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: \( 3.20437245526 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.242882165\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.171743626\) \(a_{7}=-0.973124354\) \(a_{8}=+0.353553391\) \(a_{9}=-0.941008254\) \(a_{10}=+0.316227766\)
\(a_{11}=+1.259007891\) \(a_{12}=+0.121441083\) \(a_{13}=+0.389290099\) \(a_{14}=-0.688102829\) \(a_{15}=+0.108620206\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.741707919\) \(a_{18}=-0.665393317\) \(a_{19}=+1.160170986\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.236354550\) \(a_{22}=+0.890253017\) \(a_{23}=+0.087473531\) \(a_{24}=+0.085871813\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.275269669\) \(a_{27}=-0.471436287\) \(a_{28}=-0.486562177\) \(a_{29}=-0.396547030\) \(a_{30}=+0.076806084\)
\(a_{31}=+0.472010445\) \(a_{32}=+0.176776695\) \(a_{33}=+0.305790562\) \(a_{34}=-1.231573480\) \(a_{35}=-0.435194441\)
\(a_{36}=-0.470504127\) \(a_{37}=+0.215746633\) \(a_{38}=+0.820364771\) \(a_{39}=+0.094551622\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.700690471\) \(a_{42}=-0.167127905\) \(a_{43}=+0.511644563\) \(a_{44}=+0.629503945\) \(a_{45}=-0.420831685\)
\(a_{46}=+0.061853127\) \(a_{47}=-0.707063388\) \(a_{48}=+0.060720541\) \(a_{49}=-0.053028992\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.423029790\) \(a_{52}=+0.194645049\) \(a_{53}=-1.800313270\) \(a_{54}=-0.333355796\) \(a_{55}=+0.563045446\)
\(a_{56}=-0.344051415\) \(a_{57}=+0.281784841\) \(a_{58}=-0.280401094\) \(a_{59}=+1.151346900\) \(a_{60}=+0.054310103\)
\(a_{61}=+0.176450690\) \(a_{62}=+0.333761786\) \(a_{63}=+0.915718049\) \(a_{64}=+0.125000000\) \(a_{65}=+0.174095825\)
\(a_{66}=+0.216226580\) \(a_{67}=+0.407194000\) \(a_{68}=-0.870853960\) \(a_{69}=+0.021245761\) \(a_{70}=-0.307728940\)
\(a_{71}=-1.142711001\) \(a_{72}=-0.332696659\) \(a_{73}=+0.382219000\) \(a_{74}=+0.152555907\) \(a_{75}=+0.048576433\)
\(a_{76}=+0.580085493\) \(a_{77}=-1.225171240\) \(a_{78}=+0.066858093\) \(a_{79}=-1.455320000\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.826504788\) \(a_{82}=+0.495462984\) \(a_{83}=+0.904659986\) \(a_{84}=-0.118177275\) \(a_{85}=-0.778915461\)
\(a_{86}=+0.361787340\) \(a_{87}=-0.096314201\) \(a_{88}=+0.445126509\) \(a_{89}=+0.825100000\) \(a_{90}=-0.297572938\)
\(a_{91}=-0.378827675\) \(a_{92}=+0.043736766\) \(a_{93}=+0.114642919\) \(a_{94}=-0.499969316\) \(a_{95}=+0.518844238\)
\(a_{96}=+0.042935906\) \(a_{97}=+1.290500641\) \(a_{98}=-0.037497160\) \(a_{99}=-1.184736817\) \(a_{100}=+0.099975586\)

Showing 100 of 130 available coefficients

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