Properties

Level $71$
Weight $0$
Character 71.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 71 \)
Weight: \( 0 \)
Character: 71.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 2.19775611579 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.078948130\) \(a_{3}=-0.927313506\) \(a_{4}=+0.164129067\) \(a_{5}=-0.946709297\)
\(a_{6}=-1.000523172\) \(a_{7}=+0.263743051\) \(a_{8}=-0.901861380\) \(a_{9}=-0.140089662\) \(a_{10}=-1.021450226\)
\(a_{11}=+1.088832381\) \(a_{12}=-0.152199100\) \(a_{13}=-1.036169730\) \(a_{14}=+0.284565072\) \(a_{15}=+0.877896317\)
\(a_{16}=-1.137190716\) \(a_{17}=+1.258152009\) \(a_{18}=-0.151149479\) \(a_{19}=-0.345540165\) \(a_{20}=-0.155382513\)
\(a_{21}=-0.244572493\) \(a_{22}=+1.174793661\) \(a_{23}=-1.282199014\) \(a_{24}=+0.836308238\) \(a_{25}=-0.103741506\)
\(a_{26}=-1.117973392\) \(a_{27}=+1.057220541\) \(a_{28}=+0.043287901\) \(a_{29}=-0.943689331\) \(a_{30}=+0.947204590\)
\(a_{31}=-0.591627609\) \(a_{32}=-0.325108416\) \(a_{33}=-1.009688972\) \(a_{34}=+1.357480757\) \(a_{35}=-0.249687999\)
\(a_{36}=-0.022992786\) \(a_{37}=+0.988486384\) \(a_{38}=-0.372819914\) \(a_{39}=+0.960854185\) \(a_{40}=+0.853800554\)
\(a_{41}=+0.311231915\) \(a_{42}=-0.263881034\) \(a_{43}=-0.279532072\) \(a_{44}=+0.178709042\) \(a_{45}=+0.132624186\)
\(a_{46}=-1.383426228\) \(a_{47}=-1.500448416\) \(a_{48}=+1.054532309\) \(a_{49}=-0.930439603\) \(a_{50}=-0.111931704\)
\(a_{51}=-1.166701350\) \(a_{52}=-0.170065571\) \(a_{53}=-1.189467399\) \(a_{54}=+1.140686126\) \(a_{55}=-1.030807738\)
\(a_{56}=-0.237859672\) \(a_{57}=+0.320424061\) \(a_{58}=-1.018191839\) \(a_{59}=+0.125123934\) \(a_{60}=+0.144088303\)
\(a_{61}=+1.451254209\) \(a_{62}=-0.638335502\) \(a_{63}=-0.036947675\) \(a_{64}=+0.786415599\) \(a_{65}=+0.980951517\)
\(a_{66}=-1.089402028\) \(a_{67}=+0.032146658\) \(a_{68}=+0.206499315\) \(a_{69}=+1.189000462\) \(a_{70}=-0.269400399\)
\(a_{71}=-0.118678166\) \(a_{72}=+0.126341456\) \(a_{73}=+1.261944086\) \(a_{74}=+1.066525536\) \(a_{75}=+0.096200900\)
\(a_{76}=-0.056713185\) \(a_{77}=+0.287171974\) \(a_{78}=+1.036711826\) \(a_{79}=+0.091090171\) \(a_{80}=+1.076589024\)
\(a_{81}=-0.840285224\) \(a_{82}=+0.335803093\) \(a_{83}=+1.025517976\) \(a_{84}=-0.040141455\) \(a_{85}=-1.191104205\)
\(a_{86}=-0.301600606\) \(a_{87}=+0.875095862\) \(a_{88}=-0.981975874\) \(a_{89}=-0.849406152\) \(a_{90}=+0.143094617\)
\(a_{91}=-0.273282566\) \(a_{92}=-0.210446127\) \(a_{93}=+0.548624272\) \(a_{94}=-1.618906012\) \(a_{95}=+0.327126087\)
\(a_{96}=+0.301477425\) \(a_{97}=+1.450464926\) \(a_{98}=-1.003896069\) \(a_{99}=-0.152534161\) \(a_{100}=-0.017026997\)

Showing 100 of 546 available coefficients

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