-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '265167011233271475279127887546', 'a10': [-26.00335220422581, 0], 'a2': [2.600335220422581, -4.5039127184827255], 'a3': [0, 0], 'a4': [-9.523486517140304, -16.49516251288418], 'a5': [-2.5, -4.330127018922194], 'a6': [0, 0], 'a7': [-12.200670440845162, 21.132181089947593], 'a8': [-57.45166612019674, 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': '405.136', 'coefficient_field': 'CDF', 'conductor': 405, 'conductor_radical': 15, 'conjugate': '2059603752937995741855145489744', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.600335220422581, 4.5039127184827255], [-4.0, -6.928203230275509]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.5, 4.330127018922194]], [[1.0, 0], [12.200670440845162, -21.132181089947593], [-171.5, -297.04671349806245]], [[1.0, 0], [14.49193474602573, -25.10076728008934], [-665.5, -1152.6798124370878]], [[1.0, 0], [-32.6959573910967, -56.63105940348664], [-1098.5, 1902.6578121144116]], [[1.0, 0], [68.17176162917389, 0], [4913.0, 0]], [[1.0, 0], [-104.42417579809047, 0], [6859.0, 0]], [[1.0, 0], [77.40333224039348, 134.06650411549563], [-6083.5, 10536.931087845265]], [[1.0, 0], [102.82886888400661, -178.10482539193785], [-12194.5, -21121.493572898675]], [[1.0, 0], [-9.12484623893564, -15.804697297090309], [-14895.5, 25799.76280414221]], [[1.0, 0], [337.6133289615739, 0], [50653.0, 0]], [[1.0, 0], [97.98450000523196, 169.71413236329468], [-34460.5, 59687.336854227295]], [[1.0, 0], [167.44093681921953, -290.0162098378185], [-39753.5, -68855.08177868936]], [[1.0, 0], [2.5019913587031537, -4.3335761533721495], [-51911.5, -89913.35549711177]], [[1.0, 0], [-319.9650172930576, 0], [148877.0, 0]], [[1.0, 0], [-215.3053036352643, -372.91972503532185], [-102689.5, 177863.43140384424]], [[1.0, 0], [297.29053397283843, -514.9223094502375], [-113490.5, -196571.31217639567]], [[1.0, 0], [97.93819965925115, 169.63393781164788], [-150381.5, 260468.39851841913]], [[1.0, 0], [425.95536061739125, 0], [357911.0, 0]], [[1.0, 0], [-929.1929053047203, 0], [389017.0, 0]], [[1.0, 0], [12.214809590090548, -21.1566708148164], [-246519.5, -426984.29905647587]], [[1.0, 0], [272.92930425377307, -472.7274218419595], [-285893.5, -495182.06755369285]], [[1.0, 0], [-84.13322641931794, 0], [704969.0, 0]], [[1.0, 0], [413.80666448078694, -716.7341673913305], [-456336.5, -790398.003348155]], [[1.0, 0], [-411.7880428579625, 713.2378121793415], [-515150.5, -892266.8395445109]], [[1.0, 0], [585.5947073387495, 1014.2797857541415], [-546363.5, 946329.3414011582]], [[1.0, 0], [1023.2080363003234, 0], [1225043.0, 0]], [[1.0, 0], [403.64665136550866, 0], [1295029.0, 0]], [[1.0, 0], [-541.1019115033738, -937.2160027964818], [-721448.5, 1249585.457044355]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-405-9.7-c3-0-1', 'leading_term': '0.875607251126159527005498663144297564088280556805011533', '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/t/136/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.8756072511261596, 0.6406372452934004, 0.3827017150251435, 0.10235732308766446, -0.19969957596418872, -0.5226170731311003, -0.8653702965418185, -1.2267432112461614, -1.6053104669065559, -1.9994201935723748, -2.4071786797569983, -2.826437874131006, -3.2547866324902186, -3.6895465859455467, -4.127773435545562, -4.566264384036655, -5.001572298593984, -5.43002706065435, -5.847764402144992, -6.250762353351351, -6.634885238638934, -6.995934954887779, -7.329709056961202, -7.632064958530187, -7.8989893394332205, -8.12667163739682, -8.311580297867184, -8.450540266882596, -8.540810044680303, -8.580156478605044, -8.566925369390852, -8.500105901317378, -8.379386889918251, -8.205202875932862, -7.978768185142908, -7.702097223471159, -7.378009486603563, -7.010118033086198, -6.602800497125396, -6.161152097953562, -5.690920530303719, -5.198423086862023, -4.690446858114528, -4.174133365465305, -3.656849495912805, -3.1460471056112125, -2.6491141290244182, -2.1732204532981245, -1.7251621771309067, -1.311208153592816, -0.9369529019751535, -0.6071800516139013, -0.3257404398871257, -0.09544881942614807, 0.08199716827216147, 0.20607252446035912, 0.2774522573031111, 0.2980085798002608, 0.270776721425299, 0.19988899908069746, 0.09047772323319225, -0.05145151622822489, -0.2191736622601057, -0.4054216243584841, -0.6025829590307712, -0.8029106150474669, -0.9987418779853561, -1.18271912019747, -1.3480056170313628, -1.488489551231049, -1.5989694125721479, -1.6753143195912477, -1.7145933476932371, -1.7151687374060165, -1.6767488636840104, -1.6003980485612461, -1.4885016630271508, -1.3446864495402706, -1.1736975567641004, -0.9812353597467875, -0.7737566845507153, -0.5582465067231313, -0.3419674883863538, -0.1321958017958545, 0.06404749466476144, 0.2402597544595224, 0.39070478031396255, 0.51063587703794, 0.5964847892689266, 0.6460083673247154, 