-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2333942032425924863182133902612', 'a10': [-0.12717791507655704, 0.2202786105132767], 'a2': [-0.6691306063588582, 0.7431448254773942], 'a3': [-3.061605861396318, 1.363114752602391], 'a4': [-0.10452846326765347, -0.9945218953682733], 'a5': [0.24879754499692391, -0.052883550716488766], 'a6': [1.0356225115395874, -3.187318354493477], 'a7': [-2.6453659002472234, 0.045158097935993236], 'a8': [0.8090169943749475, 0.5877852522924731], 'a9': [5.507956802697438, -6.1172057562143625], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.2296961911277184, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.6691306063588582, -0.7431448254773942]]], [7, [[1.0, 0], [2.6453659002472234, -0.045158097935993236]]], [11, [[1.0, 0], [-0.6231251281411581, 3.257562750689396]]]], 'bad_primes': [2, 7, 11], 'central_character': '154.137', 'coefficient_field': 'CDF', 'conductor': 154, 'conductor_radical': 154, 'conjugate': '304734559788904697666131522285', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.6691306063588582, -0.7431448254773942]], [[1.0, 0], [3.061605861396318, -1.363114752602391], [2.0073918190765747, -2.2294344764321825]], [[1.0, 0], [-0.24879754499692391, 0.052883550716488766], [4.567727288213004, -2.033683215379001]], [[1.0, 0], [2.6453659002472234, -0.045158097935993236]], [[1.0, 0], [-0.6231251281411581, 3.257562750689396]], [[1.0, 0], [0.2463787619209348, 0.7582758594736823], [-10.517220926874316, 7.641208279802151]], [[1.0, 0], [2.642894992660017, 2.9352322542276226], [-1.776983875550109, 16.906872221260645]], [[1.0, 0], [0.19019872240498534, -1.8096199636885413], [-18.584804413942308, -3.9503221255374275]], [[1.0, 0], [3.4754461504471235, 6.019649311544086], [-11.5, 19.91858428704209]], [[1.0, 0], [2.76276671304805, -2.0072675119869916], [8.961492836873475, -27.580638972559452]], [[1.0, 0], [1.1487928867532513, 0.2441834660792502], [28.31990918692063, 12.608835935349806]], [[1.0, 0], [-0.3009007574604261, -0.13396964865244823], [24.757832435277756, 27.496358542663586]], [[1.0, 0], [6.583093917734383, 4.782897697087454], [12.669696769372845, 38.9933171681013]], [[1.0, 0], [-2.734709699847758, 0], [43.0, 0]], [[1.0, 0], [-1.050820164320152, 9.997886019187991], [-45.97293723448887, -9.77184946843469]], [[1.0, 0], [-3.788429415151774, -0.8052555306142339], [48.41790925505785, 21.55704208301741]], [[1.0, 0], [-0.41715497595487055, -3.9689644751270974], [-57.710708443294536, 12.266789758247802]], [[1.0, 0], [5.2512850690709865, -1.1161950986308535], [55.72627291619865, -24.810935227623812]], [[1.0, 0], [0.045439633957621364, -0.07870375469193226], [-33.5, -58.023702053557386]], [[1.0, 0], [-2.7204685031183153, 8.372741125451043], [-57.440206600621266, -41.73275291276559]], [[1.0, 0], [-0.16787502731991089, -1.5972241926842055], [-71.40477485356782, 15.177553429696431]], [[1.0, 0], [9.954725501455181, -11.055842723605435], [-8.257748598144625, -78.56722973409359]], [[1.0, 0], [2.380240280604928, -7.325626326139192], [-67.14841053312064, -48.78617594027527]], [[1.0, 0], [-2.018507045875068, -3.49615675889138], [-44.5, 77.07626093681505]], [[1.0, 0], [4.596936680188782, 14.147916342054076], [-78.4746484543699, 57.01516947236989]], [[1.0, 0], [9.097409510027873, 1.9337140855556854], [92.2680912219027, 41.08040095065582]], [[1.0, 0], [-9.226051447518122, -4.10770275656741], [68.9204524549624, 76.5439170241716]], [[1.0, 0], [-0.9515093484554, 9.053006722804549], [-104.66179327851721, -22.246550917500247]], [[1.0, 0], [8.20066716493786, -14.203972185634196], [-54.5, -94.39676901250381]], [[1.0, 