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: \( 27.3725417397 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.153599190\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=-0.108611029\) \(a_{7}=+0.653560814\) \(a_{8}=+0.353553391\) \(a_{9}=-0.976407289\) \(a_{10}=+0.316227766\)
\(a_{11}=+0.072505509\) \(a_{12}=-0.076799595\) \(a_{13}=-0.932766440\) \(a_{14}=+0.462137284\) \(a_{15}=-0.068691646\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.096726257\) \(a_{18}=-0.690424215\) \(a_{19}=-0.808579197\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.100386412\) \(a_{22}=+0.051269137\) \(a_{23}=+0.770112959\) \(a_{24}=-0.054305514\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.659565475\) \(a_{27}=+0.303574559\) \(a_{28}=+0.326780407\) \(a_{29}=+1.041572724\) \(a_{30}=-0.048572329\)
\(a_{31}=-0.901569734\) \(a_{32}=+0.176776695\) \(a_{33}=-0.011136788\) \(a_{34}=+0.068395792\) \(a_{35}=+0.292281282\)
\(a_{36}=-0.488203644\) \(a_{37}=+1.430912271\) \(a_{38}=-0.571751833\) \(a_{39}=+0.143272170\) \(a_{40}=+0.158113883\)
\(a_{41}=+0.019467288\) \(a_{42}=-0.070983912\) \(a_{43}=+1.430825648\) \(a_{44}=+0.036252755\) \(a_{45}=-0.436662614\)
\(a_{46}=+0.544552096\) \(a_{47}=+0.539189305\) \(a_{48}=-0.038399797\) \(a_{49}=-0.572858262\) \(a_{50}=+0.141421356\)
\(a_{51}=-0.014857075\) \(a_{52}=-0.466383220\) \(a_{53}=+0.206495838\) \(a_{54}=+0.214659629\) \(a_{55}=+0.032425450\)
\(a_{56}=+0.231068642\) \(a_{57}=+0.124197110\) \(a_{58}=+0.736503136\) \(a_{59}=+0.424084130\) \(a_{60}=-0.034345823\)
\(a_{61}=+0.004853536\) \(a_{62}=-0.637506072\) \(a_{63}=-0.638141543\) \(a_{64}=+0.125000000\) \(a_{65}=-0.417145833\)
\(a_{66}=-0.007874898\) \(a_{67}=-0.993802556\) \(a_{68}=+0.048363129\) \(a_{69}=-0.118288727\) \(a_{70}=+0.206674076\)
\(a_{71}=-0.350609959\) \(a_{72}=-0.345212108\) \(a_{73}=-0.795613381\) \(a_{74}=+1.011807770\) \(a_{75}=-0.030719838\)
\(a_{76}=-0.404289599\) \(a_{77}=+0.047386760\) \(a_{78}=+0.101308723\) \(a_{79}=+1.304112497\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.929778483\) \(a_{82}=+0.013765451\) \(a_{83}=+1.619317124\) \(a_{84}=-0.050193206\) \(a_{85}=+0.043257297\)
\(a_{86}=+1.011746518\) \(a_{87}=-0.159984727\) \(a_{88}=+0.025634569\) \(a_{89}=-1.118404432\) \(a_{90}=-0.308767096\)
\(a_{91}=-0.609619594\) \(a_{92}=+0.385056480\) \(a_{93}=+0.138480381\) \(a_{94}=+0.381264414\) \(a_{95}=-0.361607610\)
\(a_{96}=-0.027152757\) \(a_{97}=+0.691611867\) \(a_{98}=-0.405071962\) \(a_{99}=-0.070794908\) \(a_{100}=+0.099975586\)

Showing 100 of 232 available coefficients

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