Properties

Level $2$
Weight $0$
Character 2.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 22.374933203 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106777\) \(a_{3}=+0.404844091\) \(a_{4}=+0.500000000\) \(a_{5}=-0.074803474\)
\(a_{6}=-0.286268001\) \(a_{7}=-0.241925207\) \(a_{8}=-0.353553384\) \(a_{9}=-0.836101262\) \(a_{10}=+0.052894043\)
\(a_{11}=+1.597524977\) \(a_{12}=+0.202422043\) \(a_{13}=-0.299934788\) \(a_{14}=+0.171066954\) \(a_{15}=-0.030283744\)
\(a_{16}=+0.249999994\) \(a_{17}=+1.330709040\) \(a_{18}=+0.591212868\) \(a_{19}=-1.265996372\) \(a_{20}=-0.037401737\)
\(a_{21}=-0.097941991\) \(a_{22}=-1.129620738\) \(a_{23}=-1.525515823\) \(a_{24}=-0.143133999\) \(a_{25}=-0.994404440\)
\(a_{26}=+0.212085921\) \(a_{27}=-0.743334747\) \(a_{28}=-0.120962602\) \(a_{29}=-0.753443873\) \(a_{30}=+0.021413841\)
\(a_{31}=+0.263698558\) \(a_{32}=-0.176776690\) \(a_{33}=+0.646748548\) \(a_{34}=-0.940953381\) \(a_{35}=+0.018096846\)
\(a_{36}=-0.418050626\) \(a_{37}=+0.271821987\) \(a_{38}=+0.895194614\) \(a_{39}=-0.121426827\) \(a_{40}=+0.026447021\)
\(a_{41}=-1.048184754\) \(a_{42}=+0.069255445\) \(a_{43}=-0.195289387\) \(a_{44}=+0.798762479\) \(a_{45}=+0.062543279\)
\(a_{46}=+1.078702577\) \(a_{47}=-1.416409852\) \(a_{48}=+0.101211021\) \(a_{49}=-0.941472194\) \(a_{50}=+0.703150119\)
\(a_{51}=+0.538729692\) \(a_{52}=-0.149967392\) \(a_{53}=-0.271352806\) \(a_{54}=+0.525617037\) \(a_{55}=-0.119500418\)
\(a_{56}=+0.085533476\) \(a_{57}=-0.512531151\) \(a_{58}=+0.532765269\) \(a_{59}=-1.366748472\) \(a_{60}=-0.015141872\)
\(a_{61}=+1.464253775\) \(a_{62}=-0.186463038\) \(a_{63}=+0.202273971\) \(a_{64}=+0.124999996\) \(a_{65}=+0.022436164\)
\(a_{66}=-0.457320281\) \(a_{67}=-1.039044208\) \(a_{68}=+0.665354512\) \(a_{69}=-0.617596067\) \(a_{70}=-0.012796402\)
\(a_{71}=+1.222020266\) \(a_{72}=+0.295606431\) \(a_{73}=+0.258534423\) \(a_{74}=-0.192207169\) \(a_{75}=-0.402578762\)
\(a_{76}=-0.632998179\) \(a_{77}=-0.386481561\) \(a_{78}=+0.085861732\) \(a_{79}=+0.117665802\) \(a_{80}=-0.018700868\)
\(a_{81}=+0.535166581\) \(a_{82}=+0.741178543\) \(a_{83}=-0.386974225\) \(a_{84}=-0.048970995\) \(a_{85}=-0.099541659\)
\(a_{86}=+0.138090449\) \(a_{87}=-0.305027300\) \(a_{88}=-0.564810362\) \(a_{89}=+0.381518324\) \(a_{90}=-0.044224776\)
\(a_{91}=+0.072561786\) \(a_{92}=-0.762757903\) \(a_{93}=+0.106756803\) \(a_{94}=+1.001553006\) \(a_{95}=+0.094700927\)
\(a_{96}=-0.071566999\) \(a_{97}=+0.688815957\) \(a_{98}=+0.665721369\) \(a_{99}=-1.335692649\) \(a_{100}=-0.497202214\)

Showing 100 of 1228 available coefficients

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