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: \( 31.7315288843 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.437913315\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+1.016758256\) \(a_{7}=+1.620057690\) \(a_{8}=-0.353553391\) \(a_{9}=+1.067594702\) \(a_{10}=-0.316227766\)
\(a_{11}=-1.485940942\) \(a_{12}=-0.718956658\) \(a_{13}=+1.031795477\) \(a_{14}=-1.145553779\) \(a_{15}=-0.643054384\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.429854577\) \(a_{18}=-0.754903453\) \(a_{19}=-0.926118539\) \(a_{20}=+0.223606798\)
\(a_{21}=-2.329502524\) \(a_{22}=+1.050718917\) \(a_{23}=-1.289547622\) \(a_{24}=+0.508379128\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.729589578\) \(a_{27}=-0.097195322\) \(a_{28}=+0.810028845\) \(a_{29}=-1.105289277\) \(a_{30}=+0.454708115\)
\(a_{31}=+0.211398516\) \(a_{32}=-0.176776695\) \(a_{33}=+2.136654266\) \(a_{34}=-1.011059868\) \(a_{35}=+0.724511825\)
\(a_{36}=+0.533797351\) \(a_{37}=+1.910935979\) \(a_{38}=+0.654864699\) \(a_{39}=-1.483632454\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.026073543\) \(a_{42}=+1.647207032\) \(a_{43}=+0.924290941\) \(a_{44}=-0.742970471\) \(a_{45}=+0.477442865\)
\(a_{46}=+0.911847868\) \(a_{47}=-0.518292052\) \(a_{48}=-0.359478329\) \(a_{49}=+1.624586920\) \(a_{50}=-0.141421356\)
\(a_{51}=-2.056006935\) \(a_{52}=+0.515897738\) \(a_{53}=+0.939877122\) \(a_{54}=+0.068727471\) \(a_{55}=-0.664532991\)
\(a_{56}=-0.572776889\) \(a_{57}=+1.331678179\) \(a_{58}=+0.781557543\) \(a_{59}=+0.942305755\) \(a_{60}=-0.321527192\)
\(a_{61}=+0.295849133\) \(a_{62}=-0.149481324\) \(a_{63}=+1.729565007\) \(a_{64}=+0.125000000\) \(a_{65}=+0.461432965\)
\(a_{66}=-1.510842721\) \(a_{67}=+0.109580385\) \(a_{68}=+0.714927289\) \(a_{69}=+1.854257697\) \(a_{70}=-0.512307224\)
\(a_{71}=-0.505031128\) \(a_{72}=-0.377451727\) \(a_{73}=+0.478470387\) \(a_{74}=-1.351235789\) \(a_{75}=-0.287582663\)
\(a_{76}=-0.463059270\) \(a_{77}=-2.407310051\) \(a_{78}=+1.049086569\) \(a_{79}=-1.904691786\) \(a_{80}=+0.111803399\)
\(a_{81}=-0.927836254\) \(a_{82}=-0.725543560\) \(a_{83}=-0.929772021\) \(a_{84}=-1.164751262\) \(a_{85}=+0.639450407\)
\(a_{86}=-0.653572393\) \(a_{87}=+1.589310169\) \(a_{88}=+0.525359458\) \(a_{89}=-0.651922910\) \(a_{90}=-0.337603088\)
\(a_{91}=+1.671568197\) \(a_{92}=-0.644773811\) \(a_{93}=-0.303972741\) \(a_{94}=+0.366487824\) \(a_{95}=-0.414172802\)
\(a_{96}=+0.254189564\) \(a_{97}=+0.724776937\) \(a_{98}=-1.148756428\) \(a_{99}=-1.586382677\) \(a_{100}=+0.099975586\)

Showing 100 of 240 available coefficients

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