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: \( 3.98699118875 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.577475889\) \(a_{3}=+0.148723808\) \(a_{4}=+1.488430182\) \(a_{5}=+0.924038633\)
\(a_{6}=-0.234608221\) \(a_{7}=+0.649299424\) \(a_{8}=-0.770486836\) \(a_{9}=-0.977881229\) \(a_{10}=-1.457648665\)
\(a_{11}=-0.092502284\) \(a_{12}=+0.221365004\) \(a_{13}=+0.448768307\) \(a_{14}=-1.024254186\) \(a_{15}=+0.137426544\)
\(a_{16}=-0.273005776\) \(a_{17}=+0.594800531\) \(a_{18}=+1.542584061\) \(a_{19}=+0.504820276\) \(a_{20}=+1.375366991\)
\(a_{21}=+0.096566283\) \(a_{22}=+0.145920122\) \(a_{23}=-0.574393382\) \(a_{24}=-0.114589736\) \(a_{25}=-0.146152604\)
\(a_{26}=-0.707921185\) \(a_{27}=-0.294158028\) \(a_{28}=+0.966436859\) \(a_{29}=+0.303450263\) \(a_{30}=-0.216787060\)
\(a_{31}=-0.151444421\) \(a_{32}=+1.201146864\) \(a_{33}=-0.013757292\) \(a_{34}=-0.938283497\) \(a_{35}=+0.599977752\)
\(a_{36}=-1.455507936\) \(a_{37}=+0.987525673\) \(a_{38}=-0.796341814\) \(a_{39}=+0.066742532\) \(a_{40}=-0.711959603\)
\(a_{41}=-0.044148988\) \(a_{42}=-0.152330983\) \(a_{43}=+1.337622598\) \(a_{44}=-0.137683191\) \(a_{45}=-0.903600034\)
\(a_{46}=+0.906091711\) \(a_{47}=+1.572142631\) \(a_{48}=-0.040602459\) \(a_{49}=-0.578410258\) \(a_{50}=+0.230552209\)
\(a_{51}=+0.088461000\) \(a_{52}=+0.667960293\) \(a_{53}=+1.020392293\) \(a_{54}=+0.464027197\) \(a_{55}=-0.085475684\)
\(a_{56}=-0.500276658\) \(a_{57}=+0.075078794\) \(a_{58}=-0.478685474\) \(a_{59}=+0.168902444\) \(a_{60}=+0.204549816\)
\(a_{61}=+1.220949879\) \(a_{62}=+0.238899923\) \(a_{63}=-0.634937718\) \(a_{64}=-1.621774442\) \(a_{65}=+0.414679253\)
\(a_{66}=+0.021701796\) \(a_{67}=-0.833802821\) \(a_{68}=+0.885319063\) \(a_{69}=-0.085425971\) \(a_{70}=-0.946450438\)
\(a_{71}=+0.118678166\) \(a_{72}=+0.753444614\) \(a_{73}=-0.150321423\) \(a_{74}=-1.557797939\) \(a_{75}=-0.021736372\)
\(a_{76}=+0.751389735\) \(a_{77}=-0.060061680\) \(a_{78}=-0.105284734\) \(a_{79}=-0.195521529\) \(a_{80}=-0.252267884\)
\(a_{81}=+0.934132927\) \(a_{82}=+0.069643964\) \(a_{83}=+0.858970467\) \(a_{84}=+0.143732170\) \(a_{85}=+0.549618670\)
\(a_{86}=-2.110067397\) \(a_{87}=+0.045130279\) \(a_{88}=+0.071271792\) \(a_{89}=+0.910250205\) \(a_{90}=+1.425407268\)
\(a_{91}=+0.291385003\) \(a_{92}=-0.854944446\) \(a_{93}=-0.022523391\) \(a_{94}=-2.480017095\) \(a_{95}=+0.466473438\)
\(a_{96}=+0.178639135\) \(a_{97}=-0.285489416\) \(a_{98}=+0.912428237\) \(a_{99}=+0.090456247\) \(a_{100}=-0.217537947\)

Showing 100 of 546 available coefficients

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