Properties

Level $10$
Weight $0$
Character 10.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 29.6437951433 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.657146895\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.464673026\) \(a_{7}=+1.800812017\) \(a_{8}=-0.353553391\) \(a_{9}=-0.568157958\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.865075459\) \(a_{12}=+0.328573448\) \(a_{13}=+0.916463374\) \(a_{14}=-1.273366389\) \(a_{15}=+0.293885026\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.052146295\) \(a_{18}=+0.401748345\) \(a_{19}=-1.499519830\) \(a_{20}=+0.223606798\)
\(a_{21}=+1.183398026\) \(a_{22}=+0.611700723\) \(a_{23}=+1.755351544\) \(a_{24}=-0.232336513\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.648037467\) \(a_{27}=-1.030510133\) \(a_{28}=+0.900406009\) \(a_{29}=-0.814177903\) \(a_{30}=-0.207808095\)
\(a_{31}=-0.681620456\) \(a_{32}=-0.176776695\) \(a_{33}=-0.568481652\) \(a_{34}=-0.036872999\) \(a_{35}=+0.805347617\)
\(a_{36}=-0.284078979\) \(a_{37}=-1.397204568\) \(a_{38}=+1.060320641\) \(a_{39}=+0.602251061\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.780351431\) \(a_{42}=-0.836788769\) \(a_{43}=-0.250176497\) \(a_{44}=-0.432537730\) \(a_{45}=-0.254087963\)
\(a_{46}=-1.241220980\) \(a_{47}=-1.141599517\) \(a_{48}=+0.164286724\) \(a_{49}=+2.242923922\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.034267776\) \(a_{52}=+0.458231687\) \(a_{53}=-1.432091487\) \(a_{54}=+0.728680703\) \(a_{55}=-0.386873506\)
\(a_{56}=-0.636683195\) \(a_{57}=-0.985404801\) \(a_{58}=+0.575710716\) \(a_{59}=-0.272141012\) \(a_{60}=+0.146942513\)
\(a_{61}=-0.681036399\) \(a_{62}=+0.481978447\) \(a_{63}=-1.023145679\) \(a_{64}=+0.125000000\) \(a_{65}=+0.409854881\)
\(a_{66}=+0.401977231\) \(a_{67}=-0.403813069\) \(a_{68}=+0.026073148\) \(a_{69}=+1.153523817\) \(a_{70}=-0.569466761\)
\(a_{71}=-1.522017728\) \(a_{72}=+0.200874173\) \(a_{73}=-1.507214442\) \(a_{74}=+0.987972825\) \(a_{75}=+0.131429379\)
\(a_{76}=-0.749759915\) \(a_{77}=-1.557838283\) \(a_{78}=-0.425855809\) \(a_{79}=+0.159297658\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.109038576\) \(a_{82}=-0.551791789\) \(a_{83}=+0.055204460\) \(a_{84}=+0.591699013\) \(a_{85}=+0.023320532\)
\(a_{86}=+0.176901498\) \(a_{87}=-0.535034481\) \(a_{88}=+0.305850362\) \(a_{89}=-0.599872669\) \(a_{90}=+0.179667322\)
\(a_{91}=+1.650378258\) \(a_{92}=+0.877675772\) \(a_{93}=-0.447924766\) \(a_{94}=+0.807232760\) \(a_{95}=-0.670605655\)
\(a_{96}=-0.116168256\) \(a_{97}=-1.355580691\) \(a_{98}=-1.585986715\) \(a_{99}=+0.491499507\) \(a_{100}=+0.099975586\)

Showing 100 of 238 available coefficients

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