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: \( 25.8565600192 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.518897146\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.366915691\) \(a_{7}=+0.108609679\) \(a_{8}=-0.353553391\) \(a_{9}=-0.730745752\) \(a_{10}=-0.316227766\)
\(a_{11}=+0.574395296\) \(a_{12}=-0.259448573\) \(a_{13}=+1.796058131\) \(a_{14}=-0.076798640\) \(a_{15}=-0.232057858\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.664406764\) \(a_{18}=+0.516715276\) \(a_{19}=-1.531409774\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.056357252\) \(a_{22}=-0.406158809\) \(a_{23}=+0.384945998\) \(a_{24}=+0.183457845\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.270004884\) \(a_{27}=+0.898079031\) \(a_{28}=+0.054304839\) \(a_{29}=+1.628380662\) \(a_{30}=+0.164089685\)
\(a_{31}=-1.055368703\) \(a_{32}=-0.176776695\) \(a_{33}=-0.298052080\) \(a_{34}=+0.469806528\) \(a_{35}=+0.048571725\)
\(a_{36}=-0.365372876\) \(a_{37}=+1.880495467\) \(a_{38}=+1.082870236\) \(a_{39}=-0.931969438\) \(a_{40}=-0.158113883\)
\(a_{41}=+1.576039088\) \(a_{42}=+0.039850595\) \(a_{43}=-0.087835352\) \(a_{44}=+0.287197648\) \(a_{45}=-0.326799435\)
\(a_{46}=-0.272197926\) \(a_{47}=-0.656413856\) \(a_{48}=-0.129724287\) \(a_{49}=-0.988203938\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.344758774\) \(a_{52}=+0.898029065\) \(a_{53}=+0.147142997\) \(a_{54}=-0.635037773\) \(a_{55}=+0.256877386\)
\(a_{56}=-0.038399320\) \(a_{57}=+0.794644161\) \(a_{58}=-1.151439008\) \(a_{59}=-1.190421179\) \(a_{60}=-0.116028929\)
\(a_{61}=-0.075122526\) \(a_{62}=+0.746258367\) \(a_{63}=-0.079366061\) \(a_{64}=+0.125000000\) \(a_{65}=+0.803221614\)
\(a_{66}=+0.210754647\) \(a_{67}=+0.096765736\) \(a_{68}=-0.332203382\) \(a_{69}=-0.199747380\) \(a_{70}=-0.034345396\)
\(a_{71}=+0.618412620\) \(a_{72}=+0.258357638\) \(a_{73}=-1.374468280\) \(a_{74}=-1.329711097\) \(a_{75}=-0.103779429\)
\(a_{76}=-0.765704887\) \(a_{77}=+0.062384888\) \(a_{78}=+0.659001910\) \(a_{79}=-1.302150964\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.264735106\) \(a_{82}=-1.114427927\) \(a_{83}=-0.501360514\) \(a_{84}=-0.028178626\) \(a_{85}=-0.297131738\)
\(a_{86}=+0.062108973\) \(a_{87}=-0.844962078\) \(a_{88}=-0.203079405\) \(a_{89}=-0.494647335\) \(a_{90}=+0.231082097\)
\(a_{91}=+0.195069296\) \(a_{92}=+0.192472999\) \(a_{93}=+0.547627808\) \(a_{94}=+0.464154689\) \(a_{95}=-0.684867271\)
\(a_{96}=+0.091728923\) \(a_{97}=+1.530320164\) \(a_{98}=+0.698765706\) \(a_{99}=-0.419736923\) \(a_{100}=+0.099975586\)

Showing 100 of 222 available coefficients

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