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: \( 7.41262473822 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+1.001383765\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.708085251\) \(a_{7}=+0.271646379\) \(a_{8}=-0.353553391\) \(a_{9}=+0.002769446\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.433911590\) \(a_{12}=+0.500691883\) \(a_{13}=+0.876818458\) \(a_{14}=-0.192082997\) \(a_{15}=-0.447832434\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.079159116\) \(a_{18}=-0.001958294\) \(a_{19}=+1.616812389\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.272022274\) \(a_{22}=-1.013928609\) \(a_{23}=+1.411615586\) \(a_{24}=-0.354042626\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.620004277\) \(a_{27}=-0.998610487\) \(a_{28}=+0.135823190\) \(a_{29}=-0.662609100\) \(a_{30}=+0.316665351\)
\(a_{31}=+1.086004921\) \(a_{32}=-0.176776695\) \(a_{33}=+1.435895788\) \(a_{34}=+0.055973948\) \(a_{35}=-0.121483954\)
\(a_{36}=+0.001384723\) \(a_{37}=-0.585355923\) \(a_{38}=-1.143259005\) \(a_{39}=+0.878031769\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.695165338\) \(a_{42}=-0.192348795\) \(a_{43}=+0.900750816\) \(a_{44}=+0.716955795\) \(a_{45}=-0.001238534\)
\(a_{46}=-0.998162953\) \(a_{47}=+1.241078435\) \(a_{48}=+0.250345941\) \(a_{49}=-0.926208245\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.079268654\) \(a_{52}=+0.438409229\) \(a_{53}=+0.023802119\) \(a_{54}=+0.706124247\) \(a_{55}=-0.641264758\)
\(a_{56}=-0.096041499\) \(a_{57}=+1.619049679\) \(a_{58}=+0.468535388\) \(a_{59}=-0.567135700\) \(a_{60}=-0.223916217\)
\(a_{61}=-1.307179654\) \(a_{62}=-0.767921444\) \(a_{63}=+0.000752310\) \(a_{64}=+0.125000000\) \(a_{65}=-0.392125135\)
\(a_{66}=-1.015331648\) \(a_{67}=+0.760850932\) \(a_{68}=-0.039579558\) \(a_{69}=+1.413568931\) \(a_{70}=+0.085902128\)
\(a_{71}=-0.971319017\) \(a_{72}=-0.000979147\) \(a_{73}=+1.063883268\) \(a_{74}=+0.413909143\) \(a_{75}=+0.200276753\)
\(a_{76}=+0.808406195\) \(a_{77}=+0.389516892\) \(a_{78}=-0.620862218\) \(a_{79}=-0.008118300\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.002761776\) \(a_{82}=+1.198662905\) \(a_{83}=-1.498778400\) \(a_{84}=+0.136011137\) \(a_{85}=+0.035401033\)
\(a_{86}=-0.636927010\) \(a_{87}=-0.663525996\) \(a_{88}=-0.506964305\) \(a_{89}=+0.256866001\) \(a_{90}=+0.000875776\)
\(a_{91}=+0.238184560\) \(a_{92}=+0.705807793\) \(a_{93}=+1.087507697\) \(a_{94}=-0.877574977\) \(a_{95}=-0.723060482\)
\(a_{96}=-0.177021313\) \(a_{97}=+0.276080000\) \(a_{98}=+0.654928130\) \(a_{99}=+0.003971140\) \(a_{100}=+0.099975586\)

Showing 100 of 126 available coefficients

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