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: \( 22.490200783 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.626116248\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.442731045\) \(a_{7}=+1.135474736\) \(a_{8}=-0.353553391\) \(a_{9}=-0.607978444\) \(a_{10}=+0.316227766\)
\(a_{11}=-0.758822370\) \(a_{12}=-0.313058124\) \(a_{13}=-0.467692681\) \(a_{14}=-0.802901886\) \(a_{15}=+0.280007698\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.426406682\) \(a_{18}=+0.429905681\) \(a_{19}=+1.566633874\) \(a_{20}=-0.223606798\)
\(a_{21}=-0.710939182\) \(a_{22}=+0.536568443\) \(a_{23}=-1.554746724\) \(a_{24}=+0.221365522\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.330708666\) \(a_{27}=+1.006781430\) \(a_{28}=+0.567737368\) \(a_{29}=-1.302553050\) \(a_{30}=-0.197995342\)
\(a_{31}=+1.627864838\) \(a_{32}=-0.176776695\) \(a_{33}=+0.475111015\) \(a_{34}=-0.301515057\) \(a_{35}=-0.507799739\)
\(a_{36}=-0.303989222\) \(a_{37}=-0.071447790\) \(a_{38}=-1.107777436\) \(a_{39}=+0.292829987\) \(a_{40}=+0.158113883\)
\(a_{41}=-1.092952762\) \(a_{42}=+0.502709916\) \(a_{43}=+0.383788704\) \(a_{44}=-0.379411185\) \(a_{45}=+0.271896226\)
\(a_{46}=+1.099371951\) \(a_{47}=-0.264505672\) \(a_{48}=-0.156529062\) \(a_{49}=+0.289302877\) \(a_{50}=-0.141421356\)
\(a_{51}=-0.266980152\) \(a_{52}=-0.233846341\) \(a_{53}=-1.437764994\) \(a_{54}=-0.711901976\) \(a_{55}=+0.339355680\)
\(a_{56}=-0.401450943\) \(a_{57}=-0.980894923\) \(a_{58}=+0.921044095\) \(a_{59}=-0.648266445\) \(a_{60}=+0.140003849\)
\(a_{61}=-0.722418939\) \(a_{62}=-1.151074266\) \(a_{63}=-0.690344163\) \(a_{64}=+0.125000000\) \(a_{65}=+0.209158525\)
\(a_{66}=-0.335954221\) \(a_{67}=+0.946383512\) \(a_{68}=+0.213203341\) \(a_{69}=+0.973452185\) \(a_{70}=+0.359068639\)
\(a_{71}=+0.605103994\) \(a_{72}=+0.214952840\) \(a_{73}=-1.487969124\) \(a_{74}=+0.050521217\) \(a_{75}=-0.125223250\)
\(a_{76}=+0.783316937\) \(a_{77}=-0.861623630\) \(a_{78}=-0.207062069\) \(a_{79}=-1.302242085\) \(a_{80}=-0.111803399\)
\(a_{81}=-0.022383767\) \(a_{82}=+0.772834310\) \(a_{83}=-1.606420987\) \(a_{84}=-0.355469591\) \(a_{85}=-0.190694866\)
\(a_{86}=-0.271379595\) \(a_{87}=+0.815549629\) \(a_{88}=+0.268284222\) \(a_{89}=+0.520464235\) \(a_{90}=-0.192259665\)
\(a_{91}=-0.531053224\) \(a_{92}=-0.777373362\) \(a_{93}=-1.019232625\) \(a_{94}=+0.187033754\) \(a_{95}=-0.700619968\)
\(a_{96}=+0.110682761\) \(a_{97}=+0.363273831\) \(a_{98}=-0.204568026\) \(a_{99}=+0.461347644\) \(a_{100}=+0.099975586\)

Showing 100 of 213 available coefficients

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