Properties

Level $7$
Weight $0$
Character 7.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 10.6456998611 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.503769196\) \(a_{3}=-1.801063821\) \(a_{4}=-0.746216598\) \(a_{5}=+1.497357574\)
\(a_{6}=+0.907320472\) \(a_{7}=-0.377964473\) \(a_{8}=+0.879690131\) \(a_{9}=+2.243830889\) \(a_{10}=-0.754322620\)
\(a_{11}=-0.346903165\) \(a_{12}=+1.343983717\) \(a_{13}=+0.180109985\) \(a_{14}=+0.190406859\) \(a_{15}=-2.696836554\)
\(a_{16}=+0.303055808\) \(a_{17}=+0.096544880\) \(a_{18}=-1.130372882\) \(a_{19}=-0.382772554\) \(a_{20}=-1.117353074\)
\(a_{21}=+0.680738138\) \(a_{22}=+0.174759128\) \(a_{23}=-0.114146039\) \(a_{24}=-1.584378068\) \(a_{25}=+1.242079704\)
\(a_{26}=-0.090733862\) \(a_{27}=-2.240218813\) \(a_{28}=+0.282043363\) \(a_{29}=+0.261512154\) \(a_{30}=+1.358583181\)
\(a_{31}=+0.525604455\) \(a_{32}=-1.032360311\) \(a_{33}=+0.624794739\) \(a_{34}=-0.048636336\) \(a_{35}=-0.565947966\)
\(a_{36}=-1.674383851\) \(a_{37}=+1.400239399\) \(a_{38}=+0.192829022\) \(a_{39}=-0.324389577\) \(a_{40}=+1.317210680\)
\(a_{41}=-1.713756137\) \(a_{42}=-0.342934904\) \(a_{43}=-0.814639456\) \(a_{44}=+0.258864899\) \(a_{45}=+3.359817176\)
\(a_{46}=+0.057503258\) \(a_{47}=-0.747732705\) \(a_{48}=-0.545822852\) \(a_{49}=+0.142857143\) \(a_{50}=-0.625721493\)
\(a_{51}=-0.173883490\) \(a_{52}=-0.134401060\) \(a_{53}=-1.512778508\) \(a_{54}=+1.128553229\) \(a_{55}=-0.519438081\)
\(a_{56}=-0.332491617\) \(a_{57}=+0.689397799\) \(a_{58}=-0.131741768\) \(a_{59}=+0.973606439\) \(a_{60}=+2.012424198\)
\(a_{61}=-0.627199434\) \(a_{62}=-0.264783333\) \(a_{63}=-0.848088359\) \(a_{64}=+0.217015515\) \(a_{65}=+0.269689050\)
\(a_{66}=-0.314752343\) \(a_{67}=-1.875446189\) \(a_{68}=-0.072043392\) \(a_{69}=+0.205584300\) \(a_{70}=+0.285107152\)
\(a_{71}=+0.547510173\) \(a_{72}=+1.973875888\) \(a_{73}=-0.181013544\) \(a_{74}=-0.705397476\) \(a_{75}=-2.237064819\)
\(a_{76}=+0.285631233\) \(a_{77}=+0.131117072\) \(a_{78}=+0.163417476\) \(a_{79}=-0.583551075\) \(a_{80}=+0.453782910\)
\(a_{81}=+1.790946168\) \(a_{82}=+0.863337551\) \(a_{83}=+0.028746427\) \(a_{84}=-0.507978097\) \(a_{85}=+0.144562207\)
\(a_{86}=+0.410390263\) \(a_{87}=-0.471000080\) \(a_{88}=-0.305167290\) \(a_{89}=-0.363820423\) \(a_{90}=-1.692572396\)
\(a_{91}=-0.068075175\) \(a_{92}=+0.085177669\) \(a_{93}=-0.946647167\) \(a_{94}=+0.376684703\) \(a_{95}=-0.573147383\)
\(a_{96}=+1.859346807\) \(a_{97}=+1.647522016\) \(a_{98}=-0.071967028\) \(a_{99}=-0.778392036\) \(a_{100}=-0.926860491\)

Showing 100 of 1228 available coefficients

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