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: \( 7.788215329 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.270888494\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.898653872\) \(a_{7}=+0.240524904\) \(a_{8}=+0.353553391\) \(a_{9}=+0.615157564\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.647485160\) \(a_{12}=-0.635444247\) \(a_{13}=+1.008112194\) \(a_{14}=+0.170076791\) \(a_{15}=+0.568358613\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.401907303\) \(a_{18}=+0.434982085\) \(a_{19}=-1.012060648\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.305680333\) \(a_{22}=+1.164947928\) \(a_{23}=-0.483614624\) \(a_{24}=-0.449326936\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.712842968\) \(a_{27}=+0.489091823\) \(a_{28}=+0.120262452\) \(a_{29}=-1.079357639\) \(a_{30}=+0.401890229\)
\(a_{31}=+1.001147235\) \(a_{32}=+0.176776695\) \(a_{33}=-2.093769934\) \(a_{34}=+0.991298161\) \(a_{35}=-0.107566007\)
\(a_{36}=+0.307578782\) \(a_{37}=-0.028167710\) \(a_{38}=-0.715634947\) \(a_{39}=-1.281198188\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.203215898\) \(a_{42}=-0.216148636\) \(a_{43}=+1.744735423\) \(a_{44}=+0.823742580\) \(a_{45}=-0.275106826\)
\(a_{46}=-0.341967180\) \(a_{47}=+0.781514493\) \(a_{48}=-0.317722124\) \(a_{49}=-0.942147771\) \(a_{50}=+0.141421356\)
\(a_{51}=-1.781667862\) \(a_{52}=+0.504056097\) \(a_{53}=-0.811119206\) \(a_{54}=+0.345840145\) \(a_{55}=-0.736777762\)
\(a_{56}=+0.085038395\) \(a_{57}=+1.286216233\) \(a_{58}=-0.763221106\) \(a_{59}=+1.598250113\) \(a_{60}=+0.284179306\)
\(a_{61}=-0.241689770\) \(a_{62}=+0.707917999\) \(a_{63}=+0.147960714\) \(a_{64}=+0.125000000\) \(a_{65}=-0.450841479\)
\(a_{66}=-1.480518918\) \(a_{67}=-0.263064040\) \(a_{68}=+0.700953652\) \(a_{69}=+0.614620261\) \(a_{70}=-0.076060653\)
\(a_{71}=-0.610464250\) \(a_{72}=+0.217491043\) \(a_{73}=+0.652651752\) \(a_{74}=-0.019917579\) \(a_{75}=-0.254177699\)
\(a_{76}=-0.506030324\) \(a_{77}=+0.396261210\) \(a_{78}=-0.905943926\) \(a_{79}=-0.584606914\) \(a_{80}=-0.111803399\)
\(a_{81}=-1.236738735\) \(a_{82}=+0.850802120\) \(a_{83}=+1.050817600\) \(a_{84}=-0.152840166\) \(a_{85}=-0.626952006\)
\(a_{86}=+1.233714249\) \(a_{87}=+1.371743204\) \(a_{88}=+0.582473964\) \(a_{89}=-0.640455900\) \(a_{90}=-0.194529902\)
\(a_{91}=+0.242476088\) \(a_{92}=-0.241807312\) \(a_{93}=-1.272346502\) \(a_{94}=+0.552614198\) \(a_{95}=+0.452607281\)
\(a_{96}=-0.224663468\) \(a_{97}=+0.451947998\) \(a_{98}=-0.666199077\) \(a_{99}=+1.013462958\) \(a_{100}=+0.099975586\)

Showing 100 of 136 available coefficients

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