Properties

Level $10$
Weight $0$
Character 10.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 29.9159624082 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.700375708\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-1.202347194\) \(a_{7}=-1.083873312\) \(a_{8}=+0.353553391\) \(a_{9}=+1.891277548\) \(a_{10}=+0.316227766\)
\(a_{11}=-1.717200624\) \(a_{12}=-0.850187854\) \(a_{13}=+0.153034590\) \(a_{14}=-0.766414169\) \(a_{15}=-0.760431134\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.576585829\) \(a_{18}=+1.337335180\) \(a_{19}=+0.301521613\) \(a_{20}=+0.223606798\)
\(a_{21}=+1.842991851\) \(a_{22}=-1.214244206\) \(a_{23}=-1.833899626\) \(a_{24}=-0.601173597\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.108211797\) \(a_{27}=-1.515506692\) \(a_{28}=-0.541936656\) \(a_{29}=+1.003664510\) \(a_{30}=-0.537706012\)
\(a_{31}=+0.162849737\) \(a_{32}=+0.176776695\) \(a_{33}=+2.919886226\) \(a_{34}=+1.114814531\) \(a_{35}=-0.484722881\)
\(a_{36}=+0.945638774\) \(a_{37}=-1.302256670\) \(a_{38}=+0.213207977\) \(a_{39}=-0.260216300\) \(a_{40}=+0.158113883\)
\(a_{41}=-0.448441926\) \(a_{42}=+1.303192035\) \(a_{43}=+1.318385478\) \(a_{44}=-0.858600312\) \(a_{45}=+0.845805032\)
\(a_{46}=-1.296762861\) \(a_{47}=+1.048449949\) \(a_{48}=-0.425093927\) \(a_{49}=+0.174781357\) \(a_{50}=+0.141421356\)
\(a_{51}=-2.680788245\) \(a_{52}=+0.076517295\) \(a_{53}=+0.341679498\) \(a_{54}=-1.071625059\) \(a_{55}=-0.767955465\)
\(a_{56}=-0.383207085\) \(a_{57}=-0.512700027\) \(a_{58}=+0.709697981\) \(a_{59}=+0.625645839\) \(a_{60}=-0.380215567\)
\(a_{61}=+0.755946047\) \(a_{62}=+0.115152153\) \(a_{63}=-2.049905261\) \(a_{64}=+0.125000000\) \(a_{65}=+0.068439149\)
\(a_{66}=+2.064671351\) \(a_{67}=+0.720632609\) \(a_{68}=+0.788292914\) \(a_{69}=+3.118318374\) \(a_{70}=-0.342750836\)
\(a_{71}=-1.085752782\) \(a_{72}=+0.668667590\) \(a_{73}=+0.630388510\) \(a_{74}=-0.920834522\) \(a_{75}=-0.340075142\)
\(a_{76}=+0.150760807\) \(a_{77}=+1.861227928\) \(a_{78}=-0.184000710\) \(a_{79}=+0.989737895\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.685653216\) \(a_{82}=-0.317096327\) \(a_{83}=+1.213600240\) \(a_{84}=+0.921495925\) \(a_{85}=+0.705070617\)
\(a_{86}=+0.932239312\) \(a_{87}=-1.706606751\) \(a_{88}=-0.607122103\) \(a_{89}=+1.173495770\) \(a_{90}=+0.598074474\)
\(a_{91}=-0.165870108\) \(a_{92}=-0.916949813\) \(a_{93}=-0.276905736\) \(a_{94}=+0.741366069\) \(a_{95}=+0.134844565\)
\(a_{96}=-0.300586798\) \(a_{97}=+1.021088528\) \(a_{98}=+0.123589083\) \(a_{99}=-3.247702985\) \(a_{100}=+0.099975586\)

Showing 100 of 232 available coefficients

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