0.6583861399501452, 0.6342636364695439, 0.5757382437366335, 0.4862865421695449, 0.3706343644687532, 0.23457317460467186, 0.08472868037397455, -0.07171022650107181, -0.22729215987879842, -0.37462189108145727, -0.506684080537687, -0.617158472354834, -0.7007127380302268, -0.7532595323685752, -0.7721652896567508, -0.756399831320512, -0.7066179424141295, -0.6251666428141114, -0.5160148450997206, -0.38460534796974366, -0.23763253611587118, -0.08275260483488231, 0.07176354869760994, 0.21742157776265378, 0.3459232690410313, 0.44959658293985, 0.5218169024984222, 0.5573996493954557, 0.5529446849915673, 0.5071140611256277, 0.42082671735505583, 0.2973565967207436, 0.14232428912359948, -0.036423410485357036, -0.2290468787208888, -0.424055763175855, -0.6087504430633376, -0.76974847832467, -0.8935770343073576, -0.9673082289811977, -0.9792111240615194, -0.9193918599175014, -0.7803923713226374, -0.5577183274937829, -0.25026847448469336, 0.13935957719932418, 0.6047079402599005, 1.1354569448070375, 1.7175928065553658, 2.3337467297693264, 2.9637002337807217, 3.585043867969293, 4.173969040410126, 4.706165774902587, 5.157793167979223, 5.506484457169331, 5.732345211177765, 5.81890143539437, 5.753954509663861, 5.530301920087857, 5.146286709077872, 4.606144356052628, 3.920123235149345, 3.104363612395839, 2.180530003937435, 1.1752022171845324, 0.11904108926825126, -0.9542446548851942, -2.0090943628922795, -3.009409768348504, -3.919936454762201, -4.707656565737545, -5.343134480656834, -5.8017573162577705, -6.064814855818865, -6.120368813487701, -5.9638690549073115, -5.5984842418642895, -5.035125963933088, -4.292158284727822, -3.3947982096283216, -2.374226269459413, -1.2664395802011905, -0.11089175747929451, 1.0510256527680975, 2.1775975430343553, 3.2284273952528246, 4.166036868345891, 4.957353330450736, 5.575019910228285, 5.998469796278835, 6.214716480325479, 6.218823999351948, 6.014035439264706, 5.611553370716685, 5.029981776768251, 4.294454643942137, 3.4354909634453974, 2.487628705119012, 1.4879007342874693, 0.4742231008489578, -0.5162297613423362, -1.4485878688634584, -2.2917146369934493, -3.019436691063233, -3.6115191899158545, -4.054343969669606, -4.341262615256341, -4.472612769261808, -4.4554027734878, -4.302686249523486, -4.032663606338833, -3.6675609114779184, -3.2323473674981296, -2.753360219628652, -2.2569098730376855, -1.767938098102313, -1.3087984345015364, -0.8982204636596377, -0.5505088991975001, -0.27501502403616956, -0.0759026109093116, 0.04778605510315506, 0.10177516441046333, 0.0959385054165139, 0.043462240468051604, -0.04015918253991307, -0.13823164988624953, -0.23400697103440374, -0.3117965729974226, -0.35798714281073846, -0.36189862617435165, -0.3164350386570606, -0.21849149500356493, -0.06909595468038238, 0.12671947241797982, 0.36030618949388155, 0.6200183651177318, 0.8920221647072534, 1.1612416755755937, 1.4123798432741859, 1.6309481547118778, 1.8042383437397924, 1.9221731165444242, 1.9779805997115656, 1.968648457054135, 1.895127730857089, 1.7622725801222194, 1.5785192161177342, 1.3553243993579651, 1.1063997748440466, 0.8467920520429558, 0.5918696718264055, 0.3562834144242408, 0.15297089095935723, -0.007727206057208479, -0.11877778565543422, -0.1769423900296478, -0.18300424783339622, -0.14171595279284818, -0.06146692097823928, 0.04631123424883713, 0.1679650881993087, 0.28861306830767136, 0.3932468858492972, 0.46786627689189, 0.5005684177627788], 'positive_zeros': ['0.20917988851622874198767539088213', '3.34377090671405162206838438883110', '3.79127065343419629751175203851420', '5.22898878675605127457248327250517', '6.03398827116268117935322505159667', '6.97073589207881097377120362913558', '7.67526332343942880095191301375267', '8.416562591837205285775580450275597', '9.756944080094272382340522223565679', '10.81844426164035141891002322402822'], 'prelabel': '2-405-9.7-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': 67}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.20917988851622874198767539088', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.34377090671405162206838438883', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.79127065343419629751175203851', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 23.89577355232496, 'bad_primes': [3, 5], 'central_character': '9.7', 'conductor': 405, 'conductor_radical': 15, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/405/4/e/t/136/3'], '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': '2-405-9.7-c3-0-1', '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': '2-405-9.7-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': '0.20917988851622874198767539088', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '265167011233271475279127887546', 'Lhash_array': ['265167011233271475279127887546'], 'label': '2-405-9.7-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/4/e/t/136/3'}