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: \( 6.37879720849 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.223884033\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213596\)
\(a_{6}=-0.158309918\) \(a_{7}=-0.498727833\) \(a_{8}=-0.353553391\) \(a_{9}=-0.949875940\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.646063331\) \(a_{12}=+0.111942016\) \(a_{13}=-0.087146842\) \(a_{14}=+0.352653833\) \(a_{15}=+0.100123983\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.623448822\) \(a_{18}=+0.671663718\) \(a_{19}=-1.085541190\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.111657198\) \(a_{22}=+0.456835763\) \(a_{23}=+1.036729303\) \(a_{24}=-0.079154959\) \(a_{25}=+0.200000000\)
\(a_{26}=+0.061622123\) \(a_{27}=-0.436546088\) \(a_{28}=-0.249363917\) \(a_{29}=+0.347211289\) \(a_{30}=-0.070798348\)
\(a_{31}=-1.640102194\) \(a_{32}=-0.176776695\) \(a_{33}=-0.144643265\) \(a_{34}=+1.147951673\) \(a_{35}=-0.223037867\)
\(a_{36}=-0.474937976\) \(a_{37}=+1.582737180\) \(a_{38}=+0.767593545\) \(a_{39}=-0.019510817\) \(a_{40}=-0.158113878\)
\(a_{41}=-0.966110902\) \(a_{42}=+0.078953562\) \(a_{43}=+0.297102876\) \(a_{44}=-0.323031666\) \(a_{45}=-0.424797434\)
\(a_{46}=-0.733078321\) \(a_{47}=+1.363025738\) \(a_{48}=+0.055971008\) \(a_{49}=-0.751270548\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.363464269\) \(a_{52}=-0.043573421\) \(a_{53}=+0.248896084\) \(a_{54}=+0.308684699\) \(a_{55}=-0.288928305\)
\(a_{56}=+0.176326916\) \(a_{57}=-0.243035339\) \(a_{58}=-0.245515457\) \(a_{59}=+1.956825684\) \(a_{60}=+0.050061991\)
\(a_{61}=-1.617834090\) \(a_{62}=+1.159727383\) \(a_{63}=+0.473729570\) \(a_{64}=+0.124999999\) \(a_{65}=-0.038973251\)
\(a_{66}=+0.102278231\) \(a_{67}=-0.820475496\) \(a_{68}=-0.811724413\) \(a_{69}=+0.232107139\) \(a_{70}=+0.157711587\)
\(a_{71}=-0.205066382\) \(a_{72}=+0.335831857\) \(a_{73}=-0.631980684\) \(a_{74}=-1.119164186\) \(a_{75}=+0.044776798\)
\(a_{76}=-0.542770586\) \(a_{77}=+0.322209763\) \(a_{78}=+0.013796217\) \(a_{79}=+0.479437205\) \(a_{80}=+0.111803442\)
\(a_{81}=+0.852140164\) \(a_{82}=+0.683143656\) \(a_{83}=+1.424909742\) \(a_{84}=-0.055828599\) \(a_{85}=-0.726028385\)
\(a_{86}=-0.210083458\) \(a_{87}=+0.077735063\) \(a_{88}=+0.228417881\) \(a_{89}=-0.398103991\) \(a_{90}=+0.300377146\)
\(a_{91}=+0.043462556\) \(a_{92}=+0.518364652\) \(a_{93}=-0.367192693\) \(a_{94}=-0.963804742\) \(a_{95}=-0.485468779\)
\(a_{96}=-0.039577479\) \(a_{97}=-1.937198488\) \(a_{98}=+0.531228500\) \(a_{99}=+0.613680013\) \(a_{100}=+0.100000002\)

Showing 100 of 2000 available coefficients

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