Properties

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

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Maass form invariants

Level: \( 71 \)
Weight: \( 0 \)
Character: 71.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 3.06323195764 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.607941829\) \(a_{3}=+1.736047562\) \(a_{4}=-0.630406732\) \(a_{5}=-0.231622220\)
\(a_{6}=-1.055415931\) \(a_{7}=+0.979286179\) \(a_{8}=+0.991192451\) \(a_{9}=+2.013861139\) \(a_{10}=+0.140812836\)
\(a_{11}=+0.918991453\) \(a_{12}=-1.094416070\) \(a_{13}=-0.150829941\) \(a_{14}=-0.595349031\) \(a_{15}=-0.402107191\)
\(a_{16}=+0.027819380\) \(a_{17}=-0.643013345\) \(a_{18}=-1.224310425\) \(a_{19}=+1.312261610\) \(a_{20}=+0.146016207\)
\(a_{21}=+1.700087384\) \(a_{22}=-0.558693345\) \(a_{23}=+0.005456904\) \(a_{24}=+1.720757239\) \(a_{25}=-0.946351147\)
\(a_{26}=+0.091695831\) \(a_{27}=+1.760111159\) \(a_{28}=-0.617348600\) \(a_{29}=+1.063677575\) \(a_{30}=+0.244457781\)
\(a_{31}=+0.890987532\) \(a_{32}=-1.008105016\) \(a_{33}=+1.595412873\) \(a_{34}=+0.390914710\) \(a_{35}=-0.226824439\)
\(a_{36}=-1.269551619\) \(a_{37}=-0.111501705\) \(a_{38}=-0.797778724\) \(a_{39}=-0.261847952\) \(a_{40}=-0.229582196\)
\(a_{41}=-0.011096652\) \(a_{42}=-1.033554235\) \(a_{43}=+1.059084681\) \(a_{44}=-0.579338399\) \(a_{45}=-0.466454988\)
\(a_{46}=-0.003317480\) \(a_{47}=-1.704253860\) \(a_{48}=+0.048295766\) \(a_{49}=-0.040998579\) \(a_{50}=+0.575326448\)
\(a_{51}=-1.116301751\) \(a_{52}=+0.095084210\) \(a_{53}=+1.900027427\) \(a_{54}=-1.070045198\) \(a_{55}=-0.212858841\)
\(a_{56}=+0.970661069\) \(a_{57}=+2.278148569\) \(a_{58}=-0.646654091\) \(a_{59}=-0.200412611\) \(a_{60}=+0.253491080\)
\(a_{61}=-0.227297232\) \(a_{62}=-0.541668590\) \(a_{63}=+1.972146380\) \(a_{64}=+0.585049828\) \(a_{65}=+0.034935566\)
\(a_{66}=-0.969918221\) \(a_{67}=-1.957547840\) \(a_{68}=+0.405359942\) \(a_{69}=+0.009473444\) \(a_{70}=+0.137896064\)
\(a_{71}=-0.118678166\) \(a_{72}=+1.996123959\) \(a_{73}=-1.164806008\) \(a_{74}=+0.067786550\) \(a_{75}=-1.642910602\)
\(a_{76}=-0.827258553\) \(a_{77}=+0.899955629\) \(a_{78}=+0.159188323\) \(a_{79}=-0.665224288\) \(a_{80}=-0.006443587\)
\(a_{81}=+1.041775548\) \(a_{82}=+0.006746119\) \(a_{83}=-1.178288126\) \(a_{84}=-1.071746532\) \(a_{85}=+0.148936179\)
\(a_{86}=-0.643861878\) \(a_{87}=+1.846594861\) \(a_{88}=+0.910897392\) \(a_{89}=+1.617635512\) \(a_{90}=+0.283577499\)
\(a_{91}=-0.147705677\) \(a_{92}=-0.003440069\) \(a_{93}=+1.546796734\) \(a_{94}=+1.036087209\) \(a_{95}=-0.303948947\)
\(a_{96}=-1.750118256\) \(a_{97}=-1.255465839\) \(a_{98}=+0.024924751\) \(a_{99}=+1.850721175\) \(a_{100}=+0.596586134\)

Showing 100 of 546 available coefficients

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