Properties

Level $21$
Weight $0$
Character 21.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 21 = 3 \cdot 7 \)
Weight: \( 0 \)
Character: 21.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 5.0058446716 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.281900704\) \(a_{3}=-0.577350269\) \(a_{4}=-0.920531993\) \(a_{5}=-1.298297512\)
\(a_{6}=+0.162755447\) \(a_{7}=+0.377964473\) \(a_{8}=+0.541399321\) \(a_{9}=+0.333333333\) \(a_{10}=+0.365990983\)
\(a_{11}=+1.033037728\) \(a_{12}=+0.531469394\) \(a_{13}=-1.116984500\) \(a_{14}=-0.106548451\) \(a_{15}=+0.749572418\)
\(a_{16}=+0.767911144\) \(a_{17}=-1.304842817\) \(a_{18}=-0.093966901\) \(a_{19}=+1.397214812\) \(a_{20}=+1.195124397\)
\(a_{21}=-0.218217890\) \(a_{22}=-0.291214063\) \(a_{23}=-0.126206259\) \(a_{24}=-0.312577044\) \(a_{25}=+0.685576431\)
\(a_{26}=+0.314878717\) \(a_{27}=-0.192450090\) \(a_{28}=-0.347928390\) \(a_{29}=-0.386767079\) \(a_{30}=-0.211304992\)
\(a_{31}=+0.748232690\) \(a_{32}=-0.757874013\) \(a_{33}=-0.596424610\) \(a_{34}=+0.367836109\) \(a_{35}=-0.490710335\)
\(a_{36}=-0.306843998\) \(a_{37}=+1.178564996\) \(a_{38}=-0.393875839\) \(a_{39}=+0.644891302\) \(a_{40}=-0.702897391\)
\(a_{41}=+0.254266585\) \(a_{42}=+0.061515777\) \(a_{43}=+1.709749631\) \(a_{44}=-0.950944278\) \(a_{45}=-0.432765837\)
\(a_{46}=+0.035577633\) \(a_{47}=+1.340478931\) \(a_{48}=-0.443353705\) \(a_{49}=+0.142857143\) \(a_{50}=-0.193264478\)
\(a_{51}=+0.753351352\) \(a_{52}=+1.028219968\) \(a_{53}=-1.423092121\) \(a_{54}=+0.054251816\) \(a_{55}=-1.341190312\)
\(a_{56}=+0.204629709\) \(a_{57}=-0.806682348\) \(a_{58}=+0.109029912\) \(a_{59}=-1.023603905\) \(a_{60}=-0.690005392\)
\(a_{61}=+0.269098757\) \(a_{62}=-0.210927322\) \(a_{63}=+0.125988158\) \(a_{64}=-0.554265926\) \(a_{65}=+1.450178197\)
\(a_{66}=+0.168132517\) \(a_{67}=+0.216258504\) \(a_{68}=+1.201149560\) \(a_{69}=+0.072865218\) \(a_{70}=+0.138331589\)
\(a_{71}=+1.067549028\) \(a_{72}=+0.180466440\) \(a_{73}=-0.265901985\) \(a_{74}=-0.332238302\) \(a_{75}=-0.395817737\)
\(a_{76}=-1.286180936\) \(a_{77}=+0.390451560\) \(a_{78}=-0.181795312\) \(a_{79}=+1.627677863\) \(a_{80}=-0.996977127\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.071677929\) \(a_{83}=-0.851959256\) \(a_{84}=+0.200876549\) \(a_{85}=+1.694074184\)
\(a_{86}=-0.481979624\) \(a_{87}=+0.223300077\) \(a_{88}=+0.559285924\) \(a_{89}=-0.463653144\) \(a_{90}=+0.121996994\)
\(a_{91}=-0.422180458\) \(a_{92}=+0.116176900\) \(a_{93}=-0.431992345\) \(a_{94}=-0.377881954\) \(a_{95}=-1.814000515\)
\(a_{96}=+0.437558765\) \(a_{97}=-1.581244230\) \(a_{98}=-0.040271529\) \(a_{99}=+0.344345909\) \(a_{100}=-0.631095038\)

Showing 100 of 198 available coefficients

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