0], [-9.637643855700183, -7.002158130935745], [34.91892036436906, 107.46938634135235]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-154-77.60-c1-0-2', '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/154/2/m/b/137/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.17647743433170213, 0.2559589677070464, 0.33135148139709936, 0.4042492047950989, 0.4746669064528488, 0.5410583838894015, 0.6004421134752231, 0.6485869659107673, 0.6802345696068871, 0.6893580993369125, 0.669469307087035, 0.6139865700037721, 0.516670519238, 0.3721239698630716, 0.17634159779154726, -0.07271661654999982, -0.37456482317424233, -0.7256892831994518, -1.1191569721685144, -1.5443896501416547, -1.9871563748799939, -2.429830117857718, -2.851940896745689, -3.2310386641413515, -3.5438547001450695, -3.76772174454579, -3.8821825793267695, -3.870686887710255, -3.7222501228217304, -3.432929222576833, -3.0069616411322646, -2.45741920375684, -1.8062487240146639, -1.0836078588545717, -0.32645640798707737, 0.4235725544284764, 1.1229253089968543, 1.7293339249456507, 2.2052390463913008, 2.521138350565351, 2.6585390365084933, 2.6121908187236054, 2.391307707351115, 2.019553855883345, 1.5336686426076525, 0.9807324631509949, 0.4142169470448034, -0.11089243978384247, -0.5434833401598593, -0.8416957456646249, -0.9777234339358049, -0.9414729759497237, -0.7425860152660771, -0.4104652440480256, 0.007864767681703941, 0.45200031257921364, 0.8541964108400495, 1.1466561380099576, 1.2693341685202821, 1.1773935533102995, 0.8474234518770511, 0.28159999413258224, -0.49084614657604825, -1.415216022870922, -2.4159988408645225, -3.4042399670321517, -4.286901934620751, -4.977202822877931, -5.4047265775718385, -5.52405132828435, -5.320752605741062, -4.813906551771196, -4.0546199502156846, -3.120604871626674, -2.1073354190237397, -1.1168029363805423, -0.24525466132898893, 0.4285000960814794, 0.8526421521986942, 1.0084103576113985, 0.9117764156154374, 0.6104039608185567, 0.17623128047374823, -0.3053382531673723, -0.7481238876885491, -1.07789040009728, -1.2431977340061093, -1.2226921739244057, -1.0276484025051869, -0.6992762368950283, -0.3011214711927443, 0.09230617222187877, 0.4088832639017427, 0.5920023648485154, 0.611218292526225, 0.46845576471356554, 0.1984760662601427, -0.13678752317835538, -0.45937961449311754, -0.6903173711116497, -0.7660071187797246, -0.6532375578764859, -0.3599389768812349, 0.06058295694599208, 0.5132797532904873, 0.8729485330893041, 1.0025048932309377, 0.7754221641482546, 0.09890748802672841, -1.0660121489346752, -2.691099989658546, -4.676977583669037, -6.860046441931726, -9.029967814387112, -10.955655439266605, -12.416220714485876, -13.232299345694372, -13.292883032521635, -12.573269051000624, -11.140982318847074, -9.148343944489682, -6.812473625293758, -4.385572075378771, -2.119979001535338, -0.23344336662903975, 1.119910649326101, 1.8683221814000732, 2.0279227492364735, 1.694354498464842, 1.0221366606616629, 0.19553038516148383, -0.603906251005472, -1.2273606585291916, -1.5812024756995249, -1.6380709459645255, -1.4350193251771448, -1.0595678341484034, -0.6267963885886069, -0.25228394558282924, -0.026441492803281477, 0.004565561876407144, -0.1525026454413253, -0.441324608294777, -0.7705592754639932, -1.0363391527780568, -1.1477679728944132, -1.0497647302480448, -0.7380659167605528, -0.2627831200560318, 0.2806864049191165, 0.7718636002341156, 1.0924717233231844, 1.1550383818698682, 0.9264962844375679, 0.44124409285843585, -0.19986351323793947, -0.845267892280928, -1.320732898483523, -1.4644161123369415, -1.1619756360409166, -0.37432876594713743, 0.8481482808854262, 2.368651179743812, 3.9844546211950203, 