198707025566315, -2.390902890293336, -2.6785995990790603, -2.772381680427774, -2.674834257140648, -2.4015055528825124, -1.9797697735884676, -1.4468243921409472, -0.8469574706694887, -0.22827714152095668, 0.36086138625144076, 0.8754694731147395, 1.277310223670446, 1.53779887730094, 1.640194482868654, 1.5809088239389852, 1.3698225431681996, 1.029571892213674, 0.5938470902318131, 0.1048190627891598, -0.39012048198698684, -0.8420654748930518, -1.2044704912105832, -1.4368993636386982, -1.5083577371011214, -1.3999475732106994, -1.1066298983597893, -0.6379476025148405, -0.01763804414447517, 0.7178502499697004, 1.5218378534564068, 2.340714572258015, 3.1178168438097065, 3.7975923027747758, 4.329735872694748, 4.6729804788383795, 4.798248918500137, 4.690920051157094, 4.352028900959818], 'positive_zeros': ['1.39978303334069136820862239558331', '2.60246916437341202100463681793582', '4.00653498524167697162630630571280', '4.55036436431716144292516809397703', '6.17178170140818428417941749339189', '7.13792582509322593793947896495255', '8.210662595535854973225136133602957', '8.991720875672659202206114653567361', '10.19914843527716186449526683077216', '11.14573202874587909315953686418225'], 'prelabel': '2-405-9.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8883303440259604, 'root_angle': 0.1111111111111111, 'root_number': '0.93969262078590838405410927732473146993620813426446463309 + 0.3420201433256687330440996146822595807630833675141606285*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.05555555555555555', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.39978303334069136820862239558', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.60246916437341202100463681794', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.00653498524167697162630630571', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 23.89577355232496, 'bad_primes': [3, 5], 'central_character': '9.4', 'conductor': 405, 'conductor_radical': 15, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/405/4/e/j/271/1'], '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': '2-405-9.4-c3-0-34', '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': '2-405-9.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8883303440259604, 'root_angle': 0.05555555555555555, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.39978303334069136820862239558', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1774435802403619061249066844318', 'Lhash_array': ['1774435802403619061249066844318'], 'label': '2-405-9.4-c3-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/4/e/j/271/1'}