5.4615181483563005, 6.576752144722062, 7.159677903381018, 7.125056202682392, 6.489662244255023, 5.369472377467319, 3.957492512042643, 2.4864822792655006, 1.1840545546396506, 0.22934228204960516, -0.27978658841214565, -0.34212526762715184, -0.04794879814648865, 0.44551750133902795, 0.9525398640084316, 1.302691205144389, 1.3802421443150639, 1.1502285204830707, 0.6652042221467164, 0.051003807690899454, -0.5253744946907534, -0.8984693923160285, -0.9477277218749216, -0.6312261642080137, -0.0013848120251671934, 0.8017333301786628, 1.578843758290067, 2.1157800600351466, 2.2340053719677067, 1.835720418968758, 0.9327733276985524, -0.34812224358215127, -1.7862036823544292, -3.1099745060205057, -4.054199500906242, -4.418308479916401, -4.1131648677512676, -3.185325219586079, -1.812620950463226, -0.27113224644037714, 1.119985876062175, 2.064277576608455, 2.3502168473598735, 1.8962919713404782, 0.7689531829587707, -0.8306570304848032, -2.6083816009283396, -4.238020217730838, -5.428210625549128, -5.980596562716256, -5.826746894618827, -5.036227744421147, -3.7948663206160465, -2.3590266868197154, -0.9970510619138763, 0.06834381859550831, 0.703589560828022, 0.8843519823316308, 0.6887518154557831, 0.26690699943860385, -0.20435027646010334, -0.5694048042015051, -0.7320830071795706, -0.6747917577503402, -0.4545263748545728, -0.1779955985447766, 0.03628845147785114, 0.0976775634513793, -0.02680698404103538, -0.30129209379589533, -0.6319402305130978, -0.8969929355667311, -0.9873766382111363, -0.8458614069756843, -0.4926301465161031, -0.02842487212676683, 0.3875820160657392, 0.5809177773847208, 0.4153018993216754, -0.15795462586649772, -1.069181826317122, -2.128860633730158, -3.058998263719514, -3.5524325666242627, -3.347312396536641, -2.2989951172082654, -0.43087989553840333, 2.050314629454395, 4.781391375998807, 7.308159180815914, 9.176389843885778, 10.028194750215066, 9.681548734186391], 'positive_zeros': ['1.84115562443288317534463211751586', '4.30383903105448719690115419659958', '5.84709738430355502081982646322066', '6.74777529736465679325972037015936', '7.67415400588307906480432598798586', '9.540879623098627157851680394010406', '10.29595812759999289118597597172547', '11.34423705834389612583862231571540', '12.07513189288565215556466133938946', '12.85827593635752692735731188045034'], 'prelabel': '2-154-77.60-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1089166745647385, 'root_angle': 0.4561335110299634, 'root_number': '0.13737484213892806 + 0.9905191329536773*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.228066755515', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.84115562443288317534463211752', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.30383903105448719690115419660', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.84709738430355502081982646322', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.2296961911277184, 'bad_primes': [2, 7, 11], 'central_character': '77.60', 'conductor': 154, 'conductor_radical': 154, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/154/2/m/b/137/1'], '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': '2-154-77.60-c1-0-2', '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': '2-154-77.60-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1089166745647385, 'root_angle': 0.2280667555149817, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.84115562443288317534463211752', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2333942032425924863182133902612', 'Lhash_array': ['2333942032425924863182133902612'], 'label': '2-154-77.60-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/154/2/m/b/137/1'}